Optimal Allocation of Virtual Inertia Devices for Enhancing Frequency Stability in Low-Inertia Power Systems

Tuo, Mingjian; Li, Xingpeng

doi:10.1109/naps52732.2021.9654729

Cited by 7 publications

(8 citation statements)

References 11 publications

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“…In [27], it is proved that the multiplier matrices Ω c are Xiao matrices. They coincide with Formulas ( 27) and ( 28) of Theorem 2.…”

Section: N(λ ρ )mentioning

confidence: 99%

“…Let us assume that system (54) is stable, unless otherwise stated, completely controllable, and observable, and all eigenvalues of matrix A m are different and do not coincide with the eigenvalues of matrix A. Following [27], consider the following continuous differential equations associated with these systems of the form dP(t) dt = AP(t) + P(t)A T + R, P(0) = 0 n×n , ( 55)…”

Section: Spectral Expansions Of Solutions To Sylvester Differential E...mentioning

confidence: 99%

“…It was shown that the solution matrices of the Lyapunov equations can be computed in a new way based on the use of Rouse tables that depends only on the coefficients of the characteristic equation of the dynamic matrix of the system. In recent years, due to the rapid growth of renewable generation in electric power systems, serious problems of controlling the modes of these systems have arisen due to the integration of renewable generation with conventional generation based on the use of conventional synchronous generators [27][28][29][30]. One of the directions for solving the problems of ensuring the stability of the modes of electric power systems is the use of virtual inertia devices in distributed power systems [27][28][29].…”

Section: Introductionmentioning

confidence: 99%

“…In recent years, due to the rapid growth of renewable generation in electric power systems, serious problems of controlling the modes of these systems have arisen due to the integration of renewable generation with conventional generation based on the use of conventional synchronous generators [27][28][29][30]. One of the directions for solving the problems of ensuring the stability of the modes of electric power systems is the use of virtual inertia devices in distributed power systems [27][28][29]. The main idea of virtual inertia is to use the synchronous generator model to stabilize the frequency control modes of distributed power systems.…”

Section: Introductionmentioning

confidence: 99%

“…The main idea of virtual inertia is to use the synchronous generator model to stabilize the frequency control modes of distributed power systems. In [27], a method and algorithm for the optimal control of the grid frequency based on the use of a simplified synchronous generator model for a reduced-order model based on the model optimization criterion using the H2-norm of the transfer functions of the full and simplified models were proposed. It is well-known that the Gramian method [1,6] is used to solve this problem.…”

Section: Introductionmentioning

confidence: 99%

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Spectral Decomposition of Gramians of Continuous Linear Systems in the Form of Hadamard Products

Yadykin

2023

Mathematics

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New possibilities of Gramian computation, by means of canonical transformations into diagonal, controllable, and observable canonical forms, are shown. Using such a technique, the Gramian matrices can be represented as products of the Hadamard matrices of multipliers and the matrices of the transformed right-hand sides of Lyapunov equations. It is shown that these multiplier matrices are invariant under various canonical transformations of linear continuous systems. The modal Lyapunov equations for continuous SISO LTI systems in diagonal form are obtained, and their new solutions based on Hadamard decomposition are proposed. New algorithms for the element-by-element computation of Gramian matrices for stable, continuous MIMO LTI systems are developed. New algorithms for the computation of controllability Gramians in the form of Xiao matrices are developed for continuous SISO LTI systems, given by the equations of state in the controllable and observable canonical forms. The application of transformations to the canonical forms of controllability and observability allowed us to simplify the formulas of the spectral decompositions of the Gramians. In this paper, new spectral expansions in the form of Hadamard products for solutions to the algebraic and differential Sylvester equations of MIMO LTI systems are obtained, including spectral expansions of the finite and infinite cross - Gramians of continuous MIMO LTI systems. Recommendations on the use of the obtained results are given.

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“…In [27], it is proved that the multiplier matrices Ω c are Xiao matrices. They coincide with Formulas ( 27) and ( 28) of Theorem 2.…”

Section: N(λ ρ )mentioning

confidence: 99%

Section: Spectral Expansions Of Solutions To Sylvester Differential E...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Spectral Decomposition of Gramians of Continuous Linear Systems in the Form of Hadamard Products

Yadykin

2023

Mathematics

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Effect of DFIG control parameters on small signal stability in power systems

Liu

Wang

et al. 2023

Sci Rep

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The doubly-fed induction generator (DFIG) with virtual inertia control and reactive damping control gives a renewable energy generation system inertia and damping characteristics similar to those of a thermal power plant, and the parameters of the control strategy have a direct impact on the small-signal stability of the system. This paper firstly introduces the operating characteristics and control strategies of DFIG-based damping control and virtual inertia control, establishes a small-signal model of the control-based DFIG integrated interconnected system, and investigates the effects of virtual inertia and reactive damping values on the small-signal stability of the system; then, the maximum damping ratio of the interval oscillation mode in small disturbance analysis is taken as the optimization objective, and the control parameters are the optimization variables. An optimization method of inertia and damping parameters is established for improving the small disturbance stability of the system. The results show that the optimization procedure could improve the damping ratio of the interval oscillation mode while ensuring the system frequency. The effects of virtual inertia and reactive damping values on the small signal stability of the system are investigated, and an optimal allocation model and method for virtual inertia used to improve the small disturbance stability of the system is proposed.

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An Analytical Formulation for Mapping the Spatial Distribution of Nodal Inertia in Power Systems

et al. 2023

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Mapping the spatial distribution of nodal inertia is crucial for helping system operators identify locational frequency stability issues in the power system operation planning process. Currently, index-based methods cannot retrieve the nodal inertia values for all load buses. To do so, this paper proposes an accurate analytical formulation relying only on steady-state system parameters to determine the nodal inertia values and, thus, map the spatial distribution of system inertia. The performance and reproducibility of the proposed formulation are evaluated using three test systems: a 5-bus radial system with two synchronous generators, a multimachine IEEE 68-bus benchmark system, and a larger NPCC 140-bus test system. We validate the proposed spatial distribution of nodal inertia using time-domain simulations and numerical estimations. In addition, we compare our method against the inertia distribution indexes presented in the literature. The results indicate that our formulation adequately quantifies the nodal inertia value in system buses, with low computational cost, and providing a suitable tool for operation planning analysis.

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Optimal Allocation of Virtual Inertia Devices for Enhancing Frequency Stability in Low-Inertia Power Systems

Cited by 7 publications

References 11 publications

Spectral Decomposition of Gramians of Continuous Linear Systems in the Form of Hadamard Products

Spectral Decomposition of Gramians of Continuous Linear Systems in the Form of Hadamard Products

Effect of DFIG control parameters on small signal stability in power systems

An Analytical Formulation for Mapping the Spatial Distribution of Nodal Inertia in Power Systems

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