Computational Techniques for Voltage Stability Assessment by Venkataramana Ajjarapu

By Venkataramana Ajjarapu

Voltage balance is a serious factor within the safe operation of the restructured energy process. bad voltage stipulations lead not just to voltage cave in within the method yet may also set off oscillatory instability that could reason a lack of synchronism. A serious query is tips on how to estimate the gap to voltage instability given the current nation of the system.

Computational strategies for Voltage balance evaluate and regulate brings jointly in a single position the computational instruments essential to compute the voltage balance margin. the elemental computational device for tracing the P-V curve and equilibria tracing is the continuation energy circulate. this system in addition to the set of rules is defined intimately by means of the writer. Sensitivity of the voltage balance margin to numerous parameters within the process is mentioned generally either theoretically and in a numerical context.

The key recommendations of either saddle node and Hopf bifurcation are lined. those are illustrated with the differential-algebraic equation (DAE) version of the approach. The version is advanced sufficient to incorporate Load Tap-Changing transformers in addition to HVDC versions. The dynamic version of the producing unit comprises the exciter because it performs a very important position in voltage balance. A promising decoupled dynamic simulation approach is brought for time area research.

Computational suggestions for Voltage balance evaluate and keep an eye on offers the computational instruments and algorithms wanted for improvement of online voltage defense assessment

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19b) 7,-77 = 0 Selection of the continuation parameter corresponds to the variable that has the largest tangent vector component. Therefore 7, at a particular step is the maximum of (| Tj \,\T2 |, • • • | T^^^ \). Now, once a suitable index k and value of rj are chosen, a slightly modified Newton-Raphson iterative process can be used to solve the above set of equations. 3 Detection of Bifurcation Points 35 The corrector Jacobian can be seen to have the same form as the predicted Jacobian. Actually the index k used in the corrector is the same as that of used in the predictor and rj will be equal to 7^ , the predicted value Yk.

The direct method. When the Jacobian becomes singular, F(x, X) =0 can not be solved by regular Newton-Raphson method in the present form. To avoid this singularity several methods have been published in the mathematical literature [29, 30, 31]. In these references the authors cleverly augmented the original system of equations in such a way that that for this enlarged system, the fold point becomes regular. 21b) F(x,A) ' =0 G(Y) = where {xc, Xc) is a fold point oiF^Xc, X) = 0. This procedure basically augments the original equations oiF(x, X) =0 by Fx(x, X)h =0, with hk= I.

Chiang. H. , Toward a theory of voltage collapse in electric power systems. Systems and control letters, Vol. , Observations on the geometry of saddle node bifurcations and voltage collapse in electric power systems. IEEE Trans, on CAS, part I, Vol. , Chaos (Singapore: World Scientific) 1990 Moon, F. C , Chaotic Vibration (New York: Wiley) 1987 Thomson, J. M. , Stewart, H. P. , Study of Hopf bifurcations in a simple power system model. Proceedings of the 39th IEEE Conference on Decision and Control, Vol.

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