Optimal configuration of multiple-chiller plants under cooling load uncertainty for different climate effects and building types

Accepted Manuscript Title: Optimal configuration of multiple-chiller plants under cooling load uncertainty for different climate effects and building types Authors: Pei Huang, Gongsheng Huang, Godfried Augenbroe PII: DOI: Reference:

S0378-7788(17)31501-3 https://doi.org/10.1016/j.enbuild.2017.10.040 ENB 8060

To appear in:

ENB

Received date: Revised date: Accepted date:

25-4-2017 11-10-2017 11-10-2017

Please cite this article as: Pei Huang, Gongsheng Huang, Godfried Augenbroe, Optimal configuration of multiple-chiller plants under cooling load uncertainty for different climate effects and building types, Energy and Buildings https://doi.org/10.1016/j.enbuild.2017.10.040 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Optimal configuration of multiple-chiller plants under cooling load uncertainty for different climate effects and building types Pei HUANG1, Gongsheng HUANG1,*, Godfried AUGENBROE2 1

Department of Architecture and Civil Engineering, City University of Hong Kong, Kowloon, Hong Kong

2

College of Architecture, Georgia Institute of Technology, Atlanta, USA

*

Corresponding author. Tel.: 852-34422408; fax: 852-34420427

E-mail: [email protected]

Graphical abstract

1

Highlights

    

A multiple-chiller system optimal configuration method under uncertainty is proposed. The method is based on uncertainty analysis and life-cycle cost analysis. The uncertainty in the cooling load and chiller COP is integrated into the design. Uncertain load distributions of different buildings and weathers are investigated. The optimal designs under different load conditions are analyzed and summarized.

Abstract: Configuring the number and size of chillers in a multiple-chiller plant properly is an efficient way to improve the plant energy efficiency. At the design stage, the optimal configuration can be achieved through matching the capacity to load as closely as possible across the full-load profile. However, in spite of the fact that current literature offers practical recommendations, a systematic method to optimize the configuration of multiple-chiller plants is lacking. Due to the lack of accurate information at the design stage and only limited knowledge of the eventual realization it is hard to predict the building’s cooling load. Moreover, there is no operational data to predict the system performance. Both explain the existence of uncertainty in the HVAC plant design process. This paper, therefore, proposes a strategy to optimize the configuration of multiple-chiller plants, which takes account of the load side uncertainty as well as the COP uncertainty and selects the optimal configuration through a life-cycle analysis. Both the load side uncertainty and the COP uncertainty are quantified using statistical distributions. To facilitate applications, the distributions of the cooling load profile of different types of buildings under different weather conditions are investigated and are classified into four categories, and the optimal configuration schemes under each type of cooling load distribution are analyzed and summarized in a tabulated form. Keywords: HVAC system, multiple-chiller plant, optimal configuration, uncertainty, cooling load

2

1. Introduction In modern buildings, heating, ventilation and air-conditioning (HVAC) systems have been widely installed to provide indoor thermal comfort and acceptable indoor air quality. As reported in many studies, buildings consume over 40% of end-use energy worldwide [1]. In hot or cold climates, HVAC systems in large commercial buildings always represent the largest primary energy end-use. There are many methods that can reduce the energy consumption of HVAC systems, and one of these methods is to design the HVAC system properly at the early design stage [2]. In the previous work, the authors have proposed an HVAC system sizing strategy, which can optimally siLze the capacity of the HVAC system under uncertainty by taking account of designers’/customers’ preferences so as to improve the energy efficiency [3,4]. Another efficient way to save energy is to properly configure the multiple-chiller plants of HVAC systems. For instance, as reported by Gang, the difference in the energy consumption across HVAC systems with different configurations of the multiple-chiller plant (number and size) can be as large as 69% [5]. In current practice, configuration schemes are available [6,7], and in most cases equallysized-chiller plants are recommended. As reported by Lee and Lee, 44 out of 50 HVAC systems install equally-sized-chiller plants for providing cooling in Hong Kong [8]. However, equallysized-chiller system may not operate at a high efficiency because the capacity of the chillers cannot always match the cooling load profile to achieve high partial load ratios. Therefore, ARI Standard 550/590 emphasizes that a comprehensive analysis (which reflects the actual weather data, building load characteristics, operational hours and energy consumed by auxiliaries such as pumps and cooling towers) should be conducted to predict the performance when configuring a multiple-chiller plant [9]. Several studies have proposed to configure multiple-chiller plants according to the cooling-load frequency of the building, aiming to achieve an operating 3

efficiency that is as high as possible during the plant’s operating time [8,10,11]. For instance, Deng studied the load frequency of a hotel building, and proposed to configure the capacity ratios of chillers based on a frequency analysis [11]. Lee and Lee conducted a survey about the existing multiple-chiller systems in Hong Kong and proposed configuring the multiple-chillers based on load frequency analysis using a simplified energy prediction model [8]. Even though the current practice provides recommendation of configuration ratios and some design methods propose applying the load frequency analysis, a systematic method (a complete methodology contains details about how to implement the analysis) of optimally configuring the multiplechiller system is still lacking. In recent years, the importance of the uncertainties in the HVAC design stage has been gradually recognized and there is a trend that HVAC system design should be done in a stochastic framework instead of the conventionally deterministic framework [3-5, 12-16]. For example, Gang et al. proposed selecting the optimal multiple-chiller configuration from several alternatives through using “maximum regrets” as optimality criterion which is calculated under different uncertain factors [13]. Gang’s work aimed to improve the HVAC system sizing part of the design process with a method that can properly configure multiple-chiller plants. However, this study did not really handle the uncertainties in the cooling load prediction or in the HVAC system operation, which is caused by the limited understanding of the model parameters and simplifications used to represent the system operation. Instead, several ‘uncertain’ factors were used to represent the upper limit and lower limit of the cooling load. Notably, Cheng et al. proposed an HVAC system optimal design method under peak load uncertainty [12], which sizes the capacity of the HVAC system based on the uncertainty in the peak load distribution and configures the multiple-chiller plant by maximizing the operational coefficient of performance (COP) and minimizing the annual capital cost. However, Cheng et al. only considered 4

