# V/F Speed Control of 3 phase Induction Motor using Space Vector Modulation

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2 Space vector representation of the three-phase inverter output voltages is introduced next. Space vector is defined as Vs= (2/3) (V a + a V b + a 2 V c ) (1) Where, A=exp (j 2π/3) Fig.1.Voltage-frequency under constant V/f principle. III.THREE-PHASE VOLTAGE SOURCE INVERTER AND SPACE VECTORS. A mathematical model of three-phase is presented here based on space vector representation. The power circuit topology of a three-phase VSI is shown in Fig.2. Each switch in the inverter leg is composed of two back-toback connected semiconductor devices. One of these two is a controllable device and other one is a diode for protection. Leg voltage waveforms is shown in Figure 3 for 180 conduction mode. The space vector is a simultaneous representation of all the three-phase quantities. It is a complex variable and is function of time in contrast to the phasors. Phase-to-neutral voltages of a star-connected load are most easily found by defining a voltage difference between the star point n of the load and the negative rail of the dc bus N. The following correlation then holds true, V A= V a +V nn V B= V b +V nn (2) V C= V c +V nn Since the phase voltages in a start connected load sum to zero, summation of equation (2) yields V nn =(1/3)( V A +V B + V C ) (3) Substitution of (3) into (2) yields phase-to-neutral voltages of the load in the following form: V a= (2/3) V A -(1/3)( V B + V C ) V b= (2/3) V B -(1/3)( V A + V C ) V c= (2/3) V C -(1/3)( V B + V A ) Fig.2.Power circuit of a three-phase Voltage Source Inverter. Phase voltages are summarized in Table 1 and their corresponding space vectors are listed in Table2. Fig.3.Leg voltage waveform of a three- phase VSI for 180 conduction. It is observed from Fig.3 that one inverter leg s state changes after an interval of 60 and their state remains constant for 60 interval. Thus it follows that the leg voltages will have six distinct and discrete values in one cycle (360 ). State &0 Table:1 Phase voltage values for different switching state Switch V ON A V B V C 1,4,6 (2/3)Vdc -(1/3) Vdc -(1/3) Vdc 1,3,6 (1/3) Vdc (1/3) Vdc -(2/3)Vdc 2,3,6 -(1/3) Vdc (2/3)Vdc -(1/3) Vdc 2,3,5 -(2/3)Vdc (1/3) Vdc (1/3) Vdc 2,4,5 -(1/3) Vdc -(1/3) Vdc (2/3)Vdc 1,4,5 (1/3) Vdc -(2/3)Vdc (1/3) Vdc 1,3,5 & 2,4,

3 And we have space vectors corresponding to above Phase voltages are as follows. State Table 2 Phase voltage space vectors. Phase voltage space vectors 1 (2/3)Vdc 2 (2/3)Vdc exp (j π/3) 3 (2/3)Vdc exp (j 2π/3) It is seen in the previous section that a three-phase VSI generates eight switching states which include six active and two zero states. These vectors form a hexagon in Fig.4which can be seen as consisting of six sectors spanning 60 each. The reference vector which represents three-phase sinusoidal voltage is generated using SVPWM by switching between two nearest active vectors and zero vectors. To calculate the time of application of different vectors, consider fig.5, depicting the position of different available space vectors and the reference vector in the first sector. 4 (2/3)Vdc exp (j π) 5 (2/3)Vdc exp (j 4π/3) 6 (2/3)Vdc exp (j 5π/3) 7 & 0 0 The discrete phase voltage space vector positions are shown in Fig.4 Fig.5. Principle of space vector time calculation. The time of application of active space voltage vectors is found from fig.5 as follows. t a = V s sin π 3 α V a sin 2π 3 t b = V s sin α V b sin 2π 3 Fig.4. Phase voltage space vectors. Where, t 0 = t s t a t b V a = V b = 2 3 V dc The binary numbers on the figure indicate the switch state of inverter legs. Here 1 implies upper switch being on and 0 refers to the lower switch of the leg being on. The most significant bit is for leg A, the least significant bit is related to leg C and the middle is for leg B.. IV.CONCEPT OF SPACE VECTOR PWM This section briefly discusses the space vector PWM principle. This PWM method is frequently used in vector controlled and direct torque controlled drives. In vector controlled drive this technique is used for reference voltage generation when current control is exercised in rotating reference frame. In order to obtain fixed switching frequency and optimum harmonic performance from SVPWM, each leg should change its sate only once in one switching period. This is achieved by applying zero state vector followed by two adjacent active state vector in half switching period. The next half of the switching period is the mirror image of the first half. The total switching period is divided into 7 parts, the zero vector is applied for 1/4 th of the total zero vector time first followed by the application of active vectors for half of their application time and then again zero vector is applied for 1/4 th of the zero vector time. This is then repeated in the next half of the switching period. This is how symmetrical SVPWM is obtained. The leg voltage in one switching period is depicted in fig.6 for sector I.[6]. 737

