By Giuseppe Fusco
Adaptive Voltage regulate in strength structures, a self-contained mixture of concept and novel program, bargains in-depth therapy of such adaptive keep an eye on schemes. insurance strikes from power-system-modelling difficulties via illustrations of the most adaptive keep an eye on platforms, together with self-tuning, model-reference and nonlinearities repayment to an in depth description of layout tools: Kalman filtering, parameter-identification algorithms and discrete-time controller layout are all represented. Case stories tackle purposes concerns within the implementation of adaptive voltage keep an eye on.
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Extra resources for Adaptive Voltage Control in Power Systems: Modelling, Design and Applications (Advances in Industrial Control)
15) where D δ(tc,k ) is a pulse. It can be easily recognized that v0,1 (tc,k ) is a step function. v0,1 (tc,k ) u(tc,k ) z −d B(z −1 ) A(z −1 ) + v1 (tc,k ) Fig. 8. 16) where −1 −nB + B + (z −1 ) = 1 + b+ + . . + b+ nB + z 1 z −1 −nB − B − (z −1 ) = b0 + b− + . . + b− nB − z 1 z and nB = nB + + nB − . Usually it is realistic to assume nB − = 0, except for some speciﬁc cases, such as voltage regulation at midpoint of a long transmission line , which yield to a nonminimum phase model (nB − = 0).
A suitable approach to the design the updating law of the variable forgetting factor has been proposed in  whose convergence properties have been discussed in . 11) σ02 is the expected measurement white noise covariance and N0 controls the speed of adaptation. A small value of N0 will give a large covariance matrix and a sensitive estimator while a larger value will give a less sensitive estimator thus leading to a slower adaptation. Other approaches are available to select the variable forgetting factor as well as other techniques such as the constant trace algorithm and directional forgetting factor can be utilized to prevent estimator wind-up [77,83,126,127].
Furthermore, it is useful to point out that in order to get smooth parameters estimation a minimum forgetting factor λmin has to be speciﬁed. If one wishes to keep the estimator more sensitive to the power system changes at the steady-state operating point a maximum forgetting factor λmax can be used, that is 0 < λmin ≤ λ ≤ λmax ≤ 1 However the use of a forgetting factor can cause the phenomenon known as estimator wind-up. Speciﬁcally, if no new data enter into the estimator over a long time, as in the case of absence of set-point changes, the regressor φ is small, and the matrix P grows exponentially if, as an extreme case, φ is zero.