Increasing nonlinearity in today’s grid challenges the conventional small-signal (modal) analysis (SSA) tools. For instance, the interactions among modes, which are not captured by SSA, may play significant roles in a stressed power system. Consequently, alternative nonlinear modal analysis tools, notably Normal Form (NF) and Modal Series (MS) methods are being explored. However, they are computation-intensive due to numerous polynomial coefficients required. This paper proposes a fast NF technique for power system modal interaction investigation, which uses characteristics of system modes to carefully select relevant terms to be considered in the analysis. The Coefficients related to these terms are selectively computed and the resulting approximate model is computationally reduced compared to the one in which all the coefficients are computed. This leads to a very rapid nonlinear modal analysis of the power systems. The reduced model is used to study interactions of modes in a two-area power system where the tested scenarios give same results as the full model, with about 70% reduction in computation time.

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.

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.

No abstract

No abstract

No abstract

No abstract

The power systems in developing countries are usually stressed and operated near their stability limits. Consequently, accurate sources of oscillations and their controls can present a challenge. This paper reports a comprehensive study of the oscillations in the Nigerian 48-bus power system. The dominant modes, sensitive locations for faults, and the most responsible generators were identified by modal analysis. Uniquely, the potential for nonlinear modal interaction of these modes was carefully investigated. The low-frequency modes identified are 1 Hz, 1.14 Hz, and 1.37 Hz, and they are associated mainly with the generators at Kainji, Afam, and Delta power stations. The results indicate the existence of inter-area phenomena and nonlinear modal interactions among these modes. Also, the analysis revealed that the generator at the Kainji power station is most affected by the nonlinear interactions.<br>