Comparative Analysis of Waste Heat Capture Technologies Applied to Battery Energy Storage Systems

Abstract

Waste heat capture and reuse from battery storage systems for cogeneration of heat and power has the potential to both improve their energy efficiency and reduce the carbon footprint. This study performs a comparison of technologies capable of converting the waste heat extracted to a useful purpose. This analysis is accomplished using the literature data as a basis for an analytical hierarchy process (AHP) applying technological efficiency, cost effectiveness, footprint and integration, and safety and environmental concerns as the criteria. Of these, cost effectiveness was found to be dominant, with technological efficiency also showing high importance. Heat pumps were found to be the most effective based on the objective and criteria of this analysis. This study dictates a pathway that allows stakeholders and decision makers to determine a route by which site-specific comparisons may be made, aiding them to navigate the complex interplay of competing objectives.

1. Introduction

The move from reliance upon centralised power stations towards distributed power generation has accompanied the shift towards renewable power generation. This has led to an increase in both smart grids and the Virtual Power Plant (VPP) concept [1]. Rather than centralisation, an array of distributed energy resources, such as solar photovoltaics, wind turbines, and Battery Energy Storage Systems (BESSs), along with demand response technologies, are controlled by the VPP as an energy management system [2]. To meet the ambitious targets set by many governments and local authorities, such as the UK to be net-zero by 2050, Scotland by 2045, and Glasgow to be carbon neutral by 2030, requires an extensive level of energy provision decarbonisation [3,4,5]. These VPPs represent one avenue of approach to this problem and are projected to be in high demand [1].

Due to the intermittent nature of renewable electricity generation, which may deliver either too much or too little electricity at a given time, it is the role of a BESS to help reconcile supply and demand. Capable of storing electricity during oversupply and of providing electricity during a shortfall, BESSs can provide both functions [6]. This makes BESSs ideally suited to the likes of smart grids and VPPs.

Temperature control within any BESS is required to maintain optimal performance and ensure the system attains a maximum useful lifespan. This is accomplished using a Thermal Management System (TMS), which dissipates the generated heat and smooths temperature fluctuations. Battery degradation occurs during the charging, discharging, and idle time states of the batteries. The typical acceptable temperature window of Li-ion batteries is −20 to 60 °C, for example. However, the optimum working range for Li-ion batteries reduces this to 20–40 °C. Furthermore, the temperature difference from cell to cell within the battery pack should be less than 5 °C [7]. Thus, it is also important to ensure uniformity of temperature across the battery pack in addition to the reduction of maximum temperature. Failure to properly manage overheating and over-charging/discharging can lead to the degradation of the BESS, system failure, and possibly even fire [8].

Comparison of TMS technologies has been carried out with a focus on temperature control [9]. However, there is a significant knowledge gap when comparing these technologies with a view to how the waste heat extracted could be put to use. The concept of waste heat capture and reuse from batteries for cogeneration of heat and power has the potential to improve overall energy efficiency, reduce the carbon footprint, and provide an alternative behind-meter solution to reduce operational costs of the BESS.

In light of this knowledge gap, this study aims to provide insights into the heat recuperation aspect of BESSs, reviewing the temperature ranges of the sources of this heat and discussing in detail the most promising solutions for waste heat capture. The benefits and challenges associated with the potential implementation of technologies for BESS waste heat recovery are identified and discussed. The suitability of each technology for different BESS heat grade scenarios is assessed, and the most promising options for BESS applications are identified and ranked.

This paper begins with a review of the literature in Section 2, highlighting gaps and opportunities within this field. In Section 3, a multi-criteria decision-making (MCDM) approach using the analytical hierarchy process (AHP) is introduced. This is then utilised in Section 4 to perform a detailed comparative analysis to assess and rank the heat extraction and reuse technologies from Section 2. This is based upon criteria of technological efficiency, cost effectiveness, footprint and integration, and safety and environmental concerns. Finally, Section 5 summarises the results of this analysis before recommending the most suitable heat extraction and reuse technology. Furthermore, future research to improve the reuse of waste heat in the electricity storage industry is suggested.

2. Literature Review

2.1. Heat Generation and Transfer Processes

Key to this study is the heat generation within the batteries in the BESS. A primary source of this heat is generated via ohmic resistance due to heat produced by current flow within the internal components of the BESS. Another major source of heat generation in BESSs is due to the actual electrochemical processes of the cells within the BESS that are fundamental to its function during charging and discharging processes. These contributions can be expressed in terms of the current, $I$, internal resistance, $R_{int}$, and the heat generated by electrochemical reactions, ${\dot{Q}}_{React}$, by [9]:

$${\dot{Q}}_{Gen}=I^2{R}_{int}+{\dot{Q}}_{React},$$

(1)

All parameters in this manuscript are in SI units unless otherwise stated. This formulation can be further expanded upon by considering the simplified form of the Bernardi equation [10]:

$${\dot{Q}}_{Gen}=I\left(V_{OC}-V\right)-I.T\left({\displaystyle \frac{\delta V_{OC}}{\delta T}}\right),$$

(2)

This expansion considers both the terminal voltage, $V,$ in addition to the open-circuit voltage, $V_{OC}$. The difference of these is multiplied by the current and determines the heat generation due to Joule heat and electrode overpotentials. This first term is known as the irreversible heat. The second term on the right-hand side of the equation features the temperature derivative of the open-circuit voltage, which is often referred to as the entropic coefficient. This entropic coefficient is again multiplied by the current and the cell temperature, $T$. This combined second term is known as the reversible heat term. The Bernardi formula has been found to have satisfactory accuracy in the cases of constant discharge but is shown to sometimes overpredict under pulse discharge [10].

