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Optimal control strategies for hollow core ventilated slab systems Benjamin Park, Moncef Krarti

∗

T

Department of Civil, Environmental, and Architectural Engineering, University of Colorado Boulder, ECOT 441 UCB 428, Boulder, CO 80309-0428, USA

A B S T R A C T

This paper evaluated potential operational cost savings associated with optimal control strategies for hollow core ventilated slab systems used to maintain indoor thermal comfort for oﬃce buildings. First, a simpliﬁed calculation method was developed to convert two-dimensional (2D) modeling of ventilated slab thermal performance to one-dimensional (1D) analysis in order to reduce computational eﬀorts required for optimization search while maintaining acceptable accuracy level. The total energy costs were considered to identify optimal control strategies to operate ventilated slab systems to cool and heat oﬃce spaces. Penalty functions restricted the optimization search to ensure that indoor thermal comfort was maintained during occupancy periods. Then, the consecutive time block optimization (CTBO) technique was used with a genetic algorithm (GA) based search method to identify strategies that minimize the operational costs of the ventilated slab systems. A comparative analysis was carried out to evaluate the impact of ventilated slab systems’ design properties on the optimal operational cost savings. The results of the optimization analysis showed that the proposed optimal controller can achieve up to 11% cost savings to operate ventilated slab systems.

1. Introduction Reducing energy consumption while maintaining acceptable occupant's thermal comfort is becoming a major objective in designing and operating heating, ventilating, and air conditioning (HVAC) systems. Several studies have proposed the use of thermally integrated heating and cooling systems to lower energy use needed to heat and cooling buildings [1–7]. In particular, it is reported that thermally activated systems such as ventilated slab systems can be more energy eﬃcient than conventional HVAC systems while providing the same or even better levels of indoor thermal comfort. Since thermal comfort depends on several factor including mean radiant temperature and space air temperature, ventilated slab systems oﬀer a wide range of operating strategies for energy eﬃciency. Indeed, ventilated slab systems can operate at higher space air temperature for cooling and lower space air temperature for heating compared to the conventional air-based HVAC systems. With their seamless integration with building mass structure, ventilated slab systems can provide adequate cooling to the indoor spaces by lowering surface temperatures and heating by increasing surface temperatures. Operating systems at higher air set point temperatures for cooling and lower air set point temperatures for heating lead to the reduction of cooling and heating energy consumption of ventilated slab systems. Despite the potential cooling and heating energy consumption reduction for ventilated slab systems compared to conventional HVAC systems, controlling ventilated slab systems to maintain thermal comfort within acceptable ranges are rather challenging due to the inherent heat transfer time lag associated to the building thermal mass.

∗

Ventilated slab systems have been shown to respond slowly to the thermal needs of space [1]. For this reason, ventilated slab systems need a predictive controller not only to improve the thermal comfort in spaces but also to reduce the energy cost. Limited studies on operating strategies of ventilated slabs have been reported in the literature. Some researchers have evaluated the impact of using ventilated slabs to demand shift thermal loads to night-time hours in order to take advantage of cheaper electricity tariﬀ during the oﬀ-peak periods. Winwood et al. [2] presented the application of the active hollow core slab in a real oﬃce building in UK and the building's thermal performance and the energy consumption. The building has a gross ﬂoor area of 2400 m2, and a ﬂoor of approximate 1875 m2 with active hollow core slabs. The experimental data showed that the building maintained a stable internal temperature through the year, and provided the opportunity to shift the heating demand to night-time. Based on the data, the building attained an energy target of between 50 and 70 kWh/m2 per year with more eﬃcient fans, better control and improved night-time preheating, depending on the local weather. Ciampi et al. [3] established a simpliﬁed one dimensional steady-state heat transfer model of the hollow core slab (ventilated facade). The heat transfer process in the slab mass and this process between the slab and the environment were not included. This study provided a simple analytical method for the calculation of the energy saving. The authors concluded that properly designed ventilated facades can achieve up to 40% cooling energy reduction. Using a simpliﬁed thermal model, Ren and Wright has investigated improved control strategies for ventilated slab systems [4]. Speciﬁcally, the thermal model is based on T-links to estimate heat transfer between hollow cores using thermal resistances

Corresponding author. E-mail address: [email protected] (M. Krarti).

https://doi.org/10.1016/j.jobe.2019.100762 Received 31 August 2018; Received in revised form 2 April 2019; Accepted 3 April 2019 Available online 09 April 2019 2352-7102/ © 2019 Elsevier Ltd. All rights reserved.

