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PUSystem - ECSE 486 Power Laboratory The Per-Unit System 1...

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ECSE 486 Power Laboratory The Per-Unit System 1 Introduction and Motivation Power system quantities like power, voltage, current, and impedance are often given in per unit or percent of specified base values. For instance, if a base voltage of 735 kV is specified then the voltage 765 kV is 765 / 735 = 1 . 04 per unit or 104%. Advantages of the per-unit system are many. First, by specifying appropriate base quantities, the transformer equivalent circuit can be simplified by eliminating the ideal transformer winding. As a result, voltages, currents, external impedances and admittances expressed in per-unit do not change when referred either to the primary or the secondary winding. This is a significant advantage when analyzing power systems of even moderate size, where hundreds of transformers can be found. The per-unit system avoids us the possibility of making many serious calculation errors when referring from one transformer side to the other. Another advantage of the per-unit system is that the per-unit impedances of electrical equipment of similar type usually lie within a narrow numerical range when the equipment ratings are used as base values. Thus, per-unit impedance data can be checked rapidly for gross errors by someone familiar with the per-unit quantities. Moreover, manufacturers normally specify the impedances of machines and transformers in per-unit or percent of nameplate rating. Per-unit quantities are calculated as: Per-unit quantity = Actual quantity Base value of quantity , (1) where the actual quantity is the value of the quantity in the actual (SI) units. The base value has the same units as the actual quantity, therefore making the per-unit quantity dimensionless. In addition, the base value is always a real number. Thus, the angle of the per-unit quantity is identical to the angle of the actual quantity. 2 Per-Unit System for Single-Phase Circuits Two independent base values can be arbitrarily selected at one point of a power system. Usually for single-phase systems the base voltage, E base , and the base single-phase complex power, S base , is selected. Then, in order for electrical laws to be valid in the per-unit system, the next relationships must be used for other base values: P base = Q base = S base , (2) I base = S base E base , (3) Z base = R base = X base = E base I base = E 2 base S base , (4) Y base = G base = B base = 1 Z base . (5) By convention, we adopt the following two rules for base quantities: 1. The value of S base is the same for the entire power system being studied.
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