Electric Power Generation, Transmission, and Distribution

The three-wire secondary is modeled by first applying the Carson’s equations and Kron reduction
method to determine the 22 phase impedance matrix:

½Š¼Zs Zs^11 Zs^12

Zs 21 Zs 22



(21:165)

The backward sweep equation becomes

½Š¼V 12 ½Šas½ŠþVL 12 ½Šbs½ŠI 12

where

½Š¼as

10

01



½Š¼bs ½ŠZs (21:166)

The forward sweep equation is:

½Š¼VL 12 ½ŠAs½ŠV 12 ½ŠBs½ŠI 12 (21:167)

where

½Š¼As ½Šas^1

½Š¼Bs ½ŠZs (21:168)

21.1.6 Load Models

Loads can be represented as being connected phase-to-phase or phase-to-neutral in a four-wire wye
systems or phase-to-phase in a three-wire delta system. The loads can be three-phase, two-phase, or
single-phase with any degree of unbalance and can be modeled as
.Constant real and reactive power (constant PQ)
.Constant current
.Constant impedance
.Any combination of the above

The load models developed in this document are used in the iterative process of a power-flow program.
All models are initially defined by a complex power per phase and either a line-to-neutral (wye load) or a
line-to-line voltage (delta load). The units of the
complex power can be in volt-amperes and volts or
per-unit volt-amperes and per-unit volts.
For both the wye and delta connected loads, the
basic requirement is to determine the load compon-
ent of the line currents coming into the loads. It is
assumed that all loads are initially specified by their
complex power (S¼PþjQ) per phase and a line-to-
neutral or line-to-line voltage.
21.1.6.1 Wye Connected Loads
Figure 21.25 shows the model of a wye connected
load.
The notation for the specified complex powers
and voltages is as follows:

+

+

+

−

− −

Van

Vcn

Sc

Sa

Sb

ILb Vbn

ILc

ILa

FIGURE 21.25 Wye connected load.