Applied Science, Faculty of
Engineering, School of (Okanagan)
DSpace
UBCO
Fani, Aria
Master of Applied Science - MASc
University of British Columbia
Implementing a universal high frequency induction machine model for arbitrary stator winding connections is crucial to determine and investigate the electromagnetic interference (EMI) issues concerning stator winding reflected wave overvoltage and bearing discharge current. It is also fundamental in determining proper motor dielectric insulation and optimal design of dv/dt filters. To design and characterize high frequency induction machine model accurately, the machine’s Differential Mode (DM) and Common Mode (CM) impedance characteristics should be analysed within the interested frequency range. The high frequency machine model should be able to represent all the possible stator winding connections (e.g., Y or Delta connections) to create a comprehensive universal high frequency machine model. In this thesis, a 7.5 HP dual-voltage 9-terminal/lead Baldor induction machine is selected for the high frequency machine modeling study due to its availability of different stator winding configurations. There are four possible types of stator winding connections of the Baldor induction machine as Single Y, Single Delta, Series Y, and Parallel Y winding configurations. Considering the machine high frequency phenomena under study and the limitation of the measurement equipment (impedance analyzer or frequency response analyzer), this thesis is focused on high frequency machine model with frequencies up to 10 MHz. The frequency ranges are subdivided into three sections: low frequencies (100 Hz – 10 kHz), mid frequencies (10 kHz – 500 kHz), and high frequencies (500 kHz – 10 MHz). The considered high frequency range is limited up to 10 MHz due to the complicated harmonics present above that limit generated by the output-controlled AC (Alternative Current) step voltages of the motor drive. There are also modeling complications with the capacitive and inductive couplings, extracted from 2D finite element simulations, as well as analytically estimated resistive winding losses in the frequency ranges above 10 MHz. The proposed machine model can represent the machine in arbitrary winding configurations with a simple, yet accurate circuit model and a straight-forward model characterization method. The proposed high frequency machine model is verified using hardware experiments on the Baldor induction machine connected with a commercial ABB motor drive, ACS150. The DM and CM currents are measured from the hardware setup and compared to the simulated DM and CM currents from the proposed high frequency machine model. The comparison of the simulated and hardware measured results verified the accuracy of the proposed high frequency machine model.
Simulation and Experimental Verification of Universal High Frequency Induction Machine Model for Arbitrary Stator Winding Connections by Aria Fani B. Tech., British Columbia Institute of Technology, 2015 A THESIS SUBMITTED IN PARTIAL FULLFILMENT OF THE REQUIREMENT FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE COLLEGE OF GRADUATE STUDIES (Electrical Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Okanagan) January 2022 © Aria Fani, 2022ii The following individuals certify that they have read, and recommend to the College of Graduate Studies for acceptance, a thesis/dissertation entitled: SIMULATION AND EXPERIMENTAL VERIFICATION OF UNIVERSAL HIGH FREQUENCY INDUCTION MACHINE MODEL FOR ARBITRARY STATOR WINDING CONNECTIONS submitted by Aria Fani in partial fulfilment of the requirements of the degree of Master of Applied Science . Dr. Liwei Wang, School of Engineering Supervisor Dr. Wilson Eberle, School of Engineering Supervisory Committee Member Dr. Morad Abdelaziz, School of Engineering Supervisory Committee Member Dr. Jian Liu, School of Engineering University Examiner iii ABSTRACT Implementing a universal high frequency induction machine model for arbitrary stator winding connections is crucial to determine and investigate the electromagnetic interference (EMI) issues concerning stator winding reflected wave overvoltage and bearing discharge current. It is also fundamental in determining proper motor dielectric insulation and optimal design of dv/dt filters. To design and characterize high frequency induction machine model accurately, the machine’s Differential Mode (DM) and Common Mode (CM) impedance characteristics should be analysed within the interested frequency range. The high frequency machine model should be able to represent all the possible stator winding connections (e.g., Y or Delta connections) to create a comprehensive universal high frequency machine model. In this thesis, a 7.5 HP dual-voltage 9-terminal/lead Baldor induction machine is selected for the high frequency machine modeling study due to its availability of different stator winding configurations. There are four possible types of stator winding connections of the Baldor induction machine as Single Y, Single Delta, Series Y, and Parallel Y winding configurations. Considering the machine high frequency phenomena under study and the limitation of the measurement equipment (impedance analyzer or frequency response analyzer), this thesis is focused on high frequency machine model with frequencies up to 10 MHz. The frequency ranges are subdivided into three sections: low frequencies (100 Hz – 10 kHz), mid frequencies (10 kHz – 500 kHz), and high frequencies (500 kHz – 10 MHz). The considered high frequency range is limited up to 10 MHz due to the complicated harmonics present above that limit generated by the output-controlled AC (Alternative Current) step voltages of the motor drive. There are also modeling complications with the capacitive and inductive couplings, extracted from iv 2D finite element simulations, as well as analytically estimated resistive winding losses in the frequency ranges above 10 MHz. The proposed machine model can represent the machine in arbitrary winding configurations with a simple, yet accurate circuit model and a straight-forward model characterization method. The proposed high frequency machine model is verified using hardware experiments on the Baldor induction machine connected with a commercial ABB motor drive, ACS150. The DM and CM currents are measured from the hardware setup and compared to the simulated DM and CM currents from the proposed high frequency machine model. The comparison of the simulated and hardware measured results verified the accuracy of the proposed high frequency machine model. v LAY SUMMARY Variable-frequency-drive-based induction machine systems are integral parts of our daily lives considering their applications in many engineering and scientific fields. Since many infrastructures depend on them, their reliability, durability, and efficiency are quite significant. These electrical machines run at risks of Electro-Magnetic Interference (EMI) issues by high frequency Pulse Width Modulation (PWM) techniques in the variable frequency drive, an DC-AC inverter for motor speed/torque regulation. Since the switching (rise-up and fall-down) times of the modern transistors like MOSFET and IGBT used as the building blocks of the inverters are relatively short (50ns − 250 ns), the EMI issues created by a high frequency induction machine drive system are considerable. The induced EMI could cause notable damage to the bearings, shaft, and winding insulation of induction machines leading to deteriorated reliability and even premature failure. In this thesis, a high frequency induction machine model and its model characterization method are proposed for induction machines with various stator winding configurations. Comparing the experimental and simulation results, the accuracy of the proposed high frequency induction machine model is verified. The proposed high frequency machine model will be widely used in motor drive high frequency filter designs to mitigate EMI issues. vi PREFACE This thesis is based on the research work conducted in the School of Engineering at the University of British Columbia, Okanagan Campus, under the supervision of Dr. Liwei Wang. This thesis contains research work that is to be published in future. I am the principal contributor to this thesis and related research work. For the research progress, Dr. Wang provided me the necessary guidance on how to build and construct all the necessary models and hardware lab infrastructure needed to test the high frequency characteristics of the 7.5 HP dual-voltage 9-terminal/lead induction machine safely and accurately. Dr. Wang also contributed with his insight with respect to analyzing the experimental vs simulated responses of induction machine drive system. vii TABLE OF CONTENTS ABSTRACT ........................................................................................................................................... iii LAY SUMMARY ................................................................................................................................... v PREFACE .............................................................................................................................................. vi TABLE OF CONTENTS....................................................................................................................... vii LIST OF FIGURES ................................................................................................................................ ix LIST OF TABLES ................................................................................................................................ xii ABBREVIATIONS .............................................................................................................................. xiii ACKNOWLEDGEMENT .................................................................................................................... xiv 1: INTRODUCTION ............................................................................................................................... 