# MODELLING AND SIMULATION OF SVPWM INVERTER FED PERMANENT MAGNET BRUSHLESS DC MOTOR DRIVE

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2 V c = V m sin(ωt+10 ) (1) These three vectors can be represented by a one vector which is known as space vector. Space vector is defined as, V s = V a + V b e jπ 3 + V c e -jπ 3 () V s = 3 V m [ sin ωt -j cos ωt ] (3) i.e, V s is vector having magnitude of 3 V m and rotates in space at ω rad/sec as shown in Figure 1. Fig.1: Rotating Space Vector This vector can be represented in two dimensional space by simply resolving abc in to dq axis. Fig.: abc to dq transformation Therefore space vector can also be written as V s = V d + jv q B. Principle of Space Vector PWM θ = tan 1 V q (4) V d V a Vd (5) Vb Vq V c Fig.3: Three-phase voltage source PWM Inverter SVPWM aims to generate a voltage vector that is close to the reference circle through the various switching modes of inverter. Figure 3 is the typical diagram of a three-phase voltage source inverter model. S1 to S6 are the six power switches that shape the output, which are controlled by the switching variables a, a, b, b, c and c. When an upper transistor is switched ON, i.e., when a, b or c is 1, the corresponding lower transistor is switched OFF, i.e., the corresponding a, b or c is 0. Therefore, the ON and OFF states of the upper transistors S1, S3 and S5 can be used to determine the output voltage. Hence there are 8 possible switch states, i.e.,(0,0,0), (0,0,1), (0,1,0), (0,1,1), (1,0,0), (1,0,1), (1,1,0), (1,1,1). The inverter has six states when a voltage is applied to the motor and two states when the motor is shorted through the upper or lower transistors resulting in zero volts being applied to the motor. Copyright to IJAREEIE 1948

3 Fig.4: Inverter Voltage Vectors (V 0 to V 7 ) Consider an inverter feeding a star connected load and center point of the dc link is take as reference point as shown in Figure 5, Fig.5: Inverter feeding a star connected load The potential of point a, point b & point c with respect to the center point of the dc link is known if the conducting states of the switches are known. When upper switch is ON, the potential of a, b &c is V dc ON, the potential of a, b &c is V dc. & when lower switch is V a0 = V an + V n0 V b0 = V bn + V n0 V c0 = V cn + V n0 (6) & V n0 = 1 3 [V a0+v b0 +V c0 ] (7) Van 1 1 Va0 1 Vbn 1 1 Vb0 (8) 3 V cn 1 1 Vc0 Consider the switching states, (0,0,0) & (1,1,1) V an = V bn = V cn =0; Hence, V d = V q = 0 Therefore, V s = 0 0 (9) Now consider the switching state (1,0,0), V a0 = V dc, V b0 = V c0 = - V dc V an = 3 V dc, V bn = V cn = V dc Hence, V d = 3 V an = V dc & V q =0 Therefore, V s = V dc 0 (10) Since (0,1,1) is the complementary of (1,0,0); For (0,1,1), V s = V dc 180 (11) Similarly derive the magnitude and angle of space vector for all possible switching states. They are, For (0,0,0) : V s = 0 0 V 0 For (1,0,0) : V s = V dc 0 V 1 For (1,1,0) : V s = V dc 60 V Copyright to IJAREEIE 1949

4 For (0,1,0) : V s = V dc 10 V 3 For (0,1,1) : V s = V dc 180 V 4 For (0,0,1) : V s = V dc 40 V 5 For (1,0,1) : V s = V dc 300 V 6 For (1,1,1) : V s = 0 0 V 7 There are 6 non-zero vectors (V 1 to V 6 ) and zero vectors (V 0 & V 7 ). Table 1 summarizes switching vectors along with the corresponding line to neutral voltage and line to line voltages applied to the motor. Table 1: Switching vectors, phase voltages and output line to line voltages While plotting 8 voltage vectors in complex plane, the non-zero vectors form the axes of a hexagon as shown in Figure 6.The angle between any adjacent two non-zero vectors is 60 electrical degrees. The zero vectors (or null vectors) are at the origin and apply a zero voltage vector to the motor. If the phase voltages are sinusoidal, locus of the V s is circle. The maximum value of V s for which locus is circle is the radius of the inscribing circle, i.e, 3 V dc. Fig.6: Basic switching vectors and sectors III.REALIZATION OF SPACE VECTOR PWM The space vector PWM is realized based on the following steps: A. Step 1: Determine V d, V q, V ref, and angle (α) From Equation 5, the V d, V q, V ref, and angle (α) can be determined as follows: 1 V d Vq V V 3 V V ref = V d + V q Copyright to IJAREEIE an bn cn = tan 1 V q V d (1)

