1 Robust State-Estimation Procedure using a Least Trimmed Squares Pre-processor Yang Weng, Student Member, IEEE and Rohit Negi, Member, IEEE and Qixing Liu, Student Member, IEEE and Marija D. Ili´ c, Fellow, IEEE Abstract—Based on real-time measurements, Static State Esti- mation serves as the foundation for monitoring and controlling the power grid. The popular weighted least squares with largest normalized residual removed, gives satisfactory performance when dealing with single or multiple uncorrelated bad data. However, when the bad data are correlated or bounded, this estimator has poor performance in detecting bad data, which leads to erroneous deleting of normal measurements. Similar to the Least Trimmed Squares(LTS) method of robust statistics, this paper considers a state estimator built on random sampling. However, different from previous robust estimators, which stop after estimation, we regard the LTS estimator as a pre-processor to detect bad data. A subsequent post-processor is employed to eliminate bad data and re-estimate the state. The new method has been tested on the IEEE standard power networks with random bad data insertions, showing improved performance over other proposed estimators. I. I NTRODUCTION An electric power grid is a complex network, composed of generation, transmission and distribution systems. Two fun- damental problems make power grid operations challenging. Firstly, it must monitor the voltages and powers at various buses. Then, based on the monitoring results, proper control must be applied to maintain stability of the power grid. In today’s interconnected power grid, Supervisory Control and Data Acquisition (SCADA) systems, which collect real- time data to feed a state estimator, are key components for monitoring the power grid. State estimation is defined as the procedure of obtaining the complex phasor voltages at all buses of the grid since these are sufficient to determine the operation condition of the grid. In practice, direct measurement of complex phasor voltages at every bus is currently very expensive. Thus, state estimation uses a redundant measure- ment set, including several bus voltages, bus real and reactive power injections, and branch reactive power flows. (Increased deployment of Phasor Measurement Units (PMU) will also allow direct measurement of the bus phasor). Yang Weng is with the Department of Electrical and Computer Engi- neering, Carnegie Mellon University, Pittsburgh, PA, 15213 USA e-mail: yangweng@andrew.cmu.edu Rohit Negi is a professor at Carnegie Mellon University, Pittsburgh, PA, with the department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, 15213 USA e-mail: negi@ece.cmu.edu Qixing Liu is with the Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, 15213 USA e-mail: lqx@cmu.edu Marija D. Ili´ c is a professor at Carnegie Mellon University, Pittsburgh, PA, with a joint appointment in the Electrical and Computer Engineering and Engineering and Public Policy Departments. She is also the Honorary Chaired Professor for Control of Future Electricity Network Operations at Delft Uni- versity of Technology in Delft, The Netherlands e-mail: milic@ece.cmu.edu The state estimation was initially formulated as a Weighted Least Square (WLS) error problem, due to the assumption of Gaussian background noise. Although a WLS solution is easy to obtain, it is suboptimal when bad data appear. Bad data refers to gross (non-Gaussian) measurement error. Therefore, dealing with the Gaussian noise as well as bad data is impor- tant. Bad data occurs due to equipment failure, finite accuracy, infrequency of instrument calibration and measurement scaling procedure at the control center. Besides, telecommunication errors and incorrect topology information may also cause bad data. Some bad data are easy to spot, such as a voltage magnitude several orders larger than the expected value. However, not all bad data are easy to detect. To test the existence of bad data in the measurement set, power system engineers employ the chi-square test. Upon the failure to pass the test, the measurement with the largest normalized residual is eliminated [1], [2]. This testing-eliminating procedure continues until the test is passed 1 . It can be shown that, if there is only an error in the measurement set, the maximum residual corresponds to the error with the same index. This Largest Normalized Residual Remover(LNRR) works well if there are indepen- dent uncorrelated bad data. However, as the assumption of independence does not hold in general, when correlated bad data does appear, the LNRR may fail. Furthermore, LNRR does not work satisfactorily when the multiple bad data are bounded with respect to the Gaussian noise standard deviation. These drawbacks indicate a need for an improved bad data removal method. Several methods to deal with bad data are known in the literature [2]–[10]. In particular, Handschin et al. [3] intro- duced a grouped residual search strategy that can remove all suspected bad data at once. In [4], a non-quadratic state estimator which minimizes the sum of absolute value of residual was studied and shown to have the ability to reject bad data. In [5], Jeu-Min et al. proposed a bad data sup- pression method, based on adapting the covariance matrix to the residuals. In [6], a method, based on hypothesis testing identification(HTI) was derived. However, as the initial selec- tion of suspected bad measurements is based on normalized residual, the HTI is inefficient if some bad data result in small normalized residuals. [7] did a survey which summarizes three classes of bad data(BD) identification methods, namely, the classes of identification by elimination(IBE), the non- 1 Notice that the system could be unobservable after the removal, which is an observability problem and is not considered here.