4 Fig.6.Leg voltages and space vector disposition for one switching period in sector I. The sinusoidal reference space vector form a circular trajectory inside the hexagon. The largest output voltage magnitude that can be achieved using SVPWM is the radius of the largest circle that can be inscribed within the hexagon. This circle is tangential to the mid points of the lines joining the ends of the active space vector. Thus the maximum obtainable fundamental output voltage is V s = 2 3 V dc cos π 6 = 1 3 V dc V. D-Q TRANSFORMATION. The space vector concept, which is derived from the rotating field of induction motor, is used for modulating the inverter output voltage. In this modulation technique the three phase quantities can be transformed to their equivalent two-phase quantity either in synchronously rotating frame (or) stationary frame. From these two-phase components, the reference vector magnitude can be found and used for modulating the inverter output. The process of obtaining the rotating space vector is explained in the following section, considering the stationary reference frame. Considering the stationary reference frame let the three-phase sinusoidal voltage component be, Va = VmSinωt Vb = VmSin(ωt-2π/3) Vc = VmSin(ωt-4π/3) When this three-phase voltage is applied to the AC machine it produces a rotating flux in the air gap of the AC machine. This rotating resultant flux can be represented as single rotating voltage vector. The magnitude and angle of the rotating vector can be found by means of Clark s Transformation as explained below in the stationary reference frame. To implement the space vector PWM, the voltage the stationary d-q reference frame that consists of the horizontal (d) and vertical (q) axes as depicted in figure 7. From this figure, the relation between these two reference frames is f dq0 =K s f abc Fig.7.The relationship of abc reference frame and stationary d-q frame. K s = f dq 0 = f d f q f 0 T. f abc K s = f a f b f c T Where, f denotes either a voltage or a current variable. As described in Fig.7 this transformation is equivalent to an orthogonal projection of [a b c]t onto the twodimensional perpendicular to the vector [1 1 1]t (the equivalent d-q plane) in a three-dimensional coordinate system. As a result, six non-zero vectors and two zero vectors are possible. Six non-zero vectors (V1-V6) shape the axes of a hexagonal as depicted in Fig.8, and supplies power to the load. The angle between any adjacent two non-zero vectors is 60 degrees. Meanwhile, two zero vectors (V0 and V7) and 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, 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 SVPWM technique is to approximate the reference voltage vector Vref using the eight switching patterns. One simple method of approximation is to generate the average output of the inverter in a small period T to be the same as that of Vref in the same period 738

5 Switching States: Table 3: Switching patterns and output vectors. Voltage Switching Sectors Line to neutral voltage Line to line voltage A B C Van Vbn Vcn Vab Vbc Vo V V /3-1/3-1/ V /3 1/3-2/ V /3 2/3-1/ Fig.8 Basic switching, vectors and sectors. V /3 1/3 1/ V /3 1/3 2/ V /3-2/3 1/ V For 180 mode of operation, there exist six switching states and additionally two more states, which make all three switches of either upper arms or lower arms ON. To code these eight states in binary (one-zero representation), it is required to have three bits (23 = 8). And also, as always upper and lower switches are commutated in complementary fashion, it is enough to represent the status of either upper or lower arm switches. In the following discussion, status of the upper bridge switches will be represented and the lower switches will it s complementary. Let "1" denote the switch is ON and "0" denote the switch in OFF. Table3 gives the details of different phase and line voltages for the eight states.[5] VI. MATLAB/SIMULINK MODEL In proposed work, i.e., the V/f control of three phase induction motor using space vector modulation is done by MATLAB R2010A. The DC voltage source is directly connected to inverter. The inverter is consist of cascade connected inverters i.e. 2 level inverter, which feeds three phase induction motor. An open loop speed control based on constant V/f ratio technique is tried for a 15: 5.4 HP (4KW) 400 V 50Hz 1430 RPM asynchronous machine. 739

6 Fig.9.SIMULINK Model Fig.10.Space Vector Modulation based pulse generating block 740

7 Fig.11.Three phase inverter block VII. SIMULATION RESULT Simulation of the proposed system, the space vector modulation technique is used to control the two level three phase inverter. An open loop speed control based on constant V/f ratio technique is tried for a 5.4HP, 400V, 50 Hz asynchronous machine. The torque applied to asynchronous machine is 2.5 and the speed was found to be settling from the initial value to the final value. The results are shown below. 741

8 Fig.12.Inverter output voltage V a,v b,v c Fig.13.Speed and Torque VIII. CONCLUSION This simulation work deals with V/f control of three phase induction motor through two level inverter using space vector modulation technique. The SVPWM techniques offers better harmonic reduction, fast switching frequency and better utilization of DC link. IX. REFERENCES (1) R. Linga Swamy and P. Satish Kumar, Speed Control of Space Vector Modulated Inverter Driven Induction Motor Proceedings of the International MultiConference of Engineers and Computer Scientists 2008 Vol IIIMECS 2008 March, pp (2) M Kubeitari, Space Vector PWM Simulation for Three Phase DC/AC inverter,world Academy of Science, Engineering and Technology ,pp (3) Shilpa V. Kailaswar and Prof. R.A.Keswani, Speed Control of Three Phase Induction Motor by V/f Method for Batching Motion System International Journal of Engineering Research and Fig.14.Stator Voltages Vd,Vq Applications (IJERA) ISSN: Vol. 3, Issue 2, March -April 2013, pp (4) El-Nobi A. Ibrahim1 Mohamed Elbesealy, V/F control of Three Phase Induction Motor Drive with Different PWM Techniques,Innovative Systems Design and Engineering,ISSN (Paper) ISSN (Online), March 2013Vol.4, No.14.pp (5) K. Vinoth Kumar, Prawin Angel Michael, Joseph P. John and Dr. S. Suresh Kumar, Simulation and comparison of spwm and svpwm control for three phase inverter ISSN , ARPN Journal of Engineering and Applied Sciences,Vol. 5, No. 7, July 2010 (6) Atif Iqbal,Adoum Lamine, Imtiaz Ashraf, Mohibullah, Matlab/Simulink Model Of Space Vector Pwm For Three-Phase Voltage Source Inverter. 742

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