Computational Techniques for Voltage Stability Assessment by Venkataramana Ajjarapu

By Venkataramana Ajjarapu

This ebook presents complete info on continuation energy circulate, and studies techniques in bifurcation conception and continuation tools for assessing energy procedure voltage balance. the writer proposes a uniform framework that gives computational techniques for either momentary and long term voltage balance phenomena. Readers can entry the author’s web-based simulation instruments, that are in response to the recommendation during this publication, to simulate assessments of platforms as much as the dimensions of 2 hundred busses.

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However, convergence of the direct method is very fast if the initial operating point is close to the turning point. The enlarged system can be solved in such a way that it requires the solution of nxn (n is the dimension of the Jacobian Fx(x, X)) linear systems, each with the same matrix. This method needs only one LU decomposition. At this turning point, rank F^ix, X)=nA and F^ (Xc, Xc) 8 range Fx(xc, Xc), that is rank F^ (Xc, Xc)/ Fx (x^ Xc) = n. These are called transversality conditions. Depending on the type of transversality condition, different types of static bifurcations can occur.

Solids Struct. , 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.

1) This equation is obtained by introducing a load parameter,/I, into the original system of nonlinear equations, F(x) = 0. For a range of values of >i, it is quite possible to identify each solution on the branch in a mathematical way [2]. But not every branch can be parameterized by an arbitrary parameter. 1 along a given path can be found for each value of A, although problems arise when a solution does not exist for some maximum possible X value. At this point, one of the 50 Continuation Power Flow state variables, x^, can be used effectively as the parameter to be varied, choice of which is determined locally at each continuation step.

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