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  differential-algebraic equations

Numerical integration of systems of delay differential-algebraic equations

The numerical solution of the initial value problem for a system of delay differential-algebraic equations is examined in the framework of the parametric continuation method.

Parameterization of differential-algebraic equations with retarded argument

Multistep numerical methods for functional-differential-algebraic equations

Perturbation index of linear partial differential-algebraic equations with a hyperbolic part

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  differential-algebraic equations

Numerical integration of systems of delay differential-algebraic equations

The numerical solution of the initial value problem for a system of delay differential-algebraic equations is examined in the framework of the parametric continuation method.

Parameterization of differential-algebraic equations with retarded argument

Multistep numerical methods for functional-differential-algebraic equations

Perturbation index of linear partial differential-algebraic equations with a hyperbolic part

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  differential algebraic equations

Conditions for partitioning a system of differential algebraic equations into weakly coupled subsystems

Systems of differential algebraic equations are examined.

On a nonlinear self-adjoint eigenvalue problem for certain differential algebraic equations of index 1

A method for solving nonlinear spectral problems for a class of systems of differential algebraic equations

A numerical procedure for solving the resulting differential algebraic equations is presented on the basis of the Newmark direct integration method combined with the Newton-Raphson iterative method.

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  differential-algebraic equations

Numerical integration of systems of delay differential-algebraic equations

The numerical solution of the initial value problem for a system of delay differential-algebraic equations is examined in the framework of the parametric continuation method.

Parameterization of differential-algebraic equations with retarded argument

Multistep numerical methods for functional-differential-algebraic equations

Perturbation index of linear partial differential-algebraic equations with a hyperbolic part

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in this article we study a single machine infinite bus system determin ed by a static load model. The mathematicalmodel of the power system is a differential algebraic equation (DAE). By using t he eigenvalue analysis. the upper branch ofthe equilibrium curve is stable while the lower branch is stable except for a sm all section of Q, between 11. 410 8 and 11. 411 5.This is different from the results of ordinary differential equation (ODE) model determined by both static load and dynamicload (Waive model)....

in this article we study a single machine infinite bus system determin ed by a static load model. The mathematicalmodel of the power system is a differential algebraic equation (DAE). By using t he eigenvalue analysis. the upper branch ofthe equilibrium curve is stable while the lower branch is stable except for a sm all section of Q, between 11. 410 8 and 11. 411 5.This is different from the results of ordinary differential equation (ODE) model determined by both static load and dynamicload (Waive model). To study the voltage collapse process of the system, we anal yse the bifurcation phenomenon near thesingular point. By using the singularity theory, the singular point of the DAE s ystem is found to be a limit point. Then byprojecting the differential equation on the (V, co) -plane. a singular ODE is ob tained. From the analysis of the phase portraitfor the singular ODE, the system is found to collapse by going through the singu lar surface. A simpler method is given toidentify the impasse point of the system and is used to prove that for the phase portrait near bifurcation value Q?. almostevery point on the singular surface is an impasse point. This method simplifies previous one by Chua et al.. and can beimplemented easily in numerical software.This project is supported by National Key Basic Research Special Fund of China ( No. G1998020307) and National NaturalScience Foundation of China (No. 19990510).

研究一個(gè)由靜態(tài)負(fù)荷決定的單機(jī)無窮大系統(tǒng) ,它的數(shù)學(xué)模型是一個(gè)微分代數(shù)方程 (DAE)。利用特征值分析方法 ,我們發(fā)現(xiàn)模型的平衡解曲線的上支是穩(wěn)定的 ,下支則除了介于 1 1 .41 0 8和1 1 .41 1 5之間非常小的一段曲線外 ,都是穩(wěn)定的。這與由靜態(tài)負(fù)荷以及動(dòng)態(tài)負(fù)荷 (Walve模型 )所決定的微分方程 (ODE)模型情況不同。為了研究系統(tǒng)電壓失穩(wěn)的模式 ,分析其奇點(diǎn)附近的分岔現(xiàn)象。利用奇點(diǎn)理論 ,計(jì)算出奇點(diǎn)為極限點(diǎn)。然后 ,通過把 DAE的微分方程部分投影在 (V,ω)面上 ,得到奇異微分方程。文中給出了用來判斷障礙 (impasse)點(diǎn)的一種較簡(jiǎn)單的方法 ,并用以驗(yàn)證對(duì)于分岔值處奇異面上幾乎所有的點(diǎn)都是障礙點(diǎn)。奇異微分方程的相圖顯示出系統(tǒng)在奇異面附近的失穩(wěn)過程

In this paper,the theory and method of feedback linearization technique of controlling differential algebraic system are first presented.Some new definitions of M derivative, M bracket and etc.to differential algebraic systems are given,which is similar to the definitions and theorems in classical differential geometry theory,a series of new result to differential algebraic system control is given,which extend further the applied scope of nonlinear control system geometry theory.Because many power systems...

