A direct method based on tensor calculation to determine maximum loadability power flow solutions

•The formulation of the maximum loadability power flow problem in terms of static optimisation.•The use of rectangular coordinates to express the power flow equations, with an alternative scheme of parameterisation to model the load variation.•The use of the second order information (quadratic (tensor) term of the Taylor series) of the equations representing the optimality conditions.•The use of a scheme based on the tensor calculation to treat the reactive power generation limits.•The use of alternative strategies to estimate initial Lagrange multipliers.

In this paper, the determination of critical loadability points of the power flow equations is formulated as an optimisation problem. A quadratic parameterisation scheme is used to model the load change, which is equivalent to implicitly including a non-negativity constraint in the load variation. The power flow equations are expressed in rectangular coordinates. This is suitable to exploit the second order information (tensor term) of the equations representing the optimality conditions. The use of this term improves the convergence of the iterative process and facilitates the manipulation of the reactive power generation limits. Simulation results obtained with a number of power systems, including real networks, are used to illustrate the main features of the proposed methodology.