# A Hybrid State Estimator Based on SCADA and PMU Measurements for Medium Voltage Distribution System
## 1 Introduction
Furthermore, the interval linear state estimation model is proposed in References [16; 17]. A Monte Carlo method is used in weighted least squares (WLS) to deal with the uncertainty of the measurement data [18; 19; 20; 21; 22; 23; 24; 25; 26]. Due to the increasing dynamics and changing behavior of actors in distribution systems, it is necessary to study how to effectively utilize the PMU measurement data with millisecond update rates in the DSSE. Some references utilize the high accuracy of the PMU measurements and the increased measurement redundancy to improve the performance of DSSE. In Reference [8], the numerical results show that a high level of accuracy in the state estimation task can be achieved with a much fewer number of PMUs than voltage magnitude meters. In References [18; 19], the root node voltage is extended into state variables, which can effectively deal with the voltage phasor and voltage amplitude measurements to improve the estimation accuracy. In Reference [20], an estimator is added for processing the PMU measurements, treating the SCADA measurements as prior information to obtain the final estimation results. However, the state estimation period of the above methods is still second-level, which is the same as the sampling period of the SCADA, and a great quantity of PMU measurement data are ignored. For the integration of measurements with different sampling periods in the distribution system, the researchers have proposed some different solutions. Reference [21] combines SCADA measurements with advanced metering infrastructure (AMI) measurements, whose sampling period ranges from 15 min to 24 h and converts DSSE into the power flow matching. Reference [22] uses SCADA, PMU, AMI, and load forecast (LF) data to perform DSSE. The AMI information is combined with SCADA, LF, and PMU to perform the static state estimation every 1 h. The unscented Kalmanfilter (UKF) is used to dynamically estimate the system states between polling periods, and to predict the estimated values every 15 min using SCADA, LF, and PMU measurements. Reference [23] proposes a hybrid method combined with nonlinear static state estimation, static state estimation, and linear dynamic state estimation. Nonlinear static state estimation is carried out every 1 min with AMI, remote terminal unit (RTU), and PMU measurements, while static state estimation is carried out every 10s with RTU and PMU measurements. Static state estimation and linear dynamic state estimation is carried out every 10s. There are some studies focusing on the data fusion of SCADA and PMU measurements in the transmission network such as References [24; 25; 26]. However, in the distribution system, there are not much research done on this problem. In the distribution system, bad data may be caused by communication, transducer failures, or third parties tampering. When it comes to the problem of bad data elimination during iterations, a robust estimation model based on an exponential objective function is adopted in Reference [27]. A weighted least absolute value (WLAV) estimator, Schweppe-type Huber generalized M (SHGM) estimator, and improved WLS are also introduced to the DSSE. Reference [28] compares the performance of the conventional WLS, WLAV, and SHGM in DSSE. The distribution system solves the observability problem by adding the pseudo-measurements with large errors, but the WLAV and SHGM estimators treat the pseudo-measurements as bad data and there are not enough redundant measurements to eliminate these bad data. Therefore, the estimation performance of the WLAV and SHGM estimators in the distribution system is not ideal, while the WLS has a better fitness. However, the WLS estimator is only optimal for the measurement data obeying a Gaussian distribution, while the bad data does not obey a Gaussian distribution. Considering the above shortcoming, References [29; 30] adopt the equivalent weight theory to improve the robust performance of the conventional WLS.