Patent Document ID: 9996644
Application ID: 14956461
Patent Flag: 1

Claim One:
1. An apparatus for carrying out complex computations of power flow in a power transmission system which comprises: means for calculating voltages at a bus in the power transmission system by equating power entering a bus to a summation of powers leaving the bus as represented by equation (15) for real power calculations: 
 P e i =Re{ E gi ×I gi }=Re{ E gi }×Re{ I gi }=Im{ E gi }×Im{ I gi }  (15) said means including a DC network emulation of a power system bus k of the power transmission system, said power system bus k having complex voltage values and being represented by four networks with four buses K I , K II , K III and K IV as equivalents and for feasible bus voltages the following conditions of equation (16) are satisfied: V k I = V k III = V k I V k II = V k IV = V k I } ; ( 16 ) said means for calculating the real power further including a field programmable gate array, said field programmable gate array programmed for implementation of Gaussian elimination by decomposition of a matrix into lower and upper triangulation factors and forward and backward elimination; memory operably connected to said field programmable gate array, a device for maintaining pivoting information operably connected to said field programmable gate array; and a table to track elimination progress.