# A Hybrid State Estimator Based on SCADA and PMU Measurements for Medium Voltage Distribution System
## 4 Case Studies  
The modified IEEE 33-bus distribution system and measurement configuration are shown in Figure 4. The network parameters and load values provided by Reference [40] were used as the reference condition. PMUs were installed at buses 12 and 30, assuming that all buses had pseudo-power injection measurements and the network reconfiguration was not considered in the state estimation. Note that the measurement configuration was based on the technical reasoning and without considering any optimal placement technique.  
Figure 3: The flowchart of a hybrid estimator based on SCADA and PMU measurements.  
In order to prove the validity of the proposed method, the power flow results were taken as the true values. Also, the measurement data are formed by superimposing the corresponding random measurement errors obeying the normal distribution on the basis of the power flow results as given by Equation (15):  
\[\mathbf{X}^{m}=\mathbf{X}(1+\sigma) \tag{15}\]  
where, \(\mathbf{X}^{m}\) are the measurement values. \(\mathbf{X}\) are the true values and \(\sigma\) is the random measurement error. The maximum error of the current amplitude measurement and power measurement in SCADA were 3%, while the maximum error of voltage amplitude measurement was 1%. The maximum error of amplitude measurement in PMU was 1%, and the maximum error of the phase angle measurement was 10\({}^{-2}\) rad. The maximum error of the pseudo-measurements was 50%. A Monte Carlo method was used to deal with the uncertainty and the number of Monte Carlo trails was 5000 [40].  
The dynamic state estimation process of this paper is shown in Figure 5. The period for the improved robust estimation and LSE could be set according to the request of the system and the real refresh frequency of measurement data. In this paper, the period for the improved robust estimation was set to 5 s, while the period for LSE was set to 0.5 s. Taking the SCADA data acquisition time as the starting moment, the improved robust estimation was performed with the SCADA and PMU measurements and pseudo-measurements. When reaching the start time of fast-state tracking with the LSE, the results of the last estimation time were taken as pseudo-measurements, and the estimation results were updated by the PMU measurement data. During the SCADA acquisition data period, a total of nine linear state estimations were performed. When reaching the SCADA data acquisition time again, the above process was repeated. The calculation time of the two state estimators is also shown in Figure 5.  
Figure 4: Measurements configuration diagram of IEEE 33-bus system.  
Figure 5: Schematic diagram of computation procedure and time with regard to two algorithms of state estimation.  
The performance of the proposed hybrid state estimator is verified under the normal condition and bad data condition. At the SCADA data acquisition time, the exponential equivalence robust estimation (EXP) mentioned in Reference [31] and initial IGGIII with no improvement (IGGIII) are used to be compared with the improved IGGIII (IIGGIII). During the dynamic state estimation process, the method in Reference [22] (WLS-UKF) was used to be compared with the proposed hybrid state estimator (IIGGIII-LSE).