Heat transfer processes in the BESS need to be considered, as these processes dictate the quantity of heat that is transferred from the cells within the BESS to the cooling medium used by the TMS. It is this heat from TMS cooling, which is usually wasted, that the heat capture technologies compared in this study are looking to capture. This can occur via a combination of conduction, convection, and radiation. The governing equation can be deduced by considering the energy conservation equation and rearranging to make the heat generation, ${\dot{Q}}_{Gen}$, the subject of the equation [11].

The energy balance equation is given by:

$${\nabla }^{2}T+{\displaystyle \frac{{\dot{Q}}_{Gen}}{k}}={\displaystyle \frac{1}{\alpha }}{\displaystyle \frac{\partial T}{\partial t}}$$

(3)

which (rearranged to make ${\dot{Q}}_{Gen}$ the subject)allows for relating the heat transfer processes to the previously discussed heat generation, giving:

$${\dot{Q}}_{Gen}={\displaystyle \frac{\partial \left(\rho c_{p}T\right)}{\partial t}}-\nabla (\mathrm{k}\nabla \mathrm{T})$$

(4)

where:

$t$ is the time during which heat transfer occurs;

$k$ is the thermal conductivity of the material;

$\rho$ is the density of the material;

$c_p$ is the specific heat capacity of the material;

$\alpha$ is the thermal diffusivity of the material $\alpha =k/\left(\rho c_p\right)$.

Note that ${\nabla }^2$ is the Laplacian operator representing the second-order spatial derivatives or the divergence of the gradient, as can be seen more clearly in Equation (4).

The heat generated, ${\dot{Q}}_{Gen}$, by the BESS is removed via the TMS. The means by which the heat is transferred from the battery itself to the medium (air, water, or solid-state material depending upon the TMS used) is governed by conduction, convection, and radiation. The proportion of each will vary depending upon the BESS and TMS used:

2.2. Heat Reuse Technologies

As discussed in the introduction, the BESS will require a TMS to maintain the temperature of the cells at optimal level. The form of cooling used by the TMS will lead to different forms of waste heat at different temperature ranges. Since the output of the TMS serves as the input to the heat recovery technology, this will have an impact on the form of heat recovery technology to be used. Most TMSs utilise either phase change material or air or liquid cooling methods, which themselves can be subdivided into passive air convection, forced air convection, liquid passive cooling, liquid active cooling, and heat pipe cooling. The heat generated is determined by Equations (3) and (4). Depending on which of these is used to cool the BESS, the temperature range and working fluid available for heat recovery will vary, as shown in

Table 1. Table of temperature ranges for TMS waste heat output.

Cooling Material	TMS Method	Waste Heat Form and Temperature
Air cooling	Passive air convection	Air or liquid 20–30 °C [12]
	Forced air convection	Air 20–40 °C [12,13]
Liquid cooling	Liquid passive cooling	Liquid 20–50 °C [13,14]
	Liquid active cooling	Liquid 50–70 °C [13,15]
	Heat pipe cooling	Vapour 40–80 °C [16,17]

.

With the temperature ranges known, then the categories of waste heat technologies available remain to be considered. These can be classified according to the intended use of the captured waste heat, which can be used directly (at the same or lower temperature level), can be converted into another form of energy (electrical or cooling), or could be used at high temperatures [18]. Based on this classification, four generalised uses of waste heat emerge [19]:

• Waste heat to heat: where the low-grade waste heat is converted to a higher temperature level, e.g., through heat pumps;
• Waste heat to cold: where the waste heat is used for cooling, e.g., via absorption or adsorption chillers;
• Waste heat to power: where technologies such as the Organic Rankine Cycle (ORC) or thermoelectric generators (TEGs) permit the conversion of waste heat to electricity
• Heat exchange: this simply uses or stores the heat at the same or lower temperatures, e.g., thermal energy storage.

Based on these categories the waste heat recovery technologies considered here are heat pumps, absorption chillers, ORC, thermoelectric generators, and hybrid ORC and heat pump systems (ORC-HP).

Due to the large range of sizes, both in terms of footprint and storage capacity, of BESS facilities, a degree of generalisation is applied throughout this study. All potential use scenarios would of course be subject to the scale of the facility and may also be dependent upon other factors. This study provides a generalised overview, which may then be adapted on a case-by-case basis to cover the specifics of a particular BESS that is of interest to stakeholders and decision makers.

2.2.1. Heat Pumps

The data in Table 1 shows that the temperature range of the captured waste heat from either an air or liquid-based TMS using heat pumps is compatible with reuse in district heating, for example [20]. The use of waste heat to directly provide domestic heating could lead to substantial energy savings of up to 75% and reduce CO₂ emissions compared to gas heating [21,22]. Heat pumps represent a good method to recover low-quality waste heat. The temperature ranges shown for the various means of TMS cooling, shown in Table 1, are in fact frequently referred to as ultra-low quality. Heat pumps work best when the temperature difference between the medium from which the heat is to be extracted to the desired temperature is minimised. This makes them particularly useful for higher quality waste heat (within this ultra-low quality temperature bracket) associated with liquid-cooled TMSs.

Heat pumps can increase the temperature and enhance the quality of waste heat captured from a BESS, enabling it to fulfil various heating requirements. Waste heat in the temperature ranges of 20 to 40 °C for air-cooled systems and 20–80 °C for liquid cooled, and heat pipe systems can potentially be used to meet household heating demands, household hot water production, or contribute to a district heating network using a centralised heat pump system [21,22]. Alternatively, the heat dissipated by a BESS can also be utilised in more ambient networks to minimise thermal losses, with decentralised building level heat pumps where the heat is further upgraded using the building’s heat pump [23].

