FAULT MITIGATION IN PERMANENT MAGNET SYNCHRONOUS MOTORS UNDER AN INTERNAL TURN-TO-TURN FAILURE By Jorge G. Cintron-Rivera A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Electrical Engineering - Doctor of Philosophy 2014 ABSTRACT FAULT MITIGATION IN PERMANENT MAGNET SYNCHRONOUS MOTORS UNDER AN INTERNAL TURN-TO-TURN FAILURE By Jorge G. Cintron-Rivera In this research the behavior and mitigation of turn-to-turn faults in PMSMs are studied. The challenge with PMSMs under a turn-to-turn fault is with the rotor magnets. Typically rare earth magnets are used in PMSMs, due to the high remnant flux density and excellent coercivity. These characteristics make rare earth magnets the strongest commercially available. Thanks to this, healthy PMSMs have high torque density and are suitable for traction and power generation systems. However, what makes them excellent machines also makes them dangerous in the event of a turn-to-turn fault. The problem arises when a fault occurs and the magnetic field produced by the magnets continuously contributes to the fault by electromagnetic induction. Magnets are capable of inducing high voltages in the windings and they cannot be turned off during fault conditions. In post-fault operation, if the rotor continues spinning, even a full inverter disconnection will not assist in the mitigation of the fault current. This research demonstrates how to detect a fault and reduce the fault current by controlling the current through the remaining healthy coils. The main idea is to generate a magnetic field, using the remaining healthy coils, to cancel some of the magnetic field created by the magnets. Although magnets cannot be turned off, their effect in the faulted area can be minimized using this technique. The technique applies the principle of the field-weakening control strategy to reduce the magnetic flux linking the fault, and therefore reduce and gain a degree of control over the fault current. This mitigation technique keeps the fault current within acceptable levels and if conditions allow, the faulted PMSM can continue operating with a reduced power capacity. This has the potential of extending the post-fault life span of the motor, which could allow for continuous operation at least for a limited time. Two fault tolerant PMSMs, with fractional winding configuration, were designed to test the proposed mitigation technique. The difference between the motors is in the number of layers in the winding and the slot/pole/phase combination. One machine has a single layer winding using a 2/5 slots/pole/phase combination, while the other has a double layer winding with a 1/2 slots/pole/phase combination. Through experimental and finite elements analysis this dissertation demonstrates the effectiveness of the proposed fault mitigation technique in regulating the fault current during a turn-to-turn fault. I dedicate this Dissertation to my wife Sheila Liz Luna-Miranda, who offered me unconditional love and support throughout the course of my Ph.D. career; and to my unborn baby, who brings happiness and joy to our lives. I would also like to dedicate this Dissertation to my parents Aracelis Rivera-Morales and Efrain Cintron-Rosado, for their love and unconditional support. iv ACKNOWLEDGMENTS First, I would like to thank God for the health and strength provided to me and to everyone. Without these qualities, this career would not be possible. Also, thanks for all the wisdom and knowledge gained during my Ph.D career. Special thanks to my wife, Sheila Liz Luna-Miranda, for her unconditional support with my professional and personal goals. She has been with me during this wonderful journey, helping me to overcome problems and giving me the strength to accomplish this goal. I want to thank my parents, Aracelis Rivera-Morales and Efrain Cintron-Rosado, for their unconditionally support and all the strong values and perseverance they taught me. Also, thanks to all my family members, especially to Carmen and Pedro Vazquez, who together with my parents gave me that initial push to start my Ph.D and continous support throughout my entire professional career. I would like to thank my research advisor Dr. Elias G. Strangas, for his support, guidance, confidence and motivation to pursue and complete my doctoral degree. Also, I would like thank my graduate committee; Dr. Fang Peng, Dr. Joydeep Mitra, Dr. Ranjan Mukherjee, for their guidance and support. This work was possible thanks to the collaboration and support from my excellent friends in the Electrical Machines and Drives Laboratory; thank you all. The relationships built in our Laboratory are remarkable, and for that I am grateful. Finally, I would like to thank Michigan State University for the Enrichment Fellowship, and Dr. Percy Pierre for the Sloan Engineering Program support. Also, I would like to thank the UNCF special programs corporation for the NASA’s Harriett Jenkins pre-doctoral fellowship. v TABLE OF CONTENTS LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 1 Introduction . . . . . . 1.1 Literature Review on Faults of 1.2 Problem Statement . . . . . . 1.3 Methodology . . . . . . . . . 1.4 Objectives and Contributions 1.5 Organization . . . . . . . . . . . . . . PMSMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 4 5 5 7 Chapter 2 Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Healthy PMSM Analysis and Modeling . . . . . . . . . . . . . . . . . . . . . 2.2 Non-ideal characteristics of PMSM . . . . . . . . . . . . . . . . . . . . . . . 2.3 Experimental Procedure and Characterization . . . . . . . . . . . . . . . . . 2.3.1 Line to neutral voltage estimation . . . . . . . . . . . . . . . . . . . . 2.3.2 Rotor Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3 Experimental Data Collection . . . . . . . . . . . . . . . . . . . . . . 2.3.4 Post Processing Parameter Extraction . . . . . . . . . . . . . . . . . 2.4 Field Oriented Vector Controlled PMSM . . . . . . . . . . . . . . . . . . . . 2.4.1 High Performance FOC Design for Traction Drives Applications; Including the Saturation And Cross Saturation Effects . . . . . . . . . 2.4.1.1 Parameters Extraction; To Demonstrate the Saturation Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1.2 Proposed Parameter Approximation . . . . . . . . . . . . . 2.4.1.3 Controller Performance Evaluation . . . . . . . . . . . . . . 2.4.1.4 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 8 13 15 15 16 18 18 21 Chapter 3 Modeling of Permanent Magnet Synchronous Turn-to-Turn Fault . . . . . . . . . . . . . . . . . 3.1 Winding and Fault Severity . . . . . . . . . . . . . . . . 3.2 Detailed Modeling of turn-to-turn Faults . . . . . . . . . 3.3 Frame of Reference Transformation Including the Fault . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix 25 27 28 34 39 Motors under a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 43 44 47 Chapter 4 Fault Tolerant Machines Specifications and Characteristics . . 4.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Stator and Rotor Configuration . . . . . . . . . . . . . . . . . . . . . 50 50 51 vi 4.2 4.3 Winding Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Finite Elements Analysis: Magneto Static Analysis to Extract parameters . . 4.3.1 Inductance Determination Procedure, Including a Turn-to-Turn Fault 4.3.2 Fault Study Case and Nominal Parameters . . . . . . . . . . . . . . . General Impedance Model for Turn-to-Turn Faulted PMSMs . . . . . . . . . Torque Experimental Determination . . . . . . . . . . . . . . . . . . . . . . 52 54 54 56 59 63 Chapter 5 Fault Current Analysis and Behavior . . . . . . . . . . . . . . . . 5.1 Fault Current Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1 Induced Fault Current in the Faulted Loop . . . . . . . . . . . . . . . 5.1.2 Fault Current Worst Case Scenario . . . . . . . . . . . . . . . . . . . 5.2 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Fault Current Behavior for Various Operating Conditions: Analysis using FEA and Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Transient Magnetic FEA Setup . . . . . . . . . . . . . . . . . . . . . 5.3.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.3 Drive’s Current Controller Performance Under Turn-to-Turn Fault . . 5.3.4 Fault Current Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Thermal Relief . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Chapter 5 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 64 66 68 70 4.4 4.5 Chapter 6 Proposed Methodology for Fault Mitigation 6.1 Fault Detection and Fault Current Estimation . . . . . 6.2 Control Algorithm and Experimental Results . . . . . . 6.3 Experimental case: A 0.5 Ohms fault across 15 turns . 6.4 Experimental case: A 0.25 Ohms fault across 15 turns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 73 75 76 77 84 86 88 89 95 97 98 Chapter 7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 APPENDIX A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 vii LIST OF TABLES Table 2.1 Rated Specifications for the PMSMs . . . . . . . . . . . . . . . . . . 27 Table 4.1 Stator and Rotor physical specifications . . . . . . . . . . . . . . . . 52 Table 4.2 Healthy PMSM Parameters . . . . . . . . . . . . . . . . . . . . . . . 59 Table 4.3 Machine Parameters Based on a 15 turns fault . . . . . . . . . . . . 59 Table 5.1 Simulation parameters range and step size . . . . . . . . . . . . . . 74 Table 5.2 Inverter and controller details . . . . . . . . . . . . . . . . . . . . . 75 viii LIST OF FIGURES Figure 2.1 Three phase model for a PMSM . . . . . . . . . . . . . . . . . . . . 8 Figure 2.2 Steady State space vector diagram for IPMSM . . . . . . . . . . . . 11 Figure 2.3 Equivalent circuit model in the synchronous frame of reference, healthy machine model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Figure 2.4 Experimental Setup for the characterization process . . . . . . . . . 16 Figure 2.5 Rotor alignment using the electrical position and estimated back EMF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Figure 2.6 Experimental data to determine the d- and q-axis quantities . . . . 19 Figure 2.7 Generalized torque controller for a PMSM . . . . . . . . . . . . . . . 21 Figure 2.8 Detailed FOC current controller for a PMSM . . . . . . . . . . . . . 22 Figure 2.9 PMSM operating regions . . . . . . . . . . . . . . . . . . . . . . . . 24 Figure 2.10 PMSM operating path in the dq plane . . . . . . . . . . . . . . . . . 25 Figure 2.11 Self and cross saturation of the flux linkages . . . . . . . . . . . . . 27 Figure 2.12 Generator experimentally extracted d-axis flux linkage and d-axis inductance. The Arrow points at the direction which iq is increased. . 29 Generator experimentally extracted q-axis flux linkage and q-axis inductance.The Arrow points at the direction which id is increased. . . 30 Motor experimentally extracted d-axis flux linkage and d-axis inductance. The Arrow points at the direction which iq is increased. . . . 31 Motor experimentally extracted q-axis flux linkage and q-axis inductance. The Arrow points at the direction which id is increased. . . . 32 Motor d-axis inductance piecewise linear approximation, including cross saturation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Figure 2.13 Figure 2.14 Figure 2.15 Figure 2.16 ix Figure 2.17 q-axis inductance piecewise linear approximation, including cross saturation in four sectors. . . . . . . . . . . . . . . . . . . . . . . . . . 33 Motor q-axis inductance piecewise linear approximation on top of the experimental q-axis inductance. . . . . . . . . . . . . . . . . . . . . 35 Simulation based performance evaluation, using the PMSM experimental parametric data. . . . . . . . . . . . . . . . . . . . . . . . . . 36 Generator Plosses in MTPA and field weakening mode, only considering copper losses. . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Figure 2.21 Generator Tout mismatch with the commanded torque Tcom . . . . . 38 Figure 2.22 Motor Plosses in MTPA and field weakening mode, only considering copper losses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Figure 2.23 Generator Tout mismatch with the commanded torque Tcom . . . . . 40 Figure 2.24 DSP memory utilization based on the control method, including lookup table resolution. . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Figure 3.1 PMSM with a turn-to-turn fault on phase A . . . . . . . . . . . . . 43 Figure 3.2 Three phase electrical model for a faulted PMSM . . . . . . . . . . . 44 Figure 4.1 Fault tolerant PMSM with fractional winding configuration . . . . . 52 Figure 4.2 Stator winding configuration for the fabricated PMSMs . . . . . . . 53 Figure 4.3 FEA geometry setup for the magneto static simulation, used to determinate the inductances of the 2/5SP P machine. . . . . . . . . . 55 Inductances determination; in this case current is applied only to the healthy part of phase A and the magnetic flux generated by the current across all the coils is measured. . . . . . . . . . . . . . . . . 56 Inductances determination; in this case current is applied only to the healthy phase B and the magnetic flux generated by the current across all the coils is measured. . . . . . . . . . . . . . . . . . . . . . 57 Inductances determination; in this case current is applied only to the faulted coil conductor and the magnetic flux generate by the current across all the coils is measured. . . . . . . . . . . . . . . . . . . . . . 58 Figure 2.18 Figure 2.19 Figure 2.20 Figure 4.4 Figure 4.5 Figure 4.6 x Figure 4.7 Single tooth, containing the faulted coil . . . . . . . . . . . . . . . . 60 Figure 4.8 Parametric validation, where kAl = 2.5 and rf = 0.5 Ω . . . . . . . . 62 Figure 4.9 Experimental, finite elements and modeling results comparison. Study case: 15 faulted turns, 300 RPM. . . . . . . . . . . . . . . . . . . . . 62 Torque profiles as a function of the current space vector angle (δ), legend on figure 4.10(a) applies to figure 4.10(b) . . . . . . . . . . . 63 Figure 5.1 Electrical model for the faulted phase . . . . . . . . . . . . . . . . . 65 Figure 5.2 Fault current as a function of the rotor speed and fault Severity . . 66 Figure 5.3 Open circuited PMSMs, fault current behavior . . . . . . . . . . . . 68 Figure 5.4 Open circuited PMSM at 300 RPM, worst case scenario as a function of the fault resistenace . . . . . . . . . . . . . . . . . . . . . . . . . 69 Sensitivity of vf = if rf to changes in the current space vector angle (δ). Operating conditions; ∆ = 15/300, speed = 300 rpm, |Ia | = 5 A and rf = 0.5 Ω. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Sensitivity of vf = if rf to changes in the current space vector magnitude. Operating conditions; ∆ = 15/300, speed = 300 rpm and rf = 0.5 Ω. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Figure 5.7 FEA geometry, including calculation mesh for the 2/5 SP P PMSM. 73 Figure 5.8 FEA Circuit, with the A coil divided into the healthy Aah and the faulty Aaf parts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 Experimental setup, with sectioned windings to insert the fault externally. The figure shows the winding configuration for the 2/5 SP P PMSM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Measured current vector, vd + jvq, while the 2/5 SP P PMSM experiences different fault conditions. Experiments were conducted at different angles of δ ,1200 , 1400 , 150o and 170o, throughout the experimentation process the space current vector magnitude at 10 A. . 76 Phase A current in time domain, for different angles and a fixed magnitude of 10 A. The fault case is the 1/2 Ω fault for 15 turns at 300 RPM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Figure 4.10 Figure 5.5 Figure 5.6 Figure 5.9 Figure 5.10 Figure 5.11 xi Figure 5.12 Figure 5.13 Figure 5.14 Figure 5.15 Figure 5.16 Figure 5.17 Figure 5.18 Figure 5.19 Figure 5.20 Figure 5.21 Figure 5.22 Results for a fault current thought 15 faulted turns, with rf = 0.5 Ω. Speed fixed at 300 RP M and current space vector magnitude set to 10 A. This data was taken using the 2/5 SP P machine. . . . . . . . 78 Results for a fault current thought 30 faulted turns, with rf = 0.5 Ω. Speed fixed at 300 RP M and current space vector magnitude set to 10 A.This data was taken using the 2/5 SP P machine. . . . . . . . 79 FEA and Analytical fault current RMS comparison for a 15 turns fault, with rf = 0.5 Ω. Speed fixed at 300 RP M and current space vector magnitude set to 10 A. This data was taken using the 2/5 SP P machine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 FEA and Analytical fault current RMS comparison for a 30 turns fault, with rf = 0.5 Ω. Speed fixed at 300 RP M and current space vector magnitude set to 10 A. This data was taken using the 2/5 SP P machine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Fault current rms value as a function of the current space vector angle at 300 RPM and current space vector magnitude set to 10 A. This data was taken using the 2/5 SP P machine. . . . . . . . . . . . . . 81 Fault current rms value as a function of the current space vector angle at 500 RPM and current space vector magnitude set to 10 A. This data was taken using the 2/5 SP P machine. . . . . . . . . . . . . . 81 Fault current rms value as a function of the current space vector angle at 700 RPM and current space vector magnitude set to 10 A. This data was taken using the 2/5 SP P machine. . . . . . . . . . . . . . 82 Fault current for different current angles, while the current space vector magnitude is kept at constant at 5 A. This data was taken using the 1/2 SP P machine. . . . . . . . . . . . . . . . . . . . . . . 82 Fault current rms value as a function of the current space vector angle at 300 RPM and current space vector magnitude set to 5 A. This data was taken using the 1/2 SP P machine. . . . . . . . . . . . . . 83 MotorCAD geometry approximation of the actual machine shown in figure 4.1(a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 MotorCAD slot and winding configuration . . . . . . . . . . . . . . 85 xii Figure 5.23 Thermal simulation for various current angles, healthy case and the rf = 0.5 Ω, Nf = 15 turns at 300 RPM case. The current space vector magnitude is kept constant at 10 A for all simulations. . . . . 86 Figure 6.1 Space vector plane, dq axes . . . . . . . . . . . . . . . . . . . . . . . 