Journal of Building Engineering 24 (2019) 100762

B. Park and M. Krarti

was used to solve the 2D heat conduction equation within the building envelope components that include embedded heat source/sink (i.e. ﬂoor and ceiling) [11]:

and the capacitances based on the geometrical properties of the slab. In comparison to a conventional control strategy, the annual operation of the predictive controller has shown that savings can be up to 43.6% in energy cost, and 66.2% in energy use due to the optimum control strategy making the best use of the thermal mass of hollow core ventilated slab systems, free night cooling and cheaper oﬀ-peak electricity. The peak demand load of ventilated slab systems can be reduced using night-time precooling strategies through circulating outdoor air at favorable temperatures [5,6]. Corgnati and Kindinis [7] reported a dynamic simulation of an active hollow core slab using Simulink. The transient heat transfer in the slab was solved with the explicit method. The cores of the slab were modeled as a heat exchanger using the ﬁnite diﬀerence. The researchers investigated the impact of utilizing nighttime free cooling on the demand energy reduction for microclimate control in Mediterranean countries. The results show that the application of active hollow core slabs for utilizing the cool night air can greatly reduce cooling loads in summer improving thermal comfort in Mediterranean climate. In this paper, optimal control strategies are developed for ventilated slab systems not only to improve temperature regulation but also to reduce energy costs required to maintain indoor thermal comfort in a US oﬃce building. The optimization analysis is carried using GeneticAlgorithm for a 24-h period using deterministic analysis approach. The impacts of the complexity of the thermal modeling for the ventilated slabs are investigated to determine the optimal control strategies. First, the analysis described in the paper proposes to use a two-dimensional (2-D) instead of a one-dimensional (1-D) thermal modeling approach for ventilated slab systems to determine accurately optimal control strategies. However, the 2-D thermal model was found to require signiﬁcant computational eﬀorts when combined with the optimization analysis. As a method to reduce the computational time, correlations to convert the 2-D solution to a 1-D modeling approach were developed to eﬃciently search for the optimal control settings. Moreover, the analysis presented in the paper considers the impact of various design parameters on the energy cost reduction predicted by the optimal controller.

k

∂ 2T ∂ 2T ∂T + k 2 + Q = ρcp 2 ∂x ∂y ∂t

(1)

The heat released or absorbed from the air ﬂowing into the hollow cores was calculated using Eq. (2):

˙ p)air (Tair , in − Tair , out ) Q= (mc

(2)

Since the air outlet temperature was not known, the eﬀectivenessNTU heat exchanger method was considered to calculate the amount of heat released or absorbed from the hollow cores [12]. The eﬀectiveness of the heat exchanger, ε , is deﬁned as the ratio of the actual energy transfer to the maximum amount of energy transfer. When one ﬂuid is stationary for a heat exchanger, the eﬀectiveness can be related to the number of transfer units (NTU) [13]:

ε≡

Q = 1 − e−NTU Q max

(3)

where NTU is deﬁned by:

NTU ≡

UA ˙ p)air (mc

(4)

The maximum heat transfer between the air and the slab is calculated based on the temperature at heat source or sink within the slab, Tsrc:

˙ p)air (Tair , in − Tsrc ) Q max = (mc

(5)

The results obtained by the developed simulation environment have been veriﬁed with predictions from the state-of-the-art whole-building energy modeling tool, EnergyPlus [10]. In a previously reported study, the impact of thermal bridging eﬀects on the thermal performance of ventilated slab systems was investigated by comparing the heat transfer and energy consumption of the ventilated slab system determined by both 1-D and 2-D models [10]. It was found that thermal bridging can lead to 14% more cooling energy consumption when no insulation is placed at the slab and wall joint. This diﬀerence of the energy consumption varied depending on the insulation level at the slab and wall joint. While 2-D model provides accurate results, it required signiﬁcant computational power to complete the simulation. For the optimization simulation, the required simulation time required for completing optimization simulation was increased magniﬁcently compared with the case where 1-D model was used. In particular, the required simulation time increased 12 times when the 2-D model was employed instead of the 1-D model for the optimization analysis, which was unpractically long for the optimal controller. In this study, a method to represent the results of 2-D model by adjusting the 1-D model was explored. A correlation between the 1-D and 2-D models was further studied to produce a correction curve. There is a discussion about this correlation later. The curve was developed as a function of an equivalent UA value of the slab-wall joint. The equivalent UA value for a given slab-wall joint was deﬁned by the procedure described as follows. The heat transfer through the slab and wall joint can be schematized by Y-network, as shown in Fig. 2. The Ynetwork needs to know the temperature in the middle of the slab and wall joint so as to calculate the overall heat transfer through the joint. By a reduction from Ye to Δ-network, the temperature in the middle of the network is no longer needed to calculate the heat ﬂow through the slab and wall joint. It is well proved that the heat transfer among three nodes (i.e.To , Tzone1, and Tzone2 ) are the same after the Ye to Δ-network reduction [14]. The transformation shown in Fig. 2 can be carried out using the following formulas:

