In this study, AHP-OS was used to assess the metrics that form the TMS criteria parameters and the TMSs according to their adjudged priorities and weights based on the comparative findings from other published literature and data forming respective comparison tables. The AHP-OS is a statistical analysis tool that assists via multi-criteria choice-making [
38]. On top of that, AHP-OS allows for minor judgmental discrepancies and generates ratio scales from paired criteria comparisons. Likewise, subjective views as well as precise measurements can be used as inputs. Consequently, a consistency ratio and priority (weights) are computed [
39]. In this case, the parameters used were indeterminate quantitatively despite their significance in determining the best TMS for use in BESS for VPP.
3.1. TMS Metrics Comparison
The study identified with the four key TMS metrics: heat dissipation efficiency, cost-effectiveness, response to dynamic loads, and safety & environment. These metrics were assigned weights based on their relative importance. Through a Saaty scale [
40], two elements were compared in AHP with their attributing values varying from 1 to 9. The scale determines the relative importance of an alternative when compared with another as shown in
Table 1.
Odd numbers are always preferred to ensure reasonable distinction among the measurement points, even numbers are only adopted whenever there is a need for negotiation between evaluators.
Table 2 shows the TMS metrics weights on the scale.
In this case, the first step was to determine the criteria as shown in
Figure 1 where they were evaluated in pairs to determine the relative importance between them and the relative weight to the goal. The evaluation started by determining the relative weight of the TMS metrics to produce a priority vector (Eigenvector) matrix as shown in
Table 3.
Then normalization was done to give relative weight to each criterion [
41]by dividing each value by the total column value as shown in
Table 4.
Now, the contribution of each criterion was determined by calculations made using the priority vector, which showed the relative weights between each criterion obtained by calculating the average of all criteria as indicated in
Table 5.
The total of the values per column is 1; therefore, this approximation was applied to simplify the calculation process because the difference between the exact and approximate values is designed to be less than 10% [
38].
For comparison, Python mathematical software with NumPy and SciPy was used to determine the exact Eigenvector values through the potential matrices. (Appendix A1 shows the Python Code used).
The approximate and exact Eigenvector values are very close to each other as indicated in Table 6, therefore the calculation of the exact vector requires a mathematical effort that can be exempted.
The next step was to determine the inconsistencies to capture enough information to decide whether the decisions made have been consistent with the choices. The consistency index comes in and is based on the maximum Eigenvector value calculated by summing up the product of each element in the Eigenvectors by the respective column of the original comparison matrix [
39] as shown in
Table 7.
The calculation of the consistency index is given by
equation (1).
where
CI is the consistency index,
λmax is the maximum Eigenvalue, and
n is the number of the evaluated criteria.
Now, CI == 0.015
In order to verify whether the consistency index (CI) is adequate, the consistency rate (CR) was determined.
CR is the ratio between the consistency index and the random consistency index (RI) and the matrix would be consistent if the resulting ratio was less than 10% shown by
equation (2).where
CR is the consistency ratio,
CI is the consistency index and
RI is the random consistency index.
The RI value is fixed on the number of criteria as shown by
Table 8 the AHP criteria table which provides determined values.
Now, CR = which is 1.7%
Since the value is less than 10%, the matrix was considered consistent and the priority criteria results for the first level are shown in Figure 2.
This formed the criteria level 1 computations as shown in
Figure 8, which the AHP-OS can do at a good CR. Therefore, for criteria level 2 to the end, data analyzed by the AHP software will be presented.
(Appendix A2 shows the results as given by AHP-OS for TMS metrics).
3.1. Comparison Data Concerning TMS Metrics
Using the prioritized TMS metrics, another hierarchy for criteria level 2 was established where various TMS options were evaluated based on their performance in each metric by comparing data from different previous studies to establish the Saaty scale. Pairwise comparisons were again conducted to establish the relative importance of different TMS options within each metric. The software was able to perform sensitivity analysis to assess the weight uncertainties overlap and robustness of the decision-making process [
40]. This involved varying the weights assigned to each criterion and observing the impact on the overall rankings of TMS options. It helped identify the relative importance of different criteria and their influence on the final decisions.