89 Figure 6.2 Changes in the voltage space vector for different fault conditions at 300 RP M with 10A∠120o for the 2/5 SP P machine. Starting from healthy, then moving to rf = 0.5 Ω@ 15 turns, rf = 0.25 Ω@ 15 turns, rf = 0.5 Ω@ 30 turns, and finalizing with rf = 0.25 Ω@ 30 turns . . . . . . . . . . . . . . . . . . . . . . . . . 91 Detection experiment, healthy operation progressing into a rf = 0.5 Ω fault across 15 turns of the winding. All the testing was performed in the single layer 2/5 SP P machine. . . . . . . . . . . . . . 93 Fault current estimator for a rf = 0.5 Ω fault across 15 turns of the winding, motor operating at 300 RP M with a |is | = 10 A. All the testing was performed in the single layer 2/5 SP P machine. . . . . . 94 Changes in the voltage space vector for different fault conditions at 300 RP M with 10A∠140o for the 1/2 SP P double layer machine. Starting from healthy, then moving to rf = 0.5 Ω@ 15 turns, rf = 0.25 Ω@ 15 turns, rf = 0.5 Ω@ 50 turns, and finalizing with rf = 0.25 Ω@ 50 turns . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Figure 6.3 Figure 6.4 Figure 6.5 Figure 6.6 Fault mitigation algorithm, enables the limitation of if by δ and |is |. 96 Figure 6.7 Motor controller including detection, estimation and mitigation . . . 97 Figure 6.8 Experimental case rf = 0.5 Ω across 15 turns, including detection, estimation and fault current mitigation. . . . . . . . . . . . . . . . . 99 Figure 6.9 Experimental case rf = 0.25 Ω across 15 turns, including detection, estimation and fault current mitigation. . . . . . . . . . . . . . . . . 100 Figure A.1 Generalized DSP execution mode, shown sequence of operation and interrupt. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 Figure A.2 ESI DSP system board specific case, C++ coding structure. . . . . . 107 Figure A.3 DSP and data logging computer information flow. . . . . . . . . . . 108 xiii Chapter 1 Introduction Permanent magnet synchronous motors (PMSM) are used in many commercial products. Their high power density and torque capacity make them suitable for traction drives applications. Automotive industries exploit these features to design and fabricate vehicles with exceptional MPG performance to satisfy the needs of the consumers and alleviate the air pollution problem. The outstanding performance of PMSMs overcomes their main drawback, which is that strong magnets, made from rare earth materials, are required to achieve suitable operation. Rare earth materials increase the production cost; however, the resulting performance and power capacity are worth the cost. Having strong magnets permanently inserted into a PMSM can be hazardous in the event of a failure, especially for a turn-to-turn fault in the winding. This is because having a high magnetic field contained within a faulted stator winding has the potential to induce voltages across the fault. The magnetic field produced by these magnets is not controllable and cannot be turned off. When a fault occurs, magnets contribute to the fault current, which leads to overheating and possible destruction of the machine and its surroundings. Considering that these motors are widely utilized in applications where human interaction is required, it is vital to develop a safety response protocol to any type of fault in a PMSM, a protocol that ensures the safety of the users, as well as, the overall integrity of the entire system. 1 1.1 Literature Review on Faults of PMSMs Faults in PMSMs are categorized into mechanical or electrical [1]; mechanical faults include rotor eccentricity, shaft bearings deterioration and parts breakage. On the other hand, electrical faults include, magnet demagnetization, open circuit phase, turn-to-turn contact due to insulation degradation, and failure of electronics, [2]. Open circuit phase faults occur when a phase winding breaks or when an electronic switching device fails, [3]. Extensive research has been performed for open circuited phase remedial strategies, [4–7]. It has been demonstrated that acceptable post-fault operation may be achievable in three phase machines by controlling the neutral current using a fourth inverter leg, [8–10]; other remedial strategies were developed for PMSMs with more than three phases, [11]. This Dissertation is entirely focused on the mitigation of turn-to-turn short faults, which are among the most common faults in PMSMs, 30 % to 40 %, [12–15]. Contrary to open circuit faults, there is no remedial strategy to safely achieve full post-fault operation in turn-to-turn faulted PMSMs. These faults can occur between turns of the same or different phases, [16]. However, faults tend to occur between turns of the same phase coil, especially when a fault tolerant PMSM is used. In this type of motor the phase windings do not share any of the slots; hence, the phase to phase mutual inductances are dramatically reduced, and the phases are physically isolated [17]. Yet, without a proper mitigation, an incipient turn-to-turn fault can easily propagate to more turns and worsen the severity of the contact point resistance. This is due to the rapid increase in the coil temperature, caused by a large circulating fault current, [18]. It is vital to detect and mitigate incipient turn-to-turn faults to stop and prevent further damage to the PMSM, [18]. The effects of an turn-to-turn fault 2 on the vector oriented controller are studied in [18–20]. Several detection methods have been proposed for PMSMs, [17, 21–23]; where the unbalanced operating conditions created by the fault are used for detection purposes. For example, in [24] and [25] the voltage imbalances are used to detect the fault, while [26] and [27] use sequence component and impedance changes, respectively. The third harmonic components of line currents, also contain information about the health of the machine, as demonstrated in [15]. In the majority of the mitigation techniques, the stator current is controlled to produce a magnetic flux linkages that is equal in magnitude but opposes the flux linkage produced by the magnets. This reduces the induced EMF voltage in the faulted turns and suppresses the fault circulating current. One important aspect, is that once the fault has been detected and cleared, the machine is not operational, as its torque output capacity is completely nulled by the stator current. One possible response to a turn-to-turn fault is to shut-down the drive’s electronics. This remedial strategy is known as uncontrolled generator (UCG); it is applicable for open and turn-to-turn faults and the operation principle is described in [28, 29]. In this technique the fault current is not controlled and it can easily increase the fault severity due to over-current and overheating. In [30] a method to keep the fault current within its rated limit during a turn-to-turn fault in a bar wound machine is presented. It demonstrates that injecting rated current at 90o lagging the back EMF results in a fault current that is kept within the rating limits of the coil, but the torque output capacity is completely nulled. In [30] this mitigation technique is compared to previously presented techniques, where the inverter was used to create a short across all phases of the motor, [31]. Shorting all phases of the motor, while operating, generates strong counter torque and transient currents capable of creating 3 a catastrophic failure. Welchko et al. [32] proposed a similar method to mitigate turn-to-turn faults in PMSMs. This method consists of injecting maximum current along the d-axis when a fault is detected; this technique was named flux nulling. The magnet flux nulling technique uses the d-axis current to cancel the back EMF, so that only a small voltage is induced in the faulted winding. This method minimizes the fault current and nulls the torque capacity of the motor. Other mitigation techniques have been developed for machines containing more than the standard three phases, [33]. However, having more phases increases the cost and complexity of a machine and drive. 1.2 Problem Statement PM motors contain magnets that are buried in or mounted on the surface of their rotors. As the rotor spins, the rotating magnetic field created by the magnets induce a voltage known as the electromotive force (EMF) in the stator windings. This physical phenomenon is described by Faraday’s law of induction, which states how a changing magnetic field will interact with an electrical circuit to create an EMF. The magnitude of the EMF voltage induced in the motor stator winding is directly proportional to the rotor angular speed and the magnetic strength of the magnets. The problem arises because the rotor magnets cannot be turned off during a fault. As the rotor moves inside the stator, the magnets induce a voltage in the faulted winding. This voltage will create a circulating fault current inside the motor that will generate heat and has the potential to propagate and/or destroy other areas of the motor. The work in this Dissertation is focused on the study and development of a fault mitigation method that has 4 the potential to continue the operation of a faulted PMSM. 1.3 Methodology Here a method to mitigate turn-to-turn faults is introduced. It is demonstrated that the stator currents, at the appropriate angle and magnitude, can restrict the fault current rms value and therefore decrease the power dissipated across the fault. The idea is to use the direct axis current to adjust the amount of flux linkage that induces the back emf voltage across the fault. By canceling some of the flux produced by the magnets, it is possible to reduce the voltage across the fault and hence the fault current. This concept is described as a low-speed field-weakening, where the flux linkage produced by the magnets is weakened by the flux produced by the line current, a technique that is normally used at high speeds. However, it will be demonstrated that this technique reduces the fault current, when applied at speeds below the nominal. This leads to a controller capable of reducing the fault current and allow post-fault operation of the motor, depending on the fault severity. The method is based on the flux nulling technique, but it also allows the injection of qaxis current that enables the PMSM’s torque production. The main idea of this method is to restrict the fault current rms, to limit the fault power losses and delay the fault propagation. Here, the fault current rms is not limited to the lowest possible value, instead, it is limited to a safe level that allows the machine to continue operating under reduced capacity. 1.4 Objectives and Contributions This objective of this dissertation is to provide a fault mitigation technique capable of limiting the amount of fault current, while allowing the PMSM to continue operating under restricted 5 operating conditions. High fault current levels promote the rapid propagation of the fault due to the thermal stress created by the increased fault power losses generated in a concentrated area. By using a magnetic field-weakening strategy at speeds below the nominal, to reduce the voltage induced in the faulted portion, it is possible to gain some control freedom over the fault current. The proposed method limits the amount of fault current in order to limit the fault power losses and delay the propagation of the fault; it also includes a detection strategy and a fault parameter estimation method. Estimation of the fault parameters is vital, since these parameters are used to estimate the rms value of the fault current and take action upon the fault, if necessary. The main research contributions are listed as follows: 1. A detailed analysis of the behavior and characteristics of faulted PMSMs, including simulations and experimental validation. This analysis shows how the fault current is developed and which operating conditions have higher impact on it. 2. A feasible detection and estimation algorithm for turn-to-turn faults based on the voltage space vector information. The method was successfully tested in the detection of several incipient turn-to-turn faults in the early stages; a 0.5 Ω and a 0.25 Ω faults across 15 turns out of the total 15 turns of the winding. One of the main advantages of this method is that it can be easily implemented in a DSP unit; it requires information of the machine parameters and operation prior to final development. This information comes in the form of lookup tables, a technique that is normally used in high performance controllers. 3. A mitigation algorithm capable of limiting the fault current to a predetermined safe 6 value, and allow continued operation of the PMSM under reduced capacity. Continuation of the motor operation is dependent upon the severity of the fault. Analytical, simulation and experimental data were used to test and validate the proposed methodology. Using a 3.8 kW - 25 A fault tolerant PMSM, developed at the MSU Electrical Machines and Drives Laboratory, it was possible to insert faults into the machine to test the proposed algorithm in a safe environment. 1.5 Organization First, in chapter 2 this work presents the theoretical background and modeling of healthy PMSM. The modeling of healthy PMSMs serves as a base point for the understanding of turn-to-turn faulted motors. Moreover, the models used for faulted motors are derived from the healthy models in chapter 3. The faulty models are detailed and accurate, and are utilized to estimate the amplitude and rms values of the fault current in chapter 5. Chapter 4 shows the characteristics and parameters of the single layer fault tolerant PMSM designed and assembled in the Electrical Machines and Drives Laboratory at Michigan State University. This motor was used to validate the proposed methodology in chapter 5. Chapter 5 is the core chapter of this work, as is there that the proposed methodology for detection, estimation and mitigation is presented. It is important to mention that the main contribution is the mitigation of the fault current; the detection and estimation methods were developed in order to test the mitigation. However, they were proven to work as a full fault mitigation system. Finally in chapter 7 all the conclusion are given. 7 Chapter 2 Theoretical Background 2.1 Healthy PMSM Analysis and Modeling This research is focused on three phase PMSMs with wye connected stator windings. A wiring configuration that is widely used in industry and traction drives systems. Commonly the neutral point in these machines is not accessible, only the three phases are available for the control of these machines through current controllers, iabc . The three phase stator windings and the reaction from the rotating rotor magnets in a PMSM are modeled as shown in figure 2.1. In this figure eˆabc represents the magnitude of the the induced sinusoidal EMF voltages and Mxy are the mutual inductances between the phases. La ia rs ib rs ic rs M ac M ab + eˆa = wl pm + Lb ˆ eb = wl pm M bc + Lc ˆ ec = wl pm Figure 2.1: Three phase model for a PMSM 8 For a three phase balanced system, the stator terminal voltages are given as follows, d d d ia + ωe λa + Mab ib + Mac ic dt dt dt d d d vb = rs ib + Lb ib + ωe λb + Mba ia + Mbc ic dt dt dt d d d vc = rs ic + Lc ic + ωe λc + Mac ia + Mbc ib dt dt dt va = rs ia + La (2.1) The electromagnetic torque produced by the PMSM is calculated using the power into the motor and the rotor speed as shown in 2.2. To = ea ia + eb ib + ec ic ωm (2.2) where ωm is the rotor mechanical angular speed. The rotor rotation is governed by, J dωm = To − Tload − kf ωm dt (2.3) where Tload is the load torque, J and kf are the moment of inertia and friction coefficient respectively. It is not common or convenient to use the three phase representation of the motor model to calculate terminal quantities, understand the behavior of the machine, and describe its control strategy. A better model representation is obtained by using the Park’s transformation matrix in equation 2.4. This matrix transforms the model in equation 2.1 to the rotor frame of reference dq, as shown in equation 2.5. 9  2π ) 3 2π ) 3 cos(θ +  cos(θ) cos(θ −  2 P =  sin(θ) sin(θ − 2π ) sin(θ + 2π ) 3 3 3  0.5 0.5 0.5        (2.4) The transformation matrix is invertible and used to transform bidirectionally, from (abc → dq) and (dq → abc). To transform from the abc frame of reference to the dq frame of reference the transformation matrix is used as follows, xdq0 = P · xabc (2.5) where x is the variable to be transformed. The dq frame of reference is known as the synchronous frame of reference, where all the electrical quantities are referred to the rotor position. Since PMSMs are synchronous machines, all the electrical quantities in the synchronous frame of reference do not change as in the stator reference; instead, the dq quantities become DC; this simplifies the analysis and control structure of a PMSM. The angle θ in equation 2.5 is extremely important for the transformation process, since it represents the new frame of reference. For PMSM this angle is the rotor position, which is obtained using a rotor position sensor or estimator. Fig. 2.2 shows the orientation frame to which the transformation is referred. It is a widely common practice to align the rotor position so that the flux linkage produced by the magnets, λpm , only shows up in the positive d-axis. Equations 2.6 to 2.9 show the machine model in the dq frame of reference, where the equation set 2.1 was transformed using Park’s transformation, with the alignment presented 10 q - axis Is Vs voltage - vector iq vq current - vector d vd d - axis id l pm q stator Figure 2.2: Steady State space vector diagram for IPMSM in figure 2.2. di vd = Rs id + Ld dtd − ωe Lq iq = Rs id + dλd dt − ω e λq di vq = Rs iq + Lq dtq + ωe Ld id + ωe λpm = Rs iq + dλq dt (2.6) (2.7) + ω e λd λd = Ld id + λpm (2.8) λq = Lq iq (2.9) where λd and λq represent the flux linkage in each of the axes and λpm is the flux linkage produced by the rotating magnets. This mathematical system of equations represents the equivalent circuit model shown in figure 2.3. 11 id Rs + Ld iq + - + vd we lq vq Rs + + wl e d + wl e pm - + - (a) PMSM d-axis equivalent circuit Lq (b) PMSM q-axis equivalent circuit Figure 2.3: Equivalent circuit model in the synchronous frame of reference, healthy machine model The torque in the synchronous frame of reference is given by, T = 3P λd iq − λq id . 