Hybrid (Optimal) Selection Model for Phase Change Materials Used in the Cold Energy Storage of Air Conditioning Systems

Abstract

The latent heat storage of phase change materials (PCMs) can be used in refrigeration and air conditioning systems. Storing cool energy during the nighttime (off-peak hours) and releasing the cool energy during the daytime (on-peak hours) to reduce the number of starts of the chiller and pumps is a practical approach for achieving energy saving and carbon reduction. Therefore, selecting PCMs is vital for improving energy efficiency and preventing future energy shortages. However, selecting PCMs is complicated by their unique characteristics and types. The purpose of this study was to establish a PCM selection model by combining the Delphi, analytic hierarchy process (AHP), and VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) methods to select the optimal PCM type applied in cold storage. A numerical example was used to verify the model’s usability, confirming that A9 is the optimal PCM for the cold storage of an air conditioning system. This three-stage PCM selection model combining the Delphi, AHP, and VIKOR approaches provides a more suitable selection model and considers the selection method of material criteria. Moreover, it can solve the problem of difficult PCM selection. Simultaneously, it considers mechanisms to incorporate a company’s primary considerations into material selection for real-world applications. These results can facilitate material evaluation and selection during system design and material qualification, helping companies achieve the goals of energy saving, carbon reduction, and sustainable management in the future.

1. Introduction

Refrigeration and air-conditioning systems share a remarkably high proportion of energy consumption, especially in building sectors that need air conditioning to maintain temperature [1]. Reducing the energy consumption of air conditioning and minimizing the use of fossil fuels for power generation are most critical for the environment. One practical solution for improving the performance of air conditioning is to use phase change materials (PCMs), which apply the characteristics of latent heat storage to maintain a stable internal temperature when the phase state changes [2]. Air conditioning systems using PCMs can save up to 35% on energy and store up to 89 percent of daily cooling load when compared to traditional air conditioning systems [3]. The practical use of PCMs is to supply the appropriate cooling to the air conditioner’s loading area while reducing the chiller and pump start-up frequency to conserve electricity. The primary premise of energy conservation with PCM cold storage is to shift the power use of an air conditioning system from on-peak (daytime) hours to off-peak hours (during nighttime) [4]. However, PCMs have many unique characteristics and applications, so the selection criteria and methods of PCMs are critical for energy saving and carbon mitigation in sustainable management.

To solve the problem of material selection, multi-criteria decision making (MCDM) is one of the most popular techniques [5]. Many researchers propose suitable material selection methods when studying PCMs. In selecting PCMs for construction, Imghoure et al. used the analytic hierarchy process (AHP) to select the optimal PCM from five PCMs and simulated them with a numerical model. The comparison of the results between the two was consistent [6]. Similarly, Socaciu et al. suggested the AHP method when choosing PCMs for building comfort applications. The optimal choice was made from eight PCMs [7]. Oluah et al. suggested the utilization of the entropy weight method (EWM) in conjunction with the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) approach for the purpose of choosing the most appropriate phase change material (PCM) [8]. Xu et al. proposed the combination of AHP and TOPSIS to select PCMs for latent heat storage [9]. Nicdalde et al. compared different methods when selecting PCMs for vehicle roofs, including AHP, VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR), TOPSIS, and COmplex PRoportional ASsessment (COPRAS) [10]. The results demonstrated that COPRAS and TOPSIS have high levels of correlation.

These studies propose several multi-criteria decision making (MCDM) methods for selecting PCMs in various fields. However, there is no relevant research on selecting cold storage PCMs. Moreover, these studies predominantly use MCDM as the material selection method, but the selection criteria only consider the physical properties of PCMs and the method for criteria selection is not mentioned. Furthermore, some relevant criteria for practical applications, such as toxicity, flammability, cost, and corrosion, do not provide a selection method. Therefore, in addition to establishing a selection model, the purpose of this study is to provide a modified model to enhance the selection of PCMs and be used in selecting materials for actual PCM applications. Consequently, PCMs can be used in air conditioning systems to achieve energy saving and carbon mitigation benefits.