A heat pump operates using a vapour compression cycle whereby thermal energy is transferred from the cold source (BESS waste heat streams) to a hot sink (hot water tank, heating circuit, etc.). The cycle is made up of four stages. Firstly, the waste heat is absorbed by the working fluid, causing the evaporation of the working fluid into vapour form. The working fluid is then compressed, thus increasing both its pressure and temperature. This high-temperature vapour is then passed through a condenser, where it releases heat to the hot sink. Finally, the working fluid passes through an expansion valve, which leads to the fluid returning to its initial state [24]. The heat pump system efficiency can be defined by its coefficient of performance (COP), the average ranges of which are between 2 to 5 under optimal conditions for low-grade heat use [25].

Various working fluids can be used depending on the temperature range, environmental considerations, and system design. R134a is historically a common working fluid used in heat pumps and air conditioning systems alike due to its thermal properties; however, due to the 2013 European Agreement, a gradual reduction in fluorinated greenhouse gases is required. This was then superseded by Regulation (EU) 2024/573 [26] phasing in even tighter control over fluorinated gases or “F-gases”. This has led to the entrance of working fluids such as R1234ze into the market as a more future resilient and environmentally friendly option [27]. Leveraging demand-side management systems, the heat pump can be operated to coincide with BESS discharge cycles, thus ensuring optimal use of the available waste thermal energy [28].

2.2.2. Absorption Chillers

Absorption chillers comprise both chemical and mechanical systems and, like heat pumps, require electrical input to drive the pumps. However, the power requirements of the pumps are so low as to frequently be considered negligible relative to the energy supplied as heat, which is input to the chiller, and are thus often neglected in analysis. Again, the waste heat from the TMS provides the input into this technology. A binary solution provides the working fluid in an absorption chiller comprised of a refrigerant (e.g., NH₃) and an absorbent (e.g., H₂O).

The waste heat from the TMS drives a cycle in which a refrigerant evaporates at low pressure to produce cooling and an absorbent solution draws in the refrigerant vapour. Additional heat then separates the two fluids so they can be reused, while the refrigerant condenses and returns to the evaporator. This thermo-chemical process allows the system to operate with very little electrical power, relying mainly on pumps rather than a compressor [29].

While absorption refrigeration systems can operate with input temperatures as low as 65–90 °C, below 65 °C, the refrigeration system shuts down, and there is a marked decline in performance. This implies that absorption chillers are compatible with liquid-cooled and heat pipe-cooled TMSs. Unless some form of additional heat booster is employed, they are unsuitable for air-cooled TMS. Within the temperature range produced by liquid-cooled and heat pipe-cooled systems, the LiBr-H₂O and H₂O-NH₃ working fluids provide the best performance [17].

The use of absorption cooling as a replacement for, or complement to, conventional battery cooling can lower the system’s power demand while also enabling the utilisation of BESS waste heat as the thermal input for the absorption cycle. The COP of absorption chillers ranges around 0.7 to 1.2 [30]; however, this varies with the temperature of the heat source. Since the heat supplied by the TMS will be at the lower end, the COP is also expected to be at the lower end of the scale [30]. An additional benefit of absorption chillers lies in their potential dual use as combined power and cooling systems [31]. Should this technology be required to be retrofit to existing BESSs, then issues may arise due to its relatively large footprint in comparison to the footprint of the BESS itself [17].

2.2.3. Organic Rankine Cycle

An Organic Rankine Cycle functions in much the same way as a traditional steam Rankine cycle but uses a working fluid with a significantly lower boiling point than water, allowing for evaporation to occur at reduced temperatures. The process begins with a pump that pressurises the liquid working fluid. The pressurised fluid then enters the evaporator, where it is heated and vapourised, which would be accomplished using the TMS outlet stream. The resulting vapour passes through a turbine, driving its blades and producing mechanical power that is converted into electricity by an attached generator. After expansion, the vapour is condensed at constant pressure in a condenser and returned to the pump, completing the cycle [32].

A number of criteria determine the selection of the working fluid used in an ORC technology depending upon the application, the source, and level of heat used. In addition to possessing optimal thermodynamic properties at the lowest permissible temperatures and pressures, the fluid must also ideally be non-toxic, non-flammable, environmentally friendly, achieve high net efficiency in order to achieve maximum use of the available energy from the heat supply, and be cost effective [33]. Depending on the gradient of the slope of the saturation curve on a T-s diagram, the working fluid may be classified as wet (positive slope), dry (negative slope), or isentropic (vertical) [34,35,36]. Herein lies some of the advantages of using the ORC over the classic Rankine cycle. Wet fluids, such as water, often require being superheated to prevent turbine damage [34], whereas many organic fluids are either dry or isentropic and do not need superheating. A second advantage is that turbines that have been designed for ORC systems often only need a single-stage expander, meaning that they are less complex and thus incur lower capitol and maintenance costs [35,36]. The working fluids used historically suffer from the same issues as those for heat pumps, and several are now banned. The working fluids that would be optimal within the temperature range for waste heat from TMSs are R143a, R23, R22, R290, R134a, and R227ea [36,37]. The environmentally damaging working fluids are now being replaced with more environmentally friendly options with some small losses in efficiency. It should be noted that while the Kalina cycle offers improved results for lower-temperature waste heat sources compared to the ORC, it also adds a significant degree of complexity [38], which may make it unsuitable for fitting/retrofitting to a BESS and, as such, is not considered here.

