The differentiation of functions of conjugate complex variables: application to power network analysis

The mathematical foundations of the rules used to differentiate functions of conjugate complex variables are examined and their use is illustrated with several power network analysis examples. Using conjugate complex notation in power network analysis, it is possible to obtain directly the real Jacobian matrix of the power-flow equations. The author introduces the concept of bicomplex Jacobian matrix and states the rules to invert it. The expressions which are above often permit an immediate physical interpretation.< >