1.1. Phase Change Material (PCM)

A phase change material (PCM) serves as a substance for latent heat storage, capable of capturing and releasing thermal energy while undergoing constant-temperature phase transitions over a wide spectrum of temperatures [11,12]. Depending on their phase changes, PCMs can be categorized into solid–liquid, solid–gas, liquid–gas, and solid–solid [13,14]. Because other forms of PCMs have technical restrictions such as lesser latent heat capacity and super cooling problems, solid–liquid PCMs are more appropriate for practical usage [15]. There are different melting point ranges for commercial PCMs on the market. The three most widely used categories are eutectic, inorganic, and organic [16,17,18].

Inorganic phase change materials (PCMs) offer benefits such as a greater heat of fusion, a constant melting temperature, excellent thermal conductivity, and minimal volume alterations during phase transition. They are predominantly employed for PCMs designed for moderate- and lower-temperature applications. However, general salt-type inorganic PCMs are prone to “overcooling” and “phase separation” when recycled [19]. Organic PCMs are not prone to “overcooling” and “phase separation”. They have the advantages of less corrosiveness, stable performance, and more solid molding. However, they have low thermal conductivity, low material density, volatility, significant loss, insufficient heat storage capacity per unit volume, high price, flammability, and other defects, reducing the efficiency of the heat storage system and limiting its application [20]. Inorganic or organic PCMs can be converted into organic–inorganic composite PCMs for practical use to address their shortcomings when used alone and achieved the optimal application effect [21,22].

1.2. Basic Principle of Phase Change Material

When a PCM melts, it undergoes a transition from a solid state to a liquid state. Throughout the phase transition procedure, the material can absorb a large amount of heat energy at an almost constant temperature. When the PCM freezes and solidifies, the opposite occurs: it releases the heat it absorbs [23,24]. Different materials that melt and solidify at different temperatures can absorb different amounts of heat energy.

PCMs are useful because they melt and solidify at a specific pressure and fixed temperature, making them suitable for temperature control in several applications. Compared with sensible heat energy materials, PCMs that melt and absorb heat are more efficient in absorbing heat energy. Accordingly, compared with using materials that do not change phase, the quantity of material required for PCMs to store the same amount of thermal energy is much less.

1.3. Desired Properties of PCMs for Cold Storage

The phase change temperature of PCMs used for cold storage is in the range of 7–14 °C. The primary applications for PCMs are food preservation, material transportation, construction, and air conditioning [22]. Frigione et al. suggested that when considering possible PCM candidates, some characteristics such as thermophysical, chemical, environmental, and economic properties must be considered [25]. The desired characteristics from the literature are listed in

Table 1. Required phase change material properties.

Category	Requirements	Literatures
Thermal–Physical Properties	Suitable phase change temperature	[7,10,20,25,26,27]
	High value of the latent heat of fusion	[7,10,20,25,26,27,28,29]
	High thermal conductivity	[7,10,20,25,26,27,28,29]
	High value of specific heat capacity	[7,25,26,28,29]
	Thermally reliable	[25]
	Cycling stability	[20]
	Little subcooling	[20,27]
	Large density	[7,27,28,29]
Chemical Properties	Chemically stable	[20,25,27,29]
	Non-toxic	[25,26,27,29]
	Non-flammable	[25,26,29]
	Non-explosive	[25,26,27]
	Corrosion-resistant	[25,26,27,29]
Kinetic Properties	High rate of nucleation	[25,26,29]
	High rate of crystal growth	[25,26,29]
	High melting rate	[27]
Environmental Properties	Low environmental impact	[25]
	Non-polluting during service life	[25,26]
	Easy recycling and treatment	[25,26]
Economic Properties	Cost-effective	[20,25,26,27,28,29]
	Commercially available	[25,26,29]
Technical Properties	Low vapor pressure	[20]
	Small volume change	[20,26,27,29]
	Compatibility with other materials	[25]

.

1.4. PCM Application for the Cold Storage of Air Conditioning

Said and Hassan investigated a physical model for improving the cooling efficiency of conventional air conditioners by utilizing PCM plates. The model consists of a rectangular duct containing six PCM plates, a centrifugal fan, an electric heater, a variable speed controller, a variable DC power supply, and an AC unit. The PCM plates are coupled with the condenser of the AC unit and use the cold ambient air at night to solidify and store cold energy. During the day, the hot ambient air is cooled by passing over the solidified PCM plates before entering the condenser, thus reducing the condensing temperature and increasing the coefficient of performance (COP) of the AC unit. This study investigated the effect of different PCM plate configurations, inlet air velocities, and temperatures on the charging and discharging processes of the PCM, as well as the performance of the AC unit [30].

