Modeling and identification of the cooling dynamics of a tropical island hotel

Energy and Buildings 92 (2015) 19–28

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Modeling and identification of the cooling dynamics of a tropical island hotel Boris G. Vega Lara a,∗ , Luis M. Castellanos Molina b , José P. Monteagudo Yanes c a b c

Department of Physics, Faculty of Engineering, University of Cienfuegos, Cienfuegos, Cuba Department of Mechanical Engineering, Faculty of Engineering, University of Cienfuegos, Cienfuegos, Cuba Center for Energy and Environmental Studies, Faculty of Engineering, University of Cienfuegos, Cienfuegos, Cuba

a r t i c l e

i n f o

Article history: Received 19 September 2014 Received in revised form 13 January 2015 Accepted 20 January 2015 Available online 30 January 2015 Keywords: Building modeling System identification Central chiller plant Parameter estimation

a b s t r a c t Minimizing energy consumption of heating, ventilation and air conditioning (HVAC) systems in buildings has experienced an increasing attention recently. Mainly motivated by the exploitation of building automation systems (BAS), as well as simulation tools, innovative practices and methodologies have been introduced to reduce the costs of energy required for heating and air conditioning of buildings. Outstanding has been the establishment of model predictive control (MPC) as a control strategy for the optimal operation of HVAC systems. The basis for MPC is a dynamic model, which is objectively challenging and time-consuming to obtain. This paper presents two modeling approaches of the return water temperature of a central chiller plant based on data of the real operation of a building, weather disturbances, and the temperature of a reference thermal zone. It integrates building’s real measurements with a room simulator model. In this work, an original method for accurately describing the cooling dynamics of a case study hotel on a tropical island is proposed. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Tourism plays an important role in the economical developing of tropical islands in the Caribbean Sea. In Cuba, tourism is an industry with steady annual growth and a tendency to increase the number of hotels and rooms built. Raising the quality of service, reducing costs and environmental conservation are continuous challenges in this area. The hotel sector is generally characterized by high, and sometimes irrational, energy consumption. This is because of the inherited concept that the hotel’s main function is to give maximum comfort to its customers to any price. However, there are opportunities to reduce energy consumption and costs without affecting the level and quality of services through an effective energy management. Concerning the energy costs for Caribbean hotels, electricity represents the largest bill, where the air conditioning and the lighting systems are the most power demanding. Air conditioning can account for about 65% of total electricity consumption, mainly due to the high solar radiation and ambient temperatures. For hotels

∗ Corresponding author at: Department of Physics, Faculty of Engineering, University of Cienfuegos, Carretera a Rodas Km 4, Cienfuegos, Cuba. Tel.: +53 43550991. E-mail address: [email protected] (B.G.V. Lara). http://dx.doi.org/10.1016/j.enbuild.2015.01.036 0378-7788/© 2015 Elsevier B.V. All rights reserved.

with central air conditioning systems, chiller plants are commonly used to provide cooling energy in the form of chilled water to maintain the thermal conditions required for indoor areas. The operation of chillers leads to a huge electricity consumption and a peak demand, that is why any program of energy saving and reduction of energy costs in a hotel should focus to reduce the consumption of the HVAC (heating, ventilation and air conditioning) system. A series of papers about energy efficient operations of complex chilled water systems under various working conditions are reported in references [1–3]. Ma and Wang [1,2] reported a modelbased supervisory and optimal control strategy for central chiller plants in complex building air-conditioning systems to enhance their energy efficiency and control performance. The optimal strategy is formulated using simplified models of major components and genetic algorithm (GA) [2]. Wang et al. [3] presented an adaptive optimal control strategy for online control of complex chilled water systems involving intermediate heat exchangers to enhance operation and energy performances. A simulated virtual platform representing a chilled water system in a super high-rise building was established to validate and evaluate the above strategies. An extensive research on the application of a model predictive control (MPC) of thermal energy storage in building cooling systems have been published in the literature [4–6]. These works deal with buildings, at university campus, equipped with a water tank

