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
Power utility companies have low measurement redundancy ratio and
high percentage of bad data.
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 gives a big challenge to residual-based bad data detection
which fully depends on measurement residual linearization.
Characteristics of Non-Divergent State Estimator (NDSE)
Unlike WLS based state estimator, NDSE can obtain a feasible voltage solution once the system is solvable, 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 help largely improve the data accuracy of power system
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.