Omara et al. proposed an air conditioning system combined with PCM storage to improve efficiency. This system is comprised of tanks that store PCM and ice-cold substances, refrigeration units, and cooling units. The system functions as follows: Initially, when the return water temperature in the ice tank falls to 8 °C, the PCM tank initiates the storage of thermal energy, causing the PCM to undergo solidification, while the ice tank delivers cooling to fulfill the load demands. Simultaneously, when the return water temperature in the ice tank reaches 14 °C, the PCM tank ceases its cooling storage, and the ice tank is recharged via a heat transfer fluid (HTF). The return water temperature in the ice tank rises with the decreasing building temperature. When the return water temperature reaches 14 °C, and the ice tank alone cannot meet the cooling needs, both the ice tank and the PCM tank start to release cooling to provide for the users. In the third scenario, when the building’s load diminishes, the ice tank exclusively supplies cooling to the building [3].

Zhai et al. suggested a cold-storage solar air-conditioning system. The main components of this system are solar collectors, an absorption chiller, an air handling unit (AHU), a latent heat storage unit, and a dry cooling system. Solar collectors transform solar radiation into thermal energy to drive the absorption chiller. The absorption chiller generates chilled water for the air handling unit (AHU) to provide space cooling. The latent heat storage unit consists of a heat exchanger filled with PCMs. The PCMs can store the excess heat from the solar collectors during the day and release it to the absorption chiller during the night, thus reducing the cooling load on the dry cooling system so that the dry cooling system can be switched off to save water and energy. The components are linked or connected by pipes, valves, pumps, and controllers, which regulate the flow and temperature of the working fluids (water, refrigerant, and PCM) according to the system operation mode and the cooling demand [27].

These studies illustrate that PCMs are helpful for peak load shifting and improving the performance of air conditioning systems by using different configurations and switching control. Therefore, PCMs are effective for reducing energy consumption and saving the electricity cost of air conditioning systems.

2. Material and Methods

2.1. PCMs for the Cold Storage of Air Conditioning Systems

In this study, the 17 PCMs used for cold storage were obtained based on a literature review and supplier survey. The types, performances, and characteristics of the materials are presented in

Table 2. PCM types and performances for cold storage.

PCM Component or Type	Phase Change Temperature (°C)	Heat of Fusion (KJ/kg)	Thermal Conductivity (W/m K)	Density (kg/m3)	Specific Heat Capacity (KJ/kg K)	Literature
Na2SO4, H2O, NaCl, NH4Cl	7.5	121	0.55 (liquid), 0.70 (solid)	1490	–	[31]
Na2SO4·10H2O, NaCl, NH4Cl, Na2B4O7·10H2O, NH4Br	9.5–10 (melting point) 8.0 (freezing point)	179, 122 (after 100 recycles)	0.75 (liquid), 0.93 (solid)	1470	–	[31]
S7	7	150	0.4	1700	1.85	PCM products
S8	8	150	0.44	1475	1.9	PCM products
S10	10	155	0.43	1470	1.9	PCM products
SP	8	182	0.8	1503	1.8	MGEC
A6	6	185	80	768	2.17	PCM products
A6.5	6.5	190	82	770	2.18	PCM products
A7	7	190	82	770	2.18	PCM products
A8	7	180	77	770	2.16	PCM products
A9	9.5	190	82	770	2.16	PCM products
E8	8	140		1469	0.67	PCM Products
E7	7	120		1542	0.62	PCM Products
C7	8	135	0.78	1400	1.4	ClimSel
C10	6–11	32–116	0.83	1400	1.6	ClimSel
OM08	7	175	0.235	1190	1.71	Pluss Tech.
PureTemp 8	8	178	0.22	0.86	1.85	PureTemp

. The primary physical phase properties are change temperature, latent heat capacity, thermal conductivity, and density.

2.2. PCM Selection Model for Cold Storage

Selecting materials is related to the success of design and application—often regarded as the most critical process for qualifying advanced product quality and performance to meet the design goal. Many scholars have proposed various methods for selecting PCMs such as AHP [6], TOPSIS [9], and VIKOR [10]. Although these scholars have provided useful methods for selecting phase change materials, the methods for criteria selection were not mentioned. Therefore, how to select criteria and combine these methods to enhance PCM selection has become extremely important. The criteria for PCM selection may include physical property criteria, chemical property criteria, environmental property criteria, economic property criteria, dynamic property criteria, and technical property criteria. Moreover, the TOPSIS method identifies the solution that is nearest to the ideal solution and farthest from the worst-case opposite solution. However, it does not assess the relative importance of these distances [32].

