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On the efficiency of quantization-based integration methods for building simulation

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Abstract

Models describing energy consumption, heating, and cooling of buildings usually impose difficulties to the numerical integration algorithms used to simulate them. Stiffness and the presence of frequent discontinuities are among the main causes of those difficulties, that become critical when the models grow in size. Quantized State Systems (QSS) methods are a family of numerical integration algorithms that can efficiently handle discontinuities and stiffness in large models. For this reason, they are promising candidates for overcoming the mentioned problems. Based on this observation, this article studies the performance of QSS methods in some systems that are relevant to the field of building simulation. The study includes a performance comparison of different QSS algorithms against state-of-the-art classic numerical solvers, showing that the former can be more than one order of magnitude faster.

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References

  • Åkesson J, Gäfvert M, Tummescheit H (2009). Modelica—An open source platform for optimization of Modelica models. In: Proceedings of the 6th Vienna International Conference on Mathematical Modelling.

    Google Scholar 

  • Baetens R, De Coninck R, Jorissen F, Picard D, Helsen L, Saelens D (2015). OpenIDEAS—An open framework for integrated district energy assessments. In: Proceedings of the 14th International IBPSA Building Simulation Conference, Hyderabad, India, pp. 347–354.

    Google Scholar 

  • Bergero F, Kofman E (2011). PowerDEVS: A tool for hybrid system modeling and real-time simulation. Simulation, 87: 113–132.

    Article  Google Scholar 

  • Bergero F, Floros X, Fernández J, Kofman E, Cellier FE (2012). Simulating Modelica models with a stand-alone quantized state systems solver. In: Proceedings of the 9th International Modelica Conference, Munich, Germany, pp. 237–246.

    Google Scholar 

  • Bergero F, Botta M, Campostrini E, Kofman E (2015). Efficient compilation of large scale Modelica models. In: Proceedings of the 11th International Modelica Conference, Versaille, France, pp. 449–458.

    Google Scholar 

  • Brück D, Elmqvist H, Mattsson SE, Olsson H (2002). Dymola for multi-engineering modeling and simulation. In: Proceedings of the 2nd Modelica Conference, Oberpfaffenhofen, Germany.

    Google Scholar 

  • Cellier F, Floros XF, Kofman E (2013). The complexity crisis: Using modeling and simulation for system level analysis and design. In: Proceedings of the 3rd International Conference on Simulation and and Modeling Methodologies, Technologies and Applications (SimulTech), Reykjavik, Iceland.

    Google Scholar 

  • Cellier F, Kofman E (2006). Continuous System Simulation. New York: Springer.

    MATH  Google Scholar 

  • Ceriani NM, Vignali R, Piroddi L, Prandini M (2013). An approximate dynamic programming approach to the energy management of a building cooling system. In: Proceedings of European Control Conference, Zurich, Switzerland, pp. 2026–2031.

    Google Scholar 

  • CIBSE (2006). CIBSE Guide A: Environmental Design. Norwich, UK: CIBSE Publications.

    Google Scholar 

  • Crawley DB, Lawrie LK, Winkelmann FC, Buhl WF, Huang YJ, et al. (2001). EnergyPlus: Creating a new-generation building energy simulation program. Energy and Buildings, 33: 319–331.

    Article  Google Scholar 

  • Dormand JR, Prince PJ (1980). A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics, 6: 19–26.

    Article  MathSciNet  MATH  Google Scholar 

  • Fernández J, Kofman E (2014). A stand-alone quantized state system solver for continuous system simulation. Simulation, 90: 782–799.

    Article  Google Scholar 

  • Fernández J, Kofman E, Bergero F (2017). A parallel Quantized State System Solver for ODEs. Journal of Parallel and Distributed Computing, 106: 14–30.

    Article  Google Scholar 

  • Floros X, Bergero F, Ceriani N, Casella F, Kofman E, Cellier FE (2014). Simulation of smart-grid models using quantization-based integration methods. In: Proceedings of the 10th International Modelica Conference, Lund, Sweden, pp. 787–797.

    Google Scholar 

  • Frances VMS, Escriva EJS, Ojer JMP (2014). Discrete event heat transfer simulation of a room. International Journal of Thermal Sciences, 75: 105–115.

    Article  Google Scholar 

  • Frances VMS, Escriva EJS, Ojer JMP (2015). Discrete event heat transfer simulation of a room using a Quantized State System of order two, QSS2 integrator. International Journal of Thermal Sciences, 97: 82–93.

    Article  Google Scholar 

  • Fritzson P (2015). Principles of Object-Oriented Modeling and Simulation with Modelica 3.3: A Cyber-Physical Approach, 2nd edn. Piscataway, NJ, USA: Wiley-IEEE Press.

    Google Scholar 

  • Fritzson P, Aronsson P, Lundvall H, Nystrom K, Pop A, Saldamli L, Broman D (2005). The OpenModelica modeling, simulation, and development environment. In: Proceedings of the 46th Conference on Simulation and Modeling (SIMS’05), Trondheim, Norway, pp. 83–90.