1 1.1: NECESSITY OF HIGH FREQUENCY INDUCTION MACHINE MODEL ........................................................ 1 1.2: PRIOR-ART HIGH FREQUENCY MACHINE MODELS ............................................................................. 2 1.3: REASONS FOR MULTIPLE STATOR WINDING CONFIGURATIONS IN AN INDUCTION MACHINE ................. 4 1.4: IMPORTANCE OF A UNIVERSAL HIGH FREQUENCY MACHINE MODEL .................................................. 7 1.5: CONTRIBUTIONS TO PROPOSED HIGH FREQUENCY MACHINE MODEL.................................................. 8 2: HIGH FREQUENCY IMPEDANCES OF INDUCTION MACHINE ................................................ 10 2.1: HIGH FREQUENCY IMPEDANCE MEASUREMENT .............................................................................. 10 2.2: DIFFERENTIAL MODE AND COMMON MODE IMPEDANCES ................................................................ 10 2.3: HIGH FREQUENCY IMPEDANCES FOR DIFFERENT WINDING CONNECTIONS ........................................ 11 3: PROPOSED HIGH FREQUENCY MODEL AND ITS CHARACTERIZATION .............................. 14 3.1: HIGH FREQUENCY MACHINE MODEL CIRCUIT ................................................................................. 14 3.1.1: Per-phase equivalent circuit model ......................................................................................................................................... 14 3.1.2: Differential Mode (DM) and Common Mode (CM) models ................................................................................................. 16 3.1.3: Parameter extraction analysis for Single Y winding connection........................................................................................... 18 3.2: PARAMETER CONVERSION WAY FOR ARBITRARY WINDING CONNECTIONS ....................................... 21 viii 3.2.1: Parameter conversion formulas for Single Delta winding connection.................................................................................. 22 3.2.2: High frequency model parameters for arbitrary winding connections derived from Single Y configuration .................... 28 4: SIMULATION STUDY AND EXPERIMENTAL VERIFICATION ................................................. 31 4.1: SIMULATION CONFIGURATION ...................................................................................................... 33 4.2: EXPERIMENTAL SETUP ................................................................................................................. 38 4.2.1: 7.5 HP Baldor Induction motor EM3710T ............................................................................................................................. 40 4.2.2: ABB Drive, ACS150-03U-09A8-2 ......................................................................................................................................... 41 4.2.3: Tektronix Oscilloscope ............................................................................................................................................................ 44 4.2.4: Safety features in experimental setup...................................................................................................................................... 45 4.3: COMPARISONS OF SIMULATION AND EXPERIMENTAL RESULTS ...................................................... 47 5: CONCLUSION AND FUTURE WORK ........................................................................................... 56 REFERENCES...................................................................................................................................... 58 APPENDICES ...................................................................................................................................... 62 APPENDIX A: PARAMETER CONVERSION FORMULAS FOR SERIES Y WINDING CONNECTION .................... 62 APPENDIX B: PARAMETER CONVERSION FORMULAS FOR PARALLEL Y WINDING CONNECTION ............... 63 ix LIST OF FIGURES Figure 1: Induction machine under study (a) 7.5 HP Baldor EM3710T induction motor (9 leads), (b) Lead colors (1: Blue, 2: White, 3: Orange, 4: Yellow, 5: Black, 6: Purple, 7: Pink 8: Red, 9: Grey), (c) Low/high voltage winding connections, and (d) Motor specification……………………………5 Figure 2: Motor’s leads orientation ......................................................................................................... 6 Figure 3: Stator winding connections (a) Single Y winding connection, (b) Single Delta winding connection, (c) Series Y winding connection, (d) Parallel Y winding connection, (e) Series Delta winding connection, and (f) Parallel Delta winding connection………………………………...6 Figure 4: Machine impedance measurement (a) DM, and (b) CM ......................................................... 11 Figure 5: Measured DM impedance characteristics for four different stator winding connections of 7.5 HP four-pole dual-voltage 9-terminal/lead motor [35] ………………………….………………….13 Figure 6: Measured CM impedance characteristics for four different stator winding connections of 7.5 HP four-pole dual-voltage 9-terminal/lead motor [35] ……………………………………………..13 Figure 7: Per-phase equivalent circuit ................................................................................................... 15 Figure 8: DM equivalent circuit ............................................................................................................ 17 Figure 9: CM equivalent circuit ............................................................................................................ 17 Figure 10: CM and DM impedance characteristics for the 7.5 HP four-pole dual-voltage 9-terminal/lead motor in Single Y connection, and the critical points for the motor equivalent circuit characterization [35] …………………………………………………………………………18 x Figure 11: CM and DM impedance characteristics for the 7.5 HP four-pole dual-voltage 9-terminal/lead motor in Single Y connection [35] …………………………………………………………..18 Figure 12: Distributed-parameter single winding segment model........................................................... 22 Figure 13: Connecting the proposed single-winding segment into a single-Y connection for the proposed high-frequency model…………………………………………………………………………23 Figure 14: Connecting the proposed single-winding segment into a single-Δ connection for the proposed high-frequency model…………………………………………………………………………24 Figure 15: Low-frequency three-phase machine equivalent leakage inductances and core-loss equivalent resistances: (a) Δ connection; (b) equivalent Y model of the Δ winding connection………….25 Figure 16: Low- to mid-frequency single-winding total equivalent capacitance ..................................... 26 Figure 17: Low- to mid-frequency three-phase CM total winding-to-ground capacitances: (a) Y winding connection; (b) Δ winding connection…………………………………………………………26 Figure 18: Simulink representation of the test setup .............................................................................. 35 Figure 19: Simulink representation of per phase high frequency motor model ....................................... 36 Figure 20: Simulink representation of the PWM of the motor drive ....................................................... 36 Figure 21: Simulink representation of CM and DM Currents ................................................................. 37 Figure 22: Simulink representation of the inverter and motor models .................................................... 37 Figure 23: Experimental setup of 7.5 HP Baldor EM3710T induction motor under test ......................... 39 Figure 24: Induction motor test set up for different winding connections ............................................... 40 xi Figure 25: ABB motor drive setup ........................................................................................................ 42 Figure 26: ABB motor drive and the safety block .................................................................................. 43 Figure 27: Digital phosphor oscilloscope DPO5034B from Tektronix ................................................... 44 Figure 28: An example captured image on the scope for Single Y configuration, CM analysis, ia (yellow), ib (blue), ic (purple), 3Icm (green), sampling rate=200 MS/s, 1 A/V. div., and 50 µs/H. div…45 Figure 29: Master circuit lock disconnect switch ................................................................................... 46 Figure 30: Experimental setup in operation ........................................................................................... 47 Figure 31: 3IDM comparison result for Single Y connection ................................................................... 49 Figure 32: 3IDM comparison result for Single Y connection with zoomed-in view .................................. 49 Figure 33: 3IDM comparison result for Series Y connection ................................................................... 50 Figure 34: 3IDM comparison result for Series Y connection with zoomed-in view .................................. 50 Figure 35: 3IDM comparison result for Parallel Y connection ................................................................. 51 Figure 36: 3IDM comparison result for Parallel Y connection with zoomed-in view ................................ 51 Figure 37: 3ICM comparison result for Single Y connection ................................................................... 53 Figure 38: 3ICM comparison result for Single Y connection with zoomed-in view .................................. 53 Figure 39: 3ICM comparison result for Series Y connection .................................................................... 54 Figure 40: 3ICM comparison result for Series Y connection with zoomed-in view .................................. 