On generalizations of the maximum power transfer problem

Mathematical methods for computing the extremal power values in the nodes of ac electric power systems

“…The maximum total active power transferred to a group of grid nodes without any additional constraints on the power of individual nodes can be determined by applying the results of electrical circuit theory for active power transfer maximization in the case when an active and a passive multiport are connected [55][56][57][58][59][60][61][62].…”

“…If the multiport contains emf sources, it is called active; otherwise the multiport is passive. Some results regarding the conditions when the active power transfer is maximized and the explicit form of the power transfer maximum were obtained in [55][56][57][58][59] (these results were subsequently developed and generalized by Desoer [60] and Vidyasagar [61]). However, the conditions derived by these authors are unattainable in practice, as has been shown by Calvaer [62].…”

“…The power transfer maxima for these cases are determined in explicit form. Application of the results from [55][56][57][58][59][60][61][62] involves additional difficulties, because the expressions for the maximum power transfer contain the values of the parameters of Thevenin equivalent circuits [63] for multiports, while the modeling of real power systems relies on resistances (or conductances) of different branches and voltages of different sources and the construction of a Thevenin equivalent circuit is a separate problem altogether (one of the approaches to approximate computation of equivalent circuit parameters is presented in [64]). …”

Available active power of the N‐port AC Thévenin source: A simple behavioral derivation

“…[3][4][5][6][7][8][9][10][11][12][13][14][15] Their goal was to determine the impedance matrix Z that a load N-port must exhibit to draw maximum active power from the N-port AC Thévenin source with internal phasor signal vector V T and internal impedance matrix Z T under various constraints on matrices Z and Z T , as well as the amount of the maximum active power drawn. [3][4][5][6][7][8][9][10][11][12][13][14][15] Their goal was to determine the impedance matrix Z that a load N-port must exhibit to draw maximum active power from the N-port AC Thévenin source with internal phasor signal vector V T and internal impedance matrix Z T under various constraints on matrices Z and Z T , as well as the amount of the maximum active power drawn.…”

On the maximal power transfer theorem for n‐ports

“…Desoer's method, to some extent anticipated in equation (5) of Nambiar,' is the following. The current between the networks is a vector i such that ( R + Z * ) i = e and the power dissipated in R is By (l), condition (6) is equivalent to Zi = Ri, that is, to…”