Power Electronics Design: A Practitioner's Guide

Appendix A: Converter Equations


Figure A.1: Single line diagram.

A.1 Definitions

?

Phaseback angle delay of conduction angle from earliest possible point

u

Commutation or overlap angle duration of current transfer between phases and width of commutation notch in voltage

Xpu

Source reactance per unit short circuit reactance on converter rating base

k

Ratio of reactance on line side of PCC to total reactance; k = X1/( X1 + X2)

Erms

RMS AC line-to-line voltage

Edo

Open-circuit DC output voltage of converter with no phase- back ( ? = 0)

Ed

DC output voltage under rated load

cos(?)

Displacement power factor cosine of angle between fundamental line-to-neutral voltage and fundamental current

Irms

RMS AC line current

Id

DC load current

Ipu

Per unit AC or DC load current

Ihpu

Per unit harmonic line current at harmonic, h

THDv

Voltage total harmonic distortion at PCC

Ifpu

Per unit peak asymmetric fault current

PCC

Point of common coupling between utility and customer usually the metering point

A.2 Equations at Full Load [1]

  1. Edo = 1.35 Erms

  2. Ed = Edo[cos( ?) Xpu/2)]

  3. Ed = Edo(1 Xpu/2) ( ? = 0)

  4. Edpu = cos( ?) Xpu/2

  5. Edpu = 1 Xpu/2 ( ? = 0)

  6. cos( ? + u) = cos( ?) Xpu

  7. cos( u) = 1 Xpu

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