Energy Performance Comparison of a Chiller Plant Using the Conventional Staging and the Co-Design Approach in the Early Design Phase of Hotel Buildings

Abstract

As part of the design process of a chiller plant, one of the final stages is the energy testing of the system in relation to future operating conditions. Recent studies have suggested establishing robust solutions, but a conservative approach still prevails at this stage. However, the results of some recent studies suggest the application of a new co-design (control–design) approach. The present research involves a comparative analysis between the use of conventional staging and the co-design approach in the design phase of a chiller plant. This paper analyzes the energy consumption estimations of six different chiller plant combinations for a Cuban hotel. For the conservative approach using on/off traditional staging, the results suggest that the best option would be the adoption of a chiller plant featuring a symmetrical configuration. However, the outcomes related to the co-design approach suggest that the best option would be an asymmetrical configuration. The energy savings results were equal to 24.8% and the resulting coefficient of performance (COP) was 59.7% greater than that of the symmetrical configuration. This research lays firm foundations for the correct choice and design of a suitable chiller plant configuration for a selected hotel, allowing for significant energy savings in the tourism sector.

1. Introduction

Selecting all of a chiller plant’s parameters involves considering the system’s cooling capacity and its configuration. Fang et al. [1] demonstrated that poor design of a plant causes a significant deviation in the efficiency of each element in the system from its optimum point of operation. According to ASHRAE [2], the sequential procedure suggests that a chiller plant design should involve the evaluation of the total cooling load demand of a building, which needs to be increased by an extra load for safety reasons, and, finally, the selection of the other features, i.e., the type of chiller, the number of chillers, the cooling load distribution, and the hydraulic arrangement. Several studies and recommendations related to these steps were summarized by Diaz et al. [3], and the overall procedure is shown in Figure 1.

Over time, the traditional chiller plant design methodology has been improved. Taylor [4] recommended adding the estimation of the energy consumption according to the critical operating conditions of the building to the traditional methodologies for selecting the lowest life cycle cost. An important improvement in this traditional methodology was its conversion into an iterative process, where the uncertainty analysis of cooling loads was incorporated with energy performance, considering an energy, economic, and/or life cycle cost approach called robust design. This methodology allows for selecting the chiller that meets the technical requirements of the facility and simultaneously offers the best performance from several empirically determined chiller plant combinations, where certain design parameters are modified (e.g., the number of chillers and the distribution of cooling capacity).

Cheng et al. [5] determined the capacity and number of cooling units using an uncertainty procedure to determine the cooling load demand profile and the Markov method to perform an energy analysis of the different proposed configurations. This analysis involved preventive maintenance and reliability. Using a similar methodology, Yang et al. [6] defined the optimal chiller plant configuration by modifying the chiller type and the number and size of the chillers. Figure 1 compares the results with the application of the traditional design methodology. The chiller plant savings were equal to 26% of the life cycle.

Despite the undeniable improvements presented in the previous studies, there are still aspects that need to be addressed to obtain a more decisive result in the selection of chiller plants. This is especially the case due to the fact that these cooling systems, once installed in buildings, usually incorporate automatic control systems, which allow for increasing the overall efficiency by synchronizing the cooling load of the chillers with the cooling demand. In this case, it is possible that this system would incorporate another design scenario, very different from the one considered in both traditional and robust design methodologies.

As the most suitable configuration for a certain building is being evaluated, the premise is that chiller plants usually comprise N + 1 units. As the energy performance analysis is carried out from the design stage, simple staging rules are used in different simulation software and research analyses. A common practice in chiller plant design is to consider the progressive startup according to the cooling load demand and the size of the chillers. Huang et al. [7] and Li et al. [8] recommended the startup of the chiller involving the highest cooling capacity first. Figure 2 illustrates the cooling load-based chiller sequencings of chiller on/off staging suggested by Sun et al. [9] and Huang et al. [7]. Figure 2 shows the energy consumption forecasting of the i-th chiller in the j-th hour using the PLR-COP curve of general chiller models according to a fixed capacity.

Energy consumption prediction is an important phase in chiller plant design, which involves considering the technical characteristics of the chiller and operating factors such as the characteristics of the facility and the thermal load variation to predict the interaction of the chiller plant. Designers must adapt the chilled-water system to the cooling load variations over time. However, this is when the following questions arise: Would it be possible for a chiller plant which was designed under the traditional staging principle to be able to operate efficiently when incorporating an automatic control system? Should its staging involve considering another principle?

Despite the major improvements in design methodologies presented by [5,6,7,8,10,11,12,13], where different parameters were optimized and these optimal chiller plant configurations were then finally tested under traditional staging, it is likely that in the exploitation phase, these configurations cannot meet the forecasts defined in the initial study. This is why an optimal design of the chiller plant must be guaranteed, considering the impact of the automatic control methods to be used in the future.

In this research area, a gap that persists is that there is not enough research in the literature dedicated to identifying the impact of the initial design stage of chiller plants on the subsequent exploration of the systems [14,15]. Recent studies call for extending the design concept of centralized heating, ventilation, and air conditioning (HVAC) systems to include possible interaction with the automatic control system, which usually increases efficiency in later phases. Garcia [16] defined this novelty approach, named co-design, as a conceptual design process that uses dynamic systems as a variable to achieve optimal results. Rampazzo [17] described the optimized operation of a chiller plant as a nonlinear combinatorial mathematical problem, restricted to continuous and discrete variables, being a challenge for standard optimization methods. However, few researchers have presented studies using the co-design concept in the design of HVAC systems. Bhattacharya et al. [15] carried out Bayesian optimization using black box models of the chillers. They optimized the size of the system (cooling capacity) and the cooling load chiller sequencing. They also included an economic analysis. Masburah et al. [18] used a deep reinforcement learning language to provide different control architectures to the HVAC systems during the simulation process in the design phase. Here, this study focuses on cooling storage system capacity and charging and discharging strategies.

In previous research, Diaz et al. [19,20] proposed a new methodology for the design of chiller plants for hotel facilities. This methodology integrated different procedures that consisted of multiple statistical analyses of cooling demands [20] to obtain load patterns that allowed obtaining individual chiller cooling capacities and then a mathematical procedure to create multiple chiller plant combinations, modifying several design variables and also considering compliance with technical standards. Subsequently, they presented an energy simulation procedure [19] carried out using the solution of a mathematical optimization problem of optimal chiller loading (OCL) and optimal chiller sequencing (OCS) analyses to establish an effective operating strategy. The final selection allowed designers to choose the system that best adapted to the variations in the thermal demands of the installation, working under an optimized mode, which would imply the implementation of an automatic control system for the HVAC system. However, the comparison of the effectiveness of this methodology was only based on the comparison of its results and the plant configuration selected according to the technical standard (a symmetrical chiller plant), and no comparative analysis was presented to validate its contribution with respect to the traditional methodologies currently used.