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Nomenclature T C UA I Occ t k ˙ m cp n  F G

temperature (◦ C) thermal capacity (J/◦ C) overall heat transfer coefficient (W/◦ C) intensity of solar radiation (W/m2 ) occupancy time (s) discrete time index water mass flow rate(kg/s) specific heat of water (J/kg ◦ C) total of thermal zones parameter vector state equation output equation

Subscripts room reference thermal zone additional state extra w water supply s r return amb ambient primary circuit prim bypass bypass line global global c continuous d discrete

used for actively storing cold water produced by a series of chillers. Simplified models of chillers, cooling towers, tank and buildings are developed and validated for the purpose of model based control design. A MPC for the chillers operation is designed in order to optimally store the thermal energy in the tank by using predictive knowledge of building loads and weather conditions. The precinct has a significantly enhanced level of instrumentation in order to support the development and demonstration of energy-efficient technologies and practices. The MPC presented in reference [7] uses both weather forecast and thermal model of a real building to inside temperature control. Subspace methods were applied to identify a multiple input multiple output system (MIMO), that describes the dynamics of the indoor temperature and return water temperature of the heating system. Alternatively to this black-box statistical approach, a RC ˇ y´ et al. modeling of the same building was implemented by Sirok [8]. Both modeling practices captured the thermal capacity of the building. The results from real operation on a large university building proved the supremacy of predictive controller over a well tuned weather-compensated control, with the savings of 15−28%. In the other hand, the use of simulation tools (e.g. TRNSYS, EnergyPlus, ESP-r) for model identification of buildings has become an innovative practice nowadays [9–11]. A medium weight office building with two zones separated by a concrete wall, heating by a thermo-active building system (TABS) was constructed in TRNSYS environment [10]. Using a pseudo-random binary sequence as the excitation input signal, a linear time invariant (LTI) model of the system was identified using grey-box technique. In a co-simulation framework [9,11], a real-life example of a large multi-zone office building is modeled linking EnergyPlus(EP) and Matlab via Building Controls Virtual Test Bed (BCVTB). It was shown that statistically based algorithms were the viable option for modeling such a complex structure building. Archetypal guestrooms of a tropical island hotel were constructed in TRNSYS by Lara et al. [12]. Applying a RC approach,

their total thermal load was modeled as a function of the indoor set point temperature and the weather disturbances. Subsequently, a simple model of the chilled water plant is added. Considering the whole system, a model predictive controller for respecting the comfort requirements of the building and minimizing the energy consumption is designed and evaluated in simulation. From the aforementioned review, it has clearly demonstrated the key importance of modeling buildings and HVAC systems for developing optimal control strategies, and consequently to improve the energy efficient performance of cooling and heating plants. Building modeling approaches, e.g. first-principle models used on simulation tools and statistically based models, have been the current trends that have encouraged the present investigation. In contrast with previous works, in this research we focus on the identification of suitable models for describing the cooling dynamics (i.e., the heat exchange between the chilled water, thermal zones and the environment) of a case study hotel on a tropical island. The contribution of this paper is to present two modeling approaches of the return water temperature of a central chiller plant based on (i) data of the real operation of a hotel (i.e., chilled water temperatures and hotel’s occupancy), (ii) weather disturbances (iii) and the temperature of a reference thermal zone, previously constructed and modeled in TRNSYS. The models will be used for future applications of indoor climate control and energy efficient performance reports. This paper is organized as follows. Section 2 describes the building modeling approaches. Section 3 introduces the case study building, the central chiller plant and the real operation profile of the hotel. Section 4 recalls the model identification of a reference thermal zone. In Section 5, two modeling approaches of the return water temperature are proposed, while Section 6 exposes the results. Finally, Section 7 concludes the article and remarks future works. 2. Modeling and identification for buildings 2.1. Building modeling techniques A comprehensive literature related to building modeling and identification has been published in a number of journals and conference proceedings. One approach is to use the first-principle models [13,14], which are largely used on simulation tools (e.g. Trnsys, EnergyPlus, ESP-r), but these models are not explicit and cannot be used for control directly. The alternative is to use statistically based models when large measurements data sets are available [8]. Prívara et al. [11,15,16] classified the building modeling techniques in: • Subspace methods family (4SID) is a family of algorithms estimating a model of a system in a state space form. They work purely in a statistical manner and belong to the black-box identification algorithms. The complete mathematical treatment can be found in the literature [17]. It was applied, for example, in references [7,9]. • Prediction error methods (PEM) are the most commonly used statistical identification techniques. Their objective is to minimize one-step ahead prediction error by optimizing parameters of prespecified model structure [18]. This approach was employed for modeling of a room temperature in office buildings [19,20]. • MPC relevant identification (MRI) is an approach minimizing multi-step ahead prediction errors [21]. The horizon for an error minimization commensurate with a prediction horizon of the predictive controller. • Deterministic semi-physical modeling uses resistance capacitance (RC) network analogue to an electric circuitry to describe the

