Adaptive State Estimation for Power Systems Measured by PMUs with Unknown and Time-Varying Error Statistics

Abstract : Measurement error is a crucial factor that determines the accuracy of state estimation (SE). Conventional estimators have fixed models, and can yield optimal performance only when the measurement error statistics exactly meet the assumptions. In reality, however, the error distribution is usually unknown and time-varying, resulting in suboptimal state estimates in most cases. This paper develops the concept of adaptive SE for power systems measured by phasor measurement units (PMUs). First, the Gaussian-Laplacian Mixture (GLM) model is developed to fit the body and tail of unknown measurement error distributions. Then, an adaptive estimation framework is proposed based on the Expectation-Maximization (EM) algorithm. It is capable of tracking the actual error statistics online, and adjusting the parameters of SE to maintain near-optimality of state estimates under complex measurement error conditions. Simulation results demonstrate that the proposed adaptive estimator yields more accurate state estimates than the well-known Weighted Least Squares (WLS) and Weighted Least Absolute Value (WLAV) estimators by adapting itself to the variations of measurement error statistics.
 ? In the existing commercial software, the “event playback” function is leveraged to validate dynamic models using PMU data. ? The key idea is to take the measured generator terminal voltage magnitude/phase angle or frequency as model inputs to obtain model outputs of real power P and reactive power Q. ? There are several vendors who offer commercial software for SSE implementation while there is no commercial software for DSE. However, we can leverage the capabilities of existing commercial tools and enable the DSE implementation. ? Indeed, the existing assets are reaching their conservative ampacity limits, typically defined on a seasonal basis, without due consideration to meteorological conditions (temperature, wind speed, etc.).
 ? The rectangular version is preferable, however, owing to the numerical problems (undefined Jacobian terms) that may arise for very small currents. ? Along with the branch topology error detection problem, the parameter error identification problem constitutes one of the examples where PMUs will have a unique edge over conventional measurements. ? State estimation problem is commonly formulated by choosing a reference bus (typically but not necessarily the same as the slack bus used for the power flow analysis) and setting its voltage phase angle equal to zero.
 • To deal with that, a correlation aided robust DSE for unknown input and state estimation is proposed in. • Compared with the previous works, no generator frequency measurement is required, and it has better robustness in dealing with bad data. • With the active efforts by many researchers for more than a decade, many DSE algorithms have been developed, and the DSE performance has been significantly improved, as summarized in this paper. • However, power systems are evolving to be more complex and different, so DSE core functions should continue to improve to meet the operational requirements of future power systems.
 ? Performances of a PMU device, in terms of accuracy or processing time, are dictated by its components, mainly, the instrumentation channel, the A/D converter and the parameters of the phasor estimation algorithm. ? However, this potential performance is not achieved due mainly to errors from instrumentation channels and system imbalances. ? Presently, evaluation of PMU data accuracy is still a challenging problem discussed in the scientific literature. ? Adding the contribution of the new sample while removing that of the oldest one provides the more computationally efficient recursive DFT algorithm.

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