54 Figure 41: 3ICM comparison for Parallel Y connection ........................................................................... 55 Figure 42: 3ICM comparison result for Parallel Y connection with zoomed-in view ................................ 55 xii LIST OF TABLES Table 1: Extracted parameter for Single Y winding configuration of 7.5 HP Baldor motor..................... 20 Table 2: Parameter conversion factors for different winding configurations ........................................... 29 Table 3: Calculated values of parameters for different winding configurations ...................................... 30 Table 4: Experimental parameters for each winding configuration ......................................................... 32 Table 5: Induction motor nameplate data ............................................................................................... 41 Table 6: ABB motor drive technical data............................................................................................... 43 xiii ABBREVIATIONS AC ASDs CM DC DM EMI FEA FRA HP IGBT MOSFET PWM RPM SiC tr VSC Alternate Current Adjustable Speed Drives Common Mode Direct Current Differential Mode Electro-Magnetic Interference Finite Element Analysis Frequency Response Analyser Horsepower Insulated Gate Bipolar Transistor Metal Oxide Semiconductor Field Effect Transistor Pulse Width Modulation Revolutions per Minute Silicone Carbide Rise Time Voltage Source ConverterWEC WIC Winding Exterior Circuit Winding Interior Circuit xiv ACKNOWLEDGEMENT Firstly, I would like to thank our Father in heaven and my family who have inspired, encouraged, and supported me during all my challenges in life. I would also like to express my most sincere appreciation to my supervisor, Dr. Liwei Wang, for guiding and directing my research during my Master study.1 1: INTRODUCTION 1.1: Necessity of high frequency induction machine model There are numerous challenges in design and operation of the adjustable speed drives due to the usage of wide-bandgap semiconductors such as Silicon Carbide (SiC) transistors in power electronic converters which provide variable frequency AC (Alternative Current) voltage supply to induction machines. Steep-fronted pulse voltages are created at the output of the power electronic converter because of the fast rise and fall switching times of the wide-bandgap semiconductors. This phenomenon causes wave propagation effects in long-cable-fed motor drive systems [1−7]. Since there is a mismatch between the cable characteristic impedance and motor surge impedance, the motor terminals face with the reflected-wave overvoltage ringing [3−7]. It is possible that the ringing voltages may reach at two or three times of the DC-bus voltage in magnitude [5]. These overvoltage spikes may damage the bearings, shaft, and winding insulation, causing the induction machine to age, deteriorate, and fail more rapidly [8−9]. Machine drives at its terminals also generate high dv/dt which leads to the common mode voltages at the machine bearings through the high frequency machine capacitances. Sometimes these common mode voltages get discharged via the bearings’ inner structure resulting in their failures [8−13]. Thus, high frequency modeling of induction machines plays a very crucial role in predicting motor terminal overvoltage ringing and machine bearing discharging current. 2 1.2: Prior-art high frequency machine models Induction machines are widely used in many different industries. Since the requirement for each industry regarding an induction machine depends on variety of factors including available input voltages and currents, the induction motors should be built with versatile capabilities. To address this important factor, Adjustable Speed Drives (ASDs) using Pulse Width Modulation (PWM) in voltage-source inverters with steep voltage pulse rise times (tr) have been utilized with the induction machines over the past four decades [10]. Recently, more sophisticated three-phase control algorithms, along with power devices having faster rise times (< 100 ns) has allowed higher control bandwidth and has reduced inverter switching losses and magnetic filter volume. The faster switching cycles (4–20 kHz) has decreased motor current ripple harmonics, torque ripple, and acoustical noise, which consequently has improved system performance. However, the fast rise time of the voltage transition also excites undesirable system secondary parasitic effects, such as reflected wave differential overvoltage spikes on motor terminals that reduce the motor insulation life. In this process, Common Mode (CM) current is generated which creates system Electro-Magnetic Interference (EMI) issues, and motor-bearing currents that drastically reduce the operating life of the induction machine [10]. To better understand the characteristics of the CM current, the high frequency machine model of a selected induction machine should be analyzed according applicable configurations. In the literature, there are currently two categories of high frequency machine models: First category is based on Finite Element Analysis (FEA) [14−17] which uses numerical and mathematical approaches to create high frequency induction machine model for 2-Dimension or 3-Dimension electromagnetic field analysis [18−28]. On the other hand, the second category of 3 high frequency induction machine model is derived using behavioural equivalent circuit model [10−13, 18−28, 35]. In this category, the impedances of the induction machine are measured experimentally in frequency domain using impedance analyzer or frequency response analyzer. The appropriate behavioural model of the machine is constructed using the measured impedances of the machine over the range of applicable frequencies from hundreds of Hz to tens of MHz [10−13, 18−28, 35]. Multiple high frequency machine models were proposed in previous research works, which are based on frequency dependent impedances using a high order lumped parameter equivalent winding circuit model [10−13, 18−28, 35]. The order of the lumped parameter equivalent circuits is an important parameter. The higher the order of the machine model goes, the better the accuracy of the high frequency machine model becomes. However, this comes at the price of more complicated high frequency model structures and their model characterizations. Overall, the focus of this thesis is to develop a lumped-parameter equivalent circuit model to represent high frequency behavior of induction machines with straightforward model parameterization and high accuracy for various stator winding configurations of induction machines. 4 1.3: Reasons for multiple stator winding configurations in an induction machine Most induction machines are required to adapt to different power supplies with various current and voltage capabilities depending on the applications. Thus, an induction machine should have multiple stator winding configuration possibilities to fulfill the requirements of the operation for different applications. The induction machine under study in this thesis is 7.5 HP four-pole dual-voltage 9-terminal/lead motor which can be configured in four possible stator winding connections: Single Y, Single Delta, Series Y, and Parallel Y winding connections (shown in Figures 1−3). Series Y winding connection operates on a higher voltage setting compared to Parallel Y winding connection. On the contrary, Parallel Y winding connection operates on a higher current rating compared to Series Y winding connection. In the specification chart of the induction machine shown in Figure 1 (d), there are two voltages and currents indicated: 230/460 Volts and 19/9.5 Amps. The lower voltage is associated with higher current and vice versa. If the stator windings are configured in Parallel Y connection, lower voltage (230 V) and higher current (19 A) ratings are utilized to generate the real power rating of 7.5 HP. On the other hand, when the stator windings are configured in Series Y connection, higher voltage (460 V) and lower current (9.5 A) ratings are utilized to generate the same real power rating of 7.5 HP. By applying the same analysis, Single Y winding connection may be utilized for higher voltage and lower current settings compared to Single Delta winding connection. In contrast, Single Delta connection may be utilized for higher current and lower voltage settings, compared to Single Y connection. It should also be noted Series Y winding connection can endure higher supply voltage compared with Single Y connection due to its series-connected windings at each phase compared to Single Y connection. 