Global optimal polynomial approximation for parametric problems in power systems

Abstract

The influence of parameters on system states for parametric problems in power systems is to be evaluated. These parameters could be renewable generation outputs, load factor, etc. Polynomial approximation has been applied to express the nonlinear relationship between system states and parameters, governed by the nonlinear and implicit equations. Usually, sampling-based methods are applied, e.g., data fitting methods and sensitivity methods, etc. However, the accuracy and stability of these methods are not guaranteed. This paper proposes an innovative method based on Galerkin method, providing global optimal approximation. Compared to traditional methods, this method enjoys high accuracy and stability. IEEE 9-bus system is used to illustrate its effectiveness, and two additional studies including a 1648-bus system are performed to show its applications to power system analysis.

Multi-Objective Optimal Control Approach for Static Voltage Stability of Power System Considering Interval Uncertainty of the Wind Farm Output

“…Therefore, using the PA models to replace the original model to obtain the optimal control scheme has high accuracy. To solve the PF, the utopian line is equally divided into 20 segments (i.e., w = {0, 0.05, 0.1… 1}), and the discrete PF is obtained by repeatedly solving the formula of the NNC method (25) with the w value of each division point. Meanwhile, the proposed PA method is used to calculate the continuous PF, and the comparative results are shown in Figure. 6.…”

“…Therefore, based on NNC and PA methods, this paper proposes a method to obtain the approximate continuous PF of the bi-objective optimization problem. As shown in Figure. 1, according to the NNC method, a discrete point A on the PF of the bi-objective optimization problem (24) can be obtained by solving the single-objective optimization problem shown in (25) [26,27]:…”

“…where J ) on the PF. By evenly taking the value of w in the interval (0, 1) to obtain a series of evenly distributed points on the utopian line, the evenly distributed discrete PF can be obtained by solving the optimization problem in (25). Therefore, as long as w is selected as a parameter, KKT conditions can be used to convert the optimization problem (25) into nonlinear equations, and these equations can be projected onto the polynomial basis functions.…”

“…Based on [21], the bound of the reactive power output of generators was further considered in [22], and a more accurate SVS region boundary was obtained. The PA method has also been applied in other power system analysis fields [23][24][25]. Because the relationships between the lower and upper bounds of the SVSM interval and the control variables are relatively complicated, obtaining the simplified approximate expression through the PA method can provide an effective way to solve the multi-layer optimal SVSM control problem.…”

Parametric Problems in Power System Analysis: Recent Applications of Polynomial Approximation Based on Galerkin Method

“…Hence the problems at hand, termed parametric problems (PPs) in this paper, are to seek an explicit function describing the relationship between parameters and states [4]. Since the parameter-state relationship in power system analysis is usually implicit and too complicated to obtain exactly, the PP comes down to acquire an accurate explicit approximate function that describes this relationship.…”