A Galerkin Method-Based Polynomial Approximation for Parametric Problems in Power System Transient Analysis

Xia, Bingqing; Wu, Hao; Qiu, Yiwei; Lou, Boliang; Song, Yonghua

doi:10.1109/tpwrs.2018.2879367

Cited by 26 publications

(12 citation statements)

References 23 publications

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“…Similarly, KKT conditions can be used to transform the mid-layer optimization problems (22) and (23) into nonlinear equations, and then the nonlinear equations can be projected onto each basis function. By solving the projection equations, the approximate target expressions λ1(PG0,UGref,Qc) and λ2(PG0,UGref,Qc) can be obtained.…”

Section: ) Pa Of the Mid-level Optimization Problemsmentioning

confidence: 99%

“…Based on [21], the bound of the reactive power output of generators was further considered in [22], and a more accurate SVS region boundary was obtained. The PA method has also been applied in other power system analysis fields [23][24][25]. Because the relationships between the lower and upper bounds of the SVSM interval and the control variables are relatively complicated, obtaining the simplified approximate expression through the PA method can provide an effective way to solve the multi-layer optimal SVSM control problem.…”

Section: Introductionmentioning

confidence: 99%

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Multi-Objective Optimal Control Approach for Static Voltage Stability of Power System Considering Interval Uncertainty of the Wind Farm Output

et al. 2020

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The static voltage stability margin (SVSM) of a power system considering the uncertain fluctuation range of wind farm (WF) output can be described as an interval value called the SVSM interval. A multi-objective optimal control model for SVS of a power system considering the interval uncertainty of WF output is proposed. The objective functions of the model are to increase the central value and reduce the fluctuation range of the SVSM interval, and the decision variables are the active power output and terminal voltage of generators and the switching capacity of shunt capacitors. Thus, it is a multi-layer optimization model. A parametric approximation (PA) method is used to obtain the approximate functional relationship between the optimal objective function values and the decision variables of the inner-layer and mid-layer optimization models and convert the optimization model into a single-layer bi-objective optimization model. A method for obtaining the continuous Pareto frontier of the bi-objective optimization model is proposed based on the normalized normal constraint and PA methods, and the compromise optimal solution calculated from the continuous Pareto frontier is used as the optimal control scheme. Two methods for improving the calculation efficiency of the PA method are also proposed. Finally, results from experimentation on the IEEE 39-bus system and an actual provincial power grid demonstrate the effectiveness of the proposed method.

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Section: ) Pa Of the Mid-level Optimization Problemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multi-Objective Optimal Control Approach for Static Voltage Stability of Power System Considering Interval Uncertainty of the Wind Farm Output

et al. 2020

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“…Since the bounded domain of control parameter

bold-italicp \in bold-italicD

can be transformed to a hypercube, i.e.

bold-italicp \in false[- 1, 1 false]^{d}

with a proper scaling, in this paper, the multivariate Legendre polynomials [15], which are orthogonal in

false[- 1, 1 false]^{d}

, are selected as polynomial basis functions

Φ_{k} false(bold-italicp false)

.…”

Section: Approximation Of the Mid‐long Term Model Of Power Systems Bamentioning

confidence: 99%

“…The TSM is a linearisation approximation method based on the first‐order Taylor expansion around the nominal operating point. Therefore, it will lose accuracy in the case of large parameter variation and strong non‐linearity [15]. Since the variation of parameters during stability control process might be large and the power system might be critically stable after a large disturbance happened, the non‐linearity of power systems can be strong.…”

Section: Introductionmentioning

confidence: 99%

Galerkin method‐based model predictive control for mid‐long term voltage stability enhancement

Xia

Shen

et al. 2020

IET gener. transm. distrib.

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“…Some early results using asymptotic expansion methods were introduced in [8]- [10]. Polynomial approximation based on Galerkin Method was recently introduced in [11]- [13] to deal with parametric problems in power systems. Optimization methods offer a systematic way of tuning system parameters [14], [15], however, they are less transparent as they do not provide much insight.…”

Section: Introductionmentioning

confidence: 99%

Impact of Commutation Failure Preventions on HVDC System Based on a Multi-Index Value Set Approach

et al. 2021

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This paper proposes a systematic method, based on rational approximation and value set approach, to unravel the impact of commutation failure preventions (CFPREVs) on HVDC system dynamics. First, some output variables in HVDC system dynamics are identified as performance indices, it is shown that these indices are rational functions of CFPREVs parameters. Then a numerical approximation method is used to determine the coefficients of the rational functions which describe the analytical relationship between the suggested performance indices and parameters. To help understand the connotation of the obtained expressions, a multi-index value set approach, which exploits the power of geometry and graphics, is described in detail. Finally, the results of the rational approximation and value set approach are reported.INDEX TERMS Commutation failure prevention, multi-index value set, multi-parameter analysis, rational approximation.

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A Galerkin Method-Based Polynomial Approximation for Parametric Problems in Power System Transient Analysis

Cited by 26 publications

References 23 publications

Multi-Objective Optimal Control Approach for Static Voltage Stability of Power System Considering Interval Uncertainty of the Wind Farm Output

Multi-Objective Optimal Control Approach for Static Voltage Stability of Power System Considering Interval Uncertainty of the Wind Farm Output

Galerkin method‐based model predictive control for mid‐long term voltage stability enhancement

Impact of Commutation Failure Preventions on HVDC System Based on a Multi-Index Value Set Approach

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