Techno-Economic Analysis of Waste Heat Recovery in Automotive Manufacturing Plants

Abstract

This study proposes an innovative system for recovering waste heat from exhaust air after a regenerative thermal oxidiser process, integrating a Carnot battery and photovoltaic (PV) modules. The Carnot battery incorporates an organic Rankine cycle (ORC) with a recuperator, thermal energy storage (TES), and heat pump. Waste heat is initially captured in TES, with additional energy extracted by a heat pump to increase the temperature of a secondary fluid, effectively charging TES from both direct and indirect sources. The stored heat enables electricity generation via ORC. The result of this study shows a heat pump COP between 2.55 and 2.87, the efficiency of ORC ranging from 0.125 to 0.155, and the power-to-power of the Carnot battery between 0.36 and 0.40. Moreover, PV generates 1.35 GWh annually, primarily powering the heat pump and ORC system pump. The proposed system shows a total annual net generation of 4.30 GWh. Economic evaluation across four configurations demonstrates favourable outcomes, with a return on investment between 25% and 160%. The economic evaluation examined configurations with and without the PV system and recuperation process in the ORC. Results indicate that incorporating the PV system and recuperator significantly increases power output, offering a highly viable and sustainable energy solution.

1. Introduction

In recent years, growing attention has been given to enhancing energy efficiency across various industries in support of sustainable development goals and net-zero emission targets [1,2]. One of the key areas of focus is the utilisation of waste heat generated by industrial processes, which often remains untapped despite its substantial energy potential. By capturing and reusing this excess heat, industries can significantly improve energy efficiency, reduce reliance on conventional energy sources, and lower carbon emissions [3]. This approach not only reduces energy demand, but also supports the shift toward net-zero emissions by decreasing the need for fossil fuel-based energy, thereby mitigating greenhouse gas emissions. Several innovative technologies are being developed to harness waste heat more effectively, enabling its repurposing for heating, power generation, and other industrial processes [4].

There are several manufacturing processes—all across the various fields of industries—where energy efficiency could be improved. A representative example from the automotive industry will be presented. This sector has seen significant growth in recent years, particularly with the rise of electric vehicles [5,6]. Within this industry, the car body paint shop is a critical step in manufacturing, requiring substantial amounts of both electricity and thermal energy [7]. This high demand makes it an ideal candidate for co-generated and recovered energy from other processes, enhancing overall energy efficiency.

In the literature, several studies have explored the potential of waste heat recovery in automotive paint shops to improve system efficiency [7,8]. One innovative approach focuses on recovering waste energy, specifically from the exhaust gases of regenerative thermal oxidisers (RTOs) used in the paint shop [7]. RTOs are critical for air pollution control, but they release large amounts of unused heat. By capturing this waste heat and repurposing it within the paint shop or other parts of the manufacturing processes, the factory can significantly reduce energy consumption, lower operational costs, and contribute to sustainability goals.

This study introduces a novel approach and provides a preliminary analysis of power generation by utilising waste heat from automotive paint shops. As waste heat recovery technologies continue to attract attention, this research investigates the potential of integrating a high-temperature heat pump to upgrade waste heat, storing the enhanced thermal energy in a thermal energy storage (TES) system. Moreover, it explores the use of an organic Rankine cycle (ORC) to efficiently convert low-grade waste heat into electricity, thus optimising the utilisation of available waste energy. The ORC is particularly suited for this purpose due to its capability to operate at low to medium temperatures, making it ideal for recovering heat in such industrial settings. The article explores the integration of ORC technology, a heat pump, TES, and photovoltaics (PV) and presents a techno-economic analysis to assess its feasibility in automotive paint shops. The analysis evaluates critical factors such as the amount of recoverable waste heat, the system’s efficiency, and the associated economic benefits. Four scenarios are described and examined for economic feasibility. By doing so, this research contributes to advancements in waste heat recovery, offering a thorough evaluation of how ORC technology can improve industrial sustainability. Also, the study provides valuable insights into how industries can optimise their energy consumption by recovering waste heat, thus supporting the transition toward more sustainable and energy-efficient production processes.

After the introduction, Section 2 provides a literature review that discusses the current state of the art and positions the contributions of this study within the broader research context. Section 3 explains the methodology, offering a detailed description of the proposed system, the thermodynamic mathematical model, and the economic analysis used in the study. Section 4 presents the results and includes an in-depth discussion of the findings related to thermodynamic analysis, PV energy production, the system’s annual energy production, and economic assessment. Section 5 offers the future direction of the research in this study. Then, Section 6 concludes the article by summarising the key insights and their broader implications.

2. Literature Review

Recent literature indicates a growing interest in research on waste heat recovery in automotive manufacturing plants, highlighting its potential to improve energy efficiency and reduce operational costs. Among these studies, the focus is specifically on the heat recovery potential within painting shops, where significant amounts of waste heat are generated during the drying and curing processes. These studies are summarised in Table 1 and examine various strategies and technologies for capturing and reusing this waste heat, contributing to overall energy savings and sustainability in automotive manufacturing plants, especially in painting shops.

Iglauer and Zahler [9] reported the development of an advanced solar combined heat and power system, Eco + Energy CPS Suntec, aimed at enhancing sustainability in the automotive manufacturing process. By combining a micro gas turbine with a Fresnel solar heat collector, the system effectively captures and reuses waste heat, achieving more than 90% efficiency. It also reduces reliance on fossil fuels by up to 35%, leading to significant cuts in both carbon and nitrogen oxide emissions. The system operates continuously, ensuring uninterrupted heat and power supply in industrial processes like curing automotive paint, which requires high temperatures. This case study demonstrated a 70% reduction in primary energy consumption alongside a decrease in carbon dioxide emission by 2800 tons per year. Furthermore, Chang et al. [10] reported that the waste heat recovery from flue gas should be used directly in the pretreatment tanks, bypassing the steam boiler and reducing energy losses. The proposed system achieves a 69% improvement in energy efficiency over conventional designs, reducing flue gas temperatures from 160 °C to 110 °C. This case study demonstrated a payback period (PBP) of 2.8 years, significantly reducing energy consumption and carbon dioxide emissions.

