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.

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

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

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


Sbase is the transformer power base.

Vbase is the transformer voltage base.

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

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

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

𝐙𝐩𝐮=𝐙𝐩𝐮(𝐒𝐛𝐚𝐬𝐞𝐒𝐛𝐚𝐬𝐞)\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

𝐙𝛀=𝐙𝐩𝐮(𝐕𝐫𝐚𝐭𝐞𝐝𝟐𝐒𝐫𝐚𝐭𝐞𝐝)c\mathbf{Z_{\Omega}=Z_{pu}\left(\frac{V_{rated}^{2}}{S_{rated}}\right)}c (10)


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 VA1φ{}_{\varphi} 1
Vln VA3φ{}_{\varphi} 3
Vln kVA1φ{}_{\varphi} 1/1,000
Vln kVA3φ{}_{\varphi} 3/1,000
Vll VA1φ{}_{\varphi} 1/3
Vll VA3φ{}_{\varphi} 1
Vll kVA1φ{}_{\varphi} 1/3,000
Vll kVA3φ{}_{\varphi} 1/1,000
kVln kVA1φ{}_{\varphi} 1,000
kVln kVA3φ{}_{\varphi} 3,000
kVln MVA1φ{}_{\varphi} 1
kVln MVA3φ{}_{\varphi} 3
kVll kVA1φ{}_{\varphi} 1,000/3
kVll kVA3φ{}_{\varphi} 1,000
kVll MVA1φ{}_{\varphi} 1/3
kVll MVA3φ{}_{\varphi} 1