Stevenson J. Power system analysis

30 CHAER I BASIC CONCES

The reader should note that this equation has nothing to do with transferring

the ohmic value of impedance from one side of a transformer to another. The

application of the equation is in changing the value of the per-unit impedance

of any component given on a particular base to a new base.

Rather than using Eq. (1.56) directly, the change in base may also be

accomplished by rst converting the per-unit value on the given base to ohms

and then dividing by the new base impedance.

Example 1.5. The reactance of a generator designated X" is gi\ en as 0.25 per unit

based on the generator's nameplate rating of 18 kY, 500 MVA. The base for

calculations is 20 kY, 100 MY A. Finu X" on the new base.

Solution. By Eq. (1.56)

( 18 )



( 100 )

X" = 0.25

500

0.0405 per unit

or by converting the given va l ue to ohms and dividing by the new base impedance,

I _

0.25( 182/500)

0.0405 per unit

202/100

Resistance and reactance of a device in percent or per unit are usually

available from the manufacturer. The impedance base is understood to be

derived from the rated kilovoltamperes and kilovolts of the device. Tables

A.1

and A.2 in the Appendix list some representative values of reactance for

transformers and generators. Per-unit quantities are further discussed in Chap.

2 associated with the study of transformers.

1.12 NODE EQUATIONS

The

junctions formed when two or more circuit elements (R, L, or C, or an

ideal source of voltage or current) are connected to each other at their

terminals are called nodes. Systematic formulation of equations determined at

nodes of a circuit by applying Kirchho's current law is the basis of some

excellent computer solutions of power system problems.

In order to examine some features of node euations, we begin with the

simple

circuit diagram of Fig. 1.23, which shows node numbers within circles.

Current sources are connected at nodes @ and @ and all other elements are

represented as admittances. Single-subscript notation is used to designate the

voltage of each node with respect to the reference node @' Applying Kirch