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State estimation of power system by only active and reactive line flow have good redundancy if
Assume more number of imaginary buses
Increase active and reactive line flow data by assume more imaginary line in power system
Power system has enough number of transmission lines which have two meters at each end of all transmission lines
All of above
Power system has enough number of transmission lines which have two meters at each end of all transmission lines
Quick Summary: State estimation in power systems involves calculating the state vector (bus voltage magnitudes and angles) based on redundant measurements. High redundancy is achieved when the number of measurements $m$ is significantly greater than the number of state variables $n$, which is facilitated by placing bidirectional meters on transmission lines.
State estimation in power systems involves calculating the state vector (bus voltage magnitudes and angles) based on redundant measurements. High redundancy is achieved when the number of measurements m is significantly greater than the number of state variables n, which is facilitated by placing bidirectional meters on transmission lines.
z=h(x)+e — The non-linear measurement model relating observations to states
η=nm — Redundancy factor defined as ratio of measurements to state variables
The measurement vector z is related to the state vector x via z=h(x)+e, where h(x) is a non-linear function and e is measurement noise. By placing flow meters at both ends of a line, we obtain two independent measurements for the same physical quantity (line flow), effectively doubling the redundancy of that specific branch data and providing robustness against bad data.
State estimation improves observability and filters measurement noise.
Bidirectional line flow monitoring helps in detecting and identifying bad data.
Critical observability is reached when m=n and the Jacobian is non-singular.
Improved accuracy in state calculation.
Enhanced detection capability for gross errors in data.
Higher instrumentation costs.
Increased communication bandwidth requirements for data acquisition.
Energy Management Systems (EMS).
Automatic Generation Control (AGC).
Security assessment and contingency analysis.
Option A and B are incorrect because increasing imaginary buses or lines does not physically increase the measurement count; it merely complicates the model. Redundancy is a measure of physical data availability relative to the system size.
The objective of state estimation is to minimize the weighted sum of squared residuals.
C is correct — Placing two meters at each end of transmission lines increases the total measurement count, thereby enhancing redundancy for the state estimation process.
In power system state estimation questions, always remember: redundancy = (Total Measurements) / (Total States). More measurements always lead to better observability.