### Transcription of A MULTIZONE BUILDING MODEL FOR MATLAB/SIMULINK …

1 Ninth International IBPSA Conference Montr al, Canada August 15-18, 2005. A **MULTIZONE** **BUILDING** **MODEL** FOR **MATLAB/SIMULINK** ENVIRONMENT. Zaki El Khoury*, Peter Riederer*, Nicolas Couillaud*, Julie Simon**, Marina Raguin**. *Centre Scientifique et Technique du B timent, 84, Avenue Jean Jaur s, 77421 Marne la Vall e Cedex 2, France ** Gaz de France - GDF, 361 Avenue Pr sident Wilson, 93211 Saint Denis la Plaine, France seconds) that is crucial for control purposes, has ABSTRACT modular structure (so it's easy to replace a block or **MATLAB/SIMULINK** is known in a large number of fields add a new one) and is transparent to the user (an as a powerful and modern simulation tool. In the field expert Simulink user can access internal variables of of **BUILDING** and HVAC simulation its use is also the **MODEL** ).

2 This transparency is due to the exclusive increasing. However, it is still believed to be a tool use of Simulink blocks and Matlab language (no S- for small applications due to its graphical structure functions written with C ). and not to fit well for the simulation of **MULTIZONE** buildings. This paper presents the development of a MATLAB AND SIMULINK. new **MULTIZONE** **BUILDING** **MODEL** for **MATLAB/SIMULINK** Matlab environment, implemented into the SIMBAD. **BUILDING** and HVAC Toolbox. It's general enough to Matlab is a high level language dedicated to technical **MODEL** a variety of useful cases. Conforming to the computing (Matlab, 2004). It is based on matrix Simulink philosophy, the **MODEL** is modular and operations: the matrix is the basic datatype for structured into blocks to represent the modelled Matlab.

3 Beside its built-in and main functionalities, phenomena. To simplify the description of the Matlab has a wide variety of toolboxes developed for simulated **BUILDING** , a graphical user interface specialized technologies such as control systems, SIMBDI is developed in parallel, generating an xml neural network and several other domains. **BUILDING** description file. This file can be read directly Simulink by the SIMBAD **MULTIZONE** **BUILDING** **MODEL** . Finally, a Simulink is a software package for dynamic systems simulation case is presented in order to compare the (Simulink, 2004), used in parallel with Matlab. It can new **MODEL** with the Trnsys **MULTIZONE** **BUILDING** **MODEL** . **MODEL** linear and nonlinear systems using continuous INTRODUCTION time, sampled time or a combination of both.

4 Simulink is very suitable for problems that have a The present work is intended to complete the **MODEL** known configuration. On the other hand, it is more library Simbad **BUILDING** and HVAC toolbox difficult to deal with general purpose models, such as (SIMBAD, 2003). This toolbox provides ready to use a complete **BUILDING** **MODEL** . For example, it is simple HVAC models and related utilities to perform to **MODEL** with Simulink a time independent state dynamic simulation for buildings and HVAC plants. space problem. It is given by: The development of this toolbox was motivated by the IEA annex 17 concerning virtual laboratories X& = AX + BU (1). (Annex 17, 1993), where several research groups developed principles for the realisation virtual When A and B are time independent matrices, this laboratories (Laitila, 91) and (Va zi, 91).

5 System can be easily modeled with Simulink (cf. To date, Simbad has several **BUILDING** models that are figure 1). The matrices A and B can either be defined mono-zone models. When the user needs to simulate directly (if known) or calculated in separate Matlab a **MULTIZONE** **BUILDING** , he had to break it down to functions or scripts. Simulink will initialise those several monozone blocks and to couple them matrices before the simulation start. manually, that can be a source of mistakes. Therefore, CSTB, in cooperation with GDF, started to develop a **MULTIZONE** **BUILDING** **MODEL** that facilitates the modelling of **MULTIZONE** buildings. This new **MODEL** is developed with a graphical interface SIMBDI' to draw the **BUILDING** and to enter data interactively.

6 Among other features, the Simbad **MULTIZONE** **MODEL** allows the use of small timesteps (in the order of Figure 1 A state space problem with Simulink;. - 525 - The bar above a variable indicates a vector (not a The problem is more complicated when these scalar). Aa, Ba,s and Ba,p are matrices that are matrices are time dependent. In this case, the defined by the **BUILDING** zones. This way of modeller has two possibilities: description is also used in the following sections. 1. Split down the problem to a set of time Walls **MODEL** independent blocks;. 2. Use the S-function block that allows to Multilayer walls are modelled using constant thermo- use other programming languages such as C physical properties for each layer.)

7 The heat transfer is and Fortran. assumed to be one-dimensional. The wall surfaces For this **BUILDING** **MODEL** , we have chosen the first can be of two kinds: those in contact with air and approach. Its implementation is described hereafter. those with imposed surface temperature (called boundary surfaces). **MODEL** COMPONENTS The governing equations for a wall are thus: A complete description of the mathematical and The heat conduction equation within each layer (j) of numerical treatments is not possible in this paper. So the wall: only a brief description of the assumptions and the Tw 2 Tw mathematical formulation is given for the **MODEL** = j (8). t x 2. components as well as a general description of the where different modules of the **MODEL** .

8 Kj j = (9). Air zones **MODEL** j Cp j Each air zone is assumed to be homogeneous in The boundaries conditions are: temperature. Every zone has two set points: one for cooling and one for heating. The zone air temperature If the first surface of the wall is on contact can vary between these two set points. with air: When the air temperature is allowed to fluctuate T. (inbetween the two setpoints), the zone heat balance k1 w = hc,1 (Ta ,1 Tw x =0 ) + 1 (10). is used to predict the air temperature variation: x x =0. a V Cp a T&a , z = Pw,c + Peq,c + Pg ,c + Pv + Pcpl (2) If it has an imposed temperature: where Tw x =0. = Tb,1 (t ) (11). Pw,c = hc,i Ai (Ts ,i Ta , z ) (3) If the second surface of the wall is on i contact with air: Pv = m& v ,i Cp a (Tv ,i Ta , z ) (4) T.

9 Kn w = hc,2 (Ta ,2 Tw x = L ) + 2 (12). i x x = L. Pcpl = m& cpl ,i Cp a (Ta ,az ,i Ta , z ) (5). i If it has an imposed temperature: In the case where the air temperature tends to be Tw = Tb,2 (t ) (13). outside both set points, the heat balance is used to x =L. calculate the heating or the cooling loads related to the corresponding set point: For each interface between two layers ( j and j+1): T T. kj w = k j +1 w (14). P = Pw,c + Pg ,c + Pv + Pcpl (6) x x = x j x x = x +j To be used into the **MULTIZONE** **MODEL** , the above This set of partial differential equations has been equations must be defined in a matricial format (for discretisized using a combined finite difference and all zones of the **BUILDING** ).

10 For example, the final finite volume schemes. The discretization step for format of the equation (2), used in the **MODEL** is (now each layer is calculated by: equivalent to equation (1)): x 2j = j t (15). &. Ta = Aa Ta + Ba,s Ts + Ba, p ( Peq,c + Pg ,c + Pcpl + Pv ) (7). The resulting final differential equation for all walls in matrix form is given by: - 526 - Infrared heat exchange &. Tw = Aw Tw + Bw,a Ta + B w, (16) The infrared heat exchange **MODEL** is based on the assumption that all surfaces behave as black bodies. The black body equation has been linearised. This is where is a vector that contains absorbed incident justified by relatively small differences between fluxes (IR and solar radiation) on the walls surfaces: surface temperatures in buildings.