5 Since the 7.5 HP four-pole dual-voltage 9-terminal/lead motor under the study has only nine connection leads, as shown in Figure 2, Series Delta and Parallel Delta winding connections cannot be configured using this induction machine. Therefore, the analysis in this thesis only focuses on the four previously mentioned winding configurations. However, similar analysis and high frequency modeling method can be applied to Series Delta and Parallel Delta winding connections of a 12-terminal/lead induction machine. Figure 1: Induction machine under study (a) 7.5 HP Baldor EM3710T induction motor (9 leads), (b) Lead colors (1: Blue, 2: White, 3: Orange, 4: Yellow, 5: Black, 6: Purple, 7: Pink 8: Red, 9: Grey), (c) Low/high voltage winding connections, and (d) Motor specification 6 Figure 2: Motor’s leads orientation Figure 3: Stator winding connections (a) Single Y winding connection, (b) Single Delta winding connection, (c) Series Y winding connection, (d) Parallel Y winding connection, (e) Series Delta winding connection, and (f) Parallel Delta winding connection 7 1.4: Importance of a universal high frequency machine model An accurate high frequency induction machine model with straightforward model characterization method plays an important role for EMI mitigation in induction machine drive design. By simulating the high frequency model of a particular induction machine, some of the design flaws of the machine in its shaft, bearings, winding insulation, and motor drive system can be recognized and addressed in the early stage. Thus, an induction machine drive system with higher reliability and better performance can be designed and manufactured. Since the induction machine drive system shares the same fundamentals and characteristics, it is crucial to develop a high frequency machine model which is applicable to induction machines with different power ratings and stator winding connections. This model should be accurate and universal, so that the high frequency characteristics of practical induction machines can be replicated by characterizing the associated parameters in the equivalent circuit model. According to numerous research efforts [10−13, 18−28, 35], the behavioral equivalent circuit models were proposed for their simplicity and versatility in comparison with FEA-based equivalent circuit models. Behavioral equivalent circuit models do not require the knowledge of the machine’s geometry and its construction material properties. Instead, the true focus of these models is on high frequency impedance characterization of the machine over the applicable range of frequencies. So far, numerous analysis [10−13, 18−28, 35] has been conducted using popular single- or multiple-section phase-belt winding models where small numbers of phase-belt equivalent are used to represent accurate high frequency models for different winding combinations within an induction machine. The stator winding connections can be in multiple possible combinations of Single/Double, Series/Parallel, and Y/Delta for which different 8 impedances are measured, separately. Ultimately, creating a single unified high frequency model structure which can represent all available winding connections would be highly desirable. By finding the resonant points in the measured machine impedances for all possible winding connections, the characterization of such a universal high frequency model can be facilitated. The research efforts to generate an accurate universal high frequency machine model have been continuous over the past decades according to multiple studies [10−13, 18−28, 35]. But there is still room for further improvement of the high frequency machine model. The main objective of this thesis is to propose an accurate and flexible induction machine model which can represent the high frequency characteristics of the machine for different stator winding connections. The parameters of the proposed high frequency machine model should be identified using straightforward impedance measurements. The proposed high frequency machine model should be verified by the comparison of the time domain simulation results using the proposed high frequency machine model with the hardware measured results. 1.5: Contributions to proposed high frequency machine model A universal high frequency machine model which can represent all four possible winding configurations (Single Y, Single Delta, Series Y, and Parallel Y) for a 7.5 HP dual-voltage 9-terminal/lead induction machine is proposed in this thesis. A single-section phase-belt winding model is utilized for the proposed high frequency machine model which is simple yet accurate to represent the high frequency behaviors of the induction machine. Differential Mode (DM) and Common Mode (CM) impedance measurements provide the necessary data for the characterization of the proposed high frequency machine model. A parameter conversion method is proposed 9 through which the model parameters for arbitrary stator winding connections can be analytically calculated from the impedance measurements carried out on one stator winding configuration. This conversion method eliminates the laborious work of repeated impedance measurements and model characterizations for different stator winding connections, thus making the approach universal. The effect of the high frequency capacitances caused by the shaft, bearings, and winding insulations plus all the internal inductances and resistances of the 7.5 HP four-pole dual-voltage 9-terminal/lead motor are considered when creating the universal machine model combining the previous studies [10−12, 17, 28, 35−42]. A high frequency model characterization method is proposed to establish the accurate values for the high frequency capacitive, inductive, and resistive element parameters, required to construct the proposed universal model. The proposed universal high frequency machine model is simulated in time domain to generate the CM and DM currents for each applicable stator winding configuration. Then, the obtained results are compared with the experimental measurement of the CM and DM currents. The similarity between the simulated and hardware measured results shows the accuracy of the proposed high frequency machine model. 10 2: HIGH FREQUENCY IMPEDANCES OF INDUCTION MACHINE 2.1: High frequency impedance measurement To represent high frequency behaviors of an induction machine, a high frequency machine model needs to be characterised in the range of frequencies typically from 100 Hz to 10 MHz [10−13, 18−28, 35]. This frequency range is usually divided to three sections: Low Frequency (<10 kHz), Mid Frequency (10 kHz – 500 kHz) and High Frequency (500 kHz -10 MHz). DM and CM impedances which are two important impedance characteristics of the induction machines are required to be measured accurately. The induction machine construction and stator winding connections have significant effects on DM and CM impedances [28, 35]. The induction machine under this study (7.5 HP four-pole dual-voltage 9-terminal/lead motor) can be connected in four possible stator winding configurations (Single Y, Single Delta, Series Y, and Parallel Y). So, the parameterization of a high frequency machine model needs to consider each stator winding connection using the individual DM and CM impedance measurements. 2.2: Differential mode and common mode impedances Impedance analyzer or Frequency Response Analyser (FRA) is used to measure the high frequency impedances of the induction machine under study (7.5 HP four-pole dual-voltage 9-terminal/lead motor). The induction machine is stationary and disconnected from the three-phase AC voltage source while the impedance measurements are taken. The motor impedance characteristics in mid to high frequency range are not affected by the rotor speed and stator current [10, 11, 35]. In order to set up the impedance analyzer or the FRA to measure the DM impedance, the impedance 11 analyzer’s leads should be connected between two parallel-connected phases and the single-ended phase [28, 35], as shown in Figure 4 (a). on the other hand, the CM impedance is measured between the three parallel-connected phases and the motor frame, which is normally grounded [28, 35], as illustrated in Figure 4 (b). Figure 4: Machine impedance measurement (a) DM, and (b) CM 2.3: High frequency impedances for different winding connections As discussed earlier in the introduction section, the 7.5 HP four-pole dual-voltage 9-terminal/lead motor can only engage in four possible stator winding configurations (Single Y, Single Delta, Series Y, and Parallel Y connections). Thus, the high frequency impedance analysis in this thesis is concentrated on the previously mentioned stator winding configurations. The induction machine’s DM and CM impedances behave differently based on the configurations of the stator winding connections. So, the high frequency model parameters should be adjusted accordingly, which makes the impedance measurement and parameter extraction for each winding configuration a tedious task [28, 35]. The high frequency machine model characterization process for different stator winding connections can be greatly simplified if the model parameters extracted 12 from one stator winding configuration can be used to calculate the model parameters for the other stator winding configurations. Figures 5 and 6 demonstrate the DM and CM impedances of the induction motor under study for different possible winding configurations. Since the single winding configurations (single Y or single Delta) of the motor have limited voltage or current ratings, the motor is not normally utilized in these configurations. Instead, the single winding configurations of the motor are used to illustrate the mathematical relationship of high frequency machine winding parameters for different winding configurations [28, 35]. It is observed from Figure 5 that the DM impedances from low to mid frequency range (10 kHz to 500 kHz) are inductive and are visibly different for each winding configuration. In high frequency range (above 500 kHz), the DM impedances of the series Y and single Y configurations become essentially identical, while the DM impedances of the parallel Y and single Delta configurations become nearly identical as well. By investigating Figure 6, it is noted that the CM impedances from low to mid frequency range of the series Y and parallel Y configurations are almost equal, while the CM impedances of the single Y and single Delta configurations are almost identical. In high frequency range, the CM impedance of the Series Y and Single Y configurations are almost the same, while the CM impedances of the parallel Y and Single Delta configurations are very close to each other [28, 35]. 13 Figure 5: Measured DM impedance characteristics for four different stator winding connections of 7.5 HP four-pole dual-voltage 9-terminal/lead motor [35] Figure 6: Measured CM impedance characteristics for four different stator winding connections of 7.5 HP four-pole dual-voltage 9-terminal/lead motor [35] 14 3: PROPOSED HIGH FREQUENCY MODEL AND ITS CHARACTERIZATION 3.1: High frequency machine model circuit A universal high frequency model of the induction machine, considering all its possible winding configurations (Single Y, Single Delta, Series Y, and Parallel Y) is proposed in this chapter. The DM and CM impedance measurements provide necessary information to extract the circuit model parameters for each specific winding configuration. The proposed universal machine model for all the possible winding configurations is based on the extension of the research works in [28, 35], which uses a straightforward single-section phase-belt winding high frequency equivalent circuit for each phase of an induction machine. 