5 B. Step : Determine time duration T 1, T, T 0 In space vector PWM technique, the required space vector is synthesized by two adjacent vectors and null vector. Switching time duration at Sector 1 From Figure 7, the switching time duration can be calculated as follows: Fig.7: Reference vector as a combination of adjacent vectors at sector1 According to volt-sec balance principle, T z T 1 T 1 T T z Vref dt V1dt Vdt V0dt 0 0 T1 T 1 T Tz Vref (T1 V1 T V) cos( α) 1 cos( π / 3) Tz Vref T1 V1 T V sin ( ) 0 sin ( / 3) α π Vref sin ( / 3 ) T1 Tz. Vdc sin ( / 3) Vref T sin ( ) T Tz Where 0 α 60 s 1, Tz & Ts (13) Vdc sin ( / 3) fs T0 Tz ( T1 T ) T 1 is the time for which V 1 is applied T is the time for which V is applied T 0 is the time for which null vector is applied T s is the sampling time Similarly switching time duration at any sector can be calculated. C. Step 3: Determine the switching time of each transistor (S1 to S6) Figure 8 shows Space Vector PWM switching patterns at each sector. Fig.8: Space Vector PWM switching patterns at each sector Copyright to IJAREEIE 1951

6 Based on Figure 8, the switching time at each sector is summarized in Table, and it will be built in simulink model to implement SVPWM. Table : Switching Time Calculation at each Sector IV.BLDC MOTOR BLDC motors are used in industries such as Appliances, Automotive, Aerospace, Consumer, Medical, Industrial Automation Equipment and Instrumentation. As the name implies, BLDC motors do not use brushes for commutation; instead, they are electronically commutated. BLDC motors have many advantages over brushed DC motors and induction motors. A few of these are: Better speed versus torque characteristics High dynamic response Higher speed ranges Long operating life High efficiency Noiseless operation In addition, the ratio of torque delivered to the size of the motor is higher, making it useful in applications where space and weight are critical factors. A. Mathematical modelling of the BLDC motor BLDC motor is fed by a three phase voltage source inverter as shown in Figure9. Fig.9: Configuration of BLDC motor drive system The analysis of a BLDC motor is represented as the following equations: V a = Ri a + (L-M) di a dt + e a V b = Ri b + (L-M) di b dt + e b V c = Ri c + (L-M) di c dt + e c (14) Where V a, V b,v c are the phase voltages, i a, i b,i c are the phase currents, e a, e b,e c are the phase back- EMF waveforms, R is the phase resistance, L is the phase inductance of each phase and M is the mutual inductance between any two phases. Copyright to IJAREEIE 195

7 The electromagnetic torque is obtained as: T e = 1 ω r (e a i a +e b i b +e c i c ) (15) Where ω r is the mechanical speed of the rotor and T e is the electromagnetic torque. The equation of motion is: dω r = 1 dt j (T e - T L - B ω r ) (16) B is the damping constant, J is the moment of inertia of the drive and T L is the load torque. The electrical frequency related to the mechanical speed for a motor with P number of pole pairs: ω e = P ω r (17) The rotor angle θ r is: θ r = ω e dt (18) The instantaneous induced EMFs can be written as given in equation: e a = sin θ r K b ω m e b = sin θ r π 3 K b ω m e c = sin θ r + π K 3 b ω m (19) Where, ω m is the rotor mechanical speed and θ r is the rotor electrical position. From the above equations, BLDC motor can be modelled. V.SIMULATION OF SVPWM INVERTER FED PM BLDC MOTOR DRIVE SVPWM inverter fed PM BLDC motor drive was designed & simulated successfully using MATLAB (SIMULINK) & following results were generated. Simulation parameters are given in Table 4. Table 3: Simulation Parameters DC voltage 40 V L s H Fundamental frequency 50 Hz J kg.m Switching frequency 10 khz B 0.00N.m.s.rad -1 R s 0.7 Ω K b 0.518V/rad/sec Fig.10: Simulink model of SVPWM Inverter fed PM BLDC motor drive Fig.11: Simulink model of PM BLDC motor Copyright to IJAREEIE 1953

