# Power System State Estimation Approach Considering Transmission Line Temperature
## 1 Introduction  
In recent years, the development of renewable generations and power electronic devices has been accelerated [1, 2]. The outputs of renewable generations are uncertain and fluctuant [3]. In addition, the response velocity of power electronic devices is faster than conventional synchronous generators [4]. With the development of renewable generations and power electronic devices, states of the power system are becoming more complicated and variable. The estimation of power system states is necessary under both the normal operation and contingencies [5, 6]. Therefore, it is necessary to attain power system states for the security and economic operation. State estimation (SE) serves as an essential part in the advanced application of the energy management system, whose main role is to provide a reliable and sufficient database for other applications, e.g., power flow analysis, economic dispatch, and stability control [7, 8]. The main factors influencing the accuracy of SE include measuring devices and transmission line parameters [9]. The rapid development of the phasor measurement unit (PMU) and advanced communication infrastructure has improved the precision of measured data [10]. However, parameters of transmission lines are often regarded as constant values and the effect of line temperature is ignored, which will result in parameter inaccuracy and has become an obstacle restricting the precision of state estimation. Failure to modify line parameters according to temperature may lead to significant errors in the calculation of power flow and network loss, whose errors may even exceed 30% [11, 12]. Electro-thermal coordination (ETC) that combines line temperature with electrical quantities is capable of decreasing temperature-dependent errors in power flow, SE, and related analysis [13]. The basic ETC principle is to establish an analytical relationship of the line temperature, current, and weather conditions through the heat balance equation (HBE) [14]. Line temperature is calculated by the HBE, and then line parameters can be corrected correspondingly. Studies on ETC in the power system mainly focus on the thermal rating [15; 16; 17], power flow analysis [18; 19; 20], and estimation of power system states and temperature [21; 22; 23; 24]. Based on dynamic thermal models, a real-time thermal rating method for the lines of the distribution network was proposed [15]. Considering the scenarios of normal operation and contingency, the performance of different real-time line monitoring devices on dynamic thermal rating has been assessed [16]. The dynamic thermal-line rating is conducted using online measurements so as to adjust the operational tripping scheme [17]. In addition, a temperature-dependent power flow algorithm was proposed, where the augmented equation set is solved by the Newton-Raphson method [18]. ETC was combined with optimal power flow, on which economic losses can be reduced [19]. With the consideration of temperature-related resistance and thermal rating, a weather-based optimal power algorithm was designed [20]. Moreover, the influence of temperature on SE performance was analyzed, and the results verify that the errors caused by temperature are not negligible [21]. Using Monte Carlo simulation and a variance reduction method, the critical line temperature in the presence of fluctuating power flows was estimated probabilistically [22]. Based on the analytical solution and numerical weather prediction, a simulation method for the evolution of line temperature was proposed [23]. In addition, a constrained nonlinear optimization model for estimating both the voltage phasors and the temperature of transmission line conductors was established and solved by a predictor-corrector interior point method [24]. With regard to SE, there are extensive efforts devoted to its performance modification techniques [25; 26; 27; 28; 29; 30; 31; 32; 33]. A hybrid state estimator using the measurements of remote terminal units (RTUs) and PMUs was designed with bad data detection [25].