Abstract
In this paper, we propose an efficient continuation method for locating multiple power flow solutions. We adopt the holomorphic embedding technique to represent solution curves as holomorphic functions in the complex plane. The holomorphicity, which provides global information of the curve at any regular point, enables large step sizes in the path-following procedure such that non-singular curve segments can be traversed with very few steps. When approaching singular points, we switch to the traditional predictor-corrector routine to pass through them and switch back afterward to the holomorphic embedding routine. We also propose a warm starter when switching to the predictor-corrector routine, i.e. a large initial step size based on the poles of the Pad\'{e} approximation of the derived holomorphic function, since these poles reveal the locations of singularities on the curve. Numerical analysis and experiments on many standard IEEE test cases are presented, along with the comparison to the full predictor-corrector routine, confirming the efficiency of the method.
Highlights
The electric power grid is a critical energy infrastructure for power generation, transmission, and distribution in modern society
Identifying the region of attraction about the operating condition, i.e. a stable equilibrium point (SEP) of the underlying dynamical system, can significantly improve the situational awareness and, will be of great importance to avoid blackouts. Characterizing this region requires the knowledge of a special type of unstable equilibrium point (UEP) which is called the type-1 UEP [1], [2]
HOLOMORPHIC EMBEDDING TECHNIQUE Theorem 1 states that the 1-dimensional curves derived from the elliptical formulation EFl− can be acquired alternatively from a particular parameterized power flow problem PF(U) − αE −1el
Summary
The electric power grid is a critical energy infrastructure for power generation, transmission, and distribution in modern society. In 1989, [13], [14] introduced the probability-one homotopy continuation method to find all the complex-valued solutions to the power flow problem. Though efficient, [19] provided a counter-example for [17] To rectify their method, an elliptical formulation of the power flow problem is used in [20] to restrict the curve design on high dimensional ellipses. An elliptical formulation of the power flow problem is used in [20] to restrict the curve design on high dimensional ellipses It helps solve all the standard IEEE test cases which can be verified by the homotopy method in a reasonable time, including the counter-example in [19]. 5) Computed solution sets for several large test cases which currently are intractable by homotopy continuation method or the similar
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