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## Homework Statement

Hi there. I was just wondering if anyone can conform that my method for this problem is correct so far?

The transistor-bridge converter shown below is being used to connect a PV array to the grid.

For the purpose of this coursework, you may assume that:

• The PV array behaves as an ideal DC voltage source.

• The grid is an ideal sinusoidal voltage source at 50 Hz.

• The components are ideal and lossless.

• Bipolar switching is used.

The DC voltage (Vdc) is 458 V.

The inverter switches at 1800 Hz and its output inductor is 4 mH.

The modulation index is 0.59 at angle of 15 degrees relative to the grid voltage.

The AC grid voltage is 217 V.

Question - Calculate Vi (Magnitude and angle)

## The Attempt at a Solution

The modulation index is defined as: Mi = Vi peak (of the fundamental component) / Vdc

Therefore; Vi = Mi x Vdc

Vi = 0.59 x 458

Vi = 270.22V

However this is a peak voltage. Hence the rms voltage is; 270.22/sqrt(2)

So Vi = 191.074 V (rms)

Since it is at an angle of 15 degrees to the grid voltage, use the sine rule to obtain the total length of the Vi phasor.

Vi / sin(90) = 191.074 / sin(75)

Vi = 197.814V

So we'll say Vi = 198V at an angle of 15 degrees to the grid voltage.

Is that correct??

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