An Extended Nonlinear Primal-Dual Interior-Point Algorithm for Reactive-Power Optimization of Large-Scale Power Systems with Discrete Control Variables

A new heuristic approach to deal with discrete variables in optimal power flow computations

“…The objective (17) is the minimization of the degree of constraints violation in the sense of the L 1 norm. The solution of problem (17)(18)(19)(20)(21) in the context of the proposed algorithm is very useful since it provides an optimum of the relaxed OPF which enables the derivation of sensitivities (7)(8) and hence allows to carry on the algorithm. Incidentally, the solution of the problem (17-21) yields the degree of original continuous OPF problem infeasibility.…”

“…To this end, we first initialize discrete variables to the values provided by the round-off approach. Then we solve the minimum infeasibility degree problem (17)(18)(19)(20)(21) which provides a feasible solution where two minimum voltage limits have been relaxed with 0.02 pu and 0.01 pu, respectively. Next sensitivities are derived at this optimum and discrete variables are moved to new discrete values according to the rules of the sensitivity-based approach.…”

“…Another class of heuristic approaches consists in handling discrete variables by means of penalty functions in NLP solvers such as the active-set Newton method [16] or the interior point method (IPM) [17]. The former approach uses several heuristic rules to drive the discrete variables to their discrete values, while nowadays the Newton method is seen as slightly less efficient than other NLP methods (e.g., interior point, sequential quadratic programming, etc.).…”

Evaluation of Voltage Control Approaches for Future Smart Distribution Networks

“…In [4], the primal-dual interior-point (PDIP) algorithm was applied to solve the reactive power and voltage control problems. The voltage control problem was formulated as a mixed integer nonlinear optimization problem (MINLP), and network loss minimization was defined as the optimization objective.…”

“…In addition, they are not designed for mixed-integer problems, although some methods have been previously proposed to facilitate the application of deterministic algorithms to solve mixed-integer problems. For example, the PDIP algorithm was applied to solve the mixed-integer problems in [4], by modelling the discrete control variables as continuous variables, and introducing a penalty function to force the discrete control variables to converge to their feasible values. However, the introduced penalty function increases the risk of converging to a local optimal solution or even an infeasible solution.…”