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i
Heat dissipation
Heat dissipation is an important consideration when evaluating thermal management solutions for BESS in VPPs. The restricted heat dissipation capability of natural convection, which depends on passive airflow, makes it less effective for bigger BESS installations [
42]. Forced air convection, facilitated by fans or blowers [
43], improves heat dissipation; yet, air is less efficient than other media [
44] due to its lower specific heat and heat transfer coefficient. With liquids having greater heat transfer coefficients than air, active cooling with liquids entails actively circulating [
35] cooling fluids to promote efficient heat dissipation. Heat pipes have excellent thermal conductivity, which enables fast heat transfer. [
35]. PCM offers variable but steady temperature control and modest heat dissipation [
35]. Using the Peltier effect, thermoelectric modules transform power into thermal differences, freeing thermoelectric cooling, which is frequently combined with other cooling techniques, to provide heat later [
45]. Hybrid cooling, whose efficacy varies based on particular configurations, optimizes [
45] heat dissipation by combining active and passive tactics to reduce vulnerabilities in cooling systems. From this information, the weights were assigned to every TMS as shown in
Table 9. Following that, the criteria were assessed in pairs once again using AHS-OS, yielding 28 pairwise comparisons.
Table 10 presents the criterion consolidated priorities and normalized pairwise comparison matrix for heat dissipation as produced from the run in the AHP-OS with twenty-eight (28) comparisons, and CR of 0.7%.
-
ii
Cost-effectiveness
Natural convection is cost-effective for smaller BESS due to its passive design, low energy usage, and minimal [
49] maintenance. Air-forced convection is moderately cost-effective [
50] for medium to large-scale BESS, but requires additional equipment like fans or blowers [
49]. Liquid passive cooling is suitable for medium to large-scale BESS, balancing efficiency and cost-effectiveness, while liquid active cooling, though effective for larger-scale BESS with high heat dissipation requirements, has higher upfront costs [
48]. Heat pipes provide an economical solution for medium to large-scale BESS, offering low costs, passive operation, and minimal maintenance. PCM is cost-effective across all BESS scales, with easy installation, low energy consumption, and little maintenance. Thermoelectric cooling is less economical due to additional components, higher energy consumption, and complex installations [
51]. The cost-effectiveness of hybrid cooling depends on the combination [
52] of techniques used, with optimization involving tailoring the combination to meet specific BESS requirements.
Table 11 presents the TMS performance outcome for cost-effectiveness which was applied in AHP-OS.
Table 12 shows the criterion consolidated priorities as well as normalized pairwise comparison matrix for cost-effectiveness from AHP-OS with twenty-eight (28) comparisons, and a CR of 1.1%.
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iii
Response to dynamic loads
Natural convection, while inexpensive and appropriate for smaller BESSs, may have trouble responding [
57] to abrupt changes in load because it depends on natural airflow, according to TMSs for BESS VPPs. When combined with fans or blowers, air-forced convection provides superior reactivity for medium- to large-scale BESSs experiencing recurrent load variations. [
57]. While liquid active cooling is appropriate for big load fluctuations due to its pump-driven [
58,
59] cooling loop, liquid passive cooling responds poorly [
58] but can manage tiny load changes. Heat pipes work well with both small and large-scale BESSs because of their remarkable responsiveness. At greater discharge rates [
57], pure PCM is less effective due to its modest response. Excellent responsiveness is a feature of thermoelectric cooling [
60], which makes it appropriate for specialized BESS applications that need accurate temperature control. The reactivity of hybrid cooling varies depending on which strategies are combined, but its adaptability allows it to be employed in a variety of load scenarios [
61].
Table 13 presents the TMS performance outcome for response to dynamic loads which was applied in AHP-OS and the results.
Likewise, the AHS-OS was able to generate 28 pairwise comparisons, for response to dynamic loads metric using the consolidated priorities and normalized pairwise comparison matrix as shown in
Table 14 with a CR of 0.8%.
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iv
Safety and environment
While air-forced convection can be risky if fans or blowers break, resulting in overheating, thermal runaway, and fire, together with electronic garbage, it also adds to noise pollution [
63]. Natural convection is safe and environmentally beneficial [
64]. The type of coolant used in liquid passive cooling can affect system safety as well as the environment [
65]. Because there is a risk of fluid leaks and pump failures, liquid active cooling calls for increasingly stringent safety measures. Except for leaks, heat pipes are secure and eco-friendly [
66]. Though they can break down and become pollutants over time [
54], PCM is environmentally benign and harmless. Owing to their higher energy consumption and potential for overheating, thermoelectric cooling systems need to be handled and designed carefully. Hybrid cooling systems' effects on the environment and safety are dependent upon the combination of approaches employed [
46]. Hybrid cooling maximizes temperature control and consistency in battery packs by combining the benefits of liquid and air cooling. In addition to improving battery performance and safety, this lessens the negative environmental effects of utilizing toxic coolants or using excessive amounts of energy.
Table 15 presents the TMS performance outcome for safety and environment which was applied in AHP-OS and the results displayed.
Table 16 presents the consolidated priorities and normalized pairwise matrix for safety and environment as produced from the run in the AHP-OS with twenty-eight (28) comparisons, and CR of 0.8%.