Thangavelu et al. [21] showed that chiller plants can reduce their energy consumption by up to 40% in medium-capacity plants and by up to 20% in small-capacity plants by employing these techniques. This means a significant reduction in the environmental impact associated with electricity generation and considerable economic benefits. OCL is a method that optimizes the total distribution of cooling loads in regulated time intervals through several periods subjected to optimization constraints. OCS defines the conditions in which the chillers should operate or not, according to the cooling demand. Therefore, it adjusts the number of chillers in operation to the fluctuation of the cooling load, maximizing the plant’s efficiency.

An efficient chiller plant must be designed based on the theoretical operating conditions that largely coincide with the future exploitation conditions in a building. However, there are still design standards and methodologies that include traditional sequencing staging in the energy assessment of chiller plants. Automatic control systems usually fit these systems; however, the savings achieved would likely be limited by errors during the initial design.

This research contributes to chiller plant design in buildings. Considering that this process is carried out according to the technical standards and procedures outlined in Figure 1, the use of optimization techniques contributes to a better design of the plant and ensures that it operates under an efficient operating regime. The main objective is to demonstrate, through the energy comparison of two design trends, the impact that both have on the selection of the most suitable configuration for future operating conditions. This paper aims to verify the impact on the design of a chiller plant configuration of the use of a traditional sequencing staging approach or the use of co-design methodology, using the OCL and OCS in the energy performance forecasts study. These outcomes can serve as an inflexion point in the design philosophy of chiller plants.

This paper is structured as follows: The methodology is described in Section 2, while the results are presented and discussed in Section 3. Finally, the conclusions are summarized in Section 4.

2. Materials and Methods

2.1. Methodology

To meet the thermal demand of a chiller plant, regardless of the selected approach, the following steps need to be taken:

• Calculation of the cooling load demand of the building.

• Implementation of accurate energy models of the HVAC systems for simulation purposes.

• Implementation of chiller plant sequencing algorithm and energy performance evaluation.

2.2. Cooling Load Demand of Building

In this work, the thermal load of the investigated facility, i.e., a Cuban hotel, was calculated using the deterministic method suggested by [22]. The time base for the input data and thermal properties of the building was established by using the interface TRNBuild of TRaNsient SYstems Simulation software (TRNSYS 16) [23].

Using TRNSYS 16, heat load profiles (ki) representing a 24 h scenario were obtained. In addition, the different implemented thermal demand profiles, which represented 24 h heat load scenarios (ki), suggested the use of the following steps:

• Consideration in the simulation of activity levels in public areas and the activity patterns of hotels near the case study, which have in common the type of hotel, total capacity, and type of tourism.

• Consideration of the variation in the occupancy levels in each thermal zone with the aid of the historical occupancy levels in similar hotels.

• Establishment of energy efficiency measures in the thermal zones related to the rooms’ areas according to the suggestions of Yang et al. [6].

• Establishment of the concept of a partially loaded room for thermal zones belonging to the rooms. This measure included comfort conditions in unoccupied rooms, considering a set point of 25 °C, which ensured high indoor air quality levels in tropical-climate hotels.

The sensible and latent heat portions were considered following the ASHRAE 55 recommendations [24]. The heat gained from the electrical equipment rated was calculated by considering its electrical power, duty factor, load factor, and efficiency. The heat fractions by convection and radiation were set at 0.7 and 0.3, respectively, and at 0.6 and 0.4 for artificial lighting [23]. Finally, a database was built, in which, for each ki, the thermal demand values (CLi) for each time interval (i) were reflected.

2.3. Implementation of Accurate Simulation Models of Air-Cooled Chiller Unit

The mathematical models were based on the generalized least-squares method and the use of black box methodology for the implementation and selection presented by [25]. In this study, a multiple linear regression model was carefully chosen for enhanced simulation. The cooling capacity (${\dot{\mathrm{Q}}}_{{\mathrm{ch}}_{\mathrm{i}}}$) (Equation (1)) is a function of the subsequent independent variables. Tc_air,in, Tch_w,s, and Tc_air are defined in Annex 1. x₀, x₁, and x₂ represent the regression coefficient of the mathematical model.

(1)${\mathrm{Qch}}_{\mathrm{i}}\left(\mathrm{kW}\right)={\mathrm{x}}_{\mathrm{o}}+{\mathrm{x}}_1{\mathrm{Tc}}_{\mathrm{air},\mathrm{in}}+{\mathrm{x}}_2{\mathrm{T}}_{\mathrm{ch}}{}_{\mathrm{w},\mathrm{s}}\begin{array}{ccc}& & {\mathrm{x}}_{\mathrm{j}}\in {\mathrm{Q},}_{\mathrm{j}}=\left[0,1,2\right]{,\mathrm{Tc}}_{\mathrm{air},\mathrm{in}}\mathrm{f}\left(\mathrm{Tamb}\right)\end{array}$

To calculate the power input of the i-th chiller (Pch,i), it was decided that the independent variables were those that could be operationally modified, leading to Equation (2).

(2)${\mathrm{Pch}}_{\mathrm{i}}\left(\mathrm{kW}\right)={\mathrm{a}}_{\mathrm{o}}+{\mathrm{a}}_1{\mathrm{T}}_{\mathrm{ch}}{}_{\mathrm{w},\mathrm{r}}+{\mathrm{a}}_2{\mathrm{Tc}}_{\mathrm{air}}\begin{array}{ccc}& {\mathrm{a}}_{\mathrm{j}}\in {\mathrm{Q},}_{\mathrm{i}}=\left[0,1,2\right]{,\mathrm{Tc}}_{\mathrm{air},\mathrm{in}}{,\mathrm{T}}_{\mathrm{ch}}{}_{\mathrm{w},\mathrm{r}}\in \mathrm{Q}& \end{array}$

in which T_{ch w,o} represents the chilled-water return temperature, which is given by Equation (3):

(3)${\mathrm{Tch}}_{\mathrm{w},\mathrm{r}}\left({}^{\mathrm{o}}\mathrm{C}\right)=\left(\frac{{\mathrm{Cl}}_{\mathrm{i}}}{{\mathrm{m}}_{\mathrm{i}}\mathrm{Cp}}+{\mathrm{Tch}}_{\mathrm{w},\mathrm{s}}\right)$

The statistical indices used for evaluating the error calculation of the model were the correlation coefficient (R²) (Equation (4)) and the mean of the absolute error (MAE) (Equation (5)). R² is equal to the ratio of SCE (i.e., measure of the variability of the regression model) and SCT (corresponding to the measure of the variability of Y without considering the effect of the explanatory variables X).

