# A Dynamic Modeling Permanent Magnet Synchronous Motor Drive System

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2 commonly used in motors and axial field flux have become a topic of interest for study and used in a few applications. 2. Flux Density Distribution PM motors are classified on the basis of the flux density distribution and the shape of current excitation. They are PMSM and PM brushless motors (BLDC). The PMSM has a sinusoidal-shaped back EMF and is designed to develop sinusoidal back EMF waveforms 3. Modeling of PM Drive System Detailed modeling of PM motor drive system is required for proper simulation of the system. The d-q model has been developed on rotor reference frame. At any time t, the rotating rotor d-axis makes and angle θr with the fixed stator phase axis and rotating stator mmf makes an angle α with the rotor d- axis. Stator mmf rotates at the same speed as that of the rotor. V q = R S i q + ω r λ d + ρλ q V d = R S i d - ω r λ q + ρλ d Fulx Linkage are given by λ q = L q i q λ d = L q i d + λ f Arranging equations in matrix form = + The developed torque motor is being given by T e = ( λ d i q λ q i d) C. Equivalent Circuit of Permanent Magnet Synchronous Motor Equivalent circuits of the motors are used for study and simulation of motors. From the d-q modeling of the motor using the stator voltage equations the equivalent circuit of the motor can be derived. Fig. 2. PMSM electric circuit d-axis Fig. 3. PMSM electric circuit q-axis 76 Online International, Reviewed & Indexed Monthly Journal

3 Field oriented control was invented in the beginning of 1970s and it demonstrates that an induction motor or synchronous motor could be controlled like a separately excited dc motor by the orientation of the stator mmf or current vector in relation to the rotor flux to achieve a desired objective. In order for the motor to behave like DC motor, the control needs knowledge of the position of the instantaneous rotor flux or rotor position of permanent magnet motor. This needs a resolver or an absolute optical encoder. Knowing the position, the three phase currents can be calculated. Its calculation using the current matrix depends on the control desired. Some control options are constant torque and flux weakening. These options are based in the physical limitation of the motor and the inverter. The limit is established by the rated speed of the motor, at which speed the constant torque operation finishes and the flux weakening starts as shown in figure.4. Fig. 4. Steady state Torque Vs Speed 1. Constant torque operation Constant torque control strategy is derived from field oriented control, where the maximum possible torque is desired at all times like the dc motor. This is performed by making the torque producing current iq equal to the supply current Im. 2. Flux Weakning Flux weakening is the process of reducing the flux in the d axis direction of the motor which results in an increased speed range. The motor drive is operated with rated flux linkages up to a speed where the ratio between the induced emf and stator frequency (V/f) is maintained constant. After the base frequency, the V/f ratio is reduced due to the limit of the inverter dc voltage source which is fixed. The weakening of the field flux is required for operation above the base frequency. 77 Online International, Reviewed & Indexed Monthly Journal

4 D. Speed control of PM motor Fig. 5. System flow diagram Speed controller calculates the difference between the reference speed and the actual speed producing an error, which is fed to the PI controller. PI controllers are used widely for motion control systems. They consist of a proportional gain that produces an output proportional to the input error and an integration to make the steady state error zero for a step change in the input. Block diagram of the PI controller is shown in figure 6. Fig. 6. PI controller Speed control of motors mainly consist of two loops the inner loop for current and the outer loop for speed. The order of the loops is due to their response, how fast they can be changed. This requires a current loop at least 10 times faster than the speed loop. Since the PMSM is operated using field oriented control, it can be modeled like a dc motor. The design begins with the innermost current loop by drawing the block diagram. But in PMSM drive system the motor has current controllers which make the current loop. The current control is performed by the comparison of the reference currents with the actual motor currents. 3. Drive System Simulation in Simulink The PM motor drive simulation was built in several steps like abc phase transformation to dqo variables, calculation torque and speed, and control circuit. The abc phase transformation to dqo variables is built using Parks transformation and for the dqo to abc the reverse transformation is used. For simulation purpose the voltages are the inputs and the current are output. Parks transformation used for converting Vabc to Vdqo is shown in figure Online International, Reviewed & Indexed Monthly Journal

