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# Percentage Impedance of Transformer & Its Calculation

Updated: Jun 15

### What is Percentage Impedance of Transformer?

The transformer has primary and secondary winding made up of copper or aluminium. The primary and secondary winding has many number of turns. The resistance of the winding depends on the length of the wire used.

The transformer works on AC supply. When AC supply is fed to primary the flux is generated, however entire flux does not link to both winding and some mount of flux leaks. The leakage flux is denoted by leakage reactance in the transformer. Thus the transformer winding has resistance and reactance or in other words we can say transformer primary and secondary has impedance. The secondary impedance can be transferred to primary to get the equivalent impedance of the transformer.

When supply is fed to transformer, the impedance of the transformer oppose the current and voltage drop takes place in the winding. The voltage drop in the transformer has direct relationship with the impedance or percentage impedance of the transformer. The percentage impedance of the transformer is engraved in the nameplate of the transformer.

## Definition of percentage impedance of Transformer

When transformer is fully loaded up to its rated secondary current, the voltage drop takes place due to transformer winding resistance and reactance. The voltage drop is expressed in terms of rated voltage is called the percentage impedance. If primary winding rated at 6600 Volts is fully loaded, and measured voltage drop is 600 Volts, then the percentage voltage drop is 10% and, thus the transformer percentage impedance is 10%.

So we can say,the percentage impedance is the percentage voltage of the rated voltage required to circulate rated current flow through one transformer winding when other winding is short-circuited at rated tap position of the transformer.

Impedance of transformer, expressed as the percentage of rated impedance of load at full rated current, is called percentage impedance. This impedance is calculated from short circuit test data, when a small primary voltage produces full load current in secondary of transformer. This small voltage on primary side, expressed as percentage of full rated voltage, is called percentage impedance.

### Percentage Impedance Formula? ## How to Calculate Percentage Impedance of Transformer?

The percentage impedance of the transformer can be calculated by conducting the short circuit test of the transformer. The secondary winding is short circuited and voltage is applied to HV side of the transformer. Full rated voltage at HV side should not be applied at primary side, it may damage the transformer. In this case enormous short circuit current will flow in the winding and transformer may damage. The voltage at HV side must be increased gradually starting from zero volt. Increase the voltage gradually till the current in the secondary side reaches up to secondary full load rated current. Note down the primary voltage(V) at secondary current is equal to full load current of transformer. The percentage impedance of transformer is;

% Z of transformer =( V/Vr) X 100

Where, Vr = Rated voltage of primary

V = Primary voltage at which secondary current= FLC of secondary

### Solved Problem on Percentage Impedance of Transformer

A transformer of rating 132000/6600 volts transformer has a measured impedance drop of 600 volts. What is the percentage impedance of the transformer?

Z% = (Impedance Voltage drop / Rated Voltage) x 100

percentage Impedance(% Z) = (600/6600)*100 = 10 %

By measuring the current of the HV side and voltage drop across secondary side, the primary and secondary impedance can also be calculated. The current in the primary is 70 ampere is 70 ampere, the impedance of the transformer is;

Z = 600/70 = 8.57 Ω

### Can we choose the percentage impedance at design stage?

There are two types of loading considered during design stage- electrical loading and magnetic loading. If magnetic loading is increased, fewer turns are required for primary and secondary winding and as a result percentage voltage drop will decrease. However, there is limitation of magnetic loading on transformer. The CRGO core can work up to 1.9 Tesla. The designer designs the transformer at 1.7 Tesla taking 10 % margin for over fluxing. Therefore, more or less the percentage impedance of the transformer for particular rating will be as per the Indian electricity standard or other standard.

The percentage impedance can be slightly decreased by lowering the leakage flux by selecting the quality material for transformer. The percentage impedance of the transformer has significant impact on power system. When transformer is rewound, the % impedance must be as per standard because the % Z increase with smaller diameter wire of winding, impure copper etc.

Let us see, how the percentage impedance affect the power system.

### Role of Percentage Impedance in Short Circuit Calculations

The impedance of the transformer limits the fault current. The higher the percentage impedance lower will be the fault current magnitude. The fault current of the system can be expressed with following mathematical expression. A 132/6.6 KV, 30 MVA transformer has an impedance of 9 %. The fault level at secondary side of the transformer is ; Thus, the percentage impedance of the transformer has positive as well as negative effect on power system.

1. If the percentage impedance is less, the fault MVA of the network is more. All the switchgears like breakers, CTs, Isolators need to be of higher short circuit capacity and, thus cost will increase. However, positive point of lower % impedance is better voltage regulation of the system.

2. If the percentage impedance is high, the fault MVA is less. However, voltage regulation will be poor.

Therefore, optimum percentage impedance of transformer is selected to have better trade off between fault level and voltage regulation.

### Role of Percentage Impedance in Parallel Operation of Transformers

Transformers are operated in parallel to optimum utilization of the transformer. It is desired that both the transformer must share the load equally to avoid circulation of current from one transformer to other transformer. The transformer has maximum efficiency at about 40 % loading, therefore if the transformers are operated in parallel the efficiency of both transformer improves. However, for equal sharing of the load the ratio of transformer rating to percentage impedance must be equal for both the transformers.

If the ratio of transformer rating to percentage impedance is unequal, one transformer will get loaded more than other transformer and also circulating current will flow in transformer will cause addition power loss and efficiency deterioration of one transformer.

### Transformer Permissible Percentage Impedance as per Indian standards/ IEC 60076

The transformer percentage impedance for different MVA and kV rating is specified in standard. However, after manufacturing of transformer +/- 1 % deviation is allowed. For example % Z for 33 MVA,132/6.6 KV transformer is 13%, the transformer % impedance can be in the range of 13 +/- 1%. At the time of testing after manufacturing the percentage impedance of the transformer should be in the range of 12.87 % to13.13 %.

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