Perturbation analysis of power systems: effects of second- and third-order nonlinear terms on system dynamic behavior

IEEE Trans. Power Syst.

et al. 2018

The inclusion of higher-order terms in small-signal (modal) analysis has been an intensive research topic in nonlinear power system analysis. Inclusion of second-order terms with the method of normal forms (MNF) has been well developed and investigated, overcoming the linear conventional small-signal methods used in the power system control and stability analysis. However, application of the MNF has not yet been extended to include third-order terms in a mathematically accurate form to account for nonlinear dynamic stability and dynamic modal interactions. Due to the emergence of larger networks and long transmission line with high impedance, modern grids exhibit predominant nonlinear oscillations and existing tools have to be upgraded to cope with this new situation. In this paper, first, fundamentals of normal form theory along with a review of existing tools based on this theory is presented. Second, a new formulation of MNF based on a third-order transformation of the system's dynamic approximation is proposed and nonlinear indexes are proposed to make possible to give information on the contribution of nonlinearities to the system stability and on the presence of significant third-order modal interactions. The induced benefits of the proposed method are compared to those afforded by existing MNFs. Finally, the proposed method is applied to a standard test system, the IEEE 2-area 4-generator system, and results given by the conventional linear small signal and existing MNFs are compared to the proposed approach. The applicability of the proposed MNF to larger networks with more complex models has been evaluated on the New England-New York 16-machine 5-area system. Index Terms-Interconnected power system, methods of normal forms, nonlinear modal interaction, power system dynamic, stability.

Section: Need For Inclusion Of Higher-order Termsmentioning

confidence: 99%

“…To simplify as much as possible the third order terms, the following third-order NF transformation is applied to (17) [16]:…”

Section: Simplification Of a Maximum Number Of Nonlinear Termsmentioning

confidence: 99%

Section: Simplification Of a Maximum Number Of Nonlinear Termsmentioning

confidence: 99%

See 1 more Smart Citation

An Accurate Third-Order Normal Form Approximation for Power System Nonlinear Analysis

Tian

IEEE Trans. Power Syst.

et al. 2018

“…The nullity of the denominators leads to particular relations between the complex eigenvalues called internal resonances. If no internal resonance occurs, (11) reduces to a fully linear system:ż = Λz. (13) In the other cases where internal resonances occur, all nonlinear terms cannot be eliminated from (11) and 13becomeṡ…”

Section: B Normal Form Theorymentioning

confidence: 99%

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

Ugwuanyi

IEEE Trans. Power Syst.

et al. 2020

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.

“…The increasing number of renewable-energy-basedgenerators, leading to unbalanced energy generation and presence of weak grids, associated to fast control devices [2], increases the nonlinear behavior of the system leading to the necessity of including 3rd order terms in the modal analysis. Several explorations [3], [4], [17], [18] have been done, but their applications haven't been fully developed. Among them, methods [3], [4] are advancements of a method validated by physical experiments in beam structure analysis [19]- [21].…”

Section: B Various Analysis Toolsmentioning

confidence: 99%

Normal form based analytical investigation of nonlinear power system dynamics under excitation

Tian

2017 IEEE Power &Amp; Energy Society General Meeting

2017

The increase of power exchanges through long lines makes power systems exhibiting predominant nonlinear interarea or local oscillations, for which the conventional linear analysis fails to offer an accurate picture. Existing 2nd Order and 3rd Order Normal Form methods make possible to do analytical investigations of the nonlinear interactions by including higherorder terms. However, those methods can only study the power system dynamics under free oscillations, usually used to study the effect of disturbances apply to the state variables, e.g the post-fault cases. When the system is subject to excitation, as variable power references or variable loads, there is no available Normal Form method in the literature making possible to study the higher-order oscillations. In this paper, for the first time to the author's knowledge, a methodology based on the Normal Form theory is proposed to give an analytical description of power system nonlinear dynamic response of excited power systems. The proposed method makes possible to simplify the initial problem by decomposing the complex power system dynamics into a set of simpler normal dynamics. The proposed analytical normal dynamics are validated using time-domain simulations and open the way to new analyzing tools for power grids.