Model-based multi-objective optimal control of a VRF (variable ...

Energy 107 (2016) 196e204

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Model-based multi-objective optimal control of a VRF (variable refrigerant flow) combined system with DOAS (dedicated outdoor air system) using genetic algorithm under heating conditions Wonuk Kim a, Seung Won Jeon b, Yongchan Kim a, * a b

Department of Mechanical Engineering, Korea University, Anam-Dong, Sungbuk-Gu, Seoul, 136-713, Republic of Korea Korea Institute of Civil Engineering and Building Technology, 64, 182 Beon-Gil, Mado-Ro, Mado-Myeon, Hwaseong-Si, Republic of Korea

a r t i c l e i n f o

a b s t r a c t

Article history: Received 19 November 2015 Received in revised form 10 March 2016 Accepted 30 March 2016

A VRF (variable refrigerant flow) combined system adopting a DOAS (dedicated outdoor air system) has been proposed to reduce the total energy consumption while satisfying IAQ (indoor air quality) and THC (thermal and humidity comfort) with minimum outdoor air. The objective of this study is to develop a model-based multi-objective optimal control strategy for the VRF combined system with multi-zone in order to optimize the multi-objective functions of the THC, IAQ, and total energy consumption. The performance of the VRF combined system was evaluated using the EnergyPlus model. The VRF combined system was optimized by GA (genetic algorithm) and RSM (response surface methodology) with the multi-objective functions of the THC, IAQ, and total energy consumption. The proposed multi-objective optimal control strategies (A and B) were compared with the TS (time schedule) strategy and the DCVH (demand controlled ventilation with humidifying). Optimal control strategy B reduced the total energy consumption by 20.4% and increased the ratio of the hours satisfying the extended comfort zone by 19.1% compared to the DCVH strategy. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Variable refrigerant flow Dedicated outdoor air system Model-based control Multi-objective optimization Multi-zone ventilation

1. Introduction Nowadays, building energy management is strongly influenced by IAQ (indoor air quality) and thermal comfort in working spaces. While ventilation with fresh OA (outdoor air) is essential for maintaining acceptable IAQ, it increases the thermal load of the working space. New ventilation systems using novel control methods such as DOAS (dedicated outdoor air system) and DCV (demand controlled ventilation) have been proposed to reduce the total energy consumption while satisfying IAQ with minimum OA. The conventional centralized all-air system consumes substantial energy to ventilate the air in a building for thermal comfort and IAQ, but the DOAS can reduce energy consumption by ventilating air only for IAQ [1]. In addition, the DOAS can allow easy control of IAQ by separating ventilation air from heating and cooling air [2]. The DOAS is often operated using DCV (demand controlled ventilation). The DCV controls ventilation airflow to satisfy the balance between IAQ and energy saving [3]. Therefore, the DOAS has been considered as an alternative to the centralized all-air system in commercial buildings.

* Corresponding author. Tel.: þ82 2 3290 3366; fax: þ82 2 921 5439. E-mail address: [email protected] (Y. Kim). http://dx.doi.org/10.1016/j.energy.2016.03.139 0360-5442/© 2016 Elsevier Ltd. All rights reserved.

In the centralized all-air system with multi-zone, conventional ventilation strategies often cause over-ventilation in some zones and under-ventilation in other zones when the heating/cooling loads and occupancy profiles in each zone differ significantly [4]. Therefore, several ventilation control methods for the centralized all-air system have been proposed to improve energy efficiency and provide uniform air-distribution to a multi-zone [4e6]. Xu et al. [4,6] reset the set point air temperature of the critical zone, which requires the largest fresh OA fraction, to optimize the OA ratio of SA (supply air). However, these control methods for the centralized allair system only resolved the imbalance of IAQ between zones using the set point reset of the critical zone. It is difficult to resolve the imbalance of IAQ and humidity at the same time using the set point reset of the critical zone. Therefore, it is necessary to apply multiobjective optimization to satisfy IAQ and THC (thermal and humidity comfort) in multi-zone with high energy efficiency. A VRF (variable refrigerant flow) system has been considered as a favorite heating/cooling system in commercial buildings due to the high part-load efficiency and individual control capability of thermal comfort in multi-zone [7e9]. Since the VRF system only circulates indoor air for a sensible load without in-taking OA, it is necessary to install a ventilation system to control IAQ and latent load [10,11]. Therefore, the VRF system usually adopts an additional

