## 1 Introduction  
Energy management systems (EMSs) play a vital function, serving as the backbone of smart power grids for monitoring, control, and state estimation [1, 2, 3, 4], while Supervisory Control and Data Acquisition (SCADA) systems are crucial for their implementation of monitoring and control [1, 2, 3, 4, 5]. The state of the power system is determined to be the assignment of the phasor voltage quantities, electrical current quantities to branches, and power values to generators and loads. One way to transform the existing power system to a \"modern\" grid is to measure its state in actual time, which requires continuous monitoring [1, 2, 3, 4, 5]. The state of a power network is said to be observed in the case of measuring the state variables, such as the phasors voltage at nodes and phasor currents running in the lines. Sensors are installed at appropriate nodes in the power network to measure the state variables' quantity, which is telemetered to the central control. The electricity companies are required to continually observe the state variables [1, 2, 3, 4, 5, 6]. In order to observe the power network state, phasor measurement units (PMUs) are utilized for gathering data and sending them to the system operator [1; 2; 3; 4]. The power system can be made fully observable by utilizing solely PMUs. In this case, the state estimation formulation is linear and solved without the needed iterative schemes [2; 4; 6]. PMUs are installed at substations and are crucial devices for system operation and control due to the measuring of the phasor voltages and phasor currents running the transmission lines. Global time reference can accurately measure these types of phasors, even from remote physical locations within a designated power system [1; 2; 3; 4; 5; 6]. Traditionally, state estimation (SE) is implemented using the SCADA system, whereas with the utilization of PMUs, hybrid state estimators based on SCADA-PMU and linear state estimators based on PMUs have emerged [2; 3; 4; 6]. SE is the most significant tool of the EMS, giving the transmission system operator an actual-time understanding of the current operation [2; 3; 4; 6]. In these circumstances, SE helps the system operator maintain the power grid to be reliable, secure, and economical in its service [1; 2; 3; 4; 6]. Furthermore, SE supports the monitoring and control application in the EMS [1; 2; 3; 4; 6]. SE procedures have undergone a great improvement since the introduction of the PMU [1; 2; 3; 4; 6]. The literature illustrates different methods to implement and solve the state estimation application [2; 3; 4; 6]. The SE model is classified as static or dynamic [1; 2; 3; 4; 6]. State estimation models based on a limited PMU number were recently presented in [2; 3; 4; 6]. The static algorithm principally relies on a WLS algorithm, utilizing data calculated at a given time [2; 3; 4; 6]. By comparison, a SE model based on a dynamic response and Kalman filter is presented in [6]. Both SE models are based on a mixed set including conventional measurements as well as a limited PMU number [1; 2; 3; 4; 6]. In a modern transmission system, telemetry relies on the SCADA and the wide-area monitoring system (WAMS) [1; 2; 3; 4; 5]. The WAMS is made of PMUs and phasor data concentrators (PDCs) and their communication networks [1; 2; 3; 4; 6]. PMUs play an essential part in the observation of the power transmission network [1; 2; 3; 4; 6]. This fact has caused a paradigm shift in the architecture of power grids, increasing the utilization of PMUs with their installation at selected power grid nodes [1; 2; 3; 4; 6]. PMUs have led to reconsideration of the way the state estimation is executed for reliable monitoring of the power grid state [1; 2; 3; 4; 6]. PMUs comprise the most commonly obtainable vital measurement infrastructures that consider synchro phasor technology [1; 2; 3; 4; 6]. A PMU enables real-time measuring data, which are the phasor voltage of the placing node and the phasor currents running in the branches running from that network bus [1; 2; 3; 4; 6].