(4)${\mathrm{R}}^2=\frac{\mathrm{SCE}}{\mathrm{SCT}}\begin{array}{cc},& 0\le {\mathrm{R}}^2\le 1\end{array}$

The mean of the absolute error is the average absolute value of the residuals and shows the average error in the response prediction using the fitted model.

(5)$\mathrm{MAE}={\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{N}}\frac{|{\mathrm{x}}_{\mathrm{i}}-{\underset{}{\overset{⌢}{\mathrm{x}}}}_{\mathrm{i}}|}{\mathrm{N}}}$

The development of the regression model was based on White’s test for homoscedasticity [26]. The Breusch–Godfrey test [27] allowed for checking the residual autocorrelation nonappearance in the selected mathematical model. In addition, the Jarque–Bera test [28] was employed to analyze normality. Compliance with the classical assumptions of a regression model guaranteed that the estimators obtained by the least-squares method were unbiased, consistent, and efficient.

As an initial state in the analysis, the chiller plant was assumed to be a decoupled system, i.e., composed of n air-cooled chillers arranged in parallel (Figure 3). The energy analysis was only applied to the primary circuit (section of chillers).

The water chiller plant should be composed of (n + 1) chillers. Many authors [6,9,29,30,31] have recommended that in the case of a plant with different chiller capacities, the one with the highest cooling capacity should be switched on first. Therefore, in the scenario involving the traditional principle of chiller on/off staging, the chillers were activated in order from the highest to the lowest capacity (Equation (6)):

(6)${\mathrm{Qch}}_1\left(\mathrm{kW}\right)\ge {\mathrm{Qch}}_2\left(\mathrm{kW}\right)\ge \cdots {\mathrm{Qch}}_{\mathrm{n}}\left(\mathrm{kW}\right)$

2.3.1. Approach Using the Traditional Principle of Chiller On/Off Staging

To answer how many chillers were working in a certain time interval (i) depended on the thermal demand of the installation (CL_i) and the cooling capacity of each chiller Qch_n,i in each time interval (i). Therefore, Equation (7) gives the total operating chillers.

(7)$\mathrm{Nc}\begin{array}{cc}=& \mathrm{f}\left({\mathrm{CL}}_{\mathrm{i}}{;\mathrm{Qch}}_{\mathrm{i}}\right)\end{array}$

The cooling load capacity of the water chiller plant as well as the electrical power required are in function of the variables shown in Equations (8) and (9), respectively.

(8)${\mathrm{Qch}}_{\mathrm{n},\mathrm{i}}\begin{array}{cc}=& \mathrm{f}\left({\mathrm{Tc}}_{\mathrm{air},\mathrm{in}}{;\mathrm{Tch}}_{\mathrm{w},\mathrm{s}}\right)\end{array}$

(9)${\mathrm{Pch}}_{\mathrm{n},\mathrm{i}}\begin{array}{cc}=& \mathrm{f}\left({\mathrm{Tc}}_{\mathrm{air},\mathrm{in}}{;\mathrm{Qch}}_{\mathrm{n},\mathrm{i}}\right)\end{array}$

The total cooling load supplied by the chiller plant, composed of n chillers, as well as the total electrical energy consumption are given by Equations (10) and (11), respectively.

(10)${\mathrm{Qch}}_{\mathrm{N},\mathrm{i}}\begin{array}{cc}\le & {\displaystyle \sum _{\mathrm{k}=1}^{\mathrm{n}}\left({\mathrm{Qch}}_{\mathrm{n},\mathrm{i}}\right)}\begin{array}{cc}& \mathrm{n}\in \mathrm{N}\end{array}\forall ,\mathrm{n}\ge 2\end{array}$

(11)${\mathrm{Pch}}_{\mathrm{N},\mathrm{i}}\begin{array}{cc}\le & {\displaystyle \sum _{\mathrm{k}=1}^{\mathrm{n}}\left({\mathrm{Pch}}_{\mathrm{n},\mathrm{i}}\right)}\begin{array}{cc}& \mathrm{n}\in \mathrm{N}\end{array}\forall ,\mathrm{n}\ge 2\end{array}$

Equation (12) describes the cooling load that the plant delivers to the building as constrained according to the thermal demand of the building. This also influences the total number of chillers in operation, whose constraint is shown in Equation (13).

(12)${\mathrm{CL}}_{\mathrm{i}}\begin{array}{cc}\le & {\displaystyle \sum _{\mathrm{k}=1}^{\mathrm{n}}\left({\mathrm{Qch}}_{\mathrm{n},}{}_{\mathrm{i}}\right)}\begin{array}{cc}& \mathrm{n}\in \mathrm{N}\end{array}\forall ,\mathrm{n}\ge 2\end{array}$

(13)$Nc=\{\begin{array}{c}Nc=n-1\begin{array}{cc}& {if(Cl}_i-{Qch}_i)\le 0\begin{array}{cc}& then\{\begin{array}{c}{Ch}_{1,i}\begin{array}{cc}& sj=1(on)\end{array}\\ ⋮\\ {Ch}_{n,i}\begin{array}{cc}& sj=0(off)\end{array}\end{array}\end{array}\end{array}\\ Nc=n\begin{array}{cc}& {if(Cl}_i-{Qch}_i)>0\begin{array}{cc}& then\{\begin{array}{c}{Ch}_{1,i}\begin{array}{cc}& sj=1(on)\end{array}\\ ⋮\\ {Ch}_{n,i}\begin{array}{cc}& sj=0(off)\end{array}\end{array}\end{array}\end{array}\end{array}\begin{array}{cc}& Sj\in \left\{0;1\right\}\end{array}$

The chilled-water supply temperature range is set according to Equation (14):

(14)${\mathrm{T}}_{\mathrm{chw},\mathrm{s}}\left({}^{\mathrm{o}}\mathrm{C}\right)\in {\mathrm{N},\mathrm{T}}_{\mathrm{chw},\mathrm{s}}=7\dots 13$

The “on” and “off” interval status to be analyzed is defined with the variable sj. Equation (15) defines the constraint denoted to the minimum range between the activation and deactivation time of a chiller to avoid too many on/off cycles. Chang et al. [32] recommended that the minimum time between the activation and deactivation of a chiller needs to be between 30 min and 1 h. In [33], Witkowski gives a similar range.

