Iterative linear cuts strenghtening the second-order cone relaxation of the distribution system optimal power flow problem

Abstract

International audienceWe present a novel iterative algorithm to solve the distribution system optimal power flow problem over a radial network. Our methodology makes use of a widely studied second order cone relaxation applied to the branch flow model of a radial network. Several types of conditions have been established under which this relaxation is exact and we focus here on the situations where this is not the case. To overcome this difficulty, we propose to add increasingly tight linear cuts to the second-order cone problem until a physically meaningful solution is obtained. We apply this technique to a sample system taken from the literature and compare the results with a traditional nonlinear solver

Mixed‐integer second‐order cone programming framework for optimal scheduling of microgrids considering power flow constraints

“…The non-linear relation between P i DG, aux , λ i DG and P i DG is replaced by linear inequalities (24)- (26). In other words, logical conditions in (3) can be deduced from (24)- (26), taking binary values of λ i DG .…”

“…It was proposed to allocate multiple ESSs within radial distribution networks, minimising either operational costs or total real power loss in [25]. Increasing tight linear cuts was integrated into a SOCP to guarantee an exact solution, by iteratively solving the OPF until a predefined stopping criterion is satisfied, considering storage units on the IEEE 69-bus system [26]. An innovative concept about electrical vehicles charging station was presented.…”

Multi-temporal optimal power flow for assessing the renewable generation hosting capacity of an active distribution system

“…The same SOCP convex relaxation used in [19] and [17] is implemented in a multi-temporal model in order to analyze the hosting capacity of a distribution grid. This relaxation entails the relaxation of certain equality constraints and the substitution of certain quadratic terms for linear terms.…”

“…While an SOCP relaxation has also proved to be exact under certain conditions as stated in [17], [10], [18]. However, these relaxations have been proven to be inexact during periods of high renewable energy production feeding into the grid due to elevated line losses [19]. In order to determine the hosting capacity of a distribution grid, it is critical to have a precise and accurate calculation methodology when RE production is high.…”

“…An example of this difficulty could be high photovoltaic (PV) production during the summer season. In order to overcome the challenge of inaccurate results at periods of high PV injection, [19] presents an AC optimum power flow algorithm that integrates linear cuts implemented in a iterative fashion to ensure an exact and feasible relaxation of the power flow equations. This single phase AC optimum power flow algorithm minimizes losses in the system, while also minimizing the distance between the curtailed production and the real PV production capacity.…”