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Nomenclature C CO2 concentration, ppm COP coefficient of performance CR combination ratio Cv(RMSE)coefficient of variation of the root mean squared error DCV demand controlled ventilation DCVH DCV with a humidifier DOAS dedicated outdoor air system E energy consumption, MJ EA exhaust air EEV electronic expansion valve EIR energy input ratio GA genetic algorithm HVAC heating, ventilating, and air-conditioning IAQ indoor air quality IDU indoor unit L length, m m mass flow rate, kg s1 MBE mean bias error O occupancy OA outdoor air Obj objective function ODU outdoor unit PLR part-load ratio PMV predicted mean vote R2 coefficient of determination RA return air RH relative humidity, %

ventilation system, such as DOAS [12,13] and VAV (variable air volume) [14]. Ventilation effect [13,15] and optimal load ratio between VRF and VAV [14] were reported in a VRF system combined with a VAV system (called a VRF combined system). In addition, a simulation model for the VRF combined system was developed in a multi-zone building [9,16]. In these studies, zonal temperatures in multi-zone were controlled by each IDU (indoor unit) in the VRF system, while zonal IAQ and humidity were controlled by SA using the centralized air system. However, the simultaneous control on the imbalance of zonal IAQ and humidity in multi-zone has not been studied in the VRF combined system. The simultaneous optimal control of the THC, IAQ, and total energy consumption in a VRF combined system with multi-zone has been rarely studied in the literature. The objective of this study is to develop a model-based multi-objective optimal control strategy for the VRF combined system with multi-zone in order to reduce the total energy consumption in the heating condition while achieving acceptable THC and IAQ in each zone. The VRF combined system adopted a DOAS with a humidifier to control the humidity in multi-zone, and the set point reset of the temperature in the high humidity zone was applied to reduce the humidity imbalance between zones. The VRF combined system with the humidifier was evaluated using a building performance simulation and then optimized by GA (genetic algorithm) with multi-objective functions of the THC, IAQ, and total energy consumption. Moreover, the effects of weighting factors for the objective functions were analyzed using RSM (response surface methodology).

2. VRF combined system Fig. 1 shows the model-based optimal control of the VRF combined system. The VRF combined system consisted of an air-source

RSM SA T THC TS VAV VRF wf

197

response surface methodology supply air temperature,  C thermal and humidity comfort time schedule variable air volume variable refrigerant flow weighting factor

Subscripts DOAS dedicated outdoor air system E total energy consumption high high humidity zone humidifier humidifier i ith air conditioned zone IAQ indoor air quality IDB indoor air dry-bulb in indoor max maximum min minimum out outdoor OWB outdoor air wet-bulb p pipe SA supply air sp set point sup superheat THC thermal and humidity comfort VRF variable refrigerant flow

VRF heat pump, a DOAS with a plate type total heat exchanger, and an electrically heated steam humidifier. The VRF system was designed to cover the sensible load in the conditioned multi-zone. The VRF system consisted of a single ODU (outdoor unit) and multiIDUs for multi-zone. The VRF system can handle various heating/ cooling loads in multi-zone by controlling a variable speed compressor and EEV (electronic expansion valve) according to refrigerant superheat, indoor temperature, and occupancy. The heating and cooling capacities of the VRF system were enhanced by increasing the compressor speed, and the mass flow rate through the VRF system was controlled by the EEV [17]. The DOAS with energy recovery was used as a separate ventilation unit to change indoor air with fresh OA. The DOAS reduced the additional heating/ cooling loads resulting from in-taking OA by the energy recovery between EA (exhaust air) and OA [1]. The DOAS with the humidifier was used to cover the latent load and IAQ in the conditioned multizone. An electrically heated steam humidifier was installed between the zone splitter and the outlet of the DOAS system. The VRF combined system was installed in a building with 7 aboveground floors and 1 underground floor, which is located in Seoul, Korea. Table 1 shows the details of the building. As shown in Fig. 2, the floor plan consists of six zones, a hallway, an elevator, two stairs, and a toilet. Only one floor with the six zones and a hallway was considered in the simulation. The thermal conductivity of the building envelope and the internal heat gain from the light and equipment are given in Table 1. Table 2 shows the specifications of the VRF system and DOAS. The heating capacity and COP (coefficient of performance) of the VRF system were 65.2 kW and 4.2, respectively, at the rated conditions. The heating sensible effectiveness and heating latent effectiveness of the DOAS were 76% and 54%, respectively, for the rated 100% flow condition and 79% and 56%, respectively, for the rated 75% flow condition. The effectiveness was determined by linear interpolation or

