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  • 1.
    Sturk, Christopher
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Structured Model Reduction and its Application to Power Systems2012Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    Many of today’s engineering systems have a network structure. Consider for instance power systems, where multiple grids of different geographical coverage are interconnected to form larger grids, a set of vehicles moving in formation or distributed control systems, where several controllers act locally with limited information. These systems are all comprised of multiple sub- systems and the full system can easily become very large, which can make it intractable for analysis or controller design.

    Model reduction is a means to overcome this issue. Most traditional model reduction algorithms do not preserve the network structure, however some algorithms can be used to reduce the subsystems locally, while retaining the network topology and approximating the global behavior of the interconnection. These algorithms will be the focus of this thesis.

    In the first half of the thesis we will deal with one such structure preserving model reduction algorithm. An important property of model reduction algorithms is their ability to give some performance guarantees prior to their application, for instance in terms of an upper bound of the model error. This can be achieved by formulating the reduction method as a linear matrix inequality, but since they are not always feasible it imposes a limitation on its usefulness. However it is showed in this thesis that certain network structures where the subsystems are either stable or strictly positive real always allow for solutions of their corresponding linear matrix inequalities. We show that common boiler-header systems modeled with grey-box identification belong to this class of systems and we demonstrate how the model order of them can be significantly reduced.

    In the other half of the thesis the focus lies on power systems and the model reduction of them. We formulate it as a structured model reduction problem and propose an algorithm for the reduction of part of the grid while retaining a high-fidelity model of the study area. This can be of relevance for a subsequent contingency analysis. We also demonstrate how reduced models can be of use for controller design by suppressing certain modes. The algorithm is applied to the Klein-Rogers-Kundur 2-area system which dynamics is well understood and to a much larger real-sized model of the Nordic power grid. We conclude that a significant model reduction can be done without losing critical dynamics of the study area.

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  • 2.
    Sturk, Christopher
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Franco, Elisa
    Murray, Richard M.
    Tuning a synthetic in vitro oscillator using control-theoretic tools2010Ingår i: Proceedings of the IEEE Conference on Decision and Control, NEW YORK: IEEE , 2010, s. 2554-2559Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    This paper demonstrates the effectiveness of simple control-theoretic tools in generating simulation-guided experiments on a synthetic in vitro oscillator. A theoretical analysis of the behavior of such system is motivated by high cost, time consuming experiments, together with the excessive number of tuning parameters. A simplified model of the synthetic oscillator is chosen to capture only its essential features. The model is analyzed using the small gain theorem and the theory of describing functions. Such analysis reveals what are the parameters that primarily determine when the system can admit stable oscillations. Experimental verification of the theoretical and numerical findings is carried out and confirms the predicted results regarding the role of production and degradation rates.

  • 3.
    Sturk, Christopher
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Sandberg, Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Trnka, Pavel
    Havlena, Vladimir
    Rehor, Jiri
    Structured Model Order Reduction of Boiler-Header Models2011Ingår i: Proceedings of the 18th IFAC World Congress, 2011Konferensbidrag (Refereegranskat)
    Abstract [en]

    This paper presents a model reduction of a boiler-header system. Since it is desirable that the reduced model retains the structure of the full model where the boilers are interconnected with the header, a structured model reduction technique is applied, which takes the entire system into account. This method requires the solution of two linear matrix inequalities to obtain the structured Gramians of the system, but in general it is not possible to guarantee feasibility of these linear matrix inequalities. However for stable systems that are connected in series with a negative feedback-loop with strictly positive real subsystems, we prove that solutions always exist. By showing that the boiler-header system belongs to this class of systems it follows that the structured model reduction method can be applied regardless of the system parameters.

  • 4.
    Sturk, Christopher
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Vanfretti, Luigi
    KTH, Skolan för elektro- och systemteknik (EES), Elektriska energisystem. Statnett SF Research and Development, Norway.
    Chompoobutrgool, Yuwa
    KTH, Skolan för elektro- och systemteknik (EES), Elektriska energisystem.
    Sandberg, Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Coherency-Independent Structured Model Reduction of Power Systems2014Ingår i: IEEE Transactions on Power Systems, ISSN 0885-8950, E-ISSN 1558-0679, Vol. 29, nr 5, s. 2418-2426Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper proposes a new model reduction algorithm for power systems based on an extension of balanced truncation. The algorithm is applicable to power systems which are divided into a study area which requires a high-fidelity model and an external area, making up most of the power system, which is to be reduced. The division of the power system can be made arbitrarily and does not rely on the identification of coherent generators. The proposed algorithm yields a reduced order system with a full non-linear description of the study area and a reduced linear model of the external area.