Consequently, we suggested selecting PCMs for cold storage by adding the Delphi method and combining AHP and VIKOR to make the selection more reasonable and complete. The overall model and process use the Delphi method to identify the PCM selection criteria, the AHP method to determine the weight of the material criteria, and finally, VIKOR to select the most suitable material. The model is depicted in Figure 1.

2.3. Methods and Model Calculation Steps

2.3.1. Delphi Method

The Delphi method is a decision-making process that involves multiple experts and questionnaires to obtain a consistent and reliable conclusion or solution [33,34]. The questionnaire is conducted anonymously. Each result must be analyzed and compared repeatedly to reach a consensus. In the next round of the questionnaire, the statistical results of the previous round will be provided as a reference for the experts to modify their opinions [35]. Through repeated iterations, a consensus can be finally reached. This study conducted the following steps for criteria selection:

Step 1. Construct a committee for the selection of criteria.

Step 2. Review literature for selection criteria.

Step 3. Ask each expert to select the criteria from step 2 and suggest some criteria.

Step 4. Use Delphi method to choose the agreed selection criteria.

In this study, fifteen experts were chosen for this study and participated in the Delphi method survey. These experts were elected among potential individuals, organizations, and academicians who were knowledgeable and experienced in the field of PCM applications with enough authority on both environmental and technical aspects. They all had working experience of at least 5 years or more. During the questionnaire survey, the experts gave their opinion about each of the criteria in the form of importance values of 1, 2, 3, 4, and 5. The values represent “not at all important”, “a little important”, “somewhat important”, “very important”, and “crucial”. Average and coefficient of variation (CV) were used as the judgements for criteria selection. The coefficient of variation is obtained by using the formula CV = (standard deviation/average) × 100%. It represents the relative variability of a dataset compared to its mean. If the calculation result is 0.5, it means that the standard deviation is 50% of the mean. The range of CV calculation results is between 0~100% (0~1). To control the response variation among experts, 0.5 was used as a threshold.

2.3.2. AHP Method

The AHP was created by Saaty in the 1970s to handle difficult problems with several criteria; it is useful for assessing the relative weights of various criteria in a MCDM problem [36]. According to Saaty, the AHP has three important components: (1) organizing a problem into a hierarchy consisting of a goal and subordinate characteristics (decomposition), (2) pairwise comparisons between items at each level (evaluation), and (3) propagation of level-specific, local priorities to global priorities (synthesis) [37].

In order to determine the weight of each criteria for PCM selection, the following application steps of the AHP are used for this model:

Step 1. Decide the overall goal of the problem;

Step 2. Set up criteria based on the result of the Delphi method;

Step 3. Establish a hierarchy structure based on the results of pairwise comparisons;

Step 4. Integrate expert’s opinion;

Step 5. Calculate the weight.

The process of calculating the priority weights involves three steps. Firstly, the geometric mean is calculated for each criterion from its corresponding pairwise comparison matrix. Second, the sum of the geometric mean of each row in the pairwise comparison matrix is computed. Finally, the geometric mean obtained in the first step is divided by the sum obtained from second step for each criterion to derive the priority weight values. These weights indicate the relative importance of each criterion in the decision-making process according to the analytic hierarchy process (AHP).

Step 6. Check consistency.

To check the consistency of a pairwise comparison matrix, the consistency ratio (CR) needs to be calculated. The CR is calculated by dividing the consistency index (CI) by the random index (RI). According to Thomas L. Saaty, the CR should be less or equal to 0.1. If the CR is greater than 0.1, it is necessary to revise the judgments. The consistency index is calculated from the principal eigenvalue of the pairwise comparison matrix. The random index is a value provided by Saaty for matrices of different sizes.

2.3.3. VIKOR Method

VIKOR is a multi-criteria decision-making method proposed by Oprcovicd in 1998, which uses sorting results of compromise solutions or alternatives to determine the best choice [32]. It is typically used when (1) the decision maker does not know how to choose, (2) there are conflicting criteria or different units of measurement, or (3) conflicting compromises are acceptable to the decision maker [38].