(15)$\mathrm{Sj}=\mathrm{f}\left\{{\mathrm{CL}}_{\left(\mathrm{i}\right)}\left(\mathrm{kW}\right)=\mathrm{m}á\mathrm{x}\left[{\mathrm{CL}}_{\left(\mathrm{t}-1\right)}{ :\mathrm{CL}}_{\left(\mathrm{t}\right)}\right]\begin{array}{cc}& \mathrm{t}\in \mathrm{N}, \mathrm{t}=1\dots .24\end{array}\right\}$

The constraints of the typical sequencing chiller strategy can be summarized as follows:

• Step 1: If cooling load CL_i ≤ Qch₁, then chiller 1 satisfied the system load (with Qch₁ > Qch₂);

• Step 2: If Cl_i > Qch₁, then chiller 1 provided the full cooling load and the remaining thermal demand was provided by chiller 2;

• Step 3: If Cl_i ≥ Qch₁ + Qch₂ +…Qch_n+, then chillers Ch₁, Ch₂,…, Ch_n were turned on (in which Qch₁ > Qch₂> … > Qch_n).

2.3.2. Optimal Chiller Loading and Optimal Chiller Sequence Staging Approach: Co-Design of Chiller Plant Approach

The chiller energy performance simulation is considered an optimal chiller sequence staging approach [18]. This study combined the four OCS strategies defined, the total cooling load-based sequencing control, and the direct power-based sequencing control. To ensure optimal results and to avoid an incorrect designation of the partial load ratio (PLR) value, as only one chiller can satisfy the thermal needs of the system without the use of two or more units, a strategic baseline was built, as is shown in Figure 4. The chillers were arranged from lowest to highest according to their individual cooling capacity, defined by the variable (Qchi).

The sequencing chiller strategy shown in Figure 4 can be summarized as follows:

• Step 1: If CL_i ≤ Qch_1,i, then chiller 1 satisfied the system load;

• Step 2: If Qch_1,i < CLi ≤ Qch_2,i, then chiller 2 met system load;

• Step 3: If (Qch_1,i + Qch_2,i) ≤ CLi ≤ Qch_n−1,i, the OF of chillers 1 and 2 was optimized and derived from the optimal load problem, and the results were quantified. The results were compared with the electrical power consumption of the chiller (n − 1). If (Pch_1,i + Pch_2,i) < Pch_n−1, chillers 1 and 2 were turned on. If not, chiller n − 1 turned on;

• Step 4: If CL_i≥ Qch_1,i + Qch_2,i +… Qch_n,i, then chillers 1, 2,…, n were turned on. OF was optimized for chillers 1,2,…, n.

The conditions in which the chillers operated were defined depending on the cooling demand. Therefore, the number of chillers in operation was adjusted according to the fluctuation of the thermal demand using an optimization algorithm, which allowed minimizing the required cooling capacity and energy consumption. The main goal of the optimization procedure is to maintain the comfort levels of the facility with the lowest energy consumption of the chiller plant. As an initial stage, the system (chiller plant) is decoupled, in order to analyze only the direct interaction between the chiller plant and the thermal demand of the building. The OCL problem to be solved is classified as a nonlinear optimization problem with constraints and a combinatorial optimization problem with continuous, discrete, and binary variables.

Each analyzed period was solved simultaneously and determined the on/off status, PLR_i; Pch_i, and COP_i for each chiller. OCS complemented the OCL expressed in the objective function (OF) (Equation (16)), and the constraints (Equations (17)–(20)) complemented the variable decision PLR (Equation (21)), shown below.

Objective function (OF) is as follows:

(16)$\min \mathrm{PLR}\left\{\left({\displaystyle \sum }_{\mathrm{j}=1}^{\mathrm{n}}\left({\mathrm{a}}_0+{\mathrm{a}}_1\left(\frac{{\mathrm{CL}}_{\mathrm{i}}{\mathrm{PLR}}_{\mathrm{i}}}{{\mathrm{m}}_{\mathrm{i}}\mathrm{Cp}}+{\mathrm{T}}_{\mathrm{chw},\mathrm{s}}\right)+{\mathrm{a}}_2{\mathrm{Tc}}_{\mathrm{air}}\right)\right)+\left(\left|{\mathrm{Q}}_{\mathrm{ch},\mathrm{m}á\mathrm{x}}-{\displaystyle \sum }_{\mathrm{j}=1}^{\begin{array}{c}\\ \mathrm{n}\end{array}}\left({\mathrm{Qch}}_{\mathrm{i},\mathrm{n}}{\mathrm{PLR}}_{\mathrm{i}}\right)\right|\right)+\left(\frac{\mathrm{n}}{{{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{n}}\mathrm{COP}}\right)\right\}\mathrm{sj}$

OF is subject to the following:

(17)${\mathrm{CL}}_{\mathrm{i}}\begin{array}{cc}\left(\mathrm{kW}\right)\le & {\displaystyle \sum _{\mathrm{k}=1}^{\mathrm{n}}\left({\mathrm{Qch}}_{\mathrm{i}}{\ast \mathrm{PLR}}_{\mathrm{i}}{}_{}\right)}\begin{array}{cc}\left(\mathrm{kW}\right)& \mathrm{n}\in \mathrm{N}\end{array}\forall ,\mathrm{n}\ge 2\end{array}$

(18)${\mathrm{T}}_{\mathrm{chw},\mathrm{in}}\left({}^{\mathrm{o}}\mathrm{C}\right)\in {\mathrm{N},\mathrm{T}}_{\mathrm{chw},\mathrm{in}}=7\dots 13$

(19)${\mathrm{CL}}_{\left(\mathrm{i}\right)}\left(\mathrm{kW}\right)=\mathrm{m}á\mathrm{x}\left[{\mathrm{CL}}_{\left(\mathrm{t}-1\right)}{ :\mathrm{CL}}_{\left(\mathrm{t}\right)}\right]\begin{array}{cc}& \mathrm{t}\in \mathrm{N}, \mathrm{t}=1\dots .24\end{array}$

The value of the PLR variable in Equation (20) determines the on/off status, which is a difference between the individual chiller staging and the strategy shown in Section 2.2.

