Efficient algorithm for transmission system energy loss allocation considering multilateral contracts and load variation

New reactive power flow tracing and loss allocation algorithms for power grids using matrix calculation

“…From Eqs. (21) and (26), it is easy to understand that the proposed method allocates all reactive power flows and losses of the branches to load 2, which is the sole load of the system. Hence, the load shares are not presented in the form of Tables 2 and 3.…”

“…(2) Since these methods use the admittance (Y) or impedance (Z) matrix and the load flow equations directly to derive the sources and loads' participations in the transmission costs and losses [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29], they pay more attention to the actual characteristics of the system and thus have a great advantage over the previous group of methods. In some of these methods [14][15][16][17], the basic circuit relations are combined with the game theory for the division of the branch power flow and loss among the generators and loads.…”

“…Refs. [18][19][20][21][22] also do not consider the generator as a supplier of reactive losses, notwithstanding they employ no predefined sharing ratio to split the reactive loss of each branch between the generators and loads simultaneously. In addition, since the effect of the branches' charging capacitances on providing the reactive loads and losses is not discussed in Refs.…”

“…[17][18][19][20][23][24][25]; the reactive power produced by the charging capacitance of each branch is considered as a part of its reactive loss in Refs. [16,21,22,14,15,26,27] represent every branch by the series impedance and ignore the shunt admittances from its equivalent circuit model; these references do not take into account the charging capacitance as a reactive power source. Even though the reactive power production of the charging capacitance is accounted in Refs.…”

“…Furthermore, negative loss allocation to a number of generators or loads is seen in Refs. [14][15][16]21,22,26]. This situation, which results in negative cost assignment, can be interpreted as cross subsidy and thus it is not allowable from an economics point of view.…”