https://sam.ensam.eu:443 The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material. Sat, 07 Mar 2026 00:40:38 GMT 2026-03-07T00:40:38Z http://hdl.handle.net/10985/17962 A New Fast Track to Nonlinear Modal Analysis of Power System Using Normal Form UGWUANYI, Nnaemeka Sunday; THOMAS, Olivier; MARINESCU, Bogdan; MESSINA, Arturo Roman; KESTELYN, Xavier 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-infinite-bus (SMIB) system and applied to IEEE 3-Machine, IEEE 16- Machine and IEEE 50-Machine systems. Wed, 01 Jan 2020 00:00:00 GMT http://hdl.handle.net/10985/17962 2020-01-01T00:00:00Z UGWUANYI, Nnaemeka Sunday THOMAS, Olivier MARINESCU, Bogdan MESSINA, Arturo Roman KESTELYN, Xavier 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-infinite-bus (SMIB) system and applied to IEEE 3-Machine, IEEE 16- Machine and IEEE 50-Machine systems. http://hdl.handle.net/10985/22519 A normal form-based power system out-of-step protection UGWUANYI, Nnaemeka Sunday; KESTELYN, Xavier; THOMAS, Olivier; MARINESCU, Bogdan; WANG, Bin This paper proposes a new system-level application for monitoring out-of-step (OOS) events in power systems. As already known, amplitude-dependent frequency shift is a nonlinear phenomenon of electromechanical oscillations under large disturbances. The frequency shift indicates the system’s nearness to instability. This new tool utilizes the Normal Form method to identify the named phenomenon, leading to accelerated OOS detection. The proposed strategy is illustrated and compared to the equal-area criterion method in a single-machine-infinite-bus power system. Extensive tests on IEEE 3- and IEEE 50-machine power systems prove the efficacy and potential of the proposed method for online warnings of instability and ranking of vulnerable system modes. Fri, 01 Jul 2022 00:00:00 GMT http://hdl.handle.net/10985/22519 2022-07-01T00:00:00Z UGWUANYI, Nnaemeka Sunday KESTELYN, Xavier THOMAS, Olivier MARINESCU, Bogdan WANG, Bin This paper proposes a new system-level application for monitoring out-of-step (OOS) events in power systems. As already known, amplitude-dependent frequency shift is a nonlinear phenomenon of electromechanical oscillations under large disturbances. The frequency shift indicates the system’s nearness to instability. This new tool utilizes the Normal Form method to identify the named phenomenon, leading to accelerated OOS detection. The proposed strategy is illustrated and compared to the equal-area criterion method in a single-machine-infinite-bus power system. Extensive tests on IEEE 3- and IEEE 50-machine power systems prove the efficacy and potential of the proposed method for online warnings of instability and ranking of vulnerable system modes. http://hdl.handle.net/10985/18337 Power System Nonlinear Modal Analysis Using Computationally Reduced Normal Form Method UGWUANYI, Nnaemeka Sunday; MARINESCU, Bogdan; THOMAS, Olivier; KESTELYN, Xavier 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. Wed, 01 Jan 2020 00:00:00 GMT http://hdl.handle.net/10985/18337 2020-01-01T00:00:00Z UGWUANYI, Nnaemeka Sunday MARINESCU, Bogdan THOMAS, Olivier KESTELYN, Xavier 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. http://hdl.handle.net/10985/18014 A Novel Method for Accelerating the Analysis of Nonlinear Behaviour of Power Grids using Normal Form Technique UGWUANYI, Nnaemeka Sunday; THOMAS, Olivier; MARINESCU, Bogdan; KESTELYN, Xavier 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. Tue, 01 Jan 2019 00:00:00 GMT http://hdl.handle.net/10985/18014 2019-01-01T00:00:00Z UGWUANYI, Nnaemeka Sunday THOMAS, Olivier MARINESCU, Bogdan KESTELYN, Xavier 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.