By Giuseppe Fusco
Adaptive Voltage regulate in strength platforms, a self-contained mix of idea and novel software, bargains in-depth remedy of such adaptive regulate schemes. insurance strikes from power-system-modelling difficulties via illustrations of the most adaptive keep an eye on structures, together with self-tuning, model-reference and nonlinearities repayment to an in depth description of layout equipment: 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)
Fig. 4. Constant damping ratio locus into the z-plane The circle of radius Rmin has been introduced to avoid the pole-shifting algorithm placing the two largest roots of T (z −1 ) in such a way that the resulting settling time is not feasible. In fact, it is useful to recall that, in the voltage regulation task, the settling time assumes values equal to a few times the fundamental frequency cycle. 22) i=3 is a pre-speciﬁed polynomial which deﬁnes, at each sampling period Tc , the closed-loop pole locations according to the pole-shifting approach.
The proof is induced starting from k = 1. 11) for k = 1 it is trivial that R1 is symmetric and positive deﬁnite. 14) hT 1 R1 h1 + Q. ,1 which directly shows that R1 is symmetric. 14) it can easily be shown that aT R1 a > 0 ∀ a ∈ IR2nh and a = 0 by applying the Schwartz inequality to the positive deﬁnite matrix R1 hT 1 R1 h1 aT R1 a ≥ hT 1 R1 a 2 It is interesting to analyze some further conditions to be imposed which assure that, asymptotically, the error covariance matrix Rk is not only stable but also reaches a constant value.
Conversely, in power system voltage regulation, the system undergoes small disturbances. Such disturbances change the poles of the power system model but such variations are not large because the power system is operating under normal conditions. Staring from this consideration, the pole-shifting technique can be usefully applied in the voltage regulation problem to vary the locations of the desired closed-loop poles, represented by the roots of polynomial T (ρ, z −1 ), in such a way that the limits imposed by the actuator are taken into account in the design of the control input .