Algebraic solution of the load-flow problem for a 4-nodes electrical network Original Research Article

The load-flow problem for an electrical network is formulated as a system of polynomial equations in several variables. In present Electrical Engineering it is solved using numerical methods. But the system contains parameters and must very often be solved in real time in order to simulate events. It would be, in principle, useful to reduce the system to echelon or triangular form, using algebraic techniques, as, for instance, Gröbner bases, in order to obtain the solution once for all and then use it in any simulation. In this paper, algorithms to triangulate the load-flow equations of a 4-nodes electrical network are presented. These algorithms have been implemented in Maple, and simulations using them are given. The advantages of the algebraic solution compared to the numerical one are discussed. In particular, the algebraic solution allows us to compute, in a very simple way, derivatives and the related numerical conditioning of the problem and also the numerical conditioning of the algorithm.