3.1.1: Per-phase equivalent circuit model Figure 7 shows the per-phase high frequency equivalent circuit model of an induction machine. The capacitors, Cg1 and Cg2, represent the equivalent phase to ground and neutral to ground parasitic capacitances. Rg1 and Rg2 are the winding-to-ground equivalent copper skin effect and proximity effect resistances. Ls represents stator winding’s leakage inductance, and Re represents high frequency eddy current losses of the stator core. Elements Rt, Lt, and Ct are used to represent the second resonance in the motor’s DM impedance characteristic due to stator winding’s inter-turn capacitive coupling effect. Lc represents the combined inductance of the machine’s internal feed conductors to the stator winding [12, 35] and the stator leakage inductance in the first few turns of the slot [10, 35]. The values for all the previously mentioned components within the 15 purposed model are calculated through evaluating the CM and DM impedance characteristics which will be discussed in detail in the following subsection. It is noted in Figure 7 that there is a slip dependent resistance Rr/s, included in the high frequency model where Rr stands for the rotor resistance and s represents the slip of the machine [10]. The slip dependent resistance Rr/s represents different loading conditions of the induction machine where the slip s is determined by the percentage difference of the synchronous and rotor speeds. The slip dependent resistance Rr/s is required for the machine model to represent the low frequency voltage and current behaviors of the induction machine. The proposed high frequency machine model in this thesis improves the previous model [35] in terms of its capability to represent the machine characteristics not only in the high frequency (500 kHz − 10 MHz) range but also in the low and mid frequencies (100 Hz − 500 kHz). Figure 7: Per-phase equivalent circuit Based on the per-phase equivalent circuit model shown in Figure 7, the “Phase” terminal is the stator winding terminal connected to the external voltage supply through three-phase motor drive/inverter. The “Neutral” terminal should be terminated for Y connections of three per-phase 16 equivalent circuits. By using a Y connection of three single-phase equivalent circuits, the three-phase equivalent circuit for each possible winding configuration (Single Y, Single Delta, Series Y, and Parallel Y) is generated. In other words, irrespective of the actual stator winding connections, the proposed three-phase high frequency machine model takes the form of a three-phase Y-connected circuit whose parameters are calculated considering the DM and CM impedance measurements and the associated stator winding connections. Therefore, the proposed model is universal and remains valid for representing the arbitrary stator winding connections [10, 28, 35]. 3.1.2: Differential Mode (DM) and Common Mode (CM) models The characterization of the proposed high frequency model is based on the DM and CM impedance measurements of the machine. The DM and CM equivalent circuits, shown in Figures 8 and 9 are derived based on the single-phase equivalent circuit model in Figure 7 and the Y connection of three single-phase equivalent circuits. The DM and CM equivalent circuits are used to fit the measured DM and CM impedances. The parameters of the single-phase equivalent circuit model in Figure 7 are extracted from the DM and CM impedances. Without loss of generality, it is assumed that the machine’s high frequency impedance characteristics are measured for the Single Y configuration [35]. The measured DM and CM impedance magnitudes and phases for the 7.5 HP four-pole dual-voltage 9-terminal/lead motor in Single Y connection and the critical points for the high frequency equivalent circuit model characterization are shown in Figures 10 and 11. 17 Figure 8: DM equivalent circuit Figure 9: CM equivalent circuit 18 Figure 10: CM and DM impedance characteristics for the 7.5 HP four-pole dual-voltage 9- terminal/lead motor in Single Y connection, and the critical points for the motor equivalent circuit characterization [35] Figure 11: CM and DM impedance characteristics for the 7.5 HP four-pole dual-voltage 9-terminal/lead motor in Single Y connection [35] 3.1.3: Parameter extraction analysis for Single Y winding connection The high frequency model parameters are extracted from characteristic points on the measured DM and CM impedances. Firstly, the total winding to ground capacitance, Ctotal, and the high frequency winding to ground capacitance, CHF, are extracted from the slopes of the CM impedance as shown in Figure 10. Thereafter, parasitic capacitances Cg1 and Cg2 are calculated [35]: 3CHF124CtotalLDMCM Impedance (ZCM)-20 dB/Decade20 dB/Decade-20 dB/DecadeDM Impedance (ZDM)DM Impedance (θDM)CM Impedance (θCM)19 𝐶𝑔1 =13𝐶𝐻𝐹 (1) 𝐶𝑔2 =13(𝐶𝑡𝑜𝑡𝑎𝑙 − 𝐶𝐻𝐹) (2) The winding to ground equivalent copper skin-effect resistances, Rg1 and Rg2, are calculated from the impedance Z3 of the resonant zero-point ③ and the impedance Z1 of the resonant zero-point ① in Figure 10 as follows [35]: 𝑅𝑔1 =23𝑍3 (3) 𝑅𝑔2 = 3𝑍1 (4) The stator leakage inductance, Ls, is extracted from the DM and CM inductances [27, 35]: 𝐿𝑠 = 𝐿𝐶𝑀 +49𝐿𝐷𝑀 (5) The CM inductance, LCM, is calculated using the impedance Z1 of the resonant zero-point ① as follows [27]: 𝐿𝐶𝑀 =112𝜋2𝐶𝑔2𝑓12 (6) The high-frequency iron loss resistance, Re, is calculated from the impedance ZP of the resonant pole point ④ as shown below [27, 35]: 𝑅𝑒 =23𝑍𝑃 (7) The inter-turn capacitance, Ct, is generally ten times lower than the single-phase total winding to ground capacitance [25, 35]. Therefore, 𝐶𝑡 =110(𝐶𝑔1 + 𝐶𝑔2) (8) 20 The inductance Lt and resistance Rt for the series RLC branch are calculated from the impedance Z2 of the resonant zero-point ② as follows: 𝐿𝑡 =14𝜋2𝐶𝑡𝑓22 (9) 𝑅𝑡 = 𝑍2 (10) The high frequency stator first-turn leakage inductance Lc is calculated from the resonant zero-point ③ as follows [13]: 𝐿𝑐 =23(38𝜋2𝐶𝑔1𝑓32 − 𝐿𝑐𝑎𝑏𝑙𝑒) (11) The high frequency model parameters for the considered 7.5 HP in Single Y winding connection are extracted applying (1) - (11), and they are summarized in Table 1 [35]. Table 1: Extracted parameter for Single Y winding configuration of 7.5 HP Baldor motor Parameter Value Parameter Value Cg1 371 pF Cg2 662 pF Rg1 13.33 Ω Rg2 750 Ω Ls 4.1 mH Re 2.43 k Ω Rt 1.4 k Ω Lt 2 mH Ct 103 pF Lc 0.66 µH 21 3.2: Parameter conversion way for arbitrary winding connections Based on the extracted parameters from one stator winding connection, the high frequency parameters for arbitrary stator winding connections can be analytically calculated. The parameter conversion method from one winding configuration to arbitrary winding connections is introduced in this section [35]. The following steps illustrates the general characterization procedure of the proposed universal machine model with respect to arbitrary stator winding connections of the induction machine under study, 7.5 HP four-pole dual-voltage 9-terminal/lead motor [35]. Step 1: The CM and DM impedance measurements are obtained for Single Y connection. Step 2: All the parameter values for Single Y Configuration are extracted using (1) − (11) with respect to per-phase equivalent circuit shown in Figure 7. Step 3: The extracted parameters are converted mathematically to generate associated new parameters for the rest of the winding configurations (Single Delta, Series Y, and Parallel Y). Step 4: The converted parameters are assigned to their associated per-phase equivalent model adopted from Figure 7. Using the similar analytical techniques detailed in the previous research [35] in which the exact same induction machine was utilized for the experiment, the conversion formulas for calculating all the required high frequency machine model parameters for all the possible stator winding configurations are derived as follows. To facilitate the derivation of parameter conversion for different winding configurations, the distributed-parameter single winding segment model shown in Figure 7 is used. The winding exterior circuit (WEC) which corresponds to the first few turns of the stator windings 22 can be represented by the branches LC, Cg1, and Rg1. The per-section stator’s internal leakage inductance and iron-loss resistance can be represented by the parallel branch of Lsk and Rek. The internal per-section winding-to-ground capacitive coupling can be represented by the series Cgk and Rgk branch in Figure 12. It is assumed that the high-frequency components do not penetrate the winding interior circuit (WIC) in Figure 12 due to high frequency impedance of Lsk. As such, the WIC represents the low-to-mid frequency (below 500 kHz) winding equivalent circuit. The three-phase mid-high frequency models of single-Y and Δ, series- and parallel-Y and Δ configurations can be produced by proper connection of three or six single-winding segment models of Figure 12. However, this will lead to high frequency winding models with high orders which are complicated to be characterized. This section investigates simplification of the three-phase single-/double-winding and Y/Δ connection models based on Figure 12 leading to the proposed universal Y-connected high frequency model based on Figure 7 and parameter conversion method using single-winding Y connection. Figure 12: Distributed-parameter single winding segment model. 