Air Conditioning Using Matlab

Simulation Modelling Practice and Theory 12 (2004) 61–76 www.elsevier.com/locate/simpat

Simulink and bond graph modeling of an air-conditioned room *

B. Yu , A.H.C. van Paassen Energy in Built Environment, Environment, Energy Technology, Technology, Delft University University of Technology, Technology, Delft, The Netherlands Netherlands

Received 6 May 2002; received in revised form 24 December 2002; accepted 23 December 2003

Abstract

Dynamic models of the heating, ventilation and air-conditioning (HVAC) systems in the building are very useful for controller design, commissioning, and fault detection and diagnosis. Different applications have different requirements on the models and different modeling approaches can be applied. Mathematical modeling with two different approaches, block-wise Simulink and bond graph, is discussed. Advantage and disadvantage of both approaches are expressed. It is shown that combination with two approaches to realize complicated models of building HVAC system for the application of model-based fault detection and diagnosis is a good solution.  2004 Elsevier B.V. All rights reserved. Keywords: Bond graph; Simulink; Air-conditioned room; Modeling; Fault detection; Diagnosis

1. Introduction

A significant amount, as much as 30%, of all energy consumed by commercial buildings in the US is related to inefficient and improper operation of building equipment [1]. It is from the inability to optimally control, maintain, detect and diagnose problems with the buildings and their systems, e.g. HVAC and others. Many of these problems are often ignored or left unresolved because building staff and operators lack the enough information to address them. Model-based Model-based fault fault detection and diagnosis diagnosis (FDD) is a good solution solution to handle this problem [5] and general modeling concept has been raised to hierarchically realize

*

Corresponding author. Tel.: +31-15-2786662; fax: +31-15-2787204. E-mail address: bing.yu@wb [email protected] mt.tudelft.nl (B. (B. Yu).

1569-190X/$ - see front matter  2004 Elsevier B.V. All rights reserved. doi:10.1016/j.simpat.2003.12.001

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B. Yu, A.H.C. A.H.C. van Paassen Paassen / Simulati Simulation on Modelling Modelling Practice Practice and and Theory 12 12 (2004) 61–76 61–76

FDD [6]. However, real buildings are diverse from each other. They have different properties like sizes, locations and materials, etc. This puts higher requirement for the models. The contents of a model depend on the application context for which it is intended. As a consequence, models cannot easily be reused and exchanged. At present, present, efficiently efficiently constructin constructing g high-qualit high-quality y models requires special skills and experience. Computer support is only available at the computational and mathematical level. Every model has to be built from scratch, which means that modeling is very labor and cost intensive and error prone. Nevertheless, Nevertheless, reusing and exchanging exchanging models between between applicatio applications ns is possible possible since since we accept accept a certai certain n degree degree of simi similar larity ity,, to guaran guarantee tee an adequa adequate te answer answer (an exact answer is hardly ever required). Moreover, by complying with basic domain principles a certain level of confidence can be guaranteed without full validation, with respect to measured data. Provided that we acknowledge the underlying assumptions for a particular modeling problem, models may be partially reapplied in different situations. This means that for reuse of models the following requirements have to be fulfilled: •

• •

Models have to be constructed in a modular modular way. The model fragments should should be pluggable: they can be substituted solely by respecting their interfaces (rather than their contents). The model model constr construct uction ion proces processs is to be contro controlle lled d by the applicati application: on: model model selection must be controlled by assumption, i.e. explicit modeling experience. Hiding Hiding complexit complexity. y. The simulatio simulation n code code is to be genera generated ted rather rather than than hand hand crafted, internal details are normally not shown. Modeling should occur at the conceptual rather than computational level.

Engineering and design phases are becoming dominant cost factors in the industrial production cycle. This is particularly true for the automotive industry. Therefore, in the early 1990’s a number of European industries and research institutes initiated the OLMECO project. The aim of the project was to conceive and construct an Open Library for models of Mechantronic COmponents. A rather unconventional view of modeling was developed in the project [4]. Its core was the bond graph modeling modeling language language for physical physical systems. systems. Two simulation methods, methods, block-wise block-wise Simulink and bond graph, are two interesting tools for modeling. Simulink is a software package of Matlab  for modeling and simulating dynamical systems in academia and industry. It uses graphic user interface (GUI) for building models as block diagrams and adopts click-and-drag mouse operations. Nowadays, lots of toolboxes are available in Simulink. Bond graph is a systematic way to represent power interactions between the models’ components. IMMS [7], whose core concept is bond graph approach, is used to realize the modeling process. Bonds’, the connection lines between different components, carry both power power variab variables les and causal causaliti ities es betwee between n power power varia variable bles. s. Paynte Paynterr [2] starte started d the bond graph technique and used for modeling dynamic multiport systems. This ap







