A STUDY OF THE MULTIPLICITY AND STABILITY OF THE LOAD FLOW SOLUTIONS
Abstract
The voltage stability of an interconnected power system has become an important consideration in system planning and operation. In this thesis, the solution techniques of load flow equations as well as the multiplicity and stability of the load flow solutions have been studied. A technique that reduces the redundant nonlinear equations corresponding to the change of the square of voltage magnitude in Cartesian coordinates has been developed. It is shown that the number of load flow equations, independent of the choice of coordinates, is 2N-NG-1, where N and NG are the number of total and generator buses respectively. To reduce computer storage and computational time, a fast decoupled method in Cartesian form has also been developed. This method has the same properties as Stott's polar form method, but its solution time is of the order of one-half to one-third of that in Polar form for the systems studied, because of the terms of cosine and sine which consume more computational time have been eliminated in the load flow equations. The multiplicity of load flow solutions has been illustrated in the voltage spaces and this indicates that up to 2('M) load flow solutions may exist for an N-bus system with M load buses (M < N). Also, the effects on these solutions of changing the system loadings have been studied. This demonstrates that some of the solutions may disappear when the system is heavily loaded or connected by long transmission lines. Furthermore, the stability of these solutions with consideration of machine/excitation dynamics and nonlinear loads has been investigated. A qualitative analysis of one-machine to one-load system which clearly expounds the concepts of voltage instability is given. A linear dynamic model of a multimachine power system suitable for the study of voltage stability has been developed and a method to formulate the model of nonlinear loads is also developed. Two different kind systems have been investigated for voltage stability. One represents exchange of power between two areas connected through high voltage transmission lines, and the other represents transmission of power to a load center. Also, eigenvalue sensitivities with respect to parameters and output sensitivity with respect to modes are studied. These studies indicate that the characteristics of nonlinear loads are of paramount importance in voltage stability studies and the induction motor is the most critical constituent.
Degree
Ph.D.
Subject Area
Electrical engineering
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