# Correlation b/w output voltage frequency and angle theta for Conventional Space Vector PWM 3-Phase inverter drive

Im writing code for SP-PWM for a 3 phase voltage source inverter but since im a bit naive to the topic I need some clarifications regarding some questions I have. Lets cut to the point. For 3-phase system, we can transform the 3 phase quantities it to a d-q frame via following transformation matrix. Where Van,Vbn,Vcn are phase voltages for WYE connected load at Va-Vb-Vb lines of inverter legs as shown below. Now, we need to rotate the voltage vector Vref in d-q frame. I can compute the magnitude of Vref and time required by each mosfet to change its state. But there is some nomenclature im not familiar with, such as switching freqency term, given by Tz = 1/fz. We need switching freqency, lets say 900HZ, which will give us 1.11ms Tz, using this assumption we can compute T1,T2 and To. My Questions:

Q) How does varying angle of Vref in d-p frame(lets say we increment angle by 10 degree in each sector) will affect my output voltage frequency ?

Q) How does varying switching freqency(please also define switching freqency in terms of this SVPWM) affects the voltage output freqency of the inverter ? Is there any relation b/w them ?

Q) What can I do produce a variable output voltage freqency ? (i.e how parameters will be varying in such case ? )

I reordered your questions because understanding which frequency is being referred too is important for understanding the other questions.

Q) How does varying switching frequency(please also define switching frequency in terms of this SVPWM) affects the voltage output frequency of the inverter ? Is there any relation b/w them ?

The SVPWM calculations are referring to the carrier frequency aka switching frequency of the inverter. The image below shows in black the carrier frequency the Inverter will produce. The effective sinusoidal signal the Inverter is approximating is shown in red. For AC motor control the SVPWM calculation is only a part of a larger control algorithm. The output frequency (Red line in the pic) is calculated by some other means depending on the control scheme used (V/Hz or Field Oriented Control). The control algorithm will command a Vd and Vq and the SVPWM calculations are used to calculate the needed switching pattern to produce the commanded Vd and Vq.

Q) How does varying angle of Vref in d-p frame(lets say we increment angle by 10 degree in each sector) will affect my output voltage frequency ?

Varying the angle of the applied voltage does not change the inverter's pwm frequency. What will change is the duty cycle of each state. From your diagram if the angle is increased 10 degrees toward V2 than the amount of time the inverter is switched in the V2 state will increase while the time in V1 will decrease. The average time between the two switch states will correspond to the angle between them. The amplitude of Vreff is varied by adjusting the amount of time the inverter is in V1 or V2 and a null state. The time the inverter is in the V1, V2 or null state will sum up to the switching period Tz.

Q) What can I do produce a variable output voltage frequency ? (i.e how parameters will be varying in such case ? )

The output frequency is typically determined through a simple open loop V/Hz control scheme, or some variation of closed loop Field Oriented Control. This video is helpful for understanding SVPWM You can see in the video that SVPWM is one part of a much larger control scheme. The video is a part of a series of videos of Dave Wilson's training on motor control. I can't recommend it enough for understanding how motor control is done by most modern Inverters.