Adamkiewicz and Nikończuk [10] presented the modelling simulations that highlight the significant potential of low-temperature waste heat recovery, particularly from air compressors and dryers, which together emit a substantial amount of heat up to 93% of the power supplied to the compressor, which is released as waste heat. This study proposed using an air-source heat pump to recover and store this heat in a water tank for reuse in processes like air heating in the spray booth. The simulation results showed that recovering and repurposing this heat can significantly reduce energy consumption. Another study [11] highlighted waste heat recovery potential, particularly within paint shops where significant heat is lost during processes like paint curing and drying (from old baking ovens). The study proposed the use of an ORC combined with a TES system to recover and reuse this heat. By capturing the waste heat from these baking ovens, the proposed system can generate electricity, improve the thermal comfort of the workspace, and reduce overall energy consumption.

Table 1. An overview of research progress on waste heat recovery in automotive painting shops.

Authors, Year	Heat Sources	Experiment/ Modelling	Thermodynamic Analysis	Economic Analysis	The Technology of Waste Heat Recovery
Iglauer and Zahler, 2014 [9]	Baking oven and solar thermal	Modelling	Yes	Yes	Gas turbine and solar thermal collector
Chang et al., 2018 [12]	RTO	Experiment	Yes	Yes	Direct use for other purposes
Adamkiewicz and Nikończuk, 2019 [10]	Air preparation room	Modelling	Yes	No	Heat pump and TES
Daniarta et al., 2021 [11]	Baking oven	Modelling	Yes	No	ORC and TES
Giampieri et al., 2022 [13]	RTO, compressors, and chilled water system	Modelling	Yes	Yes	TES and liquid desiccant system configuration
Broniszewski et al., 2022 [14]	n.a.	Experiment	Yes	Yes	ORC
Martire et al., 2024 [15]	RTO and solar thermal	Modelling	Yes	Yes	ORC, TES, solar thermal collector
The state of the art in the presented study	RTO	Modelling	Yes	Yes	Carnot battery (ORC, heat pump, and TES), and PV

Table 1. An overview of research progress on waste heat recovery in automotive painting shops.

Authors, Year	Heat Sources	Experiment/ Modelling	Thermodynamic Analysis	Economic Analysis	The Technology of Waste Heat Recovery
Iglauer and Zahler, 2014 [9]	Baking oven and solar thermal	Modelling	Yes	Yes	Gas turbine and solar thermal collector
Chang et al., 2018 [12]	RTO	Experiment	Yes	Yes	Direct use for other purposes
Adamkiewicz and Nikończuk, 2019 [10]	Air preparation room	Modelling	Yes	No	Heat pump and TES
Daniarta et al., 2021 [11]	Baking oven	Modelling	Yes	No	ORC and TES
Giampieri et al., 2022 [13]	RTO, compressors, and chilled water system	Modelling	Yes	Yes	TES and liquid desiccant system configuration
Broniszewski et al., 2022 [14]	n.a.	Experiment	Yes	Yes	ORC
Martire et al., 2024 [15]	RTO and solar thermal	Modelling	Yes	Yes	ORC, TES, solar thermal collector
The state of the art in the presented study	RTO	Modelling	Yes	Yes	Carnot battery (ORC, heat pump, and TES), and PV

Giampieri et al. [13] reported waste heat recovery from regenerative thermal oxidisers (RTOs), compressed air systems, and chilled water systems to regenerate the liquid desiccant solution, which controls temperature and humidity within paint booths. This solution enables energy-efficient dehumidification and humidification processes, reducing the energy demand associated with conventional air management systems. The study showed that significant energy cost reductions were achieved by 44.4% in colder climates and 33.6% in hot and humid climates. Moreover, the PBP for implementing this technology ranges from 5.74 to 9.02 years, depending on the location and specific climate conditions.

Broniszewski et al. [14] investigated the waste heat recovered to generate electricity by utilising an ORC. It is mentioned that while standalone ORC systems may not always be economically viable due to high investment costs and long PBPs, combining this system with cogeneration units can substantially reduce energy costs and achieve shorter PBPs, making the solution more attractive for energy-intensive industries like automotive manufacturing.

In a recent article, Martire et al. [15] proposed a waste heat recovery solution for automotive paint shops using a solar ORC system integrating solar energy with low-grade waste heat from RTOs. The proposed system uses waste heat to preheat the organic working fluid in the ORC, thereby improving overall system efficiency. In this study, the TES was also considered to store and accumulate the heat taken from solar sources. This study reported that the implementation of the proposed system could generate 712.2 kW of electricity, covering about 5.9% of the plant’s energy needs while achieving an energy efficiency of 31.02%.

Significant potential improvement in waste heat recovery in painting shops and automotive manufacturing plants remains. This article proposes an innovative system and presents the simulation results of a novel waste heat recovery system, which uses a heat pump to capture waste heat from the RTO. The recovered heat is stored in TES and later used to generate electricity through an ORC. This process is referred to as a Carnot battery system [16,17]. In this case, the system offers an advantage for the double exploitation of the waste heat from RTO. In some regions with limited solar thermal energy collection, PV panels offer a promising alternative to power the heat pump. By installing PV panels on the factory roof, sufficient electricity can be generated to drive the system, making this an innovative and sustainable solution for waste heat recovery.

3. Methodology

3.1. System Description

Figure 1 shows the proposed Carnot battery system that is installed to recover the waste heat from RTO. In this figure, the process operation (indicated by the number) is also illustrated. This system consists of four key technologies, including heat pump, ORC, TES, and PVs. In this system, the RTO treats volatile organic compounds present in the exhaust air from the painting processes, with the exhaust air reaching temperatures around 150 °C. This waste heat is harnessed by the heat pump through the evaporator (EVA_HP), which evaporates the working fluid of the heat pump to the vapour state. The working fluid is then compressed by a compressor (CPR), increasing the pressure and the temperature. The compressor is driven by a motor (MTR_HP) powered by electricity from PVs. Also, in a condenser of the heat pump (CDS_HP), heat is transferred from the working fluid to a secondary fluid. As a result, the secondary fluid is heated up to around 145 °C, while the working fluid of the heat pump is condensed. The secondary fluid, now carrying the stored heat, can then be used to charge the TES system, effectively storing thermal energy for later use. The working fluid of the heat pump is then expanded in the throttle valve (TRV) and recirculated to the evaporator in a closed-loop system.

