MODELING AND SIMULATION OF MULTI-ZONE BUILDINGS FOR BETTER CONTROL

Transcription

1 MODELING AND SIMULATION OF MULTI-ZONE BUILDINGS FOR BETTER CONTROL Wathala Perera and Carlo F. Pfeiffer and Nil-Olav Skeie Telemark Univerity College Department of Electrical, IT and Cybernetic Porgrunn, Norway. ABSTRACT Building are one of the larget energy conumer in mot of the countrie. Building ector in the European Union (EU) i continuouly expanding and currently utilize 40% of total energy conumption in the union. Out of that, pace heating energy demand i the highet. Norway, where a harh climate predominate, ue 48% of the total energy production for both reidential and commercial building. Recent invetigation carried out in Norway howed that there i a potential of aving 65 TWh both from reidential and commercial building in Nowaday there i a growing trend to ue building automation ytem (BAS) in building, ranging from mall room to multi-zone building with divere architectural deign. BAS help to make the environment more efficient for occupant with better facility management. Currently, BAS lack a building model, and the control i baed on temperature zone and lowering the temperature only 5 0 C when the heater are unued. A good building model may help to optimally turn the energy on and off and reach the temperature goal of the zone. Thi will give a better energy performance for the building. Thi article refer to a multi-zone mechanitic building model which can be ued for imulating the thermal behavior of a reidential building. It conit of modeling the ventilation, thermal ma of wall, floor, roof and furniture. The model tate variable are expreed uing a lumped parameter approach. The temperature and relative humidity meaurement acquired from a typical reidential building in Norway are ued to verify the model. Model imulation i carried out in MATLAB environment, and it can be applied for controlling the energy performance of complex building deign reaonably well. Hence the current reearch project i important a it contribute in achieving the energy aving goal determined in Keyword: Mechanitic building model, Multi-zone building, Reidential building, Ventilation NOMENCLATURE Q Heat flow rate [W Symbol q Heat generation rate [W A Surface area [m 2 R Ga contant [J/(molK) ĉ p Specific heat capacity of air [J/(kgK) r Radiu of phere [m E Enthalpy [J T Temperature [K ĥ Specific enthalpy [J/kg t Thickne [m I Internal energy [J U Overall heat tranfer coeff. [W/(m 2 K) M Molar ma of air [kg/mol V Volume [m 3 ṁ Air ma flow rate [kg/ α Thermal diffuivity [m 2 / n No. of mol [mol ξ Furniture temperature [K P Preure [Pa φ Ceiling temperature [K ψ Floor temperature [K Correponding author: Phone: E- ρ Denity [kg/m 3 mail:wathala.perera@hit.no τ Time [ 268

2 θ ω Subcript c f f ur g i j w α Supercript h v Inide air temperature [K Wall temperature [K ceiling Floor Furniture Ground Building unit Adjacent room Wall Outide environment Horizontal opening Surface vertical opening INTRODUCTION The total worldwide energy demand i continuouly increaing owing to the population growth, economic development and the ocial development. With the growth of the indicated determinant, building ector ha become one of the larget energy conumer and it account for nearly 40% of the total global energy conumption [1. Similarly, the building energy conumption in the EU i continuouly expanding and it ha alo rien to 40% [2. According to the tatitic in 1999, pace heating wa the key contributor, which account for 68% of total houehold energy conumption in the EU [3. Among the European nation, Scandinavian countrie experience comparatively harh climate condition during about one third of the year. Accordingly, in a country like Norway, reidential houehold and commercial building conume about 48% of the total energy production [4 mainly for pace heating. Recent invetigation in Norway, have howed that there i a feaibility of aving 65 TWh both from reidential and commercial building by 2020 [4, and to achieve thi goal Norwegian government authoritie have impoed building technical regulation.they encourage the people to ave energy uing renewable ource and building energy management ytem (BEMS). BEMS are a ubet of BAS and they monitor and control the energy of the building and building ervice a energy efficiently a poible while reducing the utility bill without compromiing the comfort level of the occupant. Thee ytem are a rapidly expanding field over the lat two decade and they have gained the attention a a tandard way of controlling the building