Abstract
This paper addresses the problem of voltage collapse in power systems. More precisely, we exhibit a voltage collapse in a power system with two buses. This study is carried out with the help of two approaches. The first is a dynamical approach where a saddle‐node bifurcation is analyzed and the second is an algebraic approach. Both approaches deal with the static behavior of the power system, but some dynamic aspects may be observed. An equivalence between the algebraic and dynamical approaches is obtained. The need to use both models comes from the fact that they are usually exploited in the literature, but a deep theoretical justification is still pending. Such a justification is meant in this work.
Highlights
Studying saddle-node in dynamical systems may help to understand and prevent some problems
Studying the loss of transversality of the curves A = 0 and B = 0 may provide some important pieces of information about voltage collapse in power systems
This paper dealt with the important problem of saddle-node bifurcation in power systems
Summary
Studying saddle-node in dynamical systems may help to understand and prevent some problems. The study of saddle-node in power systems has increased in recent years Such investigations help in understanding how a system may become unstable as a consequence of successive small parameter variations. This problem is known as voltage collapse, and deserves special attention from engineers and operators around the world [1]. Identifying the point of bifurcation plays a crucial role on power system analysis, since it may help the operator to avoid instability problems. For this purpose, continuation methods may be accurate and useful, since they identify the saddle-node point and trace the bifurcation diagram.
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