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Characterization of heat dynamics of an arctic low-energy house with floor heating

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  • Building Thermal, Lighting, and Acoustics Modeling
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Abstract

This paper presents grey-box modeling of the heat dynamics of an apartment in a highly insulated test building located in the Arctic. Data from a 16-day-long experiment is analyzed and used to fit lumped parameter models formulated as coupled stochastic differential equations. The output of the models is the measured indoor air temperature, and the models are fitted using maximum likelihood techniques with the software CTSM-R. Models are compared using likelihood-ratio tests and validated considering autocorrelation and periodograms of residuals. The fitted models facilitate description of both the fast responses to mechanical ventilation and solar radiation through a large window facade, and the slow responses to floor heating and outdoor temperature. To successfully describe the dynamics of the system, solar radiation is given special attention in modeling of both the physical system and the observational noise. The estimated physical parameters which include UA-value, total heat capacity, and time constants for the apartment are discussed. Simulations are performed to illustrate step and impulse responses of inputs.

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Abbreviations

A :

system matrix in a linear system

A s :

area with which the global horizontal solar radiation is scaled (W/m2)

A w :

area with which the projected solar radiation (P s,win) is scaled (W/m2)

A noise :

scaling of projected solar radiation in a system noise process ((K·m2·s1/2)/J)

B :

matrix describing how inputs enter in a linear system

C i :

thermal capacity of state i (or e, f) (J/K)

P el :

electric power (W)

P h :

floor heating power (W)

P s :

global horizontal solar radiation (W/m2)

P s,win :

global horizontal solar radiation projected onto the window side of the building (W/m2)

P v :

estimated ventilation heating to one apartment (W)

R ij :

thermal resistance between states or inputs I and j (W/K)

SACF:

sample autocorrelation function

T a :

outdoor temperature (°C)

T e :

temperature of the building envelope (°C)

T i :

indoor air and surface temperature (in three-state model) (°C)

T f :

floor heating system temperature (°C)

UA:

common UA-value for the building envelope (W/K)

W s :

wind speed (m/s)

c v :

scaling of ventilation heating signal

c W :

a constant related to the effect of wind speed ((K·s1/2)/m)

e k :

observational noise at discrete time k (°C)

k :

discrete time

n :

number of parameters in a model

p :

p-value of a hypothesis test

r k :

one-step-ahead prediction uncertainty of the indoor air temperature measurement at time k (°C)

t :

continuous time

Y k :

indoor temperature measurement at time t k (°C). When referring to particular observations, y k is used

∈k :

residual, i.e. one-step-ahead prediction error of the indoor temperature at time k (°C)

\(\tilde \in _k \) :

standardized residual at time k, \(\tilde \in _k = \in _k /r_k \)

ω i :

Wiener processes in state i (or e, f))(s1/2)

σ i :

scaling of Wiener process in state i (or e, f) (K/s1/2)

σ o :

standard deviation of observational noise (°C)

ℓ :

log-likelihood value

References

  • Andersen KK, Madsen H, Hansen LH (2000). Modelling the heat dynamics of a building using stochastic differential equations. Energy and Buildings, 31: 13–24.

    Article  Google Scholar 

  • Andersen PD, Iversen A, Madsen H, Rode C (2014). Dynamic modeling of presence of occupants using inhomogeneous Markov chains. Energy and Buildings, 69: 213–223.

    Article  Google Scholar 

  • Andersen PD, Rode C, Madsen H (2013a). An arctic low-energy house as experimental setup for studies of heat dynamics of buildings. Frontiers of Architectural Research, 2: 488–499.

    Article  Google Scholar 

  • Andersen PD, Rode C, Madsen H (2013b). Low-energy house in Sisimiu-Measuring equipment. Technical Report-2013-017. DTU Compute.

    Google Scholar 

  • Bacher P, Madsen H (2011). Identifying suitable models for the heat dynamics of buildings. Energy and Buildings, 43: 1511–1522.

    Article  Google Scholar 

  • Bellman R, Åström KJ (1970). On structural identifiability. Mathematical Bio-sciences, 7: 329–339.

    Article  Google Scholar 

  • Cools C, Gicquel R (1989). The PASSYS project, final reports phase 1, 1986–89. Tech. Rep. Office of the Official Publications of EU, Luxembourg.

    Google Scholar 

  • Corradi O, Ochsenfeld H, Madsen H, Pinson P (2013). Controlling electricity consumption by forecasting its response to varying prices. IEEE Transactions on Power Systems, 28: 421–429.

