By Giuseppe Fusco
Adaptive Voltage keep an eye on in strength structures, a self-contained mixture of concept and novel program, deals in-depth therapy of such adaptive regulate schemes. insurance strikes from power-system-modelling difficulties via illustrations of the most adaptive keep watch over structures, together with self-tuning, model-reference and nonlinearities reimbursement to a close description of layout tools: Kalman filtering, parameter-identification algorithms and discrete-time controller layout are all represented. Case reports tackle functions matters within the implementation of adaptive voltage keep watch over.
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Extra resources for Adaptive Voltage Control in Power Systems: Modelling, Design and Applications (Advances in Industrial Control)
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. 3. If the initialization matrix R0 is symmetric and positive deﬁnite, if ∀ k ∈ N0 Qw,k = Qw , with Qw a diagonal matrix whose diagonal elements satisfy the following condition: qw,j = qw,j−1 > 0 for j = 2, 4, .
The use of a forgetting factor [9, 10, 127] ensures that data in the distant past are forgotten. To derive the prediction model we write the output v1 (tc,k ) in recursive form as v1 (tc,k ) = − a1 v1 (tc,k−1 ) + . . + anA v1 (tc,k−nA ) + b0 u(tc,k−d ) + . . . 2) j=0 where nA v0,1 (tc,k ) = v0,1 (tc,k−1 ) + D δ(tc,k ) + D ai δ(tc,k−i ) i=1 represents the impulse response of ﬁlter A(z −1 )/Ad (z −1 ). 3) 40 4 Self-tuning Voltage Regulators in which A(1) is the value assumed by the polynomial A(z −1 ) for z −1 = 1.
27) the diﬀerence ﬁlter Ad removes the oﬀset due to the no-load voltage disturbance . 30) is rewritten as p0 Ad (z −1 ) E(z −1 ) ν(tc,k+d ) = p0 E (z −1 ) ν(tc,k+d ) − p0 ed−1 ν(tc,k ) where the sequence E (z −1 ) ν(tc,k+d ) = e0 + (e1 − e0 ) z −1 + (e2 − e1 ) z −2 + . . . 30). Nevertheless, the term p0 ed−1 ν(tc,k ) relating to the present value of the noise aﬀects the prediction at time tc,k . 31) if, for the ﬁrst nA − 1 steps following a variation of the disturbance amplitude D, polynomial E(z −1 ) has roots inside the unit circle, since p0 A(z −1 ) E(z −1 ) is a FIR ﬁlter (ﬁnite impulse response).