4 (2.10) This classical model is based on ideal conditions, where the effects of iron losses, self and cross saturation are neglected. Nevertheless, it reveals essential information about the PM motor operation and behavior. Important remarks about the dq classical model are as follows: Torque is produced by the interaction between flux linkages and currents in each of the axes. It is produced by iq , since it is perpendicular to λpm , while id serves to adjust the amount of flux linkage in de d-axis. Normally in interior PMSMs id is negative, and used to optimize the amount of reluctance torque produced by the PMSM. It also allows for field weakening at high speeds. Back EMF voltage only shows up in vq , due to the alignment shown in figure 2.2. This allows the experimental rotor alignment using back emf voltage measurements. The id can demagnetize the magnets if it is not properly controlled. The flux along 12 the d-axis is a contribution from the flux generated using id and the established flux i by the magnets, λtotal = λdd + λpm . Having excess of negative id can permanently d demagnetize the magnets. 2.2 Non-ideal characteristics of PMSM The classical d- and q- axis model presented in the previous section is useful for understanding the operation principle of the machine. However, from the control point of view, the model lacks the non-ideal characteristics of a machine such as the self and cross saturation effects. These nonlinear effects are not negligible; in fact, they are very common and expected. In order to develop a high performance controller, the knowledge of these effects is essential. Better estimates of the machine inductances can be determined if the level of self and cross saturation is known. id and iq saturate the iron paths in each corresponding axis. When this happens, the flux linkages produced by the magnetizing currents are not longer decoupled as shown in the ideal model (2.8) and (2.9). Instead, the flux linkages become coupled to both axis currents; this coupling effect can be modeled as follows: λd id , iq = Ld (id )id + Ldq (id , iq )iq + λpm (2.11) λq id , iq = Lq (iq )iq + Lqd (id , iq )id (2.12) where Ld (id ) and Lq (iq ) are the baseline inductances for each of the axes. They represent the corresponding axis self-inductance as a function of the axis current and are calculated assuming no cross saturation from the other-axis current. Ldq id , iq and Lqd id , iq are 13 the cross coupling inductances for each of axis and add the cross saturation effects to the machine to the model. Equations 2.11 and 2.12 could be written in a variety of ways to model the effect of both currents on the d and q axis fluxes. The formulation used here assigns all the cross coupling to the quasi-mutual inductances Lqd and Ldq , the rest of the saturation to Ld and Lq , and no effect of saturation to the flux due to magnets, without decreasing the model accuracy. The machine model including the saturation effects is calculated by substituting equations 2.11 and 2.12 into equations 2.6 and 2.7. After simple algebraical manipulation the modified machine model is given by di di vd = Rs id + Ld (id ) dtd + Ldq (id , iq ) dtq (2.13) −ωe Lq (iq )iq + Lqd (id , iq )id di di vq = Rs iq + Lq (iq ) dtq + Lqd (id , iq ) dtd (2.14) +ωe Ld (id )id + Ldq iq (id , iq ) + λpm T = 3P λd id , iq · iq − λq id , iq · id . 4 (2.15) The parameters required to model a PMSM are determined experimentally using a process known as characterization. In this process the terminal voltages, currents and position of the rotor are measured for all operating conditions. All the measured data is used to mathematically solve the models backward and calculate the parameters. 14 2.3 Experimental Procedure and Characterization The characterization process is divided in two main procedures, experimental data collection and offline data processing. This section describes step by step the experimental process. This technique is described and validated in [34], where a simplified characterization method for PM machines was proposed, the simplified method is based on the methods presented on [35, 36]. It has reduced components count, since no AC voltages sensors or analog filters are required to measure the machine line voltages. The components used in this process are, a TMS320F28335 Digital Signal Processor (DSP) with CAN interface, current sensors, a DC link voltage sensor, and a computer to log the data via CAN communication, as it is shown in Fig. 2.4. These are the same components used in a traditional drive system, hence the method is suitable for field, non-laboratory environment. 2.3.1 Line to neutral voltage estimation The line to neutral voltage of phase A is required for the characterization process. Normally in motor drives the voltages are not measured or used by the control system. Without sensors to measure this quantity, it is accurately estimated using the known information in the DSP unit. Figure 2.4 shows the DSP as the main control unit for the DC-AC inverter that feeds the PM machine. Therefore, the voltage level at which the control unit is operating the inverter is known and it is possible to transmit this information via CAN interface to the data logging computer. 15 w PM Motor Dyno qe ia , ib , ic Speed Controlled data logging and post-process ABC Inverter Vdc DSP system Board Delfino F28335 CAN data flow Figure 2.4: Experimental Setup for the characterization process 2.3.2 Rotor Alignment The estimated line to neutral voltage is used to align the position sensor measurement to the rotor flux axis. A careful alignment must be performed, since the torque capability of the machine is very sensitive to position errors, [36]. The rotor position sensor measurement is properly align to the rotor flux axis using the following steps: 1. Provide sufficient DC voltage to the inverter, in order to be able to match the back EMF of the machine. The DC voltage can be estimated using the machine EMF vs. speed √ SV M profile to calculate, Vdc > 2vemf . SVM, stands for Space Vector Modulation. l−l 2. Set the inverter to regulate the machine line currents to zero. Then the dynamometer is used to spin the machine at a constant speed. The speed must be high enough to produce measurable back EMF, but below base speed. 16 3. Record the electrical rotor position measurement and the estimated back EMF voltage of phase A. If the desired orientation frame of reference is the one described by Fig. 2.2, the zero reading of the electrical rotor position sensor must be aligned with the positive peak of the back EMF voltage, as shown in Fig. 2.5. The rotor magnet flux linkage lags 90o from the produced back EMF, in vector notation it takes the form q λpm = λdpm + jλpm . λdpm takes the value of the magnet flux linkage at an electrical q position of 90 degrees, while the λpm is the value at 0 degrees, as indicated in Fig. 2.5. q Therefore, λpm = λdpm + jλpm = λdpm = λpm as it is described by Fig. 2.2, where the flux linkage due to the magnets lies positively in the d-axis. 4. Finally, after aligning the rotor, apply only a negative d-axis current to verify that no torque is produced. With the position sensor measurement aligned to the rotor flux axis, only the q-axis current is capable of producing torque. If a significant amount of negative d-current is applied and the machine remains at standstill the alignment is correct. On the other hand, if the machine moves with negative d-axis current, while keeping the q-axis current at zero, the alignment is not correct and the process must be repeated until perfect alignment is achieved. 1. 5 vemf 1 qe l t 0. 5 0 0 - 0. 5 o 90 360o o l vemf -1 - 1. 5 0 2 4 6 8 10 12 14 Figure 2.5: Rotor alignment using the electrical position and estimated back EMF 17 2.3.3 Experimental Data Collection Accurate estimates of the machine parameters are essential for the development of a high performance motor controller. The estimation process starts by accurately finding the machine flux linkage, λd id , iq and λq id , iq , considering the saturation effects on the machine. The necessary information to calculate the flux linkages are van , ia , and θ. These three quantities are available in the DSP unit, in the form of feedback and estimation in the case of the phase voltage. The information is used for control purposes, but also it is transmitted to the data logging computer, where the offline computation takes place. The first step of the experimental process is to use a dynamometer to rotate the PM machine at the desired speed. The speed at which the machine is characterized should be below the rated, but sufficiently high to produce a measurable back EMF. In the case where the core losses are to be considered, the process may be repeated for different speeds. While keeping the machine rotating at a constant speed the stator current Is is varied in steps from 0 to Ismax , and for every current step the current-angle δ is varied in steps from 90 to 180 degrees, for reference see Figure 2.2. For every combination of Is and δ van , ia , and θ are recorded. 2.3.4 Post Processing Parameter Extraction Data post-processing is performed offline after collecting all the required data points. In this work the data processing was carried out using the Matlab software tool. The corresponding axis quantities, i.e vd , vq , id and iq , are determined for every collected data point using the fundamental of the recorded waveform. Figure 2.6 shows an example on how to extract these d- and q-axis quantities from the recorded data, the black square 18 Line Current Line A Current 5 0 −5 Raw−current Fundamental −100 0 100 200 300 200 300 Van command θ (Position) 200 100 0 −100 −200 Commanded Voltage Corrected Voltage −100 0 100 θ (Position) Figure 2.6: Experimental data to determine the d- and q-axis quantities indicates d-axis values and the black circle indicates the q-axis values. Determining the value of the magnet flux linkage λpm is important, since it is part of the total flux linkage on the d-axis. It is estimated using the data collected at no current. With no current the inverter has to match the back EMF of the machine, therefore the permanent magnet flux is calculated as follows: λpm = vˆemf vq dθe = , ωe = ωe ωe dt (2.16) Using the d- and q-axis quantities and the value of λpm it is possible to calculate the actual flux linkages of the machine. All the collected data points were recorded while operating at steady state conditions and only the fundamental waveforms were used to estimate the dand q-axis quantities. Therefore, the derivative terms of equations 2.13 and 2.14 are zero. By combining equations 2.11 and 2.12 with equations 2.13 and 2.14 with all the derivatives 19 set to zero, the flux linkages equations are written as: vq − iq Rs ωe (2.17) i Rs − vd λq id , iq = d ωe (2.18) λd id , iq = If the d-axis flux due only to the d-axis current is required, it can be estimated by subtracting λpm from λd , see equation 2.11. The information extracted up to this point is sufficient to develop a high performance controller, since λd id , iq , λq id , iq are the actual non-ideal flux linkages of the machine. From them the machine torque can be calculated and lookup tables can be developed. The apparent axis inductances, are estimated using the flux linkages of the machine and the corresponding axis currents as follow: λ (i , iq ) − λpm Ld (id , iq ) = d d id Lq (id , iq ) = λq (id , iq ) iq (2.19) (2.20) Equations 2.19 and 2.20 are estimates of the machine inductances, where the cross coupling terms are neglected. For better accuracy the saturation model, in equations 2.11 and 2.12 is used to represent the flux linkages of the machine. The baseline inductances, Ld (id ) and Lq (iq ), and the cross-coupling terms, Ldq (id , iq ) and Lqd (id , iq q), are calculated as follows: λ (i , 0) − λpm λq (0, iq ) Ld (id ) = d d , Lq (iq ) = id iq (2.21) λ (i , 0) − λd (id , iq ) ∆λd (id , iq ) Ldq (id , iq ) = d d = iq iq (2.22) 20 Lqd (id , iq ) = λq (0, iq ) − λq (id , iq ) ∆λq (id , iq ) = id id (2.23) Using equations 2.21 - 2.23 it is possible to reconstruct the machine non-ideal flux linkages. Ldq (id , iq ) and Lqd (id , iq q) represent the deviations from the baseline inductors as the oppositive axis current is varied. 2.4 Field Oriented Vector Controlled PMSM A typical controller for PMSM is presented in figure 2.7, the design process for a torque controller is fully covered in [37]. This type of controller is known as the field oriented controller (FOC) for PMSM, where the magnet flux is oriented in the positive direction of the d-axis, as shown in figures 2.2 and 2.8. torque controller * Tcom current controller id* Model * based iq + PI vd vd* - id + PI vq dq vq* iq idq idq ia va* vb* * abc vc - q ,w DC Source iPark ' s DC AC Inverter q q ,w ib Shaft ic PMSM iabc dq abc q Park ' s Figure 2.7: Generalized torque controller for a PMSM The concept is to separately control the the d and q axes currents, id and iq , to achieve the desired torque. These two current components must be properly controlled and coordinated for each operating point. The direct axis current is used to control and adjust the amount of flux linkage on the direct axis and is not capable of producing torque. On the other hand, 21 Figure 2.8: Detailed FOC current controller for a PMSM the quadrature axis current is the main torque producing component. To illustrate the importance of commanding the correct current vector id + jiq → is ∠δ, the torque equation 2.10 is rewritten as follow, 2 1 Te = 3P 4 λpm is sin δ + 2 Ld − Lq is sin 2δ . (2.24) Equation 2.24 shows the two torque components in a PMSM. The main torque, produced by the interaction of magnets flux and iq and the reluctance torque that comes from the difference in the axes inductances and currents. Not all PMSMs have reluctance torque, this torque component is available on interior permanent magnets where Ld = Lq . Other types of PMSM, like surface mount, are only capable of producing the main torque as their axes inductances are equal, Ld = Lq . As shown in figure 2.9 PMSMs operate in two regions, the constant torque region and 22 the constant power region. The boundary for each operating mode is the rotor speed, for speed below the nominal it is possible to minimize the current amplitude with respect to the torque without exceeding the maximin ratings of the machine. This region is also known as the Maximum Torque per Amp (MTPA) region; the optimal current angle that results in d Te MTPA is determined using equation 2.24 as dδ is = 0. The optimum current angle for the entire MTPA region is determined by equation 2.25. This operating mode is shown in figure 2.10, this mode is the line segment that extends from the origin to point A.  δopt = cos−1 − λpm 4(Ld −Lq )is + λpm 4(Ld −Lq )is 2  + 12  (2.25) Once the motor exceeds the nominal speed it is no longer possible to continue MTPA operation, since the terminal voltage of the machine will exceed its ratings. In this case, the control is switched to field weakening, where the current angle is controlled in order to maintain the PMSM operating at its rated voltage. Controlling this angle controls the amount of id current. As shown in figure 2.2, this current opposes the flux linkage from the magnets and it is capable of reducing the amount of flux in the d-axis. Reducing this flux linkage, reduces de amount of voltage in the terminals of the machine. As shown in figure 2.10 there are two possible field weakening operating modes, mode 1 and mode 2. In mode one the controller applies field weakening so that the resulting voltage magnitude is equal to the machine rated voltage. This operating mode is shown in figure 2.10, and it is depicted by the line segment AB. In this line segment the machine operates under the rating current circuit, i2s = i2d + i2q , and its only constraint is the lines voltages. Voltage form an ellipse in the dq operating plane, and this ellipse shrinks as the speed continues to increase. Point B in figure 2.10 shows the point at which the machine current 23 Constant Torque Region Constant Power Region Torque Power Corner or Base Speed Speed Figure 2.9: PMSM operating regions rating will be exceeded if the machine speed continues to increase. The behavior of the voltage ellipse is governed by equation 2.26. vs2 = ωr2 [ 2 λ id + Lpm d 1/Ld iq + 0 + 1/Lq 2 ] (2.26) Mode 2 field weakening is not always available, it depends on the machine parameters and design. If point C is outside the current rating circle, then mode 2 is not available. The λ position of point C depends on the parameters of the machine and it is given by Lpm . If d point C is inside the current circle, the field weakening mode 2 is achieved by constraining the voltage and current applied to the machine for all conditions in the operating segment BC. Finally most controllers are developed solving the motor model backwards to find the best combination if id and iq that will result in the desired torque output and speed. Lookup 24 iq A Current circle Torque hyperbolas Voltage ellipse B MTPA line δopt id C Figure 2.10: PMSM operating path in the dq plane tables are often used to obtain the commands, given and operating conditions. In [37, 38] the torque and flux linkage information are used to develop develop the tables that follow the behavior shown in figure 2.10. Other authors use model based systems to develop the controllers, as presented on [39], [40] and [41]. 