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

Abstract

Deep Neural Networks (DNNs) approaches for the Optimal Power Flow (OPF) problem received considerable attention recently. A key challenge of these approaches lies in ensuring the feasibility of the predicted solutions to physical system constraints. Due to the inherent approximation errors, the solutions predicted by DNNs may violate the operating constraints, e.g., the transmission line capacities, limiting their applicability in practice. To address this challenge, we develop DeepOPF+ as a DNN approach based on the so-called "preventive" framework. Specifically, we calibrate the generation and transmission line limits used in the DNN training, thereby anticipating approximation errors and ensuring that the resulting predicted solutions remain feasible. We theoretically characterize the calibration magnitude necessary for ensuring universal feasibility. Our DeepOPF+ approach improves over existing DNN-based schemes in that it ensures feasibility and achieves a consistent speed up performance in both light-load and heavy-load regimes. Detailed simulation results on a range of test instances show that the proposed DeepOPF+ generates 100% feasible solutions with minor optimality loss. Meanwhile, it achieves a computational speedup of two orders of magnitude compared to state-of-the-art solvers. NOMENCLATUREVariable Definition N Set of buses, N |N |. G Set of generators. D Set of loads. E Set of branches. PG Power generation injection vector, [PG i , i ∈ N ]. P min G Minimum generator output vector, [P min G i , i ∈ N ]. P max G Maximum generator output vector, [P max G i , i ∈ N ]. PD Power load vector, [PD i , i ∈ N ]. Θ Voltage angle vector. θi Voltage angle for bus i. B Admittance matrix. xijLine reactance from bus i to j. P max T ij Line transmission limit from bus i to j. NhidThe number of hidden layers in the neural network.

Unsupervised deep learning with convolutional neural networks for static parallel transmit design: A retrospective study

“…However, power or SAR constraints are substantially more difficult. To the best of our knowledge, inclusion of hard quadratic constraints with DL methods is an open question, although progress has been made in the broader artificial intelligence community 38–43 . One step in this direction would be to use a soft constraint on power or SAR by incorporating an additional term into the loss function.…”

“…To the best of our knowledge, inclusion of hard quadratic constraints with DL methods is an open question, although progress has been made in the broader artificial intelligence community. [38][39][40][41][42][43] One step in this direction would be to use a soft constraint on power or SAR by incorporating an additional term into the loss function. However, the performance and robustness will substantially depend on tuning the weight for this soft constraint term.…”

Low and Medium Voltage Distribution Network Planning with Distributed Energy Resources: A Survey

“…Then, post-processing is performed to ensure that the solution is feasible. An upgraded version of Deep-OPF is proposed in [162]. This method can achieve a computational speedup by two orders of magnitude compared to conventional solvers with minor optimality loss.…”

A Sample-Efficient OPF Learning Method Based on Annealing Knowledge Distillation

“…The researchers are currently interested in a model-free method based on deep learning, which seeks a function automatically to fit the abstract relationship between power demand and power dispatch. In [5]- [11], load variables are widely used as input features, while power generations and phase angles are considered as output variables. Other unchangeable factors can be contained in network parameters and thus excluded from the input features.…”