Transversality enforced Newton-Raphson algorithm for fast calculation of maximum loadability

The authors propose a novel modification of the conventional Newton-Raphson load flow solver for characterisation of the maximal system loadability. Within the proposed approach, the standard power flow equations are extended with (i) an algebraic representation of maximal and minimal voltage level conditions and (ii) with the so-called transversality condition restricting the set of solutions to the boundary of the solvability region. Solutions to this extended system of equation characterise the maximal load levels for which the solution of power flow equations exists and satisfies the standard feasibility constraints on voltage levels. The resulting system of equations is non-singular and can be solved with just a few standard Newton-Raphson type iterations. Different possible choices of transversality conditions are discussed together with fast algorithms for evaluating the transversality conditions and their gradients. Implementation of the algorithm is described in detail, and its performance is validated on several IEEE cases.