2.4.1 High Performance FOC Design for Traction Drives Applications; Including the Saturation And Cross Saturation Effects In this work high performance controllers were designed for two high power PMSMs, used in a traction drive system [42,43]. The application was a hybrid-electric ground vehicle capable of developing high torque and operate at higher speeds. Future ground vehicle platforms are expected to generate significantly greater levels of onboard electric power. While traditional alternators can provide approximately 600 A current at 28 V DC (16.8 kW ), emerging high-voltage generators directly driven by the engine’s crankshaft can produce nearly an order-of-magnitude increase in electric power 25 (125 − 160 kW ). Benefits of the increased electric power include greater electrification of vehicle loads and intelligent power management, including some of the most significant loads such as the main engine cooling fan(s) and air conditioning compressor. A key challenge remains to ensure that these loads along with the generator operate at maximum efficiency. The key to improving the performance and efficiency of a motor drive is to develop controllers based on real parameters, [34, 43, 44]. Such controllers are capable of acknowledging the parameters’ non-ideal behaviors and using them to operate as efficiently as possible. In this work, a method to approximate the parameters of a PMSM is proposed. The method is based on experimental data and it includes the saturation effects using piecewise linear functions. The method was validated, in the MTPA and field weakening regions, using simulations based on real parameters from two 125 kW PMSMs. The effects of iron saturation are covered in section 2.2, a graphical illustration of these effects is given in figure 2.11. Figures 2.7 and 2.8 show the typical configuration for a high performance FOC. It is important to note the relationship between torque and speed to the commands id and iq . For any operating condition (T and ωm ), there exist an optimal combination of (id and iq ) that maximizes the efficiency and delivers the required torque. The determination of all the combinations of id and iq for all operating conditions is performed prior to the development of the final controller. Often developers neglect these effects to simplify the controller design, and eliminate the need of characterizing the PMSM before the development of the controller. This can cause a serious decreases in the performance of the overall system, as the saturation effects in PMSM are considerably noticeable, [45]. 26 ! ! " # ! ! ! " # " "! #! " # !# "! ! # # # " "! #! $ " # ! # ! Figure 2.11: Self and cross saturation of the flux linkages 2.4.1.1 Parameters Extraction; To Demonstrate the Saturation Effects Two PMSMs, a motor and a generator, were characterized in order to study the effects of iron saturation. The characteristics for each machine are given in table 2.1. Table 2.1: Rated Specifications for the PMSMs Parameter Motor Generator Rated Power 125 kW 125 kW Rated Speed 1500 RP M 1900 RP M Max Speed 5000 RP M 3000 RP M Line Voltage 480 Vll 480 Vll Number of Poles 4 8 The parameters for both machines were determined at 700 RP M using the characterization technique presented in section 2.3. This speed is sufficient to generate a measurable back-EMF voltage and it is below the base speed. Therefore, it is possible to collect experimental data for all the combinations of id and iq up to rated current. The experimental results for the characterization process are shown in figures 2.12 to 2.15. 27 They demonstrate that self and cross-saturation are non-ideal characteristics and cannot be ignored or assumed to be negligible. For the motor, the flux linkage along the d-axis had as much as 38.5 % variation due to cross saturation, while along the q-axis it had as much as 23.7 % variation. The generator behavior is similar, with flux variations as high as 31.4 % on the d-axis flux and 14.5 % on the q-axis due to cross saturation. These non-ideal parametric variations have a negative impact on the torque production of the machine, since the torque is directly proportional to the flux linkages, as shown in equation 2.15. Efficiency is also affected, as the parametric variations will de-tune the motor controller. For a given operating condition, the de-tuned controller will not inject the optimal currents to generate the desired torque. This is because the saturation effects decrease the amount of flux linkages the machine can produce and the de-tuned controller has to compensate the torque mismatch by increasing the magnitude of the q-axis current. Resulting in a non-optimal id and iq commands to produce the desired torque. 2.4.1.2 Proposed Parameter Approximation In order to develop a high performance controller, accurate knowledge of the parameters is required across the entire operating range. Look Up Tables (LUTs) are commonly used to develop controllers based on real parameters. By using a controller based on a LUT, it is possible to fully include the non-ideal parameter behavior shown in figures 2.12 to 2.15 in the PMSM controller. The main drawback of a LUT is the required memory in the controller. The memory space requirement is directly proportional to the resolution of the LUT, [43]. In many applications, Digital Signal Processors (DSPs) are used to implement the controller. These DSPs are 28 125 kW PM Genertator, d−axis flux linkage 0.3 d d q λ (i ,i ) 0.2 0.1 0 Saturation due to iq −0.1 −200 −150 −100 −50 0 id −3 x 10 125 kW PM Genertator, d−axis Inductance 2 Ld(id,iq) 1.5 Saturation due to iq 1 0.5 −200 −150 −100 id −50 0 Figure 2.12: Generator experimentally extracted d-axis flux linkage and d-axis inductance. The Arrow points at the direction which iq is increased. commercially fabricated with a limited memory capacity. A LUT can be implemented in a DSP controller; however, the LUT resolution must be reduced to fit it in the available memory. This can lead to a decrease in performance of the controller, as information is removed from the table’s entries. An accurate curve-fit method to approximate the real parameters of the motor and generator is proposed in this section. The method is a dynamic piecewise linear approximation that includes the parameters’ non-ideal characteristics, i.e., the cross-saturation effect. It can perform as well as a full parametric LUT controller, but it will not overstress 29 125 kW PM Genertator, q−axis flux linkage 0.5 λq(id,iq) 0.4 0.3 0.2 Saturation due to id 0.1 20 40 60 80 100 i 120 140 160 180 200 180 200 q −3 125 kW PM Genertator, q−axis Inductance x 10 8 Lq(id,iq) 7 Saturation due to id 6 5 4 3 0 20 40 60 80 100 iq 120 140 160 Figure 2.13: Generator experimentally extracted q-axis flux linkage and q-axis inductance.The Arrow points at the direction which id is increased. the DSP/microcontroller memory, nor consume much computation time. For the case of Ld (id , iq ), the true inductance, shown in figures 2.12 to 2.14, is divided into two linear sectors, as shown in figure 2.16. The first step is to determine the baseline d-axis inductance from the experimental data, given by 2.27. Ld (id , iq ) = Ld (id , 0) (2.27) iq = 0 The two linear approximations for 2.27 are highlighted in figure 2.16 by the line with stars 30 125 kW PM Motor, d−axis flux linkage λ pm 0.8 λd(id,iq) 0.6 0.4 0.2 Saturation due to iq 0 −200 −3 x 10 −150 −100 id −50 0 125 kW PM Genertator, d−axis Inductance 6 Ld(id,iq) 5.5 Saturation due to iq 5 4.5 4 3.5 −200 −180 −160 −140 −120 −100 id −80 −60 −40 −20 0 Figure 2.14: Motor experimentally extracted d-axis flux linkage and d-axis inductance. The Arrow points at the direction which iq is increased. markers. Finally, the cross saturation for this case is added by subtracting from this baseline approximation, as the other axis current increases. It is assumed that cross-saturation in the d-axis increases linearly with the q-axis current. The incremental function is defined as Λ(iq ). By using the experimental data and inspection, it is determined that the function representing the cross-saturation terms is as shown in equation 2.28. Finally, the total inductance in these two sectors is given by equation 2.29. 1&2 (i ) = Λsec q d 31 −∆L (iq ) iq irated (2.28) 125 kW PM Motor, q−axis flux linkage 1.2 λq(id,iq) 1 0.8 0.6 0.4 Saturation due to id 0.2 20 40 60 80 100 iq 120 140 160 180 200 125 kW PM Motor, q−axis Inductance 0.025 Saturation due to id Lq(id,iq) 0.02 0.015 0.01 0 20 40 60 80 100 iq 120 140 160 180 200 Figure 2.15: Motor experimentally extracted q-axis flux linkage and q-axis inductance. The Arrow points at the direction which id is increased. 1&2 (i ) Ld (id , iq ) = Ld (id ) + Λsec q d (2.29) In figure 2.16, the two sector linear approximations and the true experimental inductances are plotted together to illustrated the approximation accuracy. The dashed straight line segments are the linear approximation, while actual parameters are represented by the solid lines. The q-axis inductance requires more linear sectors, as shown in figures 2.13 to 2.15, since it suffers higher saturation than the d-axis quantities. Instead of two sector to approximate 32 Ld including Saturation and Cross−Saturation −3 5.5 x 10 5 Sector 2 Ld(id,iq) 4.5 4 3.5 3 ΛL(iq) 2.5 2 Sector 1 1.5 −250 −200 −150 −100 −50 0 id Figure 2.16: Motor d-axis inductance piecewise linear approximation, including cross saturation. this inductance, four sectors are used as shown in figure 2.17. ! %# #$$%& *&(++,+-.#&-."(/ !"#$%&( %# '()%& !"#$%&' *&(++,+-.#&-."(/ $ # #$$%& *&(++,+-.#&-."(/ " # #$$%& $ # '()%& ! !"#$%&) !"#$%&* 0$ " # '()%& 0 0" " Figure 2.17: q-axis inductance piecewise linear approximation, including cross saturation in four sectors. The linear approximations made in each sector are discussed from right to left, beginning with sector 4. As shown in figures 2.13 to 2.15, the effect from the d-axis current is minimal 33 in this segment. Therefore, the inductance approximation is made by finding the equation of the line that passes through points ζ4 and ζ5 as shown in figure 2.17. In sector 3, the cross-saturation effects are added by introducing a slope change to the base line inductance Lq (0, iq ). In this sector, ζ4 is a fixed point, but the slope of the baseline inductance is adjusted as a linear function of id as shown in equation 2.30, and the crosssaturation is added using Λsector3 (id ) in equation 2.31. The expression to determine the d approximated q-axis inductance in sector 3 is given by equation 2.32. m(id ) = ζ3 lower − ζ3 upper ζ4 − ζ3 upper · id + id rated · (x4 − x3 ) x4 − x3 (2.30) ζ3 upper − ζ3 lower · id + ζ3 upper irated (2.31) Λsector3 (id ) = d Lq (id , iq ) sector3 = m(id ) · (iq − x3 ) + Λsector3 (id ) d (2.32) In sectors 2 and 1, the linear approximation is made using the same technique used for the d-axis inductance in equation 2.29; where the slope is constant and the cross-saturation is modeled by the linear function Λsector2&1 (id ). Note that all values of ζ are known from q the experimental data. The complete approximation for the motor q-axis inductance along with the true experimental values are shown in figure 2.18. The inductance approximations for the generator were determined using the same technique and the results are similar to those of the motor. 2.4.1.3 Controller Performance Evaluation To evaluate the accuracy of the proposed parameter approximation method, a performance simulation based on experimental data was developed for each PMSM, as shown in figure 34 Lq including Saturation and Cross−Saturation 0.03 0.025 L q Approximation (black dashed) 0.02 0.015 0.01 True Value (red) 20 40 60 80 Q axis Currentiq 100 120 Figure 2.18: Motor q-axis inductance piecewise linear approximation on top of the experimental q-axis inductance. 2.19. The simulation was performed with four different controllers; one using a highly detailed parametric LUT including the saturation effects, one LUT without the saturation effects, one using parameters determined using FEA magneto static analysis and finally one with the proposed approximation method. For this study, only the copper losses were considered. This leads to high efficiency results, but it serves as a proof of concept. First, a highly detailed controller was developed using a LUT. This controller contains all the saturation effects of the motor. Therefore, this controller is used as the baseline. The tables’ resolution has steps of 2.5 A from zero to 250 A. For each current step there is a table entry that matches a torque command and a speed to a set of id and iq . The second controller was developed using experimental data, but the cross-saturation effects were ignored. For this case the table’s resolution is the same as the first case. The third controller was developed using the proposed parameter approximation method. Finally, a controller based on parameters from FEA was developed to compare with the experimental parameters based controllers. The controllers developed using the proposed and FEA parameters are based on curve fit methods, not LUT. 35 !"#$%' "%#$%)* +,%%- !"!#$4!+"#!''&# ()*&%$!+5 67$3&")1'&%$8)#)2&"&#*$ 97$8)#)2&"&#*$:;! $$$$<#!**$*)"-#)"1!+ =7$8#!0!*&%$ &">!% ?7$@.A$B)*&%$ $$$$0)#)2&"&#* .-C D .#C !"!#$ !%&' ()*&%$!+$,#-&$ ./0 &+")'$3)") (- E.- D .# F !"#$%&' '(!))%) (# E.- D .# F Figure 2.19: Simulation based performance evaluation, using the PMSM experimental parametric data. Each controller was tested in the MTPA and field-weakening regions. For each region, the torque command was varied from 200 Nm to maximum, and the copper power losses and torque for each operating point were calculated. The results for the performance simulation are shown in figures 2.20 to 2.23. Figures 2.20 and 2.21 show the performance simulation for the generator. For both operating regions, the controller that performed almost as well as the baseline, the high resolution LUT controller, was the controller designed with the proposed parameter approximation method. This statement is based on the lower power losses and the torque tracking effectiveness. Figure 2.20 shows that minimum power losses were achieved with the base line controller and the controller using the proposed parameters approximation technique. On the other hand, the controllers designed using FEA parameters and the parameters ignoring crosssaturation are the controllers that yielded the highest power losses. Similar behavior was 36 Losses as a function of loading 1600 P Power Copper Losses 1400 1200 1000 loss w cross−sat (LUT) Ploss w/o cross−sat (LUT) P w proposed P w FEA loss loss 800 600 400 200 200 250 300 350 Tcom 400 450 500 (a) Generator power losses at nominal conditions Losses as a function of loading 1200 Power Copper Losses Ploss w cross−sat (LUT) 1000 Ploss w/o cross−sat (LUT) Ploss w proposed 800 Ploss w FEA 600 400 200 200 210 220 230 240 250 Tcom 260 270 280 290 300 (b) Generator power losses at 3000RPM, field weakening region Figure 2.20: Generator Plosses in MTPA and field weakening mode, only considering copper losses. noted for the torque performance shown in figure 2.21 where the controller designed using the proposed parameters follows the detailed LUT controller torque performance. The motor exhibited similar behavior as shown in figures 2.22 and 2.23. However, power losses are higher for the motor, this is because it has a higher line resistance and is more prompt to higher cross-saturation than the generator. The motor has higher cross-saturation 37 Generator Torque Performance 500 450 Toutput 400 350 300 Tout w cross−sat (LUT) 250 Tout w/o cross−sat T out 200 w proposed Tout w FEA 150 200 250 300 350 Tcom 400 450 500 (a) Output torque vs. commanded torque profile in the MTPA region Generator Torque Performance 320 T w cross−sat (LUT) T w/o cross−sat out 300 out T output 280 260 Tout w proposed T out w FEA 240 220 200 180 200 210 220 230 240 250 Tcom 260 270 280 290 300 (b) Output torque vs. commanded torque profile in the field weakening region, 3000 RP M . Figure 2.21: Generator Tout mismatch with the commanded torque Tcom . due to the intensity of the magnets flux linkage (λpm ), which is much higher in the motor than in the generator. The intense flux linkage saturates the iron and makes the machine prompt to suffer cross-saturation. For the motor, the controller designed using the proposed parameter approximation method had the closest performance to the detailed LUT controller. 38 Losses as a function of loading 4000 P w cross−sat (LUT) P w/o cross−sat (LUT) P w proposed P w FEA Power Copper Losses loss loss 3000 loss loss 2000 1000 0 200 250 300 350 400 Tcom 450 500 550 600 (a) Motor power losses at nominal conditions Losses as a function of loading 4000 P w cross−sat (LUT) P w/o cross−sat (LUT) Power Copper Losses loss 3500 loss Ploss w proposed Ploss w FEA 3000 2500 2000 1500 200 210 220 230 240 250 Tcom 260 270 280 290 300 (b) Motor power losses at 3000RPM, field weakening region Figure 2.22: Motor Plosses in MTPA and field weakening mode, only considering copper losses. 2.4.1.4 Remarks In this section, the effects of iron saturation on the performance of a motor drive are studied using two PMSMs. The flux linkages and inductances of each machine were determined through a characterization process and are shown in figures 2.12 to 2.15. Saturation is evident from these figures and cannot be ignored or assumed negligible. 39 Motor Torque Performance 700 Tout w cross−sat (LUT) 600 w/o cross−sat T w proposed T w FEA out out 500 Toutput T out 400 300 200 100 200 250 300 350 400 Tcom 450 500 550 600 (a) Output torque vs. commanded torque profile in the MTPA region. Motor Torque Performance 300 T w cross−sat (LUT) T w/o cross−sat out out Toutput 250 Tout w proposed Tout w FEA 200 150 200 210 220 230 240 250 T 260 270 280 290 300 com (b) Output torque vs. commanded torque profile in the field weakening region, 3000 RP M . Figure 2.23: Generator Tout mismatch with the commanded torque Tcom . It is possible to obtain the parameters required to design a motor controller through FEA simulations or experimental data collection. The inclusion of cross-saturation effects in the controller development is vital to ensure a high performance, high efficiency controller. A method to include these effects is proposed. It was tested against controllers based on high resolution LUT, LUT without cross-saturation, and FEA parameters. Figures 2.20 and 2.21 demonstrate the validity of the method. The simulations showed that the proposed 40 method results in low losses and good torque performance; both metrics are comparable to the performance of the high resolution LUT controller at both MTPA and field weakening regions. Compared with conventional approaches, the proposed method applied to a 125 kW machine contributed to a reduction in copper losses as high as 900 W , resulting in an efficiency gain of 1.36%. The proposed controller, incorporating a dynamic piecewise linear approximation of the machine flux linkages, is realizable in the majority of motor control DSPs used in high performance PMSM controllers due to its computational efficiency. This efficiency also reflects on the memory utilization in the DSP unit, figure 2.24 the memory utilization for various control techniques. The controller helps to improve the dynamic response of the drive and its improved efficiency contributes to a decreased thermal burden on the cooling system in vehicle applications. Momory (kB), DSP: TMS320F28335 DSP Memory Usage vs. Control Method 500 512 kB 400 DSP capacity 10168 entries 300 8080 entries 200 4800 entries 100 0 Total DSP Look−up Tables Implementation Method Parameters Approximations Approximation Figure 2.24: DSP memory utilization based on the control method, including look-up table resolution. 