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process dynamics and is often referred to as a grey-box modeling. This technique was used for modeling real buildings [4,8]. • Probabilistic semi-physical modeling (PSPM) utilizes stochastic differential equations for the description of the system to be identified. Then a maximum likelihood estimation (ML) is employed to obtain unknown parameters. This method naturally enables an incorporation of prior information. It was used for modeling the heat dynamics of buildings [14,22].

There is extensive flexibility in choosing various predictor structures, i.e., g functions, and this gives a corresponding freedom in defining “good” models in terms of prediction performance [18]. A measure of model quality is the Akaike’s Information Criterion (AIC), defined in Eq. (9), where the model is tested on a validation data set. Comparing different models under this criterion, the most accurate model has the smallest AIC [18].

The building modeling approach applied in this paper is based on prediction error methods. It is essential to underline that this technique will not be used to estimate parameters for a pre-specified ready-made model structure (e.g. ARX, ARMAX, BoxJenkins or Output Error), but physically parametrized ones are treated. For its significance to this work, the main aspects of this methodology are briefly discussed in the following.

AIC = log VN (, Z N ) +

2.2. Prediction error methods From a selected certain model structure M, with particular models M() parametrized using the parameter vector  ∈ DM ⊂ Rd , the set of models defined is: M∗ =



    ∈ DM .

M 

(1)

Each model represents a way of predicting future outputs. The predictor could be a linear or nonlinear filter, which corresponds to one-step-ahead prediction for a general system described in reference [18]. The task with it is to decide upon how to use the information contained in the batch of data collected from the system to select a proper value ˆ N of the parameter vector, and hence a proper member M(ˆ N ) in the set M∗ . Starting from a data set ZN (see Eq. (2)) collected from the system, with inputs and outputs recorded over a time interval 1 ≤ t ≤ N, Z N = {u(1), y(1), . . ., u(N), y(N)},

(2)

a general predictor of a parametrized model leads to: yˆ ( t| ) = g(, Z t−1 ).

(3)

A parameter estimation method is summarized as the following general procedure [18]: 1. Form the sequence of prediction errors from observed data and the predictor yˆ ( t| ), ε(t, ) = y(t) − yˆ ( t| ), t = 1, 2, . . ., N.

(4)

Here  is the finite dimensional vector used to parametrize the mapping from past inputs and outputs to the space of the model outputs. 2. Possibly filter the prediction errors through a linear filter L(q) (q denotes the shift operator, qu(t) = u(t + 1)), εF (t, ) = L(q)ε(t, ).

(5)

3. Select a scalar valued, positive function l(.). Typically, a quadratic norm would be a first candidate, l(ε) =

1 2 ε . 2

(6)

4. Minimize the sum of these norms: ˆ N = argminVN (, Z N ),

(7)



where 1 l(εF (t, )). N N

VN (, Z N ) =

t=1

(8)

2d . N

(9)

