A successive decomposition method for the solution of linear time-varying systems

Wu, Min-Yen

doi:10.1080/00207178108928547

Cited by 11 publications

(5 citation statements)

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“…On close inspection of A tv , one can conclude that it does not belong to any of the cases listed in Ref. [45]. Consequently, the transition matrix is best obtained by means of numerical integration.…”

Section: Closed‐loop Vsc Model Based On the Proposed Methodsmentioning

confidence: 89%

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Steady‐state solutions of a voltage source converter with dq‐frame controllers by means of the time‐domain method

Lian

Syai’in

2014

IEEJ Transactions Elec Engng

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A voltage source converter (VSC) is one of the most widely used power converters in a power system. In this paper, a timedomain-based accelerated steady-state method is proposed to solve for a closed-loop pulse-width modulated (PWM) VSC with dq-frame controllers, which is able to account for the harmonic interactions between the converter and the rest of the power network, between the AC and DC sides of a VSC, and between the converter and its controllers. The proposed time-domain method is based on the modified time-domain shooting method, where the Jacobian matrix is updated by the quasi-Newtons method. This will drastically increase the computation efficiency as it avoids re-evaluating and inverting the Jacobian matrix, whose size is usually very large for a PWM-VSC due to high number of times of switching. All the results are shown to be consistent with those obtained by a PSCAD/EMTDC model, which has been validated with the experiment in a previous publication.

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Section: Closed‐loop Vsc Model Based On the Proposed Methodsmentioning

confidence: 89%

“…However, a homogenous, linear, time‐varying system generally does not have a closed‐form solution, except in a few cases, as listed in Ref. [45]. On close inspection of A tv , one can conclude that it does not belong to any of the cases listed in Ref.…”

Section: Closed‐loop Vsc Model Based On the Proposed Methodsmentioning

confidence: 98%

Steady‐state solutions of a voltage source converter with dq‐frame controllers by means of the time‐domain method

Lian

Syai’in

2014

IEEJ Transactions Elec Engng

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“…If one wants to find out the sensitivity of the 2nd harmonic of and 9th harmonic of with respect to the input, one can augment their harmonic states, and in (27) and get (28) where the expressions for and are stated in (34) and (35), respectively. itself is linear time-varying, and according to [84] and [85], it does not have a closed form expression. Thus, the transition matrix of (28) is obtained by numerical integration.…”

Section: B System Equationsmentioning

confidence: 99%

Derivation of a Small-Signal Harmonic Model for Closed-Loop Power Converters Based on the State-Variable Sensitivity Method

Lian

2012

IEEE Trans. Circuits Syst. I

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An admittance or impedance matrix of a power converter is highly desirable for harmonic analysis of a power system. However, power converters are inherently nonlinear and time-varying systems. Therefore, a small-signal harmonic model needs to be derived. While there have been many methods to obtain the small-signal models of DC-DC converters, most of these methods cannot be directly applied to AC-DC converters. Moreover, while accurate methods exist for obtaining accurate models of open-loop AC-DC converters, there are few existing methods for obtaining accurate models for closed-loop AC-DC converters. This paper proposes an analytical method for obtaining an accurate small-signal harmonic model for a power converter. The proposed method is based on state-variable sensitivity methods, which have been previously used to derive a transfer function of a DC-DC converter. This paper will show what modifications are required to extend it to derive the small-signal harmonic model of a closed-loop AC-DC converter. A small-signal harmonic model of a closed-loop pulse-width modulated (PWM) voltage source converter (VSC) with synchronous frame current controllers and a dc voltage controller is derived based on the proposed method. The results are in good agreement with large-signal simulations by means of PSCAD/EMTDC.Index Terms-Harmonics, pulse width modulation, small signal harmonic model, steady state analysis, voltage source converter.

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“…The controllability Grammian matrix (CGM) [1,2] may not always be determined from the integral relation for linear time-varying systems because the state transition matrix (STM) cannot always be converted to the known matrix form, except for the state matrix A(t) being in the canonical companion [3] or the successive decomposition form [4]. There exist numerous methods for the numerical computation of the CGM in the literature [5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

“…However, it is too complex and tedious for linear time-varying systems. Furthermore, it is even impossible except for some special cases [3,4]. Instead of determining the elements of W c (t f , t 0 ) by using Equation (2), the Lyapunov differential matrix equation given by(3)…”

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confidence: 99%

State controllability computation technique for linear time‐varying systems by using Taylor series approximation

Aksoy

2008

Adaptive Control & Signal

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This article presents a technique to determine the controllability Grammian matrix (CGM) for linear timevarying systems by using truncated Taylor polynomial vector and the operational matrix of integration. An important property of this algorithm is that it starts by integrating the Lyapunov differential matrix equation in terms of the CGM. However, the algorithm does not use the mathematical integration processes actually, but uses the truncated Taylor polynomial vector and the operational matrix of integration. Thus, the problem is reduced to solving a linear set of algebraic equations with constant coefficients consisting of the Taylor polynomial constant coefficients of each of the CGM elements. Numerical results and error curves are given to illustrate the improvements achieved by the proposed algorithm.

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A successive decomposition method for the solution of linear time-varying systems

Cited by 11 publications

References 1 publication

Steady‐state solutions of a voltage source converter with dq‐frame controllers by means of the time‐domain method

Steady‐state solutions of a voltage source converter with dq‐frame controllers by means of the time‐domain method

Derivation of a Small-Signal Harmonic Model for Closed-Loop Power Converters Based on the State-Variable Sensitivity Method

State controllability computation technique for linear time‐varying systems by using Taylor series approximation

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