uncertainty in the system sizing, but neglects it when configuring the multiple-chiller plant. Essentially, the energy performance of multiple–chiller plants is determined by their COPs and the partial load profile [17,18]. Neglecting the uncertainties in the chiller COP and the cooling load profile may result in incomplete understanding of the performance of the system, and may further lead to improper decisions. Based on the facts that (1) the current practice only provides recommendations on chiller configuration ratios, but offers no systematic methods of optimally configuring the multiplechiller plants, (2) and the current design neglects the uncertainties in load prediction and system performance prediction, and offers no transparency relating to the risk of designed system meeting the required level of performance, this paper therefore tries to fill in these gaps by proposing a method to optimally configure the multiple-chiller plant based on Cheng et al.’s work [12], which will take account of the load side and COP uncertainty, and select the optimal configuration through a life-cycle cost analysis. The objective is to provide designers with a systematic way to optimize the configuration of multiple-chiller plants considering the unknown factors, so as to achieve a better understanding of the system performance, to enhance the energy efficiency and to reduce the life-cycle cost. It should be noted that the capacity of the HVAC system should be sized before configuring the multiple chillers. As the optimal sizing of the HVAC system capacity has been studied in the authors’ previous work [3,4], this study will only focus on the optimal configuration of multiple chillers. Besides the uncertainty, the variability across the building types/weather conditions are two other major factors that affect the optimal multiple-chiller plant configuration, as the building type/ weather condition (in principle) determines building peak cooling load and hourly cooling load [19-21]. The variability across building types/weather conditions is not uncertainty (which exists in the prediction of the loads for an individual building due to unknown factors), as the 5

building type/weather condition are already known before designing a HVAC system. In order to investigate the impact of variability on the optimal chiller configuration, this study will examine the loads distributions of different types of buildings under different weather conditions and investigate the optimal design in each case. This paper is organized as follows: Section 2 will introduce the proposed optimal configuration method. Section 3 will apply the configuration method to a case building. Section 4 will further apply the proposed method under different types of cooling load profile. Conclusions will be given in Section 5.

2. Methodology The process of optimizing the configuration of multiple-chiller plants is shown in Figure 1. It consists of three stages: uncertainty analysis of the cooling load, optimization of the chiller configuration, and posterior analysis. Details about the work at each stage are explained below.

Fig. 1. Process of optimal configuration of multiple-chiller systems under cooling load uncertainty for different building types and climate effects

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Uncertainty analysis of cooling load: At this stage, an uncertainty analysis will be conducted for both the peak cooling load and the hourly cooling loads. The uncertainties in the building input parameters will be quantified using different distributions (normal distribution, uniform distribution, triangular distribution, etc.) as appropriate following existing literature. Then these quantified uncertainties will be propagated through the building energy model. The estimated peak cooling load distribution will be used to determine the size of the whole HVAC system (i.e. the sum of the capacity of multiple chillers) [3,4], and the hourly cooling load distribution will be used to determine the configuration ratios of multiple chillers. How to size HVAC system optimally considering peak load uncertainty has been investigated in our previous work [3,4], this study only consider how to configure multiple-chiller plants. Optimization of chiller configuration: At this stage, a set of multiple-chiller configuration alternatives is proposed. The total number of chillers and the size of each chiller are considered in the configuration optimization. Configuration alternatives and estimated hourly loads with previous quantified uncertainties are imported into the chiller performance prediction model. Several performance indices, such as annual energy consumption, chiller switch on/off time, initial cost and maintenance cost, are evaluated. Since the load side and chiller COP uncertainty are considered, the resulting predicted performance will also be in a stochastic form. Finally, a life-cycle cost analysis is conducted to select the optimal configuration from all considered alternatives. Posterior analysis: At this stage, a recommended multiple-chiller configuration scheme, including the number of chillers, the configuration ratios of each chiller and the type of chiller, is summarized for the given building. Meanwhile, the predicted performance of the designed multiple-chiller plants, such as the energy consumption, the switching on/off times, the initial cost and the maintenance cost, etc. is organized and presented. 7

2.1 Uncertainty analysis of cooling load 2.1.1 Uncertainty quantification The uncertainties associated with the cooling load prediction have been investigated by many researchers. For example, ASHRAE Handbook [19] and Domínguez-Muñoz et al. tabulated the uncertainty descriptions for physical parameters (such as thermal property of building materials) through analyzing field data [22]. Macdonald and Hopfe quantified the uncertainties in scenario parameters, which are relative to the real-time operation of buildings, including ventilation rate and heat dissipation rate of occupants, facilities and light, and through human operated natural ventilation [23,24]. Wang investigated the uncertainties in occupancy variables, such as presence and control actions, and analysed the influence of these uncertainties on building energy consumption [25]. Notably, Wang studied the model form uncertainties of the HVAC system model through comparing the outputs from a higher fidelity module with a sub-model which is based on a low fidelity description of the governing physics [25]. In this study the uncertainties for estimating the cooling load are classified into three types following Hopfe’s and Wang’s work [3,25], namely uncertainty in the physical parameters, uncertainty in the scenario parameters and model form uncertainties. Table 1 lists the classification of these three types of uncertainties. All these potential uncertainties are qualified to follow a normal distribution, triangular distribution or uniform distribution as deemed appropriate and based on previous work. For simplicity, the model form uncertainties are not considered in this study. The results from EnergyPlus simulations are assumed to represent the physical reality well. Table 1 Classification of uncertain input parameters for estimating cooling load Types

Description

8

Refer to physical properties of materials, and they are mostly identifiable Definition Uncertainty

in

physical

as the standard input parameters in simulation and not influenced by designers. Thickness, density, thermal conductivity and heat capacity of walls,

Examples roofs and windows, etc.

parameters Sources

[19,22]

Distributions

Normal; Refer to parameters that are relative to the real-time operation of the

Definition

building during its life time. They are not measurable and hard to control.

Uncertainty

in

scenario

Weather condition, such as ambient temperature and relative humidity, solar radiation; casual heat gain, such as the number of occupants, Examples computers and light in use; Internal and external shading coefficients;

parameters

Internal and external convection transfer rate; Infiltration etc. Sources

[23-26]

Distributions

Normal; Triangular; Refer to the discrepancy between the empirical data from physical experiments or outputs from a higher fidelity module and the module

Definition Model

form

output which is based on a low fidelity description of the governing physics. Model form uncertainties exist since no model is a perfect

uncertainties representation of the physical reality. Sources

[25]

Distributions

Normal;

9

2.1.2 Cooling load uncertainty propagation The process of propagating the cooling load uncertainty is shown in Figure 2, which consists of three stages: pre-processing, processing and post-processing.

