Large Scale Optimal Power Flow

Optimization Decomposition of Resistive Power Networks With Energy Storage

“…Interestingly, the difference between two successive dual variables ´Øµ ´Ø ½µ plays a decoupling role over time: Proof: As the dynamic OPF has a zero duality gap, we use the Karush-Kuhn-Tucker (KKT) conditions (cf. [18]) to deduce the following: ¾ « Ö ´Øµ ´Øµ ´Øµ · ´Øµ ´Øµ Ø ½ ¾ Ì (27) ´Øµ ´Ø ½µ « · ´Øµ ´Øµ Ø ¾ ¿ Ì (28) ´Ìµ « ´Ì · ½µ · ´Ì · ½µ Suppose that battery never drains or saturates, i.e., ¼ ´Øµ (29) where the second equality is due to (28). In (29) …”

“…The relaxation gap (as well as the Lagrange duality gap in the OPF considered in this paper) is zero in this case. methods (predominantly Lagrange dual decomposition) have been previously used in the literature to solve the OPF [7], [8], [24], [27], [28], but these prior work use approaches (using the DC OPF linearization to approximate the OPF) different from that in this paper. Decomposition enables fundamental understanding of architectural possibilities, especially in the distributed coordination of functional modules in a large network [29], [30].…”

Introduction to Electric Power Systems

“…In [54] , the nonsparse implementation of the QP -based OPF was proposed while in [51 -53] , the sparse implementation of the QP -based OPF algorithm for large -scale power systems was presented. In [51,52] , the successive QP -based OPF problems are solved through a sequence of linearly constrained subproblems using a quasi -Newton search direction. The QP formulation can always fi nd a feasible solution by adding extra shunt compensation.…”

“…In [53] , the QP method, which is a direct solution method, solves a set of linear equations involving the Hessian matrix and the Jacobian matrix by converting the inequality constrained quadratic program (IQP) into the equality constrained quadratic program (EQP) with an initial guess at the correct active set. The computational speed of the QP method in [53] has been much improved in comparison to those in [51,52] . The QP methods in [51 -53] are solved using MINOS, developed at Stanford University.…”

Reactive Power is a Cheap Constraint

“…We adopt the more natural procedure of embedding the problem in an optimal power flow framework. Optimal power flow (OPF) is a more complex calculation than ordinary power flow because it involves a simultaneous minimization of fuel costs along with satisfying the ordinary power flow constraints (Burchett et al, 1982;Gribik et al 1991). OPF is not widely available in software packages.…”