Control Systems

Download Computational Techniques for Voltage Stability Assessment by Venkataramana Ajjarapu PDF

By Venkataramana Ajjarapu

This ebook presents accomplished info on continuation strength movement, and experiences suggestions in bifurcation concept and continuation equipment for assessing energy method voltage balance. the writer proposes a uniform framework that gives computational ways for either momentary and long term voltage balance phenomena. Readers can entry the author’s web-based simulation instruments, that are in keeping with the recommendation during this booklet, to simulate assessments of structures as much as the scale of two hundred busses.

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Additional resources for Computational Techniques for Voltage Stability Assessment and Control (Power Electronics and Power Systems)

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Here, x denotes an /^-dimensional vector. Continuation methods usually consist of the following [25]: predictor, parameterization strategy, corrector and step length control. 3 Detection of Bifurcation Points the homotopy method. 15, this corresponds to the assumption that g has a known zero point. ^j. With a predictor-corrector method, the stepy to step 7+1 is split into two parts, with (Xj^^, Xj) produced in between by the prediction. 12. The distance between two consecutive solutions is called the step size.

1 Selecting the continuation parameter The best method of selecting the correct continuation parameter at each step is to select the state variable (change the underlined to variable) with the largest tangent vector component. In short, we select the state variable (change the underlined to variable) evidencing the maximum rate of change near a given solution. To begin with, /I is a good choice, and subsequent continuation parameters can be evaluated as: x,:\t,\=max{\t,l\t,l'-,\tj} Here, t_ is the tangent vector.

12 is equivalent to solving the following differential equation. 17a) With the initial conditions x{X) = xo, where F(xo, Ao) = 0. 17b with an appropriate initial value. VF, However, here, the singularity ofFx creates numerical problems. Continuation methods can well alleviate this problem. The continuation algorithm starts from a known solution and uses a predictor-corrector scheme to find subsequent solutions at different 1 values. 17c) =0 Let T=[dx d XY, where T is a n+\ dimensional vector with Tn+i = X.

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