Fig. 2. Process of uncertainty analysis The first phase is to generate a large number of samples, each consisting of an EnergyPlus input file (IDF files) and a weather file (EPWs). Each sample is used in an EnergyPlus simulation that calculates the cooling load for that sample. The samples are generated from the uncertainties in input parameters, and each input file (sample) represents one combination of all the uncertain inputs. The procedures are illustrated as follows: firstly, a base EnergyPlus input file is generated based on the base-case scenario. Secondly, N random samples are generated from the assigned uncertainty distributions for each input parameter (there are k uncertain parameters in total). All input parameter values form an N × k input matrix. Thirdly, the corresponding parameter values in the BASE.IDF are replaced with the values in the input matrix row by row, and the replacement repeats N times which will produce N samples, i.e. N input IDF files [4,27]. In the second phase, EnergyPlus is run for all samples generated in the first phase, thus conducting a routine Monte Carlo simulation, resulting in an output for every sample which can 10

be combined in the distribution of the selected outcomes [3,4]. In order to reduce the number of simulation required (N), instead of brute force exhaustive sampling, the Latin Hypercube Sampling (LHS) method is used for generating random samples [28]. In the third phase, the cooling load data generated by the EnergyPlus simulation are extracted from the sample output files. The mean, standard deviation, distribution of the peak load distribution and the hourly load distribution are estimated using well known statistical techniques. The peak load distribution is subsequently used for determining the size of the whole HVAC system. Details about the sizing strategy can be found in literature [3,4]. A histogram is also drawn for hourly cooling loads to investigate its distribution. The uncertain hourly load will be used for estimating the HVAC system performance. In this study, the uncertainty analysis for the peak cooling load and the hourly cooling load is conducted using the Georgia Tech Uncertainty and Risk Analysis Workbench (GURA-W). It is a simulation tool developed by Georgia Institute of Technology for uncertainty analysis [29].

2.2 Optimization of the chiller configuration 2.2.1 Introduction to chiller COP The chiller nominal COP is affected by the chiller type and the chiller size [6,12,18,30]. Constant-speed-driven (CSD) chillers achieve a high COP when they operate at a high Partial Load Ratio (PLR). The PLR-COP curves reach peak approximately when PLR is larger than 0.8. Figure 3 shows the schematic diagram of PLR-COP curves for a CSD chiller. The size of a chiller is another major factor affecting chiller COP [6,31]. For instance, as required by ANSI/ASHRAE/IESNA [31], the nominal COP of centrifugal compressor, watercooled and electric-driven chillers with a capacity smaller than 150 ton (528 kW) should be larger than 5, with a capacity between 150 ton (528 kW) and 300 ton (1055 kW) should be larger 11

than 5.55, or with a capacity larger than 300 ton should be larger than 6.1. Therefore, when designing a multiple-chiller plant, the influence of individual chiller capacity on chiller COP should be considered. COP Peak COP CSD chiller

Lower Optimal Pct. Load

Upper Optimal Max Pct. Pct. Load Load

Reference: Johnson control 2015 [18]

Fig. 3. Schematic diagram of PLR-COP curve for a CSD chiller Table 2 summarized the minimum required COP at full load for chillers of different sizes and using different types of compressors. In this study, the configuration of water-cooled centrifugal chillers is studied. Table 2 Minimum COP requirementsa at full load for different types of chillers Capacity range Type of compressor

Minimum COP Reference 1 ton = 3.52 kW < 115 tons

2.8

≥ 115 tons

2.9

< 115 tons

2.8

≥ 115 tons

2.9

< 145 tons

2.9

≥ 145 tons

3.0

Reciprocating

AirScroll cooled

[32]

Screw

12

Centrifugal

All capacities

3.2

< 150 tons

4.2

≥150 and <300 tons

4.7

≥300 tons

5.3

< 150 tons

4.8

≥150 and <300 tons

5.0

≥300 tons

5.5

< 150 tons

5.00

≥150 and <300 tons

5.55

≥300 tons

6.10

Air-cooled Absorption single effect

All capacities

0.60

Water-cooled Absorption single effect

All capacities

0.70

Reciprocating/Scroll

[32,33] WaterScrew cooled

Centrifugal

Others

a

[33]

[34] Absorption double effect, Indirect-fired

All capacities

1.00

Absorption double effect, Direct-fired

All capacities

1.00

: Refer to the reference for the testing condition.

2.2.2 Configuration of chiller alternatives There is no engineering rule showing that all chillers must be equally sized. Even though symmetrical chiller capacity can bring some maintenance advantages due to the common parts, asymmetrical chiller configurations are more energy efficient under a general circumstance [7]. In this study, both symmetrical chiller capacity and asymmetrical chiller capacity are considered. Table 3 lists the configuration alternatives for a multiple-chiller plant. The capacity of each chiller is determined according to the capacity of the whole HVAC system (which is determined using the peak load distribution, as introduced in Section 2.1) and its sizing ratio. To generalize

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the research outcomes, these sizing ratios are selected based on an interval of 0.1 for asymmetrical cases. In total, there are 5 cases for 2-chiller system, 9 cases for 3-chiller system, 10 cases for 4-chiller system and 7 cases for 5-chiller system. The optimal configuration scheme will be determined from among these alternatives. Table 3 Sizing ratio alternatives of chiller configuration

