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Thursday, 15 January 2015

Per Unit Representation in Power System Studies

In a large interconnected power system, the various sections of the system are connected through transformers and have different voltage levels. In the computation of power system problems it is more convenient to express impedance, current, voltage and power in terms of per-unit (p.u.) value rather than in ohms, amperes, volts, and watts.

"The per-unit value of any quantity is defined as the ratio of its actual value to another arbitrarily chosen value of the quantity of the same dimension." 

This arbitrarily chosen value is called the base or reference value. Hence p.u. values are dimensionless.

Voltage, current, apparent power and impedance are so related that the selection of base values for any two of them determines the base values for the remaining two. 
Usually base power in kVA or MVA and base voltage in kV are the quantities selected to specify the base. 

For example; if a base voltage of 10 kV is selected, voltages of 8, 10 and 11 kV would be specified as 0.8, 1.0, and 1.1 p.u. respectively.

Advantages of p.u. system:

Some of the advantages of p.u. system are:

1.      The current, impedance, losses etc. vary considerably with the variation of terminal voltage, power rating etc., whereas the p.u. values of machines of the same type and widely different rating usually lie within a narrow range.
2.      The p.u. impedance referred to either side of a transformer, whether 1-phase or 3-phase, is the same when expressed on the proper base. For a 3-phase transformer the p.u. impedance for both the sides is the same regardless of the 3-phase connection i.e. delta or star.
3.      The computational effort required is very much reduced with the use of p.u. representation.  

Selection of Base values:

The selection of base values of apparent power and voltage is made in order to reduce the work required in computation. Normally the p.u. values of various equipments are given in terms of their own voltage and kVA rating. 

In a large power system, the various sections of the system having different equipments are connected through transformers and have different voltage and capacity levels. It is necessary to refer all the per unit values to a selected base value. At first a convenient value of MVA is selected as the base value and the same value is used as base MVA in all the sections of the power system. The base MVA so selected may be the total MVA of the system, the largest MVA of a section or any round figure as 100, 500 MVA etc. 

After the selection of base MVA, the base voltages for each section are to be selected. The rated voltage of the largest section may be taken as the base voltage of that section. The base voltages for remaining sections are then assigned according to the transformation ratio of the transformers. When a common base MVA and base voltages of different sections are made, the p.u. impedance of various sections can be calculated to draw the single-line diagram.

The base selected should be one that gives p.u.values of rated voltage and current approximately equal to one in order to simplify the calculations. Time required will be less if the base values is so selected that few p.u. quantities already given need not to be converted to a new base. 

Normally the p.u. impedance of various equipments of a power system is given corresponding to their own voltage and kVA rating. Since all impedance in any one part of a system must be expressed on the same impedance base when doing calculations, therefore it is desired to convert p.u. quantities from one base to another. It is possible to change the base of p.u. quantities with the help of a very simple formula.