Design DC link capacitor

Looks like homework.

Clues...

1. In my experience, Xd'' << 1 p.u.. Check you copied all numbers correctly and kick examiner if you did. A value of 12.5% (% not p.u.) is believable. Machine parameters seem irrelevant if "load seen by DC link capacitor as pure resistor". Is the load current 900 Amp mean (talking DC supply) or rms (talking AC motor)? N.B. It is suggested that we got 11 kV r.m.s. electrical systems because the original designers worked it out for a logical 10 kV mean magnitude value sine wave.
   
2. Ripple 10%. Is that peak, peak to peak, mean, r.m.s. or what? Good examiners do not give ambiguous definitions, that is reserved for paying customers, ask your examiner to show you the correct solution for 10% r.ms. in revenge. Hint - assume peak to peak ripple, capacitor is charged to supply peak voltage during brief diode conduction and discharging at constant load current until voltage falls to "90% of peak" and is less than rectifier voltage output got with resistive load.
3. Google or Wikipedia "3 phase full wave rectifier". Hint - with a resistive load, the output voltage over one cycle is the tops of 6 half sine waves .
4. Sketch a voltage and current against time diagram showing capacitor voltage and rectifier output voltage with resistive load - it promotes more understanding of analysis than looking for a formula.
5. Draw the circuit diagram first. Drawing it last is "walking backwards (back first)".

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I checked my value, i have copied it correctly. I will check with my prof about 900Amps being mean or rms also regarding the ripple voltage. at the moment could you tell me what Xd" stands for?

also is this the circuit diagram for my above question??

The circuit diagram is correct, if you add the reservoir capacitor.

Note that a real system would have some resistance and inductance in the supply - a proper design would ensure that the Diode maximum 1/2 cycle current was not exceeded and that subsequent cycles were within the repetitive maximum.

A good design for industrial use would have a large margin to ensure reliability. Power supplies figure large in failure rates and turn-on is a time of maximum stress.

Three phase rectifier systems usually have an inductor before the capacitor. This cuts the current surges and smooths the DC waveform.

Rectifier-Capacitor input supplies cause brutal surges and are usually tolerable only on small equipment, roughly what can be fed from a domestic socket.

Xd" is used in models of the transient behaviour of AC electrical machines since about 100 years ago, when a French man introduced the system. X means reactance, d stands for direct rotor axis (the other is q for quadrature, at 90 degrees to d); " indicates sub-transient, ' indicates transient and nothing indicates synchronous (Xs). Each axis d and q has the three reactances, each with its own time constant.

I guess that those values apply to the machine which the DC to AC part of an electronic variable speed drive feeds.

You will find the theory in textbooks like "Electric Machinery" ISBN 0-07-021134-5.

Machines with round rotors, like induction motors and turbo-generators have d and q values very similar, but salient pole machines have distinct differences.

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One item further about your diagram. Conventionally, 3 phase supplies are given as line to line voltage, 600V for a-b, b-c, c-a in this case.

Often say, 415/240, is given, the second value is line to neutral - 3 wire systems may have no neutral or star point. So your generators would be 600/√3 volts each.

3 phase systems often work with just 3 wires, as for motors. Generators of 600V in connection would be easier to analyze.

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This is an oscilloscope trace of the (steady state) voltage and current input to the laptop with which I am writing this.

It is, of course, single phase - but it is a full wave rectifier - capacitor reservoir DC supply, about 300V,feeding a DC-DC converter.

The blue trace is mains voltage, 240V rms, red is current 10.7 mV per amp.

I have not measured the inrush current at plugging - in, but there is a mighty "splat" sound and a good blue flash. The AC mains supply is about 0.2 ohm impedance at the socket. One ohm total resistance would be a ~340 amp peak with switch on at peak mains voltage.

As I wrote, rectifier-capacitor supplies are a bit brutal.

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