# State Estimation for DC Microgrids using Modified Long Short-Term Memory Networks
## 1 Introduction  
State estimation (SE) is an important component of an energy management system (EMS), since it allows the system operator to control and monitor an electric power system [1]. The state of a power system can be estimated based on the supervisory control and data acquisition (SCADA) measurements, phasor measurement unit (PMU) measurements, and a topology processor. Some of the most important functions of EMS are based on the SE, such as contingency analysis, optimal power flow, and security assessment [2, 3]. Measurement data obtained straight from the telemetry is usually not perfect, as random errors are always present. These kinds of measurements need to be processed by SE to get the closest approximation to the real value before being used by the EMS functions. This fortifies the importance of SE in the transmission system level of power systems [4]. In the last decade, there has been a paradigm shift in the distribution system technology. The conventional unidirectional model had changed as the consumers in the distribution system have evolved from passive users to active users [5]. Around the same period, the concept of microgrids started to emerge as an alternative solution for local energy systems with distributed energy resources [6]. The introduction of microgrids led to distribution systems that are more active, with more diverse dynamics and service-oriented actions compared to their predecessor. This phenomenon established a need to bring distribution systems into the operation control and monitoring circle. Consequently, the development of microgrid SE is inevitable. However, due to the differences of the transmission and distribution systems [7, 8], the tools used for transmission system SE (TSSE) might not be directly applicable for microgrids and would need some adjustment for microgrid SE application. One of the main problems in microgrid SE applications is the lack of available real-time measurements in microgrids. As a result, the input data required by the observability analysis in the SE process is not sufficient. One of the ideas to solve the measurement scarcity problem is the use of pseudo-measurements [1; 9]. Pseudo-measurements are usually generated using the daily load profile (DLP) with annual updates [10]. Nowadays, the presence of advanced metering infrastructure (AMI) might help in providing a more accurate definition of DLP, which could lead to improved pseudo-measurements [11], and as a result, a more accurate microgrid SE. Conventionally, state estimators are formulated as overdetermined systems of nonlinear equations, which are then solved by using the weighted least squares (WLS) method [1; 12]. Conventional SE use the measurement data acquired at the present time to estimate the state of the system. In [13], a fuzzy linear SE model based on [PERSON]'s fuzzy linear regression model was employed to model the uncertainty in the system. In [14], a decentralized SE method was proposed for hybrid microgrids using a dual decomposition approach, where the estimation was separately conducted for either grid, with only limited information exchanged during the process. In [15], a state estimator was developed with centralized and decentralized approaches for hybrid alternating current (AC)/high voltage DC (HVDC) grids. The optimization-oriented state estimators were proven to be functional and stable, but in terms of computational speed and accuracy further improvement is desired. In [16], a fast real-time state estimator based on the belief propagation algorithm was proposed. The model proved to be robust against ill-conditioned scenarios caused by the differences between various measurements. Different efforts towards a fast real-time SE were introduced in [17], where the artificial neural network (ANN) method was used for a smart grid SE. Another effort using a deep learning-based state estimator is shown in [18], which combines the use of a deep neural network (DNN) for TSSE and a recurrent neural network (RNN) for state forecasting.