    Article  Google Scholar 

  • Friling N, Jiménez MJ, Bloem H, Madsen H (2009). Modelling the heat dynamics of building integrated and ventilated photovoltaic modules. Energy and Buildings, 41: 1051–1057.

    Article  Google Scholar 

  • Godfrey KR (1980). Correlation methods. Automatica, 16: 527–534.

    Article  Google Scholar 

  • Gutschker O (2008). Parameter identification with the software package LORD. Building and Environment, 43: 163–169.

    Article  Google Scholar 

  • Jiménez MJ, Madsen H (2008). Models for describing the thermal characteristics of building components. Building and Environment, 43: 152–162.

    Article  Google Scholar 

  • Jiménez MJ, Madsen H, Andersen KK (2008a). Identification of the main thermal characteristics of building components using MATLAB. Building and Environment, 43: 170–180.

    Article  Google Scholar 

  • Jiménez MJ, Porcar B, Heras MR (2008b). Estimation of building component UA and gA from outdoor tests in warm and moderate weather conditions. Solar Energy, 82: 573–587.

    Article  Google Scholar 

  • Juhl R (2011). Towards Efficient Estimations of Parameters in Stochastic Differential Equations. MA Thesis, Technical University of Denmark.

    Google Scholar 

  • Kristensen NR, Madsen H (2003). Continuous time stochastic modelling-Mathematics guide. CTSM 2.3. Technical University of Denmark.

    Google Scholar 

  • Kristensen NR, Madsen H, Jørgensen SB (2004). Parameter estimation in stochastic grey-box models. Automatica, 40: 225–237.

    Article  MathSciNet  Google Scholar 

  • Ljung L (1987). System Identification: Theory for the User. Upper Saddle River, NJ, USA: Prentice-Hall.

    MATH  Google Scholar 

  • Ljung L, Söberström T (1983). Theory and Practice of Recursive Identification. Cambridge, USA: The MIT Press.

    Google Scholar 

  • Madsen H (2008). Time Series Analysis. Boca Raton, FL, USA: Chapman & Hall/CRC.

    MATH  Google Scholar 

  • Madsen H, Holst J (1995). Estimation of continuous-time models for the heat dynamics of a building. Energy and Buildings, 22: 67–79.

    Article  Google Scholar 

  • Madsen H, Thyregod P (2011). Introduction to General and Generalized Linear Models. Boca Raton, FL, USA: Chapman & Hall/CRC.

    MATH  Google Scholar 

  • Mortensen S, Nielsen HA (2010). Analysis of energy consumption in single family houses. Tech. Rep. 03EKS0009A002. Enfor.

    Google Scholar 

  • Norling CR, Rode C, Svendsen S, Kragh J, Reimann GP (2006). A low-energy building under arctic conditions-A case study. In: Proceedings of 3rd International Building Physics Conference: Research in Building Physics and Building Engineering, pp. 587–594.

    Google Scholar 

  • Øksendal B (2007). Stochastic Differential Equations, 6th edn. Berlin: Springer.

    MATH  Google Scholar 

  • Pawitan Y (2001). In All Likelihood: Statistical Modelling And Inference Using Likelihood. Oxford, UK: Oxford University Press.

    MATH  Google Scholar 

  • Wasserman L (2003). All of Statistics-A Concise Course in Statistical Inference. New York: Springer.

    MATH  Google Scholar 

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Authors and Affiliations

  1. DTU Compute, Matematiktorvet, Building 322, DK-2800, Kgs. Lyngby, Denmark

    Philip Delff Andersen & Henrik Madsen

  2. Department of Energy, Energy Efficiency in Buildings Unit, CIEMAT, Av. Complutense 22, E-28040, Madrid, Spain

    María José Jiménez

  3. DTU Civil Engineering, Brovej, Building 118, DK-2800, Kgs. Lyngby, Denmark

    Carsten Rode

Authors
  1. Philip Delff Andersen
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  2. María José Jiménez
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  3. Henrik Madsen
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  4. Carsten Rode
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Correspondence to Philip Delff Andersen.

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Andersen, P.D., Jiménez, M.J., Madsen, H. et al. Characterization of heat dynamics of an arctic low-energy house with floor heating. Build. Simul. 7, 595–614 (2014). https://doi.org/10.1007/s12273-014-0185-4

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  • DOI: https://doi.org/10.1007/s12273-014-0185-4

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