# South Asian Journal of Engineering and Technology Vol.2, No.16 (2016) 21 30

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2 II.MODELLING OF PMSM A. Machine Equations For PMSM, the model in rotor synchronous coordinate is the most popular, because all the parameters become constant. The machine equations of a PMSM in synchronous frame are expressed as follows (the components indicated by dq) ud = Rs id + dψd/d (2.1) uq = Rs iq + dψq/dt + ωψd (2.2) ψd = Ld id + ψf (2.3) ψq = Lq iq (2.4) where, Rs - stator resistance Ld, L q- d-axis and q-axis inductance Ψf- permanent magnet flux ψd, ψq- ud, uq- d-axis and q- axis stator flux d-axis and q- axis stator voltage id, iq- d-axis and q-axis stator current ω- electrical rotor speed and the torque is expressed as Te = (3/2)p (ψd iq ψq id ) (2.5) ψα = Lα iα + Lαβ iβ + ψf cos θe (2.8) ψβ = Lαβ iα + Lβ iβ + ψf sin θe II. EXISTING SYSTEM Direct Torque Control principle for PMSM: The basic principle of vector control is to get a high-performance system through controlling flux and torque independently after getting the motor decoupling model through coordinate transformation. There are 3 signals which affect the control action in a DTC system; 1. Torque - Te 2. The amplitude of the Stator Flux linkage - ψ 3. The angle of the resultant flux linkage vectors - δ A. The Implementation of DTC System 22

3 The existing DTC scheme is indicated in figure 1, torque and flux signals are obtained from the estimator. These are regulated by using two hysteresis controllers. The hysteresis controllers outputs in turn switch the three inverter legs, applying a set of voltage vectors across the motor B.Flux and Torque Estimator Flux and torque estimator are used to determine the actual value of the torque and flux linkage. Into this block enters the VSI voltage vector transformed to the qd-stationary reference frame. The three-phase variables are transformed into dq axes variables with the following transformationwhere ƒ represents the stator currents, voltages and flux linkages. The stator flux linkage is estimated by taking the integral of difference between the input voltage and the voltage drop across the stator resistance as, ψ = (V - R i ) dt (3.1) ψd = (Vd - Rsid ) dt (3.2) q q s q The flux linkage phasor is given by 2 + ψ (3.3) 2 ψ = (ψ ) s d q of stator flux linkage (θ) is In this block, the location r 23

4 Fig. 2 2-level torque hysteresis comparator PRINCIPLE OF SPACE VECTOR The space vector pulse width modulation is used to generate the voltages applied to the stator phases. It uses a special scheme to switch the power transistors to generate pseudo sinusoidal currents in the stator phases. This method is increasingly used for AC drives with the condition that the harmonic current is as small as possible and the maximum output voltage is as large as possible. Fig. 4 Switching vectors and sector Treats the sinusoidal voltage as a constant amplitude vector rotating at constant frequency. This PWM technique approximates the reference voltage Vref by a combination of the eight switching patterns (V0 to V7). Coordinate Transformation (abc reference frame to the stationary α-β frame). That is a three-phase voltage vector is transformed into a vector in the stationary α-β coordinate frame represents the spatial vector sum of the three- phase voltage. The vectors (V1 to V6) divide the plane into six sectors (each sector: 60 degrees).vref is generated by two adjacent nonzero vectors and two zero vectors. To implement the space vector PWM, the voltage equations in the abc reference frame can be transformed into the stationary αβ reference frame that consists of the horizontal (α) and vertical (β) axes, as a result, six non-zero vectors and two zero vectors are possible. Six nonzero vectors (V1 - V6) shape the axes of a hexagonal as depicted in figure 3.6 and feed electric power to the load or DC link voltage is supplied to the load. The angle between any adjacent two non-zero vectors is 60 degrees. Meanwhile, two zero vectors (V0 and V7) are at the origin and apply zero voltage to the load. The eight vectors are called the basic space vectors and are denoted by V0, V1, V2, V3, V4, V5, V6, and V7. The same transformation can be applied to the desired output voltage to get the desired reference voltage vector Vref in the d-q plane. The objective of space vector PWM technique is to approximate the reference voltage vector Vref using the eight switching patterns. The space vector pulse width modulation is used to generate the voltages applied to the stator phases. It uses a special scheme to switch the power transistors to generate pseudo sinusoidal currents in the stator phases. The space vectors technique is nowadays commonly known as space vector modulation (SVM). 24