2. Description of the building energy model A two-story building with one thermal zone per ﬂoor was considered for the study. The building had a ﬂoor area of 3200 m2. A ceiling height was set to be 3 m for both ﬂoors. The U-value of the building envelope was determined based on requirements of ASHRAE 90.1 2013 [8]. The oﬃce building was assumed to be located in Golden, CO, the U-value of the exterior walls were set to be 0.088 W K−1 m−2 while the U-value of the exterior roof and ﬂoor was set to be 0.033 W K−1 m−2. Peak occupancy was assumed to be 32 m2 per person. Based on ASHRAE recommendations, each person contributed 120 W of internal gain where 70% was assumed to be sensible and 30% latent [9]. Peak lighting power density was deﬁned as 10.8 W/m2 [8]. Table 1 provides a summary of the building model features and the control parameters considered. The length of peak period was 14 h (from 8 a.m. to 10 p.m.). The oﬃce building was occupied from 6 a.m. to 6 p.m. However, the ventilated slab system can be available to operate even when the building is unoccupied. A simulation environment that combines ﬁnite diﬀerence model and thermal network technique was developed and veriﬁed to evaluate the performance of ventilated slab systems and to assess the impact of thermal bridging eﬀects associated with the slab and wall joint. Fig. 1 illustrates the developed simulation environment. A 3R2C thermal network model was implemented to calculate heating and cooling thermal loads for spaces within the building. A 2-D ﬁnite diﬀerence method was used to model heat transfer between various element of the ventilated slab system taking into account thermal bridging through the slab and the wall joints [10]. Speciﬁcally, a control volume approach and pure implicit ﬁnite diﬀerence technique 2

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B. Park and M. Krarti

Table 1 Main characteristics of the oﬃce building model. Slab Exterior wall Roof Fenestration

U-value U-value U-value U-value SHGC Window-to-wall ratio Occupancy and Lighting

Internal load

0.033 W/m2-K 0.088 W/m2-K 0.033 W/m2-K 2.96 W/m2-K 0.385 34.6% (East and West) Number of people: 32 m2 per person Lighting Power density: 10.4 W/m2

Schedule:

Ventilated slab system

0.015 m3/s

Inﬁltration Core diameter Throttling range Set-point temperature

Heating Cooling Min. heating Max. heating Min. cooling Max. cooling Heating Cooling

Air inlet temperature

Air mass ﬂow rate

Rwall, floor =

0.10 m ± 1 °C 20 °C 24 °C 25 °C 30 °C 10 °C 15 °C 0.1 kg/s 0.05 kg/s

Rwall Rfloor + Rwall R ceiling + Rfloor R ceiling

Rwall, ceiling =

R ceiling

Rfloor , ceiling =

(6)

Rwall

(8)

where, Rwall is the thermal resistance of exterior wall, Rfloor is upper half of the thermal resistance of the slab, R ceiling is lower half of the thermal resistance of the slab. The Δ-network shown in Fig. 2 can be redrawn to produce an equivalent thermal network in parallel as shown in Fig. 3.

Rwall Rfloor + Rwall R ceiling + Rfloor R ceiling Rfloor

Rwall Rfloor + Rwall R ceiling + Rfloor R ceiling

(7)

Fig. 1. Schematic of the FDMRC simulation environment. 3

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B. Park and M. Krarti

Fig. 2. Reduction from Ye to Δ-network.

Fig. 3. Parallel thermal network.

The total heat ﬂow Q˙ total from zone 1 node to zone 2 node is made up of the heat ﬂow in the two parallel paths, Q˙ total = Q˙ wall, floor + Q˙ wall, ceiling + Q˙ floor , ceiling . Thus, the equivalent UA can be deﬁned as follows:

1 1 ⎞ UAeq = ⎜⎛ As ⎟ Ae + R + R R wall , floor wall , ceiling floor , ceiling ⎝ ⎠

(9)

where,

•A •A

e

s

= area of slab edge (i.e. slab and wall joint), = area of slab surface.

Rearranging Eq. (9) yields:

UAeq =

Fig. 4. The structure of the optimal controller for a deterministic simulation analysis.

