A Decoupled Method for Systematic Adjustments of Phase-Shifting and Tap-Changing Transformers

Exact matrix-vector representations of the power flow equations are used to develop a scheme for systematic adjustment of regulating transformers. The real and reactive power models are both written in matrix-vector form as Ax= ь. The unknowns in the real and reactive power models are the sets of voltage phase angles and unspecified voltage magnitudes at PQ busses, respectively. The real power model includes specified power flows through phase-shifting transformers as injections into busses where such transformers are connected. The reactive power model has a dimensionality equal to the number of load busses less the number of tap-changing transformers. Two separate submodels allow the calculations of phase shifter angle and tap settings. The application of the algorithm to the IEEE standard test systems shows that the algorithm adjusts transformer settings in about the same number of iterations as that for unadjusted solutions.