with regard to the claical technique uch a thermotat control [5. Currently, the mot of the BEMS ytem utilize on/off control, PID control or optimum tart-top routine a the control algorithm [5. PID control i the mot ued technique in uch ytem [5. However the ue of claical control algorithm uch a PID and on/off may not be the bet to be combined with BEMS [6. In building, thermal interaction between different zone and HVAC (Heating, Ventilation and Air-Conditioning) ytem lead to multivariable behavior. Claical control technique have ome deficiencie in handling uch ytem. For example, claical controller are eay to tune for SISO (Single Input - Single Output) ytem and not eay or even impoible to tune for MIMO (Multiple Input - Multiple Output) ytem. Advanced control technique appear with a mathematical model of the building and have the potential to approach thee contraint [5. The required model in advanced control could be multivariable and conequently ha a higher probability of delivering improved performance with fewer etpoint deviation and high energy aving when compared with the claical control. Therefore, it i eential to chooe a good quality building model to produce a favorable outcome by BAS. Building heating model can be categorized into three broad categorie: (i) mechanitic model (white box or phyical model); (ii) empirical or black box model; and (iii) grey box model ([7 - [11). Mechanitic building model are developed baed on the phyical principle of ma, energy and momentum tranfer. They conit of everal equation with numerou coefficient to repreent the building geometry and the thermal propertie of the building. Large number of numerical oftware tool are available for olving uch ytem. However, there are problem aociated with mechanitic model regarding the calibration of the phyical parameter. Software tool like Energy Plu, TRN- SYS, Modelica and Fluent provide comprehenive mechanitic model for building imulation. Thee model may have a very high accuracy, but they may have a high computational burden when applied to online control. Further, it may not be eay to calibrate thee model with repect to the experimental data. Therefore, the election of a mechanitic 269

3 model for a building i a balance between model complexity and the deired accuracy [7. Application of phyical principle to building and developing mechanitic type model are available in [12 - [19. Sytem identification baed model, regreion model [20, genetic algorithm [21, fuzzy logic model [22, neural network model [23, neurofuzzy model [24 and upport vector machine [25 are ome example of black box model. Thee model are generated baed on the data meaured from a particular building uch a inide and outide temperature, relative humiditie, wind peed, olar radiation and air flow rate. Accordingly, thee model do not ue any phyical data of the building and hence the model coefficient do not have a phyical meaning. Black box model may perform better than phyic baed model, but it will only work for a pecific building where the data i meaured. When the input are outide the modeled data range thee model may give unrealitic and non-phyical reult. Grey box model [26 are a combination of both mechanitic and black box model and information about thee model i partly known [11. They are motly ued for parameter etimation and only a limited work ha been done on them [11. The preent tudy focue on the development of imple but comprehenive mechanitic type building heating model for multi zone building, which can alo be applied in online control in BAS. The development i baed on the ingle zone building model preented in [19. There are a number of reearch article that explain the modelling of multi-zone building uing phyical principle. [12 preent the development of a multi zone building model for MATLAB/SIMULINK environment implemented into the SIMBAD Building and HVAC Toolbox. Wall thermal ma i conidered in the model and it i aumed to have contant thermo phyical propertie for each layer of the multilayered wall. A window model and olar radiation model are alo included in [12. In [15, a reduced order tate pace thermodynamic model i developed. Each zone i aumed to be well mixed and inter zone air mixing, air infiltration and olar radiation alo modeled. A variety of multi zone building thermal modelling technique can be found in [27, [17, [16 and [28. However, the indicated multi zone building model lack either one or everal feature: (i) zonal ma balance; (ii) thermal ma of wall, floor and roof; (iii) thermal torage capability of building