The heat can then be stored in TES and used to generate power when needed. In this case, the thermal energy stored in the TES system can be utilised to heat and evaporate the working fluid of the ORC in the evaporator (EVA_ORC). Once evaporated, the working fluid expands in an expander (denoted as EXP), converting thermal energy into mechanical work and then generating electricity by a generator (GTR_ORC). After the expansion process, the fluid is cooled and condensed in the condenser (CDS_ORC). Following the condensation process, the pressure of the working fluid is increased by a pump (PMP), allowing it to be recirculated through the system in a continuous closed-loop process of the ORC system. It is important to note that because of the time shift between the application of heat pump and ORC units, some parts (like the motor-generator and the compressor-expander) can be one bi-functional unit [18], but usually, this solution decreases the efficiency; therefore, in this work, the two units will be completely separated.

The model proposed in this study was developed using MATLAB R2024a, and the simulation utilised thermal property data obtained from REFPROP 10.0 [19]. The mathematical description of the proposed system is listed in

Table 2. A list of the components and specific processes shown in Figure 1.

List of Components	Specific Process
TES	$Q_{\mathrm{TES}}=V_{\mathrm{TES}}{\rho }_{\mathrm{TES}}{c}_{\mathrm{TES}}\mathsf{\Delta }{T}_{\mathrm{TES}\to \mathrm{env}}$ ${\dot{Q}}_{\mathrm{TES}}={\dot{Q}}_{\mathrm{s}1\to \mathrm{s}2}+{\dot{Q}}_{\mathrm{s}7\to \mathrm{s}8}$
	${\dot{Q}}_{\mathrm{s}1\to \mathrm{s}2}={\dot{m}}_{\mathrm{wh}}\left(h_{\mathrm{s}1}-h_{\mathrm{s}2}\right)$
	${\dot{Q}}_{\mathrm{s}7\to \mathrm{s}8}={\dot{m}}_{\mathrm{sf}}\left(h_{\mathrm{s}8}-h_{\mathrm{s}7}\right)$
EVAORC	${\dot{Q}}_{{\mathrm{EVA}}_{\mathrm{ORC}}}={\dot{m}}_{\mathrm{sf}}\left(h_{\mathrm{s}4}-h_{\mathrm{s}3}\right)={\dot{m}}_{\mathrm{ORC}}\left(h_2-h_1\right)$
EXP	$P_{\mathrm{EXP}}={\dot{m}}_{\mathrm{ORC}}\left(h_2-h_{3,is}\right){\eta }_{\mathrm{EXP},\mathrm{is}}$ ${\eta }_{\mathrm{EXP},\mathrm{is}}=\left(h_2-h_3\right)/\left(h_2-h_{3,\mathrm{is}}\right)$
RECORC	${\dot{Q}}_{{\mathrm{REC}}_{\mathrm{ORC}}}={\dot{m}}_{\mathrm{ORC}}\left(h_3-h_4\right)={\dot{m}}_{\mathrm{ORC}}\left(h_1-h_6\right)$
CDSORC	${\dot{Q}}_{{\mathrm{CDS}}_{\mathrm{ORC}}}={\dot{m}}_{\mathrm{air}}\left(h_{\mathrm{a}1}-h_{\mathrm{a}2}\right)={\dot{m}}_{\mathrm{ORC}}\left(h_4-h_5\right)$
PMPb	$P_{\mathrm{PMP}}={\dot{m}}_{\mathrm{ORC}}\left(h_{6,\mathrm{is}}-h_5\right)/{\eta }_{\mathrm{PMP},\mathrm{is}}$ ${\eta }_{\mathrm{PMP},\mathrm{is}}=\left(h_{6,\mathrm{is}}-h_5\right)/\left(h_6-h_5\right)$
EVAHP	${\dot{Q}}_{{\mathrm{EVA}}_{\mathrm{HP}}}={\dot{m}}_{\mathrm{wh}}\left(h_{\mathrm{s}6}-h_{\mathrm{s}5}\right)={\dot{m}}_{\mathrm{HP}}\left(h_8-h_7\right)$
CPR	$P_{\mathrm{CPR}}={\dot{m}}_{\mathrm{HP}}\left(h_{9,\mathrm{is}}-h_8\right)/{\eta }_{\mathrm{CPR},\mathrm{is}}$ ${\eta }_{\mathrm{CPR},\mathrm{is}}=\left(h_{9,\mathrm{is}}-h_8\right)/\left(h_9-h_8\right)$
CDSHP	${\dot{Q}}_{{\mathrm{CDS}}_{\mathrm{HP}}}={\dot{m}}_{\mathrm{sf}}\left(h_{\mathrm{s}8}-h_{\mathrm{s}7}\right)={\dot{m}}_{\mathrm{HP}}\left(h_9-h_{10}\right)$
TRV	$P_{\mathrm{TRV}}={\dot{m}}_{HP}\left(h_{10}-h_{7,\mathrm{is}}\right)/{\eta }_{\mathrm{TRV},\mathrm{is}}$ ${\eta }_{\mathrm{TRV},\mathrm{is}}=\left(h_{10}-h_7\right)/\left(h_{10}-h_{7,is}\right)$

, where $\dot{m}$, $\dot{Q}$, $Q$, $h$, $P$, $T$, $\rho$, $c$, $V$, and $\eta$ refer to mass flow rate, heat transfer rate, heat transfer, specific enthalpy, power, temperature, density, specific heat capacity, volume, and efficiency, respectively. In addition, the subscripts of sf, is, wh, and env refer to secondary fluid, isentropic, waste heat (exhaust air), and environment, respectively. In addition, a detailed calculation related to the heat exchanger can be seen in Equations (1) and (2).

$$A={\displaystyle \frac{\dot{Q}}{U\Delta T_{\mathrm{LMTD}}}}$$

(1)

$$\Delta T_{\mathrm{LMTD}}={\displaystyle \frac{\Delta T_{\max }-\Delta T_{\min }}{\ln \frac{\Delta T_{\max }}{\Delta T_{\min }}}}$$

(2)

The heat transfer surface area ($A$) of heat exchangers, such as the evaporator, recuperator, and condenser, can be calculated using Equation (1). In this equation, $U$ represents the overall heat transfer coefficient, and $\Delta T_{\mathrm{LMTD}}$ refers to the logarithmic mean temperature difference. In this study, the assumed overall heat transfer coefficients are as follows: 1.875 kW/m²K for the evaporator, 1.200 kW/m²K for the recuperator, and 2.029 kW/m²K for the condenser. The assumed overall heat transfer coefficients are chosen based on several factors related to the thermal properties and heat transfer behaviour of the specific processes involved [20]. It is worth noting that in the case of the evaporator, a portion of the heat exchanger is responsible for increasing the temperature of the working fluid in its liquid phase. For this part of the heat exchanger (pre-heater), an overall heat transfer coefficient of 1.200 kW/m²K is assumed. The logarithmic mean temperature difference can be calculated using Equation (2), where $\Delta T_{\max }$ and $\Delta T_{\min }$ refer to the maximal and minimal temperature differences at the end of the heat exchangers. For the purpose of this analysis, the heat exchangers are assumed to operate in a counter-current flow configuration.

