摘要
为应对新型电力系统以最优潮流为核心的精细化资源配置与运行分析需求,基于深度神经网络的最优潮流计算方法受到广泛关注。然而深度神经网络具有“黑箱特性”,现有方法普遍仅基于有限训练、测试集进行深度神经网络的训练与评估,难以从理论上量化计算误差,导致可信度缺乏理论保障。为此,该文提出基于可信深度神经网络的最优潮流计算方法。首先,以理论定量评估深度神经网络映射误差为核心,提出基于min-max双层规划问题的深度神经网络可信训练模型,实现深度神经网络的可信度量化训练;然后,基于KKT最优性条件与激活函数解析表征技术,将所提可信训练模型解析构建为以混合整数规划模型为基础的双层规划问题,并提出基于Danskin定理的精确求解策略;最后,提出基于凸松弛技术与模式识别思想的快速近似求解策略以减轻整数变量计算负担。仿真算例表明:所提方法可将基于有限测试集的深度神经网络映射评估精度提升28.73%,可更为精准地量化深度神经网络可信度;相较于基于有限训练集的现有深度神经网络训练方法,该方法可将计算误差减少87.49%,实现更为可信的深度神经网络训练。
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 0.0220(pu),while the mapping error of the proposed method is only 0.0019(pu).Numerical experiments in the IEEE 118-bus sys
作者
冉晴月
林伟
杨知方
余娟
Ran Qingyue;Lin Wei;Yang Zhifang;Yu Juan(State Key Laboratory of Power Transmission Equipment Technology Chongqing University,Chongqing 400044 China;Department of Electrical and Electronic Engineering The Hong Kong Polytechnic University,HKSAR 999077 China)
出处
《电工技术学报》
EI
CSCD
北大核心
2024年第21期6687-6699,共13页
Transactions of China Electrotechnical Society
基金
国家重点研发计划资助项目(2021YFE0191000)。
关键词
新能源
最优潮流
深度神经网络
可信训练
Renewable source
optimal power flow calculation
deep neural network
trustworthy training