41 Chapter 3 Modeling of Permanent Magnet Synchronous Motors under a Turn-to-Turn Fault Modeling is an essential tool to understand the behavior of PMSMs and develop new techniques for PMSMs. It enables researchers to study operational characteristics and come up with control techniques before trying them in a real system. This chapter develops a faulty machine modeled to predict the behavior of a faulted PMSM and design a controller capable of mitigating the fault. Modeling is an important part of fault mitigation systems. Faulted PMSMs models are derived from the healthy operational characteristics and models. There are two types of models, FEA parameters based and analytically derived. The first one, consist in calculating all the machines parameters using FEA, including the parameters of the faulted winding and the remaining healthy windings. While in the second modeling method, the faulted parameters are estimated from the healthy parameters. These models are similar for detection, control and characterization techniques, [3, 20, 46, 47]. 42 3.1 Winding and Fault Severity A turn-to-turn fault is modeled by splitting a portion of a healthy phase coil into two separate coils, denoted as ah for the healthy part and af for the faulted area. The number of turns involved in the fault is denoted as Nf and the total number of turns per phase is Ntotal . The schematic representation for a faulted machine is shown in figure 3.1. A fault resistor, rf , is included in the model to take into account the severity of the damaged winding. A turn-to-turn fault starts with low severity, rf → ∞, and as the winding insulation continues to deteriorate it has the potential to become a highly severe fault or short circuit, where rf → 0, [12]. Winding insulation deterioration is due to many possible reasons, among these possibilities are: high voltage spikes from the DC link and PWM phase voltages, aging, overheating and mechanical stress. b if rf a ah Ntotal af Ntotal ( Ntotal - N f ) Nf c Figure 3.1: PMSM with a turn-to-turn fault on phase A Once a fault is developed, a circuit path is created through rf . This circuit allows the fault current, if , to flow, and it puts in danger the integrity of the whole PMSM. This dissertation shows that this current has the potential to grow as high as or even higher than 43 the current ratings of the winding. Therefore, a method to detect and correct is required in applications where lives could be in danger. For researchers, the term fault mitigation means to completely extinguish the fault current, if . In this work the mitigation technique is aimed to gain a degree of control over the fault current, not necessarily achieve complete suppression of it. 3.2 Detailed Modeling of turn-to-turn Faults A turn-to-turn fault affects the electrical quantities in the phase it resides. It directly reduces the flux that links the coil, the voltage and increases the line current. This presents challenges in the control, as the system is no longer three phase balanced. This type of fault is modeled with the electrical circuit shown in figure 3.2 and has been adopted and validated by others; [19], [24], [21]. M a f ah faulted winding (a f ) rf if L af icf + healthy winding (ah ) Lah ia + M ah c eˆah = Dwl pm Maf b M ahb ib + Lb ˆ eb = wl pm M bc ib + Lc eˆaf = Dwl pm Maf c eˆc = wl pm Figure 3.2: Three phase electrical model for a faulted PMSM Each coil is modeled using its own resistance, self and mutual inductances and its induced back EMF. The induced voltage across rf depends on the number of turns involved in the 44 fault, and is estimated using the ratio (∆) between Nf and Ntotal . Nf Ntotal (3.1) Ntotal − Nf = (1 − ∆) Ntotal (3.2) ∆= ¯ = ∆ The mathematical expressions for the faulted machine shown in figure 3.2 are determined using circuit analysis techniques. This mathematical model is shown in the system of equations 3.3.     vah          vaf      =      vb         vc  rah 0 0 0   0   ia      raf 0 0    ia − if ·    ib 0 rs 0      ic 0 0 rs 0  Lah    Ma a  h f +   Ma b  h  Mah c 0 Mah af Ma b Mah c h Laf Ma b Maf c f Ma b f Lb Mbc Maf c Mbc Lc where the back emf voltages are given by,                   eah          ea    f  + +      eb        ec      ia          ia − if   d    dt         ib       ic ¯ pm · sin(θ) eah   ωe · ∆λ      eaf    ωe · ∆λpm · sin(θ) =   eb   ωe · λpm · sin(θ − 2π 3 )     ec ωe · λpm · sin(θ + 2π 3 ) (3.3)            (3.4) The back EMF in the total phase is the sum of the healthy and faulted induced back 45 EMFs voltages. From figure 3.2, the voltage equation for each of the coils in phase A is given by, va = vah + vaf (3.5) vaf = if · rf (3.6) By replacing equations 3.5 and 3.6 into the model equation 3.3, it is possible to rearrange the system of equations with the turn-to-turn fault as shown by the new system of equations 3.7.                    ia   ea          ib    eb  + +     ec  ic        −ef if    (3.7) La Ma b + Ma b Mah c + Maf c −(Laf + Mah af )   ia  h f          Ma b + Ma b Lb Mbc −Ma b i b d    h f f     dt      Mah c + Maf c Mbc Lc −Maf c i c       −(Laf + Mah af ) −Ma b −Maf c Laf if f           0 0 −raf va   rs      rs 0 0 vb    0 =    0 rs 0 vc    0   −raf 0 0 raf + rf 0           ·         The system of equations 3.7 is more suitable to represent and model a faulted PMSM and it can be divided in two parts. First, rows 1 → 3 represent the remaining healthy part of the motor and the influence of the fault current. This part of the model shows that the PMSM is capable of keep on operating and producing torque after a turn-to-turn fault takes place. The second part is the faulted circulating current model, this is the fourth row in the system of equations. This fault current is governed by the number of turns involved in the 46 fault, the line currents and the rotor speed as ef ∝ ωe . Some remarks deducted from this model are as follows: 1. The fault current is directly proportional to the fault resistance, this includes the winding internal resistance raf and the resistance due to the damage to the insulation rf , named the fault point of contact. 2. High mutual inductances between coils have a negative impact in the performance of a faulted PMSM. This is because mutual inductances between the coils enable the remaining phases in the machine to contributed toward the fault current in a indirect manner. 3. Parameters are dependent on the PMSM topology and the number of turns involved in the fault. For accuracy, these parameters are determined using finite element analysis, (FEA). 3.3 Frame of Reference Transformation Including the Fault As shown in equation 3.7 the system has four variables. This complicates the transformation as Park’s in equation 2.4 transforms three variables to two. This problem is solved by augmenting Park’s transformation matrix. The resultant matrix is known as the Concordia transformation and is given in equation 3.8, [19]. 47  2π ) 3 2π ) 3 cos(θ +  cos(θ) cos(θ −   2π 2π 2  sin(θ) sin(θ − 3 ) sin(θ + 3 ) Γ(abcf →dqh f ) =  0 3 1 1 1  2 2 2   0 0 0  0    0     0    (3.8) 3 2 This transformation is used to change from the stator frame of reference to the rotor frame of reference, (3.9), including the fault.              d        q     = Γ    h0      f  ia    ib     ic    if (3.9) In this new set of equations, h0 is the zero sequence component. For a faulted machine h0 = 0 as the fault throws off the electrical symmetry of the stator windings. Equations 6.1 to 3.13 show the faulted model of a PMSM in the dq frame of reference. dif di vd = 2/3(id rs + ed + Ld d −if raf sin(θ) − (L + Mah af ) sin(θ)) dt dt af (3.10) = v¯d + v˜d vq = 2/3(iq rs + eq + Lq dif diq −if raf cos(θ) − (L + Mah af ) cos(θ)) dt dt af = v¯q + v˜q where v¯ is the expected healthy value and v˜ is the variation cause by the fault. 48 (3.11) The zero sequence component of the applied voltage vector and the fault voltage are calculated using equations 3.9 and are shown in equations 3.12 and 3.13. vo = ho = vf = f = 3 2 dif 1 −if raf − (Laf + Ma1 a2 ) + eo 2 dt dif dia −ia raf + if (raf + rf ) − ef − (Laf + Ma1 a2 ) + Laf dt dt Equation 3.13 comes from the extended Concordia Park’s transformations. 49 (3.12) (3.13) Chapter 4 Fault Tolerant Machines Specifications and Characteristics Two PMSMs were designed and built to study the effects of turn-to-turn faults in PMSMs, a fractional 2/5 SP P single layer machine and a fractional 1/2 SP P double layer machine. These types of motors are used in transportation products, such as hybrid powertrains, where any type of failure can endanger lives. This drives the motivation and the interest in studying how different winding configurations affect the fault behavior and determine which type of winding has better fault tolerance. Extensive experimentation was performed to both machines to demonstrate and study the fault behavior for each winding configuration. The detailed design process for the machines is fully described in [48], and the background theory comes from [49]. This work is focused on fault current mitigation for turn-to-turn faulted PMSMs and therefore, only a brief description about the motor parameters is presented in this chapter. 4.1 Design Standard induction motor WEG frames were used to house the fractional winding permanent magnet machines. This fabrication method is simple, fast and low cost, but the final product has poor cooling properties. Cooling issues were overcame by performing short duration 50 experiments under controlled operating conditions. Having poor cooling is bad for any electrical component; however, for research purposes, this bad quality offers a way to study the thermal effects due to a fault under accelerated conditions. 4.1.1 Stator and Rotor Configuration Figure 4.1 shows the motors used to study the behavior of turn-to-turn faults and the possibility of fault current mitigation. Both motors have concentrated windings, this type of winding has better fault toleration than distributed windings. The reason is that in concentrated windings the phases are wound physically separated from each other. The difference in the two windings is the number of layers. Figure 4.1(a) shows a single layer machine vs. figure 4.1(b) that is a double layer machine. As shown in figure 4.1(a), single layer machines offer better physical isolation between the phases. In this winding topology the phase coils do not share the stator teeth nor the slot opening, therefore, maximum physical isolation is archived. The advantage of having physically isolated coils is that in the event of a controlled failure, only the affected phase suffer the effects of the fault, not the remaining phases. The double layer machine, figure 4.1(b), also has a concentrated winding, where each coil is separately wound. The disadvantage with this winding configuration is that the coils share the slot openings. Depending on the fault severity, a healthy coil sharing the slot with a faulted coil could be affected by the effects of the fault. 51 (a) A single layer 2/5 SP P concentrated fractional (b) A double layer 1/2 SP P concentrated fracwinding PMSM tional winding PMSM Figure 4.1: Fault tolerant PMSM with fractional winding configuration Table 4.1: Stator and Rotor physical specifications 4.2 Motor parameters 2/5 SP P machine 1/2 SP P machine number of phases 3 3 number of slots 12 6 number of poles 10 4 number of turns per coils 150 152 Rotor Diameter 69 mm 49.2 mm Stator Diameter 110 mm 91 mm Airgap 1 mm 1 mm Machine Length 72 mm 72 mm Magnet type NdFeB NdFeB Winding Configuration A detailed study of turn-to-turn faults is not feasible with off-the-shelf PMSMs, as the windings are internally connected and only the three input phases are accessible. Therefore, the fault current, induced by an insulation failure between two or more turns, is not measurable from the input terminals. This problem was solved by constructing the two PMSMs with the phase A winding sectioned into coils as shown in figure 4.2. Each of these coils is wired and 52 connected to an interconnection box, where it is possible to externally insert a fault resistor and monitor the circulating fault current. Stator 120 turns Coil 4 15 turns Coil 3 14 turns 1 turn Coil 2 Coil 1 h toot 150 turns Phase B Coil 150 turns - total Phase A Coil 150 turns Phase C Coil (a) Stator Winding configuration for the double layer 2/5 SP P concentrated fractional winding PMSM Stator 121 turns Coil 4 15 turns Coil 3 15 turns 152 turns Phase B Coil Coil 2 1 turn h toot Coil 1 152 turns - total Phase A Coil 152 turns Phase C Coil (b) Stator Winding configuration for the double layer 1/2 SP P concentrated fractional winding PMSM Figure 4.2: Stator winding configuration for the fabricated PMSMs Splitting of a phase coil into separated coils, as shown in figure 4.2, allows for the study of the fault current behavior as a function of the number of turns involved. For example, it is possible to study a one turn failure by inserting any fault resistance across coil 1. Coils 1 and 2 can be combined to represent 10% of the turns in the coil faulted; while the combination 53 of coils 1, 2 and 3 can be used to represent a 20% coil failure. The resistance of the coils, rs , is determined analytically by estimating the length of the coil and the its cross sectional area using the resistance equation 4.1. These quantities are estimated using the wire gauges and winding configuration information. R=ρ l A (4.1) The resistance value is verified using accurate measurements once the machine is assemble. In this work the resistance was measured using a multi-meter. 4.3 Finite Elements Analysis: Magneto Static Analysis to Extract parameters This chapter is focused on the determination of the machine parameters using finite elements analysis, which is a reliable tool for electro-mechanical simulations. These parameters are used to populate and solve the faulted PMSM model presented in chapter 3. Through FEA it is possible to determine all the parameters for any specific fault scenario. 4.3.1 Inductance Determination Procedure, Including a Turn-toTurn Fault To determine the inductances of the phases and the faulted coil a magneto static FEA simulation was performed without the rotor magnets, as it is shown in figure 4.1. This eliminates the magnetic flux due to the magnets and allows for the determination of the coil inductances. The geometry used for the inductance determination is shown in figure 4.3, 54 where phasef models the turns involved in a fault. phase B phase f phase C phase A phase f phase C ' phase A ' Air phase B ' Figure 4.3: FEA geometry setup for the magneto static simulation, used to determinate the inductances of the 2/5SP P machine. In the finite elements analysis each phase region, including the faulted region phasef , is assigned to a coil conductor. The analysis is performed by applying current in only one of the coils conductors, while measuring the magnetic flux across all the coils conductors. Using this information the self and mutual inductances for a given fault scenario are calculated using equation 4.2. inductance = λ i (4.2) The same finite elements analysis and geometric alteration procedures were performed for the 1/2SP P machine. 55 4.3.2 Fault Study Case and Nominal Parameters In this section the inductances required to develop model equation 3.3 are determined for the specific case of a fifteen turns insulation failure. The technique described in section 4.3.1 is used to determine these inductances for the specific case, but it is applicable to any other fault scenarios. 150 L Inductance (mH) ah M ah−af 100 Mah−b M ah−c 50 0 0 50 100 150 Rotor angle θ (degrees) 200 r (a) Phase A remaining healthy coil ah inductance Lah and the mutual inductances between the other coils, including the faulted region. Specific case: Nf = 15 turns - 2/5 SP P single layer machine. 150 L Inductance (mH) ah 100 Mah−af 50 Mah−b M ah−c 0 −50 −100 0 50 100 150 Rotor angle θ (degrees) 200 r (b) Phase A remaining healthy coil ah inductance Lah and the mutual inductances between the other coils, including the faulted region. Specific case: Nf = 15 turns - 1/2 SP P double layer machine. Figure 4.4: Inductances determination; in this case current is applied only to the healthy part of phase A and the magnetic flux generated by the current across all the coils is measured. 56 150 L Inductance (mH) b M b−c Mb−af 100 50 0 0 50 100 150 Rotor angle θr (degrees) 200 (a) Healthy phase B coil ab inductance Lb = Ls and the mutual inductances between the other coils, including the faulted region. Specific case: Nf = 15 turns - 2/5 SP P single layer machine. 200 L b Inductance (mH) 150 Mb−c 100 Mb−af 50 0 −50 −100 0 50 100 150 Rotor angle θ (degrees) 200 r (b) Healthy phase B coil ab inductance Lb = Ls and the mutual inductances between the other coils, including the faulted region. Specific case: Nf = 15 turns - 1/2 SP P double layer machine. Figure 4.5: Inductances determination; in this case current is applied only to the healthy phase B and the magnetic flux generated by the current across all the coils is measured. It is important to notice the inductance behavior differences between the single layer 2/5 SP P machine and the double layer 1/2 SP P . Figures 4.4, 4.5 and 4.6 show the main and most important difference between the machines, where high mutual inductances were detected in the double layer winding. The mutual inductances between the phases for the double layer machines oscillates between 36.65 mH and 83.45 mH as shown in figure 4.5(b). 