⎛ As ⎜1 + Rfloor , ceiling ⎜ ⎝ 1

1 A Rwall, floor + Rwall, ceiling e 1 Rfloor , ceiling

Fig. 5. The schematic of Consecutive Time Block Optimization (CTBO) technique. 4

As

⎞ ⎟ ⎟ ⎠

(10)

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B. Park and M. Krarti

Fig. 6. Normalized cost as a function of 6-h interval set-point temperature schedule combinations obtained from brute-force simulation. Table 2 The optimal solutions obtained from the brute-force simulation and the optimization simulation using Matlab Global Optimization Toolbox. Normalized energy cost

Daily set-point temperature schedule

Brute-force simulation

0.41

Optimization simulation

0.41

1 7 1 7 1 7 1 7

fs, w =

(

1 Rwall, floor + Rwall, ceiling

(

1 Rfloor , ceiling

)A

e

)A

s

(11)

The indoor thermal comfort within spaces is calculated based on ANSI/ASHRAE Standard 55 [15]. This standard deﬁnes thermal comfort zone on the psychrometric chart as a function of operative temperature that depends on the mean radiant temperature (MRT). The ANSI/ASHRAE Standard 55 indicates that the operative temperature can be approximated with suﬃcient accuracy using Eq. (12) for spaces where occupants are engaged in near sedentary physical activity with metabolic rates between 1.0 and 1.3; not in direct exposure to sunlight and to air velocities greater than 0.20 m/s; and where the diﬀerence between MRT and dry-bulb is less than 4 °C:.

a.m.–6 a.m.: 23 °C a.m. to 12 p.m.: 26 °C p.m.–6 p.m.: 27 °C p.m. to 12 a.m.: 27 °C a.m.–6 a.m.: 23 °C a.m. to 12 p.m.: 26 °C p.m.–6 p.m.: 27 °C p.m. to 12 a.m.: 27 °C

The heat transfer factors (the ratio of heat transfer rate through exterior walls to heat transfer rate through a slab) can be expressed as follows:

to =

tmr + tdb 2

where,

Fig. 7. The optimal solution (a daily set-point temperature schedule) of the ventilated slab system. 5

(12)

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B. Park and M. Krarti

Fig. 8. Hourly zone air temperature proﬁles.

Fig. 9. Hourly total cooling energy use proﬁles.

•t •t •t

= operative temperature [K], = mean radiant temperature [K], db = dry-bulb air temperature [K].

t mr(standing)

o

mr

=

{0.08[tpr , up + tpr , down] + 0.23[tpr , right + tpr , left ] + 0.35[tpr , front + tpr , back ]} [2(0.08 + 0.23 + 0.35)] (13)

In this study, MRT was calculated from the plane radiant temperatures in six directions (i.e. up, down, right, left, front, back) and for the projected area factors of a person in the same six directions [8]. The larger and closer the surface is to an occupant, the more potential it has to thermally inﬂuence the occupant. The plane radiant method recognizes the position of the occupant in the space and considers two options standing or seated. The plane radiant temperature can be calculated using Eqs. (13) and (14) for standing and seated position, respectively. A seated occupant is assumed to be located in the middle of the space [16].

and,

t mr(seated) =

{0.18[tpr , up + tpr , down] + 0.22[tpr , right + tpr , left ] + 0.30[tpr , front + tpr , back ]} [2(0.18 + 0.22 + 0.30)] (14)

where,

•t •p •p •p

= plane radiant temperature, [°C], = ceiling temperature above the occupant, r,down = ﬂoor temperature below occupant, r,right = wall temperature to the right of the occupant,

pr

r,up

6

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B. Park and M. Krarti

Fig. 10. Comparison of normalized operation cost.

Fig. 11. Percent diﬀerence of cooling energy use between 1-D and 2-D model after optimization process as a function of percent diﬀerence of cooling energy consumption between 1-D and 2-D model for various slab sizes and utility rate ratios.

•p •p •p

indoor thermal comfort using the Fanger's model described in the ASHRAE Standard 55 [15].

= wall temperature to the left of the occupant, temperature in front of the occupant, r,back = wall temperature behind the occupant. r,left

r,front = wall

3. Optimization objective function

The following equation is used to calculate a plane radiant temperature:

tpr =

4

∑ Fpi (ti + 273)4

− 273

The objective of an optimal controller is to minimize an output value of the optimization objective function. The total daily operational cost associated with the ventilated slab system is considered as the optimization objective function throughout this study. The total daily operational cost is a virtual cost function that is deﬁned to represent the daily utility cost penalized when a constraint, that is the occupant thermal comfort in this study, is violated. Using the penalty option within the daily utility cost, the optimal controller search for solutions that ensure that the indoor thermal comfort is maintained within acceptable and desired range. The optimal controller searches for a space set-point temperature schedule that minimizes the total daily

(15)

where,

• t = surface temperature of surface i [°C], • F = view angle factor of a small plane i

pi

(person) to surface i

(∑ Fpi = 1) .

The predicted mean vote (PMV) is considered as an indicator of 7

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B. Park and M. Krarti

Fig. 12. Percent diﬀerence of operation costs between 1-D and 2-D numerical model as a function of ratio of heat transfer rate through exterior walls to heat transfer rate through a slab.