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Humidity controller DOAS EA

Supply fan

Set point from optimizer

Optimal set point to predictor

SA RA

Set point from optimizer

OA flow rate controller

Humidifier Set point from optimizer

EEV controller

Tsp reset controller

Tsup Tin RH O Tout Refrigerant flow controller

IDU 1

Zone 1

Tsup Tin RH O

VRF Outdoor unit

Tsup Tin RH O IDU i

Constraints Damper

Damper

Zone 2 ...

IDU 2

Genetic algorithm

Iterative calls during optimizing

Data from predictor

...

OA

Multi-objective function estimator

User-define weight factors

Damper

Zone i

Model-based predictor (EnergyPlus)

Multi-objective optimizer (MATLAB)

Fig. 1. Model-based optimal control of the VRF combined system.

Table 1 Brief description of the case building. Section

Details

Location Building Total floor area Plan and height Operating/office hours HVAC design parameter

Seoul (latitude 37.6N, longitude 127.0E) Office building, 7 floors above grade, 1 below grade 756.76 m2 Rectangle, floor-to-floor 3.5 m Mon. to Fri.: 08:00e18:00/09:00e18:00 Lighting load ¼ 20 W m2, Equipment load ¼ 13.78 W m2 Space design temperature: Cooling ¼ 26  C, Heating ¼ 20  C DOAS operates at 9:00 AM, 13:00 PM, 17:00 PM, and 21:00 PM for an hour. Infiltration (air change rate): 0.732 h1 3 mm granite cladding, 65 mm expanded polystyrene, 75 mm extruded polystyrene, 25 mm gypsum board (U-value ¼ 0.22 W m2 K1) 80 mm concrete, 110 mm extruded polystyrene, 150 mm concrete, 25 mm gypsum board (U-value ¼ 0.22 W m2 K1) 3 mm granite cladding, 30 mm mortar cement, 150 mm concrete, 50 mm extruded polystyrene (U-value ¼ 0.35 W m2 K1) 3 mm double clear glass, 13 mm air-space (U-value ¼ 2.76 W m2 K1)

Building envelope

External wall Roof Floor Window

Note: Based on the Korean building regulation, the minimum ventilation air flow rate requirement for the office building is 34.2 m3 h1 per person. In the ventilation air flow rate, the exhaust air from the kitchen and bathrooms can be included. In addition, the minimum occupant load requirement is 9.3 m2 per person.

extrapolation from the values for the 100% and 75% flow rate conditions. In addition, the air flow rate was specified at 2000 m3 h1. The thermal load of each zone was strongly dependent on the OA temperature, occupancy density, heating load from the lighting and equipment, set point SA-mass flow rate (msp,SA) in the DOAS, and set point air temperature (Tsp) in the VRF system. The operation schedules of the occupancy, lighting, and equipment were determined by an on-the-spot survey by the previous study [18] in the same building. In addition, the air change rate for building infiltration was assumed to be 0.732 h1, which was estimated based on the volume of the building space and the capacity of the exhaust fans in toilets [19]. Fig. 3 shows the temperature and humidity ratio

of the OA in the design day, and Fig. 4 shows the variation of occupancy density in each zone. msp,SA was estimated to satisfy IAQ, which was represented by CO2 concentration. The CO2 concentration was dependent on the occupancy density and msp,SA. The CO2 concentration of the OA was assumed to be constant with 400 ppm. 3. Development of multi-objective optimal control strategy 3.1. Computational model for multi-objective optimal control The energy performance of the VRF combined system installed in a research office building was simulated using the EnergyPlus

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199

Fig. 4. Variation of occupancy density in each zone.

Fig. 2. Typical floor plan of the case building.