57 0.8 L Inductance (mH) af Maf−c 0.6 0.4 0.2 0 0 50 100 150 Rotor angle θr (degrees) 200 (a) Faulted coil af inductance Lf and the mutual inductances between the other coils, including the healthy phases Ma c = Ma b . Specific case: Nf = 15 turns f f 2/5 SP P single layer machine. Inductance (mH) 10 Laf 5 Maf−c 0 −5 −10 −15 0 50 100 150 Rotor angle θ (degrees) 200 r (b) Faulted coil af inductance Lf and the mutual inductances between the other coils, including the healthy phases Ma c = Ma b . Specific case: Nf = 15 turns f f 1/2 SP P double layer machine. Figure 4.6: Inductances determination; in this case current is applied only to the faulted coil conductor and the magnetic flux generate by the current across all the coils is measured. In the double layer machine the slot opening contains two different coils from two different phases, as shown in figure 4.2; therefore, high coupling between all the coils exists. This behavior does not exist in the single layer winding machine, since each coil is wound around a tooth and dosn’t share any slot opening. This gives the advantage to the single layer 58 2/5 SP P machine as a fault tolerant PMSM. Another peculiarity on the 1/2 SP P machine is the magnitude of the inductances variation as a function of the rotor position. Figure 4.5(b) is a clear example of these inductances variation, in the 2/5 SP P machine the Lb varies from 110.5 mH to 115.3 mH, whereas in the 1/2 SP P the variations are from 81.5 mH to 150.0 mH. A summary of the machine parameters is given in tables 4.2 and 4.3. Table 4.2: Healthy PMSM Parameters Motor parameters 2/5 SP P machine 1/2 SP P machine Ls = La = Lb = Lc Ms = Mbc = Mca = Mab 112 mH average 122 mH average 62 mH average λpm Rs ≈0 0.23 V.s 1.51 V.s 1.5 Ω 1.5 Ω Table 4.3: Machine Parameters Based on a 15 turns fault 4.4 Motor parameters 2/5 SP P machine 1/2 SP P machine Lah 107 mH average 92 mH average Laf 0.655 mH average 8.8 mH average Ma a h f M a b = M af c f 6.35 mH average 13.7 mH average ≈0 11.7mH General Impedance Model for Turn-to-Turn Faulted PMSMs In section 4.3.2 a technique to determine the parameters of the faulted machine, for a specific number of faulted turns, using finite elements analysis is described. The technique is accurate and detailed; however, it only models one specific fault scenario. A model that accounts for fault severity changes is important in order to facilitate the study of the progression of a fault and its implication on the PMSM performance. In this 59 section the fault parameters are modeled using the information of the healthy machine with an analytical model based approximation. This allows the estimation of the fault quantities for any fault scenario in a relatively simplistic way. First, the inductance of a Ntotal turns coil conductor around a tooth is calculated using P, the permeance, as shown in equation 4.3. 2 P L = Ntotal (4.3) If an insulation failure occurs, the coil conductor is modeled by dividing the entire coil into two: a healthy and a faulted area as shown in figure 4.7. af zf ah tooth Nf Ntotal Figure 4.7: Single tooth, containing the faulted coil The inductances for each of the coils is calculated as follows; A l (4.4) Af lf (4.5) 2 Ls = µNtotal Laf = µNf2 A Lah = µ(Ntotal − Nf )2 ah lah 60 (4.6) where Ls , Laf and Lah are the healthy inductance, the inductance of the faulted coil and the inductance of the remaining healthy coil, respectively. To find an analytical expression for the faulted coil inductance Lf , as a function of the number of turns involved in the fault and the healthy inductance, equation 4.5 is divided by equation 4.4. The resultant expression is given by equation 4.7. Laf = Ls ∆2 kAl (4.7) kAl is a constant that represents the changes in the permeance of each coil due the fault. In this research the value of kAl is determined using finite elements analysis. The value is dependent on the fault location and the turns involved in the fault. Other important quantities to model the fault behavior are the mutual inductances between the faulted coil and all other healthy coils. This quantities are calculated using the healthy data of the machine as follows; Mah af = ∆(1 − ∆)Ls (4.8) Ma b = Maf c = ∆Ms f (4.9) The proposed parametric modeling technique presented in section 4.4 is validated using FEA data as shown in figure 4.8. The FEA data was obtained using the parameter determination process presented in section 4.3 for different fault case scenarios; the results are compared to the analytically determined values as shown in figure 4.8. Both FEA and model based parameters are in agreement for the range of fault scenarios in figure 4.8. Experimental validation of the proposed parametric modeling is shown figure 4.9, for 61 0.03 L Model af Coil Inductances 0.025 0.02 L FEA af M ahaf Model Mahaf FEA 0.015 0.01 0.005 0 0 0.05 0.1 0.15 0.2 Percentage of Faulted Widing 0.25 0.3 Figure 4.8: Parametric validation, where kAl = 2.5 and rf = 0.5 Ω two operating conditions. For this validation the fault current was determined using FEA, calculated using the model with the analytical approximation of the parameters and experimentally measured. Experimental FEA Model 6 Fault Current (A) Fault Current (A) 10 Experimental FEA Model 8 5 0 −5 4 2 0 −2 −4 −6 −10 −8 −15 20 40 60 Rotor Angle θr 80 60 80 100 120 140 Rotor Angle θr 160 180 (a) Comparison for for commanded current I = (b) Comparison for commanded current I 10 A < 90o 10 A < 150o = Figure 4.9: Experimental, finite elements and modeling results comparison. Study case: 15 faulted turns, 300 RPM. The same modeling technique applies to the 1/2 SP P machine. 62 4.5 Torque Experimental Determination Figure 4.10 shows the torque profile for each of the PMSMs, determined from experimental data. These curves are required for the development of high performance motor drives. From them, it is possible to determine the conditions for which maximum torque per amp is achieved. |i|com = 5 A 50 |i|com = 10 A Torque (Nm) 40 |i|com = 15 A |i|com = 20 A 30 |i| com = 25 A 20 10 0 100 120 140 160 Current Sapace Vector angle (degrees) 180 (a) 2/5 SP P machine torque as a function of the current space vector angle 80 Torque (Nm) 60 40 20 0 100 120 140 160 Current Sapace Vector angle (degrees) 180 (b) 1/2 SP P machine torque as a function of the current space vector angle Figure 4.10: Torque profiles as a function of the current space vector angle (δ), legend on figure 4.10(a) applies to figure 4.10(b) 63 Chapter 5 Fault Current Analysis and Behavior This chapter explores the behavior of the fault current under different operating conditions. Through modeling, FEA and experimental data it is demonstrated that some degree of control is gained over if by controlling the current angle δ. The concept is to use the angle of the space vector current to keep if at bay. It is demonstrated that using a field weakening technique at speeds below the rated gives sufficient controllability over if , enough to limit the current to a predetermined value. 5.1 Fault Current Analysis The fault current in vector form is given by equation 5.2, it is calculated from the fault model described by figure 3.2 and equation 3.7. In this form it is clear that the fault current is fed by three quantities. The first one is the current in the phase where the fault resides (ia (t)), the second quantity is the back EMF produced by the machine, and finally (ib (t)) and (ic (t)) through the mutual inductances between the faulted coil to the remaining healthy coils. Zaf = rf + raf + jωLaf where Zaf is the equivalent impedance across EMF eaf . 64 (5.1) if = ia · raf + jω · (Laf − Maf ah ) ∆λpm ω jω · (Maf b · ib + Maf c · ic ) + − Z af Z af Z af (5.2) The fault current contribution due to the mutual inductances, Ma b and Maf c , in equaf tion 5.2 can be neglected depending on the topology of the PMSM. The electrical circuit shown in figure 5.1 must be carefully studied using the motor winding structure and geometry to determine the impact of the mutual inductances. Generally PMSMs are designed with low mutual inductances, such as the single layer winding PMSM presented in chapter 4. rf ia Lah coilah raf M ah a f Laf Maf b if + Dwl pm ib ic coilc coilb Maf c Figure 5.1: Electrical model for the faulted phase Mah af plays an important role in the development of fault current in the faulted area. This mutual inductance, Mah af , is not negligible as the faulted coil shares the same slot with the remaining healthy part of the coil. This coupling between the healthy and faulted parts of the coil allows ia (t) to contribute toward the fault current in a direct manner, as it is electrically connected and indirectly through Mah af . Assuming that Ma b and Maf c are nearly zero, the fault current phasor in equation 5.2 f is simplified to equation 5.3. For the purposes of this work, this assumption is valid, since 65 the 2/5 SP P machine presented in chapter 4 is used for experimental validation. ia contribution if = ia · raf + jω · (Laf − Maf ah ) Z af ∆λpm ω Z af + (5.3) Back EMF contribution With this assumption the main contributors to the fault current are ia (t) and the back emf induced by the magnets across the faulted coil. The line current ia (t) is a quantity that depends on the operating conditions of the PMSM, speed, power and torque. Therefore, it is important to regulate these operational conditions under post-fault operation. 5.1.1 Induced Fault Current in the Faulted Loop In this subsection the fault current contribution from the back emf, as shown in the second terms of equation 5.3 is analyzed. The fault severity (rf ) and the rotor speed are contributors to the fault current by magnetic induction. To understand this behavior the line currents are set to zero. Under this condition, if exist only if the PMSM rotor moves inside the stator. The electrical model for this case is given by the circuit shown in figure 5.2 and the fault current in the time domain is calculated as shown in equation 5.4. rf raf ia = 0 if + Laf e af = Dwl pm Figure 5.2: Fault current as a function of the rotor speed and fault Severity if (t) = ∆ωλpm sin(ωt) Zaf 66 (5.4) The magnitude of the fault is calculated as a function of the speed and the fault severity (rf ) as shown in equation 5.5. |i|f = eaf Zaf = ωe ∆λpm Rf2 + ωLaf 2 = ∆λpm 2 · ω2 Rf2 + ωLaf 2 (5.5) where Rf = rf + raf Having knowledge of the fault current magnitude helps to determine which operating conditions exceeds the current limits of the winding. Equation 5.5 is analyzed at its extreme conditions, when the impedance approaches a pure resistor and when it approached an inductive behavior. First let assume that Rf ≫ XL af , where the fault impedance is mostly inductive. Under this condition the fault current magnitude is approximated as, |i|f ≈ ∆λpm · ωe Rf (5.6) For a PMSM with a low severity faults, where Rf is reasonably larger, it is concluded that the fault current is directly proportional to the speed. The fault current shows a linear behavior with a slope equal to ∆λpm R . This slope is directly related to the number of f turns involve in the fault and the characteristic rotor magnets flux linkage. The second case to study, is the case when the impedance is dominated by the inductance term, XL af ≫ Rf . For this case the fault current is estimated as follows, |i|f ≈ ∆λpm ∆λpm λpm N λpm ≈ 2 = = total Laf ∆Las Nf Las ∆ Las where Las is the healthy characteristic line inductance. 67 (5.7) For this extreme case, the fault current is only dependent on the number of turns involved in the fault and the PMSM characteristics, not the rotor speed. Figure 5.3 shows the complete fault behavior dictated by equation 5.5. It also demonstrates that fault tolerant PMSMs designed with relatively high inductive characteristics are better at limiting the fault current, as it is bounded by ∆λpm /Laf . |i | f Δλ pm L af r > r > r >r af1 af2 af3 af4 X >> R f Laf raf4 r af3 r af2 r af1 Rf >> XLaf m= Δλ pm L af ω Figure 5.3: Open circuited PMSMs, fault current behavior 5.1.2 Fault Current Worst Case Scenario It has been reported that the worst case scenario for a PMSM is the single turn fault. This statement is based on the fact that this fault has the lowest impedance and, therefore can allow the highest fault current flow. However, this statement is only valid for full short faults, where rf = 0 Ω, as shown in figure 5.4. Table 4.2 shows the parameters used for this case study of the worst case scenario. The goal of this work is to study the behavior of the fault current in the early stages of 68 a turn-to-turn fault, where rf > 0 Ω, and before the fault becomes a full short circuit. The idea to to develop a controller capable of adjusting the operating conditions of the motor, that maintains acceptable currents and temperature levels, in order to stop the propagation of the fault. 25 rf=2 mΩ rf=10 mΩ rf=1 Ω rf=0.5 Ω Fault Current Magnitud 20 15 10 5 0 0 0.05 0.1 0.15 0.2 Percentage of Faulted Widing 0.25 0.3 Figure 5.4: Open circuited PMSM at 300 RPM, worst case scenario as a function of the fault resistenace Special consideration must be taken when dealing with incipient faults, as the maximum fault current no longer occurs when there is a single turn fault. Figure 5.4 shows the displacement of the maximum fault current peak as rf increases. This behavior is due to the change in impedance across the fault. For low severity faults the worst scenario happens when the number of turns involved in the fault is considerably large. For this case, the current is primary driven by the emf voltage, if ≈ eaf /rf , and in order to create high fault current high eaf is required, which means more faulted turns. The worst case for the fault current, in terms of the number of turns involved in the fault, is entirely coupled to the fault across the turns. In order to avoid over-stressing the faulted PMSM, this behavior must be well understood, since there is the possibility of operating 69 under the worst case scenario, and the control algorithm must recognize all the possible operating conditions. 5.2 Sensitivity Analysis Sensitivity analysis is used to determine the effects upon the fault behavior due to changes in a parameter. The sensitivity, Sf ault→ξ , is calculated as shown in equation 5.8. With this analysis it is possible to determine how the current space vector, magnitude and angle, affects the fault current. The model shown in equation 5.3 is used to find the sensitivity of fault related quantities to changes in a parameter or input quantities as follows: Sf ault→ξ = ∂F ∂ξ (5.8) ∂F = F + Fchange (5.9) ∂ξ = ξ + ξchange (5.10) where ∂ξ is the quantity changed by ξchange and ∂F is the change in the behavior due to ∂ξ. The sensitivity of the fault voltage vf = if rf is determined in equation 5.11, in order to understand the effect of the current space vector angle upon the fault voltage. The results for Si r →∂δ are shown in figure 5.5. This figure shows how the sensitivity of the fault f f voltage to the control angle δ increases as the current space vector angle is increased. It is important to notice that as the angle (δ) is increased, the voltage across the fault decreases. Having higher sensitivity as δ increases and the fact that the slop is positive, means that the voltage across the fault becomes more alterable as the angle δ is increased. 70 Si r →∂δ = f f ∂(if rf ) ∂δ (5.11) where ∂δ = 90o − δchange . Since the fault current becomes more alterable as the angle δ is increased, a degree of control is gained upon this fault current. This translates to a gain of control over if by controlling the current angle δ. This serves as the basis for the mitigation technique proposed in this Dissertation. 0.3 0.2 f f S = δ i *r / δ δ 0.25 0.15 0.1 0.05 90 100 110 120 130 140 150 160 Current Space Vector Angle (δ) 170 180 Figure 5.5: Sensitivity of vf = if rf to changes in the current space vector angle (δ). Operating conditions; ∆ = 15/300, speed = 300 rpm, |Ia | = 5 A and rf = 0.5 Ω. A similar behavior is noticed with the sensitivity of the voltage across the fault due to changes in the current space vector magnitude is calculated. This calculation was performed according to equation 5.12 for different values of the angle δ, and the results are shown in figure 5.6. It is concluded that the changes in |Is | have more effect upon the voltage across the fault as the angle δ is increased. This is in accordance this figure figure 5.5 and means that at higher angles the if becomes more alterable; and therefore, the magnitude of the current space vector has higher impact upon if . 71 ∂(if rf ) Si r →∂|Is | = f f ∂ |Is | (5.12) where ∂ |Is | = |Is | − |Is | · %change. 0.85 with 20% with 40% with 60% 0.75 f f S = δ i *r / δ i am 0.8 0.7 0.65 90 100 110 120 130 140 150 160 Current Space Vector Angle (δ) 170 180 Figure 5.6: Sensitivity of vf = if rf to changes in the current space vector magnitude. Operating conditions; ∆ = 15/300, speed = 300 rpm and rf = 0.5 Ω. 5.3 Fault Current Behavior for Various Operating Conditions: Analysis using FEA and Experimental Results In this section the fault current behavior is tested using FEA and experimental data for different operating conditions. The FEA and experimental setups are discussed in subsections 5.3.1 and 5.3.2 respectively. The goal of this subsection is to test the effects of the current angle δ upon the fault current. As mentioned in previous sections, this angle plays a vital role in the behavior of 72 the fault current. 5.3.1 Transient Magnetic FEA Setup The geometry with the detailed mesh and the electric coupled circuit, used to simulate the fault, are shown in figures 5.7 and 5.8 respectively. These were developed using the electrical and mechanical specifications for the machines described in chapter 4. The regions for each of the areas are the same as in figure 4.3, where the faulted area is denoted by the black regions. Figure 5.7: FEA geometry, including calculation mesh for the 2/5 SP P PMSM. The circuit shows the different coils and passive elements in the machine, where Rs and Ls represent the line resistances and inductances. The faulted coil component is denoted by Aaf , while Aah represents the remaining healthy part of phase A coil, where the fault is inserted. The healthy phases B and C are represented by the coils components B and C. Equations 5.13 to 5.15 shows the expressions for each of the current sources in figure 5.8. The parameters swept and step size for the FEA simulations are given in table 5.1. 73 r f Ia Ls Aah Rs Aaf Ib B C Ic Ls Rs Ls Rs Figure 5.8: FEA Circuit, with the A coil divided into the healthy Aah and the faulty Aaf parts. Table 5.1: Simulation parameters range and step size Simulation parameter Range Rotor Angle Movement θ 0 to 180o 90 to 180o Current Angle δ ia (t) = I sin(θp + δ) Step size 2o 10o (5.13) ib (t) = I sin(θp − 2π + δ) 3 (5.14) ic (t) = I sin(θp + 2π + δ) 3 (5.15) where p are the pole pairs of the machine. 74 5.3.2 Experimental Setup Figure 5.9 shows the block diagram of the setup utilized to collect all the experimental data. The top level controller in this figure controls the inverter in current mode; this control structure is described by the vector control setup shown in figure 2.7. The main characteristics of the electronics are given in table 5.2. 