Transmission Line Maximum Powers And Clarke's Deduction For Reactance Networks

Abstract

Results of a maximum power transfer theorem for transmission systems are presented. The theory is based on conditions referenced to a single node voltage constraint with the other voltages coming out as a result of maximum received power. The analytic solution for the Single Node Constraint (SNC) circuit uses for verification a 3-node configuration comprising a source defined by ( E , jX ) connected to a line defined by ( s V , R + jX ,V) . The resulting statement of maximum received power reduces to s E2 / 4R as X tends to zero, which corresponds to the celebrated Jacobi's law of impedance matching for resistive circuits; and to V X s 2 / as R tends to zero, which is Miss Clarke's deduction for the steady-state stability limit (SSSL) of a Reduced Two-Node Constraint (RTNC) reactance network. While presentation time and space limitations do not allow for solution details of the outstanding SSSL problem in circuits with resistance and node voltage constraints, the results given for reactance networks will disclose the existence of a second SSSL mode for the SNC transmission system.