A comparison study between mathematical models of Static VAR Compensators aimed at optimal power flow solutions

In this paper two positive sequence mathematical models for two types of most commonly used Shunt VAR Compensators - i.e. STATCOM and SVC - have been given, which are suitable for carrying out optimal power flow solutions. The OPF solution algorithm is chosen to be the already well-established Newton´s method for augmented Lagrangian functions. In this method, instead of directly penalizing the objective function, a Lagrangian function is created based on the problem definition and the set of equality constraints, which is then penalized for points outside the feasible solution space. The linearized system of equations is solved for the primal variables using Newton´s method whilst preserving its strong convergence characteristics (quadratic). The principles of formulating a non-linear programming problem such as the OPF has been already well established in open literature and will only be briefly mentioned in this paper.