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Register a new userFast Calculation of Probabilistic Optimal Power Flow: A Deep Learning Approach
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Probabilistic optimal power flow (POPF) is an important analytical tool to ensure the secure and economic operation of power systems. POPF needs to solve enormous nonlinear and nonconvex optimization problems. The huge computational burden has become the major bottleneck for the practical application. This paper presents a deep learning approach to solve the POPF problem efficiently and accurately. Taking advantage of the deep structure and reconstructive strategy of stacked denoising auto encoders (SDAE), a SDAE-based optimal power flow (OPF) is developed to extract the high-level nonlinear correlations between the system operating condition and the OPF solution. A training process is designed to learn the feature of POPF. The trained SDAE network can be utilized to conveniently calculate the OPF solution of random samples generated by Monte-Carlo simulation (MCS) without the need of optimization. A modified IEEE 118-bus power system is simulated to demonstrate the effectiveness of the proposed method.
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The AC Optimal Power Flow (AC-OPF) is a key building block in many power system applications. It determines generator setpoints at minimal cost that meet the power demands while satisfying the underlying physical and operational constraints. It is non-convex and NP-hard, and computationally challenging for large-scale power systems. Motivated by the increased stochasticity in generation schedules and increasing penetration of renewable sources, this paper explores a deep learning approach to deliver highly efficient and accurate approximations to the AC-OPF. In particular, the paper proposes an integration of deep neural networks and Lagrangian duality to capture the physical and operational constraints. The resulting model, called OPF-DNN, is evaluated on real case studies from the French transmission system, with up to 3,400 buses and 4,500 lines. Computational results show that OPF-DNN produces highly accurate AC-OPF approximations whose costs are within 0.01% of optimality. OPF-DNN generates, in milliseconds, solutions that capture the problem constraints with high fidelity.
Scenario reduction is an important topic in stochastic programming problems. Due to the random behavior of load and renewable energy, stochastic programming becomes a useful technique to optimize power systems. Thus, scenario reduction gets more attentions in recent years. Many scenario reduction methods have been proposed to reduce the scenario set in a fast speed. However, the speed of scenario reduction is still very slow, in which it takes at least several seconds to several minutes to finish the reduction. This limitation of speed prevents stochastic programming to be implemented in real-time optimal control problems. In this paper, a fast scenario reduction method based on deep learning is proposed to solve this problem. Inspired by the deep learning based image process, recognition and generation methods, the scenario data are transformed into a 2D image-like data and then to be fed into a deep convolutional neural network (DCNN). The output of the DCNN will be an image of the reduced scenario set. Since images can be processed in a very high speed by neural networks, the scenario reduction by neural network can also be very fast. The results of the simulation show that the scenario reduction with the proposed DCNN method can be completed in very high speed.
This paper introduces for the first time a framework to obtain provable worst-case guarantees for neural network performance, using learning for optimal power flow (OPF) problems as a guiding example. Neural networks have the potential to substantially reduce the computing time of OPF solutions. However, the lack of guarantees for their worst-case performance remains a major barrier for their adoption in practice. This work aims to remove this barrier. We formulate mixed-integer linear programs to obtain worst-case guarantees for neural network predictions related to (i) maximum constraint violations, (ii) maximum distances between predicted and optimal decision variables, and (iii) maximum sub-optimality. We demonstrate our methods on a range of PGLib-OPF networks up to 300 buses. We show that the worst-case guarantees can be up to one order of magnitude larger than the empirical lower bounds calculated with conventional methods. More importantly, we show that the worst-case predictions appear at the boundaries of the training input domain, and we demonstrate how we can systematically reduce the worst-case guarantees by training on a larger input domain than the domain they are evaluated on.
An equivalent circuit formulation for power system analysis was demonstrated to improve robustness of Power Flow and enable more generalized modeling, including that for RTUs (Remote Terminal Units) and PMUs (Phasor Measurement Units). These measurement device models, together with an adjoint circuit based optimization framework, enable an alternative formulation to Power System State Estimation (SE) that can be solved within the equivalent circuit formulation. In this paper, we utilize a linear RTU model to create a fully linear SE algorithm that includes PMU and RTU measurements to enable a probabilistic approach to SE. Results demonstrate that this is a practical approach that is well suited for real-world applications.
The stochastic and dynamic nature of renewable energy sources and power electronic devices are creating unique challenges for modern power systems. One such challenge is that the conventional mathematical systems models-based optimal active power dispatch (OAPD) method is limited in its ability to handle uncertainties caused by renewables and other system contingencies. In this paper, a deep reinforcement learning-based (DRL) method is presented to provide a near-optimal solution to the OAPD problem without system modeling. The DRL agent undergoes offline training, based on which, it is able to obtain the OAPD points under unseen scenarios, e.g., different load patterns. The DRL-based OAPD method is tested on the IEEE 14-bus system, thereby validating its feasibility to solve the OAPD problem. Its utility is further confirmed in that it can be leveraged as a key component for solving future model-free AC-OPF problems.
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