2.2.4. Thermoelectric Generators

Thermoelectric generation is a process with the potential to directly convert TMS waste heat into electricity. Using semiconductors, TEG modules operate via thermoelectricity by leveraging a phenomenon called the Seebeck effect [39]. This occurs by utilising the difference in temperature of two different conductors or semiconductors linked at two junctions. Alternatively, heat energy can be converted to pyroelectricity, whereby materials’ structures undergo a transformation with the application of heat, which changes the polarisation of the material, generating an electric potential [40]. For TEG technologies operating using the Seebeck effect, arrays of N- and P-type semiconductors are positioned such that the heat source is attached to one end and the heat sink to the other. In the case of the conversion of waste heat from a TMS to electricity, the hot side is coupled to the waste heat source. The energy absorbed at this junction provides enough additional energy, above the bandgap level to bridge the energy gap between the N- and P-type semiconductors and initiate electrical flow. In this way, the thermoelectric generators convert the waste thermal energy from the BESS into electrical energy [39].

Due to the variable nature of TMS thermal output, it is necessary to consider carefully the selection of a suitable semiconductor with adequate performance in that temperature range [41]. The primary advantage of using a TEG system to convert waste heat to electricity is its very small size compared to other technologies considered. TEG systems are suitable waste heat above 80 °C, which would be available in liquid active cooling and heat pipe BTMSs only [39]. Using TEG electricity generation, small, localised power loads such as the pumping of the thermal management cooling system could be achieved, reducing the costs of this cooling process.

2.2.5. Hybrid ORC and Heat Pump Systems

Waste heat is often categorised into low, medium, and high temperature, with low temperature being below about 150 °C. This means that waste heat from TMSs occupies the bottom end of the low temperature scale, and even then, many are found not to be at a viable temperature. One way to circumvent this issue is to upgrade the temperature from the TMS waste heat output using a heat pump. A prime example of this is the ORC-HP system. Of course, this means that the hybrid system also has the combined expense and footprint of both the ORC and heat pump systems.

The method by which this operates first involves the recovery of the waste heat from the TMS by the heat pump using a refrigerant before passing through a compressor (if a refrigerant-based heat pump is used). The compressed fluid then reaches the heat exchanger, forming the link between the heat pump and the ORC. The heat exchanger takes the heat supplied by the compressed refrigerant in the heat pump cycle and heats up the refrigerant in the ORC. This heated refrigerant is then expanded through a turbine which is the electricity generation part of the process. It is then condensed and pumped back round to the heat exchanger again. In the heat pump cycle, after the refrigerant passed through the heat exchanger, it reaches an expansion valve and is circled back round to collect heat from the TMS once again [42]. The ORC-HP system uses compressors and pumps in its workings and, as such, requires electrical input to drive these devices. Despite this, the ORC-HP system has higher electrical output efficiency when compared to the ORC system alone, primarily due to the upgraded temperature of the waste heat source [13,42].

As has been discussed in the cases of both heat pumps and ORC systems, the issue of refrigerant choice once again needs to be considered.

2.2.6. Summarising Critical Parameters

For the sake of brevity, additional information regarding each technology, its potential application scenarios, and suitable TMS and temperature matches are summarised in tabular format in

Table 2. Temperature ranges and matching technologies to TMSs.

Technology	Minimum Driving Temperature (°C)	Optimum Driving Temperature (°C)	Matching TMS Cooling Technology	Application Scenario	References
Heat pump	Ambient	20–90	Liquid cooling, air cooling, and heat pipe	Preheating for space heating, space heating, and district heating network	[13,17,20,25,28]
Absorption chillers	65	70–90	Liquid active cooling and heat pipe	Refrigeration and chilled water production	[17,43,44]
ORC power generation	65	60–100	Liquid active cooling and heat pipe	Device power supply	[17,32,45]
TEG	80	>80	Liquid active cooling and heat pipe	Localised small power loads	[13,39]
ORC-HP	40	60–100	Liquid cooling, active air cooling, and heat pipe	Localised small power loads	[20,42]

. With regard to the potential TMS configurations, consideration must be given to the best options for TMSs. The choice of TMS determined using the AHP method [9] has revealed the best option to be hybrid cooling as the first option and heat pipes as the second-best option. In both cases, heat pipe active cooling was involved, and as detailed in Table 2, the temperature range of this cooling system waste heat output is 40–80 °C [16,17]. The operating conditions required for the technologies such as the ORC and TEG operate at the higher end of this temperature range but still fall within it and, as such, are considered feasible options.

Similarly, information on the efficiency/COP, combined capital, maintenance and running costs, along with associated payback periods are given in

Table 3. Summary of technology efficiency, costs, and footprint from the literature.

Technology	Efficiency	Capital Cost	Payback Period	Footprint	References
Heat pump	high	low	short	medium	[17,25,46,47,48]
Absorption chillers	medium–high	low–medium	short–medium	high	[17,25,43,44]
ORC power generation	low	medium	medium	medium	[17,25,32,45,49]
TEG	low	high	long	low	[13,39,50]
ORC-HP	medium	medium	medium	high	[20,25,42]

, aiming to facilitate pairwise comparison of technologies. Due consideration was given to the shear range of possible variations of each system within technology types [44]. The exact technology would also vary depending on the individual BESS application of interest. With this in mind, specific numerical values of COP/efficiency, capital cost, and footprint are not used. In place of this, a low, low–medium, medium, medium–high, and high scale is used to allow systematic comparison. Similarly, the payback period will also be dependent upon the scale of the BESS under consideration, and so again, numerical values are replaced by comparative values of short, short–medium, medium, medium–long, and long.

