## 1 Introduction  
The use of machine learning techniques in power systems research has been an increasing trend in recent years due to the transition to the Smart Grid (SG). As utility companies move towards SG implementation, the new technology being used will provide more data to be analyzed. This is a natural fit for the integration of machine learning techniques into the power systems field. One area in particular that can take advantage of machine learning is cyber-physical security of the SG. Besides all of the benefits that come with the transition to the SG, the increasing reliance on communication, automation and information technology systems adds vulnerability to cyber-security threats [1, 2, 3, 4, 5, 6, 7]. Cyber-attacks have already been successfully executed with major consequences. In Ukraine, a cyber-attack led to a major blackout that impacted 225,000 customers [8]. This draws a lot of awareness from academic circle and industrial practitioners which fueled research in the cyber-security of the power grid, including solutions based on machine learning techniques. When considering cyber-security of the SG monitoring systems, a critical process is the state estimation (SE), which is the core real-time monitoring tool used by utility companies. SE analyzes measurements from throughout the system to estimate the voltages of each bus. The results of SE are then used in many applications, including bad data analysis, which can be used to detect and identify a variety of different potential cyber-attacks on the SG. However, most research only focuses on false data injection (FDI) attacks on measurements used in SE. Further, research that involves machine learning so far focuses on either creating more accurate SE results or aiding in the detection of measurement FDI attacks [9; 10; 11; 12; 13; 14; 15; 16]. In the authors' previous works [17; 18], hybrid data-driven and physics-based methods for anomaly detection on the SG are developed, but they still only deal with measurement FDI attacks. On the other hand, there is no real-time monitoring for these network parameters which are used in SE process. The database of network parameters can be stealthily attacked [19; 20] or can be corrupted due to several reasons such as human entry error or failure to update replaced equipment parameters etc. Therefore, inaccuracy in the database information may lead system operators to blame errors in the SE results on measurements accuracy. Hence, the quality of SE solution can be severely impacted due to these two main sources: measurement or network parameter errors. In the literature though, the work on addressing network parameter FDI is seldom covered as measurements, giving that both sources of cyber-attacks can greatly impact the SE. Bad data processing is an important sub-routine function which mainly aims to detect, identify and correct measurement errors in SE. Different from tampering the sensor measurements, the database of network parameters is stored at a control center, and as previously stated, are not monitored. These are ideal conditions for maliciously adversaries, which might attempt to modify the network parameters database with the intent to change state estimation results. There are several methods developed to detect, identify and correct errors pertaining to network parameters. The aim in this work pertains though to model parameter FDI correction in bad data processing. Regarding parameter errors processing, in [21], the author uses an augmented state vector-based approach. Similarly, refs. [2; 22; 23; 24; 25; 26] all depend heavily on high measurement redundancy, since they are based on the state vector augmentation approach. Considering stealthy parameter FDI, this can easily lead to observability issues in the SE. Still, these approaches cannot handle multiple simultaneous attacks. In previous works of the authors, parameter FDI cyber-attack correction models have been presented [19; 27; 28].