5 The SVPWM switching pattern is shown in the fig. 5, it consists of eight vectors starting from V0 to V7. Fig.5 SVPWM switching pattern IV. PROPOSED SYSTEM WITH SINUSOIDAL PULSE WIDTH MODULATION Pulse width modulation is the process of modifying the width of the pulses in a pulse train in direct proportion to a small control signal. There are different types of pulse width modulations. Among them, the well known are Sinusoidal pulse width modulation (SPWM). Sinusoidal PWM has been very popular technique used in AC motor control. This method employs a triangular carrier wave compared with a sine wave and the points of intersection determine the switching points of the power devices in the inverter. However, this method is unable to make full use of the inverter s supply voltage and the asymmetrical nature of the PWM switching characteristics produces relatively high harmonic distortion when compared to SVPWM. A. Generation of Gating Signals Instead of maintaining the width of all pulses as same, the width of each pulse is varied in proportion to the amplitude of a sine wave evaluated at the center of the same pulse. The SPWM is commonly used in industrial applications. The frequency of the reference signal fr determines the inverter output frequency fo, and the reference peak amplitude controls the Modulation Index (MI), and in turn the rms output voltage. The generations of gating signals with SPWM are shown in fig. 6. There are three sinusoidal reference waves and each shifted by 120º. A carrier wave is compared with the reference signal corresponding to a phase to generate the gating signals for that phase. Comparing the carrier signal with the reference phases it produces the gating pulses. When the sinusoidal wave has magnitude higher than the triangular wave, the comparator output is high, otherwise low. The number of pulses per half cycles depends upon the carrier frequency. When the triangular wave has its peak coincident with zero of the reference sinusoidal, there are N=fc/2f pulses per half cycle. If zero of the triangular wave coincides with zero of the reference sinusoidal, there are (N-1) pulses per half cycle. The normalized carrier frequency should be odd multiple of three. Thus, all phase voltage are identical, but 120º out of phase without even harmonics; moreover, at frequencies multiples of three are identical in amplitude and phase in all phases. The rms output voltage can be varied by varying the Modulation Index (MI). It can be observed that the area of each pulse corresponds approximately to the area under the sine wave between the adjacent midpoints of off periods on the gating signals. B. Advantages The Distortion Factor (DF) is reduced. The Lowest Order Harmonic (LOH) content is also reduced significantly. 25

6 Easy implementation when compared to SVPWM. As shown in fig. 6, the frequency of Vtri and Vcontrol is: Frequency of Vtri = fs Frequency of Vcontrol = f1 where, fs = PWM frequency and f1 = Fundamental frequency The inverter output voltages are determined as follows: When Vcontrol > Vtri, VA0 = Vdc/2 When Vcontrol < Vtri, VA0 = Vdc/2 where, VAB = VA0 VB0, VBC = VB0 VC0, VCA = VC0 VA0 C. Modulation Index The ratio of sinusoidal reference wave to triangular carrier wave is called modulation index. The magnitude of fundamental component of output voltage is proportional to MI. MI can never be more that unity and hence by varying MI, we can control the output voltage. The frequency modulation ratio is given by, m f f s f1 Frequency modulation ratio (mf) should be a multiple of 3 for three-phase PWM inverter, an odd multiple of 3 and even harmonics are suppressed. D. Overmodulation: Further increase in the amplitude of load voltage, the amplitude of the modulating signal can be made higher than the amplitude of the carrier signal which leads to overmodulation. The relationship between the amplitude of the fundamental ac output line voltage and the dc link voltage becomes nonlinear. Large values of MI in SPWM leads to full overmodulation. This case is known as square-wave operation, where the power devices are ON for 180º. Here the inverter cannot vary the load voltage except by varying the dc supply voltage. V. RESULT AND DISCUSSION The simulation results for DTC based PMSM drive using SPWM technique are discussed. The system built in 26

7 simulink for a PMSM drive system has been tested at the constant power-region of operation. The motor was controlled by SPWM technique and the waveform of electromagnetic torque output and dynamic torque output is shown if fig. 7, 8. Fig Fig 7 Electromagnetic Torque Output (Torque=0.4Nm) Dynamic Torque output Fig. 8 27

