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Linear state estimation operates in a similar way, but instead, the analog measurements are voltage and current phasors.
Linear state estimation uses a fully observable set of PMU measurements to determine the system state using linear equations and a non-iterative procedure.
Examples of these online WAMS applications include the real time estimation of oscillation parameters (e.g. inter area oscillations), the dynamic rating of transmission lines, and hybrid and linear state estimation.
Coupled with a synchrophasor analytic applications engine and real-time visualization, the system provides dynamic visibility of the grid by a complete solution of data validation and conditioning, linear state estimation, data analytics, and visualization.
At the coordination level, the linear state estimation with PMUs is carried out to coordinate the voltage states of boundary buses where the computational time can be significantly reduced.
The formulation of linear state estimation problem is described as follows, left{ begin{array}{lll} { hbox{min} }quadvarvec{sigma}^{text{T}} varvec{Wsigma } hfill {text{s}}.{text{t}}.quad ;varvec{Z} = left[ {begin{array}{*{20}c} varvec{I} varvec{Y} end{array} } right]varvec{X} +varvec{sigma}hfill end{array} right.
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Extended Kalman Filter (EKF) is a non-linear state estimation technique which is used to produce values that close to the true value when given with measurement containing noise and other inaccuracies.
In addition, for the linear state estimator, the state estimation performance with beforehand given attenuation parameter is established by the design of a compensative controller.
These performance criteria include guaranteed-cost suboptimal versions of estimation objectives like H2, H∞, stochastic passivity, etc. Linear state estimators that satisfy these criteria are presented.
This model is non-autonomous, non-linear and has a continuous state space; thus, linear tools for state estimation are not applicable.
The best sensor location for the reactor is found by specifying scalar measures on the observability Gramian integral from the linear least-squares state estimation problem.
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