Convex Restriction of Power Flow Feasibility Sets

Lee, Dong‐Chan; Nguyen, Hung D.; Dvijotham, Krishnamurthy; Turitsyn, Konstantin

doi:10.1109/tcns.2019.2930896

Cited by 44 publications

(38 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The resulting convex restriction represents a convex inner approximation of the feasible region in the OPF problem. This is proven by the following Theorem from [17], which we extend to include transmission line flow limits. and (s f , s t ) such that…”

Section: < L a T E X I T S H A 1 _ B A S E 6 4 = " K T 6 F X B A S H mentioning

confidence: 92%

“…In summary, the main contributions of this paper are: 1. We formulate the AC OPF problem based on convex restrictions from [17]. This is the first formulation of an OPF with convex restriction, which requires extending the convex restriction to include line flow constraints.…”

Section: Convex Restrictionmentioning

confidence: 99%

“…The convex restriction provides a convex condition on the control variable u such that there exists a state variable x that satisfies both the AC power flow equations in (2) and the operational constraints in (3). A sufficient convex condition for AC power flow feasibility was developed in [17], and we extend its application to solve full OPF problem including line flow limits.…”

Section: Optimal Power Flow With Convex Restrictionmentioning

confidence: 99%

“…Further, (23) ensures the operational constraints are satisfied for all x ∈ P(b). A more detailed proof is in [17].…”

Section: Proof Conditionmentioning

confidence: 99%

“…In contrast to previous work, our proposed feasible path algorithm is not limited to specific classes of systems, considers the nonlinear AC power flow model, and is tractable for large problems. Based on a quadratic convex restriction of the AC power flow feasible space [17], we compute a piece-wise linear path connecting an initial point to a desired operating point such that all points along the path are feasible. The proposed algorithm is illustrated in Fig.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Feasible Path Identification in Optimal Power Flow With Sequential Convex Restriction

Lee

Turitsyn

Molzahn

et al. 2020

IEEE Trans. Power Syst.

Self Cite

View full text Add to dashboard Cite

Nonconvexity induced by the nonlinear AC power flow equations challenges solution algorithms for AC optimal power flow (OPF) problems. While significant research efforts have focused on reliably computing high-quality OPF solutions, identifying a feasible path from an initial operating to a desired operating point is a topic that has received much less attention. However, since the feasible space of the OPF problem is nonconvex and potentially disconnected, it can be challenging to transition between operating points while avoiding constraint violations. To address this problem, we propose an algorithm which computes a provably feasible path from an initial operating point to a desired operating point. The algorithm solves a sequence of quadratic optimization problems over conservative convex inner approximations of the OPF feasible space, each representing a so-called convex restriction. In each iteration, we obtain a new, improved operating point and a feasible transition from the operating point in the previous iteration. In addition to computing a feasible path to a known desired operating point, this algorithm can also be used to locally improve the operating point. Extensive numerical studies on a variety of test cases demonstrate the algorithm and the ability to arrive at a high-quality solution in few iterations. I. INTRODUCTIONAC optimal power flow (OPF) is a fundamental optimization problem in power system analysis The classical form of an OPF problem [1] seeks an operating point that is feasible (i.e., satisfies both the AC power flow equations that model the network physics and the inequality constraints associated with operational limits on voltage magnitudes, line flows, generator outputs, etc.) and economically efficient, i.e., achieves minimum operational cost. Significant research efforts have focused on obtaining locally and globally optimal OPF solutions using algorithms based on local search, approximation, and relaxation techniques [2]- [5]. While previous research has improved the computational tractability of OPF algorithms and the quality of the resulting solutions, a number of challenging issues remain. One such issue is to determine a sequence of control actions that facilitate a safe transition from the current operating point to the desired operating point [6], [7].Previous literature has considered the problem of determining a limited number of active and reactive power redispatch [8]-[10] required to bring the system to a new safe or optimal operating point. References such as [9], [10] consider the sequence as a set of individual control actions, where the operating point after each action must be steady-state feasible. While this improves security relative to a setting where intermediate feasibility is not considered, the feasible space of the AC OPF problem is nonconvex and sometimes disconnected [11]. Hence, a feasible path connecting the two steady-state operating points (where each intermediate state is

show abstract

Section: < L a T E X I T S H A 1 _ B A S E 6 4 = " K T 6 F X B A S H mentioning

confidence: 92%

Section: Convex Restrictionmentioning

confidence: 99%

Section: Optimal Power Flow With Convex Restrictionmentioning

confidence: 99%

“…Further, (23) ensures the operational constraints are satisfied for all x ∈ P(b). A more detailed proof is in [17].…”

Section: Proof Conditionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Feasible Path Identification in Optimal Power Flow With Sequential Convex Restriction

Lee

Turitsyn

Molzahn

et al. 2020

IEEE Trans. Power Syst.

Self Cite

View full text Add to dashboard Cite

show abstract

The Reform and Practice of Computer Public Teaching in University

Zhang

2019

Lecture Notes in Electrical Engineering

View full text Add to dashboard Cite

Many problems in power systems involve optimizing a certain objective function subject to power flow equations and engineering constraints. A long-standing challenge in solving them is the nonconvexity of their feasible sets. In this paper, we propose an analytical method to construct the convex restriction of the feasible set for AC power flows in radial networks. The construction relies on simple geometrical ideas and is explicit, in the sense that it does not involve solving other complicated optimization problems. We also show that the construct restrictions are in some sense maximal, that is, the best possible ones. Optimization problems constrained to these sets are not only simpler to solve but also offer feasibility guarantee for the solutions to the original OPF problem. Furthermore, we present an iterative algorithm to improve on the solution quality by successively constructing a sequence of convex restricted sets and solving the optimization on them. The numerical experiments on the IEEE 123-bus distribution network show that our method finds good feasible solutions within just a few iterations and works well with various objective functions, even in situations where traditional methods fail to return a solution.

show abstract

Hidden invariant convexity for global and conic-intersection optimality guarantees in discrete-time optimal control

Baayen

Postek

2021

J Glob Optim

View full text Add to dashboard Cite

Non-convex discrete-time optimal control problems in, e.g., water or power systems, typically involve a large number of variables related through nonlinear equality constraints. The ideal goal is to find a globally optimal solution, and numerical experience indicates that algorithms aiming for Karush–Kuhn–Tucker points often find solutions that are indistinguishable from global optima. In our paper, we provide a theoretical underpinning for this phenomenon, showing that on a broad class of problems the objective can be shown to be an invariant convex function (invex function) of the control decision variables when state variables are eliminated using implicit function theory. In this way, optimality guarantees can be obtained, the exact nature of which depends on the position of the solution within the feasible set. In a numerical example, we show how high-quality solutions are obtained with local search for a river control problem where invexity holds.

show abstract

Convex Restriction of Power Flow Feasibility Sets

Cited by 44 publications

References 33 publications

Feasible Path Identification in Optimal Power Flow With Sequential Convex Restriction

Feasible Path Identification in Optimal Power Flow With Sequential Convex Restriction

The Reform and Practice of Computer Public Teaching in University

Hidden invariant convexity for global and conic-intersection optimality guarantees in discrete-time optimal control

Contact Info

Product

Resources

About