8 The stator currents and dynamic static current output waveforms are shown in fig. 9, 10. Stator Current Output Fig. 9 ` Fig. 11 Dynamic Static Current Torque pulsations are less in case of the proposed system. It is clear that a SPWM techinque based torque controller achieves the minimum torque ripple. Also, SPWM based DTC as better current and torque characteristics. The percentage of ripples obtained by using SPWM the ripple is 4.2%. This percentage ripple obtained by using SPWM is similar to SVPWM technique. Thus by using simple implementation like SPWM, the torque ripple is reduced similar to that of using complicated technique SVPWM. Also the current waveform is similar as in the case of SVPWM. 28

9 VI. CONCLUSION This paper explains the mathematical equations related to the application of DTC in PMSM. The equations show that the change of torque can be controlled by keeping the amplitude of the stator flux linkage constant and increasing the rotating speed of the stator flux linkage as fast as possible. The simulink block of DTC in PMSM using SPWM is presented. The simulation results examined the implementation of the direct torque control in permanent magnet synchronous motor using SPWM and compared its performance with using SVPWM. The torque and flux linkage reference are kept constant at the same level. VII. APPENDIX MOTOR PARAMETERS Type PMSM Rated Power 1HP Number of phases 3 Number of poles (P) 8 Base current 2.5 A Rated voltage 300 V Stator resistance per ohm phase( R) q-axis inductance(lq) H Stator flux linkages per p H due to rotor magnet ( A f ) (rad/s) Moment of inertia (J) Friction Factor (F) (N.m.s) d-axis inductance (Ld ) VII. REFERENCES [1] Helsinki. Tech.Guide, Direct torque control-the world moat advanced Ac drive technology,abb Finland [2] BIMBAL.K.Bose (2002) Modern power electronics and AC drives Englewood Chiffs, Prentice-Hall. [3] Krishnan R. (2002) Electric motor drives modelling, analysis, and control, Eastern Economy Edition [4] V. Ambrozic, G. S, Buja and R. Menis, Band constrained technique for direct torque control of induction motor, IEEE Trans. Ind. Electron., vol. no. 4, pp , Aug [5] G. S. Buja and M. P. Kazmierkowski, Direct torque control of PWM inverter- fed AC motors- A survey, IEEE Trans, Power Electron., vol.51, no.4,pp, , Aug [6] Bimal K. Bose, A High-Performance Inverter-Fed Drive System of an Interior Permanent Magnet Synchronous Machine, IEEE Transactions on Industry Application, vol 24, no.6. [7] Pragasen Pillay, Modelling, Simulation and Analysis of Permanent Magnet Motor Drives, IEEE Transaction On Industry Application, vol 25. [8] V. Ambrozic, G. S, Buja and R. Menis, Band constrained technique for direct torque control of induction motor, IEEE Trans. Ind. Electron., vol. no. 4, pp , Aug [9] S. Kouro, R. Bernal, H. Miranda, C. Silva, and J. Rodriguez, Highperformance torque and flux control for multilevel inverter fed induction motors, IEEE Trans. Power Electron., vol. 22, no. 6, pp , Nov [10] Y. Zhang, J. Zhu,Y. Guo,W. Xu,Y.Wang, and Z. Zhao, 29

10 A sensorlessdtc strategy of induction motor fed by three-level inverter based on discrete space vector modulation, in Proc. Australasian Univ. Power Eng. Conf. (AUPEC 2009), pp [11] K. D. Hurst, T. G. Habetler, G. Griva, and F. Profumo, Zero-speed tacholess IM torque control: Simply a matter of stator voltage integration, IEEE Trans. Ind. Appl., vol. 34, no. 4, pp , Jul [12] J. Hu and B. Wu, New integration algorithms for estimating motor flux over a wide speed range, IEEE Trans. Power Electron., vol. 13, no. 5, pp , Sep [13] B. K. Bose and N. R. Patel, A programmable cascaded low-pass filter based flux synthesis for a stator flux-oriented vector-controlled induction motor drive, IEEE Trans. Ind. Electron., vol. 44, no. 1, pp , Feb [14] T.-W. Chun, M.-K. Choi, and B. K. Bose, A novel startup scheme of stator-flux-oriented vector-controlled 30

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