In selecting the best PCM, the proposed steps of the VIKOR method in this research are as follows. The optimum PCM is finally selected with the minimum Q value calculated with Formula (3), which is a measure of the closeness of the compromise solution to the ideal solution.

Step 1 Calculate the best performance of each criterion selected with the Delphi method $f_i^{*}$ (positive ideal solution, PIS) and the worst performance of each criterion $f_i^{-}$ (negative ideal solution, NIS), i = 1, 2, …, n.

$$f_i^{\mathrm{*}}=\underset{j}{\max }{f}_{ij}{f}_i^{-}=\underset{j}{\min }{f}_{ij}$$

where $f_{ij}$ is the performance values of criteria.

Step 2 Calculate S_j and R_j for j = 1, 2, …, J

$$S_j=\sum _{i=1}^n{w}_i\left(f_i^{*}-f_{ij}\right)/\left(f_i^{*}-f_i^{-}\right)$$

(1)

$$R_j=\underset{i}{\max }\left[w_i\left(f_i^{*}-f_{ij}\right)/\left(f_i^{*}-f_i^{-}\right)\right],$$

(2)

$w_i$ is the weight of criteria from AHP results. It indicates the relative importance of criteria.

Step 3 Compute the values $Q_j$, j = 1, 2,…, J

$$Q_j=v \left(S_j-S^{*}\right)/\left(S^{-}-S^{*}\right)+\left(1-v\right)\left(R_j-R^{*}\right)/\left(R^{-}-R^{*}\right)$$

(3)

where $S^{*}=\underset{j}{\min }{S}_j$, $S^{-}=\underset{j}{\max }{S}_j$, $R^{*}=\underset{j}{\min }{R}_j$, $R^{-}=\underset{j}{\max }{R}_j$.

v represents the weight of the strategy that is based on the majority of criteria, here v = 0.5.

Step 4 Arrange the PCM options in descending order based on the S_j, R_j, and Q_j values to establish their rankings.

Step 5 Choose the best PCM type with the lowest Q_j value calculated with Formula (3).

3. Model Calculation

In verifying the model, this section uses the PCMs listed in Table 2 to select the optimal cold storage PCM with the suggested model and steps to confirm the model’s applicability and usability. The results are presented in the following sub-sections.

3.1. Criteria Selection Using Delphi Method

In this study, we first identified the properties and relevant criteria of the PCM for cold storage based on a literature review [7,10,20,25,26,27,28,29] and suggestions from experts. Then, 15 experts were surveyed to choose the most suitable selection criteria for the PCM used in cold storage. All experts had working experience of over 5 years. They also had to be independent and not be influenced by any external factors such as personal interests, political affiliations, or financial incentives. This is to ensure they had the ability to provide unbiased opinions. Experts needed to fill the questionnaires with 1, 2, 3, 4, and 5 importance values for the 24 criteria identified by the first step and listed on questionnaires. Finally, the thresholds with an average greater than 3 and the coefficient of variation less than or equal to 0.5 were applied for determining the important criteria.

The selected criteria from the Delphi method are phase transition temperature, material density, heat of fusion, specific heat capacity, thermal conductivity, material cost, and environmental impact. Compared with the physical properties in previous studies, selecting materials using the Delphi method can increase other relevant properties that must be considered in the practical application of PCMs. The results are presented in

Table 3. Criteria selection results from Delphi method.

Item	Criteria	Average (1~5)	Coefficient of Variation (0~1)	Result
1	Phase change temp.	4.6000	0.1979	Selected
2	Material density	4.5333	0.1412	Selected
3	Heat of fusion	4.7333	0.0967	Selected
4	Specific heat capacity	4.6667	0.1323	Selected
5	Thermal conductivity	4.7333	0.0967	Selected
6	Material cost	4.6000	0.1102	Selected
7	Environmental impact	4.8000	0.0863	Selected

.

3.2. Criteria Weighting from Using AHP Method

The weighting of each selection criterion was confirmed by surveying 15 experts and conducting a pairwise comparison with the AHP method for the phase change temperature, density, heat of fusion, specific heat capacity, thermal conductivity, material cost, and environmental impact, which were selected from the Delphi method.

Table 4. Comparison matrix of the criteria.