3. Case study: tropical island hotel 3.1. Building and system description This case study considers a colonial mansion built in 1869, one of the most charming boutique hotels in Cuba. After a recent period of restoration, the hotel was rebuilt with 36 standard rooms, 11 junior suite rooms, and 2 suite rooms. The central chiller plant of the hotel is a primary-secondary chilled water system that consists of: two screw compressor units with partial heat recovery (229.9 kW of cooling capacity and R134a as refrigerant) to provide cooling energy for the building, and constant speed primary and secondary pumps to distribute chilled water across the chiller evaporator and thermal zones, respectively. The primary loop is decoupled with the secondary loop through the bypass line, as shown in Fig. 1. A building automation system (BAS) was installed in the hotel to monitor the chiller plant, the sanitary hot water system, the quality of pool water, the cold chambers, and to control the starting or stopping of pumps, lighting systems, air handling units (AHU), etc. A database for energy management contains historical records of supply and return chilled water temperatures, sanitary hot water temperatures, active power of the hotel, etc. The present study is based on data from the real operation of the hotel, collected by the BAS during periods between April to October 2013. Time series of supply and return water temperatures from the chiller, the weather, and the occupancy profile of the hotel for April 2nd–6th and 8th–16th can be found in Figs. 2 and 3, respectively. The weather data were provided by the Provincial Weather Institute of Cienfuegos, and the occupancy by the commercial staff of the hotel. It is important to remark that nearly persistent excitation tests for the building took place throughout April; the normal operation of the hotel was stopped due to foreseen shutdowns of chiller compressors, and that is evident when both temperatures, the supply and return water temperatures from the chiller, become practically equal during this time. Further, the incidence of outliers caused by signal spikes or by measurement malfunctions, can be seen in the figures. Hence, after extracting the informative data portions into segments and merge them into one multiexperiment data set, these measurements (i.e., the estimation data) were conveniently used for input-output statistical identification experiments. Each magnitude was recorded with a sampling interval of 5 min. The interaction of the hotel with the chilled water system is divided into two parts. Initially, the temperature of a reference thermal zone (i.e., a critical guestroom) is modeled as a function of weather and the temperature of the water supplied to the actuator (i.e., a fan coil unit) located inside the room, as discussed in the next section. This model will be useful for evaluating the occupants’ thermal comfort in a near future climate control application. Finally, the return water temperature from the building is modeled as a function of this reference room temperature, the hotel’s occupancy, the ambient temperature and the chilled water supply temperature, which is a control variable.

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Fig. 1. Hotel primary-secondary chilled water system.

4. Model identification of a reference thermal zone 4.1. The zone and HVAC system description Measuring and recording of real temperatures of guestrooms, offices or other parts of the hotel, ideal for building mathematical models using identification techniques, have not been a common practice in such facilities. Alternatively, an original solution is proposed: to construct, simulate and model a reference thermal zone on a simulation tool, in this case TRNSYS. In view of the case study hotel has a diversity of room types, to model each guestroom, office rooms, small shop, etc. might be a complex and tedious task. A reference zone for evaluating the

occupants’ thermal comfort for the worst scenario (i.e., the room with the highest cooling load) was chosen. It means that, if the reference zone is “comfortable”, consequently the comfort for the rest of the zones is ensured. In this plan, the selected thermal zone was the corner Suite Room 208, located in the 3rd floor. This guestroom has one of the biggest space area (66.8 m2 ) for air conditioning as a single thermal zone, only exceeded by the hotel’s restaurant and the summit meeting room, not considered in this study. It has fac¸ade orientations to the East (31.28 m2 of front area) and the South (39.4 m2 of front area), balconies with doors made of wood (4.05 m2 of area) and (2.84 m2 of area) glass, and consequently receiving the effects of solar radiation on the external walls, doors and the roof. This reference thermal zone was constructed in

Fig. 2. The data set for April 2nd–6th.

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Fig. 3. The data set for April 8th–16th.

TRNSYS environment (component Type56), taking into account the geometry of the room, solar orientation, materials and dimensions of walls, windows and doors, internal heat gains due to equipment and occupants, and the HVAC system used. The HVAC system used in the building is a fan coil unit (i.e., chilled water is circulated through a series of fluid-to-air heat exchangers to provide cooling energy to the building zones). For this case, a real prototype of fan coil unit is firstly modeled from a manufacturer data-sheet, and latterly implemented in TRNSYS. Considering that the fan coil unit is working at its maximum cooling capacity (i.e., highest and constant water flow by the pipes and air flow by the fan), a static model for describing the sensible cooling power, as a function of the room temperature and the chilled water temperature, was achieved. This cooling power is put into practice in the environment as a mechanical ventilation.