Table 2 Specifications of the VRF system and DOAS. System

Details

VRF system Rated cooling/heating capacity (kW): 58.0/65.2 Rated cooling/heating COP: 4.02/4.20 DOAS Cooling/heating sensible effectiveness at 100% air flow (%): 76/76 Cooling/heating latent effectiveness at 100% air flow (%): 53/54 Cooling/heating sensible effectiveness at 75% air flow (%): 78/79 Cooling/heating latent effectiveness at 75% air flow (%): 55/56 Power consumption (kW): 1.5 Air flow rate (m3 h1): 2000

0.0028

o

Outdoor air temperature ( C)

2

Outdoor air temperature Outdoor air humidity ratio 0

0.0024

-2

0.0020

-4

0.0016

-6

0.0012

0.0008

-8 0

2

4

6

8

10

12

14

16

18

20

22

Outdoor air humidity ratio (kgv/kga)

model [20]. The VRF system was simulated using Raustad's model [21] with the manufacturer's data. The heating performance curves for the VRF system are given in Table 3. The capacity and power consumption of the VRF system are expressed in terms of the

24

Time (h) Fig. 3. Variation of outdoor air temperature and humidity ratio on the test day.

following variables: (1) indoor and outdoor conditions (TIDB and TOWB), (2) the PLR (part-load ratio), (3) the CR (combination ratio), which is defined as the ratio of the total IDU rated capacity to the total ODU rated capacity, and (4) the losses associated with the refrigerant distribution piping. Additional energy consumptions such as defrost operation, oil return operation, and long refrigerant lines [22] were also considered in the simulation. The DOAS containing a plate heat exchanger and a single air duct was simulated using the effectivenesseNTU method [23]. The sensible and latent effectiveness of the plate heat exchanger were determined based on the manufacturer's data. The optimization of the VRF combined system was conducted using GA [6,24] with the EnergyPlus program. The building energy performance data from the EnergyPlus were used as the input for MATLAB [25]. The objective function of the optimization was estimated by MATLAB. The GA generated the population of the candidate solutions for the input variables. The population size of the GA was 200 and the number of generations was determined by twenty times of the number of the control variables. The proper solutions remained, while the other solutions were reset in the next generation by the genetic rules. This procedure was repeated until the final solution was reached. Finally, the optimized input variables were determined in the model-based multi-objective optimization. All calculations for the EnergyPlus model were carried out using the hourly measured weather data [18] for Seoul, Korea from November, 2011 to October, 2012. For the optimization study, the measured weather data in a single winter design day were used, and the EnergyPlus model was initialized using the simulations on previous warm-up days. The EnergyPlus model was validated in a real building by comparing the predicted monthly total energy consumption with the measured data in 2012. The measured energy consumption represents the total energy used in the HVAC (heating, ventilating, and air-conditioning) systems, lighting, and equipment. As shown in Fig. 5, the simulation results were consistent with the measured data with the MBE (mean bias error) of 4.1%, and the coefficient of variation of the RMSE (root mean squared error), Cv of 7.6%. Based on the M&V Guidelines 3.0 [26], the recommended MBE and Cv (RMSE) were ±5% and 15%, respectively. The errors of the EnergyPlus model were within the acceptable range. 3.2. Multi-objective optimal control strategy In this study, two multi-objective control strategies (A and B) were applied in the VRF combined system. The control strategy A

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Table 3 Heating performance curves for the VRF system. ODU Curve input Piping description correction factor X Y Z a b c

Lp e Normalized factor 1.006 1.304E-3 3.699E-6

d

7.000E-9

e f g X min X max Y min Y max

e e e 7.5 225 e e

IDU Capacity Capacity ratio modifier ratio boundary function for low T

EIR EIR modifier EIR modifier EIR modifier EIR modifier Capacity ratio boundary function for function for function for function for modifier high PLR low PLR high T low T function for high T

Combination ratio EIR correction factor

Capacity ratio modifier function for T

TIDB e TOWB

TIDB TOWB Normalized factor 1.170 4.903E-3 2.815E-4

TIDB TOWB Normalized factor 2.044 6.447E-2 7.594E-4

e

e

TIDB TOWB Normalized factor 29.73 2.074 1.817 0.1105 3.280E- 1.997E-3 2 1.713E-3 e

