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A novel optimisation-based model of the power flow (PF) problem is proposed using complementarity conditions to properly represent generator bus voltage controls, including reactive power limits and voltage recovery processes. This model is then used to prove that the Newton-Raphson (NR) solution method for solving the PF problem is basically a step of the generalised reduced gradient algorithm applied to the proposed optimisation problem. To test the accuracy, flexibility and the numerical robustness of the proposed model, the IEEE 14-bus, 30-bus, 57-bus, 118-bus and 300-bus test systems and large real 1211-bus and 2975-bus systems are used, benchmarking the results of the proposed PF model against the standard NR method. It is shown that the proposed model yields adequate solutions, even in the case when the NR method fails to converge.

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An affine-based stochastic power flow problem is proposed in this paper. First, a novel optimization-based model of the power flow problem using complementarity conditions to properly represent generator bus voltage controls, including reactive power limits and voltage recovery is presented. This model is then used to solve the stochastic power flow problem to obtain operational intervals for power flow variables based on an Affine Arithmetic (AA) method to consider active and reactive power demand uncertainties. The proposed AA algorithm is tested on a 14-bus test system and the results are then compared with the Monte-Carlo Simulation (MCS) results. The AA method shows slightly more conservative bounds; however, it is faster and does not need any information regarding statistical distributions of random variables.Index Terms-Power flow problem, mixed complementarity problem, stochastic power flow problem, affine arithmetic, monte-carlo simulation.

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