Furthermore, the efficiency of the ORC system (${\eta }_{ORC}$) and the coefficient of performance (COP) of the heat pump can be calculated using Equations (3) and (4), respectively. These equations are used to calculate the overall power-to-power (P2P) efficiency of the Carnot battery, as shown in Equation (5). This calculation assumes that the TES operates at ideal conditions with no thermal losses (an efficiency of one). Evaluating these parameters is crucial for accurately assessing the system. The model has been validated against similar boundary conditions, as referenced in [21], demonstrating a difference of less than 5% in the results. This minimal difference highlights the reliability and robustness of the model.

$${\eta }_{\mathrm{ORC}}={\displaystyle \frac{P_{\mathrm{EXP}}-P_{\mathrm{PMP}}}{{\dot{Q}}_{{\mathrm{EVA}}_{\mathrm{ORC}}}}}$$

(3)

$$CO{P}_{\mathrm{HP}}={\displaystyle \frac{{\dot{Q}}_{{\mathrm{CDS}}_{\mathrm{HP}}}}{P_{\mathrm{CPR}}}}$$

(4)

$$P2P=CO{P}_{\mathrm{HP}}{\eta }_{\mathrm{ORC}}$$

(5)

3.2. Working Fluids and Boundary Conditions of the Proposed System

This study selected toluene as the working fluid for the ORC and heat pump operating at temperatures up to 145 °C due to its favourable thermal properties and environmental impact. The critical temperature of toluene is 318.6 °C. This working fluid has high thermal stability, which ensures reliability and efficient heat transfer within the operating temperature range of the cycle. The environmental impact is considered based on the low global warming potential (GWP) and zero ozone depletion potential (ODP). Based on a selection of working fluids, toluene demonstrated good performance in various studies [22,23].

In addition, Ethylene glycol has been selected as the secondary fluid to transfer heat from the heat pump to the TES and from the ORC to the TES. This fluid was chosen for its favourable thermal properties and environmentally friendly effects. Another advantage is that it remains in liquid form within the operating temperature range of the proposed system at atmospheric pressure. This makes it safer to use and requires less energy to circulate compared to when it is in the vapour phase.

In this study, several assumptions were made for simplification. All components are assumed to operate under steady-state conditions. For the heat exchanger, changes in the kinetic and potential energy of the working fluid are considered negligible, and there are no heat or pressure losses. It operates at constant pressure, with a constant overall heat transfer coefficient and specific heat. The pinch temperature difference between the heat source and the evaporator is set to 5 °C. Moreover, the isentropic efficiencies of the pump, compressor, and expander are assumed to be 0.75. The waste heat temperature (at s1) was assumed to be constant at 150 °C, and the mass flow rate was 34.25 kg/s [15], while the ambient air temperature (at a1) varied between 25 °C and 35 °C.

3.3. Boundary Conditions for Thermal Energy Storage

Performing an assessment is essential to determine the necessary mass for the TES system in relation to the proposed system design. This evaluation includes the calculation of the mass sizing parameter for TES, introduced in [24] and denoted as $\zeta$. This parameter represents the ratio between the mass of the TES material and the mass flow rate of the secondary fluid. As an alternative approach, $\zeta$ can be determined as the ratio of enthalpy change between the TES material and the secondary fluid. In this study, phase change material (PCM) was chosen as the TES material, with the assumption that no energy losses occur during either the charging or discharging phases. The mathematical model for calculating the TES mass sizing parameter is described in Equation (6).

$$\zeta ={\displaystyle \frac{m_{\mathrm{TES}}}{{\dot{m}}_{\mathrm{sf}}t}}={\displaystyle \frac{c_{\mathrm{sf}}\mathsf{\Delta }{T}_{\mathrm{sf}}}{\mathsf{\Delta }{h}_{\mathrm{TES}}}}$$

(6)

Furthermore, the mixture of 53% KNO₃, 40% NaNO₂, and 7% NaNO₃ was selected as the TES material as a case study due to its favourable thermophysical properties. The specific melting enthalpy of 80 kJ/kg, measured at a melting temperature of 142 °C [25], indicates a high energy storage capacity, making it an efficient choice for thermal applications. This composition was chosen to optimise both thermal conductivity and melting behaviour, ensuring reliable performance within the targeted temperature range for TES systems. In this study, the TES temperature of 142 °C was selected as the target set point for the heat pump operation to raise the temperature of the system. In this case, the temperature of the outlet of the compressor in the heat pump was around 146.5 °C. This choice ensured that the heat pump efficiently transferred thermal energy until the TES material reached its melting point, optimising the energy storage process. The system maximises energy efficiency during the phase change process by aligning the set point of the heat pump with the melting temperature of PCM.

In this situation, the TES system can be charged through two distinct methods, which have been discussed in recent literature [26]. The first method involves utilizing waste heat, while the second method relies on a heat pump. The temperature of waste heat at the outlet of the TES (at s2) is assumed to be 80 °C. These dual charging mechanisms provide flexibility and enhance the overall efficiency of the TES system. By utilising these two charging sources, the TES system can optimize energy utilization and contribute to improved thermal performance.

3.4. Boundary Conditions for Photovoltaics

In this study, the PVWatts Calculator [27], which is provided by National Renewable Energy Laboratory USA, was employed to estimate and predict the electricity generation needed to power the heat pump. The primary goal was to ensure that the PV system could meet the energy demands of the heat pump, at the very least. To achieve this, a simulation was conducted to model the annual global energy production of the PV system based on its location and physical characteristics. An article [28] reported a comparative analysis of PVWatts, PVGIS, and RETScreen for PV energy modelling tools. PVGIS and PVWatts are free, user-friendly tools that offer a range of flexibility options. PVGIS and PVWatts also provide accurate simulations that closely match real-world data, making them reliable choices for PV energy modelling [28,29]. In addition, PVWatts includes options for configuring inverter input parameters. Although the PVWatts Calculator uses simplified assumptions regarding detailed PV system components, certain general information about the system is still required to perform accurate simulations. These general parameters include the location’s solar irradiance, system size, orientation, and other key factors that influence PV performance. This approach allows for a reliable estimate of the PV system’s energy production despite the inherent simplifications in the PVWatts tool, making it suitable for the early-stage planning and feasibility analysis of PV installations.