PCM Criteria	Phase Change Temp. (°C)	Material Density (kg/m3)	Heat of Fusion (KJ/kg)	Specific Heat Capacity (KJ/kg K)	Thermal Conductivity (W/m K)	Material Cost (USD/Kg)	Environmental Impact (1~9)
Phase Change Temp. (°C)	1.000	3.117	3.431	3.431	3.550	3.416	3.117
Material Density (kg/m3)	0.321	1.000	0.250	0.250	0.333	0.374	0.333
Heat of Fusion (KJ/kg)	0.291	4.000	1.000	2.111	3.000	2.111	2.111
Specific Heat Capacity (KJ/kg K)	0.291	4.000	0.474	1.000	3.117	3.178	3.178
Thermal Conductivity (W/m K)	0.282	3.000	0.333	0.321	1.000	1.320	3.000
Material Cost (USD/Kg)	0.293	2.671	0.474	0.315	0.758	1.000	1.000
Environmental Impact (1~9)	0.321	3.000	0.474	0.315	0.333	1.000	1.000

presents the AHP decision matrix,

Table 5. Calculation results of geometric mean, priority weighting, and matrix.

Criteria	Geometric Mean	Priority Weight	Matrix Calculation Result
Phase Change Temp. (°C)	2.811	0.32904	7.91633
Material Density (kg/m3)	0.363	0.04251	7.76713
Heat of Fusion (KJ/kg)	1.647	0.19281	7.61527
Specific Heat Capacity (KJ/kg K)	1.504	0.17601	7.68281
Thermal Conductivity (W/m K)	0.863	0.10106	7.70480
Material Cost (USD)	0.707	0.08276	7.15044
Environmental Impact (1~9)	0.648	0.07581	7.54589

presents the results of each criterion weighting, and

Table 6. Calculation results of λ_max, CI, and CR.

λmax	CI	RI	CR	Consistence Check
7.62610	0.10435	1.32000	0.07905	PASS

presents the results of the consistency check. The AHP weighting results were used in the VIKOR method calculation when choosing the optimal alternative PCM.

Table 4 shows the comparison matrix of the criteria for selecting phase change materials (PCMs) for cold storage in air-conditioning systems. The criteria from row by row are phase change temperature, material density, heat of fusion, specific heat capacity, thermal conductivity, material cost, and environmental impact. The values in the table represent the relative importance of each criterion with respect to another criterion, based on a scale of 1 to 9, where 1 means equal importance and 9 means extreme importance.

Table 5 shows the calculation results of geometric mean, priority weighting, and the matrix calculation result required for further calculation of the maximum eigenvalue (λmax). The geometric mean of each criterion was calculated from Table 4. For instance, the value 2.811 in Table 5 was obtained from the calculation (1.000 × 3.117 × 3.431 × 3.550 × 3.461 × 3.117)^(1/7) of Table 4. The priority weight values were derived by dividing the geometric mean of each criterion by the row sum of geometric mean of each criterion based on Section 2.3.2. Step 5. For example, the priority weight 0.32904 in Table 5 was derived from the geometric mean 2.811 of the first cell in Table 5 divided by the column sum of the geometric mean (2.811 + 0.363 + 1.647 + 1.504 + 0.863 + 0.707 + 0.648). The weighting result will be used for further calculations in the VIKOR method.

The “Matrix Calculation Result” column represents the computed values obtained from pairwise comparison matrix (A matrix) multiplied by priority weight (B matrix), then divided by priority weight (B matrix). In other words, matrix calculation = (A matrix × B matrix)/(B matrix). This calculation is part of the calculation process of the maximum eigenvalue (λmax) and it can be easily computed with an Excel function.

Table 6 outlines key parameters in the analytic hierarchy process (AHP). The maximum eigenvalue (λmax) signifies the principal eigenvalue derived from pairwise comparisons. The consistency index (CI) measures the coherence of these comparisons, calculated using (λmax − n)/(n − 1), where ‘n’ stands for the number of criteria or alternatives. The random index (RI) provides a reference value for the consistency ratio (CR) computation, evaluating the consistency of judgments by comparing CI to RI. CR is computed as CI divided by RI and serves as a pivotal metric to assess judgment consistency, ensuring the validity of decisions made through AHP. The “Consistence Check” verifies whether the CR meets predefined thresholds, affirming the consistency of judgments within acceptable limits, often set below 0.1. These parameters and their calculations ensure the reliability and validity of the decision-making process in AHP based on pairwise comparisons. The CR value in this study is 0.0795, which meets the requirement below 0.1.

