# Optimizing CNN-LSTM for the Localization of False Data Injection Attacks in Power Systems
## 1 Introduction  
With the rapid advancement of information technology, the degree of information in power systems is continuously improving, offering numerous conveniences and opportunities to the power industry. Power systems comprise both a physical and an information system. The integration of information and physical systems represents the long-term developmental trajectory of power systems. Following the deep integration of these systems, failures in the information system and network attacks will not only disrupt the information system's function but also pose additional risks to the physical system, endangering its secure operation [1]. As power systems are critical national infrastructure and key drivers of economic and social progress, any cyber attacks on them would not only jeopardize their safe and stable operation but also result in significant economic losses and potentially disrupt normal social functions, thereby endangering personal safety [2]. The false data injection attack (FDIA) is one of the common cyber attacks in power systems, first proposed by [PERSON] et al. in 2009 [3]. The attacker constructs false measurement values that can bypass bad data detection and mislead the system's state estimation by tampering, deleting, or forging measurement data, thereby disrupting the system control and interfering with its normal operation. Therefore, designing an effective FDIA detection and localization method to promptly identify the attacked data, respond quickly to attacks, and mitigate their impact is of great significance for ensuring the secure and stable operation of power systems. Since [PERSON] et al. first introduced the concept of FDIA, numerous researchers have developed a spectrum of detection methodologies, predominantly categorized into model-based [4; 5] and data-driven approaches [6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16]. The model-driven method does not need the training of historical data sets and can build the FDIA detection model only by the relationship between the measured data and the system state. However, the accuracy of this detection can be significantly swayed by the system parameters, and the ongoing expansion of power grids invariably amplifies the model complexity. Conversely, data-driven FDIA detection algorithms bypass the need for parameter tuning, focusing instead on the volume of available data. With an abundance of power system data acting as a robust foundation, these algorithms are garnering increasing attention. For example, to capture the spatial difference between false data and normal data, the literature [6; 7; 8] employs the multi-layered structure of convolutional neural networks (CNNs) to extract spatial features from measured data, which is then integrated with bad data detection for identifying FDIAs. Addressing the challenge of hyperparameter selection inherent in CNNs when localizing faults within power systems, such as the size of convolutional kernels and the number of convolutional layers, the literature [9] introduces the sparrow search algorithm (SSA). It proposes an SSA-augmented CNN optimization method to tackle the intricate issue of CNN hyperparameter tuning, thereby enhancing detection accuracy. To capture the temporal characteristics of power grid measurement data during the FDIA process, the literature [10; 11] leverages the robust memory capabilities of long short-term memory (LSTM) networks in time series prediction to identify potentially compromised measurement values. In order to effectively capture the dependency between the nodes of the power systems and consider the spatial correlation of various measurement devices, the literature [12; 13] proposes employing graph neural networks (GNNs) to extract spatial features of the measurement data through the power system's inherent graph topology and identify FDIAs.