  • 5.
    Sturk, Christopher
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Vanfretti, Luigi
    KTH, Skolan för elektro- och systemteknik (EES), Elektriska energisystem. Statnett SF, Res & Dev, Oslo, Norway.
    Chompoobutrgool, Yuwa
    KTH, Skolan för elektro- och systemteknik (EES), Elektriska energisystem.
    Sandberg, Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Coherency-Independent Structured Model Reduction of Power Systems2015Ingår i: 2015 IEEE POWER & ENERGY SOCIETY GENERAL MEETING, IEEE , 2015Konferensbidrag (Refereegranskat)
  • 6.
    Sturk, Christopher
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Vanfretti, Luigi
    KTH, Skolan för elektro- och systemteknik (EES), Elektriska energisystem.
    Chompoobutrgool, Yuwa
    KTH, Skolan för elektro- och systemteknik (EES), Elektriska energisystem.
    Sandberg, Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Structured Power System Model Reduction of Non-Coherent Areas2012Ingår i: Power and Energy Society General Meeting, 2012 IEEE, IEEE , 2012, s. 6344913-Konferensbidrag (Refereegranskat)
    Abstract [en]

    This paper demonstrates how structured model reduction can be used to reduce the order of power systems without the need to identify coherent groups of generators. To this end the Klein-Rogers-Kundur 2-area system is studied in detail. It is shown how different modes of the system are captured as the model order is varied, which is of interest in e.g. distributed controller design, where the objective is to damp these oscillations. The power system is divided into a study area and an external area and the proposed algorithm is used to reduce the external area to a low order linear system, while retaining the nonlinear description of the study area. It is shown that this approach permits greater deviations from the steady-state than if a reduced system that is entirely linear is used, while still yielding accurate simulation results.

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  • 7.
    Sturk, Christopher
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Vanfretti, Luigi
    KTH, Skolan för elektro- och systemteknik (EES), Elektriska energisystem.
    Milano, Federico
    Sandberg, Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Structured Model Reduction of Power Systems2012Ingår i: 2012 American Control Conference (ACC), American Automatic Control Council , 2012, s. 2276-2282Konferensbidrag (Refereegranskat)
    Abstract [en]

    This paper shows how structured model order reduction can be applied to power systems. For power systems divided into a study area and an external area, the proposed algorithm can be used to reduce the external area to a low order linear system, while retaining the nonlinear description of the study system. The reduction of the external area is done in such a way that the study system is affected as little as possible. It is shown that a lower model order can be attained when information about the study system is taken into consideration, than if the external system is reduced independently of it

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  • 8. Trnka, Pavel
    et al.
    Sturk, Christopher
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Sandberg, Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Havlena, Vladimir
    Rehor, Jiri
    Structured Model Order Reduction of Parallel Models in Feedback2013Ingår i: IEEE Transactions on Control Systems Technology, ISSN 1063-6536, E-ISSN 1558-0865, Vol. 21, nr 3, s. 739-752Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Parallel working units in closed-loop operation are frequently encountered in industrial applications of advanced process control (boilers, turbines, chemical reactors, etc.). Control strategies typically require different low-order models for each configuration of parallel units. These different models are usually obtained by heuristics applied to the parallel models. To replace these heuristics, this paper proposes a systematic solution based on structured model order reduction. Two methods are considered, the first has general applicability to stable closed-loop systems, but gives no a priori error bounds; the second linear matrix inequality (LMI)-based method comes with an explicit error bounds, but cannot be applied to general models. However, it is shown that for models composed of cascades of stable subsystems and negative feedbacks of strictly positive real subsystems, the LMIs are always feasible. Both methods are demonstrated on a practical example of a cogeneration power plant with multiple boilers. It is proved that the second LMI-based method can always be applied to general problems with structures similar to the boiler-header systems considered in this paper.

1 - 8 av 8
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