5 Fig. 7.Vabc to Vdqo Block The d and q axis motor circuits built using Simulink elements are shown in figure 8. And 9. Fig. 8. d axis circuit Fig. 9. q axis circuit 4. Results The system built in Simulink for a PMSM drive system has been tested with the two current control methods, Hysteresis and PWM, at the constant torque and flux-weakening regions of operation. The motor parameters used for simulation are given in table 1. These parameters were taken from reference. The motor is operated with constant torque up to its rated speed and beyond that rated speed fluxweakening mode is adopted. Simulation results are given at electrical speeds of 200 radians per second (31 Hz) and 600 radians per second (95 Hz). The above speeds represent below and above rated speed of the motor. Table 1: Interior Permanent Magnet Motor Parameters 79 Online International, Reviewed & Indexed Monthly Journal

6 The simulation was carried out using two current control techniques to study the performance of the motor drive. The techniques are Hysteresis current control and PWM current control. The plots of current, torque and speed are given for both cases. B. Simulation for Operation at 200 rad/s Fig. 10 Iabc Currents with Hysteresis Control at 200 rad/s Fig. 11 Idqo Currents with Hysteresis Control at 200 rad/s 80 Online International, Reviewed & Indexed Monthly Journal

7 Fig. 12 Developed torque with Hysteresis Control at 200 rad/s Fig. 13Motor Electrical speed with Hysteresis Control at 200 rad/s Fig. 14 Iabc Currents with PWM Control at 200 rad/s 81 Online International, Reviewed & Indexed Monthly Journal

8 Fig. 15 Idqo Currents with PWM Control at 200 rad/s Fig. 16 Developed torque with PWM Control at 200 rad/s Fig. 17Motor Electrical speed with PWM Control at 200 rad/s 82 Online International, Reviewed & Indexed Monthly Journal

9 5. Conclusion Usually in such a drive system the inverter is driven either by hysteresis or by PWM current controllers. A comparative study has been made of the two current control schemes in terms of switching frequency, device losses, power quality, speed error and current control ability. This study proves that PWM current controllers are better than hysteresis current controllers because of having constant switching frequency and lower THD of the input voltage waveforms. The error between the speed command and the actual speed is also greatly reduced. Hysteresis current controllers have a variable switching frequency that depends of the hysteresis band and if the bandwidth is very small it may affect the device switching capability. However, the simulation with hysteresis current controller allows faster simulations with reduced time and computational resources. A speed controller has been designed successfully for closed loop operation of the PMSM drive system so that the motor runs at the commanded or reference speed. The simulated system has a fast response with practically zero steady state error thus validating the design method of the speed controller. References 1. Ambrish Pati Tripathi,Vikram Singh, Ankush Patidar, " Permanent Magnet Synchronous Motor Voltage Vector Control By Simulation "International Journal of Scientific & Engineering Research Volume 3, Comparison of various pwm techniques for field oriented control vsi fed pmsm drive-p.ramana, B.Santhosh Kumar, Dr.K.Alice Mary, Dr.M.Surya Kalavathi 3. Li Chuan-Fang, Li Feng, QU Ji-Sheng and so on. Thechnology characteristic and optional method of the space vector polse-duration modulation(svpwm).shan Dong university Journal, 2005, pp M.T. Benchouia, Zouzou S.E., Golea A., Ghamri A., Modeling and Simulation of Variable Speed DriveSystem with Adaptive Fuzzy Controller Application to PMSM, IEEE International Conference onindustrial Technology (ICIT), pp ,December, Matlab/simulink model of field oriented control of pmsm drive using space vectors- Remitha K Madhu1 and Anna Mathew,Department of EE Engineering, Rajagiri Institute of Science and Technology, Kochi, India Assistant Professor, Rajagiri Institute of Science and Technology, Kochi, India 6. Nour M., Aris I., Mariun N., Mahmoud S., Hybrid Model Reference Adaptive Speed Control for Vector Controlled Permanent Magnet Synchronous Motor Drive IEEE Power Electronics and Drive System, pp , April, Sung Yu J., Mo Hwang S., Yuen Won C., Performances of Fuzzy Logic Based Vector Control for Permanent Magnet Synchronous Motor Used in Elevator Drive System, The 30th Annual Conference of the IEEE Industrial Electronics Society, pp , November, Online International, Reviewed & Indexed Monthly Journal

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