furniture; (iv) olar irradiation; and (v) occupancy. Hence, it i important to develop a reliable multi-zone mechanitic building model that depict all thee effect. The ret of the paper i organized to preent a detailed overview of the multi zone model development, imulation to validate the propoed approach uing real experimental data and finally ome concluding remark. MODELLING APPROACH In thi ection, a mechanitic dynamic heating model for a multi zone building unit i developed. The modeled building unit i preented in Figure 1. It i connected to four adjacent room, outide environment and ground. Heat i tranferred from the main unit to the urrounding via wall, roof and floor. The mechanical ventilation ytem control the air flow rate into and out of the building unit. There i a taircae to acce the room above the building unit via the horizontal opening in the ceiling. Air i exchanged in between the adjacent room owing to the interaction caued by vertical and horizontal opening. A heater i intalled inide the building unit to upply the energy for heating. Further, the other electrical appliance dicharge their wate energy which can alo increae the inide temperature. The furniture inide the unit may behave a a heat ink or heat ource depending on the temperature difference between the furniture and the urrounding. Adjacent room 1 Horizontal Opening Heater Window Sun irradiation Adjacent room 3 Door Outide Door Furniture + Appliance Air in & out Adjacent room 2 Room above Ground Figure 1: Configuration of the building unit 270

4 Application of ma balance for ventilated pace i vital a ventilation play a key role in convective mode of heat tranfer. The ma balance equation for the indicated multi zone building unit can be expreed a in the equation 1. dρ i dτ = 1 [ ṁα,i ṁ i,α + ṁ v j,i V i ṁ v i, j + ṁh j,i ṁh i, j (1) Energy balance for the building unit i derived uing the tandard energy balance equation, the relation E = I + PV, the relation de = d(mĉ p θ) and the ideal ga law PV = nrθ. dθ i dτ = ṁ α,i ĥ α ṁ i,α ĥ i + Q i + ṁ v j,iĥ j ṁ v i, jĥi + ṁ h j,iĥ j ṁ h i, jĥi ρ i V i (ĉ pi R/M i ) θ i dρ i ρ i dτ (2) Modelling the heat tranfer via the building envelope i eential in thermal modelling a it thermal ma ha a ignificant contribution to the temperature fluctuation inide the building. Wall, ceiling, roof and floor uually conit of everal layer of diimilar material uch a wooden panel and inulation material. In thi tudy, all the layer are recognized a one element of contant thermal propertie for ( implicity of the model. ) Tranient heat equation T dτ α 2 T q ρĉ p = 0 i dicretized uing the finite difference method to obtain the repective energy balance equation for the wall, floor and ceiling of the building unit baed on the aumption of one-dimenional heat tranfer. The deduced ordinary differential equation for heat tranfer through wall, floor and ceiling are given by equation 3, 4 and 5 repectively. dω dτ = α w dψ dτ = α f dφ dτ = α c [ ω i 2ω ω j (t w /2) 2 [ ψ i 2ψ ψ g (t f /2) 2 [ φ i 2φ φ j (t c /2) 2 + q w ρ w ĉ p,w (3) + q f ρ f ĉ p, f (4) + q c ρ c ĉ p,c (5) The preence of furniture in a building prolong the time required to heat a building to a pecified temperature. Correpondingly, it take a longer time to cool down the building a the heat releae from the furniture i low. To implify the modelling of heat tranfer in furniture, all the furniture with different propertie are aggregated into a ingle large pherical object having equivalent average thermal diffuivity. ( Heat ( equation ) in pherical ) coordinate, r 2 ξ τ α r r 2 ξ r r 2 q ρĉ p = 0, i dicretized to obtain the repreentative energy balance equation for the furniture (equation 6). dξ dτ = α [ f ur ξ i 2ξ ξ centre + ξ i ξ centre r (r/4) r/2 (6) Equation 1 to 6 preent the ordinary differential equation decribing the model for the multi zone building unit. The ret of thi ection how the algebraic equation required to obtain the complete model. It i neceary to evaluate the air ma flow rate via vertical and horizontal opening of the building unit to the neighboring zone. Figure 2 preent the air flow pattern through a vertical and a horizontal opening. Figure 2: Air flow through (a) Vertical and (b) Horizontal opening [29 Many author ([29, [30, [31 and [32) have developed equation for air flow acro a vertical opening conidering a contant air denity for each zone. Intereted reader can refer to the above mentioned reference to admit a relation for the ma flow rate (m v j,i, mv i, j ) addreed in the equation 1. The ma flow rate through horizontal opening could be either one way or two way depending on the preure difference between the zone [29. Conequently, to determine the direction of the flow, it i neceary to undertand the preure of each zone. Equation 7 i uggeted by [33 to determine the air ma flow rate along a taircae. A o and H o are the area and thickne of the opening while C d i the coefficient of dicharge. [ 0.5 ṁ h θgho = ρa o C d (7) θ 271

