DeepOPF: Deep Neural Network for DC Optimal Power Flow

Abstract

We develop DeepOPF as a Deep Neural Network (DNN) approach for solving security-constrained direct current optimal power flow (SC-DCOPF) problems, which are critical for reliable and cost-effective power system operation. DeepOPF is inspired by the observation that solving the SC-DCOPF problem for a given power network is equivalent to depicting a highdimensional mapping between load inputs and generation and phase-angle outputs. We first construct and train a DNN to learn the mapping between the load inputs and the generations. We then directly compute the phase angles from the generations and loads by using the (linearized) power flow equations. Such a two-step procedure significantly reduces the dimension of the mapping to learn, subsequently cutting down the size of the DNN and the amount of training data/time needed. We further characterize a condition that allows us to tune the size of our neural network according to the desired approximation accuracy of the load-to-generation mapping. Simulation results of IEEE test cases show that DeepOPF always generates feasible solutions with negligible optimality loss, while speeding up the computing time by up to 400x as compared to a state-of-the-art solver.1 There are two types of SC-DCOPF problems, namely the preventive SC-DCOPF problem and the corrective SC-DCOPF problem. In the preventive SC-DCOPF problem, the system operating decisions cannot change once they are determined, thus they need to guarantee feasibility under both the preand post-contingency constraints. For the corrective SC-DCOPF problem, the system operator can have a short time (e.g., 5 minutes) [12] to adjust the operating points after the occurrence of each contingency. Our DeepOPF approach is applicable to both problems. We focus on the preventive SC-DCOPF problem in this paper for easy illustration.

Recent Developments in Machine Learning for Energy Systems Reliability Management

“…More recently, several papers proposed to exploit Deep Learning (DL) for this purpose. Pan et al [153] use deep learning to predict the decision of a DC-OPF while in [154], [155] the authors predict the decision of an AC-OPF. In all these papers a post-processing method ensuring the feasibility of the solution is described.…”

“…In all these papers a post-processing method ensuring the feasibility of the solution is described. In [153], if the predicted solution is not feasible, the authors solve an optimisation problem to find the feasible solution closest to the predicted one. In [155], the output of the DL model is constrained with a sigmoid function to adhere to active power generation and voltage magnitude constraints and a power flow problem is then solved based on the predictions.…”

A Data-driven Method for Fast AC Optimal Power Flow Solutions via Deep Reinforcement Learning

“…Two other important concepts of RL are state-value and action-value functions as defined in (9) and (10), respectively.…”

“…In [9], a graph neural network (NN) has been applied to approximate the solutions of PF solvers. Deep NNs (DNN) are similarly utilized to solve the DC OPF [10], [11] and AC OPF problems [12], [13]. A commonality among all these methods is that they primarily depend on supervised learning techniques to train the NNs while using massive simulations that must be obtained ahead of time for approximating optimal solutions.…”

Real-Time Optimal Power Flow Using Twin Delayed Deep Deterministic Policy Gradient Algorithm

“…As such, it is a challenging task to obtain general real-time ACOPF solutions from existing algorithms. Therefore, ACOPF solutions with DNN (Deep Neural Network) and DRL (Deep Reinforcement Learning) were introduced to speed up the calculation process [6], [7], [8]. It has been noted that DNN and DRL approaches can solve the ACOPF problem of complex, larger dimensions, and continuous state space.…”