# Space Vector Modulation

**Topics:**Electric motor, Brushless DC electric motor, Vector space

**Pages:**5 (1441 words)

**Published:**March 16, 2010

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I.INTRODUCTION

*II.*BASIC CONCEPT OF SVPWM

Space Vector Modulation treats the two level inverter of fig.1 as a single unit which can be driven to eight unique states that each state creates a corresponding voltage vector. An electric-motor control system, comprising: *a two level voltage source inverter.

III.*IMPLE*MENTATION OF SPACE VECTOR PWM

For the three phase two-level PWM inverter as shown in Fig.1, the switch function is denoted by (1) ,shown below. where x=R,Y,B;"1"denotes Vdc/2 at the inverter output (a,b,c)with reference to point neutral;"0"denotes –Vdc/2;O is the neutral point of the dc bus. {draw:frame}

Fig. 1. Three phase two level inverter

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Fig.2 eight switching states

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Fig. 3 Voltage vector space.

In the vector space, according to the equivalence principle the following conditions are obtained. The following steps are carried out to implement SVPWM

Step.1 Determine the possible switching vectors in the output voltage space. Step.3 Calculate the time variables

Step.4 switching time calculation to each sector

There are eight possible switching states for the inverter at any instant of time. The eight states of the inverter and the corresponding space- phasors of the output voltages are shown in fig 2 and 3 respectively. It can be observed that at any instant of time there are only eight possible positions for the voltage space phasor. *2. DEFINING V*REF

VRN=13 (VRY-VBR)=13 (2VRO-VYO-VBO)

VYN=13 (VYB-VRY)=13 (2VYO-VBO-VRO)

VBN=13 (VBR-VYB)=13 (2VBO-VRO-VYO) (3)

Given a set of inverter pole voltages (VRO, VYO, VBO) the vector components (Vα, Vβ) in this frame are found by the forward Clarke transform Equation 4 denotes the magnitude of the reference vector

The phase angle can be evaluated by

The continuously moving reference vector VREF is sampled at a sampling frequency f s. During this interval Is =1fs between samples the reference vector VREF is assumed to be constant. 3. CALCULATION OF TIME VARIABLES

Now consider VREF is situated in sector 1 as shown in fig 4. The angle Φ represents the position of the references vector each respect to the beginning of the sector Assume that the sampling period IS is divided into the three sub-intervals T1, T2 and T0. The inverter is turned ON to produce the vector V1 for T1 seconds. V2 for T2 seconds. And zero (i.e. either V7orV8) for T0 seconds. From fig.4

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Fig.4 Sampled Reference Vector Located in Sector 1

Where

│VS*│is the amplitude of the reference vector.

From equation (5)

It is important to note that each sector has different pattern and also different value of ta, tb and to as the value of phase (or) angle differs from time to time. {draw:frame} Fig.5 Output signal based on Symmetrical Sequence algorithm in sector 1 Fig.6 shows the reason for some distortion in the phase voltage in addition that the ideal maximum realizable modulation index for low distortion phase voltages is described by a circle of radius Tp –T min.The maximum achievable modulation index is thus 4/3(1-Tmin/Tp).Where Tp is the PWM period. {draw:frame}

Fig.6 A space vector diagram showing aspects of the operation of the system. The space vectors are calculated using standard space vector modulation technique and we obtained corresponding results as follows: The alpha and beta voltage are calculated and normalized with respect to half of the DC link voltage. The SVM sector that the voltage demand vector lies in is determined mathematically. The nominal duration, Ta, Tb, of the two non-zero SVM adjacent to that sector are calculated to produce a compound vector equal to the demanded voltage vector to control the speed of the BLDC motor. *IV.IMPLEMENTATION *OF SVPWM BASED INVERTER FOR BLDC MOTOR. The following circuit and a method for controlling the rotating speed of the brushless direct...

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