DeepOPF+: A Deep Neural Network Approach for DC Optimal Power Flow for Ensuring Feasibility

Zhao, Tianyu; Pan, Xiaojun; Chen, Minghua; Venzke, Andreas; Low, Steven H.

doi:10.48550/arxiv.2009.03147

Cited by 2 publications

(9 citation statements)

References 13 publications

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“…Though end-to-end methods have been actively studied for constrained optimizations with promising speedups, the lack of feasibility guarantees presents a fundamental barrier for practical application, e.g., infeasibility due to inaccurate active/inactive limits identification. Infeasible solutions from the end-to-end approach are also observed [5], [13], especially considering the DNN worst-case performance under adversary input with serious constraints violations [14], [45], [46]. This echoes the critical challenge of ensuring the DNN solutions feasibility.…”

Section: Related Workmentioning

confidence: 99%

“…For example, existing works belong to the "learn to optimize" field, using RNN to mimic the gradient descent-wise iteration and achieve faster convergence speed empirically [43], [44]. Other works like [6], [7], [13] directly used the DNN model to predict the final solution (regarded as end-to-end method), which can further reduce the computing time compared to the iteration-based approaches. These approaches, in general, can have better speedup performance compared with the hybrid approaches.…”

Section: Related Workmentioning

confidence: 99%

“…These approaches generally depends on the network relaxation with accuracy as the metric. Our work differs significantly from the one in [13] in that our framework provides some fundamental understanding in ensuring DNN solution feasibility for optimization problems, including determining both the inequality constraint calibration magnitude and DNN size necessary for ensuring universal feasibility and deriving the active training scheme considering both optimality and feasibility.…”

Section: Related Workmentioning

confidence: 99%

“…1. The framework first adopts the predict-and-reconstruct idea [6], [7], [13] to guarantee the equality constraints satisfaction by predicting a subset of N − p variables in P and recovering the remaining p ones by solving the linear equations in (2). This way, we not only guarantee equality constraints but also exploit them to reduce the number of variables to be predicted by DNN.…”

Section: A Overview Of the Frameworkmentioning

confidence: 99%

“…This is due to the inherent prediction errors of neural network models. Failing to respect the system physical and operational constraints can be fatal and lead to system instability or incur higher operating cost for the system operator [13]. Existing works address the feasibility concern mainly by incorporating the constraints violation (e.g., a penalty function of the dual variables corresponding to the constraints) into the loss function to guide the neural network training.…”

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confidence: 99%

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Ensuring DNN Solution Feasibility for Optimization Problems with Convex Constraints and Its Application to DC Optimal Power Flow Problems

Zhao¹,

Peng²,

Chen³

et al. 2021

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Ensuring solution feasibility is a key challenge in developing Deep Neural Network (DNN) schemes for solving constrained optimization problems, due to inherent DNN prediction errors. In this paper, we propose a "preventive learning" framework to systematically guarantee DNN solution feasibility for problems with convex constraints and general objective functions. We first apply a predict-and-reconstruct design to not only guarantee equality constraints but also exploit them to reduce the number of variables to be predicted by DNN. Then, as a key methodological contribution, we systematically calibrate inequality constraints used in DNN training, thereby anticipating prediction errors and ensuring the resulting solutions remain feasible. We characterize the calibration magnitudes and the DNN size sufficient for ensuring universal feasibility. We propose a new Adversary-Sample Aware training algorithm to improve DNN's optimality performance without sacrificing feasibility guarantee. Overall, the framework provides two DNNs. The first one from characterizing the sufficient DNN size can guarantee universal feasibility while the other from the proposed training algorithm further improves optimality and maintains DNN's universal feasibility simultaneously. We apply the preventive learning framework to develop DeepOPF+ for solving the essential DC optimal power flow problem in grid operation. It improves over existing DNN-based schemes in ensuring feasibility and attaining consistent desirable speedup performance in both light-load and heavy-load regimes. Simulation results over IEEE Case-30/118/300 test cases show that DeepOPF+ generates 100% feasible solutions with <0.5% optimality loss and up to two orders of magnitude computational speedup, as compared to a state-of-the-art iterative solver. I. INTRODUCTIONRecently, there have been increasing interests in developing neural network schemes, including those based on deep neural networks (DNN), to solve constrained optimization problems in various problem domains, especially those needed to be solved repeatedly in real-time. The idea behind these machine learning approaches is to leverage the universal approximation capability of DNNs [1]- [3] to learn the mapping between the input parameters to the

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: A Overview Of the Frameworkmentioning

confidence: 99%

mentioning

confidence: 99%

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Ensuring DNN Solution Feasibility for Optimization Problems with Convex Constraints and Its Application to DC Optimal Power Flow Problems

Zhao¹,

Peng²,

Chen³

et al. 2021

Preprint

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Learning to Solve AC Optimal Power Flow by Differentiating through Holomorphic Embeddings

Lange,

Chen,

Berges

et al. 2020

Preprint

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Alternating current optimal power flow (AC-OPF) is one of the fundamental problems in power systems operation. AC-OPF is traditionally cast as a constrained optimization problem that seeks optimal generation set points whilst fulfilling a set of non-linear equality constraints -the power flow equations. With increasing penetration of renewable generation, grid operators need to solve larger problems at shorter intervals. This motivates the research interest in learning OPF solutions with neural networks, which have fast inference time and is potentially scalable to large networks. The main difficulty in solving the AC-OPF problem lies in dealing with this equality constraint that has spurious roots, i.e. there are assignments of voltages that fulfill the power flow equations that however are not physically realizable. This property renders any method relying on projected-gradients brittle because these non-physical roots can act as attractors. In this paper, we show efficient strategies that circumvent this problem by differentiating through the operations of a power flow solver that embeds the power flow equations into a holomorphic function. The resulting learningbased approach is validated experimentally on a 200-bus system and we show that, after training, the learned agent produces optimized power flow solutions reliably and fast. Specifically, we report a 12x increase in speed and a 40% increase in robustness compared to a traditional solver. To the best of our knowledge, this approach constitutes the first learning-based approach that successfully respects the full non-linear AC-OPF equations.

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DeepOPF+: A Deep Neural Network Approach for DC Optimal Power Flow for Ensuring Feasibility

Cited by 2 publications

References 13 publications

Ensuring DNN Solution Feasibility for Optimization Problems with Convex Constraints and Its Application to DC Optimal Power Flow Problems

Ensuring DNN Solution Feasibility for Optimization Problems with Convex Constraints and Its Application to DC Optimal Power Flow Problems

Learning to Solve AC Optimal Power Flow by Differentiating through Holomorphic Embeddings

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