5 The term Q i in the equation 2 repreent the net heat flow to the building unit, and it can be approximated uing the equation 8. Heat loe through wall, floor, roof, window and door can be etimated uing the equation 9 for each component. [ Q i = Q heater + Q olar + Q appliance Q w Q f Q c Q window Q door Q f ur ) (8) Q = UA T (9) THE TEST BUILDING Thi ection yield a decription of the tet building which i located in Norway. It i a three toreyed reidential building located near Langeund and built in x x60 60x120 2x170x60 90x x x x x x (a) 100x210 (b) (c) 90x x x x60 130x50 90x210 2x110x x x x Temperature meaurement Humidity meaurement Figure 3: Sketche with the inner dimenion of the tet building (a) econd floor (attic) (b) firt floor (main floor) (c) baement. All the dimenion are in cm. The building inner dimenion, window and door dimenion are given in Figure 3. The three torey are acceible via two inner taircae. The main floor 100x60 and the attic are equipped with a mechanical ventilation ytem while the baement i not provided with mechanical ventilation. Total average air inflow rate into the building i 230 m 3 /h. There i a heat exchanger intalled acro the ventilation ytem to heat the incoming air uing the outgoing air. Thi heat recovery ytem ha an efficiency of 90%. The exterior wall of the attic have a thickne of 30 cm (average) and the roof thickne i 30 cm. It ha a volume of 93 m 3. Both attic and main floor are contructed uing wood and mineral wool inulation. The furniture volume inide the econd floor i etimated to be 3 m 3. There are no heater fixed in thi torey, but four peronal computer are running all the time which upply around 700W. The main floor ha the ame roof thickne imilar to attic with a volume of 196 m 3. It wall thickne i 15 cm. It i filled up with 25 m 3 of furniture and 3200 W power i upplied for heating purpoe. The electrical heater are controlled by a imple BAS with a et temperature of 20 0 C when the building i occupied. In the imulation, the heater i preciely controlled by an On/Off controller having an operating band of ± C, to maintain the temperature at 20 0 C. In addition to the electrical heater, wood firing i ued to heat the building only during the colder period, which i not modelled in thi article. The thicker wall of the baement and it ground floor are built uing concrete and the ret i wood. Outer wooden wall of the baement have a thickne of 20 cm and concrete wall have a thickne of 40 cm. The thickne of the ceiling i 30 cm, and the wall height i 235 cm. The total volume of the baement i m 3 and the furniture account for 40 m 3. There are four heater intalled in the baement. Out of that, two are wall heater (2x750 W), controlled by the ame BAS in the firt torey. The other are full time running floor heater. The floor heater have witche to turn them OFF or ON(1), ON(2) and ON(3). ON poition 1 ( W) i the lowet power uage and ON poition 3 i the highet power uage. All the floor heater are running at poition 1 for mot of the time. However, in reality, thee heater are manually brought to poition 2 depending on the outide temperature. The experiment of the tet building i carried out for 79 day/1897 hour in the period 24 October January The location where the temperature and relative humiditie are meaured, are 272

6 Table 1: Model parameter of the tet building Parameter 2 nd Storey 1 t Storey Baement α w,wood α w,concrete α f α c α f ur U w,wood U w,concrete 1.15 U f U c U f ur U door U window ymbolized in the ketch (Figure 3). No meaurement were collected from the attic of the building during the tet period. To eliminate the outlier and the noie preent in the data, they are moothed uing 30 th order Savitzky-Golay filter. For the conidered period, olar irradiation meaurement are not available. Hence, it i roughly etimated uing the intant outide temperature. A implified form of the equation 7 ha been ued to determine the value of the convective air ma flow rate inide the building in between each torey. To define the air movement direction, it i eential to recognize the preure and denity fluctuation of each torey. However, preure meaurement are not