3. Materials and Methods

The examination of possible technologies for waste heat recovery and reuse requires a hierarchical structure to be investigated. The primary purpose of any BESS is the storage of electricity and release for later use. If the BESS were to overheat, then the efficiency of this primary purpose would be inhibited, and as such, a TMS would be needed to dissipate heat as the secondary requirement. To avoid waste of this valuable resource, this study examines the application of waste heat recovery and reuse techniques as the tertiary requirement. While a given waste heat recovery technology may, for example, prove to be most effective in terms of reuse of the heat captured, if it reduces the heat dissipation to the extent that the heat is no longer properly managed or requires some condition that reduces the BESS’s effectiveness, then it is not the optimal choice despite its effectiveness at heat capture. Complications such as this can be navigated through use of an AHP as a means of MCDM tool.

The AHP is a statistical tool developed by Saaty [51] that has the advantage of being capable of processing both subjective assessments and precise data and outputting a consistency ratio and priority weighs [52,53]. This allows for comparisons between metrics that may not be precise quantitative values and are more subjective by nature but still represent essential criteria for decision making. This statistical process has been successfully applied in numerous fields to determine the priority order for decision makers [54] and has already been applied to various functions associated with thermal management [9,52]. To perform calculations for multi-decision problems of moderate scale, a spreadsheet program is sufficient. However, for highly complex and large-scale problems, the number of pairwise comparisons may require use of a more advanced software tool [55]. To this end, an online software tool for AHP calculations was developed by Goepel, called AHP-OS [53].

The initial phase of an AHP calculation is to define the hierarchy tree for the problem at hand. The following steps denote the basic process of defining the hierarchy tree prior to performing AHP calculations [54]:

• Define the problem objectives;
• Identify the relevant criteria or attributes;
• Select the appropriate available alternatives;
• Arrange in the hierarchy tree structure: objectives, criteria, and alternatives.

To generate the hierarchy tree, there are three levels, with the chief objective of the study at the top, the decision alternatives at the bottom, and, however, as many criteria layers as required by the problem at hand in the middle [56]. A hierarchy tree for $N$ criteria and $M$ alternatives is shown in Figure 1.

The AHP takes an element from an upper level and uses it to perform a comparison between the elements on the level immediately below it with respect to it, as detailed in Equations (5)–(11). However, for such calculations to be performed, a numerical scale is required to render qualitative or subjective data into a numerical quantity. To do this, Saaty’s 9-point scale of pairwise comparison is used (see

Table 4. Saaty’s 9-point scale of pairwise comparison.

Preference Level	Preference Score	Description
Extremely Preferred	9	Importance of one factor over the other is extreme
Very Strongly Preferred	7	Very strong preference for one factor in the pair but not extreme
Strongly Preferred	5	Clear preference for one factor over the other
Moderately Preferred	3	There is only a moderate preference for one factor
Equally Preferred	1	There is equal preference for both factors
Intermediate Values	2, 4, 6, 8	Values falling between the adjacent levels

) [9,57]. This translates the subjective judgments into a numerical scale from 1 (equally preferred) to 9 (extremely preferred). For example, for Criterion 1 in Figure 1, this is done by taking Alternatives 1 to M and comparing them pairwise to determine each rank with respect to the others. So, Alternative 1 is compared to each other alternative (1 to M) individually, assigning a comparison score on the Saaty scale (see Table 4) each time. Clearly, the comparison of any Alternative to itself will equal 1 (see Equation (5)). Then, this process is repeated for each Alternative 2 to M to create the decision matrix (matrix A in Equation (5)).

When it comes to the date presented in Table 3, it is vital to keep in mind the nature of the pairwise comparison used to construct the comparison matrix. This means that the qualitative categories in Table 3 (e.g., “high”, “medium”, and “low”) serve to facilitate this comparison and do not themselves represent Saaty numerical (Table 4) values. Thus, just because a technology has a “medium” level in Table 3 does not imply it has a Saaty value of 5, for example. When generating the comparison matrix, the levels in Table 3 were used in comparison with one another, where two similar levels (e.g., “low” vs. “low”) from Table 3 when compared against one another would typically lead to a value of 1 (there is equal preference to both factors) or 3 (there is only a moderate preference for one factor). In the case where, for example, two “lows” were compared and a Saaty value of 3 showing a moderate preference was chosen, this was due to additional factors considered from the details given in Section 2.2.1, Section 2.2.2, Section 2.2.3, Section 2.2.4 and Section 2.2.5.

Using the Saaty scale, it becomes possible to construct a matrix such that the pairwise comparison can take place. Consider the generalised decision tree shown in Figure 1. If the set of criteria to be analysed is $C=\left\{C_k, k=1, 2, \dots , N\right\}$, then the results of the pairwise comparison yield an $N\times N$ matrix, $A$. In $A$, each element, $a_{ij} (i,j=1, 2, \dots , N)$, indicates the relative importance of criterion $i$ as compared to criterion $j$ [52,54]. It should be noted that for the entry where the comparison is the reverse, this yields the reciprocal value (as shown in Equation (5)):

$$A= \left[\begin{array}{ccc}{a}_{11}& \dots & a_{1N}\\ ⋮& \ddots & ⋮\\ a_{N1}& \dots & a_{NN}\end{array}\right] ,a_{i=j}=1; a_{ij}\ne 0, a_{ji}={\displaystyle \frac{1}{a_{ij}}}$$

(5)

Having now defined matrix $A$, it remains to normalise it. This is achieved by summing each column, ${SUM}_j$, and then dividing each entry by its respective column sum. This results in the normalised matrix, $AN$. The Priory Vector, $W$, is then calculated by taking the arithmetic mean of each row of the normalised matrix [9,58]. This means of approximating the eigenvector is used to facilitate the calculation process without having to directly solve the eigenvalue problem.