2

Cases

1

2

3

4

5

Chiller 1

0.1

0.2

0.3

0.4

0.5

Chiller 2

0.9

0.8

0.7

0.6

0.5

Cases

6

7

8

9

10

11

12

13

14

chillers Chiller 1

0.1

0.1

0.1

0.1

0.2

0.2

0.2

0.3

0.33

Chiller 2

0.1

0.2

0.3

0.4

0.2

0.3

0.4

0.3

0.33

Chiller 3

0.8

0.7

0.6

0.5

0.6

0.5

0.4

0.4

0.33

Cases

15

16

17

18

19

20

21

22

23

24

Chiller 1

0.1

0.1

0.1

0.1

0.1

0.1

0.1

0.2

0.2

0.25

Chiller 2

0.1

0.1

0.1

0.1

0.2

0.2

0.3

0.2

0.2

0.25

Chiller 3

0.1

0.2

0.3

0.4

0.2

0.3

0.3

0.2

0.3

0.25

Chiller 4

0.7

0.6

0.5

0.4

0.5

0.4

0.3

0.4

0.3

0.25

Cases

25

26

27

28

29

30

31

Chiller 1

0.1

0.1

0.1

0.1

0.1

0.1

0.2

chillers Chiller 2

0.1

0.1

0.1

0.1

0.1

0.2

0.2

Chiller 3

0.1

0.1

0.1

0.2

0.2

0.2

0.2

Chiller 4

0.1

0.2

0.3

0.2

0.3

0.2

0.2

Chiller 5

0.6

0.5

0.4

0.4

0.3

0.3

0.2

chillers

(5 cases)

3 (9 cases)

4

chillers

(10 cases)

5 (7 cases)

14

This study considers the configuration of CSD chillers. Figure 4 presents the schematic diagrams of a typical multiple-CSD-chiller plant. It has two chilled water loops: a primary loop with constant speed pumps and a secondary loop with variable speed pumps [12].

Chiller 1

By-pass

Secondary VSD pumps

…

Chiller 2 Chiller N

Air Handling Units

Primary CSD pumps

Fig. 4. Schematic diagram of a typical multiple-CSD-chiller system

2.2.3 Performance evaluation Energy consumption prediction In this study, the energy consumption of the ith chiller in the jth hour is predicted based on the PLR-COP curve [12,35]. 𝐶𝑂𝑃𝑖,𝑗 = 𝑓(𝑃𝐿𝑅𝑖,𝑗 )

(1)

where 𝐶𝑂𝑃𝑖,𝑗 is the COP of the ith chiller in the jth hour, 𝑓(∙) is the function to calculate COP from PLR which can be fitted using the operational data of existing chillers, and 𝑃𝐿𝑅𝑖,𝑗 is the partial load ratio of the ith chiller in the jth hour, which is calculated by 𝐶𝐿𝑗

𝑃𝐿𝑅𝑖,𝑗 = 𝐶𝐴𝑃

(2)

𝑠𝑢𝑚,𝑗

where 𝐶𝐿𝑗 (kW) is the cooling load required by all the conditioning zones in the jth hour, and 𝐶𝐴𝑃𝑠𝑢𝑚,𝑗 (kW) is the available cooling capacity that can be supplied by all the operating chillers in the jth hour (i.e. the sum of the cooling capacity of each operating chiller). 15

The energy consumption of the ith chiller in the jth hour (𝐸𝑖,𝑗 (𝑘𝑊 ∙ ℎ)) is calculated by 𝐸𝑖,𝑗 =

𝐶𝐴𝑃𝑠𝑢𝑝𝑝𝑙𝑦,𝑖,𝑗

(3)

𝐶𝑂𝑃𝑖,𝑗

where 𝐶𝐴𝑃𝑠𝑢𝑝𝑝𝑙𝑦,𝑖,𝑗 (kW) is the cooling capacity supplied by the ith chiller in the the jth hour. It is determined by 𝐶𝐴𝑃𝑠𝑢𝑝𝑝𝑙𝑦,𝑖,𝑗 = 𝐶𝐴𝑃𝑖 ∙ 𝑃𝐿𝑅𝑖,𝑗

(4)

where 𝐶𝐴𝑃𝑖 (kW) is the maximum cooling capacity of the ith chiller. The annual energy consumption of all the chillers in the multiple-chiller system (n chillers) is calculated by 𝑛 𝐸𝑎𝑛𝑛𝑢𝑎𝑙,𝑡𝑜𝑡 = ∑8760 𝑗=1 ∑𝑖=1 𝐸𝑖,𝑗

(5)

Switch on/off times counting Corresponding to the schematic diagram of the multiple-chiller system in Figure 4, Figure 5 illustrates the principle of staging chillers on or off. The staging-on and -off criterions are explained below [36]: Stage-on criterion: IF the cooling load is larger than a predefined switch-on threshold and this state lasts for a period longer than the time limit, THEN a chiller will be switched on. For example, if the total supply cooling capacity of the (z-1) online chillers (which equals cooling load) is greater than 𝑄𝑧𝑡ℎ and this state lasts for a while, the zth chiller will be switched on. Stage-off criterion: IF the total capacity of online chillers is smaller than the predefined switch-off threshold and this state lasts for a period larger than the time limit, THEN a chiller will be switched off. For example, if the total supply cooling capacity of the (z+1) online chillers 𝑡ℎ decreases to below 𝑄𝑧+1 for a while, the (z+1)th chiller will be switched off.

16

Fig. 5. Principle of chillers staging on or off The threshold is determined by the upper optimal percent load value [18]. For instance, if a plant has chillers running with a combined capacity of 400 kW and the Upper Percent Load is 80%, the application considers staging up when the current load exceeds 320 kW. In this study, the staging on/off are controlled by the cooling load in the system (cooling load-based sequence control). The impact of detailed control and operation strategy of chiller plant is not considered. This is because: (1) in system design, the main focus is to match the chiller capacity with the hourly cooling load to improve the system efficiency. Adjusting the operation (such as the control and optimization of building management system) can also improve the system efficiency, but it is too complex to be considered. For instance, even for a staging on/off action, there are four different control methods (T-based, Q-based, F-based and Pbased) [36]. (2) The proposed framework for configuring multiple chillers under uncertainty does not change for different ways of chiller operations. Designers only need to adjust the performance evaluation module (in Figure 1) when the chiller operation strategy changes.

