The QC Relaxation: A Theoretical and Computational Study on Optimal Power Flow

Coffrin, Carleton; Hijazi, Hassan; Hentenryck, Pascal Van

doi:10.1109/tpwrs.2015.2463111

Cited by 293 publications

(274 citation statements)

References 40 publications

(74 reference statements)

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“…Starting from an initial optimization problem with a given set of variable bounds, optimization-based bound tightening solves a sequence of optimization problems to find the upper and lower achievable values for, e.g., the voltage magnitudes and angle differences. The obtained values are then used to tighten the bounds on these quantities, which in turn improves the quality of certain convex relaxations of the AC power flow equations [5], [6]. The effectiveness of these methods in obtaining tighter variable bounds implies that many of the bounds are implicitly satisfied through other constraints in the problem, such as the power flow equations and the generation constraints.…”

Section: Introductionmentioning

confidence: 99%

Implied Constraint Satisfaction in Power System optimization: The Impacts of Load Variations

Roald

Molzahn

2019

2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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In many power system optimization problems, we observe that only a small fraction of the line flow constraints ever become active at the optimal solution, despite variations in the load profile and generation costs. This observation has farreaching implications not only for power system optimization, but also for the practical long-term planning, operation, and control of the system. We formalize this empirical observation for problems involving the DC power flow equations. We use a two-step constraint screening approach to identify constraints whose satisfaction is implied by other constraints in the problem, and can therefore be removed from the problem. For the first screening step, we derive analytical bounds that quickly identify redundancies in the flow limits on parallel lines. The second screening step uses optimization-based constraint screening, where we solve a (relaxed) optimization problem for each constraint to identify redundancies. Different from existing methods, we specifically focus our approach on large ranges of load variation such that the results are valid for long periods of time, thus justifying the computational overhead required for the screening method. Numerical results for a wide variety of standard test cases show that even with load variations up to ±100% of nominal loading, we are able to eliminate a significant fraction of the flow constraints. This large reduction in constraints may enable a range of possible applications. As one illustrative example, we demonstrate the computational improvements for the unit commitment problem obtained as a result of the reduced number of constraints.

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Section: Introductionmentioning

confidence: 99%

Implied Constraint Satisfaction in Power System optimization: The Impacts of Load Variations

Roald

Molzahn

2019

2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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“…In this section, we summarize the procedure of obtaining a convex restriction for the AC OPF problem. 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%

Feasible Path Identification in Optimal Power Flow With Sequential Convex Restriction

Lee

Turitsyn

Molzahn

et al. 2020

IEEE Trans. Power Syst.

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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

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“…(z c , y c ) ← Solve coarse problem (23) ← 0, r ← ∞, s ← ∞ Initialize ADMM coordination. (z , y ) ← Map coarse solution to fine space using (25) while r ≥ pr and s ≥ du do for (in parallel) k ∈ K do x +1 k ← Solve subproblem (10) with (x , z , y ). end for z +1 ← Update coupling states using (13).…”

Section: Algorithm 1 Hierarchical Optimization Schemementioning

confidence: 99%

A Hierarchical Optimization Architecture for Large-Scale Power Networks

Shin

Hart

Jahns

et al. 2019

IEEE Trans. Control Netw. Syst.

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We present a hierarchical optimization architecture for large-scale power networks that overcomes limitations of fully centralized and fully decentralized architectures. The architecture leverages principles of multigrid computing schemes, which are widely used in the solution of partial differential equations on massively parallel computers. The top layer of the architecture uses a coarse representation of the entire network while the bottom layer is composed of a family of decentralized optimization agents each operating on a network subdomain at full resolution. We use an alternating direction method of multipliers (ADMM) framework to drive coordination of the decentralized agents. We show that state and dual information obtained from the top layer can be used to accelerate the coordination of the decentralized optimization agents and to recover optimality for the entire system. We demonstrate that the hierarchical architecture can be used to manage large collections of microgrids.

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The QC Relaxation: A Theoretical and Computational Study on Optimal Power Flow

Cited by 293 publications

References 40 publications

Implied Constraint Satisfaction in Power System optimization: The Impacts of Load Variations

Implied Constraint Satisfaction in Power System optimization: The Impacts of Load Variations

Feasible Path Identification in Optimal Power Flow With Sequential Convex Restriction

A Hierarchical Optimization Architecture for Large-Scale Power Networks

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