In this paper,the theory and method of feedback linearization technique of controlling differential algebraic system are first presented.Some new definitions of M derivative, M bracket and etc.to differential algebraic systems are given,which is similar to the definitions and theorems in classical differential geometry theory,a series of new result to differential algebraic system control is given,which extend further the applied scope of nonlinear control system geometry theory.Because many power systems are modeled by differential algebraic model,and the loads of power systems are frequently the nonlinear expression of voltage and frequency,in addition,there are many problem of optimal control in practical engineering,these control problem above can be solved by using the M derivative, M bracket and so on.The designs of nonlinear excitation control of power systems with nonlinear loads can be applied by the feedback linearization technique of controlling differential algebraic systems,which make the differential geometry methods get more extensive application in the study of power system control.

首次提出了用于控制微分代數(shù)系統(tǒng)的反饋線性化技術(shù)理論和方法 ,類似于經(jīng)典的微分幾何理論中的定義和定理 ,給出關(guān)于微分代數(shù)系統(tǒng)的M導(dǎo)數(shù)、M括號(hào)等一些新的定義 ,并給出了有關(guān)微分代數(shù)系統(tǒng)控制的一系列新結(jié)果 ,進(jìn)一步拓廣了非線性系統(tǒng)幾何理論的應(yīng)用范圍。考慮到大多數(shù)電力系統(tǒng)模型都是采用微分代數(shù)模型 ,而且電力系統(tǒng)的負(fù)荷往往是電壓和頻率的非線性表達(dá)式 ,另外在實(shí)際工程中也�；痦�(xiàng)目 :國(guó)家重點(diǎn)基礎(chǔ)研究發(fā)展規(guī)劃項(xiàng)目 (G19980 2 0 30 0 ) ;中國(guó)博士后基金資助項(xiàng)目。ProjectSupportedbySpecialFundoftheNationalPriorityBasicResearch(G19980 2 0 30 0 ) .常遇到求非線性微分代數(shù)方程的最優(yōu)控制解 ,引入微分代數(shù)系統(tǒng)的M導(dǎo)數(shù)、M括號(hào)等定義可較好地解決這類控制問題。利用控制微分代數(shù)系統(tǒng)的反饋線性化技術(shù) ,能很好地應(yīng)用于具有非線性負(fù)荷的電力系統(tǒng)非線性勵(lì)磁控制的設(shè)計(jì) ,使微分幾何方法在電力系統(tǒng)控制研究中得到更廣泛的應(yīng)用

It is very important for an interconnected power system under the m arketing circumstance to quantitatively analyze its stability on- line for tracking the actual operation condition and make decision for stability control adaptively.Preventive control and emergency control have been studied separately till now.In this paper,coordination between them is form ulated as a nonlinear hybrid programm ing on logic- difference- differential- algebraic equations with m any constraints including stability. The objective...

It is very important for an interconnected power system under the m arketing circumstance to quantitatively analyze its stability on- line for tracking the actual operation condition and make decision for stability control adaptively.Preventive control and emergency control have been studied separately till now.In this paper,coordination between them is form ulated as a nonlinear hybrid programm ing on logic- difference- differential- algebraic equations with m any constraints including stability. The objective function is the sum of the daily cost for preventive control and the probabilistic cost for em ergency control. An optimization procedure is proposed for the coordination,which integrates the unique EEAC technique for quantitative analysis of stability and a hybrid programm ing for non- convex nonlinear optim ization. This procedure refreshes the decision table in a sub- real- time fashion.

研究了預(yù)防控制與緊急控制的互補(bǔ)性 ;強(qiáng)調(diào)在線預(yù)決策對(duì)暫態(tài)穩(wěn)定控制的重要性 ;指出量化分析是決策優(yōu)化的一個(gè)關(guān)鍵。指出預(yù)防控制和緊急控制的協(xié)調(diào)對(duì)電力市場(chǎng)下互聯(lián)電網(wǎng)安全經(jīng)濟(jì)運(yùn)行非常重要 ,并提出協(xié)調(diào)控制的數(shù)學(xué)模型、框架和邏輯—差分—微分—代數(shù)方程的穩(wěn)定性分析和控制優(yōu)化方法。

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