"Weighted Least Square state estimator is an optimal estimator in power systems"

This statement holds true when only noise is present in the measurements and system model. However, in power systems, bad data are unavoidably present in the measurements and system model. Considering that WLS SE is essentially an average estimator in statistics, WLS SE is actually a biased state estimator in power systems.

Zero injection measurements are given a huge weight in power companies

In traditional state estimation theory, zero injection measurements are often given significant weight due to their perceived reliability. However, this practice can create leverage points in the estimation process. Leverage points are data points that strongly influence the solution, and when associated branches to a zero injection measurement have topology or parameter errors, they can lead to divergence or biased solutions in conventional state estimators.

SE+ offers a notable advantage in handling this issue. It effectively addresses erroneous zero injection measurements by appropriately rejecting them during the estimation process. By doing so, SE+ avoids the adverse effects of leverage points caused by faulty or erroneous measurements associated with zero injection measurements. This capability of SE+ contributes to more accurate and reliable state estimation outcomes, ensuring the integrity and quality of the estimated results even in the presence of problematic zero injection measurements or associated errors in power system topology or parameters.

It was said: "Our SE converges most of the time, so it works very well."

In the power industry, it is widely recognized that a good state estimator should not only achieve convergence but also effectively reject bad data to ensure an accurate solution. Using erroneous data in the voltage estimation process can introduce biases, leading to issues such as negative loads, significant mismatches, or branches generating real power. These inaccuracies can adversely affect critical functions like contingency analysis, Locational Marginal Price (LMP) calculation, and security assessment.

Consequently, the primary goal of a state estimator is to provide an accurate solution. While convergence is a basic requirement, accuracy is of greater significance as it directly affects the reliability and quality of subsequent analyses and operational decisions in the power industry.

In summary, a state estimator must not only converge but also effectively identify and reject bad data to ensure accurate results. This emphasis on accuracy is crucial for reliable power system operation and robust decision-making processes.

Moreover, when the system is highly stressed due to heavy load, a least squares state estimator often struggles to reach a solution. IEEE test results have shown that Weighted Least Squares (WLS) estimators have a high probability of divergence under these conditions. In 2011, "The Future of the Electric Grid: An Interdisciplinary MIT Study" highlighted that "the algorithm (of the 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." WLS static state estimators fail to accurately recover true values from bad measurements, exacerbating challenges during critical times.

It was said: "SE at our company converges more than 99%, therefore we will not put efforts on 1% convergence improvement."

You raise an important point regarding the impact of divergence in state estimators, especially during critical or emergency conditions. While a convergence rate of 99.8% may seem high, it still implies the possibility of at least one divergence per day on average if state estimator runs every 5 mintes. In normal operating conditions, such occasional divergences may not have significant consequences. However, during alert states or extreme situations like the 2003 Northeast blackout, where the system is already under stress, even a small probability of divergence can have substantial implications, including economic losses and potential blackouts.

The Challenges of State Estimation in Emergency Conditions

State estimators often face significant challenges in accurately estimating system states during unusual or emergency conditions, precisely when their performance is most crucial. The complexity of these situations, coupled with the limitations of current state estimators, makes it difficult to achieve reliable and accurate estimations. During alert states, the system is more prone to errors and instability, exacerbating the risk of divergence and its associated consequences.

Implications of a 1% Divergence Rate

Addressing the 1% divergence rate in state estimators becomes even more challenging during alert states. The risk of system-scale blackouts increases significantly in such cases, and rectifying this divergence becomes exceptionally difficult due to the limitations of current state estimation algorithms. The consequences of even a single divergence during critical conditions can be severe, leading to:

• Economic Losses: Power outages and instability can result in substantial economic losses, impacting businesses and consumers.
• System Reliability: Divergence during emergency conditions can undermine the reliability of the entire power system, making it difficult to maintain stability and control.
• Operational Challenges: State estimators must provide accurate and timely information to support decision-making during emergencies. Divergence can hinder this process, delaying response times and complicating recovery efforts.

The Need for Robust and Accurate State Estimation Techniques

Recognizing these limitations and working towards the development of more robust and accurate state estimation techniques is vital to improve the resilience of power systems and enhance their ability to handle emergency conditions effectively. Developing advanced state estimators, such as the SE+ algorithm, which guarantees convergence and accurately rejects bad data, is essential for:

• Improved Resilience: Enhancing the power system's ability to withstand and recover from extreme conditions and emergencies.
• Accurate Decision-Making: Providing operators with reliable data to make informed decisions during critical situations.
• Reduced Risk of Blackouts: Minimizing the likelihood of system-scale blackouts by ensuring consistent and accurate state estimation.

In conclusion, while a high convergence rate is important, the focus must also be on improving accuracy and robustness to handle the challenges posed by emergency conditions. By advancing state estimation techniques, we can significantly enhance the reliability and stability of power systems, ensuring they remain resilient in the face of increasing complexities and extreme weather events.