Extending the perturbation technique to the modal representation of nonlinear systems

Soltani, Sepehr; Pariz, Naser; Ghazi, Reza

doi:10.1016/j.epsr.2009.02.011

Cited by 6 publications

(3 citation statements)

References 13 publications

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“…Technique for handling internal resonances is outside the scope of this paper and the interested reader can refer to [20]. At the end, system (14) has two advantages. Due to the normal transform, it is first much simpler than system (2) since it has much less nonlinear terms and second, it can be consistently truncated to a few modes, thanks to the concept of nonlinear modes and invariant manifolds (see [45], [47], [48] and references therein).…”

Section: B Normal Form Theorymentioning

confidence: 99%

“…Due to the normal transform, it is first much simpler than system (2) since it has much less nonlinear terms and second, it can be consistently truncated to a few modes, thanks to the concept of nonlinear modes and invariant manifolds (see [45], [47], [48] and references therein). System (14) can then be used for nonlinear modal analyses, time integration and many more, and can be reversed to its original coordinates x by applying successively, the change of variables (10) and (5).…”

Section: B Normal Form Theorymentioning

confidence: 99%

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

Ugwuanyi

Kestelyn

Thomas

et al. 2020

IEEE Trans. Power Syst.

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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.

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Section: B Normal Form Theorymentioning

confidence: 99%

Section: B Normal Form Theorymentioning

confidence: 99%

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

Ugwuanyi

Kestelyn

Thomas

et al. 2020

IEEE Trans. Power Syst.

View full text Add to dashboard Cite

show abstract

“…The modal series method, which was first introduced in Ref. [21], gives a good view of nonlinear systems' dynamical behaviours [22][23]. This method was firstly developed for the analysis of dynamical systems with nonlinear terms [24][25][26], and recently it was extended for the optimal control and MPC of nonlinear dynamical systems [27][28][29].…”

Section: Introductionmentioning

confidence: 99%

On a New and Efficient Numerical Technique to Solve a Class of Discrete-time Nonlinear Optimal Control Problems

Abadi¹,

Vaziri²,

Jajarmi³

2019

JESA

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This article proposes a new and efficient iterative procedure to solve a class of discrete-time nonlinear optimal control problems. Based on the Pontryagin's maximum principle, the necessary optimality conditions are formulated in the form of a nonlinear discrete boundary value problem (BVP). This problem is then reduced into a sequence of linear discrete BVPs by applying a series expansion approach called the modal series method. Solving the aforementioned sequence by using the techniques of solving linear difference equations, the optimal control law is derived in the form of a uniformly convergent series. In order to demonstrate the efficiency of the proposed method in practice, an iterative algorithm with a fast rate of convergence is provided. In a recursive manner, only a few iterations are needed to find a suboptimal control law with enough accuracy. The effectiveness of this new technique is verified by solving some numerical examples.

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