(20)${\mathrm{S}}_{\mathrm{j}}=\{\begin{array}{c}\begin{array}{cccc}\mathrm{if}& \mathrm{PLR}=0& \mathrm{then}& {\mathrm{S}}_{\mathrm{j}}=0\begin{array}{c}\left(\mathrm{off}\right)\end{array}\end{array}\\ \begin{array}{ccccc}\mathrm{if}& 0<\mathrm{PLR}\le 1& \mathrm{then}& {\mathrm{S}}_{\mathrm{j}}=1& \left(\mathrm{on}\right)\end{array}\end{array}\mathrm{Sj}\in \left\{0;1\right\}$

In OCL and OCS problems, the literature commonly uses the PLR as a decision variable, as can be seen in different papers [34,35,36,37]. The theoretical (PLR_n,i) of each chiller is as shown in Equation (21).

(21)${\mathrm{PLR}}_{\mathrm{n},\mathrm{i}}=\frac{{\mathrm{CL}}_{{}_{\mathrm{i}}}}{{\mathrm{Qch}}_{{}_{\mathrm{i}}}}$

For the OCL solution, a genetic algorithm (GA) was used. GA is a metaheuristic method offering an optimal solution to an optimal combinatorial problem, which has many possibilities for a solution. The variables to be processed were the decision variable (PLR_n,i) of the chiller unit and the arrangement of the chiller working in parallel.

After the variables were encoded into chromosomes, the information built into the chromosomes was the total PLRs of the units running in parallel. A GA flowchart for OCL problems is presented in Figure 5.

3. Case Study

The methods described in the previous subsections applied to a hotel being built in Cienfuegos (Cuba) and involving three functional areas: rooms, public areas, and service areas. The room area has 87 rooms, 45 of which are part of the main building and 42 of which are individual modules and cabins. One of the functional areas includes public areas, such as a lobby designed with natural air ventilation, a gift store, a specialized restaurant, a kitchen, and a nightclub. Finally, the service area, including different office modules, was also considered in the total cooling chiller plant capacity. The main characteristics of the functional areas are summarized in Table 1.

For the cooling demand analysis of the facility, the thermal properties of the hotel walls were obtained from TRNSYS 16 library [22] and are listed in Table 2.

The detailed composition of each functional area, the thermal properties of their construction materials, the heat gains deriving from occupation, and the use of equipment were considered (Table 3 and Table 4).

The hotel design criteria were establishing according to thermal inside comfort Cuban standard NC 217:2002 [38].

Using TRNSYS 16, the standard procedure for thermal demand analysis recommended in ASHRAE Fundamentals [2] was applied, taking into consideration the worst operating conditions scenario at the hotel and other future operating scenarios that reflected the great variation in the nature of activities in the facility.

Different cooling profiles suggest the need for energy efficiency measures to mitigate the different occupancy levels of the hotel. In addition, this analysis considered the occupancy and employment patterns of a hotel in operation (from the same hotel chain) based on a previous study [19,22,39,40]. Furthermore, the hotel featuring these partners was characterized by a service disruption between 10:00 am and 4:00 pm (defined as transit hotel classification). The occupied room indicator (Hdo) fluctuated according to the tourist season from low occupancy (Hdo ≤ 10%) to medium occupancy (45% ≤ Hdo ≤ 50%) to high occupancy (75% ≤ Hdo ≤ 90%) to full hotel occupancy (Hdo = 100%). Therefore, several cooling load profiles (ki) in the functional areas, i.e., the rooms, public areas, and service areas, were implemented.

In addition, for the ki calculation:

• (1). The concept of a “partially loaded” room (unoccupied rooms which were kept at 26 °C by an air conditioner) was applied [32].

• (2). Different occupancy rates between 10%, 50%, 75%, and 100% for the hotel in the rooms and public areas were considered.

• (3). The load diversity through occupancy strategies was eliminated using the lowest-thermal-demand rooms for occupancy rates of 75% and 50%.

Six chiller plants with an arrangement of two air-cooled screw-type water chillers were proposed to be installed in the hotel; see Table 5. The primary circuit was characterized by a constant chilled-water mass flow rate. The installed cooling capacity varied between 538 kW and 589 kW, representing the common practice of a load safety factor between 10% and 20% of the total installed capacity (as recommended in [2]). The plant configurations are presented in Table 5.

Using the manufacturer’s data set of the chillers selected, the mathematical models that represent the Qch and Pch, using Equations (1) and (2), were determined through the least-squares method. The regression coefficients and the quality of the black box models were defined using the software Eviews 12 [41]. The results of the adjustability as well as the quality of the models are shown in Table 6.

In the performed tests, the p-value for compliance with the null hypothesis was ≥ 0.05. It was observed that the selected models fulfilled the established statistical assumptions. The selected models did not fulfil the assumption of the nonexistence of autocorrelation. This is a consequence of the cyclical nature of the data used for their construction. Finally, the fourth assumption, i.e., the null hypothesis that dictated normality in the data, was fulfilled as well. It is emphasized that this is an inviolable requirement of regression.

The regression coefficients of each of the investigated chiller plant configurations, as well as the results of the adjustment measurement, are shown in Table 7. It was found that they have a high explanatory percentage with an R² above 99% and lower values of MAE and AIC. Considering these results and considering that the violation of the third assumption did not invalidate the estimators obtained by the least-squares method, this can establish that the regression coefficients (x₀, x₁, x₂; a₀, a₁, a₂) and the chillers’ black box models obtained are unbiased, consistent, and efficient.

4. Results and Discussion

The cooling thermal demand of each feasible scenario was calculated according to the elements and design criteria exposed in Section 3. The thermal profiles k₁ and k₂ are the critical scenarios of the hotel, i.e., the maximum demand and minimum demand, respectively. The other thermal profiles simulate different occupation scenarios and activity levels which could occur in the hotel. The eight load profiles of the hotel were generated using TRYNSYS 16 [22]. The time interval for the analysis was 24 h in a typical summer day profile, obtained using METEONORM data [42]. For each thermal zone, a graphical interface was built into the program. For the infiltration gains, a factor of 0.8 was assumed. The convection/radiation fraction of the heat gain due to the use of electronic equipment was 0.3/0.7.

The simulation in TRNBuild [22] was carried out using the power level control, while the cooling loads of the building were calculated considering the information above. The results of the demand load values are shown in Table 8.

For the comparison of the energy performance of the chiller plants presented in Table 5 with the eight thermal demand profiles calculated in Section 3, Equations (1)–(3) were used by substituting the correlation coefficients listed in Table 7 and setting a fixed temperature setpoint value equal to 7 °C. In addition, the ambient temperature profile corresponding to the same day when the thermal demand was calculated was extracted. Subsequently, the mathematical algorithm described by Equations (12)–(15) was implemented using MATLAB 2018 [43]. The on/off schedule of each chiller plant and the PLRi values of each chiller are shown in Figure 6 and Figure 7, respectively.

