Electric Power Generation, Transmission, and Distribution

Phase a:jjffSa ua¼PaþjQa andjjffVan da (21:169)

Phase b:jjffSb ub¼PbþjQb andjjffVbn db (21:170)

Phase c:jjffSc uc¼PcþjQc andjjffVcn dc (21:171)

1. Constant real and reactive power loads

ILa¼

Sa

Van

*

¼

jjSa

jjVan

ffdaua¼jjffILa aa

ILb¼

Sb

Vbn

*

¼

jjSb

jjVbn

ffdbub¼jjffILb ab

ILc¼

Sc

Vcn

*

¼

jjSc

jjVcn

ffdcuc¼jjffILc ac (21:172)

In this model the line-to-neutral voltages will change during each iteration until convergence is
achieved.

2. Constant impedance loads

The ‘‘constant load impedance’’ is first determined from the specified complex power and line-to-
neutral voltages according to the following equation:

Za¼

jjVan^2

Sa*

¼

jjVan^2

jjSa

ffua¼jjffZa ua

Zb¼

jjVbn^2

S*b

¼

jjVbn^2

jjSb

ffub¼jjffZb ub

Zc¼

jjVcn^2

Sc*

¼

jjVcn^2

jjSc

ffuc¼jjffZc uc (21:173)

The load currents as a function of the constant load impedances are given by the following equation:

ILa¼

Van

Za

¼

jjVan

jjZa

ffdaua¼jjffILa aa

ILb¼

Vbn

Zb

¼

jjVbn

jjZb

ffdbub¼jjffILb ab

ILc¼

Vcn

Zc

¼

jjVcn

jjZc

ffdcuc¼jjffILc ac (21:174)

In this model the line-to-neutral voltages will change during each iteration until convergence is
achieved.

3. Constant current loads

In this model the magnitudes of the currents are computed according to Eq. (21.172) and then held
constant while the angle of the voltage (d) changes during each iteration. In order to keep the power
factor constant, the angles of the load currents are given by

ILa¼jjffILa daua

ILb¼jjffILb dbub

ILc¼jjffILc dcuc (21:175)