A way to understand Weighted Least Square (WLS) based State Estimator

As the most commonly used state estimator in power industry, weighted least square (WLS) based SE is essentially an average estimator, and therefore, the influence of a bad data is shared (or hidden) by the neighbor buses around the location of bad data. This feature of WLS based SE makes the bad data detection very hard, if not impossible. 

The convergence issue of WLS based SE

Considering WLS is essentially an average estimator, if the average value go beyond the stop criterion due to the huge inconsistence caused by the bad data, the state estimator will definitely diverge. 

The difficulty of bad data detection

The difficulty of bad data detection lies in the following aspects:

1) Measurements and System Data

    Our observation on real-time data from limited power utility companies

    shows that power utility companies have low measurement redundancy

    ratio and high percentage of bad data.

2) Algorithms

• Weighted Least Square based state estimator forces the influence of bad data shared by its neighbor buses, which makes the bad data detection very hard, especially the nonlinearity of power grids give a big challenge to residual-based bad data detection which fully depends on measurement residual linearization.
• Leverage Point is one of the main reasons that bad data is hard to be detected by Weighted Least Square based SE and Least Absolute Value based SE. If a bad data (typical three types) exists in a measurement which is related to leverage point, this bad data will affect the state estimation results for sure. Unfortunately, leverage points very commonly exist in power system state estomation. NDSE has effectively solved the problem of Leverage Point.

Characteristics of Non-Divergent State Estimator (NDSE)

Unlike WLS based state estimator, NDSE can obtain a feasible voltage solution once the system is observable, and it has the following charcteristics:

1) No human involvement. Examples of human involvement include:

    adjusting the measurement weights to make it convergent; removing

    suspecious measurements; changing the measurement values and/or

    system parameters, etc.

2) The voltage estimate completely depends on the given measurements

    and system data/parameters.

3) NDSE can largely improve the data accuracy of power system

    operations.

4) NDSE is robust because it is Not sensitive to bad data. Its breakdown

    point value is 0.5. Breakdown point is a statistic index to evaluate the

    robustness of a state estimator, which takes value from 0.0 to 0.5.