Unlimited point algorithm for OPF problems

Abstract

A non-linear Optimal Power Flow (OPF) algorithm is presented which allows to solve the KarushKuhn-Tucker (KKT) optimality conditions using a pure Newton-Raphson solution procedure. The method is similar to interior point algorithms. However, due to a simple transformation, the variable space becomes unlimited (Unlimited Point) and variables do not need to be forced to stay within the feasible region during all OPF iterations as is the case for interior point algorithms. As a consequence only a pure Newton-Raphson iterative process to algebraically transformed KKT conditions is applied. The algorithm has been successfully applied to various networks up to size 700 buses with the active power loss objective function.

Constrained optimization applying decomposed unlimited point method based on KKT condition

“…It is not clear from a theoretical point of view what the best values for p and q are. However, it is advised that choosing p = 2 and q = 1 leads to good convergence for all tested numerical examples [10]. Applying these steps to the primal KKT condition, it can be transformed into the following equations: ⎡…”

“…The equations' characteristics remain the same as (10) while there will be a non-smooth point when applying NCPM. Accordingly, (10) can be converted into the following equations:…”

“…In most of the literature, the equivalent equations are solved by Newton-type methods, such as Newton-Raphson method (NRM) [10], [11], [12]. Nevertheless, NRM has a strict requirement that the Jacobi matrix must be non-singular, which will undoubtedly limit its application.…”

Constrained Potential Function—Based Control of Microgrids for Improved Dynamic Performance

“…Network interface requires solution of a set of algebraic equations relating voltages and currents of the network to those of the devices. Injected currents are calculated from the network equations (28) where represents the vector of bus voltages. The injected currents obtained from the network equations are set equal to those obtained from generators and nonlinear loads (29) where , , and show the generators current injection, admittance, and internal voltage, respectively.…”

“…The common approach to handle inequality constraints is to convert them into equality constraints using a barrier function. Different barrier functions can be defined [27], [28]. In this work, a logarithmic barrier function is used that includes slack variables for inequality constraints.…”