A Novel Method for Accelerating the Analysis of Nonlinear Behaviour of Power Grids using Normal Form Technique

Abstract

Today's power systems are strongly nonlinear and are becoming more complex with the large penetration of power-electronics interfaced generators. Conventional Linear Modal Analysis does not adequately study such a system with complex nonlinear behavior. Inclusion of higher-order terms in small-signal (modal) analysis associated with the Normal Form theory proposes a nonlinear modal analysis as an efficient way to improve the analysis. However, heavy computations involved make Normal Form method tedious, and impracticable for large power system application. In this paper, we present an efficient and speedy approach for obtaining the required nonlinear coefficients of the nonlinear equations modelling of a power system, without actually going through all the usual high order differentiation involved in Taylor series expansion. The method uses eigenvectors to excite the system modes independently which lead to formulation of linear equations whose solution gives the needed coefficients. The proposed method is demonstrated on the conventional IEEE 9-bus system and 68-bus New England/New York system.

Power System Nonlinear Modal Analysis Using Computationally Reduced Normal Form Method

“…The NF solution obtained with this reduced model shall be referenced as NF-9310 against the full model referenced as NF-35,000. The computation of the remaining coefficients is easy since one just has to solve a set of linear equations (please see [32,37]). Figure 2 shows drastic reduction in computation time brought by the proposed method.…”

“…The time considered in Figure 2 is only for computing the coefficients. The fast NF computation method proposed in [32,37] was used. It can be seen that more significant reduction is achieved by skipping some interactions.…”

“…The main goal of this paper is to reduce the computational burden associated with NF application to power systems, especially when it is applied to understand the significant modal interactions and the accompanying new frequencies. In previous works, an alternative method for computing selectively any desired term rapidly by avoiding the usual Taylor expansion was proposed [32,33,37]. The present paper investigates further reduction of NF computation by considering fewer terms in the nonlinear approximation based on the information provided by the linear analysis.…”

“…This however, does not reduce any operation in NF analysis other than the grid size. A method which facilitates the computation of the polynomial coefficients required for NF application has been proposed in [32,33], however, much reduction is still needed as there are still too many terms being considered.…”