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. Normally convergent solution contains Bias if bad measurements and/or system modeling errors are not all effectively detected and removed. 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 of a state estimator does not mean the obtain solution is accurate.

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 extremenly hard to fix this 1% divergence because today's state estimators are prone to fail when the system is in an alert state.