3.2.1: Parameter conversion formulas for Single Delta winding connection Single-winding segment equivalent circuits of Figure 12 can be used to form three-phase Y or Δ circuits for the corresponding three-phase high-frequency models with stator windings in Y and Δ 23 configurations, as shown in Figures 13 and 14. It is noted the WICs are effectively disconnected from the circuits in Figures 13 and 14, because the stator windings have high impedances at high frequencies. Therefore, the Y and Δ configurations have their per-phase high-frequency equivalent circuits shown in two dotted boxes of Figures 13 and 14. Thus, the stator-winding-to-ground capacitance, Cg1, for single-winding Δ connection can be derived, based on Figures 13 and 14, as follows: 𝐶𝑔1,𝑠𝑖𝑛𝑔𝑙𝑒∆ = 2𝐶𝑔1,𝑠𝑖𝑛𝑔𝑙𝑒𝑌 (12) Like (12), the high-frequency stator-winding-to-ground resistances Rg1 and the stator first-turn leakage inductances Lc of the single-winding Δ, are given as: 𝑅𝑔1,𝑠𝑖𝑛𝑔𝑙𝑒∆ =12𝑅𝑔1,𝑠𝑖𝑛𝑔𝑙𝑒𝑌 (13) 𝐿𝑐,𝑠𝑖𝑛𝑔𝑙𝑒∆ =12𝐿𝑐,𝑠𝑖𝑛𝑔𝑙𝑒𝑌 (14) Figure 13: Connecting the proposed single-winding segment into a single-Y connection for the proposed high-frequency model 24 Figure 14: Connecting the proposed single-winding segment into a single-Δ connection for the proposed high-frequency model The distributed-parameter stator winding model in Figure 12 becomes inductive at low frequencies (below 10 kHz). The winding-to-ground capacitances, Cg1 and Cgk, have large impedance and become effectively open circuit. Thus, they can be removed from Figure 12. The low-frequency machine winding equivalent leakage inductance Lsn and the equivalent core-loss resistance Ren can be derived from Figure 12 as follows: 𝐿𝑠𝑛 = 2𝐿𝑐 + 𝑛𝐿𝑠𝑘 ≈ 𝑛𝐿𝑠𝑘 (15) 𝑅𝑒𝑛 = 𝑛𝑅𝑒𝑘 (16) where n is the number of sections in the single-winding model. The high-frequency inductance 𝐿𝑐 in (15) corresponds to the leakage inductance of the first turn of the winding, which implies 𝐿𝑐 ≪ 𝐿𝑠𝑘 . This simplification leads to the low-frequency three-25 phase machine equivalent circuit for the Δ connection shown in Figure 15 (a). The machine winding equivalent leakage inductance Lsn and the equivalent core-loss resistance Ren can be characterized from the single-Y connection as in (5) and (7): 𝐿𝑠𝑛 = 𝐿𝑠,𝑠𝑖𝑛𝑔𝑙𝑒𝑌 (17) 𝑅𝑒𝑛 = 𝑅𝑒,𝑠𝑖𝑛𝑔𝑙𝑒𝑌 (18) Since the proposed model takes the universal form of Y connection for arbitrary winding configurations, the Δ circuit is transformed into the equivalent Y circuit as shown in Figure 15 (b). The equivalent Y circuit in Figure 16 (b) has the following per-phase inductance and resistance. 𝐿𝑠,∆ =13𝐿𝑠𝑛 =13𝐿𝑠,𝑠𝑖𝑛𝑔𝑙𝑒𝑌 (19) 𝑅𝑒,∆ =13𝑅𝑒𝑛 =13𝑅𝑒,𝑠𝑖𝑛𝑔𝑙𝑒𝑌 (20) Figure 15: Low-frequency three-phase machine equivalent leakage inductances and core-loss equivalent resistances: (a) Δ connection; (b) equivalent Y model of the Δ winding connection. The machine’s CM impedance behaves capacitively at low- to mid-frequencies (below 100 kHz). 26 Therefore, we can neglect the winding inductances Lc, Lsk, and the core resistance Rek from the distributed-parameter stator winding model in Figure 12. The single-winding total equivalent winding-to-ground parasitic capacitance, Ctotal,1p, can be formed in Figure 12 and is shown in Figure 16. Thus, the low- to mid-frequency three-phase CM Y- and Δ-winding equivalent circuits can be constructed based on Figure 16, as shown in Figures 17 (a) and (b). Figure 16: Low- to mid-frequency single-winding total equivalent capacitance Figure 17: Low- to mid-frequency three-phase CM total winding-to-ground capacitances: (a) Y winding connection; (b) Δ winding connection Hence, three-phase CM total winding-to-ground parasitic capacitance for Y- and Δ-winding connections are equal, i.e., 𝐶𝑡𝑜𝑡𝑎𝑙,𝑠𝑖𝑛𝑔𝑙𝑒∆ = 𝐶𝑡𝑜𝑡𝑎𝑙,𝑠𝑖𝑛𝑔𝑙𝑒𝑌 = 3𝐶𝑡𝑜𝑡𝑎𝑙,1𝑝 (21) 27 Therefore, the winding-to-ground capacitances Cg2 of the Δ-winding connection can be calculated from (2) using (12) and (21). The copper skin-effect resistance Rg2 is evaluated at the mid-frequency resonant zero point from 100 kHz to 500 kHz, as shown in Figure 10. For single-winding Δ- and Y-connections, the relationship between the resistances Rg2,singleΔ and Rg2,singleY is given as follows: 𝑅𝑔2,𝑠𝑖𝑛𝑔𝑙𝑒∆ =12𝑅𝑔2,𝑠𝑖𝑛𝑔𝑙𝑒𝑌 (22) This relationship comes from the fact that two-phase windings are effectively paralleled in Δ-connection at mid- to high-frequencies, which reduces the winding-to-ground resistance, to half of that in single-winding Y-connection. The 2nd resonant zero point in the DM characteristic in Fig. 10 is modeled by the inter-turn winding capacitance Ct and the series elements Lt, Rt. It is shown in (21) and (26-28) that analytical derivation of the inter-turn capacitance Ct is difficult. Therefore, Ct is usually approximated as one tenth of the total per-phase winding-to-ground capacitance (21), (26-28) in the corresponding winding configurations: 𝐶𝑡,𝑠𝑖𝑛𝑔𝑙𝑒𝑌 ≈110(𝐶𝑔1,𝑠𝑖𝑛𝑔𝑙𝑒𝑌 + 𝐶𝑔2,𝑠𝑖𝑛𝑔𝑙𝑒𝑌) (23) 𝐶𝑡,𝑠𝑖𝑛𝑔𝑙𝑒∆ ≈110(𝐶𝑔1,𝑠𝑖𝑛𝑔𝑙𝑒∆ + 𝐶𝑔2,𝑠𝑖𝑛𝑔𝑙𝑒∆) (24) The resonant zero point in the DM impedance characteristics of the single-winding Y connection in Figure 10 is used to extract the values of Lt,singleY and Rt,singleY. 28 The values of Lt and Rt for single-winding Δ connection are half of those of the single-winding Y configuration in (25) and (26). This is because the two-phase windings are effectively paralleled in Δ connection at mid to high frequencies, as shown in Figure 14. 𝐿𝑡,𝑠𝑖𝑛𝑔𝑙𝑒∆ =12𝐿𝑡,𝑠𝑖𝑛𝑔𝑙𝑒𝑌 (25) 𝑅𝑡,𝑠𝑖𝑛𝑔𝑙𝑒∆ =12𝑅𝑡,𝑠𝑖𝑛𝑔𝑙𝑒𝑌 (26) 3.2.2: High frequency model parameters for arbitrary winding connections derived from Single Y configuration The distributed parameter winding models for series and parallel connections of the stator windings, as shown in Figure 3, can be generated using the single winding segment model of Figure 12. The resulting models can be simplified into the proposed universal high-frequency machine per-phase equivalent circuit of Figure 7, like the derivation of the single Δ connection. The parameters of per-phase equivalent circuit model for the series- and parallel-Δ connections can be calculated based on those from single-Y connection [35]. Thus, the laborious impedance measurements and parameter extractions are avoided. The parameter conversion method for series and parallel connections of the stator windings using single-Y connection are summarized in Appendix. The high frequency parameter conversion factors for all possible winding configurations are summarized in Table 2. 29 Table 2: Parameter conversion factors for different winding configurations Parameter Single Y Single Delta Series Y Parallel Y 𝐶𝑔1 1 2 1 2 𝐶𝑔2 1 0.44 2.56 2 𝐶𝑡𝑜𝑡𝑎𝑙 1 1 2 2 𝑅𝑔1 1 1/2 1 1/2 𝑅𝑔2 1 1/2 1 1/2 𝐿𝑠 1 1/3 2 1/2 𝑅𝑒 1 1/3 2 1/2 𝑅𝑡 1 1/2 1 1/2 𝐿𝑡 1 1/2 1 1/2 𝐶𝑡 1 1 2 2 𝐿𝑐 1 1/2 1 1/2 By applying the previously calculated parameters values of Single Y configuration, shown in Table 1, the high frequency parameter values for all the possible winding configurations, illustrated in Table 3 [35]. 30 Table 3: Calculated values of parameters for different winding configurations Parameter Single Y Single Delta Series Y Parallel Y 𝐶𝑔1 371 pF 742 pF 371 pF 742 pF 𝐶𝑔2 662 pF 291 pF 1,695 pF 1,324 pF 𝐶𝑡𝑜𝑡𝑎𝑙 3,099 pF 3,099 pF 6,198 pF 6,198 pF 𝑅𝑔1 13.33 Ω 6.67 Ω 13.33 Ω 6.67 Ω 𝑅𝑔2 750 Ω 375 Ω 750 Ω 375 Ω 𝐿𝑠 4.1 mH 1.367 mH 8.2 mH 2.05 mH 𝑅𝑒 2.43 k Ω 0.81 k Ω 4.86 k Ω 1.215 k Ω 𝑅𝑡 1.4 k Ω 0.7 k Ω 1.4 k Ω 0.7 k Ω 𝐿𝑡 2 mH 1 mH 2 mH 1 mH 𝐶𝑡 103 pF 103 pF 206 pF 206 pF 𝐿𝑐 0.66 µH 0.33 µH 0.66 µH 0.33 µH 31 4: SIMULATION STUDY AND EXPERIMENTAL VERIFICATION In the previous chapter, the measured impedances ranging from 100 Hz to 10 MHz for different possible stator winding configurations (Single Y, Single Delta, Series Y, and Parallel Y) of the induction machine under study, 7.5 HP four-pole dual-voltage 9-terminal/lead motor, were used to extract the high frequency machine model parameters for various stator winding connections. In this chapter, the high frequency machine model is validated in time domain simulation in induction motor drive application where the motor drive PWM generates high frequency switching, leading to CM current in the induction machine. The simulated DM and CM currents using the proposed high frequency model are compared with the hardware measured DM and CM currents to verify the effectiveness of the proposed high frequency model for various stator winding connections. It is noted that the proposed machine model is built upon a similar model framework to the previous study [35]. In this study, the same induction machine, 7.5 HP four-pole dual-voltage 9-terminal/lead motor, is used to facilitate the high frequency model characterization and experimental verification. However, this thesis improves the high frequency machine model in [35] by adding the slip dependent rotor resistance Rr/s to the high frequency model, as illustrated in Figure 7, to capture the low frequency transients of the induction machine. Here, Rr stands for the rotor winding resistance while s represents the slip of the machine [10]. It should be noted that Rr/s values for each winding configuration are extracted through the associated experimental results. Table 4 illustrates all the experimental values of Rr/s with respect to different stator winding configurations. 32 Table 4: Experimental parameters for each winding configuration Parameter Single Y Single Delta Series Y Parallel Y ns (synchronous speed) 1800 RPM 1800 RPM 1800 RPM 1800 RPM nr (mechanical speed) 1756 RPM N/A 1763 RPM 1761 RPM s (slip) = (ns - nr)/ ns 0.0079 N/A 0.0040 0.0051 Rr (rotor DC resistance) 0.133 Ω 0.089 Ω 0.267 Ω 0.067 Ω Rr/s 17 Ω N/A 67 Ω 13 Ω A tachometer is used to measure the mechanical speed of the motor for different winding configurations. This is done by pointing the tachometer’s laser beam at the rotating shaft of the motor. The tachometer counts the number of Revolutions Per Minute (RPM) with respect to each test set up. After finding out the mechanical speed of the motor for each winding configuration, the slip (s) of the motor is calculated using the slip formula, s = (ns - nr)/ ns, and the known synchronous speed of the motor as summarized in Table 4. It should be noted that the Single Delta configuration leads to higher stator current per phase. Since the utilized motor drive (ABB, ACS150-03U-09A8-2) has limited output current rating and cannot be used for the Single Delta configuration, the mechanical speed (nr) for the Single Delta configuration is measured. Nevertheless, the motor drive can supply the input currents for the rest of the possible stator configurations nto measure the rotor speed ns as shown in Table 4. Overall, the inclusion of the slip dependent rotor resistance, Rr/s, in the motor equivalent model helps to represent the motor low frequency characteristics. The comparison analysis between experimental 33 and simulated CM and DM currents in time domain verifies that the inclusion of Rr/s in the high frequency machine model produce more accurate simulation results for machine low frequency responses for various stator winding configurations. 