Initial cost

17

The initial cost includes the cost of chillers and relevant accessories. The initial cost 𝐼𝐶𝑖 (US$) of the ith chiller in the multiple-chiller system is calculated following Taal et al.’s [37] and Cheng et al.’s [12] work by Eqn. (8) 𝐼𝐶𝑖 = 𝐼𝐶0 ∙ (𝐶𝐴𝑃𝑖 ⁄𝐶𝐴𝑃0 )𝜏

(8)

where 𝐼𝐶0 (US$) is the initial cost of a reference chiller with the capacity 𝐶𝐴𝑃0 (kW), 𝐶𝐴𝑃𝑖 (kW) is the maximum cooling capacity of the ith chiller, and 𝜏 is a coefficient, which is set to 0.4 in this study [12, 38]. Following Cheng et al.’s work [12], a 900 kW CSD chiller is used as the reference chillers. The capital cost of the CSD chiller is 154,300 US$. The initial cost of the multiplechiller plant with n chillers is calculated by Eqn. (9) 𝐼𝐶 = ∑𝑛𝑖=1 𝐼𝐶𝑖

(9)

Maintenance cost The maintenance cost of a multiple-chiller plant is calculated based on some engineering practice [39]. The maintenance cost of each chiller is determined by its cooling capacity, as shown in Eqn. (10). 𝑀𝐶𝑖 = 𝐶𝐴𝑃𝑖 ∙ 𝑀𝐶𝑢𝑛𝑖𝑡 , 𝑀𝐶𝑢𝑛𝑖𝑡

6.17 𝑈𝑆$/𝑘𝑊 (𝐶𝐴𝑃𝑖 < 528 kW) (528 kW ≤ 𝐶𝐴𝑃𝑖 < 1055 kW) { 4.63 𝑈𝑆$/𝑘𝑊 = (𝐶𝐴𝑃𝑖 ≥ 1055 kW) 2.57 𝑈𝑆$/𝑘𝑊

(10)

The maintenance cost of the whole multiple-chiller plant (𝑀𝐶 (𝑈𝑆$)) is calculated by Eqn. (11) 𝑀𝐶 = 𝜇 ∙ ∑𝑛𝑖=1 𝑀𝐶𝑖

(11)

where 𝜇 is a calibration factor, which equals 0.8 for 2-chiller plants and 0.7 for 3-chiller systems or systems with more than 3 chillers if the multiple chillers are identical.

18

2.2.4 Life-cycle cost analysis The life-cycle cost of the configured multiple-chiller plant is estimated using the following formula of Eqn. (12) [40]. It should be noted that only the price of the multiple chillers is considered in the life-cycle cost analysis. The chilled water pumping system and the condensate water pumping system are not considered since this study only optimize of the number, size and type of each chiller in a multiple-chiller plant. 𝐴𝐶

𝑡 LCC = IC + ∑𝑁 𝑡=1 (1+𝑟)𝑡

(12)

where LCC is the life-cycle cost (US$), IC is the initial cost (US$), ∑ is the sum over lifetime from year 1 to year N, N is the lifetime of the appliance, r is the discount rate, t is the year that annual cost is determined, and 𝐴𝐶𝑡 is the annual cost (US$) in the tth year which is determined by Eqn. (13) AC = MC + EC𝑎𝑛𝑛𝑢𝑎𝑙

(13)

where MC (US$) is the annual maintenance cost and EC𝑎𝑛𝑛𝑢𝑎𝑙 (US$) is the annual electricity cost, which is calculated by Eqn. (14) EC𝑎𝑛𝑛𝑢𝑎𝑙 = 𝐸𝑎𝑛𝑛𝑢𝑎𝑙,𝑡𝑜𝑡 ∙ C𝑒𝑙𝑒

(14)

where 𝐸𝑎𝑛𝑛𝑢𝑎𝑙,𝑡𝑜𝑡 is the annual electricity consumption (𝑘𝑊 ∙ ℎ) and C𝑒𝑙𝑒 is the price of 1 𝑘𝑊 ∙ ℎ electricity. It should be noted that the life-cycle cost analysis only indicates the best multiple-chiller plant configuration in terms of cost. Other performance indices, such as the on/off switch time and the maintenance difficulty, are not considered. Therefore, there are other configuration schemes that may perform equally well or even better. The optimal configuration scheme selected through the life-cycle cost analysis only provides a reference for a new system design.

19

3. Case study In this section, a case study is used to illustrate the procedure of the proposed optimal configuration strategy. A case building is selected from the reference buildings summarized by the U.S. Department of Energy [41]. This building is a hospital building with 5 floors. Each floor has a dimension of 70.1 m × 53.3 m (230 ft × 175 ft) and a height of 4.3 m (14 ft). The temperature was set to 21.1oC (70℉) during winter time and was set to 23.9 oC (75 ℉) during summer time. The building was assumed to be located in Miami. Figure 6 shows the layout of the building.

Fig. 6. Appearance of the building model

3.1 Uncertainty analysis of cooling load The uncertainties in the input parameters were quantified according to a generic uncertainty quantification (UQ) repository, which includes uncertainty information for general building envelope and materials, and usage scenarios and operation [29,42]. Table 4 lists the main uncertain parameters. Table 4 Quantification of uncertain parameters Parameter

Mean

Min.

Max.

Parameter

Thermal properties 20

Mean

Min.

Max.

Conductivity

–

±15%

Visible transmittance

–

±3%

Density

–

±3%

Front side visible reflectance

–

±3%

Specific heat

–

±36.75%

Back side visible reflectance

–

±3%

±12%

Infrared transmittance

–

±3%

–

±3%

–

±3%

Thermal absorptance –

Front Solar absorptance

–

side

infrared

±12% hemispherical emissivity Back

Visible absorptance

–

side

infrared

±12% hemispherical emissivity

Solar transmittance Front

side

–

±3%

Dirt correction factor

–

±30%

–

±3%

U-factor

–

±15%

–

±3%

Solar heat gain coefficient

–

±15%

–

±15%

2.60

0.26

solar

reflectance Back

side

solar

reflectance Thermal resistance

Internal load Occupancy

Infiltration density

Effective –

±20%

–

±20%

(ft²/person) Lighting (W/ft²)

leakage

window area (cm2/m2)

area/ 4.94

400 samples were generated for the parameters listed in Table 4 using the Latin Hypercube Sampling method. Simulations were conducted for all 400 samples, which produced 400 annual cooling load data. Statistical analysis was conducted for evaluating the uncertainty in the peak cooling load and the uncertainty in the distribution of the hourly cooling load, as shown in Figure 7. The peak cooling load follows approximately a normal distribution, with a mean of 845.5 kW 21

and a standard deviation of 33.7 kW. This peak load distribution was used for sizing the HVAC system using the method proposed by the author in 2015 [3,4].

