An Explainable Deep Learning Method For Power Flow Linearization

Linear power flow model is widely used in scenarios such as economic scheduling,planning optimization,and static safety analysis.In order to reduce the error of the linear power flow model,a deep neural network based on the dual drive of "data mechanism" is designed to capture the correlation between the operating state and the linearization map.From the perspective of function approximation theory,the neural network approximation function avoids two difficult problems existing in polynomial approximation functions,so this thesis uses deep neural networks to approximate the linearization coefficient of linear power flow model,which is superior in principle to using polynomial approximation linearization coefficient.On the basis of summarizing the existing linear power flow model,this thesis constructs a general linear power flow model,and summarizes and proves the three characteristics of the linear power flow model in the linearization process.Inspired by the physical information neural network,this thesis embeds the constructed linear power flow model into the deep neural network,and uses two methods,soft punishment and hard constraint,to integrate the three characteristics of the linear power flow model into the deep neural network and guide the output of the deep neural network.Thus,interpretable deep neural networks that are physically reasonable,mathematically accurate,computationally stable and efficient are constructed.In order to solve the problem of difficulty in weight adjustment using the mechanism guidance method using soft punishment,this thesis proposes to use the hard constraint method to embed the mechanism into the deep neural network,which accelerates the model convergence speed and limits the maximum error of the linear power flow model by limiting the output range of the deep neural network,further enhancing the reliability and practicality of the model,and meeting the reliability requirements of the power system.In order to maintain high linearization accuracy under the condition of changing the operating state of the power system and the network topology,the constructed deep neural network can still maintain high linearization accuracy.Based on mathematical derivation and power system mechanism,this thesis selects the feature vectors embedded in the network topology.Due to the mechanism embedded in deep neural networks,general data preprocessing methods are no longer applicable,and this thesis designs targeted data preprocessing methods,which not only do not change the mechanism of embedding models,but also accelerate the training speed of models and prevent the phenomenon of information annihilation.A case study was carried out on the IEEE118 and IEEE33 systems.The accuracy of the constructed linear power flow model is verified in the IEEE118 node system.Validate the model’s ability to cope with topology changes in IEEE33 node system;The model trained on IEEE118 node is migrated to the IEEE33 node system to verify the portability of the model.The model is trained using 2000 samples to verify the linearization accuracy of the model under small-sample training.Finally,the node linearization of 30 nodes of the IEEE118 node system is carried out to verify the linearization accuracy of the model nodes.