3.3. VIKOR Calculation and Ranking

VIKOR was used to determine the ranking of 10 PCM types, and the best PCM type was finally selected with the minimum Q_j value calculated with Formula (3). Q_j expresses how close the compromise solution is to the ideal solution. First, the performance value for each criterion is obtained from Table 2, and materials with incomplete or missing data are pre-eliminated. The performances of criteria are presented in

Table 7. Performance matrix for each criterion.

PCM Type	Phase Change Temp. (°C)	Material Density (kg/m3)	Heat of Fusion (KJ/kg)	Specific Heat Capacity (KJ/kg K)	Thermal Conductivity (W/m K)	Material Cost (USD/Kg)	Environmental Impact (1~9)
S7	7	1700	150	1.85	0.4	6	1
S8	8	1475	150	1.9	0.44	6	2
SP	9	1503	182	1.8	0.8	5	0
A6	6	768	185	2.17	80	7	2
A6.5	6.5	770	190	2.18	82	7	2
A7	7	770	190	2.18	82	7.5	1
A8	7	770	180	2.16	77	9	2
A9	9.5	770	190	2.16	82	7.2	1
C7	8	1400	135	1.4	0.78	8.2	2
OM08	7	1190	175	1.71	0.235	9.3	3
$w_i$	0.329	0.043	0.193	0.176	0.101	0.083	0.076

. Then, the positive ideal solution (PIS) and negative ideal solution (NIS) are determined based on the ideal solution in

Table 8. Positive ideal solution and negative ideal solution.

Criteria	Phase Change Temp. (°C)	Material Density (kg/m3)	Heat off Fusion (KJ/kg)	Specific Heat Capacity (KJ/kg K)	Thermal Conductivity (W/m K)	Material Cost (USD/Kg)	Environmental Impact (1~9)
Ideal Solution	Higher is Better	Higher is Better	Higher is Better	Higher is Better	Higher is Better	Lower is Better	Lower is Better
f*j (PIS)	9.50	190.00	82.00	1700.00	2.18	5.00	0.00
f−j (NIS)	6.00	135.00	0.24	768.00	1.40	9.30	3.00

. Finally, the S_j, R_j, and Q_j values are calculated using the VIKOR method formulas. The results and ranking are listed in

Table 9. VIKOR calculation results and ranking.

Material	Sj	Rj	Qj (v = 0.5)	Ranking
S7	0.54564	0.23503	0.48147	6
S8	0.51282	0.19232	0.30906	3
SP	0.35035	0.19147	0.14185	2
A6	0.60396	0.32904	0.84690	10
A6.5	0.54670	0.28204	0.63575	8
A7	0.48404	0.23503	0.41913	4
A8	0.56030	0.23503	0.49631	7
A9	0.26123	0.17563	0.00000	1
C7	0.64490	0.19152	0.44014	5
OM08	0.75521	0.23503	0.69360	9

.

Table 7 shows the performance matrix of different materials for each criterion based on the VIKOR method. The 10 different material types (S7, S8, SP, A6, A6.5, A7, A8, A9, C7, OM08) and their performance values are from Table 2. The last row ($w_i$) shows the weights of each criterion based on the pairwise comparison matrix from the AHP method. The weights reflect the relative importance of each criterion in the decision-making process.

Table 8 shows the positive ideal solution (PIS) and negative ideal solution (NIS). Positive ideal solution (PIS) represents the highest achievable values for each criterion. For instance, a higher phase change temperature, material density, heat of fusion, specific heat capacity, and thermal conductivity are considered desirable. Lower material cost and environmental impact are preferred. Negative ideal solution (NIS) represents the lowest values for each criterion. For example, lower phase change temperature, material density, heat of fusion, specific heat capacity, and thermal conductivity are desired. Conversely, higher material cost and environmental impact are less preferable.

Table 9 shows the Q_j (v = 0.5) values calculated with Formula (3) and ranking orders for each of the phase change materials (PCMs). These values represent the quality of each material with respect to the criteria used in the VIKOR analysis. Lower Q_j (v = 0.5) values indicate better performance.