logged in thi experiment. Therefore, the preure increment in each zone i calculated by analyzing the volume of air flowing into each torey through the ventilation ytem. RESULTS AND DISCUSSION In thi ection, the performance of the developed multi-floor building model i analyzed for the elected tet building after it implementation in MAT- LAB. The thermal propertie like thermal conductivity, pecific heat capacity and denity of the building material are obtained from the literature, and they are ued to calculate the thermal diffuivity of the building component. The overall heat tranfer coefficient are determined uing the experimental data. Parameter identification from tet data ha revealed that calibrating the parameter preented in the model to normal operating data from a building may lead to groly inaccurate etimate. The predicted overall heat tranfer coefficient, which can admit a favorable olution to the propoed criteria, and the computed thermal diffuivitie are given in Table 1. It hould be noted that only the thermal parameter oberved in the model equation which are acknowledged to be ignificant are tabulated. The predicted temperature of the three torey of the building are preented in the Figure 4. According to the figure, it can be noticed that the inide temperature have a cloe relationhip with the outide temperature fluctuation. In the econd torey, only the predicted temperature i hown becaue of the unavailability of enor meaurement. The temperature i wavering while maintaining 20 0 C, which i acceptable according the reident feedback. The firt torey of the building maintain 20 0 C throughout the 79 day, which can be oberved by the meaured temperature profile. The prediction alo produce a conitent 20 0 C for more than 90% of the time with the benefit of an ON/OFF temperature controller. Even though the meaured temperature i retricted to 20 0 C, the predicted temperature i coniderably lower cloe to day 30 and day 45. The low outide temperature predominating over the period i the reaon for thi cenario. However, in actuality the inide temperature i preerved at the et temperature by wood firing, which i not reflected in the imulation. The deviation of the baement temperature profile are proportionately higher compared to the firt torey. The maximum divergence between the predicted temperature and the meaured temperature approache C at day 47. The dicrepancie could be owing to the action of floor heater at ON poition 2 during the cold period. CONCLUSION Mechanitic building heating model have peeded up the deign, contruction and operational activitie of building and ucceeded in etablihing the new technologie in building operation. Hence, the identification of a proper model of the heat dynamic of a building baed on frequent reading will be very ueful in defining the energy performance of the building, forecating the energy conumption and controlling the indoor environment. 273

7 Figure 4: Inide and outide temperature variation of the tet building. No temperature meaurement data i available for the attic. The main floor and the baement temperature prediction cloely follow the meaured temperature profile. 274

8 In thi paper, a lumped parameter model illutrating the long term heat dynamic of a reidential building baed on firt principle i preented. The model alo take the thermal ma of the building envelope and vertical air mixing into conideration. Hence, it ha been hown that the ued methodology can provide rather detailed knowledge of the heat dynamic of the building. Moreover, the propoed criteria i imple, computationally attractive and require limited input information. The developed model accomplihe the application independability and, therefore, the application of thi methodology to a broad cla of building type i traightforward. The deficiencie met in the model validation are: requirement for more temperature enor at repreentative poition in each floor; olar irradiation meaurement; and preure meaurement. Thee deficiencie can be eliminated, and accurate thermal imulation can be achieved if ufficient and precie input data of the building i available. Integration of the developed model with a BAS may help to optimize the uage of energy conumption. Further, it will help to achieve the temperature goal of each zone with le energy compared to uing a time chedule to control the temperature. REFERENCES [1 World Energy Council, World energy reource, [2 EBPD, On the energy performance of building. Official Journal of the European Union, Directive 2010/31/EU of the European Parliament and of the council, 2010: p [3 Douni, A.I. and C. Caraico, Advanced control ytem engineering for energy and comfort management in a building environment - A review. Renewable and Sutainable Energy Review, (6 7): p [4 Valmot, O.R., Enormt potenial for energiparing, in Teknik Ukeblad p [6 Perera, D.W.U., C.F. Pfeiffer, and N.