Distributed algorithms for optimal power flow problem

Abstract

Abstract-Optimal power flow (OPF) is an important problem for power generation and it is in general non-convex. With the employment of renewable energy, it will be desirable if OPF can be solved very efficiently so its solution can be used in real time. With some special network structure, e.g. trees, the problem has been shown to have a zero duality gap and the convex dual problem yields the optimal solution. In this paper, we propose a primal and a dual algorithm to coordinate the smaller subproblems decomposed from the convexified OPF. We can arrange the subproblems to be solved sequentially and cumulatively in a central node or solved in parallel in distributed nodes. We test the algorithms on IEEE radial distribution test feeders, some random tree-structured networks, and the IEEE transmission system benchmarks. Simulation results show that the computation time can be improved dramatically with our algorithms over the centralized approach of solving the problem without decomposition, especially in tree-structured problems. The computation time grows linearly with the problem size with the cumulative approach while the distributed one can have sizeindependent computation time.

Physics of power networks makes hard optimization problems easy to solve

“…For instance, [28] simplifies the SDP formulation by exploiting the sparsity in the structure of a power network. The paper [29] proposes a distributed algorithm for solving this SDP problem. [30] and [31] prove that the SDP relaxation is guaranteed to work for tree networks under certain assumptions.…”

Dynamic Network Energy Management via Proximal Message Passing

“…In the second phase, these prices allow individual devices to jointly optimize their power flows with minimal (if any) additional coordination over the time horizon. More recently, building on the work of [39], a distributed algorithm was proposed [38] to solve the dual OPF using a standard dual decomposition on subsystems that are maximal cliques of the power network.…”

Stochastic loss minimization for power distribution networks

“…Sufficient conditions guaranteeing that the convex relaxation is exact, ensure that solving the relaxed problem is equivalent to solving the original non-convex one [10], [11], [26], [13]. A centralized approach for inverter VAR control using the SOCP relaxation has been devised in [12], while a distributed algorithm based on a semidefinite program relaxation can be found in [17].…”