2.504E-2 3.888E-7 2.834E-4 16 24 20 2.2

5.335E-5 9.665E-7 2.138E-6 16 24 10 13.7

e e e 16 24 e e

259.5 35.04 1.573 2.428E2 e e e 16 24 e e

TIDB e TOWB

1.828E-2 8.816E-4 2.863E-3 16 24 20 0.7

TIDB TOWB Normalized factor 0.8193 1.623E-3 6.109E-4

PLR e Normalized factor 0.5309 1.144 2.532

PLR e Normalized factor 1.221E3 3.304E3 2.969E3

CR e Normalized factor 9.115 23.16 17.46

TIDB TOWB Normalized factor 0.9646 1.029E-2 6.118E-4

e

0.9199

8.856E2

4.417

e

3.616E-2 5.779E-4 2.152E-3 16 24 7.6 13.7

e e e 0.5565 1 e e

e e e 1 1.201 e e

e e e 1 1.4 e e

5.335E-5 9.665E-7 2.138E-6 16 24 20 13.7

Note: Z ¼ a þ bX þ cX2 þ dX3(for cubic curves); Z ¼ a þ bX þ cX2 þ eY þ fY2 þ gXY (for bi-quadratic curves).

included two control variables: set point SA-mass flow rate (msp,SA) and set point relative humidity at the humidifier outlet (RHsp,SA). In control strategy A, the set point air temperature (Tsp) was fixed at 20  C. In addition to the control variables included in control strategy A, Tsp was added in control strategy B as a control variable in the high humidity zone to overcome humidity imbalance. In control strategy B, Zones 1, 3, and 6, which had high occupancy density, were selected as the high humidity zone. The control strategy B adopted a dual mode control; Tsp was fixed at 20  C except for the high humidity zone, but Tsp,high (Tsp for the high humidity zone) was optimized in the range of 20  Ce24  C. As the zone air temperature increases, more water vapor needs to be added to the zones due to the decreased RH (relative humidity), reducing the humidity imbalance between the zones. THC and IAQ are significantly influenced by the control variables such as msp,SA, RHsp,SA, and Tsp. THC and IAQ can be enhanced by

increasing msp,SA, RHsp,SA, and Tsp, but the total energy consumption is also substantially increased. Therefore, it is necessary to control THC and IAQ simultaneously using the multi-objective optimal control strategy, while minimizing the total energy consumption. THC can be expressed by the PMV (predicted mean vote) [27,28] and RH. The common ranges of winter comfort zone are 0.5  PMV  0.5 and 30%  RH  60% [27,29,30]. In this study, the lower limit of PMV was extended to 1.0 in order to reduce the total energy consumption according to Korean design standards [31], which yielded the extended winter comfort zone. In addition, an 8-hour average CO2 concentration must be lower than 1000 ppm [32,33] to satisfy IAQ. Finally, the objective functions of the THC, IAQ, and total energy consumption are expressed by Eqs. (1)e(3), respectively.

ObjTHC ¼ 300

i¼1

Measured Predicted Energy consumption (GJ)

7 1X Maxð0; PMVi  0:5Þ þ Maxð0;  1:0  PMVi Þ 7 ð0:5  ð  1:0ÞÞ

Cv(RMSE) = 7.6%

þ

MBE = -4.1%

7 1X Maxð0; RHi  60Þ þ Maxð0; 30  RHi Þ 7 ð60  30Þ i¼1

(1) 200

ObjIAQ ¼

(2)

i¼1

100

ObjE ¼ 0

11 Dec. 012 Feb. Mar. Apr. May Jun. 20 2 v., n., o Ja N Month

7 1X Maxð0; Ci  1000Þ þ Maxð0; 400  Ci Þ 7 ð1000  400Þ

. l. Ju Aug

Fig. 5. Comparison between the measured and the predicted monthly energy consumption.

X

EDOAS þEHumidifier þEVRF þElight þEequipment



(3)

The total objective function was derived in terms of the THC, IAQ, and total energy consumption to determine the optimal control strategy. As given in Eq. (4), the multi-objective functions were transformed into the total objective function by combining the weighting factors with each objective function [34e36]. The optimal control variables were determined by minimizing ObjTotal, as given in Eq. (5).

