Join 60,000+ competitive exam aspirants
or with email
Your Cart
Subtotal₹0
Total₹0
Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
Join 60,000+ competitive exam aspirants
When WLSE method is applied for only reactive power injection measurement vector then the estimation of ‘x’ is
x e s t ( v ) P + 1 = x e s t ( v ) P + H 4 P T W q H 4 P H 4 P T W q Z q - h q x e s t P
x e s t ( v ) P + 1 = x e s t ( v ) P + H 3 P T W q H 3 P H 3 P T W q Z q - h q x e s t P
x e s t ( v ) P + 1 = x e s t ( v ) P + H 4 P T W q H 4 P Z q - h q x e s t P
None of above
xest(v)P+1=xest(v)P+H4PTWqH4PH4PTWqZq-hqxestP
Quick Summary: The Weighted Least Squares Estimation (WLSE) method computes the state vector $x$ by iteratively minimizing the sum of the squares of the weighted residuals. When specifically estimating based on reactive power injection measurements ($Z_q$), the Jacobian matrix $H_4$ is utilized, where $H_4 = \frac{\partial h_q(x)}{\partial x}$ represents the sensitivity of reactive power measurements to the state variables.
The Weighted Least Squares Estimation (WLSE) method computes the state vector x by iteratively minimizing the sum of the squares of the weighted residuals. When specifically estimating based on reactive power injection measurements (Zq), the Jacobian matrix H4 is utilized, where H4=∂x∂hq(x) represents the sensitivity of reactive power measurements to the state variables.
J(x)=[z−h(x)]TW[z−h(x)] — Objective function for WLSE
Δx=(HTWH)−1HTWΔz — Normal equation for state update
The WLSE method linearizes the non-linear measurement function h(x) around the current estimate xP using a Taylor series expansion. The update rule is derived by solving the normal equations: (Δx)=(HTWH)−1HTWΔz. For reactive power, the Jacobian H becomes H4, and the residual vector is Δz=Zq−hq(xP).
The Jacobian H4 specifically relates reactive power injections to voltage magnitudes and angles.
Weighting matrix Wq is the inverse of the covariance matrix of the reactive measurement errors.
The process is iterative, typically utilizing the Gauss-Newton approach for convergence.
Efficiently filters out measurement noise
Provides an optimal estimate in the presence of Gaussian noise
Computationally intensive for large systems due to matrix inversion
Sensitive to bad data without pre-processing
Power System State Estimation (PSSE)
Online monitoring of reactive power flow
The matrix H3 (often found in option B) is typically associated with active power flow or different power components.
WLSE relies on the assumption that measurement errors are normally distributed with zero mean.
A is correct — It correctly defines the iterative update step for the state vector using the reactive Jacobian matrix H4 and the reactive weights Wq.
Always verify the Jacobian index (H1,H2,H3,H4) in power system estimation problems, as they map specifically to active/reactive power and voltage measurements.