Fig. 7. Histogram of uncertain peak cooling load and hourly cooling load In order to analyze the uncertainty in the hourly load distribution, one stairstep graph is drawn based on the statistical analysis of a year of hourly cooling load data, and hence 400 curves were generated. These 400 curves were accumulated to represent the uncertainty in the distribution of the annual hourly cooling load. As shown in Figure 7 (b), the minimum hourly cooling load is 168 kW and the maximum hourly load is 945 kW. As the hourly cooling load increases from the minimum to the maximum value, its occurrence frequency increases linearly and reaches a peak at the load of 350 kW, then the occurrence frequency decreases gradually and becomes 0. The white curve in the middle shows the average distribution of the hourly load file.

3.2 Performance evaluation of different configured alternatives After an optimal HVAC system size is determined, 31 alternatives for the multiple-chiller plant are produced based on the configuration ratios listed in Table 3. In the performance evaluation process, 3 PLR-COP curves are used to describe the cooling performance of chillers of different sizes (large/ medium/ small), corresponding to Section 2.2.1 (Table 2). The uncertainties in the chiller COP is also considered. These uncertainties are quantified by normal distributions 22

following Liao et al.’s work [36]. Figure 8 presents these PLR-COP curves and their associated uncertainties. The points in Figure 8 represent the uncertainties in COP. They are samples generated from the quantified normal distributions (the mean is set as the base COP, and the standard deviation is set as 10% of the mean). Given a PLR, the COP value of the sample point, instead of the point on the COP-PLR curve, is used for performance evaluation.

Fig. 8. PLR-COP curves of CSD chillers of different sizes The types of compressors mainly determine the maximum COP that the chillers can achieve, not the trend of PLR-COP curves. In this study, the CSD chillers use centrifugal compressors (refer to Table 2 for their COPs). Four performance indices, namely the annual energy consumption, the annual switching on/off numbers, the initial cost and the annual maintenance cost, were evaluated for each of the 31 alternatives. The predicted performance of each option under the given cooling load is shown in Figure 9. As it can be seen, the initial cost increases as the number of chillers increases. The maintenance cost is mainly determined by configuration ratios, since the size of the whole system has already been determined at the sizing stage.

23

Fig. 9. Comparison of the four performance indices between 31 alternatives (All-CSD-chiller) The following general findings can be obtained through analyzing the predicted performance above. 

For all-CSD-chiller systems, as the number of chillers increase, the average energy consumption of the alternatives of different configuration ratios decreases. This is because in all-CSD-chiller system, dividing a large sized chiller into several small sized chillers can guarantee the small sized chillers to operate at full load condition, which can help improve the system COP.



For all-CSD-chiller systems, even though the number of chillers is identical, different configuration ratios can lead to large difference in energy consumption.

3.3 Optimization of chiller configuration A life-cycle cost analysis is conducted to select out the optimal configuration for the case building. A discount rate of 5% and a unit electricity price of 0.1049 US$/(kW·h) are used [43]. 24

The lifespan of the HVAC system is set to 20 years [44]. Figure 11 shows the comparison of the life-cycle cost of the 31 configuration alternatives for the case building. As can be seen, Alternative 3 has the smallest average life-cycle cost (1.307×106 US$). Therefore, a 2-chiller system with a configuration ratio of 0.3 and 0.7 is recommended for the HVAC system for the case building. Meanwhile, the performance of the configured multiple-chiller system can be predicted: the annual energy consumption will lie in the range (816,047, 862,091) kW·h at a 90% confidence level with a mean of 836,278 kW·h. The switching on/off time will lie in the range (291, 346) times at a 90% confidence level with a mean of 315.6 times. The initial cost will be around 163,450 US$, and the annual maintenance cost will be around 4,043 US$.

Fig. 10. Comparison of life-cycle cost of each alternative It can be found that the varying trend of the life-cycle cost with configuration alternatives is similar to the trend of annual energy consumption. However, as the number of chillers increases, the average life-cycle cost will increase. As can be seen Figure 9, Alternative 15 is superior to Alternative 7 and superior to Alternative 3 in terms of energy consumption. However, in terms of life-cycle cost, Alternative 3 (2-chiller system) is slightly better than Alternative 7 (3-chiller system) and Alternative 15 (4-chiller system), as shown in Figure 10. The reason why the life25

cycle cost of 2-chiller system is slightly better than 3-chiller system and 4-chiller system is that the initial cost of 2-chiller system is significantly smaller than the 3-chiller or 4-chiller system, which even makes up the deficiency in energy consumption. Therefore, only when the improvement in the energy performance is larger than the increase in the initial cost, adding one more chiller should be recommended. Figure 11 compares of the uncertain life-cycle cost of Alternative 3 (0.3+0.7), Alternative 5 (0.5+0.5) and Alternative 7 (0.1+0.2+0.7). Alternative 3 is the optimal design for this building, Alternative 7 is the second optimal design, and Alternative 5 is the design from the popular configuration. As can be seen, the possibility that Alternative 3 is superior to Alternative 5 reaches as high as 100%. The average life-cycle cost of Alternative 3 reduced 1.13 × 105 US$ (8.67% cost saving) compared with Alternative 5. Therefore, the proposed configuration strategy can help improve the design dramatically. Alternative 7 has similar performance with Alternative 3. It can be considered as a second choice in the configuration process.

Fig. 11. Comparison of uncertain life-cycle cost of different alternatives

26

4. Extended studies In order to study the influence of the cooling load distribution on the optimal configuration of multiple-chiller system, extended studies are conducted by applying the proposed method under different cooling load file (It comes from EnergyPlus simulation of models which combines different types of buildings and different weather conditions). In this section, several different weather conditions and building prototypes are selected and combined. Then the uncertainty analysis is conducted for these different combinations of weather condition and building type. In the end the optimal configuration is determined under each cooling load file.

4.1 Selection of weather condition and building prototypes Five cities from five typical climate zones in the U.S. are selected according to the climate zone designations used by the U.S. Department of Energy Building America Program [45]. These five cities are Miami, Phoenix, San Francisco, Salem and Chicago. The locations of the five cities are marked in Figure 12.

