the system's current condition. The system condition or state is a function of several variables: bus voltages, relative phase angles, and tap changing transformer positions. A state estimator can typically identify bad analog telemetry, estimate non‐telemetered flows and voltages, and determine actual voltage and thermal violations in observable areas.”
According to [5], SSE has evolved rapidly to online implementations beginning with the Norwegian Tokke installation [8] followed by the larger AEP installation [9] soon after. Not long later, T. E. Dy Liacco [10] stated: “Although the number of control centers with State Estimation is still rather small, the number is increasing at a rapid rate. The requirement for State Estimation at a modern control center has become the rule, rather than the exception.”
The fundamental problem of state estimation can be defined as an over determined system of nonlinear equations solved as an unconstrained weighted least squares (WLS) minimization problem. The WLS estimator minimizes the weighted sum of the squares of the residuals. Residuals are the error or difference between the estimated and the actual values [11]. Many papers and books treat the broad generic area of “state estimation” in system theory [12–14]. State estimation concepts can be applied in other power systems areas [15–20].
1.3 THE NEED FOR STATE ESTIMATION
Security control is the main strategy used in the operation of electric power systems, where actions are taken to prevent an impending emergency, to correct an existing emergency, or to recover from an emergency. Knowing the state of the system under steady‐state conditions is the key to security control.
Control centers may be classified into two types, according to the information base available. In one type of control center, the raw power system data as obtained in real time is an adequate information base for operation. The other type of control center goes beyond the mere acquisition of data. By applying state estimation, a far better and a more comprehensive information base than raw data is obtained.
The importance of the real‐time load flow fed by state estimation lies in its use as basis for security analysis. With the load flow as a base, reference allows analyzing the effects on the system of any contingency event. In contrast, without state estimation, there is not much to be done with raw data except to check it for abnormal values.
A further important feature of state estimation is the ability to detect the presence of bad data (outliers) and to identify which data is in error. Corrections can then be expedited in the field on the faulty instrumentation. Without state estimation, there is no effective, systematic way of finding measurement errors. Some sort of data validation has been attempted wherein power measurements around a bus are summed up and flows at both ends of a branch checked against each other, but these checks apart from being inconclusive end up being too complicated as it has to take into account the topology of the network. Now network topology is handled systematically and correctly by state estimation. Hence for all the checking done by so‐called data validation programs, it is best to go directly to state estimation.
In the modeling of power systems for security control functions, there are usually external networks, i.e. networks or subnetworks, which are not being telemetered by the control center and which are not observable. There are two approaches for estimating the state of these external networks. One approach is to use pseudo‐measurements, based on statistics and forecasts, of the injections at the nodes of the external network. The pseudo-measurements are then assigned relatively low weights and included as part of the measurement set in the state estimation routine. The second approach is to perform the state estimation only on the observable part. The state of the external network is then obtained by finding a load flow solution using the pseudo-measurements as inputs with the boundary node voltages held at the values determined by the state estimation of the observable part.
For bad data identification, early state estimators singled out measurements with the highest values of the weighted residual. Newer bad data identification techniques use both the weighted residual and the normalized residual. Either the values of the normalized residual or the ratios of the normalized ones from the weighted residual are used to identify bad data. Bad data rejection is a time‐consuming procedure at control centers especially if there are more than one measurement in error.
The concept of security control cannot be fully realized without a complete information base that is derived from the voltage magnitudes and phase angles of all buses in a power system obtained via state estimation [1–3].
1.4 STATIC STATE ESTIMATION IN PRACTICE
The material in this section is based on a NERC Task Force report [7]. To quote the Task Force:
This report presents the findings and recommendations of the North American Electric Reliability Corporation (NERC) Real‐Time Tools Best Practices Task Force (RTBPTF) concerning minimum acceptable capabilities and best practices for real‐time tools necessary to ensure reliable electric system operation and reliability coordination. RTBPTF's undertaking is based on the U.S.‐Canada Power System Outage Task Force findings that key causes of the August 14, 2003 northeast blackout included absence of situational awareness and inadequate reliability tools. That report also notes the need for visualization display systems to monitor system reliability.
RTBPTF's recommendations result from an extensive, three‐year process of fact‐finding and analysis supported by the results of the Real‐Time Tools Survey, the most comprehensive survey ever conducted of current electric industry practices.
RTBPTF's findings and recommendations are firmly grounded in the results of the Real‐Time Tools Survey, a more than 300‐page, web‐based document with nearly 2,000 questions on a broad scope of current industry practices and plans for using real‐time tools.
While [21] referred to RTUs as the eyes and ears and hands of the master station, the phrase came to be commonly used to refer to the state estimator as the eyes and ears of the real‐time operator. Indeed, in current practice the state estimator prevails as an “essential” tool for power system operators' “situational awareness.” Existing NERC reliability standards assume the use of state estimators to aid RCs and TOPs in maintaining situational awareness for the bulk electric system. The state estimator must be available and able to produce an accurate solution because many applications rely on the state estimator solution as base case.
State estimators are commercially available allowing SCADA/EMS vendors to provide viable state estimators off the shelf with some customization and fully integrated with users' production SCADA/EMS systems. State estimators are used as input to monitor MVA/ampere loadings and low and high bus voltages, voltage drop, voltage node angle separation, SCADA, and visualization. Therefore, it is important that it be available and produce an accurate solution.
Single‐pass methods execute one estimation that simultaneously includes internal and external networks, observable/internal network, and nonobservable/external network solved together. The two‐pass method deals with two state estimates, one for the internal system and another for the external system or for the entire system (observable/internal network and nonobservable/external network solved separately). Many in the power industry prefer using a single‐pass over a two‐pass solution.
According to [22], the single‐pass method suffers from numerical instability. An enhancement to the one‐pass method uses a set of critical external pseudo‐measurements. Some alternative two‐pass state estimators require a load flow study for the external system. Both two‐pass methods reduce the effects of boundary errors in the internal system solution by properly weighing the external pseudo‐measurements, but they may result in very high or negative loads and generations in the external system. Zero‐injection buses are more commonly treated as high‐confidence