$${SUM}_j=\left(a_{1j}+a_{2j}+\dots +a_{Nj}\right)$$

(6)

$$AN=\left[\begin{array}{ccc}{\displaystyle \frac{a_{11}}{{SUM}_1}}& \dots & {\displaystyle \frac{a_{1N}}{{SUM}_N}}\\ ⋮& \ddots & ⋮\\ {\displaystyle \frac{a_{N1}}{{SUM}_1}}& \dots & {\displaystyle \frac{a_{NN}}{{SUM}_N}}\end{array}\right]$$

(7)

$$W=\left[\begin{array}{c}{w}_1\\ ⋮\\ w_N\end{array}\right]=\left[\begin{array}{c}{\displaystyle \frac{\left(\frac{a_{11}}{{SUM}_1}+\frac{a_{12}}{{SUM}_2}+\dots +\frac{a_{1N}}{{SUM}_N}\right)}{N}}\\ ⋮\\ {\displaystyle \frac{\left(\frac{a_{N1}}{{SUM}_1}+\frac{a_{N2}}{{SUM}_2}+\dots +\frac{a_{NN}}{{SUM}_N}\right)}{N}}\end{array}\right]$$

(8)

The Priority Vector is a normalised version of the dominant (right) eigenvector (also known as the Perron eigenvector) such that the sum of the values in the vector is one. This permits ready identification of the order of priority of the criteria and facilitates the conversion to percentage values, making it easier for the reader to compare. Since this is the dominant eigenvector, it is associated with the maximum eigenvalue, ${\lambda }_{max}$. A close approximation for this can be found by taking each value of the Priority Vector, multiplying it by the relevant column total ${SUM}_j$, and then adding the resulting values together, as detailed in Equation (9).

$${\lambda }_{max}\cong [\left({SUM}_1\times w_1\right)+\left({SUM}_2\times w_2\right)+\dots +\left({SUM}_N\times w_N\right)]$$

(9)

The consistency index, $CI,$ can be examined with the random inconsistency, $RI,$ to yield the consistency ratio, $CR,$ which is used to verify the consistency of the matrix. First, the consistency index is calculated as shown in Equation (10):

$$CI={\displaystyle \frac{{\lambda }_{max}-N}{N-1}}$$

(10)

The average random inconsistency is used based on the value of $N,$ as shown in

Table 5. The average random inconsistency as a function of N.

N	1	2	3	4	5	6	7	8	9	10	11
RI	0	0	0.58	0.9	1.12	1.24	1.32	1.41	1.45	1.49	1.51

[51,59].

Using the requisite value from Table 5 and the value calculated using Equation (10), the consistency ratio is calculated using Equation (11):

$$CR={\displaystyle \frac{CI}{RI}}$$

(11)

The accepted upper limit of the consistency ratio is 0.1 [9,54,56,59]. If this criterion is not satisfied, then a new comparison matrix must be constructed [60].

This study employs an AHP-Excel method to first evaluate the criteria for the overall objective of creating an order of preference for heat recovery and reuse technologies. Once these criteria are ranked, the technologies themselves are ranked using literature-based weighting to perform the comparison.

4. Results and Discussion

This study employs an AHP-Excel method to evaluate heat recovery and reuse technologies using literature-based weighting to perform the comparison. There are a number of choices of method for gathering the expert opinion used to conduct the pairwise comparisons. Some investigators use a system involving expert surveys [61]; other authors have performed this analysis based on existing data in the literature [9]. Additional methods for performing such comparative studies have also been reviewed [62]. This study follows the second of these routes, combining data and expert opinions found in the literature.

4.1. Comparison of Heat Recovery Technology Criteria

The AHP system requires pairwise comparison between criteria for each layer so that finally stakeholders will be in a position to make informed decisions regarding the installation of heat recover technology to a BESS. To accomplish this, the criteria for the first layer need to be defined by consideration of the key requirements the heat recovery system needs to fulfil regardless of the particular technology used.

The first layer to be examined covers the four key metrics: heat capture technology efficiency, cost effectiveness, footprint and integration, and safety and environment. These metrics were given weights reflecting their significance with respect to one another in terms of the overall objective of determining the optimum choice for heat recovery technology for the BESS.

Following the steps outlined in Section 3, a pairwise comparison matrix is generated as described in Equation (5). The columns are then summed as described in Equation (6), with the summation values shown at the bottom of the appropriate column in

Table 6. Comparison matrix for the objectives.

Comparison Matrix	Technology Efficiency	Cost Effectiveness	Footprint and Integration	Safety and Environmental Considerations
Technology Efficiency	1	3	3	5
Cost Effectiveness	0.33	1	3	3
Footprint and Integration	0.33	0.33	1	3
Safety and Environmental Considerations	0.2	0.33	0.33	1
Summation	1.87	4.67	7.33	12

.

The next step involves creating the normalised priority matrix, as shown in Equation (7). The normalised priority matrix for the comparison of heat recovery technology criteria is shown in

Table 7. Priority matrix for the objectives. The Priority Vector is shown in bold in the final column.

Priority Matrix	Heat Capture Efficiency	Cost Effectiveness	Response to Dynamic Loads	Safety and Environmental Considerations	Priority Vector
Heat Capture Efficiency	0.535714286	0.642857143	0.409090909	0.416666667	50.11%
Cost Effectiveness	0.178571429	0.214285714	0.409090909	0.25	26.30%
Response to Dynamic Loads	0.178571429	0.071428571	0.136363636	0.25	15.91%
Safety and Environmental Considerations	0.107142857	0.071428571	0.045454545	0.083333333	7.68%

, with the Priority Vector (see Equation (8)) shown in the final column as a percentage.

