reactive power case 5 similar to case 4 except that it has been installed with one additional statcom 103 the statcom 103 has one shunt branch and it is in parallel with bus 81 to control its voltage magnitude in the above test cases the coupling transformers have the same impedances as 0 01 j0 05 p u the allowable tolerance of newton raphson algorithm is set to 10 u2212 12 the initial values for the state variables are 1 u2220 0 u00b0 for the bus voltages and 0 for i sh d and i sh q table 1 shows the iteration numbers required for obtaining the power flow solution in different test systems the simulation results showed that incorporating the steady state model of the generalized power flow controller will not increase the iteration number for obtaining the power flow solution within the same allowable tolerance fig7 shows the convergence pattern of state variables of the gupfc as shown the current components i sh q and i sh d converge to their target values after six iterations respectively case 3 is designed to demonstrate a distinguishing feature of the present invention even through the sending ends of the shunt branch and series branches of the gpfc connect to different buses the power flow solution converges as rapidly as the base case does fig8 shows the power mismatches at the sending end and receiving end buses of the gpfc after six iterations the power mismatches are within a tight tolerance and thus a precise power flow solution is obtained therefore it is well demonstrated that the power flow calculation achieves a rapid convergence characteristic using the steady state model of the generalized power flow controller according to the present invention fig9 shows a quadratic convergence pattern.