"Weighted Least Square state estimator is an optimal estimator in power systems"
This statement is true when only noise exists in the measurements and system model. However, it is observed that bad data are unavoidably present in the measurements and system model in power systems. Considering WLS SE is essentially an average estimator in statistics., therefore WLS SE is actually a biased state estimator in power systems.
Zero injection measurements are given a huge weight in power companies
It is common in power companies that zero injection measurements are given a huge wight because zero injection measurements are considered to be trustworthy by traditional state estimation theory. Assigning a huge weight just creates a leverage point and all leverage points are forced to be satisfied to obtain a minimum objective function value in today's state estimators. When associated branches to a zero injection measurement have topology error or parameter error, leverage points will cause divergence or at least biased solution for today's state estimators. SE+ does not have such an issue and erroneous zero injection measurements will be effectively rejected by SE+.
It was said: "Our SE converges most of the time, so it works very well."
This is a common understanding in power industry which however may not be true. A good state estimator should be able to not only provide a feasible solution under any circumstances but also to effectively rejcet the bad data to reach an accurate solution. If bad data are used in the voltage estimate, the solution must contain bias. Therefore, some weird problems occur from the convergent solution, such as negative loads at some buses, big mismatch at some buses, branches generating real power, etc. The biased solution will have negative impacts on the performance of other functions including contingency analysis, LMP calculation, security assessment, etc.
In summary, convergence is just a basic requirement for a state estimator. The accuracy of the solution is more important for a state estimator which is the primary goal of it.
It was said: "SE at our company converges more than 99%, therefore we will not put efforts on 1% convergence improvement."
Let us take the best convergence rate 99.8% as an example. Normally state estimator runs every 5 minutes (it is even shorter for some companies), which means state estimator needs to run 288 times every day. 99.8% implies that there is at least one-time divergence every day in average. One-time divergence per day is not a big deal unless the system is in alert state or is under extreme tense, like what happened in 2003 Northeast blackout which led $7-10 billions economic loss.
In 2011 it was reported in "The Future of the Electric Grid: An Interdisciplinary MIT Study" that “the algorithm (of state estimator) is not perfect, and state estimators have trouble estimating a system state during unusual or emergency conditions – unfortunately, when they are most needed”.
In another word, the 1% divergence rate of state estimator will cause system-scale blackout with a big probability if the system is in an alert state. And it is extremely hard to fix this 1% divergence because today's state estimators are prone to fail when the system is in an alert state.