4.2. Modeling the reference thermal zone The objective of modeling the reference thermal zone is to find out the relationship between the selected room’s temperature with the chilled water supply and return temperatures, as well as the weather disturbances. Before going into the modeling details, two simplifying suppositions were considered. (i) The fan coil unit dynamics are faster than the one of the room temperature, then the actuator’s static model is suitable for simulations, (ii) and relative humidity is not controlled in the room (60% is fixed in simulations). Meteorological conditions (i.e., ambient temperature and solar radiation) are simulated using TRNSYS Type109 with the year weather profile corresponding to Havana, Cuba. Timebase and TRNSYS simulation time-step equal to 1/12 h for Type56 was chosen, allowing good compromise between simulation accuracy and execution time. Once the thermal zone is constructed in TRNSYS environment and the fan coil unit attached, the system is excited with a pseudorandom multilevel sequence of the chilled water temperature, Tw . In the following and relied on black-box modeling approach, different model structures (ARX, ARMAX, Box-Jenkins, Output Error and state space form) were tested. The discrete-time state space model

Eq. (10) led to one of the most accurate structure for representing the dynamics of the room temperature, xroom (k + 1) = Axroom (k) + Buroom (k),

(10)

yroom (k) = Cxroom (k) + Duroom (k),

where xroom ∈ R2 , uroom ∈ R3 and yroom ∈ R, and A, B, C and D are matrices of appropriate dimensions. These system matrices are a canonical version of a black-box linear model in free parametrization, estimated by subspace identification method, using simulation data from TRNSYS. The manipulated variable and



T

disturbances are combined in vector uroom = Tw , Tamb , Iglobal . The output vector is yroom = [Troom ]. The vector of system states is composed as xroom = [Troom , Textra ]T , where the state Textra has no physical meaning. The sampling period of the model is 1/12 h. Due to the bypass line, the water leaving the chiller plant (i.e., the water with the supply temperature Tw,s ) is mixed with the return water (i.e., the water with the temperature Tw,r ) from the hotel before they flow into the fan coil units, as it can be seen in Fig. 1. For that reason, the temperature of the chilled water reaching the fan coil units, Tw , was substituted by a proper expression obtained from an energy balance, Eq. (11). ˙ w,prim + m ˙ w,bypass )cp Tw = m ˙ w,prim cp Tw,s + m ˙ w,bypass cp Tw,r . (m

(11)

Taking into account the nominal water flows of the constant speed pumps in the primary (60 m3 /h) and secondary (80 m3 /h) circuits, Tw is a linear combination of the measured chilled water supply and return temperatures. Tw = 3/4Tw,s + 1/4Tw,r .

(12)

To conclude this section, the actual temperature of the reference thermal zone can be estimated, using Eqs. (10) and (12), from real values of chilled water supply and return temperatures and weather disturbances. From now on, this estimation will be considered as a “measured” temperature of the reference thermal zone, Troom .

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5. Model identification of the return water temperature In this section two approaches for modeling the return water temperature were considered. At first, a deterministic semiphysical approximation was regarded. Afterward, a black-box strategy was implemented.

parameters the constant terms of the right hand side of Eq. (17), the continuous-time nonlinear (CNL) model for explaining the return water temperature resumes as: dT w,r = c,1 (Tw,s − Tw,r ) + c,2 (Tamb − Tw,r ) dt + c,3 · Occ (Troom − Tw,r ).

5.1. Simplifying assumptions In order to reduce the complexity of the problem, some realistic suppositions were taking into account. • As constant speed pumps were installed, the water mass flow rates in primary and secondary circuits are assumed to be constant during the experiments. • As the water circuit is closed, the water thermal capacitance is assumed to be time invariant. • Based on the fact that the same fan coil unit, considering the manufacturer cooling capacity, was installed in most of the guestrooms for air conditioning, it is assumed that the overall heat transfer coefficient (thermal transmittance/conductance) for each actuator is the same and time invariant. • The amount of thermal zones for air conditioning is mainly defined by the number of occupied guestrooms, i.e., the occupancy of the hotel in this instant of time.