Fig. 13. Comparison of adjusted daily operation cost obtained from 1-D model (the cost adjusted by the correction factor) and 2-D model.

charges. The objective function can be expressed as indicated by Equation (16). The ﬁrst term in the right-hand side of the equation refers to the penalized energy charge for any 24-h period. The second term in the right-hand side of the equation is speciﬁc the on- and oﬀpeak demand charges.

operational cost of the ventilated slab system while thermal comfort is maintained during occupied period. The utility rate structure considered for the US commercial buildings consists of time-of-use (TOU) charge and demand charge. The TOU charge rate varies depending on the time of the day and includes onpeak or oﬀ-peak periods. The demand charge is the highest average demand during each month, and the demand expressed in kW is billed during each month. For the results presented in this paper, the TOU and demand charges are assumed to be $0.10 per kWh and $10 per kW, respectively. The monthly demand charge is extrapolated to daily utility cost by assuming that all days in the month are identical in order to simplify the utility cost calculation. Speciﬁcally, sum of the estimated peak demand charge is divided by the number of days in a month (i.e., 28, 29, 30, or 31 depending on the month), and added to the daily TOU

24

E=

∑ {re,onpeak,k EConpeak,k + re,offpeak,k ECoffpeak,k + f (PMVk )} k=1

rd, onpeak Donpeak + rd, offpeak Doffpeak

+

nd

where,

•E •r

= the total operational cost, = on-peak electricity rate,

e, onpeak

8

(16)

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B. Park and M. Krarti

Fig. 14. Percent energy cost savings of precooling vs. conventional control as a function of a hollow core slab thickness: (a) Ru = 4 and (b).Ru = 10

= oﬀ-peak electricity rate, •r = hour, k • = on-peak demand charge, •r = oﬀ-peak demand charge, •r • EC = on-peak energy consumption at hour k [kWh], • EC = oﬀ-peak energy consumption at hour k [kWh], • D = on-peak demand [kW], • D = oﬀ-peak demand [kW], • n = number of days in a month, • f (PMV ) = penalty cost function.

• 15°C ≤ T

set

e, offpeak

There are two techniques widely used to penalize the ﬁtness value of infeasible solutions. One is the simple rejection of infeasible solutions, and the other is to penalize the ﬁtness value based on the degree of infeasibility. In this paper, the latter technique was used since it allows the optimal controller to choose the solution that saves the maximum operational cost even if the solution violates the thermal comfort constraint slightly. The PMV penalty cost function is calculated by using Equation (17).

d, onpeak

d, offpeak

onpeak

offpeak

onpeak

offpeak

d

2

f (PMV ) = w (e PMV − 1)

The objective function is constrained by the thermal comfort levels set for the occupants. The predicted mean vote (PMV) is chosen as the index for assessing the thermal comfort of occupants. PMV value ranging between −0.5 and + 0.5 is generally acceptable [8]. To maintain the thermal comfort within the acceptable range during occupied hours, the zone set-point temperatures are generally limited as follows:

• 20°C ≤ T

set

≤ 30°C (During the unoccupied period)

(17)

where,

•w

= weighting factor that can be adjusted depending the penalty level desired to maintain indoor thermal comfort.

≤ 24°C (During the occupied period) 9

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Fig. 15. Comparison of slab surface temperatures of diﬀerent control strategies with various slab thickness: (a) conventional set-up control and (b) precooling control.

4. Optimal controller

controller uses Genetic Algorithm (GA) to perform the optimization search. In this paper, Consecutive Time Block Optimization (CTBO) technique is employed to search for an optimal solution. CTBO performs an optimization simulation over a planning horizon L [48]. The CTBO controller carries out an optimal solution for the entire predeﬁned planning horizon. Once the optimization process is completed for a current horizon L, the optimization process for the next horizon L will be executed. The planning horizon L of 24 h is typically considered throughout this study, as shown in Fig. 5. The essential assumption in this study is that weather, occupancy, lighting loads are perfectly predicted and known to perform a deterministic optimization analysis. The use of CTBO and perfect predictions are assumed since the main idea of this paper is to investigate the potential improvement levels of the performance associated with better operation of ventilated slab systems.

The selection of suitable optimization algorithm depends generally on the objective function and how well the diﬀerent methods can be tuned to ﬁt the particular optimization search [17–28]. Genetic Algorithm (GA) was chosen in this study because this approach shows a good performance when the number of parameters is large and the objective function is noisy. GA is known to be one of the most thorough methods in ﬁnding the global optimum in various ﬁeld of applications [29–32]. GA-based optimization has been widely used in building energy system design and operation applications. In particular, GA has been used to ﬁnd an optimal building shape [33,34], building envelope design [35–38], and control strategy of HVAC systems [39–49]. Fig. 4 shows the structure of the optimal controller developed to operate the ventilated slab system in order to maintain both heating and cooling building needs. The controller searches for the solution that maximizes the operational cost savings. Speciﬁcally, the controller varies the zone air set-point temperature schedule until it reaches the optimal solution. The zone air set-point temperatures for the optimal solution form the optimal zone air set-point temperature schedule. The

5. Discussion of analysis results A series of optimization analyses are carried out using the developed 10

Journal of Building Engineering 24 (2019) 100762

B. Park and M. Krarti

Fig. 16. Optimal solutions (daily set-point schedules) of the ventilated slab system with various solution space sizes.