4.1: Simulation Configuration MATLAB/Simulink Simscape/Specialized Technology toolbox is utilized for the simulation studies of high frequency induction machine model. As shown in Figure 18, the Simulink model configuration consists of a PWM generator, Voltage Source Converter (VSC), motor’s equivalent circuit which can be adjusted to represent each winding configuration by changing the respective parameters within the model accordingly. The multiple scopes within the simulation model are implemented to show the relevant signals for analysis of the operation. Since the input AC supply voltage per phase (Vac) to the three-phase diode rectifier is 120 V, the output DC-link voltage (Vdc) of the DC-AC inverter is calculated as 𝑉𝑑𝑐 = 𝑉𝑎𝑐√2√3 = 294𝑉. The switching frequency fs of the simulated AC-DC inverter is set to 4 kHz to match the switching frequency of the ABB variable frequency drive, ACS150. The per phase high frequency motor model is illustrated in Figure 19 which can be used to represent all the stator winding connections by changing the associated parameter values listed in Tables 3 and 4. The high frequency machine model is verified using the comparison results of the DM and CM currents predicted by the proposed model and the experimental measurements. The CM current is defined by the phase current signals 𝑖𝑎 , 𝑖𝑏 , and 𝑖𝑐 as (27): 𝐼𝑐𝑚 =𝑖𝑎+𝑖𝑏+𝑖𝑐3 (27) The DM current components are defined for each phase as: 34 𝐼𝑑𝑚,𝑘 = 𝑖𝑘 − 𝐼𝑐𝑚 for 𝑘 = 𝐴, 𝐵, 𝐶. (28) Substituting 𝐼𝑐𝑚 into 𝐼𝑑𝑚,𝑘 , the DM current can be further simplified. For example, the DM current for phase A is represented as: 𝐼𝑑𝑚,𝐴 =2𝑖𝑎−𝑖𝑏−𝑖𝑐3 (29) 35 Figure 18: Simulink representation of the test setup 36 Figure 19: Simulink representation of per phase high frequency motor model Figure 20: Simulink representation of the PWM of the motor drive 37 Figure 21: Simulink representation of CM and DM Currents Figure 22: Simulink representation of the inverter and motor models 38 4.2: Experimental Setup As illustrated in Figure 23, there is a custom-built experimental setup which provides the necessary safety protocols with unique designed features to plug in multiple meter probes for various analysis required. The experimental setup consists of the motor drive part (ABB, ACS150-03U-09A8-2) and the induction motor part (7.5 HP Baldor, EME3710T). Digital phosphor oscilloscope (Tektronix, DPO5034B) is used to collect all the voltage and current measurements. The following subsections detail the motor drive setup and measurement equipment for the high frequency induction motor studies. 39 Figure 23: Experimental setup of 7.5 HP Baldor EM3710T induction motor under test 40 4.2.1: 7.5 HP Baldor Induction motor EM3710T As shown in Figure 24, the induction machine under the study is 7.5 HP four-pole dual-voltage 9-terminal/lead motor, which is equipped with flexible stator winding connection features to carry out the experiment for different stator winding connections (Single Y, Single Delta, Series Y, and Parallel Y). These possible winding configurations of the motor are discussed at introduction section. The nine terminals are labeled in the set up illustrated in Figure 24. By connecting these terminals accordingly, different stator winding connections are achieved conveniently. Figure 24: Induction motor test set up for different winding connections 41 According to the manufacturer datasheet, some of the important technical parameters of the 7.5 HP Baldor EM3710T induction motor are shown in Table 5. Table 5: Induction motor nameplate data Output power 7.5 HP, 5.6 kW Input voltage 230/460 V Input current 19/9.5 A RPM 1770 Input frequency 60 Hz Input phase 3 Input current @ high voltage Full load: 9.4 A, locked rotor: 70.1 A Full load torque 22.4 Lb. Ft. Efficiency ½: 92.2 %, ¾: 92.7 %, full load: 91.7% Power factor ½: 63%, ¾: 75%, full load: 81% 4.2.2: ABB Drive, ACS150-03U-09A8-2 The ACS150 motor drive is a wall or cabinet mountable power electronic inverter for controlling induction motor speed. Figure 25 shows the simplified main circuit diagram of the motor drive. 42 The diode rectifier converts three-phase AC voltage to DC voltage. In this study, the three-phase AC supply (120 V per phase) is rectified to a DC voltage of 294 V. The DC-link capacitor bank of the intermediate stage stabilizes the DC voltage. Then, the inverter converts the DC voltage to a controlled AC voltage for the AC induction motor. When the DC voltage in the circuit exceeds its maximum limit, the brake chopper, connecting the external brake resistor, is activated to reduce DC voltage within the rated values. Figure 25: ABB motor drive setup The ABB motor drive and its hardware connection are shown in Figure 26. The custom-made safety block, shown in Figure 26, secures the input and output terminals of the motor drive and makes the test probing application more secure and convenient. Table 6 demonstrates the specification and technical data of ABB motor drive, ACS150-03U-09A8-2. It is noted that the ABB motor drive has the semiconductor switching frequency of 4 kHz. 43 Figure 26: ABB motor drive and the safety block Table 6: ABB motor drive technical data I1Nnc (Continuous input current without choke or reactor) 14.3 A I1Nc (Continuous input current with choke or 5% reactor) 9.2 A f1 (Input frequency) 48-63 Hz I2N (Continuous output current) 9.8 A I2, 1min/10min (Continuous output current 1/10 minutes, max. 50% overload) 14.7 A I2max (Maximum output current, available 2 seconds at start) 17.2 A PN (Typical output power for 4-pole motor) 2.2 kW, 3 HP f2 (Output frequency) 0-500 Hz 44 4.2.3: Tektronix Oscilloscope Tektronix DPO5034B is a sophisticated four channel oscilloscope which can measure the voltages and currents of the induction motor under study at high sampling rates. Thus, the hardware measured data and waveforms can be used to verify the high frequency motor model proposed in the thesis. Tektronix DPO5034B, as shown in Figure 27, provides exceptional signal fidelity, along with advanced analysis and math function capabilities. It can run Windows-based analysis software right on the oscilloscope. By pointing and clicking the visual triggers, complex signals can be captured easily. This oscilloscope has 16 digital timing channels, and can be equipped to decode common serial protocols, providing a comprehensive view of the systems under study. Figure 27: Digital phosphor oscilloscope DPO5034B from Tektronix Figure 28 illustrates an example image captured by Tektronix DPO5034B which is taken when the experimental setup is configured for the Single Y winding connection of the induction motor under study. The green waveform represents common mode current (3Icm), and the rest of the waveforms represent the phase currents ia, ib, and ic. The sampling rate is set to be at 200 MS/s. so it means that 200,000,000 samples per second could be exported for each waveform in order to accurately analyse them and compare them to the simulated waveforms, respectively. 45 Figure 28: An example captured image on the scope for Single Y configuration, CM analysis, ia (yellow), ib (blue), ic (purple), 3Icm (green), sampling rate=200 MS/s, 1 A/V. div., and 50 µs/H. div. 4.2.4: Safety features in experimental setup Since collecting experimental data is involved with three-phase high voltages and currents, extra precautions must be taken into consideration when performing the hardware motor drive tests. As shown in Figure 23, there is a red beacon connected to the AC grid voltage supply which flashes when the induction motor is in operation. There is also a master breaking switch for AC grid voltage supply, as illustrated in Figure 29, which is locked up once the experimental setup is not used. 46 Figure 29: Master circuit lock disconnect switch To provide a secondary protection, another lock switch is utilized between the motor drive and the induction motor as shown in Figure 30. This kill switch is for the motor and provides an immediate disconnection possibility in case of an emergency. The acrylic shields surrounding the induction motor and motor drive terminals also provide extra layer of security and help avoiding accidental short circuits. Ultimately, safety is always a major concern when operating a high-power device, e.g., 7.5 HP induction motor. It is worth mentioning that the ABB motor drive output and the secondary kill switch nearby the induction motor are coupled using a one-meter-long cable (AWG 16). The short cable length reduce/avoid over-voltage spikes at the induction motor terminals due to fast semiconductor switching transients. Having stated that, this connecting cable could be replaced by cables with different lengths for analysing over-voltages caused by them in the motor drive system. The experimental set up is equipped with all the extra connecting terminal jacks for future studies regarding this research direction. 