Salem

D

E

San Francisco Phoenix

Chicago

C B

A

Miami

Fig. 12. Location of five cities from five different weather conditions Table 5 lists the detailed information about weather condition in these five cities. The maximum value and range of dry-bulb temperature on the design day of these five cities is

27

presented. As this study investigates the optimal configuration of multiple-chiller plants, only the cooling load is estimated. Table 5 Description about weather condition in five selected cities Design Day Dry-Bulb Temperature (℃) No.

City

Climate Zone Characteristics Max.

Range

A

Miami

Zone 1A

very hot, humid

33.6

8.4

B

Phoenix

Zone 2B

hot, dry

43.4

12

C

San Francisco Zone 3C

warm, marine

28.3

8.5

D

Salem

Zone 4C

mild, marine

33.3

15.4

E

Chicago

Zone 5A

cold, humid

33.3

10.5

Five prototype commercial buildings are selected from the reference buildings summarized by the U.S. Department of Energy [41]. The first building is the hospital building (shown in Figure 5) which has been analyzed in Section 3, the other four buildings include a large hotel, a large office, a restaurant and a secondary school. These building models are available from the DOE website and are designed for EnergyPlus simulation. Figure 13 shows the exterior of the five reference buildings. Table 6 further describes the configuration of each building. Each of these buildings represents a specific category of commercial building. They have different functions, implying that their usage schedules are different. Details about the five reference commercial buildings can be found in DOE website [41]. Table 6 Description about five selected commercial prototype buildings Building No. Type Name

Floor Area (ft2) Number of Floors

1

Hospital

241,351

5

2

Large Hotel

122,120

6

28

3

Large Office

498,588

4

Full Service Restaurant 5,500

1

5

Secondary School

2

210,887

12

Fig. 13. Exterior of five prototype buildings Figure 14 shows the internal gain schedule of the five reference buildings. As the function of each building is different, the internal gain schedules are also different. It can be seen that hospital, office, and school (normal) have similar occupancy schedules, which reach peak during daytime from 10:00 to 17:00. The occupancy schedule of the restaurant has two peaks, namely from 12:00 to 14:00 and from 19:00 to 21:00. However, occupancy schedule of the hotel is different from the other four building types. It reaches peak during nighttime from 23:00 to 6:00 the following day. Lighting schedules for hospital, office, school and restaurant are similar, which reach peak during daytime from 9:00 to 17:00. Lighting schedule for the hotel reaches a small peak between 8:00 and 10:00, and reaches a large peak at around 21:00. There are five climate zones (Weather A to E) selected and five type of commercial buildings (Building 1 to 5) selected. This leads to 25 combination cases. Through analyzing these 25

29

combinations, the influence of building type and weather condition on cooling load characteristics can be revealed to some extent. Lighting schedule

1

1

0.8

0.8

0.6

0.6

Friction

Friction

Occupancy schedule

0.4

0.4 0.2

0.2

0

0 1

3

5

7

9

11 13 15 Hour in a day h

17

19

21

1

23

3

5

7

9

11 13 15 Hour in a day h

17

19

21

23

Fig. 14. Occupancy schedule and lighting schedules of the five prototype buildings

4.2 Uncertainty analysis of the cooling load The uncertainties in the input parameters are quantified according to the generic uncertainty quantification (UQ) repository as introduced in Section 3 [29,42]. 400 sample simulations are conducted in each case, which produces 400 annual cooling load outcomes. The following conclusions can be drawn by comparing the histograms of the 25 cases in Figure 15. 

The distribution of the hourly load profile is affected by two major factors: weather condition and building type (to be specific, the schedule of building usage).



In hot climates, if the building is used at night (i.e. there is nightly occupancy and facility usage), the hourly cooling load distribution approximates uniform distributions, as observed in Case 1A and 2A. This is because the variance in daily hourly cooling load is not large (the building is in use during 24h in a day).

30



In hot climates, if the building is not used at night, the distribution of the hourly load file approximates an exponential distribution, as observed in Case 3A, 3B, 4A, 4B, 5A, 5B. This is because large hourly load only occurs during daytime within limited hours (12:00 to 16:00), which accounts for only a small percentage of total hours (8760h) in one year.



In colder climates, most of the hourly cooling load distributions approximate exponential distributions, as shown in Case 2D, 2E, 3D, 3E, 4D, 4E, 5D and 5E. This is because the larger cooling load (which only occurs during summer time) only accounts for a small percentage of the annual cooling load, while smaller cooling load (which occurs during winter and most nighttime) make up most of the percentage. 1 Hospital

2 Large hotel

3 Large office

4 Restaurant

5 Secondary school

A. Miami

Counts

B. Phoenix

C. San Francisco

D. Salem

E. Chicago

Cooling load kW

Fig. 15. Histogram of hourly cooling load distributions of the five building prototypes under different weather condition

31

Analyzing the characteristics of hourly load distributions can help determine the optimal configuration of multiple-chiller system. The hourly cooling load distribution is categorized into four types, as listed in Table 7 and highlighted in Figure 15 using four colors. Table 7 Categorization of hourly cooling load distributions Types

Characteristics

Example cases

1

The occurrence frequency doesn’t change much over the middle cooling load 1A,1B,2A range. There is no salient peak.

2

3

The occurrence frequency has a flat peak at a small cooling load (even 0).

1C,1D,1E,

After the peak, the occurrence frequency decreases gradually to 0.

2B,2C,3A,3B,4A

The occurrence frequency has a very sharp peak at a small cooling load.

2D,2E,3C,3D,3E

After the peak, the occurrence frequency decreases to 0 slowly at an 4B, 5A,5B exponential trend (a long tail).

4

The occurrence frequency has a very sharp peak at a small cooling load.

4C,4D,4E,5C,5D,

After the peak, the occurrence frequency drops to 0 very fast (a short tail).

5E

4.3 Life-cycle cost analysis As the performance evaluation process and the life-cycle cost analysis process are the same as introduced in Section 3, this section skips these details and presents the final results directly. Table 8 summarizes the optimal multiple-CSD-chiller system configurations under different combinations of building types and climate. The optimal option is the one with the smallest average life-cycle cost. Other options represent the configurations that result in the 2 nd and 3rd smallest average life-cycle cost. The four colors filling Table 8 are corresponding to the four types of hourly cooling load distribution in Figure 15.