As shown in Figure 6, this operating staging forced the first chiller to always be running, regardless of the thermal demand. The second chiller covered the remaining demand if requested, regardless of the load regime to which it was subjected. Figure 7 describes this type of operation causing at least one of the chillers to work in a critical partial regime.

The total energy consumption as well as the average COP of each investigated chiller plant are listed in Table 9. According to the results, there were no significant differences in energy performance between the proposed chiller plant configurations. The highest energy consumption was given by the chiller plant configuration #6, which consumes 5.3% greater than the one offering the minimum consumption of electricity (chiller plant #5).

Using the traditional load-based sequencing methodology and without the application of optimization procedures, chiller plant configuration #5 was selected for the hotel facility, being the highest-performing.

For the energy performance of the chiller plants using the mathematical optimization shown in Equations (16)–(20), the same operating conditions used in the investigated hotel were employed. The principle of simultaneously reaching the optimum operating point of each chiller and the chiller plant was defined using the methodology depicted in Figure 4. For the evaluation of the objective function and the constraints, a genetic algorithm was used to adjust the control parameters (Table 10). MATLAB Simulink 2018 [43] was used for carrying out the evaluation.

The proposed procedure allowed identification of the optimal PLRi of each chiller at each demand point, through the established optimal sequence, the on/off status, and the number of chillers in operation. The on/off schedule and PLI-COP curve diagrams are shown in Figure 8 and Figure 9, respectively.

Figure 8 shows a marked difference between the operation of the chiller plant and the cooling demand profile obtained in Table 9, concerning the mode of operation shown in Figure 6. In this case, it can be seen how the staging sequencing of the chillers is adjusted to the individual cooling capacity and in correspondence to the specific cooling demand. This mode of operation has a positive influence on the individual efficiency of each chiller and in turn on the overall efficiency of the chiller plant, as shown in Figure 9.

Figure 9 demonstrates that the strategy designed for the chiller plant allows for a more efficient operating regime (range of the PLR greater than 0.5) for the chiller with the largest cooling capacity by sacrificing the efficiency of the chiller with the smallest cooling capacity. Table 11 shows the energy consumption and average COP values of all the chiller plant options. The results reveal that the best configuration was chiller plant configuration #1 (i.e., an asymmetric chiller plant with a cooling distribution of 33/67% and safety factor of 10.2%).

Considering that the GA tool provided an approximated result, three runs of the program were carried out to verify the results of the OCL and OCS optimization procedures. The results obtained were corroborated using the relative standard deviation (RSD). Table 12 reveals an RSD of less than 1%, proving the existence of a great fit in the control parameters of the GA.

As mentioned above, the results obtained revealed the following:

• The application of the traditional load-based sequencing methodology suggested the adoption of chiller plant configuration #5, which showed an energy consumption of 13,882.52 kWh and an average COP of 2.78.

• The implementation of the proposed optimization approaches suggested that the best option would be the adoption of chiller plant configuration #1 (asymmetric configuration, chiller cooling capacity distribution of 33/67%, safety factor of 10.2%), which showed an energy consumption of 10,446.25 kWh and an average COP of 4.44.

The proposed optimization procedures led the chillers operating in the investigated hotel to energy savings of about 24.8% and an increment in the average COP by about 59.7% compared with chiller plant configuration #5 selected by the traditional load-based sequencing methodology. In addition, the results obtained supported the adoption of asymmetric configurations rather than symmetric arrangements. In particular, it was observed that chiller plant configuration #5, which featured the best-performing arrangement in the energy analysis carried out under traditional staging and the cooling distribution recommended by the Cuban standard NC 220-3:2009 [44] (a requirement for building design companies), was actually the one with the worst energy performance after implementing the optimization procedures (Figure 10). However, the main conclusion of this research is that the use of the proposed approaches prevents engineers from making an incorrect decision regarding the chiller plant to be installed in a building. It is very important to keep in mind that in the design phase, it is not only enough to consider the installation of the most advanced system supported by an efficient control system. It is also necessary to analyze the future operating conditions as close to reality as possible, so that the design and the operation of the project are in line with each other.

5. Conclusions

Implementing energy-efficient chillers can significantly help in the fight against global warming. To promote the adoption of highly performing chillers for hotel facilities, this research studied the energy impact of the selection of the most appropriate chiller configuration for a Cuban hotel. Six different chiller plant combinations and two different approaches to evaluating their energy performance have been considered. The first methodology was based on the traditional staging approach that relies on the on/off principle, whereas the second procedure used a co-design principle and involved the solution to a mathematical optimization problem. The two selected optimization procedures were optimal chiller loading (OCL) and optimal chiller sequencing (OCS).

The energy simulation using the two approaches in the earlier chiller plant design stage for buildings demonstrated the following:

As regards the traditional principle of chiller on/off staging, the chiller plant with the best energy performance was the solution, featuring a symmetric configuration, chiller cooling capacity distribution of 50/50%, and a safety factor of 11.7%.

As regards the co-design approach with staging using OCL and OCS optimization procedures, the best energy performance was provided by the solution involving an asymmetric configuration, chiller plant #1 (featuring an asymmetric configuration, chiller cooling capacity distribution of 33/67%, and a safety factor of 10.2%), showing an energy consumption of 10,446.25 kWh and an average COP of 4.44. The approach based on mathematical optimization offers a reduction in energy consumption by 24.8% and an increase in COP by 59.7%.

Therefore, it can be concluded that both analyzed approaches lead to different results that imply selecting different configurations as optimal. However, in terms of practical issues, it is known that for the case study analyzed, the implementation of an automatic control system for the hotel air conditioning system was proposed. Therefore, the chiller plant that is best adapted to the future operation of the system was chosen through the co-design methodology. An erroneous selection of the chiller plant configuration can result in significant energy consumption, environmental impact, and economic losses. It is also highly recommended that different thermal load profiles are considered due to the diversity of cooling load demand scenarios that hotels face during the exploitation phase, and the energy performance analysis of the proposed chiller plant should be set under this premise.

However, the present research still has limitations that will be addressed in the future, such as the extension of the energy analysis to the rest of the secondary circuits of the chiller plant. In this way, it will be possible to determine more accurately the impact of the operating strategies on the whole chiller plant system. Another aspect that can enhance the analysis is the establishment of the OCS analysis through other approaches such as chilled-water return temperature-based (T-based) sequencing control or bypass flow-based (F-based) sequencing control, in which, although the energy savings are lower, they do not involve on/off chiller operating regimes, thus preserving the technology better.