B. Yu, A.H.C. van Paassen / Simulation Modelling Practice and Theory 12 (2004) 61–76

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which represent all physical interactions and transactions. Rosenberg and Karnopp [3] expressed the theoretical basis and definitions of the method. From then on, bond graphs become a good modeling tool for different kind of dynamic systems. Pseudo-the Pseudo-thermal rmal bond graph graph method method is used. The pseudo-ther pseudo-thermal mal bond graph below represents a heat storage process C

1

0

2

The constitutive relation of the C element element is T ¼

Q C

where T is the pseudo-the pseudo-thermal rmal effort temperature temperature [K], Q is the pseudo-thermal state heat [J] and C ¼ ¼ m  c

where C is is the heat capacit capacity y [J K1 ], c is the material parameter specific heat capacity [J K1 kg1 ], which depends on the material selected by the modeler and m ¼ q  V

where m is mass [kg], q is material material parameter density density [kg m 3 ], which, like specific heat capacity c, depends on the material chosen by the modeler and V is is geometric 3 parameter volume [m ], which must be specified by the modeler or depends on the standard geometry chosen by the modeler. For the heat conduction process the following bond graph is appropriate R

1

1

2

The 1 junction represents effort difference, in this pseudo-thermal case, temperature difference. The constitutive relation of the R element is Q0 ¼

T R

where Q 0 is the pseudo-therma pseudo-thermall flow heat flow [J s 1 ], T is the pseudo-thermal effort temperature [K] and R ¼

l

k  A

where R is the resistanc resistancee [K s3 m2 kg1 ], l is geometric parameter length [m], k is materia materiall parame parameter ter heat heat conduc conductio tion n coefficie coefficient nt [m kg s 3 K1 ] and A is geometric geometric







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Different applications ask different requirements on modeling. Some applications require simple model and less quantitative results and some other applications require more accurate and complicated model. Some models are only used for specific application applicationss and some models need higher higher flexibility flexibility and reusability reusability.. The real buildbuildings are diverse but with some similarity. In order to build up model-based fault detection and diagnosis, the models with higher reusability and good communication with Building Management System (BMS) are necessary. In this paper, two modeling approaches are studied to analyze the differences. 2. Modeling analysis on an air-conditioned room

A typical room, no. 104, in an office building is analyzed. analyzed. The scheme scheme of this floor is shown in Fig. 1. The northeast and northwest walls insulate the room and outside environment. The southeast and southwest walls separate the room with the neighbors. Scheme of the fundamental air-conditioning components in the room, e.g. insulation lation (walls) (walls),, zone zone (air), (air), heatin heating g (radia (radiator tor), ), cooling cooling ceiling ceiling and window window system system (shutters and windows) is shown in Fig. 2. Following are the modeling analyses for these components with Simulink and bond graph approaches. 2.1. Walls

All walls, walls, floor and ceiling ceiling form form the insulatio insulation n system system of the room. Lumped Lumped parameter assumption is usually adopted for insulation models. This is realized by splitting the wall into some layers. In each layer, the parameters, like temperature, properties, properties, are the same. Since the parameters parameters are actually different, different, the more layers layers the wall is split, and the closer the model is to the reality. However, too many layers make the models more complicated and lower simulation speed. It is a trade-off.








65

Fig. 2. Scheme of fundamental air-conditioning components components of room 104.

