A method for high order linear system reduction and nonlinear system simplification

Desrochers, A.A.; Al-Jaar, Robert Y.

doi:10.1016/0005-1098(85)90101-3

Cited by 10 publications

(5 citation statements)

References 16 publications

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“…To present in more detail the difference between approaches, the root mean square errors of all states are calculated using the following expression: (19) where N is the number of simulation steps; ij x and ˆi j x are respectively the values of i-th state variable of generator 23 of the original system and the reduced system at time step j. The results of calculation are shown in Table II.…”

Section: A Temporary Bus Fault Testsmentioning

confidence: 99%

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Adaptive Nonlinear Model Reduction for Fast Power System Simulation

Osipov

Sun

2018

IEEE Trans. Power Syst.

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The paper proposes a new adaptive approach to power system model reduction for fast and accurate time-domain simulation. This new approach is a compromise between linear model reduction for faster simulation and nonlinear model reduction for better accuracy. During the simulation period, the approach adaptively switches among detailed and linearly or nonlinearly reduced models based on variations of the system state: it employs unreduced models for the fault-on period, uses weighted column norms of the admittance matrix to decide which functions to be linearized in power system differential-algebraic equations for large changes of the state, and adopts a linearly reduced model for small changes of the state. Two versions of the adaptive model reduction approach are introduced. The first version uses traditional power system partitioning where the model reduction is applied to a defined large external area in a power system and the other area defined as the study area keeps full detailed models. The second version applies the adaptive model reduction to the whole system. The paper also conducts comprehensive case studies comparing simulation results using the proposed adaptively reduced models with the linearly reduced model on the Northeast Power Coordinating Council 140-bus 48-machine system.Index Terms--Linear model reduction, nonlinear model reduction, power system partitioning, power system simulation.

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Section: A Temporary Bus Fault Testsmentioning

confidence: 99%

“…In this paper, a model reduction method is proposed as a hybrid of nonlinear and linear model reduction techniques. As shown in [19]- [20], the transformation matrices T and T  can be used to reduce the nonlinear system as well. In this case, the system can be represented as follows:…”

Section: ) Proposed Hybrid Model Reductionmentioning

confidence: 99%

Adaptive Nonlinear Model Reduction for Fast Power System Simulation

Osipov

Sun

2018

IEEE Trans. Power Syst.

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“…Faßt man die Fehlervektoren d 2 nebeneinander angeordnet zur Matrix D 2 zusammen und außerdem die Gewichtungsfaktoren q in der Diagonalmatrix Q, so läßt sich das Gütemaß J 2 in Matrixschreibweise J2 = ^m{D2QQ T D T 2} (18) angeben. Um hierin leicht einsetzen zu können, werden nun ebenfalls die Vektoren χ(/,) und xdo(tj) zu Matrizen X und Xdo zusammengesetzt, so daß D2 = XWXdo gilt.…”

Section: Wird Durch Einsetzen Dieser Beziehungen Xdo(r) = a Xdo(t) + unclassified

Ordnungsreduktion und Dominanzanalyse nichtlinearer Systeme

Lohmann¹

1994

at - Automatisierungstechnik

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at 10/94 ιΉΒΟΜΒΠΒ^η THEORETISCHE ARBEITEN Dr.-Ing. Boris I.ohmann arbeitet in der Entwicklungsabteilung für Briefsortieranlagen der AEG Electrocom. Konstanz. Hauptarbeitsfelder: Anlagensteuerung und -regelung. Theorie linearer und nichtlinearer Mehrgrö-ßensysteme. Es wird ein Verfahren zur Verringerung der Gleichungsanzahl nichtlinearer Systemmodelle vorgestellt. Der Grundgedanke ist dabei, die Nichtlinearitäten des Originalsystems ihrem Charakter nach ins reduzierte System zu übernehmen, jedoch alle Kopplungen von Zustandsgrößen untereinander und mit nichtlinearen Funktionen neu festzulegen. Forderungen nach stationärer Genauigkeit des reduzierten Systems können berücksich-tigt werden. Ergänzend werden anschauliche Dominanzmaßzahlen eingeführt, die Hinweise auf günstige Systemordnungengeben und den Entwerfer bei der Vorgabe wesentlicher Zustandsgrößen unterstützen. Als Anwendungsbeispiel wird das Modell einer aktiven hydropneumatischen Kraftfahrzeugfederung behandelt. Order reduction and dominance analysis of nonlinear systemsA method is presented which reduces the number of equations of nonlinear system models. The main idea is to take over the nonlinearities from the original system into the reduced system but to renew all couplings of state variables and nonlinear functions. Steady state error can be avoided by additional measures. Furthermore dominance numbers are introduced which help chosing a favourable system order and dominant state variables. As a technical example the model of an active hydropneumatic vehicle suspension is considered.

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“…This can be caused by strong numerator dynamics (i.e., RHP zeros). The methods of dominant eigenvalue retention (Kim and Friedly, 1974), Routh approximations (Hutton and Friedland, 1975), impulse energy approximations (Lucas, 1985), and least-squares approximations (Desrochers and Al-Jaar, 1985) preserve the stability of the high-order model in the approximate one, but they can be applied only to rational transfer functions.…”

Section: Previous Workmentioning

confidence: 99%

Approximate dynamic models for chemical process systems

Papadourakis¹,

Doherty²,

Douglas³

1989

Ind. Eng. Chem. Res.

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Modern integrated chemical plants can be viewed as consisting of a number of smaller interconnected subsystems. Approximate dynamic models for both individual process units and subsystems are the necessary tools for preliminary dynamic studies of plantwide operability and control. A variable-order method is presented that can be used to develop simple dynamic models for such systems. The method is successful in retaining the dominant dynamic modes of the process, and examples are given to demonstrate this point.

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A method for high order linear system reduction and nonlinear system simplification

Cited by 10 publications

References 16 publications

Adaptive Nonlinear Model Reduction for Fast Power System Simulation

Adaptive Nonlinear Model Reduction for Fast Power System Simulation

Ordnungsreduktion und Dominanzanalyse nichtlinearer Systeme

Approximate dynamic models for chemical process systems

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