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Examoogle • User • info@examoogle.com • EE-2024-8821
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Suppression of bad data is done by selecting estimation index function as
Quadratic
Non-quadratic
Square
None of above
Quadratic
Quick Summary: State estimation in power systems involves calculating the state vector (bus voltage magnitudes and angles) from redundant measurements. To suppress the influence of bad data or outliers (gross measurement errors), estimators replace the standard Weighted Least Squares (WLS) objective function, which is quadratic, with a non-quadratic 'robust' estimator objective function.
State estimation in power systems involves calculating the state vector (bus voltage magnitudes and angles) from redundant measurements. To suppress the influence of bad data or outliers (gross measurement errors), estimators replace the standard Weighted Least Squares (WLS) objective function, which is quadratic, with a non-quadratic 'robust' estimator objective function.
J(r)=∑i=1mρ(σiri) — Generalized objective function where ρ is non-quadratic
ri=zi−hi(x) — Measurement residual calculation
The standard WLS method uses a quadratic penalty J=rTR−1r, where r is the residual. Because the quadratic function grows rapidly with the residual magnitude, it is highly sensitive to bad data. Non-quadratic estimators, such as the Least Absolute Value (LAV) or Huber function, reduce the penalty for large residuals, preventing outliers from significantly skewing the estimated state.
Quadratic estimators (WLS) are optimal only when measurement errors follow a Gaussian distribution.
Gross errors (bad data) deviate significantly from the Gaussian distribution.
Non-quadratic estimators are inherently 'robust' to bad data without requiring separate identification routines.
The Huber estimator is a common hybrid that acts quadratically for small residuals and linearly for large ones.
Automatic rejection of gross errors (outliers).
Improved stability of state estimation under sensor failure.
Increased computational complexity compared to simple WLS.
Non-linear optimization often requires iterative numerical methods.
Power System Energy Management Systems (EMS).
Smart Grid Wide Area Monitoring Systems (WAMS).
The 'Quadratic' option refers to Weighted Least Squares (WLS), which is prone to error magnification when bad data is present.
Non-quadratic methods are often referred to as Robust State Estimation.
B is correct — Non-quadratic estimation functions limit the influence of large residuals, effectively suppressing the impact of bad data.
Always remember that in statistical signal processing, quadratic penalty functions (like in standard regression) give maximum weight to large deviations; therefore, 'non-quadratic' is the universal requirement for outlier robustness.