Now that the Priority Vector has been determined, it remains to be verified that the priority matrix is in fact consistent. To accomplish this, the maximum eigenvalue is calculated using Equation (9); this is used to determine the consistency index using Equation (10). In turn, this is used to reveal the consistency radio in accordance with Equation (11) and

Table 8. Consistency checks for the decision matrix.

${\lambda }_{max}$	4.25
$CI$	0.083
$CR$	0.093

. In order for the matrix to be considered consistent, the consistency ratio must be below 0.1. The results of this check show that the decision matrix is indeed consistent (see Table 8).

The Priority Vector allows for the determination of the relative importance of each criterion examined. From Figure 2, it can clearly be observed that the criteria in order of importance are cost effectiveness, technology efficiency, footprint and integration, and safety and environmental concerns, with the latter sharing the joint lowest score.

The prevalence of the cost effectiveness criterion can be understood from the standpoint of the heat reuse being a tertiary system after the TMS as a secondary and the BESS itself as primary. Clearly the BESS must exist in order for the electricity storage purpose to be fulfilled. When it comes to the TMS, this is very much a necessity also, as without it, the risk of significantly reduced battery lifetime or even catastrophic failure due to thermal runaway events become very real. This is why when performing an MCDM analysis on the choice of TMS, the cost effectiveness was the lowest criterion, with heat dissipation as the highest [9]. The heat capture and reuse technology, on the other hand, is more of a “nice to have” component. Without it, the system will still function perfectly well. Any spending, be it capital, maintenance, or otherwise, needs to be able to cover itself or it is merely a financial drain on the facility. With the financial aspect considered, then it is of interest to ensure that the technology to be used is best able to recover the available heat in an efficient manner. The greater the quantity of heat able to be reused as heat or electrical energy, the better. Finally, there come the twin concerns of how much extra space and added complexity the addition of the technology will bring to the facility and what are the safety and environmental considerations. Barring excessive complexity and a prohibitively large footprint, this is not an aspect that will decide the overall course of action. To address the second part, since this is just an add-on to the primary purpose of the BESS, which will likely be using Lithium-based cells, the increase in environmental impact to that of the BESS itself will not be substantial.

This has resolved the criteria levels of the hierarchy tree, as shown in Figure 1. Now that the criteria rankings have been determined, it falls to the next level of the hierarchy tree to undergo pairwise comparison with respect to each criterion in turn.

4.2. Comparison of Heat Recovery Technologies

For the sake of brevity, the initial comparison matrix for each criterion will be shown to facilitate the reproduction of the results, along with the Priority Vector; however, individual steps will not be explicitly shown. Additionally, the consistency ratio will be added to the table to demonstrate the consistency of the comparison matrix.

4.2.1. Heat Capture Technology Efficiency

Based on the details presented in Section 2.2, its source references, and Table 2 and Table 3, the priority matrix for the heat capture technology efficiency is shown below in

Table 9. Comparison matrix for heat capture efficiency. The Priority Vector is shown in bold in the final column.

Comparison Matrix	Heat Pump	Absorption Chillers	ORC Power Generation	TEG	ORC-HP	Priority Vector
Heat Pump	1	3	9	9	5	50.48%
Absorption Chillers	0.33	1	7	7	5	30.16%
ORC Power Generation	0.11	0.14	1	1	0.33	4.38%
TEG	0.11	0.14	1	1	0.33	4.38%
ORC-HP	0.2	0.2	3	3	1	10.60%
${\lambda }_{max}$			5.3149
$CI$			0.0787
$CR$			0.0703

. In addition to the raw efficiency values, the ability of the technology to adapt to the fluctuating nature of the thermal input is considered. It is recognised that the COP of a heat pump and the thermal-to-electric efficiency of an ORC represent fundamentally different physical metrics. However, a method to make a fair comparison is necessary for the purpose of this study. To do so, it is vital to keep in mind the research focus on waste heat capture and reuse. As such, the efficiency of heat pumps is considered in terms of waste heat input compared to useful heat output. Similarly, for ORCs, the thermal efficiency, defined as the net electrical work output compared to the heat input [63], is the metric of interest. Here, heat pumps are still very effective, and so they scored well in this comparison (see Table 9).

4.2.2. Cost Effectiveness

Using the details presented in Section 2.2, its source references, and Table 2 and Table 3, the priority matrix for the cost effectiveness is shown below in

Table 10. Comparison matrix for cost effectiveness. The Priority Vector is shown in bold in the final column.

Comparison Matrix	Heat Pump	Absorption Chillers	ORC Power Generation	TEG	ORC-HP	Priority Vector
Heat Pump	1	3	5	7	5	48.34%
Absorption Chillers	0.33	1	3	7	3	25.08%
ORC Power Generation	0.2	0.33	1	5	1	11.44%
TEG	0.14	0.14	0.2	1	0.2	3.70%
ORC-HP	0.14	0.33	1	5	1	11.44%
${\lambda }_{max}$			5.3721
$CI$			0.0930
$CR$			0.0830

. This takes into account not just the capital costs and payback time but also the complexity of the system, which leads to increased maintenance costs.

4.2.3. Footprint and Integration

From the information presented in Section 2.2, its source references, and Table 2 and Table 3, the priority matrix for the footprint and integration is shown below in

Table 11. Comparison matrix for footprint and integration. The Priority Vector is shown in bold in the final column.