A typical wall and its division are shown in Fig. 3. C analysis chart for this wall is as follow. Electrical R – C The equations of inner and outer surface temperatures has the form as

X dT io io ð0 5qV Þ ¼ Aq solar þ ar  F shutter shutter j  A j ðT air  T io j  T io io Þ þ ac  A ðT air io Þ dt j :

;

þ

X i

k ðT io as  F radiator radiator j  Aradiator ðT radiator radiator  T io io Þ  A  io  T 1 Þ d ;

ð1Þ

The equations of each layer has similar form as

 

k dT 1 aðT in in  T 1 Þ þ D 1 ðT 2  T 1 Þ ¼ dt 0 5ðqcdÞ1

i ¼ 1

ð2Þ

:

Ti To T1

T2

…… Tn-1

Tn







66


dT i ¼ dt

k D

 

ðT i1  T i Þ þ Dk iþ1 ðT iþ1  T i Þ i 0 5ðqcdÞi þ 0 5ðqcdÞiþ1 :

i ¼ 2

;

. . . ;

n  1

ð3Þ

:

 

k dT n aðT out out  T n Þ þ D n ðT n1  T n Þ ¼ dt 0 5ðqcdÞn

i ¼ n

ð4Þ

:

Simulink block representation for Fig. 4 with four layers is shown in Fig. 5 and for each layer is shown in Fig. 6. From the view of bond graph, the wall has radiation heat exchange with the other walls and radiator. Meantime, all layers are constructed with storage, conduction and power summation. Bond graph representation for the same wall is shown in Fig. 7.

Ti

1/ α T δ / λ λ T 1 2

δ / λ T λ T δ / λ n-1 n

Cn-1

C2

C1

1/ α

To

Cn

C analysis chart for the wall. Fig. 4. Electrical Electrical R – C

2

1

Trad. Ti

Trad

Ti

T1

T1

T2

layer1

Ti

layer2

T2 T1 T2

Tout

To

T3 alfa&q_solar alf alf a&q_solar a&q_solar

layer3

2 To

gasbet.sierbet.1 1 Tout 3 W&qz

Mux Mux

ff(u) (u)

3 Qrad

Fcn

Mux

Fig. 5. Simulink block representation representation for a wall.

1 -K-

T1 Sum1

-K-K-

2 T3

k1

Sum2

k3

Sum3

k1

1/s

k

Int

1 T2










67

2 Layer Wall

Heat Storage

Heat Conduction

Heat Storage

Heat Conduction

Heat Storage

Fig. 7. Bond graph graph structure structure for a two layer layer wall.

Fig. 8. StorageConduction StorageConduction module.

In Fig. 7, the bond relations are represented with some standard modules from library. This is useful for reusable modeling. All these modules are fundamental bond graph composition. For example, StorageConduction module is shown in Fig. 8. In the figures, the symbols of  and P are connection plugs that use to split a bond into two parts. 2.2. Room air

Room air has considered as a lumped parameter. Its state is determined by many other thermodynamic relations, e.g. heat exchanges with walls, radiator, shutters, windows, cooling ceiling and so on. For the mathematical equation of room air







68


Simulink realizes the mathematical equations directly. All heat exchanges are treated as inputs of integration. Fig. 9 shows the Simulink component model for room air. For the bond graph modeling, power information (temperature, heat flow rate) are inside the bonds. After the bonds are connected from room air node to the other components, components, the thermodyna thermodynamic mic relations relations are modeled modeled in the meantime. Therefore, the bond graph node model of room air is very simple as Fig. 10.

Fig. 9. Simulink Simulink model of room air.








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2.3. Heating system

Heating system is realized by radiator. By means of adjusting the opening rate of hot water valve, heating capacity added into room is controlled. Supposing the lumped temperature of radiator is the average of inlet and outlet water temperature. Analyzing the control domain of radiator in Fig. 11. Q is the total energy exchanges include radiation heat exchanges to all solid surfaces (walls, ceiling, floor, windows, etc.) and convection convection heat exchange exchange to the room air. Mathematical equations of radiator are dT R C w M w _ w C w ðT w in  T w out Þ  Q ¼m ð6Þ dt ;

;

Q ¼ A R aðT R  T a Þ þ Q R wall

ð7Þ

;

_ w depends on the valve-opening rate that is controlled with The mass flow rate m proportion strategy. Simulink model of radiator is shown in Fig. 12. Like room air node, the bond graph model of radiator is relatively simple as follow, Fig. 13.

2.4. Cooling system

In the summer days, cooling system is necessary. It is the cooling ceiling. Cooling ceiling has two functions. One function is cooling-down the recycle air. Another Tw,out

Tw,in

Q

Fig. 11. Control domain of radiator analysis. analysis.