Fig. 17. Hourly cooling energy use proﬁles with various solution space sizes.

simulation environment outlined above. In this section, select results of the analyses are presented including: (a) optimization veriﬁcation, (b) impact of slab modeling, and (c) parametric analysis. Results of each of the analysis are brieﬂy discussed in the following subsections.

levels. The set-point schedules obtained from the Global Optimization Toolbox and the brute-force simulation are found to provide identical solutions to minimize building energy consumption as shown in Fig. 6 and Table 2.

5.1. Optimization approach veriﬁcation

5.1.2. Optimal control strategy compared to conventional night setup control The dimension of the s for one day is 24 on an hourly basis to obtain optimal solution that includes temperature settings for each hour of the day. However, the search for one day (24-h horizon) can be reduced using a set of periods that considers both occupancy patterns and utility rate structure during the day. This simpliﬁcation can be considered in order to reduce the computational eﬀorts required to search for the optimal solution. For instance, when the search domain is reduced from 24 to 5, ﬁve time periods can be deﬁned to account for both occupancy levels and TOU utility rate structure considered in this study, as follow:

5.1.1. Optimization accuracy For the optimization simulation, GA provided by Matlab Global Optimization Toolbox was used [50]. The accuracy of the optimization search is veriﬁed for the speciﬁc case of the oﬃce building deﬁned in Table 1. In particular, the optimal set-point temperature schedule and the operational cost of the ventilated slab system predicted by the optimization simulation are veriﬁed against the results obtained by the brute-force simulation that considers all possible set-point schedule combinations in the search domain. For this analysis, the set-point temperatures are constrained to integer values within the range of 23°C ≤ Tset ≤ 27°C in terms of the acceptable indoor thermal comfort

• 12:00 a.m.–6:00 a.m., unoccupied and oﬀ-peak period 11

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Fig. 18. Normalized energy cost savings with various solution space sizes.

Fig. 19. Comparison of normalized operation cost savings for diﬀerent utility structures with various slab thickness.

• 6:00 a.m.–8:00 a.m., occupied and oﬀ-peak period • 8:00 a.m.–6:00 p.m., occupied and on-peak period • 6:00 p.m.–10:00 p.m., unoccupied and on-peak period • 10:00 p.m.–12:00 a.m., unoccupied and oﬀ-peak period

identiﬁed by the optimal controller. In particular, the optimal controller of the ventilated slab systems suggests a precooling operation strategy for the building prior to occupancy. The optimal set-point temperature is initially deﬁned as 20 °C during the unoccupied and oﬀ-peak period. The optimal set-point temperature is then slightly increased to 22 °C for the occupied and oﬀ-peak period. The zone air temperature remains at 24 °C, the upper limit of the comfort zone, during the occupied and onpeak period. The zone air temperature ﬂoats freely as soon as the occupied period ends by returning to the high value for the set-point temperature. Fig. 8 shows the hourly variations for the zone air temperature when the ventilated slab system operates with both the conventional night setup control and the optimal control strategy. The zone air temperature has decreased on average by 0.8 °C with the optimal control strategy outlined in Fig. 8. The precooling operation shifted the cooling energy consumption to the unoccupied and oﬀ-peak period

For each zone within the building, the optimal controller searches for 5 instead of 24 set-point temperatures. The TOU utility rate structure has a strong incentive for peak-demand shifting with on-to-oﬀ peak ratio of 4. Speciﬁcally, the energy and demand charges are respectively, $0.10/kWh and $10/kW during on-peak period, and $0.025/kWh and $2.5/kW during oﬀ-peak period. During the unoccupied period, a lower bound of 15 °C and an upper bound of 30 °C are set for the set-point temperatures. During the occupied period, the lower and upper bounds are set to 20 °C and 24 °C, respectively. Fig. 7 compares the set-point temperature schedule for the conventional night setup control with the set-point temperature schedule 12

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5.3. Parametric analysis

reducing the cooling energy consumption during the occupied and onpeak period, as shown in Fig. 9. This temperature-setting shift essentially results in 8.5% of overall building cooling energy cost reduction, as shown in Fig. 10.

A series of sensitivity analyses is performed to investigate the eﬀect of design and operating parameters on the performance of the optimal controls on the potential energy cost savings associated with the operation of a ventilated slab system to maintain thermal comfort for an oﬃce building described in Table 1. In this section, selected results are brieﬂy outlined for the following parameters: dimension of search domain, building thermal mass level, and TOU utility rate structure.