    Google Scholar 

  • Fuchs M, Constantin A, Lauster M, Remmen P, Streblow R, Müller E (2015). Structuring the building performance Modelica model library AixLib for open collaborative development. In: Proceedings of the 14th International IBPSA Building Simulation Conference, Hyderabad, India, pp. 331–338.

    Google Scholar 

  • Grinblat GL, Ahumada H, Kofman E (2012). Quantized state simulation of spiking neural networks. Simulation, 88: 299–313.

    Article  Google Scholar 

  • Hairer E, Nørsett S, Wanner G (1993). Solving Ordinary Differential Equations I. Nostiff Problems, 2nd edn. Berlin: Springer.

    MATH  Google Scholar 

  • Hairer E, Wanner G (1996). Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems. Berlin: Springer.

    MATH  Google Scholar 

  • Hindmarsh AC, Brown PN, Grant KE, Lee SL, Serban R, Shumaker DE, Woodward CS (2005). SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers. ACM Transactions on Mathematical Software, 31: 363–396.

    Article  MathSciNet  MATH  Google Scholar 

  • Jorissen F, Helsen L, Wetter M (2015). Simulation speed analysis and improvements of Modelica models for building energy simulation. In: Proceedings of the 11th International Modelica Conference, Versaille, France, pp. 59–69.

    Google Scholar 

  • Kofman E (2002). A second-order approximation for DEVS simulation of continuous systems. Simulation, 78: 76–89.

    Article  MATH  Google Scholar 

  • Kofman E (2004). Discrete event simulation of hybrid systems. SIAM Journal on Scientific Computing, 25: 1771–1797.

    Article  MathSciNet  MATH  Google Scholar 

  • Kofman E (2006). A third order discrete event simulation method for continuous system simulation. Latin American Applied Research, 36: 101–108.

    Google Scholar 

  • Kofman E, Junco S (2001). Quantized-state systems: A DEVS approach for continuous system simulation. Transactions of the Society for Computer Simulation International, 18: 123–132.

    Google Scholar 

  • Mattsson SE, Elmqvist H, Otter M (1998). Physical system modeling with Modelica. Control Engineering Practice, 6: 501–510.

    Article  Google Scholar 

  • Migoni G, Kofman E, Bergero F, Fernández J (2015). Quantizationbased simulation of switched mode power supplies. Simulation, 91: 320–336.

    Article  Google Scholar 

  • Migoni G, Bortolotto M, Kofman E, Cellier FE (2013). Linearly implicit quantization-based integration methods for stiff ordinary differential equations. Simulation Modelling Practice and Theory, 35: 118–136.

    Article  Google Scholar 

  • Nytsch-Geusen C, Huber J, Ljubijankic M, Rädler J (2013). Modelica BuildingSystems—eine Modellbibliothek zur Simulation komplexer energietechnischer Gebäudesysteme. Bauphysik, 35: 21–29.

    Article  Google Scholar 

  • Perfumo C, Kofman E, Braslavsky JH, Ward JK (2012). Load management: Model-based control of aggregate power for populations of thermostatically controlled loads. Energy Conversion and Management, 55: 36–48.

    Article  Google Scholar 

  • Petzold LR (1982). A description of DASSL: A differential/algebraic system solver. In: Proceedings of Scientific computing, Montreal, Canada, pp. 65–68.

    Google Scholar 

  • Wetter M, Haugstetter C (2006). Modelica versus TRNSYS—A comparison between an equation-based and a procedural modeling language for building energy simulation. In: Proceedings of the 2nd National IBPSA-USA Conference, Cambridge, MA, USA.

    Google Scholar 

  • Wetter M, Zuo W, Nouidui TS, Pang X (2014). Modelica Buildings library. Journal of Building Performance Simulation, 7: 253–270.

    Article  Google Scholar 

  • Wetter M, Nouidui TS, Lorenzetti D, Lee EA, Roth A (2015). Prototyping the next generation EnergyPlus simulation engine. In: Proceedings of the 14th International IBPSA Building Simulation Conference, Hyderabad, India.

    Google Scholar 

  • Wetter M, Bonvini M, Nouidui TS (2016). Equation-based languages—A new paradigm for building energy modeling, simulation and optimization. Energy and Buildings, 117: 290–300.

    Article  Google Scholar 

  • Zeigler B, Praehofer H, Kim TG (2000). Theory of Modeling and Simulation, 2nd edn. San Diego, USA: Academic Press.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Laboratorio de Sistemas Dinámicos, CIFASIS-CONICET, Rosario, Argentina

    Federico Martín Bergero, Ernesto Kofman & Joaquín Fernández

  2. Politecnico di Milano, Milan, Italy

    Francesco Casella

  3. FCEIA-UNR, Rosario, Argentina

    Ernesto Kofman

Authors
  1. Federico Martín Bergero
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  2. Francesco Casella
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  3. Ernesto Kofman
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  4. Joaquín Fernández
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Correspondence to Federico Martín Bergero.

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Bergero, F.M., Casella, F., Kofman, E. et al. On the efficiency of quantization-based integration methods for building simulation. Build. Simul. 11, 405–418 (2018). https://doi.org/10.1007/s12273-017-0400-1

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  • DOI: https://doi.org/10.1007/s12273-017-0400-1

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