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A NUMBER OF METHODS have been described for developing a set of loss constants for a power system network with which the total or incremental losses can be calculated by matrix multiplications. These values then may be applied to the dispatching of power systems through comparisons of incremental fuel costs and incremental transmission losses. A new approach determines the per unit incremental loss incurred by increasing the generation at one plant by a small amount and reducing the generation at another plant by the amount required to maintain con stant loads. This per unit incremental loss then is com pared with the ratio of the incremental fuel costs of the two plants, complete co-ordination being provided by the economic balancing of pairs of plants. The two basic assumptions are in harmony with practicable power system operation. They are 1. When small amounts of power are exchanged between generating plants of a power system, the mag nitudes of the bus voltages of these plants are unchanged. 2. Multiple transmission paths between any two gen erating plants may be represented by a single impedance, commonly known as the transfer impedance. From these assumptions, equations have been developed showing that the incremental loss incurred by increasing generation of a plant by a small amount and decreasing another by an appropriate amount to maintain constant loads is = (2 tan θι-2)/{Κ + tan ^1-2)where ^1-2 is the angle by which the voltage at plant 1 leads that of plant 2, and Κ is the ratio of reactance to resistance of the open-circuit transfer impedance between these plants.This formula is rigorous except for the influence of inter-Fig. 1. Economic fuel cost ratio as a function of phase angle and react ance/resistance ratio, Κ i:o 120 no ^100 I CO to 3 90 UJ ^ 80 70 i / / --1 / --/ / Ξ LC iASL ADir IG/ Θ 1 / Δ \ \ 1 /j \ί .2--200 300 400 PLANT NO. I LOADING -MW (Vs NO. 13) 500 Fig. 2. System loss changes with exchanges in generation between plants 1 and 13 Curve plotted from angle equations Ο = PR calculated values Δ = Calculated from Β constants • = From modified Β constants mediate plants, which tend to maintain constant voltages at points along the path. A more accurate expression recognizing the presence of intermediate plants is dL/dP,-2 = (4^ tan 1/2 θι-,)/{Κ + tan 1/2 θι-2? (2) Co-ordination of incremental fuel costs and incremental transmission losses then is expressed as: dF2/dP2 (K + tan 1/2 ^1-2)2 dF,/dPi (K -tan 1/2 Θ1-2Υ (3) 10 20 30 40 50 ANGLE Θ.-2-DEGREES where άΡχ/άΡχ is the incremental fuel cost of plant 1. Fig. 1 illustrates the variation of economic fuel cost ratio with the angle θ for three values of K. With such a series of curves and with tables or curves of incremental fuel costs, it is feasible to adjust the generation represented on a net work analyzer in a rapid series of approximations.Equations for deriving incremental losses may be ex panded to deal with substantial exchanges of generation. Fig. 2 includes a curve plotted from such equations to gether with the corresponding loss...

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