A Two-level ADMM Algorithm for AC OPF with Global Convergence Guarantees

Sun, Kaizhao; Sun, Xu Andy

doi:10.48550/arxiv.2008.12139

Cited by 3 publications

(5 citation statements)

References 27 publications

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“…Peng and Low (2014, 2016 applied ADMM to some convex relaxation of ACOPF on radial networks. The numerical success of ADMM has also been observed on nonconvex ACOPF (Chung et al 2005, 2011, Sun et al 2013, Erseghe 2014, Mhanna et al 2019 with the convergence studied under certain technical assumptions (Erseghe 2014, Sun andSun 2020).…”

Section: Literature Reviewmentioning

confidence: 92%

Solving Large-Scale Security Constrained AC Optimal Power Flow Problems

Gholami¹,

Sun²,

Zhang³

et al. 2022

Preprint

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In this paper, we study efficient and robust computational methods for solving the securityconstrained alternating current optimal power flow (SC-ACOPF) problem, a two-stage nonlinear mixed-integer optimization problem central to the operation of electric power grids. The first-stage problem in SC-ACOPF determines the operation of the power grid in normal condition, while the second-stage problem responds to various contingencies of losing generators, transmission lines, and transformers. The two stages are coupled through disjunctive constraints, which model generators' active and reactive power output changes responding to system-wide active power imbalance and voltage deviations after contingencies. Real-world SC-ACOPF problems may involve power grids with more than 30k buses and 22k contingencies and need to be solved within 10-45 minutes to get a base case solution with high feasibility and reasonably good generation cost. We develop a comprehensive algorithmic framework to solve SC-ACOPF that meets the challenge of speed, solution quality, and computation robustness. In particular, we develop a smoothing technique to approximate disjunctive constraints into a smooth structure which can be handled by interior-point solvers; we design a distributed optimization algorithm with convergence guarantee to solve the two-stage SC-ACOPF model; we propose a screening procedure to prioritize contingencies; and finally, we develop a reliable and parallel architecture that integrates all algorithmic components. Extensive tests on industry-scale systems demonstrate the superior performance of the proposed algorithms.

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Section: Literature Reviewmentioning

confidence: 92%

Solving Large-Scale Security Constrained AC Optimal Power Flow Problems

Gholami¹,

Sun²,

Zhang³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…As the cardinality of K increases, the accuracy of the demand estimated by ( 6) increases while sacrificing computation. We denote by K a collection of various K and by D ẑl (K) a demand estimated by (6) with K ∈ K.…”

Section: ) Motivating Example (Data Leakage)mentioning

confidence: 99%

“…First, we consider various K(T ) when constructing the adversarial problem (6). As T increases, theoretically, the accuracy of the demand estimated by solving (6) with K ∈ K(T ) increases. We report in Figure 4 an average demand estimation error (DEE):…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…Distributed OPF consists of (i) a set of OPF subproblems defined for each zone of the power grid and (ii) consensus constraints that link the subproblems. Distributed OPF can be solved by the existing distributed algorithms (e.g., [3], [4], [5], [6]), which do not require sharing private data information (e.g., demand data from each zone) but send the local solutions to the central machine. Unfortunately, an adversary may be able to estimate the data based on the solutions (e.g., reverse engineering [7]), thus motivating the need for solution encryption.…”

Section: Introductionmentioning

confidence: 99%

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A Privacy-Preserving Distributed Control of Optimal Power Flow

Ryu¹,

Kim²

2021

Preprint

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We consider a distributed optimal power flow formulated as an optimization problem that maximizes a nondifferentiable concave function. Solving such a problem by the existing distributed algorithms can lead to data privacy issues because the solution information exchanged within the algorithms can be utilized by an adversary to infer the data. To preserve data privacy, in this paper we propose a differentially private projected subgradient (DP-PS) algorithm that includes a solution encryption step. We show that a sequence generated by DP-PS converges in expectation, in probability, and with probability 1. Moreover, we show that the rate of convergence in expectation is affected by a target privacy level of DP-PS chosen by the user. We conduct numerical experiments that demonstrate the convergence and data privacy preservation of DP-PS.

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“…The computational bottleneck of the master problem solution can be avoided by decomposing the network into two subnetworks and by parallelizing each subproblem solution. For example, we can use ADMM (e.g., [28]) for solving each subproblem in parallel. We will address this issue in our future work.…”

Section: Concluding Remarks and Future Workmentioning

confidence: 99%

On the Tightness of the Lagrangian Dual Bound for Alternating Current Optimal Power Flow

Zhang¹,

Kim²,

Zavala³

2021

Preprint

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We study tightness and scalability properties of a Lagrangian dual (LD) bound for the nonconvex alternating current optimal power flow (ACOPF) problem. We show that the LD bound is as tight as that provided by the powerful and popular semidefinite programming relaxation. However, a key advantage of the proposed bound is that it can be computed in a parallel, decentralized manner. Specifically, in the proposed approach we partition the network into a set of subnetworks, we dualize the coupling constraints (giving the LD function), and we maximize the LD function with respect to the dual variables of the coupling constraints (giving the desired LD bound). The dual variables that maximize the LD are obtained by using a bundle method and we provide a proof of convergence for such method. We demonstrate our developments using PGLib test instances.

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A Two-level ADMM Algorithm for AC OPF with Global Convergence Guarantees

Cited by 3 publications

References 27 publications

Solving Large-Scale Security Constrained AC Optimal Power Flow Problems

Solving Large-Scale Security Constrained AC Optimal Power Flow Problems

A Privacy-Preserving Distributed Control of Optimal Power Flow

On the Tightness of the Lagrangian Dual Bound for Alternating Current Optimal Power Flow

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