Author Contributions

Conceptualization, Y.D.T. and P.G.; methodology, M.T.d.T.; software, Y.D.T., R.R.C. and J.G.S.; validation, Y.D.T., P.G. and R.R.C.; formal analysis, M.T.d.T. and H.H.H.; investigation, Y.D.T.; resources, Y.D.T., R.R.C. and J.G.S.; data curation, Y.D.T.; writing—original draft preparation, Y.D.T.; writing—review and editing, P.G., H.H.H. and J.I.S.O.; visualization, P.G.; supervision, P.G., H.H.H. and J.I.S.O.; project administration, H.H.H.; funding acquisition, P.G. and H.H.H. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The data presented in this study are available in: [19,20,25].

Conflicts of Interest

The authors declare no conflict of interest.

Nomenclatures

Annex 1: Nomenclature
a0, a1, a2	Correlation coefficients of the black box model of electrical power
BLR	Building load ratio
CI	Specific consumption index
CLi	Building cooling load for each interval of time i (kW)
Comb	Combinations of chiller plant
COP	Coefficient of performance
cp	Specific heat at constant pressure of water at 7 °C (kJ/(Kg·K))
GA	Genetic algorithm
Hdo	Occupied room indicator
ki	Simulation scenario
ṁ	Chilled-water mass flow (Kg/s)
nch	Total of chiller selected in each chiller plant
OCL	Optimal chiller loading
OCS	Optimal chiller sequencing
Pch	Power consumption of chiller (kW)
PLR	Partial load ratio
Qch	Cooling load for the chiller (kW)
Qcl	Total cooling load (kW)
Qchstd	Cooling capacity of the chiller at standard conditions according to manufacturer (kW)
Qcho	Cooling capacity of the reference chiller (kW)
Sj off	Stage off threshold
Sj on	Stage on threshold
Tc air,in	Condenser air inlet temperature (°C)
Tc hw,s	Chiller water supply temperature (°C)
Tc hw,r	Chiller water return temperature (°C)
x0, x1, x2	Correlation coefficients of the black box model of nominal cooling capacity
Subscripts
ch	Chiller water
i	ith
max	Maximum
min	Minimum
c	Condenser
in	Inlet
s	Supply
r	Return

Footnotes

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Figures and Tables

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Figure 1. A traditional methodology for designing the primary circuit of centralized chiller/heat pump plants [3].

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Figure 2. Cooling load-based chiller sequencing representation of the traditional principle of chiller on/off staging. Reprinted/adapted with permission from Ref. [9].

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Figure 3. The general framework of the decoupled chiller plant.

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Figure 4. Baseline schedule of OCS strategy [18].

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Figure 5. General GA flowchart for OCL problems.

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Figure 6. On/off schedule of chiller plant options using the traditional on/off approach of chiller staging.

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Figure 6. On/off schedule of chiller plant options using the traditional on/off approach of chiller staging.

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Figure 7. COP-PLR curves of chiller plant configuration ns.

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Figure 8. On/off schedule of chiller plant options using the optimized on/off principle of chiller staging.

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Figure 8. On/off schedule of chiller plant options using the optimized on/off principle of chiller staging.

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Figure 9. COP-PLR performance curves of chiller plant options.

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Figure 10. Comparative analysis of the results obtained by different energy simulation approaches. (a) Energy consumption. (b) COP.

Table 1

Main characteristics of the functional areas of the hotel.

Type of Thermal Zone	Functional Areas	Thermal Zone ID	Type of Thermal Zone	Functional Areas	Thermal Zone ID
Top floor (East)	Rooms	1	Restaurant	Public areas	9
Top floor (West)		2	Cabaret		10
Top floor (Intermediate rooms)		3	Shops		11
Low levels (Intermediate rooms)		4	Double office	Service areas	12
Low levels (Intermediate rooms–east–west corner)		5	North office		13
Cabins (West corner)		6	South office		14
Cabins (East corner)		7	Intermediate office		15
Cabins (Intermediate rooms)		8

Table 2

Thermal properties of the hotel’s walls.

Wall Type	Nomenclature	Thermal Conductivity (W·m−2·K−1)	Overall Transmittance (W·m−2·K−1)	Material (Thickness (m))
Outwall	O	2.05954	11.40879	Concrete block (0.15); Cement+clay (0.02); Cement+clay (0.01)
Inwall	I	2.09029	11.67302	Brick (0.15); Cement+clay (0.01); Cement+clay (0.01)
Ground	G	3.40909	29.18919	Concrete (0.24); Ceramics (0.01); Cement+clay (0.01)
Roof	R	3.25960	26.31854	Concrete (0.24); Rasilla (0.02)
Window	W	5.8	5400	Single crystal (0.008)

Table 3

Thermal comfort features of main building rooms and cabins (room area).

Thermal Zone ID	Number of Rooms	Dimensions (m3)	Wall Type	Heat Gains
1	3	108	W(1); O (1); I (2); R(1);	Electronic appliances: 1643 WLighting: 13 W·m−2People: Max 3 guests (sensible/latent: 65/55 W)
2	3	108	W(1); O (1); I (2); R(1);
3	9	108	W(1); I (4);
4	18	108	W(1); I (3); G (1)
5	12	108	W(1); O (1); I (2); G(1);
6	3	111.38	W(1); O (1); I (1); R(1); G(1);
7	3	111.38	W(1); O (1); I (1); R(1); G(1);
8	36	111.38	W(1); I (2); R(1); G(1);

Table 4

Thermal comfort features of public areas and service area.

Thermal Zone ID	Number of Rooms	Dimensions (m3)	Wall Type	Heat Gains
9	1	951.34	W(2); O (2); R(1); G(1);	Electronic appliances: 21,080 WLighting: 16 W·m−2Max 58 guests (sensible/latent: 65/55 W)Max 9 employees (sensible/latent: 75/55 W)
10	1	1463	O (2); R(1); G(1)	Electronic appliances: 7317.61 WLighting: 10 W·m−2Max 500 guests (sensible/latent: 90/160 W)Max 9 employees (sensible/latent: 65/55 W)
11	2	111.38	W(2); O (2); R(1); G(1);	Electronic appliances: 700 WLighting: 13 W·m−2Max 12 guests (sensible/latent: 65/55 W)Max 3 employees (sensible/latent: 75/55 W)
12	3	47.73	W(1); O (1); I(1); R(1); G(1);	Electronic appliances: 413 WLighting: 13 W·m−2Max 2 employees (sensible/latent: 63/52 W)
13	1	23.4	W(1); O (1); I(1); R(1); G(1);
14	1	23.4	W(1); O (1); I(1); R(1); G(1);
15	4	23.4	W(1); R(1); G(1); I(2);

Table 5

Chiller plant configurations.

