# 2.1 Leakage Impedance

A transformer’s leakage impedance is determined empirically through a short-circuit test. Leakage impedances provided by equipment manufacturers are usually expressed in percent using the device’s rated power as the base. To convert the impedance from percent to per unit, just divide it by a hundred.

 $\mathbf{Z_{pu}}=\frac{\mathbf{Z_{\%}}}{100}$ (7)

To express the impedance in per unit on the system base rather than the transformer base

 $\mathbf{{Z\prime}_{pu}=Z_{pu}\frac{{S\prime}_{base}V_{base}}{S_{base}{V\prime}% _{base}}}$ (8)

where

Sbase is the transformer power base.

Vbase is the transformer voltage base.

$\mathbf{{S\prime}_{base}}$ is the system power base.

$\mathbf{{V\prime}_{base}}$ is the system voltage base.

When the transformer voltage base coincides with the system voltage base, this equation simplifies to

 $\mathbf{{Z\prime}_{pu}=Z_{pu}\left(\frac{{S\prime}_{base}}{S_{base}}\right)}$ (9)

The transformer’s impedance may also be expressed in ohms

 $\mathbf{Z_{\Omega}=Z_{pu}\left(\frac{V_{rated}^{2}}{S_{rated}}\right)}c$ (10)

where

Vrated is the transformer’s rated voltage. The computed impedance is referred to the transformer’s primary or secondary by the appropriate choice of Vrated.

Srated is the transformer’s power rating.

c is a constant that keeps the units straight. The value of c depends on how the transformer’s power and voltage ratings are specified. Variations in c over a wide range of unit systems are found in Table 1.

Table 1: Per Unit to Ohm Conversion Constants
Voltage Unit Power Unit Constant
Vln VA1${}_{\varphi}$ 1
Vln VA3${}_{\varphi}$ 3
Vln kVA1${}_{\varphi}$ 1/1,000
Vln kVA3${}_{\varphi}$ 3/1,000
Vll VA1${}_{\varphi}$ 1/3
Vll VA3${}_{\varphi}$ 1
Vll kVA1${}_{\varphi}$ 1/3,000
Vll kVA3${}_{\varphi}$ 1/1,000
kVln kVA1${}_{\varphi}$ 1,000
kVln kVA3${}_{\varphi}$ 3,000
kVln MVA1${}_{\varphi}$ 1
kVln MVA3${}_{\varphi}$ 3
kVll kVA1${}_{\varphi}$ 1,000/3
kVll kVA3${}_{\varphi}$ 1,000
kVll MVA1${}_{\varphi}$ 1/3
kVll MVA3${}_{\varphi}$ 1