Furthermore, specific assumptions made about the PV system’s performance and efficiency are outlined and summarised in

Table 3. Boundary conditions of PV.

Parameters	Unit	Value
System losses	%	14.08
Tilt	°	35 [30]
Azimuth	°	−2
DC-to-AC size ratio	–	1.2
Inverter efficiency	%	96%

. One of the automotive manufacturing plants in Karawang, Indonesia, was chosen for analysis for the PV simulation. This study utilises a standard PV module with a fixed roof-mounted array configuration. Key input parameters include total system losses in the PV setup, calculated at 14.08%, accounting for factors such as soiling, shading, wiring, mismatch, and system availability. The tilt angle of the array was set at 35°, approximating the optimal angle for the site’s location, while a slight azimuth adjustment of −2° provides a westward orientation, which can enhance energy capture at specific times of the day. This tilt angle of 35° is typical for Bandung, Indonesia, [30] and may be suitable for nearby locations like Karawang, Indonesia, allowing for effective adaptation. The direct current-to-alternating current (DC-to-AC) ratio of 1.2 was applied alongside a 96% inverter efficiency, reflecting the use of high-quality inverters common in modern PV systems. This setup helps ensure consistent, reliable energy conversion over time. In addition, it is important to note that the solar radiation was taken from the NREL National Solar Radiation Database, which has been integrated with PVWatts.

3.5. Cost Estimation and Economic Analysis

The economic analysis evaluates the cost-generation process associated with internal operations and final products in energy systems and industrial plants. The analysis provides a comprehensive view of operational efficiency by assessing the costs involved in each energy production stage. It enables a more accurate evaluation of the financial implications of different energy generation methods and technologies. Furthermore, understanding these costs helps to identify opportunities for optimising resource allocation and improving overall performance. This detailed economic insight is essential for making informed investment decisions, cost reductions, and long-term financial sustainability in energy projects.

The investment cost is determined by the additional components purchased for the system, including the ORC, heat pump, TES, and PV. The estimated cost ($C_p^0$) of each component can be estimated based on its specific capacity ($X$) or relevant parameters. For instance, the cost of rotary components, such as turbines and pumps, can be estimated based on their output power ($P$) or volumetric flow rate ($\dot{V}$). Similarly, the cost of stationary components, like evaporators, condensers, and TES units, can be estimated using factors such as heat exchanger area ($A$), heat transfer rate ($\dot{Q}$), or other relevant parameters. Several estimated cost functions used in this study are described and listed in Table 4, and some of them use Equation (7).

$$C_{\mathrm{p}}^0={10}^{K_1+K_2{\log }_{10}\left(X\right)+K_3{\left({\log }_{10}\left(X\right)\right)}^2}$$

(7)

Based on a recent market survey, the estimated cost for a 100-kW heat pump is approximately 18,000 EUR. A recent review article [31] highlights that TES can be integrated into ORC systems in multiple configurations, offering flexibility in its application. Given this adaptability, it is reasonable to approximate the cost of TES at a similar level to the estimated cost of the evaporator used in this study.

Some component purchase costs were sourced from different years, so these costs need to be adjusted to reflect the base year for this calculation in 2023. All purchase costs were converted from USD to EUR using the annual average exchange rate. Also, the costs were adjusted using the chemical engineering plant cost index (CEPCI) [32]. To estimate the bare module capital cost ($C_{\mathrm{BM}}$), the total purchase cost is multiplied by the bare module factor ($F_{\mathrm{BM}}$), which accounts for the development of the existing system [20]. The bare module factor for each component is taken from this study [20]. To account for additional expenses such as contractor fees, auxiliary facilities, system integration, installation, and project costs, the capital cost of the bare module is further multiplied by 1.18 [33] to estimate the total module capital cost ($C_{\mathrm{TM}}$). The bare module and total module capital costs are determined using Equations (8) and (9), respectively.

$$C_{\mathrm{BM}}={\displaystyle \sum }_{i=1}^n{C}_{\mathrm{p},\mathrm{i}}{F}_{\mathrm{BM}}$$

(8)

$$C_{\mathrm{TM}}=1.18{\displaystyle \sum }_{i=1}^n{C}_{\mathrm{BM},\mathrm{i}}$$

(9)

Table 4. The estimated cost functions for the components.

Components	Unit for the Capacity	The Range of the Capacity	Currency and Year	Estimated Cost Function or Value
				${\mathit{K}}_1$	${\mathit{K}}_2$	${\mathit{K}}_3$
Generator [34]	kW	80–10,000	USD, 2013	4.1055	0.0570	0.0797
ORC pump [20]	kW	1–100	USD, 2001	3.4771	0.1350	0.1438
ORC expander [35]	kW	100–20,000	USD, 2010	$C_{\mathrm{p},\mathrm{EXP}}^0=-14\times {10}^3+1.9\times {10}^3{\left(P_{\mathrm{EXP}}\right)}^{0.75}$
Air-cooled heat exchanger for condenser [20]	m2	200–2000	USD, 2001	4.0336	0.0234	0.0497
Heat exchanger for the evaporator [36]	m2	80–4000	USD, 2000	$C_{\mathrm{p},\mathrm{EVA}}^0=328000{\left({\displaystyle \frac{A_{\mathrm{EVA}}}{80}}\right)}^{0.68}$
Heat exchanger for preheater and recuperator [20]	m2	10–1000	USD, 2001	4.6656	−0.1557	0.1547
PV [37]	kW	-	USD, 2023		$758P_{\mathrm{PV}}$
Mounting rack [38]	-	-	USD, 2023		10% of PV cost
Inverter cost [38]	kW	-	USD, 2021		$300P_{\mathrm{PV}}$
Battery bank [38]	kWh	-	USD, 2021		$160E_{\mathrm{BB}}$
A 100 kW heat pump [39]	-	-	EUR, 2023	~18,000

Table 4. The estimated cost functions for the components.

