# Compensation of reactive energy absorbed by the transformer

Where metering is carried out at the MV side of a transformer, the reactive-energy losses in the transformer may need to be compensated (depending on the tariff)

## The nature of transformer inductive reactances

All previous references have been to shunt connected devices such as those used in normal loads, and power factor-correcting capacitor banks etc. The reason for this is that shunt connected equipment requires (by far) the largest quantities of reactive energy in power systems; however, series-connected reactances, such as the inductive reactances of power lines and the leakage reactance of transformer windings, etc., also absorb reactive energy.

Where metering is carried out at the MV side of a transformer, the reactive-energy losses in the transformer may (depending on the tariff) need to be compensated. As far as reactive-energy losses only are concerned, a transformer may be represented by the elementary diagram of **Figure** L20. All reactance values are referred to the secondary side of the transformer, where the shunt branch represents the magnetizing-current path. The magnetizing current remains practically constant (at about 1.8% of full-load current) from no load to full load, in normal circumstances, i.e. with a constant primary voltage, so that a shunt capacitor of fixed value can be installed at the MV or LV side, to compensate for the reactive energy absorbed.

## Reactive-power absorption in series-connected (leakage flux) reactance XL

The reactive power absorbed by a transformer cannot be neglected, and can amount to (about) 5% of the transformer rating when supplying its full load. Compensation can be provided by a bank of capacitors. In transformers, reactive power is absorbed by both shunt (magnetizing) and series (leakage flux) reactances. Complete compensation can be provided by a bank of shunt-connected LV capacitors

A simple illustration of this phenomenon is given by the vector diagram of **Figure** L21.

The reactive-current component through the load = I sin φ so that QL = VI sin φ.

The reactive-current component from the source = I sin φ so that QE = EI sin φ'.

It can be seen that E > V and sin φ' > sin φ.

The difference between EI sin φ' and VI sin φ gives the kvar per phase absorbed by XL.

It can be shown that this kvar value is equal to I^{2}XL (which is analogous to the I^{2}R active power (kW) losses due to the series resistance of power lines, etc.).

From the I^{2}X_{L} formula it is very simple to deduce the kvar absorbed at any load value for a given transformer, as follows:

If per-unit values are used (instead of percentage values) direct multiplication of I and X_{L} can be carried out.

### Example

A 630 kVA transformer with a short-circuit reactance voltage of 4% is fully loaded.

What is its reactive-power (kvar) loss?

X_{L} = 0.04 pu and I = 1 pu

loss = I^{2}X_{L} = 1^{2} x 0.04 = 0.04 pu kvar

where 1 pu = 630 kVA

The 3-phase kvar losses are 630 x 0.04 = 25.2 kvar (or, quite simply, 4% of 630 kVA).

At half load i.e. I = 0.5 pu the losses will be

0.5^{2} x 0.04 = 0.01 pu = 630 x 0.01 = 6.3 kvar and so on...

This example, and the vector diagram of **Figure** L21 show that:

- The power factor at the primary side of a loaded transformer is different (normally lower) than that at the secondary side (due to the absorption of vars)
- Full-load kvar losses due to leakage reactance are equal to the transformer percentage reactance (4% reactance means a kvar loss equal to 4% of the kVA rating of the transformer)
- kvar losses due to leakage reactance vary according to the current (or kVA loading) squared

To determine the total kvar losses of a transformer the constant magnetizing-current circuit losses (approx. 1.8% of the transformer kVA rating) must be added to the foregoing “series” losses. **Figure** L21 shows the no-load and full-load kvar losses for typical distribution transformers. In principle, series inductances can be compensated by fixed series capacitors (as is commonly the case for long MV transmission lines). This arrangement is operationally difficult, however, so that, at the voltage levels covered by this guide, shunt compensation is always applied.

In the case of MV metering, it is sufficient to raise the power factor to a point where the transformer plus load reactive-power consumption is below the level at which a billing charge is made. This level depends on the tariff, but often corresponds to a tan ϕ value of 0.31 (cos φ of 0.955).

Rated power (kVA) | Reactive power (kvar) to be compensated | |
---|---|---|

No load | Full load | |

100 | 2.5 | 6.1 |

160 | 3.7 | 9.6 |

250 | 5.3 | 14.7 |

315 | 6.3 | 18.4 |

400 | 7.6 | 22.9 |

500 | 9.5 | 28.7 |

630 | 11.3 | 35.7 |

800 | 20 | 54.5 |

1000 | 23.9 | 72.4 |

1250 | 27.4 | 94.5 |

1600 | 31.9 | 126 |

2000 | 37.8 | 176 |

As a matter of interest, the kvar losses in a transformer can be completely compensated by adjusting the capacitor bank to give the load a (slightly) leading power factor. In such a case, all of the kvar of the transformer is being supplied from the capacitor bank, while the input to the MV side of the transformer is at unity power factor, as shown in **Figure** L23.

In practical terms, therefore, compensation for transformer-absorbed kvar is included in the capacitors primarily intended for power factor correction of the load, either globally, partially, or in the individual mode. Unlike most other kvar-absorbing items, the transformer absorption (i.e. the part due to the leakage reactance) changes significantly with variations of load level, so that, if individual compensation is applied to the transformer, then an average level of loading will have to be assumed.

Fortunately, this kvar consumption generally forms only a relatively small part of the total reactive power of an installation, and so mismatching of compensation at times of load change is not likely to be a problem.

**Figure** L22 indicates typical kvar loss values for the magnetizing circuit (“no-load kvar” columns), as well as for the total losses at full load, for a standard range of distribution transformers supplied at 20 kV (which include the losses due to the leakage reactance).