Chiller Plant Configuration	*(kW)	*(kW)	Chiller Cooling Capacity Distribution (%)	Total Cooling Capacity (kW)	Safety Factor
1	180.1	357.8	33/67	537.92	10.2
2	198.7	357.8	36/64	556.59	14.1
3	201.6	357.8	36/64	559.82	14.7
4	228.9	310.6	42/58	539.53	10.6
5	271.2	271.2	50/50	542.46	11.7
6	271.2	310.6	47/53	581.85	19.2

* Chiller cooling capacity in standard conditions (STD): chilled-water supply/return of 7/12 °C, air temperature at the condenser inlet of 32 °C.

Table 6

Quality measurement of the selected chiller black box models [41].

Diagnostic Test	t Student	White	Breusch–Godfrey	Jarque–Bera
Stadígraph	−7.822 × 10−14	10.947	29,046	4.152
p-value	0.990	0.952	4.929 × 10−7	0.125

Table 7

Regression coefficients and fitting measurements of the models.

Chiller Cooling Capacity at STD	ṁ (kg·s−1)	Cooling Capacity Model						Electrical Power Model
		Regression Coefficients			Fitting Measurements of the Models			Regression Coefficients			Fitting Measurements of the Models
		x0	x1	x2	R2	MAE	AIC	a0	a1	a2	R2	MAE	AIC
180.1	8.67	203.1	−2.30	7.21	99.6	1.08	0.32	19.55	0.84	0.24	99.0	0.60	0.40
198.7	9.56	221.0	−2.42	7.91	99.7	0.97	0.28	22.93	0.92	0.33	98.8	0.74	0.40
201.6	9.72	226.0	−2.51	8.07	99.7	1.04	0.29	22.69	0.93	0.37	98.9	0.71	0.39
228.9	11	257.0	−2.87	9.12	99.8	0.93	0.27	24.57	1.18	0.26	98.8	0.96	0.40
271.2	13	302.7	−3.37	10.9	99.6	1.64	0.32	30.15	1.29	0.37	99.0	0.93	0.40
310.6	14.9	345.3	−3.80	12.4	99.7	1.51	0.27	34.96	1.39	0.53	98.8	1.10	0.41
357.8	17.2	403.5	−4.55	14.2	99.6	2.15	0.32	39.07	1.68	0.47	99.1	1.18	0.40

Table 8

Cooling load demand values of the 8 analyzed profile schedules.

Time (h)	Cooling Load Demand Values Cli (kW)
	k1	k2	k3	k4	k5	k6	k7	k8
01:00	387.74	96.04	345.74	289.30	241.30	154.79	146.45	142.45
02:00	387.38	90.41	345.50	293.56	240.44	154.19	150.38	141.26
03:00	347.84	84.47	308.20	255.96	203.32	117.04	112.93	104.29
04:00	342.10	79.59	300.86	248.02	195.66	109.07	104.52	96.36
05:00	340.69	76.32	299.47	245.88	194.00	107.80	102.50	94.82
06:00	339.16	73.67	299.01	245.12	193.56	105.96	100.58	93.42
07:00	338.36	85.59	321.25	259.69	208.61	196.54	180.10	170.42
08:00	337.45	94.15	324.88	261.63	211.11	156.40	137.89	128.37
09:00	383.76	105.42	339.18	273.98	223.42	150.03	132.46	125.50
10:00	388.71	115.99	337.89	270.96	220.60	148.47	129.14	122.38
11:00	415.22	120.71	347.08	290.72	239.84	150.19	141.46	134.18
12:00	436.97	147.52	388.49	325.39	274.35	239.18	227.26	223.02
13:00	456.91	166.02	410.54	344.90	293.54	207.44	193.01	188.45
14:00	473.62	179.50	427.18	361.45	309.25	223.27	208.75	203.35
15:00	483.59	187.89	425.09	357.58	304.90	220.91	204.77	199.09
16:00	488.26	192.69	429.24	362.48	309.00	225.00	209.61	203.13
17:00	487.54	182.40	417.64	362.43	307.99	315.73	264.88	214.84
18:00	476.32	171.97	402.85	349.18	293.42	224.23	215.08	200.12
19:00	439.19	165.65	402.86	356.05	299.13	278.36	276.51	260.79
20:00	424.56	168.73	410.88	345.47	288.27	232.83	212.25	196.05
21:00	418.87	158.23	406.21	340.41	283.37	227.59	206.81	190.97
22:00	411.23	129.84	384.29	333.80	277.40	206.63	200.85	185.45
23:00	399.14	115.54	358.72	306.89	251.49	181.54	174.26	159.66
00:00	401.53	105.80	360.86	309.27	254.51	183.68	176.64	162.68

Table 9

Energy consumption and average COP values of the investigated chiller plant options.

Chiller Plant Configuration	Energy Consumption (kWh)	Average COP
1	14,088.54	2.43
2	14,187.96	2.35
3	14,162.84	2.22
4	14,186.33	2.68
5	13,882.52	2.78
6	14,619.42	2.53

Table 10

GA control parameters.

Population size	150.00
Selection operator	uniform stochastic
Reproduction: elitism	2.00
Crossover factor	0.80
Mutation uniform	0.01
Crossover heuristic	1.50

Table 11

Energy consumption and average COP values of chiller plant options.

Chiller Plant Configuration	Energy Consumption (kWh)	Average COP
Chiller plant #1	10,446.251	4.491
Chiller plant #2	10,681.532	4.312
Chiller plant #3	10,696.964	4.304
Chiller plant #4	10,596.201	4.481
Chiller plant #5	11,953.838	3.872
Chiller plant #6	11,707.874	3.991

Table 12

Results obtained with the GA tool.

Chiller Plant Configuration	Test 1	Test 2	Test 3	RSD (%)
1	10,446.25	10,446.29	10,446.25	0.02
2	10,681.53	10,681.51	10,681.55	0.02
3	10,696.96	10,696.82	10,696.90	0.07
4	10,596.20	10,595.67	10,594.91	0.61
5	11,953.83	11,953.83	11,953.83	0.00
6	11,707.87	11,708.70	11,709.26	0.60

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