8 Fig.1: Reference voltage waveform of SVPWM Fig.13: Switching pulses of T 1,T 3 & T 5 in Sector 1 Fig.14: Motor Output Voltage waveforms Fig.15: Motor Current waveforms Fig.16: Sinusoidal back-emf waveforms Copyright to IJAREEIE 1954

9 VI. ADVANTAGES OF SVPWM COMPARED TO SINUSOIDAL PWM 1. Since the triplen order harmonics are appeared in the phase-to-centre voltage of SVPWM, it has higher modulation index compared to the Sinusoidal PWM. When the modulation index increases the THD of the output voltage decreases. Hence SVPWM has less amount of current and torque harmonics than those of sinusoidal PWM.. For Sinusoidal PWM (SPWM) V max = V dc / For Space Vector PWM V max = V dc / 3 Where, V dc is DC-Link voltage. From this it is clear that Space Vector PWM can produce about 15 percent higher than Sinusoidal PWM in output voltage. 3. In SPWM different phases may switch simultaneously. But in SVPWM only one phase is switch at a time. Hence SVPWM has reduced switching losses compared to SPWM. 4. The SPWM inverter can be thought of as three separate driver stages which create each phase waveform independently. But Space Vector Modulation treats the inverter as a single unit. VI.CONCLUSION Space vector Modulation Technique has become the most popular and important PWM technique for Three Phase Voltage Source Inverters for the control of AC Induction, Brushless DC, Switched Reluctance and Permanent Magnet Synchronous Motors. In this paper analysis and simulation of space vector pulse width modulation is presented. The Modulation Index is higher for SVPWM as compared to SPWM. The current and torque harmonics produced are much less in case of SVPWM. In case of SVPWM the output voltage is about 15% more as compared to SPWM. The SVPWM technique utilizes DC bus voltage more efficiently and generates less harmonic distortion in a three-phase voltage-source inverter. SVPWM is very easy to implement. There are modern digital signal processors (DSP) with dedicated pins which give a pulse width modulated waveforms using SVM. REFERENCES [1] B. K. Bose, Power Electronics and Variable Frequency Drives: 39 Technology and Applications. IEEE Press, [] Rashid, M. H., Power Electronics Handbook, Academic Press, 001. [3] Mohan, N., First Course on Power Electronics and Drives, MNPERE, 003. [4] R. Krishnan, Electric Motor Drives Modelling, Analysis and Control, Prentice Hall, 001. [5] J. Holtz, Pulse width modulation A Survey, IEEE Transactions on Industrial Electronics, Vol. 30, No.5, Dec 199, pp [6] H. W. V. D. Brocker, H. C. Skudenly and G. Stanke, Analysis and realization of a pulse width modulator based on the voltage space vectors, in Conf. Rec. IEEE-IAS Annu. Meeting, Denver, CO, 1986, pp [7] Dorin O. Neacsu, Space Vector Modulation an introduction, The 7th annual conference of the IEEE industrial electronics society. [8] Keliang Zhou, and Danwei Wang, Relationship between space vector modulation and three phase carrier- based PWM: A Comprehensive Analysis, IEEE Transactions on Industrial Electronics, vol. 49, No.1, February 00, pp [9] Yi Huang, Chunquan Li Model and system simulation of Brushless DC motor based on SVPWM control nd International Conference on Electronic & Mechanical Engineering and Information Technology (EMEIT-01) BIOGRAPHY Devisree Sasi was graduated from Government Engineering College, Idukki, Kerala, India in Electrical and Electronics Engineering in the year 010. Currently she is pursuing her M.Tech in Power Electronics in Mar Athanasius College of Engineering, Kothamangalam, Kerala, India. Jisha Kuruvilla P completed her B.Tech in Electrical and Electronics Engineering from LBS College of Engineering, Kasargode, Kerala, India in the year 001. She got her M.Tech in Power Electronics and Drives from PSG Tech., Coimbatore, Tamil Nadu, India in the year 011. Now, she is working as Assistant Professor in Mar Athanasius College of Engineering, Kothamangalam, Kerala, India. Copyright to IJAREEIE 1955

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