Grouping together Eqs. (18) with the continuous-time version of (10) and (12), the full model that represents the interaction of the reference thermal zone with the chilled water system is a set of first-order differential equations: ˙ x(t) = Fc (t, x(t), u(t), c,1 , c,2 , c,3 ), y(t) = Gc (t, x(t)),

in which the state, output and input variables are respectively defined according to:

⎡ ⎢

dT w,r ˙ w cp (Tw,s − Tw,r ) + UAamb (Tamb − Tw,r ) =m dt + UA1 (Troom,1 − Tw,r ) + · · · + UAn (Troom,n − Tw,r ).

UA1 = UA2 = . . . = UAn ≡ UA.

(13)

(14)

Therefore, extracting UA as a common factor, and posterior n, the terms of the heat exchange between the return water temperature and the thermal zones can be transformed to:

= n · UA

room,1 + · · · + Troom,n − Tw,r n

,

Troom,1 + · · · + Troom,n . n

(15)

˙ w cp m dT w,r UAamb = (Tw,s − Tw,r ) + (Tamb − Tw,r ) Cw Cw dt UA · Occ (T room − Tw,r ), Cw

Tw,r

y=

⎡

Troom Tw,s

,

⎤

(20)

⎢ ⎥ ⎢ Tamb ⎥ ⎢ ⎥. u=⎢ ⎥ I ⎣ global ⎦ Finally, the unknown parameters of this nonlinear grey-box model should be estimated according to the procedures described in Section 2.2, using measured data collected in April, 2013. The drawback of this scheme is the nonlinear dynamic behavior of the return water temperature, in this case bi-linear between inputs and states. An MPC based on this model will result in a nonconvex optimization problem, which can be challenging to solve [23]. Therefore, a linear model version could be an alternative to this disadvantage.

Inspired in the black-box identification techniques, the following model was found after a series of trial-and-error experiments. Regardless from physical principles, the primary interests of the model in Eq. (21) were in fitting the data and being a linear structure oriented to future control applications. Tw,r (k + 1) = d,1 Tw,r + d,2 Troom + d,3 Tw,s + d,4 Tamb + d,5 Occ .

(16)

Subsequently, the lumped capacitance model for the return water temperature can be rewritten as:

+

⎥

x = ⎣ Troom ⎦ ,

5.3. Black-box approach



where n is the total of thermal zones for air conditioning, precisely the occupancy (Occ) of the hotel in this instant of time. Denoting T room as the average temperature of the thermal zones, it is calculated as: T room =

⎤

Occ

As the overall heat transfer coefficient for each fan coil unit was assumed equivalent, then

T

Tw,r

 Textra 

Initially, a deterministic semi-physical approach is concerned for modeling the return water temperature. From first principles, the differential equation describing the heat exchange between the return water with the supply water, the ambient and the thermal zones for air conditioning is as follows:

UA(Troom,1 + · · · + Troom,n − n · Tw,r )

(19)

x(0) = x0 ,

5.2. Deterministic semi-physical approach

Cw

(18)

(17)

where T room is substituted by the temperature of the reference thermal room, i.e., Troom , modeled in Section 4.2. Combining in

(21) Gathering Eqs. (20), (10) and (12), the full discrete-time linear (DL) model that represents the interaction of the reference thermal zone with the chilled water system is a set of first-order difference equations: x(k + 1) = Fd (k, x(k), u(k), d,1 , d,2 , d,3 , d,4 , d,5 ), y(k) = Gd (k, x(k)), x(0) = x0 ,

(22)

B.G.V. Lara et al. / Energy and Buildings 92 (2015) 19–28 Table 1 Parameters of CNL model.

25

Table 2 Parameters of DL model.

Parameters

Value

Standard dev.

Unit

Parameters

Value

Standard dev.

