Development and Analysis of Pulse Width Modulation Techniques for Induction Motor Control

SVPWM (Space Vector Pulse Width Modulation) technique is type of traditional PWM method that efficiently utilizes its dc link voltage and generates high voltage pulses with low harmonic content and high modulation index. VSI (Voltage Source Inverter) with SVPWM generates adjustable voltage and frequency signals for VSDs (Variable Speed Drives). This research work presents the simplified SVPWM technique for controlling the speed and torque of induction motor. The performance of developed SVPWM technique is analyzed in terms of its switching losses and harmonic content and compared with SPWM (Sinusoidal Pulse Width Modulation). Mathematical modeling for induction motor control through two-level VSI with SVPWM and SPWM is presented. The voltage and current TDHs (Total Harmonic Distortions) of the drive with SVPWM technique are 73.23 and 63.3% respectively as compared to 101.99 and 77.89% with SPWM technique. Similarly, the switching losses with SVPWM technique are 178.79 mW and that of with SPWM are 269.45 mW. Simulink modeling and laboratory setup are developed to testify the efficacy of SVPWM and SPWM techniques. The modulation factor of SVPWM technique is 0.907 which is higher as compared to SPWM technique with 0.785 modulation factor.

Since, induction motor is inherently being supplied with constant input voltage and frequency and it generates unvarying torque at constant speed [2]. In order to adjust the torque and speed of induction motor, its input voltage and frequency should be regulated. The Converter-Inverter topology is set to produce variable voltage and frequency for VSDs.VSI is invariably being used in VSDs.
The PWM technique is used to harmonize the output of VSI. With PWM technique, the desired output waveform can be obtained by varying its switching time. With three pole-two level inverter, the output voltage is based on condition of dc link voltage at different eight states. The two-level-three pole inverter consisted of six IGBTs as shown in Fig.2

Space Vector Pulse Width Modulation
SVPWM is the modified switching technique in which three voltage phasors are transformed into two vectors in orthogonal coordinates [12][13]. For two-level inverter all the active voltage states lie along the radii of hexagon as shown in Fig.3 [12][13]. With greater sampling frequency, accurate sine wave can be obtained but it causes higher switching losses too.
The reference vector is obtained by joining the two respective supply voltage vectors to gathers. When the reference vector is located in sector 1 as shown in Fig.4, the switching time is calculated by Equations (1-2) [12][13].
Where T Z = 1/f Z and f Z is carrier frequency.
In the way, the switching timings for other remaining five sectors can be calculated by using Equations (1-2) with respective input variables.
Since the VSI is consisted of six IGBT switches arranged in pair of two in three different arms, as shown in Fig.5.
The upper switches are designated as T1, T2, and T3 while the bottom switches are T2, T4 and T6, to control the drive. The states of uppers switch determine the output voltage.

Sinusoidal Pulse Width Modulation
SPWM is one the most commonly used PWM techniques.
The SPWM is also called carrier-based PWM. It uses reference modulation signal to generate the desired output voltages. It is called SPWM because it uses sinusoidal modulating signal whose maximum value is always less than the maximum value of carrier signal [14]. The principle of SPWM is shown in Fig.7. The sinusoidal modulating signal of 50 Hz, also called reference signal is modulated by high frequency triangular carrier signal.
By comparing modulating wave with carrier wave, switching signal is generated. The pulse is generated when magnitude of modulating wave is larger than carrier wave and this switching pulse is then used to activate the switches of VSI.

Induction Motor
Three Equations (8-10) Where: V h is magnitude of harmonics voltage and V 1 is magnitude of fundamental voltage.

Switching Losses
The performance of inverter mainly depends upon its conduction and switching losses, which collectively are power losses. However, the switching losses depend upon the supply frequency, supply voltage, load current and dynamics of inverter [17]. These losses can be Equation (12)

Simulink Modeling
The Simulink models of IM (Induction Motor) controlled through VSI switched by SVPWM and SPWM are shown in Figs. 8-9 respectively. The common parameters of circuit are shown in Table1. The PI speed controller is used to set the reference values both SVPWM and SPWM.
The step load torque is applied to IM drive.

Simulink Results
The technique is shown in Fig.15. The trend of switching losses in VSI with SVPWM technique is shown in Fig.16.
The RMS value of switching losses in case of SVPWM is 178.79 mW.
The FFT analysis of output voltage and current of VSI with SPWM method is shown in Figs. 17-18. Fig.17 shows that voltage THD is 101.99%, which is huge because the reference modulating signal is generated with the help of feedback speed signal. Fig.18 shows that the current THD is 77.89%. The speed of motor reaches to 150 rpm and normalizes to 20 rpm with SPWM, due to consequent fluctuations, as shown in Fig.19. The torque of motor reaches to 200 N.m, as shown in Fig. 20. The switching signal for VSI with SPWM is shown in Fig.21. The switching loss of inverter with SPWM is shown in Fig.22 and reaches to 269.45 mW.

Practical Results
The laboratory setup for induction motor drive control is shown in Fig.23. The motor is supplied with 400 V/230 V Y/". The name plate data of motor is shown in Fig. 24.