W. Kim et al. / Energy 107 (2016) 196e204

ObjTotal ¼ wfTHC $

  ObjTHC  ObjTHC;min

4. Simulation results and discussion

 ObjTHC;max  ObjTHC;min   ObjIAQ  ObjIAQ ;min  þ wfIAQ $ ObjIAQ ;max  ObjIAQ ;min   ObjE  ObjE;min  þ wfE $ ObjE;max  ObjE;min

MinðObjtotal Þ 0 kg s1  m_ SA  1:77 kg s1 30%  RHSA  80% 20 C  Tsp  24 Cðonly for control strategy BÞ

(4)

(5)

In Eq. (5), the upper limit of msp,SA was determined by the peak ventilation load, and the maximum RHsp,SA was determined to avoid water condensation and mold growth [37]. 3.3. Optimal weighting factors with response surface methodology Since the objective functions were significantly influenced by the weighting factors, the optimal weighting factors for the control strategies A and B were determined by the RSM. The relationships between the weighting factors and objective functions were analyzed using the Box-Behnken design method. As shown in Table 4, a total 13 runs were performed. As a result, the second-order response surface model for each objective function is expressed by Eq. (6). The coefficients in Eq. (6) are given in Table 5. The coefficients of determination (R2) for ObjTHC, ObjIAQ, ObjE, and ObjTotal were found to be 0.96, 0.92, 0.97, and 0.86 for the control strategy A, and 0.94, 0.89, 0.95, and 0.99 for the control strategy B, respectively. Finally, the optimal weighting factors for the THC, IAQ, and total energy consumption were determined as 0.71, 0.64, and 1.00 for the control strategy A, and 0.57, 0.69, and 0.72 for the control strategy B, respectively. 2 2 Y ¼ b0 þ b1 wfTHC þ b2 wfIAQ þ b3 wfE þ b11 wfTHC þ b22 wfIAQ

þ b33 wfE2 þ b12 wfTHC wfIAQ þ b13 wfTHC wfE þ b23 wfIAQ wfE (6)

Table 4 Weighting factors assignment using the BoxeBehnken design method. Case wfTHC, weighting assigned to THC

wfIAQ, weighting assigned to IAQ

wfE, weighting assigned to energy

1 2 3 4 5 6 7 8 9 10 11 12 13

0.0 0.5 0.0 0.0 1.0 1.0 0.5 0.5 0.5 1.0 0.0 1.0 0.5

0.0 0.0 0.5 0.5 0.5 0.5 0.0 1.0 1.0 0.0 1.0 1.0 0.5

0.5 0.0 0.0 1.0 0.0 1.0 1.0 0.0 1.0 0.5 0.5 0.5 0.5

201

The performances of the VRF combined system, applying optimal control strategies A and B with the optimal weighting factors were compared with those using the TS (time schedule) strategy and the DCVH (demand controlled ventilation with humidifying) strategy in the case building. The TS strategy operates the DOAS four times a day with a constant msp,SA without having an additional humidifier. In the DCVH strategy, msp,SA was determined by considering the occupancy and floor area, and RHsp,SA was controlled so that the RHs in all zones did not fall below 30%. msp,SA was evaluated by the summation of each zonal ventilation rate. The zonal ventilation rate was determined to be a higher value between the estimated values based on the occupancy density and the floor area [38]. In optimal control strategies A and B, msp,SA and RHsp,SA were optimized by applying the multi-objective functions of the THC, IAQ, and total energy consumption. In addition, in optimal control strategy B, Tsp,high was also optimized to minimize humidity imbalance. Fig. 6 shows the variations of the control variables for the four control strategies. msp,SA varied periodically in the TS strategy and DCVH strategy, while it was optimized for each time step in optimal control strategies A and B. In optimal strategies A and B, the control variables experienced large oscillations between consecutive time steps because they were controlled for daily optimization considering the time-lag effect by thermal inertia [25]. The average msp,SA in the TS strategy, DCVH strategy, optimal control strategy A, and optimal control strategy B were 0.65 kg s1, 1.39 kg s1, 0.98 kg s1, and 1.06 kg s1, respectively. As shown in Table 6, the energy consumption in the DOAS (EDOAS) significantly increased with increasing the average msp,SA. The average msp,SA was the highest in the DCVH strategy because IAQ needs to be satisfied in each zone for all times. RHsp,SA was optimized for each time step in the DCVH strategy, and optimal control strategies A and B. However, RHsp,SA was 0% in the TS strategy because the TS strategy did not have an additional humidifier. The average RHsp,SA in the DCVH strategy, optimal control strategy A, and optimal control strategy B were 59.5%, 51.8%, and 50.8%, respectively. As shown in Table 6, the DCVH strategy showed the highest energy consumption in the humidifier (EHumidifier) due to the high msp,SA and RHsp,SA. Optimal control strategy B showed higher EHumidifier than optimal control strategy A due to the elevated Tsp in the high humidity zone, even though these strategies had comparable msp,SA and RHsp,SA. In addition, the energy consumption in the VRF (EVRF) for optimal control strategies A and B was lower than that for the TS strategy and DCVH strategy due to the optimized control. Fig. 7 presents the indoor thermal conditions for the four strategies in the psychrometric chart. The ratios of the hours satisfying the extended winter comfort zone (1.0  PMV  0.5 and 30%  RH  60%) [27,30,31] over the total occupied hours were 5.6%, 35.9%, 47.9%, and 55.0% for the TS, DCVH, optimal control strategy A, and optimal control strategy B, respectively. The TS strategy represented the lowest hour ratio satisfying the extended winter comfort zone with very lower RH because it did not include the extra humidifier. Optimal control strategy B showed the highest hour ratio satisfying the extended winter comfort zone. Optimal control strategy B reduced the humidity imbalance between zones because it showed a higher air temperature than the other strategies. Generally, the inflow of water vapor increases with the increase in the air temperature. In addition, the DCVH strategy showed an over-humidification problem because it humidified the SA until the RHs in all zones exceeded 30%. Table 7 shows the environmental performance and objective function for the four control strategies. In the TS strategy, the daily means of PMV and RH were very low at 1.38% and 20.7%,

