AC optimal power flow (AC-OPF) problems need to be solved more frequently in the future to maintain stable and economic power system operation. To tackle this challenge, a deep neural network-based voltage-constrained approach (DeepOPF-V) is proposed to solve AC-OPF problems with high computational efficiency. Its unique design predicts voltages of all buses and then uses them to reconstruct the remaining variables without solving non-linear AC power flow equations. A fast post-processing process is also developed to enforce the box constraints. The effectiveness of DeepOPF-V is validated by simulations on IEEE 118/300-bus systems and a 2000-bus test system. Compared with existing studies, DeepOPF-V achieves decent computation speedup up to four orders of magnitude and comparable performance in optimality gap, while preserving feasibility of the solution.

Distributed generator (DG) volatility has a great impact on system operation, which should be considered beforehand due to the slow time scale of distribution network reconfiguration (DNR). However, it is difficult to derive accurate probability distributions (PDs) for DG outputs and loads analytically. To remove the assumptions on accurate PD knowledge, a deep neural network is first devised to learn the reference joint PD from historical data in an adaptive way. The reference PD along with the forecast errors are enveloped by a distributional ambiguity set using Kullback-Leibler divergence. Then a distributionally robust model for three-phase unbalanced DNR is proposed to obtain the optimal configuration under the worst-case PD of DG outputs and loads within the ambiguity set. The result inherits the advantages of stochastic optimization and robust optimization. Finally, a modified column-and-constraint generation method with efficient scenario decomposition is investigated to solve this model. Numerical tests are carried out using an IEEE unbalanced benchmark and a practical-scale system in Shandong, China. Comparison with the deterministic, stochastic and robust DNR methods validates the effectiveness of the proposed method.

The rapid growth of renewables and dynamic loads has highlighted the short-term voltage stability (STVS) issue in distribution network operation. With the advances in metering, communication and control technologies, deep learning-based distribution network reconfiguration (DNR) becomes available to maintain secure and economic system operation. However, STVS is traditionally evaluated for a specific network topology using time-domain simulations, which cannot be expressed explicitly as a function for optimization, making it intractable to consider STVS in DNR. In this paper, an efficient deep learning-based method is proposed to address this issue. An STVS evaluation network is customized from deep convolution neural networks (CNNs) and trained to learn the relationship between network topology and STVS performance from historical data. To find the optimal topology, a well-trained evaluation network is applied in DNR, where STVS with various network topologies is evaluated without resorting to time-domain simulations. Then, the number of candidate topologies is significantly reduced by a threshold of STVS performance, which enables the direct solution of the DNR for STVS enhancement. The application of the proposed method in large-scale systems is also discussed via integration with heuristic algorithms. Case studies of a modified 69-bus distribution system and a real large-scale distribution system validate the necessity of considering STVS enhancement in DNR and the effectiveness of the proposed solution method.

Multi-microgrids (MMGs) are emerging as a cost-effective solution to provide ancillary services. To reconcile external reserve provision and internal risk hedging for MMGs, a novel comprehensive multi-area dynamic optimal power flow (MADOPF) model is established, where energy-reserve co-optimization, three-phase unbalanced network intrinsics and dual control time-scales are all addressed. To better hedge the uncertainties of distributed generation and loads, distributionally robust model predictive control (MPC) is applied to the MADOPF problem. To preserve operational independence and information privacy for each microgrid, decomposition of the nonconvex model is devised with guaranteed convergence. Numerical tests on a two-area system and a real large-scale 16-area system derived from Shandong Power Grid validate the effectiveness of the proposed method. The advantages are demonstrated by the comparison with the conventional MPC, stochastic and robust methods.

With the increasing penetration of renewables, AC optimal power flow (AC-OPF) problems need to be solved more frequently for reliable and economic power system operation. Supervised learning approaches have been developed to solve AC-OPF problems fast and accurately. However, due to the non-convexity of AC-OPF problems, it is non-trivial and computationally expensive to prepare a large training dataset, and multiple load-solution mappings may exist to impair learning even if the dataset is available. In this paper, we develop an unsupervised learning approach ( $\mathsf{DeepOPF-NGT}$ ) that does not require ground truths. $\mathsf{DeepOPF-NGT}$ utilizes a properly designed loss function to guide neural networks in directly learning a legitimate load-solution mapping. Kron reduction is used to remove the zero-injection buses from the prediction. To tackle the unbalanced gradient pathologies known to deteriorate the learning performance, we develop an adaptive learning rate algorithm to dynamically balance the gradient contributions from different loss terms during training. Further, we derive conditions for unsupervised learning to learn a legitimate load-solution mapping and avoid the multiple mapping issue in supervised learning. Results of the 39/118/300 /1354-bus systems show that $\mathsf{DeepOPF-NGT}$ achieves optimality, feasibility, and speedup performance comparable to the state-of-the-art supervised approaches and better than the unsupervised ones, and a few ground truths can further improve its performance.

Power distribution networks are approaching their voltage stability boundaries due to the severe voltage violations and the inadequate reactive power reserves caused by the increasing renewable generations and dynamic loads. In the broad endeavor to resolve this concern, we focus on enhancing voltage stability through stochastic distribution network reconfiguration (SDNR), which optimizes the (radial) topology of a distribution network under uncertain generations and loads. We propose a deep learning method to solve this computationally challenging problem. Specifically, we build a convolutional neural network model to predict the relevant voltage stability index from the SDNR decisions. Then we integrate this prediction model into successive branch reduction algorithms to reconfigure a radial network with optimized performance in terms of power loss reduction and voltage stability enhancement. Numerical results on two IEEE network models verify the significance of enhancing voltage stability through SDNR and the computational efficiency of the proposed method.