5.2. Impact of slab modeling 5.2.1. Thermal bridging A correlation between optimal solutions obtained from 2-D model and 1-D model is investigated. Then, a method to represent 2-D model's optimization solutions by adjusting the 1-D model's optimization solutions is explored. It is observed that percent diﬀerences of energy consumption between 1-D and 2-D models before and after the optimization simulation are in linear relationship for various ﬂoor sizes and various utility rate ratios, as shown in Fig. 11. The R2 value of 0.9711 indicates a good ﬁt. The correlation between 1-D and 2-D models before the optimization simulation is further investigated to produce a curve as a function of the heat transfer factor in Eq. (11). The heat transfer factor is determined by the dimension and thermal resistances of a slab. Fig. 12 shows the results of the linear regression analysis applied to ﬁt the percent diﬀerence between 1-D and 2-D models associated with the heat transfer factors. The R2 value of the linear regression model is found to be greater than 0.90 indicating a good ﬁt. Given the slab dimension and thermal properties, the curve provides a correction factor that can be applied to the 1-D model's optimization solution represent the 2-D model's optimization solution. The linear regression correlation is then used to adjust the optimal solution predicted by 1-D model in order to mimic the optimal solution calculated by 2-D. Four diﬀerent slab sizes are considered; 4-m slab, 8m slab, 12-m slab, and 16-m slab. For 4-m slab case, two on-to-oﬀ peak ratios are considered; a ratio of 1 and 4. The impact of on-to-oﬀ peak ratio on the optimization simulation will be discussed later. Fig. 13 compares the adjusted daily operation cost obtained from 1D model with the cost obtained from 2-D model. The adjusted daily operation costs obtained from 1-D model is appeared to match those of 2-D model with R2 value of 0.9998. In other words, when an optimal solution obtained by 1-D model is adjusted by a proper correction factor, a relevant optimal solution obtained by 2-D model can be inferred.

5.3.1. Eﬀect of search domain dimension As noted earlier, the dimension for the optimization search domain can be reduced by deﬁning a set of periods within a day in order to decrease the computational eﬀorts. In this section, the impact of the search domain dimension is assessed on the optimal solution settings and associated operating cost savings. Speciﬁcally, ﬁve diﬀerent search domain dimensions are considered in this analysis:

• Base case: 24 °C for occupied period and 30 °C for the unoccupied period (this represents the conventional set-up schedule) • 3 dimensions: zone set-point temperatures for each occupancy • • •

period (0:00–6:00 (unoccupied), 6:00–18:00 (occupied), 18:00–24:00 (unoccupied)) 5 dimensions: zone set-point temperatures for each combination of occupancy period and utility rate structure during a day. 12 dimensions: the day is divided into 2-h periods. 24 dimensions: the day is simply divided into 1-h periods.

Fig. 16 illustrates the temperature settings for the ﬁve options described above for the dimension of the optimization search domain. For the analysis presented in this section, the building operated with a setpoint temperature of 24 °C during the occupied period and 30 °C during the unoccupied period is considered as the base case. The optimization results and the performance of the ventilated slab system operated using the ﬁve resulting control strategies are summarized in Fig. 17 and Fig. 18. As expected, the total operation cost is the lowest when using any optimized set-point schedule instead of the conventional set-up operation. More operation cost savings can be achieved by using ﬁner set-point schedule discretization as shown in Fig. 18. Fig. 17 shows the hourly cooling energy use proﬁles obtained for diﬀerent control strategies. The peak demand and energy consumption during on-peak period are consistently reduced with larger dimensions for the optimization search domain. The most eﬀective strategy is obtained using the hourly optimal control scheme reducing the total energy cost by 11.1% compared to the base case.

5.2.2. Impact of slab thickness This section investigates the eﬀect of the thickness of the hollow core slab on the potential operation cost savings associated with optimally operated ventilated slab systems. Speciﬁcally, optimal control strategies are identiﬁed using diﬀerent search domains (i.e. 3 dimensions, 5 dimensions, 12 dimensions, 24 dimensions) for various slab thicknesses. The optimal operation performance is compared with that of the conventional set-up control. Two TOU utility rate structures are considered with an on-to-oﬀ peak charge ratio of 4 and 10. Fig. 14 shows that when there is a strong incentive for demand shifting, a precooling strategy can save up to 19% of total cooling energy cost when a 0.25-m-thick slab is utilized. When the thickness of the hollow core slab varies, a 0.25-m-thick slab appears to result in the most operational cost savings, as shown in Fig. 14. This ﬁnding is speciﬁc to the US oﬃce building described in Table 1 and to the weather conditions of Golden, CO and is associated to the fact that the slab thickness aﬀects both the level of slab thermal mass and the building structure time constant (τ= RC ) [51]. In one hand, the energy storage capacitance increases with the slab thickness. In the other hand, when the slab is too thick it becomes diﬃcult to cool the slab surfaces by the air ﬂowing within the hollow cores due to higher thermal resistance. Thus, the slab surface temperatures for thicker slabs remain higher than those obtained for thinner slabs, as shown in Fig. 15.