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Table 5 Coefficients of the second-order response surface model. Coefficient

b0 b1 b2 b3 b11 b22 b33 b12 b13 b23

Strategy A

Strategy B

ObjTHC

ObjIAQ

ObjE

ObjTotal

ObjTHC

ObjIAQ

ObjE

ObjTotal

1.16 0.28 0.09 0.22 0.10 0.03 0.05 0.13 0.05 0.09

0.07 0.09 0.21 0.14 0.04 0.15 0.02 0.09 0.04 0.13

1,472,926 264,477 6846 389,010 32,450 21,162 112,581 123,663 6789 175,731

0.05 0.31 0.26 0.99 0.25 0.25 0.74 0.74 0.44 0.08

0.94 0.36 0.29 0.27 0.13 0.24 0.01 0.11 0.06 0.08

0.08 0.02 0.25 0.06 0.04 0.18 0.06 0.08 0.01 0.14

1,604,301 311,675 289,049 428,187 69,211 248,840 113,706 82,715 9088 134,198

0.17 0.46 0.43 0.55 0.34 0.24 0.30 0.16 0.60 0.12

Fig. 6. Variations of control variables in the TS strategy, DCVH strategy, optimal control strategy A, and optimal control strategy B: (a) set point SA-mass flow rate and (b) set point RH.

respectively. ObjTHC and ObjIAQ were relatively high at 1.72 and 0.27, respectively, which indicates large deviation from the extended winter comfort zone with poor IAQ. In the DCVH strategy, the daily mean PMV and RH were improved from the TS strategy, which led to better satisfaction for the THC and IAQ with ObjTHC, and ObjIAQ of 1.26 and 0, respectively. However, the DCVH strategy showed the largest standard deviation of RH, which indicates severe humidity imbalance between zones. Optimal control strategies A and B showed better daily mean PMVs of 1.06 and 0.83, respectively, compared with the TS and DCVH strategies. Optimal control strategy B showed the lowest ObjTHC of 0.9 with a very low ObjIAQ of 0.004. However, optimal control strategy B showed higher total energy consumption than the TS strategy and optimal control strategy A due to the elevated set point air temperature. The DCVH strategy showed the highest total energy consumption due to the over-humidification and strict regulation for IAQ. The energy savings of optimal control strategies A and B against the DCVH strategy were 29.0% and 20.4%, respectively. Overall, optimal control strategy B can be recommended as the best control strategy in the VRF combined system because it yielded satisfactory THC and IAQ with reasonable energy savings compared to the DCVH strategy. Fig. 8 shows the variation of the CO2 concentration in Zone 3 for the four strategies. Zone 3 was selected as an extreme IAQ condition because it had the lowest IAQ with the highest occupancy density. The variation of the CO2 concentration between zones was due to the use of a central DOAS for ventilation in a multi-zone having different occupancy densities. The 8-hour average CO2 concentrations for Zone 3 with the TS strategy, DCVH strategy, optimal control strategy A, and optimal control strategy B were 1704, 964, 1032, and 998 ppm, respectively. Therefore, the TS strategy and optimal control strategy A did not satisfy the IAQ guideline [32,33] in Zone 3 in terms of the 8-hour average CO2 concentration. The TS strategy showed very high CO2 concentration, but it represented lower CO2 concentration below 1000 ppm during DOAS operations (9:00 AM, 13:00, 17:00, and 21:00 PM). The CO2 concentration for the DCVH strategy was always controlled below 1000 ppm because msp,SA was adjusted only for IAQ. Optimal control strategy B showed a slightly higher CO2 concentration than the DCVH strategy, because msp,SA was controlled for the multi-objective functions. In optimal control strategy B, as the occupancy density increased rapidly (9:00 AM and 19:00 PM) and the OA humidity decreased sharply (15:30 PM),

