Data Recovery for False Data Injection Attacks of Power Systems Based on Lightweight Variational Convolution Auto-Encoder

Power system state estimation (PSSE) plays a vital role in stable operation of modern smart grids, while it is vulnerable to cyber attacks. False data injection attacks (FDIA), one of the most common cyber attacks, can tamper with measurement data and bypass the bad data detection (BDD) mechanism, leading to incorrect PSSE results. This paper proposes a data recovery framework for FDIA based on variational convolution auto-encoder (VCAE) to ensure continuous monitoring of PSSE. VCAE combines deep learning ideas with Bayesian inference. Besides, VCAE uses convolution and deconvolution operations with excellent feature capture capabilities in the encoder and decoder network, respectively, to effectively restore the abnormal values after FDIA to the values close to normal operation. Moreover, knowledge distillation (KD) is used to compress the VCAE model, making it possible to deploy a lightweight model on equipment with limited resources. Case studies are undertaken on IEEE 14-bus system under different attack intensities and degrees to evaluate the recovery performance of VCAE. Simulation results show that the mean absolute error (MAE) and mean absolute percentage error (MAPE) of VCAE are lower than the comparative generative models. Moreover, the satisfactory recovery performance of IEEE 30-bus and 118-bus systems verifies the scalability of the proposed model. In addition, KD allows the lightweight VCAE scale to reach about one-tenth of the original VCAE scale with almost no increase in MAE and MAPE.

电力系统状态估计（Power system state estimation, PSSE）对于现代智能电网的稳定运行至关重要，但其极易受到网络攻击。虚假数据注入攻击（False data injection attacks, FDIA）作为最常见的网络攻击类型之一，可篡改测量数据并绕过坏数据检测（Bad data detection, BDD）机制，导致电力系统状态估计结果出错。本文提出一种基于变分卷积自编码器（Variational convolution auto-encoder, VCAE）的虚假数据注入攻击数据恢复框架，以保障电力系统状态估计的持续监测。变分卷积自编码器将深度学习思想与贝叶斯推理相结合，其编码器与解码器网络分别采用具备优异特征捕获能力的卷积与反卷积操作，可有效将虚假数据注入攻击后的异常值恢复至接近正常运行的数值。此外，本文采用知识蒸馏（Knowledge distillation, KD）对变分卷积自编码器模型进行压缩，使得在资源受限设备上部署轻量化模型成为可能。本文在不同攻击强度与攻击程度下的IEEE 14节点系统上开展案例研究，以评估变分卷积自编码器的恢复性能。仿真结果表明，变分卷积自编码器的平均绝对误差（Mean absolute error, MAE）与平均绝对百分比误差（Mean absolute percentage error, MAPE）均低于对比生成式模型。此外，在IEEE 30节点与118节点系统上取得的优异恢复性能验证了所提模型的可扩展性。同时，知识蒸馏可将轻量化后的变分卷积自编码器规模压缩至原模型的十分之一左右，且平均绝对误差与平均绝对百分比误差几乎未出现增长。