30 turn fault connection Data Logging i f , ia if Scope ia A' 15 turn fault 1 turn fault connection connection if if if A30 A CAN Top-level controller ia , ib , DC B B' C C' ic , va , AC qe Inverter A15 A1 PMSM Winding Configuration Figure 5.9: Experimental setup, with sectioned windings to insert the fault externally. The figure shows the winding configuration for the 2/5 SP P PMSM. Table 5.2: Inverter and controller details Specification value Specification value Imax Vdc max CAN transmission speed 300 A TI-DSP TMS320F28335 800 V fsw 10 kHz 1 M bit/sec Sampling Rate 100 µs The experimental data is recorded through the electric drive controller area network (CAN), to log the voltages command, rotor position and measured line currents. Using a high resolution oscilloscope the fault current and line current are measured. Information from the CAN unit and the scope are stored in the data logging computer. 75 10 8 Healthy R05 10% R05 20% R025 10% R025 20% iq 6 4 2 0 −10 −9 −8 −7 id −6 −5 −4 Figure 5.10: Measured current vector, vd + jvq, while the 2/5 SP P PMSM experiences different fault conditions. Experiments were conducted at different angles of δ ,1200 , 1400 , 150o and 170o , throughout the experimentation process the space current vector magnitude at 10 A. 5.3.3 Drive’s Current Controller Performance Under Turn-to-Turn Fault Faults create harmonics, unbalanced conditions and other disturbances that can affect the performance of a motor drive. In this work the performance is defined as the capacity of the drive to maintain the commanded currents, under any operational condition. The controller performance is tested in this section because maintaining the correct current vector is crucial in the control of the fault current, especially the current angle δ. The effectiveness of the current controller was tested for all the fault cases shown in fig. 5.10. As shown in this figure, the current controller was able to keep the desired direct and quadrature axis currents, regardless of the fault condition. Each data cluster in fig. 5.10 results from the angles 1200 , 1400 , 150o and 170o of the current space vector; the magnitude of the vector was kept constant at 10 A throughout the experiment. The current waveforms for the fault case, rf = 1/2 Ω with 15 turns at 300 RPM, are 76 Phase A current for different angles Phase A current 10 o 5 δ=120 δ=140o 0 δ=150o o δ=170 −5 −10 500 550 600 650 samples 700 750 800 Figure 5.11: Phase A current in time domain, for different angles and a fixed magnitude of 10 A. The fault case is the 1/2 Ω fault for 15 turns at 300 RPM. shown in fig. 5.11. This figure demonstrates that the controller is capable of tracking the commanded current, without having significant harmonic distortion. 5.3.4 Fault Current Behavior FEA and experimental data were collected for faults across 15 and 30 turns with rf = 0.5 Ω; while the speed was kept constant at 300 RP M. The current magnitude |I| is kept constant to show only the effect of the current angle δ on the fault current. Normally in a motor drive both quantities, |I| and δ change depending on the operating conditions. However, in this section the interest is to only show the dependence of the fault current on the angle, not the magnitude. Figures 5.12 and 5.13 show the resultant fault current when the commanded line current magnitude |I| is kept constant at 10 A, but its angle δ is swept from 90o to 120o and finally to 150o. An important remark, is the decrease of the fault current magnitude as the current angle increases. This behavior was consistent for the 15 and 30 turns faults. The fault progression and severity are mainly aided or caused by excess of heat in the 77 FEA i vs δ, for 300 RPM, R =0.5 Ω f f 15 o δ = 90 Fault Current 10 o δ = 120 5 o δ = 150 0 −5 −10 −15 0 50 100 150 Rotor Position θ (a) Finite elements simulation for 90o , 120o and 150o . Experimental if vs δ, for 300RPM, Rf=0.5 Ω 15 o δ = 90 Fault Current 10 o δ = 120 δ = 150o 5 0 −5 −10 −15 0 0.5 1 Samples 1.5 2 4 x 10 (b) Experimental results for 90o , 120o and 150o Figure 5.12: Results for a fault current thought 15 faulted turns, with rf = 0.5 Ω. Speed fixed at 300 RP M and current space vector magnitude set to 10 A. This data was taken using the 2/5 SP P machine. faulted location. This heat is caused by the increased power losses which depend on the true rms of the fault current; it is important to understand how the fault current true rms value changes as a function of the current angle. The effects of the true rms of the fault current are determined using the FEA and experimental data shown in figures 5.14 and 5.15. Figures 5.14 and 5.15 show the resultant rms values for the 15 and 30 turns faults. Both figures show the attenuation of the true rms fault current. This shows how applying a field weakening d-axis current at speeds below the nominal reduces the fault current true rms value. Since, both data sets are in accordance with very similar results, it is concluded 78 FEA i vs δ, for 300 RPM, R =0.5 Ω f f 30 o δ =90 Fault Current 20 o δ =120 o 10 δ = 150 0 −10 −20 −30 0 50 100 150 Rotor Position θ (a) Finite elements simulation for 90o , 120o and 150o Experimental if vs δ, for 300RPM, Rf=0.5 Ω 30 δ = 90o Fault Current 20 δ = 120o δ = 150o 10 0 −10 −20 −30 0 0.5 1 Samples 1.5 2 4 x 10 (b) Experimental results for 90o , 120o and 150o Figure 5.13: Results for a fault current thought 30 faulted turns, with rf = 0.5 Ω. Speed fixed at 300 RP M and current space vector magnitude set to 10 A.This data was taken using the 2/5 SP P machine. that the analysis and the FEA simulation setup are correct and closely resemble the real experimental results. The effects of the current angle upon the fault current rms value were also tested at higher speeds, at 300 RP M, 500 RP M and 700 RP M, using experimental and FEA data; for different faulted turns conditions, 15 and 30 turns; and for different contact point resistances, rf = 0.5 Ω and rf = 0.25 Ω. Figures 5.16, 5.17 and 5.18 show the fault current rms values behavior for δ = 120o, 140o , 150o and 170o . The swept on the current angle δ starts at 120o , since it is the optimal angle for maximum torque per amp (MTPA) operation and 79 Fault Current rms 9 FEA Experimental 8 7 6 5 4 90 100 110 120 130 140 150 160 Current Space Vector Angle 170 180 Figure 5.14: FEA and Analytical fault current RMS comparison for a 15 turns fault, with rf = 0.5 Ω. Speed fixed at 300 RP M and current space vector magnitude set to 10 A. This data was taken using the 2/5 SP P machine. 20% fault with 0.5 Ω fault Fault current rms value 16 FEA Experimental 14 12 10 8 6 90 100 110 120 130 140 150 160 170 180 θ r Figure 5.15: FEA and Analytical fault current RMS comparison for a 30 turns fault, with rf = 0.5 Ω. Speed fixed at 300 RP M and current space vector magnitude set to 10 A. This data was taken using the 2/5 SP P machine. the machine never operates below this angle. Even at higher speed and for different fault conditions, fault current mitigation is achieved as the angle δ is increased. As the current angle δ increases, as a mitigation strategy to decrease the fault current causes, the output torque of the machine to be reduced. The worst case scenario studied in this work is shown in figure 5.17, where rf = 0.5 Ω and Nf = 30 turns at 500 RPM. Under normal operation the PMSM should be operating at the MTPA current angle, with 80 if vs. δ at 300 RPM 15 turns with Rf=0.25Ω Fault Current rms 18 30 turns with Rf=0.25Ω 16 14 12 10 120 130 140 150 160 Current Space Vector Angle 170 Figure 5.16: Fault current rms value as a function of the current space vector angle at 300 RPM and current space vector magnitude set to 10 A. This data was taken using the 2/5 SP P machine. if vs. δ at 500 RPM Fault Current rms 18 16 15 turns with Rf=0.5Ω 14 30 turns with Rf=0.5Ω 12 15 turns with R =0.25Ω f 10 8 120 130 140 150 160 Current Space Vector Angle 170 Figure 5.17: Fault current rms value as a function of the current space vector angle at 500 RPM and current space vector magnitude set to 10 A. This data was taken using the 2/5 SP P machine. i∗ = 10 A∠120o , producing 24.7 Nm as shown in figure 4.10(a). However, once the fault occurs, the fault current rms value becomes 18.8 A, as shown in figure 5.17, which is higher than the winding rated value. In order to mitigate the fault and continue safe operation, the controller must increase the angle δ until a safe point in reached. Assuming the new angle be δ = 150o , the fault current rms becomes 16.2 A and the machine torque drops to 17 Nm. With this new angle, the machine torque output is reduced, but the fault current rms value is kept below the rated value. 81 if vs. δ at 700 RPM Fault Current rms 16 15 turns with Rf=0.5Ω 15 14 13 12 11 120 130 140 150 160 Current Space Vector Angle 170 Figure 5.18: Fault current rms value as a function of the current space vector angle at 700 RPM and current space vector magnitude set to 10 A. This data was taken using the 2/5 SP P machine. The work and results presented above in this section 5.3.4 were performed for the 2/5 SP P single layer PMSM. The same technique was experimentally tested using the double layer 1/2 SP P PMSM. The double layer 1/2 SP P PMSM exhibited the same behavior as the single layer 2/5 SP P PMSM. That is; the reduction of the fault current rms Experimental Measured Fault Currents value as the current angle δ increases. o Is = 5 ∠ 90 Amps 10 I = 5 ∠ 140o Amps s o Is = 5 ∠ 150 Amps 5 0 −5 −10 0 0.2 0.4 0.6 0.8 1 Samples 1.2 1.4 1.6 1.8 2 4 x 10 Figure 5.19: Fault current for different current angles, while the current space vector magnitude is kept at constant at 5 A. This data was taken using the 1/2 SP P machine. 82 In figure 5.20 the rms value for each current angle was calculated, while the magnitude was kept at 5 A. It is important to notice the fault current reduction as the angle δ is increased. This behavior confirms that the fault current can be reduced in the double layer machine as well, regardless of the value of mutual inductances. However, higher reduction Experimental Measured Fault Current rms of fault current was achieved for the single layer machine. 5 4.5 4 3.5 3 2.5 90 100 110 120 130 140 Current Space Vector Angle 150 160 Figure 5.20: Fault current rms value as a function of the current space vector angle at 300 RPM and current space vector magnitude set to 5 A. This data was taken using the 1/2 SP P machine. Some important remarks about the machines are: Higher fault current reduction was noted for the single layer 2/5 SP P PMSM. This is primary due to the machine’s lower mutual inductances and the fact the inductance, Ls , is large and limits the fault current. Better experimental stability during a fault event was achieved on the single layer machine. High torque and mechanical vibration were noted in the double layer 1/2 SP P PMSM. 83 Although, the single layer machine showed better fault tolerant characteristics, fault current reduction was achieved in both machines. 5.4 Thermal Relief A thermal simulation was performed using MotorCAD to show how changes in the current angle δ to mitigate the fault current can relieve the temperature rise caused by the turn-toturn fault. MotorCAD uses built-in templates that utilize the actual measurements of the machine to generate the simulation geometry. This presents a modeling problem, since it is impossible to generate the exact geometric of the machine under study. The actual geometry of the machine utilized in this work is shown in figure 4.1(a) and it was approximated using the MotorCAD built in templates as shown in figure 5.21(a). The winding configuration inside each of the slots is shown in figure 5.22. (a) MotorCAD motor geometry front view (b) MotorCAD motor geometry 3D view Figure 5.21: MotorCAD geometry approximation of the actual machine shown in figure 4.1(a) 84 Figure 5.22: MotorCAD slot and winding configuration MotorCAD is designed to simulate the thermal behavior in healthy machines. Therefore, it is not possible to simulate a PMSM with a turn-to-turn fault in a straight manner. To approximate the behavior of a turn-to-turn faulted three phase machine, a forth winding is added in the simulation. This forth winding is set to represent the loss distribution in the faulted coil Aaf , while the other three are configure to represent the loss distributions in Aah , B and C winding coils. The loss distribution in the simulations are calculated from the experimentally measured quantities in each specific case. Because MotorCAD does not provide any means to add a fault, and it is approximated using a fourth phase windings, it is not possible to simulate a transition from healthy to faulted conditions. However, it is possible to simulate each of the operational conditions, for each current angle δ. The simulations were performed for the rf = 0.5 Ω, Nf = 15 turns at 300 RPM fault case, for the different current angles. To study the temperature rise and fall, the machine was simulated running at the corresponding load for 60 sec, followed by a 60 sec no-load condition. The results of this simulations are shown in fig. 5.23; (H 120d) stands for 85 healthy at δ = 120o , (R05 120d) stands for faulted with rf = 0.5 Ω at δ = 120o, the same nomenclature is used for the rest of the cases. The loading condition for each angle is shown in fig. 4.10(a); where the torques corresponding to of the each angles are the following: (δ = 120o → 24.7 Nm), (δ = 140o → 21.3 Nm) and (δ = 150o → 17 Nm). Temperature Rise vs. time Winding HotSpot (C) 36 34 32 30 H 120d R0.5 120d R0.5 140d R0.5 150d 28 26 24 0 20 40 60 time (sec) 80 100 120 Figure 5.23: Thermal simulation for various current angles, healthy case and the rf = 0.5 Ω, Nf = 15 turns at 300 RPM case. The current space vector magnitude is kept constant at 10 A for all simulations. For this fault, operating at δ = 1400 , instead of the MTPA angle δ = 120o is better in terms of thermal stress. Operating with this angle reduces the output torque by only 3.4 Nm. However, the fault current is kept within acceptable limits, with a 10% drop as shown in figure 5.14, and the operating temperature is restored to nominal conditions, as shown in fig. 5.23. 5.5 Chapter 5 Remarks Analytical sensitivity calculations showed that the fault current becomes susceptible to the current angle δ, as δ increases into the field weakening region. Equation 5.3 shows how the line current in the faulted phase and the back emf contribute toward 86 the fault current. The induced current by the back emf can be controlled using the line current angle. Various experimental results demonstrated that changes in the current angle δ can reduce the fault circulation current, reducing the fault power losses and hence the operating temperature. The idea is to operate the faulted machine in the field weakening region, even if the speed is below base, to reduce the voltage induced in the faulted area. Thermal simulations demonstrate the thermal relief when the machine operated in field weakening below nominal speed, as a fault current reduction remedial technique. 87 Chapter 6 Proposed Methodology for Fault Mitigation This chapter discusses a fault mitigation technique and its effectiveness in reducing the fault current. Once a fault takes place in the stator windings there is a high possibility of having overcurrent in the faulted area. This over-current condition has a negative effect on the motor performance and its operating temperature. It is essential to mitigate these effects to avoid a catastrophic event. The key objectives of this technique are denoted as follows: Maintain healthy current levels across the lines and the fault circuit loop. Keep all motor components operating under the maximum allowed temperature. If conditions allow continue operation under limited torque conditions. The proposed method uses the current angle δ to mitigate the fault; and it also limits the machine capacity to avoid over current conditions. Figure 6.1 shows the space vector plane for the PMSM, it demonstrates how the increasing current angle δ cancels some of the flux linkage due to the magnets λpm . The induced voltage in the faulted coil depends on the total flux linkage, vemf = ωe λtotal . As the angle increases, id becomes more negative and produces a flux λd that opposes the magnet flux λpm . The flux cancelation effect reduces the fault current due to the reduction of induced voltage. 88 q-axis Is iq δ id λ pm d-axis ϴ λd = id Ld Figure 6.1: Space vector plane, dq axes A fault mitigation technique relies on the ability to detect and estimate the fault conditions. A turn-to-turn fault creates unbalanced operating conditions that serve as indicators for fault detection purposes. 6.1 Fault Detection and Fault Current Estimation In this work, fault detection is made using the variations in the voltage space vector, vd = vd +jvq . As stated in the introduction this topic has attracted a lot of work and contributions. Here we base the method on [24] and [25]. The effects of the fault in the voltage vector are analyzed using the model shown in equation 3.7. This model is simplified by neglecting the mutual inductances between the phases. A valid assumption, since a single layer fault tolerant PMSM with negligible mutual inductances is used for experimental validation. To derive the space vector form, equation 3.7 is transformed into the dq rotor frame of reference; the direct and quadrature axes voltages are shown in equations 6.1 and 6.2. 89 di vd = 2/3(id rs + ed + Ld d dt dif −if raf sin(θ) − (L + Mah af ) sin(θ)) dt af (6.1) = v¯d + v˜d vq = 2/3(iq rs + eq + Lq −if raf cos(θ) − diq dt dif (L + Mah af ) cos(θ)) dt af (6.2) = v¯q + v˜q where v¯ is the expected healthy value and v˜ is de variation cause by the fault. The fault current fundamental value depends on the induced emf voltage and the line current commands, which are relatively sinusoidal. By considering only the fundamental component of if , of the form if = if cos(θ), equations 6.3 and 6.4 are determined. These equations only show the variations on the voltage space vector due to the fault. 