DeepOPF: A Feasibility-Optimized Deep Neural Network Approach for AC Optimal Power Flow Problems

Abstract

The AC-OPF problem is the key and challenging problem in the power system operation. When solving the AC-OPF problem, the feasibility issue is critical. In this paper, we develop an efficient Deep Neural Network (DNN) approach, DeepOPF, to ensure the feasibility of the generated solution. The idea is to train a DNN model to predict a set of independent operating variables, and then to directly compute the remaining dependable variables by solving the AC power flow equations. While this guarantees the power-flow balances, the principal difficulty lies in ensuring that the obtained solutions satisfy the operation limits of generations, voltages, and branch flow. We tackle this hurdle by employing a penalty approach in training the DNN. As the penalty gradients make the common first-order gradient-based algorithms prohibited due to the hardness of obtaining an explicit-form expression of the penalty gradients, we further apply a zero-order optimization technique to design the training algorithm to address the critical issue. The simulation results of the IEEE test case demonstrate the effectiveness of the penalty approach. Also, they show that DeepOPF can speed up the computing time by one order of magnitude compared to a state-of-the-art solver, at the expense of minor optimality loss.

Deep Reinforcement Learning Based Real-time AC Optimal Power Flow Considering Uncertainties

“…However, if the DNN is only trained by adopting (2), the feasibility of the AC OPF problem cannot be guaranteed after running the power flow (PF) solver during online implementation even though the loss is small due to operational security limit violations defined in (1). Although [8] - [10] adopt the penalty function to deal with the feasibility issue, the penalty coefficient needs to be further tuned regarding the training performance. In this paper, the DRL framework is adopted to address the feasibility issue.…”

“…Due to the consideration of system topology information, the input state dimension is two times larger compared with those in [8]- [10]; therefore, to further effectively extract the features from the inputs for the "actor", one convolutional layer from the convolutional neural network (CNN) is utilized first and then connects a fully connected (FC) layer with the following hidden layers shown in Fig. 2.…”

“…there are constraint violations 1000 -0.01Costs gen solutions are feasible (10) where R pg_v , R v_v , and R br_v are shown in (11) corresponding to negative rewards if violations of any inequality constraints are detected, including: ① the active power limits of generators; ② the voltage magnitude limits of buses; and ③ the thermal flow limits (in both directions) of transmission lines. Variable Costs gen in (10) is the total generation cost value of the power system.…”

“…To deal with this issue, [8] and [9] utilize the penalized loss function to capture the operational constraints. Reference [10] adopts the zero-order optimization technique on the IEEE 30-bus system that achieves the feasibility among 98% of the testing data. With the recent success of deep reinforcement learning (DRL) algorithms adopted in power system controls, multiagent Q(λ) learning is implemented to perform OPF tasks under discretized action spaces in [11].…”

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

“…It uses a large amount of historical data to approximate the variable relationship and achieve the real-time response. Compared with traditional solvers, the deep learning approach has a computation speed improvement of up to 200 times for DC-OPF and 35 times for alternating current OPF (AC-OPF) [4], [6]. In addition, the deep learning technique provides a feasible solution to address OPF solving in online settings and state combinations.…”