Components	Unit for the Capacity	The Range of the Capacity	Currency and Year	Estimated Cost Function or Value
				${\mathit{K}}_1$	${\mathit{K}}_2$	${\mathit{K}}_3$
Generator [34]	kW	80–10,000	USD, 2013	4.1055	0.0570	0.0797
ORC pump [20]	kW	1–100	USD, 2001	3.4771	0.1350	0.1438
ORC expander [35]	kW	100–20,000	USD, 2010	$C_{\mathrm{p},\mathrm{EXP}}^0=-14\times {10}^3+1.9\times {10}^3{\left(P_{\mathrm{EXP}}\right)}^{0.75}$
Air-cooled heat exchanger for condenser [20]	m2	200–2000	USD, 2001	4.0336	0.0234	0.0497
Heat exchanger for the evaporator [36]	m2	80–4000	USD, 2000	$C_{\mathrm{p},\mathrm{EVA}}^0=328000{\left({\displaystyle \frac{A_{\mathrm{EVA}}}{80}}\right)}^{0.68}$
Heat exchanger for preheater and recuperator [20]	m2	10–1000	USD, 2001	4.6656	−0.1557	0.1547
PV [37]	kW	-	USD, 2023		$758P_{\mathrm{PV}}$
Mounting rack [38]	-	-	USD, 2023		10% of PV cost
Inverter cost [38]	kW	-	USD, 2021		$300P_{\mathrm{PV}}$
Battery bank [38]	kWh	-	USD, 2021		$160E_{\mathrm{BB}}$
A 100 kW heat pump [39]	-	-	EUR, 2023	~18,000

Some of the key economic indicators used in this study include specific investment cost (SIC), net present value (NPV), PBP, and levelized cost of electricity (LCOE). The SIC refers to the total capital cost required for the project, expressed per unit of capacity, which helps to compare the cost efficiency of different projects, which is described in Equation (10). The NPV measures the overall profitability of an investment by calculating the difference between the present value of cash inflows and outflows over the lifetime of the project; a positive NPV indicates a profitable investment, which can be determined using Equation (11). In this case, $C_{\mathrm{ncf}}$ refers to the annual economic savings of the system, calculated by subtracting the operational and maintenance costs ($C_{\mathrm{t}}$) from the total cost of electricity production ($C_{\mathrm{pr}}$). The PBP is the time it takes for the initial investment to be recovered from the project’s net cash inflows, providing insight into the risk and financial feasibility of the project. Moreover, the LCOE represents the per-unit cost of electricity generated over the lifetime of the project, accounting for capital, operating, and maintenance costs, and it serves as a standard metric for comparing the cost-effectiveness of different energy generation technologies. The LCOE can be determined using Equation (12). In this study, several assumptions are made. The installed system is expected to have a lifespan ($y$) of 20 years, with an annual discount rate ($d$) of 6.00% and an inflation rate of 2.00%. Also, the rate of operation and maintenance costs ($C_{\mathrm{t}}$) are set at 0.01 EUR per kWh. The business electricity price in Indonesia was assumed 0.065 EUR per kWh. Additionally, the return on investment (ROI) was determined using Equation (13) to provide insight into how well the investment generates returns relative to the resources invested.

$$SIC={\displaystyle \frac{C_{\mathrm{TM}}}{P_{\mathrm{net}}}}$$

(10)

$$NPV=-C_{\mathrm{TM}}+{\displaystyle \sum }_{i=1}^y{\displaystyle \frac{C_{\mathrm{ncf}}}{{\left(1+d\right)}^i}}$$

(11)

$$LCOE={\displaystyle \frac{C_{\mathrm{TM}}+{{\displaystyle \sum }}_{i=1}^y\frac{C_t}{{\left(1+d\right)}^i}}{{{\displaystyle \sum }}_{i=1}^y\frac{P_{\mathrm{net}}t}{{\left(1+d\right)}^i}}}$$

(12)

$$ROI=\left({\displaystyle \frac{-C_{\mathrm{TM}}+{{\displaystyle \sum }}_{i=1}^y{C}_{\mathrm{ncf},\mathrm{i}}}{C_{\mathrm{TM}}}}\right)100\%$$

(13)

4. Results and Discussion

This section presents a discussion of the results obtained from the thermodynamic and economic analyses. The thermodynamic analysis provides insights into the efficiency of the system and power (both consumption and generation) under various operating conditions, while the economic analysis evaluates the cost-effectiveness and financial feasibility of the proposed solutions.

4.1. Thermodynamic Analysis of the Proposed Carnot Battery

Figure 2 presents the simulation results for the Carnot battery in the temperature of air and the temperature of waste heat at the outlet. Figure 2a shows the COP of the heat pump ranging from 2.55 to 2.87, which varies based on the temperatures of the waste heat and the air. When the temperature of the waste heat at the outlet is 60 °C and the air temperature is 25 °C, the COP is 2.55. If the air temperature increases to 35 °C while maintaining the same waste heat outlet temperature of 60 °C, the COP improves to 2.87. In addition, when the waste heat outlet temperature is lowered to 50 °C with an air temperature of 25 °C, the COP remains at 2.55. However, at a waste heat outlet temperature of 60 °C and an air temperature of 35 °C, the COP rises to 2.87. These COP values are based on the assumption that the heat pump consumes 100 kW of power.

Figure 2b,c display the efficiency and net output power of the ORC, respectively. The efficiency of the ORC ranges from 0.125 to 0.155, while the net output power varies between 444.5 kW and 581.3 kW. At a waste heat outlet temperature of 60 °C and an air temperature of 25 °C, the ORC achieves its highest efficiency of 0.155 and the greatest net output power of 581.3 kW. However, when the air temperature rises to 35 °C while maintaining a waste heat outlet temperature of 60 °C, the efficiency drops to 0.139, and the net output power decreases to 509.9 kW. In the case where the waste heat outlet temperature is reduced to 50 °C and the air temperature remains at 25 °C, the ORC efficiency is 0.142, with a net output power of 514.5 kW. If the air temperature increases to 35 °C with a waste heat outlet temperature of 50 °C, the efficiency falls further to 0.125, and the net output power decreases to 444.5 kW. To achieve the desired results, the mass flow of the ethylene glycol from TES to ORC varies between 37.2 and 62.3 kg/s. The ORC system operated with a mass flow rate ranging between 7.4 and 7.7 kg/s. The primary energy source for charging the TES was the waste heat recovered from the exhausted air, which played a dominant role in the system’s overall energy efficiency. Moreover, the heat pump contributed approximately 9.5% to 10.6% of the total energy required to charge the TES. This approach highlights the integration of both waste heat recovery and additional heat pump, optimising the energy storage process for better sustainability. Therefore, the outlet temperature of the waste heat can be maintained between 50 °C and 60 °C.

