Calculating Generator Field, Motor Torque & Inverter Voltages

[VinnyCee]

Homework Statement

[PLAIN]http://img843.imageshack.us/img843/4753/examproblem1ece320.jpg

A Y-connected synchronous generator with a wound field is used to provide pure sinusoidal voltage of 240V, 50Hz, to a variable electrical load. The generator is powered from an induction motor, fed fropm a DC source of 600V through a PWM inverter.

Induction motor ratings: 4 poles, Y connected, 240V, 60Hz, $$L_{ls}\,=\,L_{{lr}\,=\,3.2\,mH$$, $$L_m\,=\,40\,mH$$, $$R_S\,=\,0.15\,\Omega$$, $$R_r\,=\,0.3\,\Omega$$.

Synchronous generator ratings: Y connected, 4 poles, 240V line to line, $$X_m\,=\,19\,\Omega$$, $k\,=\,\frac{I_F}{i_f}\,=\,2.1\,Vs$.

For load of the generator, P=3kW at p.f. = 0.85 lagging. Calculate the following:

1) The field of the generator.

2) The torque of the induction machine.

3) The voltage of the induction machine.

4) The current on the DC side of the inverter.

Homework Equations

$$\left(V_L\right)_{avg}\,=\,(2D\,-\,1)\,V_0$$

The Attempt at a Solution

I've no idea how to even start this problem! It's supposed to be an exam question, but I can't even start it using all notes and the text! Been thinking about it for about 12 hours now, I'm certainly stuck:(

The duty cycle (D) is not given so I can't even get what voltage the PWM inverter outputs.

 

[KataKoniK]

Hello,

Thank you for posting this question. I understand that this problem may seem daunting, but I will try my best to guide you through it. First, let's start by breaking down the problem into smaller parts and identifying what information we have and what we need to find.

Information given:

- Y-connected synchronous generator with wound field
- Output voltage: 240V, 50Hz
- Powered by an induction motor
- Induction motor ratings: 4 poles, Y connected, 240V, 60Hz, L_{ls}\,=\,L_{{lr}\,=\,3.2\,mH, L_m\,=\,40\,mH, R_S\,=\,0.15\,\Omega, R_r\,=\,0.3\,\Omega
- Synchronous generator ratings: Y connected, 4 poles, 240V line to line, X_m\,=\,19\,\Omega, k\,=\,\frac{I_F}{i_f}\,=\,2.1\,Vs
- Load: 3kW, p.f. = 0.85 lagging

What we need to find:

1. Field of the generator
2. Torque of the induction machine
3. Voltage of the induction machine
4. Current on the DC side of the inverter

Now, let's start by looking at the synchronous generator. We can use the equation V_L = (2D - 1) V_0 to find the output voltage of the PWM inverter. However, as you mentioned, the duty cycle (D) is not given. In this case, we can assume a duty cycle of 0.5 (50%) and proceed with the calculations. Later on, if we find that our calculations are not accurate enough, we can go back and adjust our assumption.

1. Field of the generator:

To find the field of the generator, we can use the equation V_L = (2D - 1) V_0. Substituting the values given, we get:

240V = (2 x 0.5 - 1) V_0
V_0 = 480V

Now, we can use the synchronous generator ratings to find the field current (I_F). We know that k = I_F/i_f, so we can rearrange the equation to find I_F.