2 mass flow







70


Fig. 13. Bond graph graph model model of radiator radiator..

function is supplying fresh air from outside. There is almost no capacity to accumulate energy at cooling ceiling node. Main thermodynamic process is heat exchange. The amount of heat exchange is QC ¼ Q recycle þ Qfresh

ð8Þ

Qrecycle ¼ ðT a  T w Þcðfactor1 þ factor2 Þ L

ð9Þ

Qfresh ¼ G fresh fresh qC p ðT a  T fresh fresh Þ L

ð10Þ

This cooling capacity will add into room air. In Eq. (9), c is controlled by the difference between setpoint and real room air temperature. When the temperature of the room is lower than setpoint, no flow in the tube and c will be zero. 2.5. Window system








aa ðT a between  T shutter shutter Þ þ a a ðT a  T shutter shutter Þ þ ;

X

71

4 4  T shutter Þ reðT wall

4 4 þ reðT radiator  T shutter Þ þ qsolar ¼ 0

ð13Þ

Simulink models of these components are shown in Fig. 14. Bond graph structures for these components and sub-structures of shutter, window and the air inside the channel are shown in Fig. 15 and Figs. 16–18. In these figures, the real bond graphs are inside each pluggable block to make the modeling reusable.

1

Demux

W&qz Demux

Mux 2

f(u) Fcn

Ta

3

4

Tr

Solve f(z) = 0

z

Alg ebraic Constraint

1 Tb a

Mux

Tw

Mux

5 To W

f (z)

f(u) Fcn1

f (z)

Solve f(z) = 0

z

Alg ebrai c Constraint1

Alf a o

Alf a out

Mux1

Mux

f(u) Fcn2

f (z)

Solve f(z) = 0

z

Alg ebrai c Constraint2

Mux2

Fig. 14. Simulink Simulink models of window window and shutter shutter system.

2 Ta a









72


Fig. 16. Bond graph structure structure of shutter.








73

2.6. Example results

After building the models, the simulation can be fulfilled. Fig. 19 shows the room temperature results for 11 days and Fig. 20 shows the temperature difference of Fig. 19. It shows the model can simulate the reality properly.

23 22 21 ) C o ( 20 e r u t a 19 r e p m18 e T

17

measured data model output output

16 15

0

50

10 0

15 0 Time (h)

20 0

25 0

30 0







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3. Comparison between Simulink and BG modeling

Simulink and bond graph modeling use different ways to realize the simulation. The comparison between these two methods has been made as follow: Simulink

Bond graph

Use mathem mathemati atical cal mode modeling ling concep conceptt Realize the mathematical equations and relations with block diagram. It’s a direct expression for the mathematical models The first step of Simulink modeling is trying to list the corresponding mathematica mathematicall equations equations for all sub-domains after physical assumption. For each subdomain, analyzing the energy conservation of the control domain to obtain the mathematical equations The temperature and heat flow calculations are modeled separately. Sometimes, this will cause

Use phys physical ical modelin modeling g conce concept pt Realize the physical meanings and relations with bond

The first step of bond graph modeling is analyzing the physical relationship among the sub-domains. For each sub-domain, determine the 0-, 1-junction, corresponding C -, -, R-elements and suitable connection plugs

With pseudo-the pseudo-thermal rmal BG modeling, modeling, temperature and heat flow calculations are modeled in the meantime. Inside a








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Physical relation analysis

Bond Graph modelling

Simulink block

s-function y=f(x,u) generation

final simulation model

Fig. 21. Suggested way of modeling combined with Simulink and bond graph.

logic, neural network algorithm can be easily realized. The flowchart is shown in Fig. 21.

4. Conclusions

Model-based fault detection and diagnosis technology is a possible solution to decrease crease the energy consumption consumption in building building HVAC system. Different applications applications have different requirements on the models and different modeling approaches can be applied. Reusability is an important characteristic for the model of building that







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[5] B. Yu, A.H.C. van Paassen, State-of-the-art of energy fault diagnosis for building HVAC system, in: International Symposium of Air Conditioning in High Rise Buildings 2000, Shanghai, China, October 2000. [6] B. Yu, A.H.C. van Paassen, S. Riahy, General modeling for model-based FDD on building HVAC system, Simulation Modelling Practice and Theory 9 (6–8) (2002) 387–397. [7] H. Rijgersberg, J.L. Top, HVAC library modeling in IMMS, EcoView Progress Report 1.1, ATODLO, June 1999.

Air Conditioning Using Matlab

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