Unit

 c,1  c,2  c,3

1.17 × 101 1.48 × 100 3.63 × 10−2

6.82 × 10−1 9.48 × 10−2 2.26 × 10−3

h−1 h−1 h−1

 d,1  d,2  d,3  d,4  d,5

3.05 × 10−1 4.57 × 10−2 5.85 × 10−1 5.03 × 10−2 1.67 × 10−2

2.09 × 10−2 6.27 × 10−3 1.75 × 10−2 5.28 × 10−3 9.22 × 10−4

– – – – ◦ C

in which the state, output and input variables are in correspondence with Eq. 20, respectively. In this case, 5 unknown parameters should be estimated using the methods discussed in Section 2.2, and measured data collected in April, 2013. 6. Results Real measurements were used as input-output data for estimating parameters in black-box and grey-box models that describe

the cooling dynamics of a case study hotel, using prediction error method. The estimated parameters for the resultant models are presented in the following. In Table 1, parameters and their standard deviations estimated for the CNL model are listed. In Table 2, idem for the DL model. A cross-validation process was performed as a method to validate the models. As it was stated before, measurements from

Fig. 4. Validation of models’ responses versus measurements. (a) Return water and room temperatures for April’s validation data set. (b) Return water and room temperatures for June 28th–July 3rd.

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Fig. 5. Validation of models’ responses versus measurements. (a) Return water and room temperatures for August–September, experiment I. (b) Return water and room temperatures for August–September, experiment II.

several days of April was used as estimation data. Validation data corresponded to periods of April (not considered in the estimation data), June, July, August, September and October. Comparison of the simulated outputs of the models with the measured data are depicted in Figs. 4–6. For evaluating the models’ quality, a normalized root mean square error (NRMSE) fitness value, defined as Eq. (23), was used:

 NRMSE fit =

1−



  yk − yˆ k 

  yk − E (yk ) 2

100%,

(23)

2

where E stands for the expected value operator. As it can be seen in Figs. 4 and 5, the identified models capture satisfactorily well the dynamics of the return water temperature, with NRMSE fitness values around 70%, and even better of the room temperature (in case of Troom , “measured” data versus simulated outputs for the models was considered), with NRMSE fitness

values higher than 90%, for the periods of April, June-July, and August-September. Likewise, there is a wide coincidence between the outputs of both models, shown in the large intersection of each response in the figures. A similar behavior between the room temperature and the chilled water return temperature was observed. At the end of September and the beginning of October, Fig. 6, the models’ quality decreased due to the change of the experimental conditions for estimating the parameters; the operating point of the primary and secondary pumps was moved (i.e., they were pumping different water mass flow rate regarding the initial settings) with the replacing of the central chiller plant for a new one. Finally, both models were compared using the Akaike’s Information Criterion, Eq. (9). The CNL model (AICCNL = 2.59) is slightly more accurate than the DL one (AICDL = 2.90). This small difference between both AIC factors can be explained recalling that the CNL model has only 3 parameters to be estimated, instead of 5 for the DL model, with practically the same NRMSE fitness values.

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Fig. 6. Validation of models’ responses versus measurements. (a) Return water and room temperatures for September 23rd–29th. (b) Return water and room temperatures for October 1st–9th.

7. Conclusions and future works This work has revealed a novel integration of a building simulation software, for modeling a reference thermal zone, with data of the real operation of a hotel and weather disturbances, to present two modeling approaches of the return water temperature of a central chiller plant. Two appropriate models were found for describing precisely the cooling dynamics of a case study hotel on a tropical island. The first proposed model, based on a deterministic semi-physical approach, conducted to reproduce the response of the return water temperature with good accuracy. However, this model led to a bi-linear dynamic behavior between one of the input and the states, which will not be suitable for predictive control. The second proposed scheme, founded on a black-box paradigm, produced comparable results, but in a linear discrete-time structure proper for an optimal control application.

Apart from the methodology for modeling the return water temperature, the reference thermal zone’s model was simulated with data of the real operation of the case study hotel. This analysis showed that the currently used open-loop strategy for controlling the central chiller plant, considering empirical criterions, has sometimes carried on violations of the occupants’ thermal comfort (i.e., Troom > 24◦ C). Hence, future works will be directed to develop control applications for minimizing energy consumption of the HVAC system whereas the comfort requirements of the hotel are satisfied. Acknowledgements B. Vega deeply thanks the Swiss Federal Commission for Scholarships for Foreign Students (FCS) for their financial support provided to his research stay at the Automatic Control Laboratory at ETH Zurich, as well as Prof. Dr. Manfred Morari for very valuable discussions and suggestions to his investigation. Moreover, the authors

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