Table 6 Energy components for the four control strategies. Energy components

TS strategy

DCVH strategy

Optimal strategy A

Optimal strategy B

EDOAS (MJ) EHumidifier (MJ) EVRF (MJ)

28 e 1039

101 513 973

52 298 637

53 323 770

W. Kim et al. / Energy 107 (2016) 196e204

203

CO2 concentration (ppm)

3000 TS strategy DCVH strategy Optimal strategy A Optimal strategy B

2500

2000

1500

1000

500 0

2

4

6

8

10

12

14

16

18

20

22

24

Time (h) Fig. 8. Variation of CO2 concentration in Zone 3 for the four control strategies.

consumption increased when THC was focused as a major objective function. On the contrary, THC decreased when the energy consumption was considered as a major objective function. In addition, the effects of wfIAQ on ObjTHC and ObjE were relatively smaller than those of the other weighting factors. However, ObjIAQ rapidly decreased with increasing wfIAQ. The sensitivities of the weighting factors on the objective functions can be utilized for the optimal control of the VRF combined system.

5. Conclusions

Fig. 7. Indoor thermal conditions for (a) the TS strategy and DCVH strategy, and (b) optimal control strategies A and B.

the CO2 concentration peaked due to the decrease in msp,SA to prevent a rapid increase in the total energy consumption. Even though optimal control strategy B showed higher CO2 concentration than the DCVH strategy, it yielded lower total energy consumption with satisfactory IAQ by controlling msp,SA for the multiobjective functions. Fig. 9 shows the effects of the weighting factors on the objective functions predicted by the RSM model in optimal control strategy B. When one weighting factor was changed, the others were fixed at their optimum values. ObjTHC almost linearly decreased with wfTHC, while it increased with wfE. However, ObjE almost linearly increased with wfTHC, while it decreased with wfE. The energy

A model-based multi-objective optimal control strategy was proposed in a VRF combined system adopting a DOAS in order to satisfy THC and IAQ in the conditioned multi-zone while minimizing the total energy consumption for a single winter design day. The performance of the VRF combined system was simulated using the EnergyPlus model. The VRF combined system was optimized by the GA in terms of the THC, IAQ, and total energy consumption, and the optimal weighting factors were determined by the RSM. The multi-objective optimal control strategies A and B were compared with the TS strategy and DCVH strategy. The TS strategy showed poor THC and IAQ. The DCVH strategy represented improved THC and high IAQ, but showed an over-humidification problem and excessive energy consumption. Optimal control strategies A and B reduced the total energy consumption by 29.0% and 20.4%, respectively, and increased the ratio of the hours satisfying the extended comfort zone by 12.0% and 19.1%, respectively, compared to the DCVH strategy. Optimal control strategy B can be recommended as the best control strategy because it yielded satisfactory THC and IAQ with substantial energy savings compared to the

Table 7 Environmental performance and objective functions for the four control strategies. Environmental performance and objective function Environmental performance Daily mean of PMV Daily mean of RH (%) Standard deviation of RH (%) Ratio of the winter comfort zone over the total occupied hour (%) Objective function THC IAQ Energy consumption (MJ)

TS strategy

DCVH strategy

Optimal strategy A

1.38 20.7 4.9 5.6

1.26 43.1 9.5 35.9

1.06 33.0 8.5 47.9

1.72 0.27 1371

1.26 0 1801

1.13 0.01 1279

Optimal strategy B 0.83 33.0 7.4 55.0 0.90 0.004 1433

204

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Fig. 9. Effects of weighting factors on objective functions.

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