47 Figure 30: Experimental setup in operation 4.3: Comparisons of Simulation and Experimental Results As introduced in Section 4.1, the DM and CM currents predicted from the high frequency machine model and measured from the experimental setup are compared to verify the proposed high frequency machine model. The definitions of the DM and CM currents are given in Section 4.1, respectively. Different stator winding configurations (Single Y, Series Y, and parallel Y 48 connections) are used to validate the proposed universal high frequency model framework. It is noted that the single  connection of the stator winding is not performed in the experiment setup since the required motor stator current is beyond the motor drive output current rating. However, the experimental results collected for the other possible winding configurations are sufficient to demonstrate the validity of the proposed high frequency motor model. Figures 31−36 demonstrate the simulated and experimental waveforms of the DM currents for Single Y, Series Y, and parallel Y winding connections. Two snap shots for the DM currents of each winding connection, wide screen and zoomed-in views, are captured in order to compare them more precisely. It is shown in Figs. 31−36 that the high frequency machine model accurately predicted the low frequency components of the DM currents for the three winding connections. The zoomed-in views of the DM currents in Figures 32, 34, and 36 shows that the stator current ripples predicted by the proposed model match the hardware measured ones in general for the single Y, Series Y, and parallel Y connections. However, the stator current ripples predicted by the proposed model has slightly large errors compared to the hardware measurements for smaller current values of the stator currents. This may be due to the inaccurate characterization of the motor low frequency parameters such as the stator and rotor resistances and stator leakage inductances. 49 Figure 31: 3IDM comparison result for Single Y connection Figure 32: 3IDM comparison result for Single Y connection with zoomed-in view 50 Figure 33: 3IDM comparison result for Series Y connection Figure 34: 3IDM comparison result for Series Y connection with zoomed-in view 51 Figure 35: 3IDM comparison result for Parallel Y connection Figure 36: 3IDM comparison result for Parallel Y connection with zoomed-in view 52 The simulated and experimental waveforms of the CM currents for Single Y, Series Y, and parallel Y winding connections are shown in Figures 37−42. Similar to the DM current figures, two snap shots for the CM currents of each winding connection, wide screen and zoomed-in views, are captured for precise waveform comparisons. It is shown in Figures 37−42 that the high frequency CM current waveforms predicted by the proposed motor model are similar to the CM currents measured from the experimental setup for the single Y, Series Y, and parallel Y connections. The peak values and the ringing frequency of the CM currents predicted by the high frequency motor model in Figures 37−42 are close to the ones measured from the hardware setup. According to [27], the spikes of the CM currents in Figures 37−42 are due to the high dV/dt during the semiconductor commutations. The current oscillations following each spike in the CM currents are in the range of 100−200 kHz as shown in Figures 37−42, which corresponds to the resonant frequency of the CM impedance in Figure 6. Figures 31−42 demonstrate the closely matching results between simulated and experimental waveforms for DM and CM currents with respect to Single Y, Series Y, and Parallel Y configurations for the 7.5 HP four-pole dual-voltage 9-terminal induction machine under the study. This verifies the proposed high frequency induction machine model and the associated model parameter extraction method. There are minor discrepancies between the simulated and experimental DM and CM currents, e.g., extra ringing effects in CM experimental current waveforms. These discrepancies are expected, because the proposed model uses low order lump circuit in Figure 7 to approximate a complicated frequency dependent system. It is expected a higher order high frequency machine model can improve the simulation accuracy of the CM and DM currents. 53 Figure 37: 3ICM comparison result for Single Y connection Figure 38: 3ICM comparison result for Single Y connection with zoomed-in view 54 Figure 39: 3ICM comparison result for Series Y connection Figure 40: 3ICM comparison result for Series Y connection with zoomed-in view 55 Figure 41: 3ICM comparison for Parallel Y connection Figure 42: 3ICM comparison result for Parallel Y connection with zoomed-in view 56 5: CONCLUSION AND FUTURE WORK A universal high frequency induction machine model for motor drive EMI studies which can represent the machine in different stator winding configurations is proposed in this thesis. The proposed high frequency model is based on characterization of a 7.5 HP 9-terminal/lead induction motor which can be connected in four stator winding configurations (Single Y, Single Delta, Series Y, and Parallel Y). The DM and CM impedances are characterization in the frequency range up to 10 MHz. The proposed high frequency model uses a simple and accurate lump parameter circuit model with a straight-forward model characterization method which is inspired by the endeavors in the previous studies [10−12, 17, 28, 35−42]. The high frequency characterization method in frequency domain using impedance measurements is implemented to determine the necessary parameters for the Single Y configuration. Then, the parameter conversion techniques are utilized to evaluate the respective parameters for the other stator winding configurations of the induction machine. The parameter conversion methods are derived using the simplification of distributed parameter stator winding model. All the calculated parameters are constant except Rr/s which is slip/load dependent resistance to capture the low frequency transients of induction machines. By measuring the mechanical speed for each winding configuration, the Rr/s values are calculated accordingly. The commercial 7.5 HP 9-terminal/lead induction machine (Baldor, EM3710T) and motor drive (ABB, ACS150-03U-09A8-2) are used to demonstrate the validity and accuracy of the proposed high frequency machine model. The experimental measurements of the CM and DM current waveforms with regards to different possible winding configurations are gathered using Tektronix DPO5034B oscilloscopes. The proposed high frequency machine model for different stator 57 winding configurations are also constructed using MATLAB/Simulink Simscape Power System toolbox to produce simulated CM and DM currents for different stator winding connections. By overlapping simulated and experimental results of the CM and DM currents with respect to each winding configuration, the validity and accuracy of the relative proposed high frequency machine model is demonstrated in time domain. The experimental data for the CM and DM currents associated with Single Delta configuration cannot be collected at the thesis due to incapability of the utilized motor drive to provide sufficient input current per phase for the induction motor under study. Having stated that, the experimental data collected for other possible stator winding configurations are sufficient to demonstrate the validity of the proposed high frequency model. Overall, the similarity between experimental and simulated results shows the effectiveness of the proposed machine model and its adaptability for various stator winding configurations. Although the proposed high frequency machine model has shown to be accurate using single phase belt equivalent circuit with straightforward model characterization procedure, future research efforts can be dedicated to further improve the accuracy of the high frequency machine model. 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Binder, "The High-Frequency Induction Machine Parameters and Their Influence on the Common Mode Stator Ground Current," IEEE 978-1-4673-0142-8/12, pp. 505-511, 2012. 62 APPENDICES Appendix A: Parameter conversion formulas for Series Y winding connection The following are Single Y (singleY) to Series Y (seriesY) parameter conversion formulas [35]: 𝐶𝑔1,𝑠𝑒𝑟𝑖𝑒𝑠𝑌 = 𝐶𝑔1,𝑠𝑖𝑛𝑔𝑙𝑒𝑌 (30) 𝑅𝑔1,𝑠𝑒𝑟𝑖𝑒𝑠𝑌 = 𝑅𝑔1,𝑠𝑖𝑛𝑔𝑙𝑒𝑌 (31) 𝐿𝑐,𝑠𝑒𝑟𝑖𝑒𝑠𝑌 = 𝐿𝑐,𝑠𝑖𝑛𝑔𝑙𝑒𝑌 (32) 𝐿𝑠,𝑠𝑒𝑟𝑖𝑒𝑠𝑌 = 2𝐿𝑠,𝑠𝑖𝑛𝑔𝑙𝑒 𝑌 (33) 𝑅𝑒,𝑠𝑒𝑟𝑖𝑒𝑠𝑌 = 2𝑅𝑒,𝑠𝑖𝑛𝑔𝑙𝑒𝑌 (34) 𝐶𝑡𝑜𝑡𝑎𝑙,𝑠𝑒𝑟𝑖𝑒𝑠𝑌 = 2𝐶𝑡𝑜𝑡𝑎𝑙,𝑠𝑖𝑛𝑔𝑙𝑒𝑌 (35) 𝐶𝑔2,𝑠𝑒𝑟𝑖𝑒𝑠𝑌 =23𝐶𝑡𝑜𝑡𝑎𝑙,𝑠𝑖𝑛𝑔𝑙𝑒𝑌 − 𝐶𝑔1,𝑠𝑒𝑟𝑖𝑒𝑠𝑌 (36) 𝑅𝑔2,𝑠𝑒𝑟𝑖𝑒𝑠𝑌 = 𝑅𝑔2,𝑠𝑖𝑛𝑔𝑙𝑒 𝑌 (37) 𝐶𝑡,𝑠𝑒𝑟𝑖𝑒𝑠𝑌 ≈110(𝐶𝑔1,𝑠𝑒𝑟𝑖𝑒𝑠𝑌 + 𝐶𝑔2,𝑠𝑒𝑟𝑖𝑒𝑠𝑌) (38) 𝐿𝑡,𝑠𝑒𝑟𝑖𝑒𝑠𝑌 = 𝐿𝑡,𝑠𝑖𝑛𝑔𝑙𝑒𝑌 (39) 𝑅𝑡,𝑠𝑒𝑟𝑖𝑒𝑠𝑌 = 𝑅𝑡,𝑠𝑖𝑛𝑔𝑙𝑒𝑌 (40) 63 Appendix B: Parameter conversion formulas for Parallel Y winding connection The following are Single Y (singleY) to Parallel Y (parallelY) parameter conversion formulas [35]: 𝐶𝑔1,𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑌 = 2𝐶𝑔1,𝑠𝑖𝑛𝑔𝑙𝑒𝑌 (41) 𝑅𝑔1,𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑌 =12𝑅𝑔1,𝑠𝑖𝑛𝑔𝑙𝑒 𝑌 (42) 𝐿𝑐,𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑌 =12𝐿𝑐,𝑠𝑖𝑛𝑔𝑙𝑒𝑌 (43) 𝐿𝑠,𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑌 =12𝐿𝑠,𝑠𝑖𝑛𝑔𝑙𝑒𝑌 (44) 𝑅𝑒,𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑌 =12𝑅𝑒,𝑠𝑖𝑛𝑔𝑙𝑒𝑌 (45) 𝐶𝑡𝑜𝑡𝑎𝑙,𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑌 = 2𝐶𝑡𝑜𝑡𝑎𝑙,𝑠𝑖𝑛𝑔𝑙𝑒𝑌 (46) 𝐶𝑔2,𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑌 =23𝐶𝑡𝑜𝑡𝑎𝑙,𝑠𝑖𝑛𝑔𝑙𝑒𝑌 − 𝐶𝑔1,𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑌 (47) 𝑅𝑔2,𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑌 =12𝑅𝑔2,𝑠𝑖𝑛𝑔𝑙𝑒𝑌 (48) 𝐶𝑡,𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑌 ≈110(𝐶𝑔1,𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑌 + 𝐶𝑔2,𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑌) (49) 𝐿𝑡,𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑌 =12𝐿𝑡,𝑠𝑖𝑛𝑔𝑙𝑒𝑌 (50) 𝑅𝑡,𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑌 =12𝑅𝑡,𝑠𝑖𝑛𝑔𝑙𝑒𝑌 (51)
Thesis/Dissertation
eng
Electrical Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Wang, Liwei
Simulation and experimental verification of universal high frequency induction machine model for arbitrary stator winding connections
Text