A New Fast Track to Nonlinear Modal Analysis of Power System Using Normal Form

Abstract

The inclusion of higher-order terms in small-signal (modal) analysis augments the information provided by linear analysis and enables better dynamic characteristic studies on the power system. This can be done by applying Normal Form theory to simplify the higher order terms. However, it requires the preliminary expansion of the nonlinear system on the normal mode basis, which is impracticable with standard methods when considering large scale systems. In this paper, we present an efficient numerical method for accelerating those computations, by avoiding the usual Taylor expansion. Our computations are based on prescribing the linear eigenvectors as unknown field in the initial nonlinear system, which leads to solving linear-only equations to obtain the coefficients of the nonlinear modal model. In this way, actual Taylor expansion and associated higher order Hessian matrices are avoided, making the computation of the nonlinear model up to third order and nonlinear modal analysis fast and achievable in a convenient computational time. The proposed method is demonstrated on a single-machine-infinitebus (SMIB) system and applied to IEEE 3-Machine, IEEE 16-Machine and IEEE 50-Machine systems.

A normal form-based power system out-of-step protection

“…The frequency shift phenomenon occurs in power systems as well, but it is not given the attention it deserves. These critical applications sparked a slew of studies aimed at easing NF's computational burden [24][25][26]. In the following subsections, the NF theory for first and second-order systems is reviewed.…”

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.…”

Solving Magnetodynamic Problems via Normal Form Method

“…More recently, it is being applied to reduce the size of finite element models [4]. It is also applied to study the nonlinear behavior of stressed power systems [5], [6]. It is attractive because it leads to an analytical (closed-form) expression for the solution.…”