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Register a new userLearning to Solve AC Optimal Power Flow by Differentiating through Holomorphic Embeddings
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Added by
Henning Lange
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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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 learning-based 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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Recently, there has been a surge of interest in adopting deep neural networks (DNNs) for solving the optimal power flow (OPF) problem in power systems. Computing optimal generation dispatch decisions using a trained DNN takes significantly less time when compared to using conventional optimization solvers. However, a major drawback of existing work is that the machine learning models are trained for a specific system topology. Hence, the DNN predictions are only useful as long as the system topology remains unchanged. Changes to the system topology (initiated by the system operator) would require retraining the DNN, which incurs significant training overhead and requires an extensive amount of training data (corresponding to the new system topology). To overcome this drawback, we propose a DNN-based OPF predictor that is trained using a meta-learning (MTL) approach. The key idea behind this approach is to find a common initialization vector that enables fast training for any system topology. The developed OPF-predictor is validated through simulations using benchmark IEEE bus systems. The results show that the MTL approach achieves significant training speeds-ups and requires only a few gradient steps with a few data samples to achieve high OPF prediction accuracy.
We explore machine learning methods for AC Optimal Powerflow (ACOPF) - the task of optimizing power generation in a transmission network according while respecting physical and engineering constraints. We present two formulations of ACOPF as a machine learning problem: 1) an end-to-end prediction task where we directly predict the optimal generator settings, and 2) a constraint prediction task where we predict the set of active constraints in the optimal solution. We validate these approaches on two benchmark grids.
The existence of multiple solutions to AC optimal power flow (ACOPF) problems has been noted for decades. Existing solvers are generally successful in finding local solutions, which satisfy first and second order optimality conditions, but may not be globally optimal. In this paper, we propose a simple iterative approach to improve the quality of solutions to ACOPF problems. First, we call an existing solver for the ACOPF problem. From the solution and the associated dual variables, we form a partial Lagrangian. Then we optimize this partial Lagrangian and use its solution as a warm start to call the solver again for the ACOPF problem. By repeating this process, we can iteratively improve the solution quality, moving from local solutions to global ones. We show the effectiveness of our algorithm on standard IEEE networks. The simulation results show that our algorithm can escape from local solutions to achieve global optimums within a few iterations.
This chapter presents recent solutions to the optimal power flow (OPF) problem in the presence of renewable energy sources (RES), {such} as solar photo-voltaic and wind generation. After introducing the original formulation of the problem, arising from the combination of economic dispatch and power flow, we provide a brief overview of the different solution methods proposed in the literature to solve it. Then, we explain the main difficulties arising from the increasing RES penetration, and the ensuing necessity of deriving robust solutions. Finally, we present the state-of-the-art techniques, with a special focus on recent methods we developed, based on the application on randomization-based methodologies.
Optimal power flow (OPF) is the fundamental mathematical model in power system operations. Improving the solution quality of OPF provide huge economic and engineering benefits. The convex reformulation of the original nonconvex alternating current OPF (ACOPF) model gives an efficient way to find the global optimal solution of ACOPF but suffers from the relaxation gaps. The existence of relaxation gaps hinders the practical application of convex OPF due to the AC-infeasibility problem. We evaluate and improve the tightness of the convex ACOPF model in this paper. Various power networks and nodal loads are considered in the evaluation. A unified evaluation framework is implemented in Julia programming language. This evaluation shows the sensitivity of the relaxation gap and helps to benchmark the proposed tightness reinforcement approach (TRA). The proposed TRA is based on the penalty function method which penalizes the power loss relaxation in the objective function of the convex ACOPF model. A heuristic penalty algorithm is proposed to find the proper penalty parameter of the TRA. Numerical results show relaxation gaps exist in test cases especially for large-scale power networks under low nodal power loads. TRA is effective to reduce the relaxation gap of the convex ACOPF model.
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