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The fuel cost formula is developed for optimal real-and reactive-power dispatch for the economic operation of power systems. The problem is decomposed into a P-optimisation and a Q-optimisation module, where both modules use the same fuel cost objective function resulting in the optimal load flow. The control variables are generator real-power outputs for the real-power module; and generator reactive-power outputs, shunt capacitors/reactors and transformer tap settings for the reactive-power module. The constraints are the operating limits of the control variables, power-line flows and busbar voltages. The optimisation problem is solved using the gradient projection method (GPM) for the quadratic objective function and linear constraints. The GPM allows the use of functional constraints without the need of penalty functions or Lagrange multipliers among other advantages. Mathematical models are developed to represent the sensitivity relationships between dependent and control variables for both real-and reactive-power optimisation modules; and thus eliminate the use of B-coefficients. Results of two test systems are presented and compared with conventional methods.

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