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
The rank of jacobian matrix is depends on
Location of measurement
Type of measurement
Network topology
All of above
All of above
Quick Summary: In Power System State Estimation, the Jacobian matrix $H$ links the measurement vector $z$ to the state vector $x$ via $z = h(x) + e$. The rank of this matrix determines the observability of the power system, specifically whether the internal states (bus voltages and angles) can be determined from the available measurements.
In Power System State Estimation, the Jacobian matrix H links the measurement vector z to the state vector x via z=h(x)+e. The rank of this matrix determines the observability of the power system, specifically whether the internal states (bus voltages and angles) can be determined from the available measurements.
z=h(x)+e — Non-linear measurement model
H=∂x∂h(x) — Definition of the Jacobian matrix
The Jacobian matrix is defined as H=∂x∂h(x). Its rank depends on the number and type of measurements (P, Q, V, I) provided, the specific location of these sensors within the grid, and the physical network topology which dictates the connectivity matrix (Admittance matrix Ybus). If the rank of H is less than the number of unknown states, the system is unobservable.
Observability analysis is a prerequisite for State Estimation.
A system is observable if the Jacobian matrix has full column rank.
Network topology changes (e.g., line outages) directly alter the structure of the Jacobian.
Redundant measurements improve the robustness of state estimation.
Allows identification of critical measurements
Essential for real-time monitoring and security analysis
Computationally intensive for large-scale grids
Requires high-quality, synchronized data
Power System State Estimation (PSSE)
Contingency Analysis
Optimal Power Flow
If Rank(H)<n (number of states), the system is unobservable and the state vector cannot be calculated uniquely.
Option A, B, and C are all partial contributors to the matrix configuration; hence D is the encompassing answer.
D is correct — The rank of the Jacobian matrix is a function of the entire measurement configuration and the network parameters.
Always remember that in state estimation, 'observability' is synonymous with the condition that the Jacobian matrix is full rank.