THE PER UNIT SYSTEM

In many engineering situations it is useful to scale, or normalize, dimensioned quantities. This is commonly done in power system analysis. The standard method used is referred to as the per-unit system. Historically, this was done to simplify numerical calculations that were made by hand. Although this advantage is eliminated by the calculator, other advantages remain.

• Device parameters tend to fall into a relatively narrow range, making erroneous values conspicuous.

• Using this method all quantities are expressed as ratios of some base value or values.

• The per-unit equivalent impedance of any transformer is the same when referred to either the primary or the secondary side.

• The per-unit impedance of a transformer in a three-phase system is the same regardless of the type of winding connections (wye-delta, delta-wye, wye-wye, or delta-delta).

• The per-unit method is independent of voltage changes and phase shifts through transformers where the base voltages in the winding are proportional to the number of turns in the windings.

• Manufactures usually specify the impedance of equipment in per-unit or percent on the base of its nameplate rating of power (usually kVA) and voltage (V or kV). The per-unit system is simply a scaling method. The basic per-unit scaling equation is

Per Unit = Actual Value/ Base Value

The base value always has the same units as the actual value, forcing the per-unit value to be dimensionless. The base value is always a real number, whereas the actual value may be complex. The subscript pu will indicate a per-unit value. The subscript base will indicate a base value, and no subscript will indicate an actual value such as Amperes, Ohms, or Volts.

Per-unit quantities are similar to percent quantities. The ratio in percent is 100 times the ratio in per-unit. For example, a voltage of 70kV on a base of 100kV would be 70% of the base voltage. This is
equal to 100 times the per unit value of 0.7 derived above.

APPLICATION OF PER-UNIT SYSTEM

Appling this to relay settings, a practical example can be shown in calculation of the settings for a relay on a transmission line. For distance relays a common setting for zone 1 is 85% of the line impedance. Zone 2 should be set not less than 125% of the line, with care to not over reach the zone 1 of the next line section. If this does then zone 2 will need to be coordinated with the next line section zone 2.

Comments

Anurag Segekar said…

explain the per unit system for DC quantities.

Wednesday, 16 May, 2018

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