1 v˜d = { if raf sin(2θ) 3 (6.3) + if (Laf + Maf ah )(cos(2θ) − 1)} 1 v˜q = { if raf + if raf cos(2θ) 3 (6.4) + if (Laf + Maf ah ) cos(2θ)} A turn-to-turn fault introduces oscillations of double angle and a dc offset shift on the axes voltages. The oscillations on the voltage vector are not a practical indicator for fault 90 detection purposes. A more practical approach is to use the dc offset shift, as a simple digital filter in the controller can extract the information. Figure 6.2 shows the dc offset shift tendency for the voltage vector. Experimental and finite element data agree with the vector movement and tendency as the fault progresses. 19 Experimental FEA Tendency 18 17 Vq 16 15 14 13 Healthy 12 11 −112 −110 −108 −106 −104 Vd −102 −100 −98 −96 Figure 6.2: Changes in the voltage space vector for different fault conditions at 300 RP M with 10A∠120o for the 2/5 SP P machine. Starting from healthy, then moving to rf = 0.5 Ω@ 15 turns, rf = 0.25 Ω@ 15 turns, rf = 0.5 Ω@ 30 turns, and finalizing with rf = 0.25 Ω@ 30 turns Estimates of the parameters of a fault, Nf and rf , are used to determine the severity of the fault and the amount of fault circulating current. Nf and rf are estimated based on the position of the voltage vector, as shown in figure 6.2, it takes a particular position depending on Nf and rf . As a fault progresses the tendency of the voltage space vector is to increase more on the q-axis than in the d-axis, as shown in figure 6.2. This behavior observed in FEA and experiments validates equation 6.3 and 6.4, since for the machine under study raf >> (Laf + Maf ah ) and the dc offset in the q-axis is proportional to if raf . 91 In this work, v˜q is used to detect and estimate the fault, given that the dc shift of the vector is more significant in the q-axis. As discussed in section 2.4.1.3, high performance controllers use lookup tables to control the machine for different operating conditions. These tables are generated by characterizing the PMSM over the operating range prior to the development of the control algorithm. Therefore, the controller has information and predictions of the expected axes voltages, for all the desired operating range of the motor. In this work we treat any persistent discrepancy in vq as a turn-to-turn fault; and the magnitude of this discrepancy is used to estimate Nf and rf . Figure 6.3 shows the detection technique experimental performance, when a 0.5 Ω fault is inserted across 15 turns of winding A. The delay between the fault insertion point and the detection time is due to the heavy moving average filtering of vq . Detection, using the mean of v˜q , requires a heavy moving average filtering to remove the controller noise, as shown in figure 6.3. The decision to rise the fault flag is only taken using the mean of v˜q when the machine is operating under steady state conditions. This is to avoid false alarms during transitory operation. Once, Nf and rf are estimated the fault current magnitude is estimated using the system model on figure 3.2. This model can be solved for |if | as follows, Rf = rf + raf X= Rf2 + (ωLaf a = id raf Rf + ∆λpm ωRf − iq ω(La2 − Ma1 a2 )Rf +ω 2 Laf id (La2 − Ma1 a2 ) + ωLaf iq raf 92 (6.5) )2 (6.6) 30 Vq 20 Raw data Post−Filter 10 0 1 1.5 2 2.5 3 3.5 2.5 3 3.5 time Flag, Nf and Rf 20 15 10 Flag Nf r *10 f Fault Inserted 5 0 1 1.5 2 time Figure 6.3: Detection experiment, healthy operation progressing into a rf = 0.5 Ω fault across 15 turns of the winding. All the testing was performed in the single layer 2/5 SP P machine. b = id ω(La2 − Ma1 a2 )Rf + iq raf Rf − ωLaf id raf 2 (6.7) 2 −ω Laf ∆λpm + ω Laf iq (La2 − Ma1 a2 ), |if | = a 2 + X b 2 . X (6.8) Figure 6.4 shows the solution of equation 6.8 for rf = 0.5 Ω fault across 15 turns, while the motor is operating at 300 RP M with a |is | = 10 A. The solution of equation 6.8 in figure 6.4 closely resembles the experimentally measured current shown in figure 5.14. The voltage movement tendency technique, presented on figure 6.2 and used to detect and estimate the fault parameters in the 2/5 SP P machine in figure 4.1(a), was also tested on the 1/2 SP P machine in figure 4.1(b). Different fault scenarios were used to study the 93 9 8.5 Fault Current Estimator 8 7.5 7 6.5 6 5.5 5 4.5 4 90 100 110 120 130 140 150 160 170 180 Angle Figure 6.4: Fault current estimator for a rf = 0.5 Ω fault across 15 turns of the winding, motor operating at 300 RP M with a |is | = 10 A. All the testing was performed in the single layer 2/5 SP P machine. voltage vector tendency using finite elements analysis as shown in figure 6.5. On this double layer machine the voltage vector showed considerably measurable voltage changes in both axes. These voltage changes are used to detect and estimate the fault, in the same way it was performed on the 2/5 SP P single layer machine in figure 6.3. The double layer 1/2 SP P machine showed more variation on the d-axis than on the q-axis. Contrary to the 2/5 SP P single layer machine where the q-axis variation dominated the variations on the d-axis. This behavior change is attributed to the higher self and mutual inductances in the machine. The different parameters for both machines are presented in tables 4.2 and 4.3. 94 44 42 40 Healthy R0.5 10% R0.5 20% R0.25 10% R0.25 20% Vq 38 36 Tendency 34 32 30 −75 −70 −65 −60 −55 Vd −50 −45 −40 −35 Figure 6.5: Changes in the voltage space vector for different fault conditions at 300 RP M with 10A∠140o for the 1/2 SP P double layer machine. Starting from healthy, then moving to rf = 0.5 Ω@ 15 turns, rf = 0.25 Ω@ 15 turns, rf = 0.5 Ω@ 50 turns, and finalizing with rf = 0.25 Ω@ 50 turns 6.2 Control Algorithm and Experimental Results Based on the results shown in previous chapters, a fault mitigation technique is proposed. Upon detection of a fault, the motor drive controller must; limit the operating speed, restrict the amount of torque the machine can develop by restricting the line current and start fieldweakening at speed bellow nominal to reduce the amount of induced voltage in the fault. The mitigation algorithm is shown in figure 6.6. It was developed to mitigate and gain some degree of control over the fault current. The algorithm checks for the RMS value of if and if it is larger than a predetermined value, it reacts by applying a current vector that weakens the magnets field, known as flux nulling. In the case, the commanded current do not permit the limitation of if , the algorithm will automatically de-rate or lower the commanded |is |. 95 .#)$# ! % !, ' $ !"# ,! % !, " ! % !!! % ! " !" !"#$!%%&$' !(()"*+ -! $ !"# ,&+ &'( ! % ! %"#$ ! % !!! % ! &$* " ! " & $" ,&+ ! %" !!! %" ! $* ! $* % % ,&+ ,&+ &'( ! % ! %"#$ * " ! %& ) &'( ! %" !! %"#$ $" '$" (%) $" '$" &'( ! %" ! %"#$ $" '$" % %) ,&+ " # %& ) ,&+ &'( ! % !#! %"#$ * " %+ $" '$" ) -! Figure 6.6: Fault mitigation algorithm, enables the limitation of if by δ and |is |. Figure 6.7 shows the full controller used to collect the experimental data. The fault resistor is inserted at a random time using a switch box. This box connects rf to the desired number of turns in the fault Nf . The proposed algorithm is tested using two rf resistances across a 15 and 30 turn fault. 96 &-30$4+.56%$+#.47#8 -" ." !*'() !! ! "+$+,-$+#. /0,#%+$12 !+'() "#$#% &'( ,* * ,+ ! " * #$%& !" )" "#$#% !* * !+ ! :6$6;$+#. 95$+2-$+#. Figure 6.7: Motor controller including detection, estimation and mitigation 6.3 Experimental case: A 0.5 Ohms fault across 15 turns In this experimental case, the mitigation technique, the detection and estimation procedures were tested using a rf = 0.5 Ω across 15 tuns fault. The experiment starts with the PM motor operating at 300 RP M with is = 10∠120o under healthy conditions. Then the fault is inserted and the speed is increased to test the controller’s ability to maintain the fault current magnitude bellow a predetermined value. In this work the predetermined maximum iset max is set to 10 A, which is 40% of the rated winding current. The experiment is finalized by a decreasing the speed, to test the controller’s ability to restore δ when the conditions allow. As seen in figure 6.8 the mitigation algorithm successfully limited the fault current to the 97 desired maximum level of 10 A. For this fault case as shown in figure 6.8(d), only δ alterations were necessary to kept the current within the limit. No limitation on the commanded line current magnitude were applied for this fault case. 6.4 Experimental case: A 0.25 Ohms fault across 15 turns The experiment performed in section 6.4 was implemented for a fault of rf = 0.25 Ω across 15 tuns, and the results are shown in figure 6.9. Due to the severity of this case, the algorithm altered δ and |is |, in order to keep the fault current within the allowed limit. For this fault, even a full flux weakening at δ = 180o did not lower if to 10A. Therefore, the algorithm automatically de-rated the amount commanded line current, as it is shown in figure 6.9(d). Encircled in figure 6.9(c) is a particular behavior in the detection of this rf = 0.25 Ω fault. Because the heavy filtering in vq , the detection algorithm first detects a rf = 0.5 Ω before it detects the correct fault of rf = 0.25 Ω. This behavior occurs because the voltage vector transitions through the rf = 0.5 Ω vector position before it reaches its final faulted vectorial position. The vectorial movement and tendency are shown in figure 6.2. 98 50 v q vd and vq 0 −50 −100 v d −150 0 5 10 15 20 25 time (a) vd and vq response to the operating conditions. 20 I s Id and Iq 10 iq 0 i −10 i d d i q −20 0 5 10 15 20 time I s 25 (b) id , iq and |is | response to the operating conditions. 20 Flag Nf Flag, Nf and Rf N f 15 r *10 f Flag 10 r *10 f 5 0 0 5 10 15 20 25 time (c) Number of faulted turns, fault flag indicator and rf estimation. 200 i *10 estimate 150 δ ω if, δ, ωm f δ m i *10 f 100 50 ω m 0 0 5 10 15 20 25 time (d) Response to a fault, δ, if estimation and mechanical speed ωm . Figure 6.8: Experimental case rf = 0.5 Ω across 15 turns, including detection, estimation and fault current mitigation. 99 50 v q Vd and Vq 0 −50 v d −100 −150 0 5 10 15 20 25 30 35 40 45 time (a) vd and vq response to the operating conditions. 20 i 10 iq d I s s Is i , i and I i q d q 0 −10 i d −20 0 5 10 15 20 25 30 35 40 45 time (b) id , iq and |is | response to the operating conditions. 20 Flag N Flag, Nf and Rf N f 15 f r *10 f Flag 10 5 r *10 f 0 0 5 10 15 20 25 30 35 40 45 time (c) Number of faulted turns, fault flag indicator and rf estimation. i *10 estimate 200 f δ δ ω if, δ, ωm 150 m i *10 f 100 50 ω m 0 0 5 10 15 20 25 30 35 40 45 time (d) Response to a fault, δ, if estimation and mechanical speed ωm . Figure 6.9: Experimental case rf = 0.25 Ω across 15 turns, including detection, estimation and fault current mitigation. 100 Chapter 7 Conclusion The proposed mitigation algorithm presented in this work and sumarized in figure 6.6 successfully regulated the fault current, limiting it to a predetermined value. Limiting the amount of fault current, lowers the power losses and the dissipated heat. Heat is the main contributor to fault propagation and deterioration of a PMSM winding. Controlling the amount of heat, by controlling the power losses, can extend the post-fault life span of a PMSM. The goal of the technique is to act upon a fault in its early stages, while it is an incipient fault, before it becomes a highly severe fault. As shown in figures 6.8 and 6.9, it is possible to control and limit if for incipient faults by applying field weakening at low speeds and/or derating the lines current. This controllability, allows the controller to auto-protect and attempt to delay the propagation of the fault. Although the method is intended for incipient faults, it is also applicable for severe faults to minimize the risk of a catastrophic even. Mitigation is the main focus of this in this research; however, a mitigation technique is as good as the detection and estimation algorithm it relying upon. Quick detection of a fault is vital to ensure that the fault propagation is stopped or delayed by the mitigation technique. A simple, but effective way to detect the fault is presented in section 6.1. As shown in figure 6.2 it uses the deviations from the expected value of the voltage space vector as an early sign of a fault. The tendency and how far the voltage vector moves away from the expected value are used to estimate the parameters of the fault. This technique was successfully tested for 101 two fault cases in figures 6.3, 6.8 and 6.9. Throughout the experimentation process excellent control performance was maintained, as it is demonstrated in figures 5.10 and 5.11. Having a robust controller capable of controlling the line currents during a fault event is vital for the proposed technique to properly work. The technique relies on the controller to inject currents at the correct angle and magnitude, in order to minimize fault current oscillations and mitigate the fault. 102 APPENDIX 103 APPENDIX A DSP Controller and Data Handling Experimental procedures and testing where performed using the system shown in figure 2.4. Its main components are: An industrial DC/AC inverter, fed by an uncontrolled diode rectifier. An ESI DSP system board, equipped with the Texas Instruments 32 bit Delfino TMS320F28335. Peak CAN adapter, CAN BUS to USB line converter, used to transfer data from the DSP unit to a computer equipped with LabView and the peak CAN data management software. This chapter deals with the details about programming the DSP unit and data logging structures. Figure A.1 show the general execution structure for a DSP unit. The two main components of the structure are the void main(void) function and the interrupt. The void main(void) function is where all the submodules, like the Analog to Digital Converter, the PWM enable, the encoder reading module and interrupt timers are set. Once all modules are properly set, the rest of the code, including the control algorithm, resides on the interrupt function. Note that the void main(void) function can handle several interrupts simultaneously and executed based on a priority flag. The basic DSP controller configuration show in figure A.1 is based on a single interrupt. 104 DSP units operate in discrete time, and the step change is set by a counter that runs at the DSP clock speed. This time change is known as the interrupt speed. For example the TMS320F28335 DSP has a internal clock speed of 150 MHz, but the time step can be set to a lower value. In this work the interrupt or step time is set equal to the switching frequency of the PWM signals. In this way, every interrupt triggers all the submodules to gather all the feedback signals, update all PWM signals and transmit available information using the CAN BUS. Figure A.2 shows a detailed programming structure, that expands the the interrupt function shown in figure A.1. The FOC controller shown in figure 2.7 and 2.8 is implemented using the DSP structure shown in figure A.2. All proportional integral controllers were transform to the discrete domain in order to close the current loops. Instead of placing external measuring equipment, to measure the line currents, the rotor position and the commanded voltages, the inherent system sensors and estimators were utilized. In this work the technique was utilized to demonstrated that using the inherent system sensors is as accurate as using high end measurement devices. Differences between both techniques were studied in detail in [44]. Figure A.3 shows the information flow from the feedbacks signals to the data logging computer. Experimental data can be recorded using the LabView interphase and the Peak CAN software. 105 Starting header 1. #include: It adds the required files to declare the sub-modules. 2. Declarations and Initializations ü Interrupt Define ü Variable Declaration ü Module variable assignment ü CAN shadow register define ü RAM to Flash memory copy void main(void) In this part of the code is where the operating conditions for the DSP and the sub-modules are coded. Some of these operating conditions are: ü CPU timer ü GPIO operation ü Modules Initialization ü Main Interrupt setup ü Idle loop, waiting for interrupt mode Sub-modules When the interrupt happens: Each Sub-module, performs its function and send their outcomes to the interrupt code structure. The most common modules are: 1. Encoder read module 2. PWM enable/disable module 3. Analog to Digital converter read Information flow Interrupt This is the core code for the DSP program. Once every sub-module in the void main(void) part is properly coded, the programmer only needs to change this part of the code. The structure is as follow. 1. All the feedback signals are measured 2. Position and Speed are acquired from the encoder. 3. Clarke, Park and inverse Park transformations, as required by programmer. 4. Programmers Core CODE 5. Update the SVPWM signals 6. CAN, send and received data Figure A.1: Generalized DSP execution mode, shown sequence of operation and interrupt. 106 Start Starting Header, (Definitions) void main(void) Setup Operating conditions for DSP and sub-functions Idle Loop, DSP waits for interrupt NO Interrupt? Run all the sub-functions defined on the #include yes PWM ON or OFF? OFF Disable Module ON Engage Module Internal and External ADC functions are called. Lines currents, line voltages and DC link voltage are read. Encoder function is called. It returns position and speed yes END Software protection Failure flag is set Continue? NO Park, inverse Park and Clarke transforms are available for the programmers needs CAN, send and receive “Programmers control ” Space Vector PWM Update Park, inverse Park and Clarke transforms are available for the programmers needs Figure A.2: ESI DSP system board specific case, C++ coding structure. 107 !?=*03 @00-9.AB=#.(#A2(*126#=)7(.6= 8.9:)05 ;2/#80:06# $2(*126601 !"#$%&# '()* "+%,#$%& %-./*01 <=01#>(/'* "+%,#$%& !24*5.10 .*.#6277)(7 $23/'*01 Figure A.3: DSP and data logging computer information flow. 108 BIBLIOGRAPHY 109 BIBLIOGRAPHY [1] J. Neely and E. Strangas, “Fault types and mitigation techniques of PMAC machines,” in 2006 IEEE International Conference on Electro/information Technology, 2006, pp. 97–102. [2] B. Welchko, T. Lipo, T. Jahns, and S. Schulz, “Fault tolerant three-phase AC motor drive topologies; a comparison of features, cost, and limitations,” in Electric Machines and Drives IEEE International Conference, vol. 1, 2003, pp. 539–546 vol.1. [3] K. H. Kim, D.-U. 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