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# Per Phase and Per Unit Representation

During the power system analysis, it is a usual practice to represent current, voltage, impedance, power, etc., of an electric power system in per unit or percentage of the base or reference value of the respective quantities.

PER PHASE AND PER UNIT REPRESENTATION

During the power system analysis, it is a usual practice to represent current, voltage, impedance, power, etc., of an electric power system in per unit or percentage of the base or reference value of the respective quantities. The numerical per unit (pu) value of any quantity is its ratio to a chosen base value of the same dimension. Thus a pu value is a normalized quantity with respect to the chosen base value.

Definition: Per Unit value of a given quantity is the ratio of the actual value in any given unit to the base value in the same unit. The percent value is 100 times the pu value. Both the pu and percentage methods are simpler than the use of actual values. Further, the main advantage in using the pu system of computations is that the result that comes out of the sum, product, quotient, etc. of two or more pu values is expressed in per unit itself.

## Per unit value.

The per unit value of any quantity is defined as the ratio of the actual value of the any quantity to the base value of the same quantity as a decimal.

## Advantages of per unit system

i.          Per unit data representation yields valuable relative magnitude information.

ii.        Circuit analysis of systems containing transformers of various transformation ratios is greatly simplified.

iii.     The p.u systems are ideal for the computerized analysis and simulation of complex power system problems.

iv.     Manufacturers usually specify the impedance values of equivalent in per unit of the equipment rating. If the any data is not available, it is easier to assume its per unit value than its numerical value.

v.        The ohmic values of impedances are refereed to secondary is different from the value as referee to primary. However, if base values are selected properly, the p.u impedance is the same on the two sides of the transformer.

vi.     The circuit laws are valid in p.u systems, and the power and voltages equations are simplified since the factors of √3 and 3 are eliminated.

In an electrical power system, the parameters of interest include the current, voltage, complex power (VA), impedance and the phase angle. Of these, the phase angle is dimensionless and the other four quantities can be described by knowing any two of them. Thus clearly, an arbitrary choice of any two base values will evidently fix the other base values.

Normally the nominal voltage of lines and equipment is known along with the complex power rating in MVA. Hence, in practice, the base values are chosen for complex power (MVA) and line voltage (KV). The chosen base MVA is the same for all the parts of the system. However, the base voltage is chosen with reference to a particular section of the system and the other base voltages (with reference to the other sections of the systems, these sections caused by the presence of the transformers) are then related to the chosen one by the turns-ratio of the connecting transformer.

If Ib is the base current in kilo amperes and Vb, the base voltage in kilo volts, then the base MVA is, Sb = (VbIb). Then the base values of current & impedance are given by

Base current (kA), Ib = MVAb/KVb

= Sb/Vb

Base impedance, Zb = (Vb/Ib) = (KVb2 / MVAb)

Hence the per unit impedance is given by Zpu = Zohms/Zb

= Zohms (MVAb/KVb2)

In 3-phase systems, KVb is the line-to-line value & MVAb is the 3-phase MVA. [1-phase MVA = (1/3) 3-phase MVA].

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Power System Analysis : Introduction : Per Phase and Per Unit Representation |