5.3.2. Eﬀect of on-peak to oﬀ-peak charges ratio and slab thickness Fig. 19 illustrates the eﬀect of the ratio of on-peak to oﬀ-peak TOU utility charges, Ru, on the operation cost savings associated with the optimal control of the ventilated slab system. The results are presented for various slab thickness including: 0.12-, 0.25- and 0.50-m-thick slab. The ratio of on-peak to oﬀ-peak is varied from 1 to 10, and is applied to both energy and demand charges. For instance, the ratio of 4 means that the energy charges and demand charges during the oﬀ-peak period are ¼ times lower than those during the on-peak period. If the cost incentive is not suﬃcient to shift cooling load to the oﬀpeak period (i.e., the ratio of on-peak to oﬀ-peak charges is close to unity or Ru = 1.0), the optimal controller would operate the ventilated slab system using the conventional set-up operation since pre-cooling would increase cost. Thus, there is no energy cost savings relative to the base case when the utility on-peak/oﬀ-peak ratio is 1. For the speciﬁc case of the oﬃce building described in Table 1 and located in Golden, CO, it appears that even a ratio of Ru = 2 does not oﬀer enough incentives for the ventilated slab system to be operated using a pre-cooling control strategy when the slab thickness is set to 0.12 m- and 0.50 m. However, for a 0.25-m-thick slab, some energy cost 13

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References

savings can be achieved through pre-cooling when Ru = 2.0. These results are due to the conﬂicting eﬀects of both storage capacitance and thermal resistance as the slab thickness varies. Fig. 19 indicates that operational cost savings can be achieved by the optimized control strategies for all slab sizes when the utility on-peak/oﬀ-peak ratio is greater than 3.

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6. Summary and conclusions Optimized control strategies to operate ventilated slab systems to maintain thermal comfort within oﬃce buildings are identiﬁed using GA search technique and a detailed simulation environment. For the analysis, Fanger's thermal comfort model is implemented in the simulation environment to calculate the predicted mean vote (PMV). The mean radiant temperature (MRT) is calculated by using the plane radiant method to compute thermal comfort. As part of the study described in this paper, a simpliﬁed method is developed and applied to convert optimal solutions determined from a 1-D heat transfer model to those obtained by the 2-D model considered for accounting thermal bridging associated with slab and wall joints. The conversion approach has been shown to be eﬀective and robust since it allows to reduce computational eﬀorts while achieving accurate predictions. The optimal control strategies are determined as hourly temperature set-points for operating the ventilated slab systems using a cost function that minimizes the energy cost with speciﬁc thermal comfort constraints over a one-day operation horizon. A genetic algorithm optimization technique is used to reduce the computational eﬀorts for the optimization search. The results of the GA optimization have been evaluated and veriﬁed against predictions obtained from a brute-force search approach that considers all the possible solution options within the search domain. A series of analyses has been performed to determine and evaluate the performance of the optimal control strategies under various design settings and utility rates to operate ventilated slab systems to maintain desired thermal comfort for an oﬃce building located in Golden, CO. The results of the sensitivity analyses clearly indicate that operating ventilated slab systems using optimized controls oﬀer opportunities to reduce energy costs to cool US oﬃce buildings. Some of the main results of the sensitivity analyses include:

• When compared to a conventional control strategy, the optimum

• •

control is found to always reduce energy costs while maintaining similar or even better indoor thermal comfort conditions. Using hourly time step, the optimal control was able to reduce energy costs by over 11% compared to the conventional night setup control for a 2-story oﬃce building located in Golden, CO. The performance of the optimized controls for ventilated slab systems depend signiﬁcantly on the thickness of the slab. A thick slab (i.e., 0.5 m) is found to require more energy to pre-cool the building and lower energy cost savings compared to 0.25-m thick slab. Suﬃcient utility incentives, through for instance higher diﬀerence between on-peak to oﬀ-peak energy or demand charges, are needed in order for the optimal controls of the ventilated slab systems to eﬀectively reduce energy costs compared to the conventional operation strategies

As part of future work to the analysis presented in this paper, an alternate optimization technique, a closed-loop optimization (CLO), can be employed. The CLO will make the model capable of dealing with uncertainties associated with forecasting building thermal loads and climatic conditions. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.jobe.2019.100762. 14

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