Resistance and Reactance of Power System | Electricity

Resistance and reactance (and consequently impedance) may be expressed in percentage or ohmic terms. In the case of rotating machines and transformers, manufacturer values are always in percentage terms while tables for cables and overhead lines are always in ohmic terms. Calculations can be made using either but not a mixture. For short-circuit calculations, generally the percentage values are employed and therefore their understanding is essential.

Percentage Resistance of Power System:

It is the voltage drop across the given resistance expressed as percentage of normal voltage when carrying full-load current pertaining to normal rating, i.e.,

%R = (IR/V) × 100 … (1.1)

where R is the resistance in ohms, I is the full-load current and V is the rated voltage.

Percentage Reactance of Power System:

Percentage reactance can be defined in the same way as percentage resistance. It is the voltage drop across the given reactance expressed as percentage of normal voltage when carrying full-load current pertaining to normal rating, i.e.,

%X = (IX/V) × 100 … (1.2)

where X is the reactance in ohms, I is the full-load current and V is the rated voltage. From Eq. (1.2) we have-

X = [(%X) × V] / [I × 100] ohms

Multiplying and dividing the right hand expression by V, we have-

X = [(%X) × V × V] / [V × I × 100] = [(%X) V²] / [(Output in VA) × 100] ohms … (1.3)

when the voltage and the output are expressed in kV and kVA respectively, then,

or % X = [(X)(kVA)] / [10 (kV)²] … (1.5)

Thus if actual reactance in ohms is given, percentage reactance can be determined and vice-versa.

Base kVA:

If number of equipment’s such as generators, transformers, transmission lines etc., are connected in parallel and their percentage resistances and reactances also refer to their respective kVA ratings, it is difficult to compare these percentage resistances and reactances and their combined effect until and unless they are all referred to a common kVA. This common kVA which is taken as an arbitrary one is known as the base kVA of the system.

A base kVA may be chosen in the following manner:

(i) Equal to the kVA rating of the largest unit connected in the network.

(ii) Equal to the sum of the kVA ratings of all the units connected in the network.

(iii) Any arbitrary value.

It must, however, be clearly understood that the value of the base kVA, has no bearing whatsoever on the results; since in the ultimate formula for the calculation of short-circuit current base MVA is to be taken into consideration.

The conversion of percentage reactance at rated kVA to the percentage reactance at base kVA can be made by using the following expression:

Percentage reactance at base kVA = (Base kVA/Rated kVA) × percentage reactance at rated kVA … (1.6)

Thus if a transformer is rated for 10,000 kVA and has percentage reactance of 7.5 %, then the percentage reactance at the base kVA of 25,000 shall be,

= (25,000/10,000) × 7.5% = 18.75%

Base kV:

In some cases it is convenient to work in ohmic values of the various reactances rather than in percentage values. The method would become simple if all the reactances relate to the same voltage but if step-up or step-down transformers or other equipment operating at different voltages are also included, all the ohmic values will have to be reduced to a common base voltage.

Reactances can be converted from one operating voltage to the other by the following relation:

X₂ = [(E₂/E₁)]² × X₁ … (1.7)

where X₁ is the reactance at voltage E₁ and X₂ is the reactance at voltage E₂.

It must, however, be remembered clearly that all the values discussed above i.e., resistances, reactances and voltages refer to the phase values and not to the line values.