Figure 2d illustrates the P2P of the Carnot battery ranges between 0.36 and 0.40 under various operating conditions. When the waste heat temperature at the outlet is 60 °C and the ambient air temperature is 25 °C, the P2P is 0.40, representing the higher end of the efficiency range. This suggests that a larger temperature difference between the waste heat and ambient air contributes to greater P2P. In another scenario, when the waste heat outlet temperature remains at 60 °C, but the ambient air temperature increases to 35 °C, the P2P remains at 0.40, indicating that the impact of ambient temperature may plateau under certain conditions. However, when the waste heat outlet temperature drops to 50 °C while the air temperature stays at 25 °C, the P2P decreases to 0.36. This reduction in temperature difference results in lower P2P, as expected in thermodynamic processes. Furthermore, when the waste heat outlet temperature remains at 60 °C and the ambient air temperature is increased to 35 °C, the P2P again drops to 0.36. This highlights that an increase in the ambient air temperature reduces the efficiency of ORC, especially when the temperature difference between the waste heat and the air is narrower. Therefore, the P2P is low.

This study also presents a comparison of the thermodynamic assessment of the ORC system, both with and without a recuperator. The analysis focuses on the efficiency differences between the ORC system and their impact on the P2P of the Carnot battery, as shown in Figure 3. The results show that the ORC with a recuperator achieves higher efficiency compared to the system without one. This improvement is due to the recuperator recovering some of the heat of the working fluid after the expansion process, which is used to raise the temperature of the working fluid after the pump. As a result, the ORC requires less heat input, leading to an increase in overall efficiency. A literature study [40] also reported a theoretical analysis of the ORC with a recuperator using various organic working fluids, which improved efficiency. When the waste heat outlet temperature is assumed to be around 60 °C and the air temperature is 25 °C, the efficiency of the ORC without a recuperator is lower than with a recuperator, with a difference of 0.0080. Similarly, under the same conditions, the P2P of the Carnot battery for the ORC without a recuperator is also lower compared to the system with a recuperator, with a difference of 0.0230.

In this study, a PCM mixture consisting of 53% KNO₃, 40% NaNO₂, and 7% NaNO₃ was selected for its optimal thermal properties in the TES system. The results show that incorporating a recuperator in the ORC significantly influences the TES mass sizing ratio, $\zeta$. Specifically, when a recuperator is included, the $\zeta$ ratio ranges from 5.86 to 6.16. In contrast, without a recuperator, the $\zeta$ ratio increases to a range of 6.15 to 6.54. This suggests that using a recuperator can reduce the PCM mass requirement for TES, thereby improving cost effectiveness.

The mean squared error (MSE) was used to determine the average of the squared difference between the efficiency of the ORC both with and without a recuperator, as well as the P2P of the Carnot battery and $\zeta$ ratio for TES. The square root of MSE or RMSE was also used in this assessment. Both MSE and RMSE can be calculated using Equations (14) and (15), where $\check{y}$ is the data of the system with a recuperator, $\widehat{y}$ is the data of the system without a recuperator, and $N$ is the total number of the data points. The results of the MSE and RMSE are really low, which can be seen in

Table 5. The MSE and RMSE between the proposed system both with and without a recuperator in the ORC.

Parameter	${\mathit{\eta }}_{\mathit{O}\mathit{R}\mathit{C}}$	$\mathit{\zeta }$	P2P
MSE (–)	5.5947 × 10−5	0.1121	4.0907 × 10−4
RMSE (–)	0.0075	0.3348	0.0202

.

$$MSE={\displaystyle \frac{1}{N}}{\displaystyle \sum }_{i=1}^N{\left({\check{y}}_i-\widehat{y}\right)}^2$$

(14)

$$RMSE=\sqrt{MSE}$$

(15)

4.2. System Performance of Photovoltaic

Figure 4 presents the monthly performance results of the PV system, showing energy output in AC MWh alongside corresponding average solar radiation in kWh/m²/day for a full year. The data span from January to December, illustrating variation in radiation and PV energy output; the PV energy output closely follows the solar radiation levels throughout the year. The total energy produced by PV is around 1.35 GWh AC. The peak output is in August, which marks the highest energy output at 145,917 kWh AC, with the highest average solar radiation of 6.42 kWh/m²/day. In this case, the lowest output is in December, which records the lowest energy output at 76,427 kWh AC and the lowest solar radiation at 3.34 kWh/m²/day. Indonesia’s tropical climate brings two main seasons: a dry season (April–September) and a wet season (October–March). The PV system performs optimally in the dry season, when solar radiation increases from April (5.28 kWh/m²/day) to September (6.18 kWh/m²/day), contributing to high energy outputs. During the wet season, energy output declines due to cloud cover and reduced sunlight hours, indicating solar radiation between 3.34 and 4.95 kWh/m²/day.

The PV system, which is integrated with battery banks and an inverter, is designed to meet the energy needs of a 100-kW heat pump, which operates in a manufacturing plant running 24 h a day for about 20–22 days each month. The PV system harnesses solar energy during the day to power the heat pump while also charging the battery bank. The battery bank is essential for storing surplus energy produced by the PV system. This stored energy ensures that the heat pump can operate reliably at night and during times when solar power is unavailable. Utilising the stored energy allows the heat pump to function continuously, even after sunset, minimising the need for external power sources and providing a consistent energy supply throughout the day and night. Based on the system’s performance data, the daily energy produced is generally sufficient to support the heat pump and charge the battery bank (for the operation of the heat pump at night), especially during months with higher solar radiation. In peak months like August, when daily solar radiation reaches 6.42 kWh/m², the PV system not only meets the heat pump’s demand, but also generates excess energy. This surplus can be redirected to support other operations in the manufacturing plant, thereby optimising energy use and reducing dependence on external sources. For instance, from May through September, the PV output consistently exceeds the heat pump’s requirements, allowing the additional energy to be utilised for other purposes, such as powering auxiliary equipment and supporting additional heating and cooling processes. Even in months with lower radiation, like December and January, the PV system’s output remains close to or meets the heat pump’s daily energy requirements, ensuring reliable operation year-round.