32

Table 8 Recommended multiple-chiller configurations under load side uncertainty for different building types and weather condition (All-CSD-chiller system) Building 5.Secondary Weather

type

1. Hospital

2. Large Hotel

3. Large Office

4. Restaurant School

condition Optimal opt. A.

0.3+0.7

0.4+0.6

0.33×3

0.4+0.6

0.5×2

(1.3 × 106)

(4.16 × 105)

(9.84 × 105)

(4.15 × 105)

(3.44 × 106 )

0.1+0.2+0.7

0.3+0.7

0.33×3

0.3+0.7

0.3+0.7

0.1+0.1+0.1+0.7

0.5+0.5

0.1+0.2+0.7

0.5×2

0.4+0.6

0.3+0.7

0.4+0.6

0.33×3

0.2+0.8

0.5×2

(1.35 × 106)

(3.98 × 105)

(9.73 × 105 )

(6.17 × 105)

(3.9 × 105)

0.1+0.2+0.7

0.5+0.5

0.3+0.7

0.1+0.9

0.3+0.7

0.1+0.1+0.1+0.7

0.3+0.3+0.4

0.1+0.2+0.7

0.3+0.7

0.4+0.6

0.2+0.8

0.4+0.6

0.3+0.3+0.4

0.1+0.9

0.3+0.7

(1.18 × 106)

(2.07 × 105)

(5.32 × 105)

(2.96 × 105)

(1.26 × 105)

0.1+0.1+0.8

0.3+0.7

0.3+0.7

0.2+0.8

0.4+0.6

0.2+0.3+0.5

0.5+0.5

0.2+0.3+0.5

0.3+0.7

0.1+0.9

0.2+0.8

0.4+0.6

0.2+0.2+0.6

0.1+0.9

0.1+0.9

(1.16 × 106)

(2.21 × 105)

(5.33 × 105)

(3.25 × 105)

(1.25 × 105)

0.1+0.1+0.8

0.5+0.5

0.2+0.3+0.5

0.2+0.8

0.2+0.8

0.1+0.2+0.3+0.4

0.3+0.7

0.3+0.7

0.3+0.7

0.3+0.7

0.3+0.7

0.4+0.6

0.2+0.2+0.6

0.1+0.9

0.4+0.6

(1.14 × 106)

(2.61 × 105)

(6.10 × 105 )

(4.05 × 105)

(4.15 × 105)

0.1+0.2+0.7

0.5+0.5

0.2+0.3+0.5

0.2+0.8

0.3+0.7

0.1+0.1+0.1+0.7

0.3+0.7

0.3+0.7

0.3+0.7

0.5×2

(Cost US$) Miami Other opts.

Optimal opt. B. (Cost US$) Phoenix Other opts.

Optimal opt. C.

San (Cost US$)

Francisco Other opts.

Optimal opt. D. (Cost US$) Salem Other opts.

Optimal opt. E. (Cost US$) Chicago Other opts.

33

The following findings about configuring multiple-chiller system can be made from analyzing the optimal configurations in each case. 

Peak cooling load is the dominant factor affecting the optimal number of chillers in the HVAC system. When the peak cooling load is smaller than 500 kW, a 2-chiller configuration is recommended (see Building 2, 4 and 5). This is because in such circumstance the size of each chiller is already very small, the energy saving brought by adding one more chiller cannot make up the increase in the initial cost.



In most cases, an equally-sized-chiller system is not the optimal configuration. As can be seen in Table 8, only Case 3A, 3B and 5A can benefit the most from the equally-sizedchiller system. This is different from the popular design (as mentioned in the introductory section) in the existing HVAC systems that use multiple equally-sized chillers.



When the peak cooling load is smaller than 500 kW, a 2-chiller configuration should be given priority for Type 1 cooling load distribution.



When the peak cooling load is smaller than 500 kW, a 2-chiller configuration should be given priority for Type 2 cooling load distribution. However, if the hourly cooling load file has a long tail, adding one more chiller is recommended. When the peak cooling load is larger than 500 kW, more chillers may be added and the configuration of chillers can be determined using the proposed method.



When the peak cooling load is larger than 500 kW, a configuration with more than 3 chillers is recommended for Type 3 cooling load distribution. This is because the hourly cooling load varies in a large range and the occurrence frequency of large cooling load is small. The cooling load in the tail part can be satisfied by adding one or two more small chillers.



When the peak cooling load is smaller than 500 kW, a 2-chiller configuration is recommended for Type 4 cooling load distribution. 34

The selection of the optimal configuration ratio is more difficult. It cannot be determined directly based on the hourly load distribution (i.e. Figure 15). Even for two hourly cooling loads with a similar trend, the optimal configurations can be different. For instance, the hourly load distributions of Case 1D and 1E are similar, but the optimal configurations for the two cases are 0.2+0.8 and 0.3+0.7, respectively. The configuring strategy introduced in Section 2 has been applied in order to select the optimal configuration ratios for these cases.

5. Conclusion This study has proposed an optimal configuration strategy for multiple-chiller plants, which consists of the following main steps: load side uncertainty analysis, configuration of chiller alternatives, performance evaluation and life-cycle cost analysis. Both the load side uncertainty and COP uncertainty have been quantified using statistical distributions and have been integrated into the configuration strategy to show their influence on the optimal configuration of multiplechiller system. The uncertainties in the cooling load profile of different combinations of weather conditions and building types has been studied. The distributions of the cooling load profile have been classified into four categories based on their varying trends, and the optimal configuration schemes under each type of the cooling load distribution has been analyzed and summarized. The configuration strategy proposed in this study provides a systematic way to design a multiplechiller system considering the cooling load uncertainty and COP uncertainty. The findings enable designers to understand the influence of building type and weather condition on the final optimal configuration of chillers. Moreover, the results from this study can be generalized so that some chiller configuration parameters, such as chiller number and chiller sizing ratio, can be recommended when designing a new multiple-chiller plant.

35

The proposed method can be directly used to find the optimal configuration of multiple variable-speed-driven (VSD) chiller system under cooling load uncertainties. Given a building type and its cooling load profile, a systematically comparison on the performance of multipleCSD-chiller system and multiple-VSD-chiller system would be interesting, which will be our future work to continuously help improve the multiple-chiller system design.

Acknowledgement This work was supported by the Guangdong Basic and Applied Basic Research Fund (No. 2015A030313814) and the grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. 11201215).

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