-O. Skeie, Control of temperature and energy conumption in building - A review International Journal of Energy and Environment, (4): p [7 Lu, X., D. Clement-Croome, and M. Viljanen, Pat, preent and future mathematical model for building. Intelligent Building International, (1): p [8 Kramer, R., J. van Schijndel, and H. Schellen, Simplified thermal and hygric building model: A literature review. Frontier of Architectural Reearch, (4): p [9 Foucquier, A., et al., State of the art in building modelling and energy performance prediction: A review. Renewable and Sutainable Energy Review, (0): p [10 Spindler, H.C. and L.K. Norford, Naturally ventilated and mixed-mode building Part I: Thermal modeling. Building and Environment, (4): p [11 Zhao, H.-X. and F. Magoulè, A review on the prediction of building energy conumption. Renewable and Sutainable Energy Review, (6): p [12 Khoury, Z.E., et al., A multizone building model for MATLAB/SIMULINK environment, in Ninth International IBPSA Conference2005: Montreal, Canada. [13 Fraie, G., et al., Development of a implified and accurate building model baed on electrical analogy. Energy and Building, (10): p [14 Lü, X., Modelling of heat and moiture tranfer in building: I. Model program. Energy and Building, (10): p [15 O Neill, Z., S. Narayanan, and R. Brahme, Model-baed thermal load etimation in building, in Fourth National Conference of IBPSA2010: New York, USA. [5 Virk, G.S., J.M. Cheung, and D.L. Loveday. Development of adaptive control technique for BEM. in International Conference on CONTROL [16 Yao, Y., et al., A tate-pace model for dynamic repone of indoor air temperature and humidity. Building and Environment, (0): p

9 [17 Lü, X., et al., A novel dynamic modeling approach for predicting building energy performance. Applied Energy, (0): p [18 Mende, N., G.H.C. Oliveira, and H.X.d. Araújo, Building thermal performance analyi by uing MATLAB/SIMULINK, in Seventh International IBPSA Conference2001: Rio de Janeiro, Brazil. [19 Perera, D.W.U., C.F. Pfeiffer, and N.-O. Skeie, Modelling the heat dynamic of a reidential building unit: Application to Norwegian building. Modeling, Identification and Control, (1): p [20 Mauda, H. and D.E. Claridge, Statitical modeling of the building energy balance variable for creening of metered energy ue in large commercial building. Energy and Building, (0): p [21 Xu, X. and S. Wang, Optimal implified thermal model of building envelope baed on frequency domain regreion uing genetic algorithm. Energy and Building, (5): p [22 Fraie, G., J. Virgone, and J.J. Roux, Thermal control of a dicontinuouly occupied building uing a claical and a fuzzy logic approach. Energy and Building, (3): p [23 Li, K., H. Su, and J. Chu, Forecating building energy conumption uing neural network and hybrid neuro-fuzzy ytem: A comparative tudy. Energy and Building, (10): p [26 Berthou, T., et al., Development and validation of a gray box model to predict thermal behavior of occupied office building. Energy and Building, (0): p [27 Hong, T. and Y. Jiang, A new multizone model for the imulation of building thermal performance. Building and Environment, (2): p [28 Anderen, K.K., H. Maden, and L.H. Hanen, Modelling the heat dynamic of a building uing tochatic differential equation. Energy and Building, (1): p [29 Allard, F., et al., Air flow through large opening in building, J.V.D. Maa, Editor 1992, International Energy Agency. [30 Brown, W.G. and K.R. Solvaon, Natural convection through rectangular opening in partition 1: Vertical partition. International Journal of Heat and Ma Tranfer, (9): p [31 Allard, F. and Y. Utumi, Airflow through large opening. Energy and Building, (2): p [32 Riffat, S.B., Algorithm for airflow through large internal and external opening. Applied Energy, (3): p [33 Peppe, A.A., M. Santamouri, and D.N. Aimakopoulo, Buoyancy-driven flow through a tairwell. Building and Environment, (2): p [24 Alaha ary, H., et al., A neuro fuzzy model for prediction of the indoor temperature in typical Autralian reidential building. Energy and Building, (7): p [25 Zhijian, H. and L. Zhiwei. An Application of Support Vector Machine in Cooling Load Prediction. in Intelligent Sytem and Application, ISA International Workhop on