4. Results and Discussion

4.1. Delphi Results

The results of the Delphi method showed that in addition to the physical characteristics, the cost and environmental impact of PCMs in practical applications must also be considered. Cost is related primarily to the market competitiveness of the cold storage system, and environmental impact is related to whether the material will affect the health of the human body. Therefore, the choice of PCMs is linked to environmental management and sustainable management. The addition of the Delphi method results in selecting PCMs closer to practical applications and provides more complete criteria considerations.

4.2. AHP Results

The AHP weight analysis showed that the phase change temperature is the most critical selection criterion for cold storage systems. Therefore, PCMs that do not meet this criterion should be avoided. The weight distribution of each criterion is depicted in the pie chart of Figure 2. The weight of phase change temperature is 0.329, and the others in order are heat of fusion, specific heat, thermal conductivity, cost, environmental impact, and material density.

4.3. VIKOR Results

The bar chart provides a visual result of the rankings for the phase change material (PCM) selection based on the VIKOR calculations. As depicted in Figure 3, the x-axis represents the material types and ranking orders, and the y-axis shows the ranking number of materials. Materials are ranked from 1 (the best) to 10 (the worst) based on their overall performance in the VIKOR analysis. From the chart, it is evident that “A9” has the best ranking (lowest Q_j (v = 0.5) value), indicating it performs the best according to the criteria considered. Oppositely, A6 is ranked 10, which suggests that it is among the worst-performing materials. The order for the other alternatives is SP > S8 > A7 > C7 > S7 > A8 > A6.5 > OM08.

4.4. Discussion

Our proposed model provides a valuable process and method for selecting PCM materials, from criteria selection to material property selection. This model is more practical and realistic than others that do not use the selection method of criteria required for real-world applications. Moreover, it can be used to evaluate new materials in the research and development stage for possible environmental impacts. During the production stage of a system, the material cost can significantly affect the system cost and competitiveness of the company. Therefore, the PCM selected by the model should be included in the list of qualified suppliers, and its performance and economic benefits should be further evaluated in follow-up research to achieve the company’s management, energy-saving, and carbon-reduction goals. Finally, PCMs are the cleanest energy source. The use of fossil fuels can therefore be minimized to save energy and enable companies to achieve cleaner, more sustainable production by applying the selected PCMs to air conditioning systems.

4.4.1. Limitations

Due to the wide variety and temperature ranges of phase change materials, it is not possible to consider all usable PCMs. Therefore, It is important to consider other factors and criteria specific to your application when selecting a phase change material. The model analysis provides valuable insights, but it should be complemented with a broader assessment.

4.4.2. Future Study

For future study, we recommend using this model to select PCMs of different types, temperatures, and fields. Project management and advance quality planning is also suggested for the application of selected PCMs in high-technology companies (Figure 4) since the industry shares the highest proportion of energy consumption. The process involves four stages: development, design test and verification, pilot run, and system integration. The first stage is the one related to material selection and qualification, which is also the most critical step of early failure detection.

After the selection of the PCM, it must be used to set up a PCM cold storage system. As depicted in Figure 5, the PCM tank is coupled with a heat exchanger and then connected with air handling units and chillers. The PCM is charged during the nighttime (off-peak time) and releases the cold during the daytime (peak time). Shifting the daytime peak loads to off-peak nighttime periods reduces actual power consumption and, most importantly, avoids daytime punitive electricity rates to reduce annual running costs dramatically. With the reduction in energy consumption, carbon mitigation can also be estimated. Therefore, a cost–benefit analysis should be carried out to ensure the application of phase change materials aligns with sustainable energy goals.

PCM is useful for reductions in energy consumption and carbon mitigation. Therefore, it is suggested to connect the performance of PCMs with the key performance indicators of energy management, environmental management, and sustainability management such as ISO5001 [39], ISO14001 [40], and sustainability standards.

5. Conclusions

The optimal selection model of cold storage PCMs proposed in this study combines the Delphi method with the AHP and VIKOR methods for a more reasonable, complete selection of PCMs. It considers the material characteristics required for practical applications and possible factors for environmental and design requirements during the material qualification and feasibility study. For the application of this model, a total of seven criteria were selected to evaluate 10 PCMs. The results confirmed that material A9 as the optimal PCM based on the Q_j value after the VIKOR calculation. The next-best, SP, can also be considered as a substitute material in practical applications of PCM, primarily because of its lower cost when compared to that of the other materials and its other characteristics that can achieve high performance.