Distributed algorithm for optimal power flow on a radial network

Peng, Qiuyu; Low, Steven H.

doi:10.1109/cdc.2014.7039376

Cited by 88 publications

(89 citation statements)

References 15 publications

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“…Since the optimization problem inherits the structure of the power network, one can likely design distributed algorithms to solve the resulting optimization problems using techniques like ADMM [11]. In a future work we plan to develop efficient ADMM algorithms for this and related problems (see below), also taking advantage of recent exploration of ADMM and related techniques on a variety of PF settings [12], [13], [14], [15], [16], [17], [18], [19].…”

Section: Solving Power Flow Equations Via Convexmentioning

confidence: 96%

Convexity of structure preserving energy functions in power transmission: Novel results and applications

Dvijotham

Chertkov

2015

2015 American Control Conference (ACC)

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It is well-known in the power systems literature that the behavior of the transmission power system (under certain simplifying assumptions) can be used to study the post-fault dynamics of a power system and provide principled estimates on dynamic stability margins. In this paper, we study a special feature of the energy function that has previously received little attention: convexity. We prove that the energy function for structure preserving models of power systems is convex under certain reasonable conditions on phases and voltages. Beyond stability analysis, these convexity results have a number of applications, noticeably, building a provably convergent PF solver, which we discuss in detail in this paper. We also outline potential applications to reformulating Optimum Power Flow (OPF), Model Predictive Control (MPC) and identifying the most probable failure (instanton) as convex optimization problems.

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Section: Solving Power Flow Equations Via Convexmentioning

confidence: 96%

Convexity of structure preserving energy functions in power transmission: Novel results and applications

Dvijotham

Chertkov

2015

2015 American Control Conference (ACC)

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“…In our work we consider each customer to be independent, for privacy reasons, and we also allow for meshed microgrid topologies.Šulc et al [31] use the relaxed DF (SOCP) equations to perform reactive power control on radial networks. For a similar problem, Peng et al [23] provide closed-form solutions for ADMM subproblems, greatly reducing the computational requirements. Again these works focus on radial networks.…”

Section: Related Workmentioning

confidence: 99%

“…This is because we have placed the buses and non-bus components into separate phases. As an additional benefit, some sub-problems are simple enough when separated that they have closed-form solutions [23]. We adopt a closed-form solution for buses as proposed in [19].…”

Section: Algorithmmentioning

confidence: 99%

Distributed Multi-Period Optimal Power Flow for Demand Response in Microgrids

Scott

Thiébaux

2015

Proceedings of the 2015 ACM Sixth International Conference on Future Energy Systems

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Abstract. With the arrival of electric vehicles, battery storage and smart appliances, households now have the opportunity to actively participate in balancing supply and demand in electricity networks. We propose to coordinate this multi-agent system using distributed optimisation, in order to scale to large systems whilst preserving agent privacy. However, the practical applicability of distributed optimisation remains an open question in this context, as AC power flows are inherently nonconvex and households often make discrete decisions about how to schedule their loads. In this paper we show that one such method, the alternating direction method of multipliers (ADMM), can be adapted to remain practical in this challenging microgrid setting. We formulate and solve a multi-period optimal power flow (OPF) problem featuring household agents with shiftable loads, and study the results obtained with a range of power flow models and approaches to managing discrete decisions. Our experiments on a suburb-sized microgrid show that the AC power flows and a simple two-stage approach to handling discrete decisions do not appear to cause convergence issues, and provide near optimal results in a time that is practical for receding horizon control. This brings distributed control of microgrids several steps closer to reality.

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“…The ADMM method when applied to a convex program, generates a sequence of the convex programs combined with the dual update that approximately solves the targeting optimization. For a convex problem, it is guaranteed to converge to a global optimal solution and has been used to develop distributed algorithm for the OPF problem in [17], [18], [19]. In contrast, for a nonconvex problem, each step requires the non-convex program which is hard to solve, and there is no convergence result, so it is not an interesting algorithm for a general non-convex optimization.…”

Section: Introductionmentioning

confidence: 99%

A non-convex alternating direction method of multipliers heuristic for optimal power flow

You

Peng

2014

2014 IEEE International Conference on Smart Grid Communications (SmartGridComm)

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Abstract-The optimal power flow (OPF) problem is fundamental to power system planing and operation. It is a nonconvex optimization problem and the semidefinite programing (SDP) relaxation has been proposed recently. However, the SDP relaxation may give an infeasible solution to the original OPF problem. In this paper, we apply the alternating direction method of multiplier method to recover a feasible solution when the solution of the SDP relaxation is infeasible to the OPF problem. Specifically, the proposed procedure iterates between a convex optimization problem, and a non-convex optimization with the rank constraint. By exploiting the special structure of the rank constraint, we obtain a closed form solution of the non-convex optimization based on the singular value decomposition. As a result, we obtain a computationally tractable heuristic for the OPF problem. Although the convergence of the algorithm is not theoretically guaranteed, our simulations show that a feasible solution can be recovered using our method. NOTATIONi is the imaginary unit. W * is the Hermitian of W , Tr (W ) is a trace of W , and W F = Tr (W W * ) is the Frobenius norm of W . The generalized inequality, W 0, means W is a positive semidefinite matrix.The projection operator Π S (W ) = argmin Z∈S W − Z 2 F , is the projection of W onto the set S.

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Distributed algorithm for optimal power flow on a radial network

Cited by 88 publications

References 15 publications

Convexity of structure preserving energy functions in power transmission: Novel results and applications

Convexity of structure preserving energy functions in power transmission: Novel results and applications

Distributed Multi-Period Optimal Power Flow for Demand Response in Microgrids

A non-convex alternating direction method of multipliers heuristic for optimal power flow

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