Comparison Matrix	Heat Pump	Absorption Chillers	ORC Power Generation	TEG	ORC-HP	Priority Vector
Heat Pump	1	3	1	0.2	3	15.59%
Absorption Chillers	0.33	1	0.33	0.14	1	6.10%
ORC Power Generation	1	3	1	0.2	3	15.59%
TEG	5	7	5	1	7	56.62%
ORC-HP	0.33	1	0.33	0.14	1	6.10%
${\lambda }_{max}$			5.1751
$CI$			0.0438
$CR$			0.0391

. One of the factors involved in the consideration of the integration aspect is that of the effect of the driving temperature. Additionally, the flexibility of the technology to be adapted to different TMS cooling mechanisms is considered.

4.2.4. Safety and Environmental Concerns

The primary concern regarding the consideration of the environmental and safety concerns priority matrix is the working fluid. Issues may arise here involving the global warming potential of the fluid, its toxicity, acidity, flammability, etc. With TEGs, the consideration focuses mainly on the semi-conductor materials used in their manufacturing. The priority matrix for the safety and environmental concerns is developed using the information in Section 2.2 and its source references, and the results are shown below in

Table 12. Comparison matrix for safety and the environment. The Priority Vector is shown in bold in the final column.

Comparison Matrix	Heat Pump	Absorption Chillers	ORC Power Generation	TEG	ORC-HP	Priority Vector
Heat Pump	1	0.33	1	1	3	17.26%
Absorption Chillers	3	1	3	1	5	37.21%
ORC Power Generation	1	0.33	1	1	3	17.26%
TEG	1	1	1	1	3	21.91%
ORC-HP	0.33	0.2	0.33	0.33	1	6.37%
${\lambda }_{max}$			5.1576
$CI$			0.0394
$CR$			0.0352

.

4.3. Heat Capture and Reuse Technologies Ranked

The consolidated weights computed for heat reuse technologies across all the metrics are calculated using the priorities of the objectives and those of the individual technology for that objective. The results are visually expressed in the pie chart in Figure 3.

The overall result of the AHP showed that heat pumps are the prime choice, followed by absorption cooling, TEG, and finally ORC-HP. The high weighting for the technological efficiency strongly favoured heat pumps, which are well known for having a high COP. This, in part, led to their high position and was complemented by the relatively low payback time, which itself is, in part, precisely due to this high COP [25]. Heat pumps are able to increase the quality of the heat at a comparatively low cost, so when this heat can be sold on or used to save other heat costs, there is a clear advantage, though, of course, this is dependent upon the location. By way of example, when comparing provision of hot water via heat pump heating to cold water provision from absorption chillers using waste heat from data centres, it was found that the payback period was below 2 years for the heat pumps, but for the absorption chillers, it was unfavourable [48]. It was noted that this result was location specific and that payback periods and capital costs will vary with geographic location. In general, in the comparison process, the absorption chillers performed well, having good efficiency and reasonable costs, but was hampered by its large footprint, which could add complexity either in terms of retrofitting or on additional land/building requirements for a new build. TEGs suffered from the worst efficiency but by far the lowest footprint. That said, their score in the footprint and integration was not maximised due to the high driving temperature requirements making them unsuitable for all but the highest temperature waste heat from TMSs. The ORC suffered from poor efficiency compared to heat pumps and absorption chillers; this had a knock-on effect on the payback time and thus reduced its performance in terms of the costs. Since, when combined, efficiency and costs make up three quarters of the weighting, this left the ORC in a poor position. While the addition of a heat pump to give the ORC-HP system did indeed help boost the poor efficiency, it also increased the footprint and complexity of the system and also its costs.

5. Conclusions

The use of waste heat captured by the TMS of a BESS was examined with a view to deciding on the best waste heat capture and reuse technology in the general case using the multi-criteria decision-making system. This was accomplished through a comparative review and the application of the AHP in Excel. Through this analysis, heat pumps appeared as the most effective heat capture and reuse technology due to their superior efficiency and low capital and maintenance costs. While absorption chillers were found to be the second-best option, their suitability was hampered by their large footprint, leading to potential challenges in both retrofit and new projects. Attempts to increase the efficiency of an ORC system through use of heat pumps to provide the ORC-HP hybrid system were found to be unsatisfactory for the purpose of capturing the ultra-low-temperature waste heat.

It is noted that the results shown in this study may be different in different circumstances, such as the geographic location of the installation. Such differences may be due to effects such as external temperature, which may make chilling rather than heating favourable in a hot climate or vice versa in a cold one. Additionally, costs associated with capital expense, electricity supply, labour, and maintenance will also vary across different geographic locations. Additional variations may arise due to differences in research interpretation of the literature. As such, the study provides a pathway for stakeholders to utilise with the specifics of any upcoming project. Following the process outlined in this study, stakeholders and decision makers can use Saaty values appropriate to their individual project in the workflow outlined in this analysis to guide their own project.

It would be ideal to have some experimental data on the waste heat available for capture and its variation with time through charge/discharge cycles as a topic for future work. Additionally, the life-cycle analysis for the entire life through to disposal should also be analysed, as this is key concern for circular economy models as an additional topic of potential future work. As mentioned above, site-specific limitations may impact the rankings, and a sensitivity analysis would be a useful piece of future work to help understand how such limitations affect the final rankings. When considering expert opinions with respect to areas of research priority for electric vehicles, alternative approaches to the calculation of the weighting of these expert opinions were compared [61], and a similar comparison could be applied by considering a weighting system.

The issue of comparing heat pumps and electricity production from heat using other metrics for comparison is also a route for future work, and looking at it through the lens of exergy analysis is one potential approach for this [64].