Optimal Power Flow Calculation Based on a Trustworthy Deep Neural Network
Ran Qingyue1, Lin Wei2, Yang Zhifang1, Yu Juan1
1. State Key Laboratory of Power Transmission Equipment Technology Chongqing University Chongqing 400044 China; 2. Department of Electrical and Electronic Engineering The Hong Kong Polytechnic University HKSAR 999077 China
Abstract To conduct the optimal power flow (OPF) for resource allocation and system analysis within small time resolutions in renewable power systems, deep neural network-based (DNN-based) optimal power flow calculation methods have gained much attention. Nevertheless, since DNNs possess a black-box nature, the existing methods generally rely on limited training and testing sets for DNNs in the training and evaluation process. This makes difficulties in theoretically quantifying computational errors, and lacks the theoretical support for their trustworthiness. Consequently, this paper proposes an optimal power flow calculation method based on a trustworthy DNN. First, this paper focuses on the theoretical quantitative evaluation of mapping errors in DNNs and introduces a trustworthy DNN training model based on a bi-level min-max programming problem, enabling a training process with trustworthiness quantifications. Furthermore, based on the KKT conditions and the analytical representation of activation functions, this paper explicitly reformulates the proposed model as a bi-level programming problem by introducing integer variables, followed by developing an exact solution strategy based on Danskin's theorem. Moreover, this paper proposes a fast approximate solution strategy using convex relaxation and pattern recognition to alleviate the computational burden of integer variables. Numerical experiments in a 4-bus test system showcase: (1) Compared with existing methods, the proposed trustworthy DNN training model solved by our exact solution strategy can more accurately quantify the trustworthiness of DNNs. The mapping error evaluated based on a limited testing set (in existing methods) is smaller than that based on the proposed trustworthy DNN model (in the proposed method), even if the sample number in the testing set has been set to 1×104. (2) The mapping error of DNNs which are trained based on existing methods can reach up to 0.022 0(pu), while the mapping error of the proposed method is only 0.001 9(pu). Numerical experiments in the IEEE 118-bus system further verify: (1) Compared with existing methods, the average maximum mapping error of generation levels can decrease from 0.502 6(pu) to 0.120 5(pu) once the proposed trustworthy DNN training model and our solved by our fast approximate solution strategy with convex relaxation. (2) When pattern recognition is additionally added in our fast approximate solution strategy, the average maximum mapping error can decrease to 0.062 8(pu). Compared with the exact solution strategy which cannot complete one solution iteration within 1 440 minutes, the computational time of our fast approximate solution strategy with convex relaxation and pattern recognition can decrease to 25 minutes. These observations indicate the synergic combination of the proposed trustworthy DNN training model and the fast approximation solution strategy can contribute to improving the trustworthiness of a DNN with improved computational efficiency. The following conclusions can be drawn from this paper: (1) The proposed trustworthy DNN training model can theoretically quantify the computational performance of DNNs. This distinguishes us from existing methods, which quantify the computational performance of DNNs using limited testing sets, by paving a promising way for precise quantification of the trustworthiness for DNN-based OPF calculations. Furthermore, the proposed model can be exactly solved using our gradient-descent method based on Danskin's theorem. (2) Our fast approximate solution strategy, which considers convex relaxation and pattern recognition, can alleviate the computational burden of integer variables involved in our previous exact solution strategy, while still maintaining the direction of updating DNN parameters toward improved trustworthiness.
Ran Qingyue,Lin Wei,Yang Zhifang等. Optimal Power Flow Calculation Based on a Trustworthy Deep Neural Network[J]. Transactions of China Electrotechnical Society, 2024, 39(21): 6687-6699.
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2024, Vol. 39 