4.3. Monthly Power Production and Consumption

Figure 5 illustrates the heat pump’s monthly energy production (indicated by positive values) from ORC and PV, alongside the energy consumption (indicated by negative values). In this study, the total net energy generation was calculated by subtracting the energy consumed by the heat pump from the combined energy produced by the ORC and PV system. The results show that the operational schedule of the ORC and heat pump adheres to working days, running for 21–23 days each month rather than a full 29–31 days. This scheduling contributes to variations in monthly energy generation and consumption.

A significant reduction in operating days was observed in April due to an annual maintenance and improvement project, leading to lower energy production from both the ORC and PV systems and, correspondingly, reduced energy consumption by the heat pump. Therefore, April recorded the lowest total net energy production at 229.79 MWh, while August, with full operational days, showed the highest net production, reaching 408.86 MWh. Furthermore, the monthly energy production from the ORC varied between 137.05 MWh and 318.5 MWh, with the highest output in July (318.49 MWh) and the lowest in April. Meanwhile, the PV system’s monthly energy production ranged from 75.35 MWh to 145.92 MWh. The heat pump’s energy consumption varied between 24 MWh and 55.2 MWh, following fluctuations in operational days and system performance requirements. The lowest energy consumption of the heat pump was also observed in April. It is important to note that, while both the heat pump and ORC systems showed the lowest energy production and consumption during non-operational periods, such as annual maintenance, the PV system continued to produce electricity. This ongoing PV production can help support essential power needs during these maintenance downtimes. Also, it is worth noting that the total annual net generation from the system with PV was 4307.29 MWh.

4.4. Economic Analysis of Different Scenarios

The economic viability of the proposed system, as illustrated in Figure 1, was carefully assessed. To provide a comprehensive evaluation, this study introduces three additional scenarios, each aimed at further analysing the economic potential of the project. These scenarios examine the economic impact of integrating or excluding a PV system and a recuperation process within the ORC system. The scenarios are described as follows.

-

Case 1 baseline scenario evaluates the project by considering both the PV system and the recuperation process within the ORC, as illustrated in Figure 1.

-

Case 2 analyses the economic performance of the project with the recuperation process in the ORC, but without including the PV system. In this scenario, the ORC-heat pump-TES system, functioning as a Carnot battery, can continue to operate even without the PV system. The electricity needed to power both the heat pump and the ORC pump is obtained from the grid.

-

Case 3 examines the project setup where only the PV system is included, omitting the recuperation process in the ORC.

-

Case 4 assesses the project without incorporating either the PV system or the recuperation process in the ORC.

Figure 6 shows the breakdown of investment costs for each project scenario, categorised into four main components: the ORC system, heat pump, TES, and PV system. For clarity in this study, the investment costs associated with the ORC, heat pump, and TES are collectively considered as the investment cost of the Carnot battery. This grouping highlights the cost associated with the energy storage and conversion components, distinguishing them from the PV system, which serves as an optional energy source. This cost distribution provides insight into how each component contributes to the overall investment, offering a clear basis for economic comparison across different configurations.

The following cases highlight how various configurations impact the total investment costs. The total investment cost of Case 1 is approximately 2.56 million EUR. Here, the PV system accounts for 61.3% of the cost (~1.57 million EUR), while the Carnot battery contributes 38.7%, divided into 33.9% (~0.99 million EUR) for the ORC, 4% for the TES, and 0.8% for the heat pump. Moreover, without the PV system, but including a recuperation process in the ORC system, described as Case 2, the total investment cost is reduced to approximately one million EUR, representing only the Carnot battery costs. This distribution is 87% for the ORC, 10.3% for the TES, and 2.1% for the heat pump. In addition, Case 3, which includes the PV system, but excludes a recuperator in the ORC system, offers about 2.49 million EUR, with the PV system contributing 64.3% (~1.57 million EUR) and the Carnot battery covering 35.7% (30.6% ORC, 4.2% TES, and 0.9% heat pump). Excluding a recuperator necessitates a larger liquid heater area, increasing its investment cost. In this study, Case 4 offers the lowest total investment cost, approximately 0.87 million EUR, achieved in this configuration, which excludes both the PV system and the recuperator. This cost was allocated to the Carnot battery, with a breakdown of 85.9% for the ORC (around 0.75 million EUR), 11.7% for the TES (approximately 0.10 million EUR), and 2.4% for the heat pump (around 21.24 thousand EUR).

From the investment mentioned above, the discounted cash flow can be estimated and evaluated using a specific discount of 6%. This discounted rate value presents the case in Indonesia and reflects the value of the money and the associated risks of the investment. By discounting the future cash flow to their present value, the NPV can then be determined. This discounted cash flow can be seen in Figure 7. It is important to note that the cumulative discounted cash flow is presented, so the NPV and PBP can be evaluated. The discounted cash flow for each case varies depending on electricity production and investment. Each case has a different investment cost between 0.87 and 2.57 million EUR, indicated in year 0 as initial installation expenses. Starting in year 1, the system is expected to be able to generate electricity and contribute revenue. The revenue rates of each case depend on the capacity of electricity generation. Therefore, Figure 7 shows that Case 4 has the quickest positive cumulative discounted cash flow due to the lowest investment and SIC.

Furthermore, the economic assessments for each case, including key metrics such as estimated power output, annual energy production, investment cost, SIC, NPV, PBP, LCOE, and ROI, are presented in

Table 6. Summary of the economic assessment.

Parameters	Unit	Case 1	Case 2	Case 3	Case 4
Recuperator	-	Yes	Yes	No	No
PV system	-	Yes	No	Yes	No
Estimated power production	kW	1310.31	476.97	1310.31	476.97
Estimated annual total energy production	MWh	4307.29	2953.29	4307.29	2953,29
Investment cost	EUR	2,568,404.57	993,590.97	2,448,520.97	873,707.37
SIC	EUR/kW	1960.15	2083.10	1868.66	1831.76
NPV	EUR	654,541.23	1,216,220.71	774,425.83	1,336,103.31
PBP	years	14.06	7.13	13.31	6.20
LCOE	EUR/kWh	0.064	0.041	0.061	0.037
ROI	%	25.48	122.41	31.63	152.92

. In terms of output power, Cases 1 and 3 generate approximately 1.31 MW each, as both incorporate PV systems. By contrast, Cases 2 and 4, which exclude the PV component, produce a lower power output of around 0.47 MW. This difference highlights the contribution of PV integration to enhanced power generation. Regarding annual energy production, Cases 1 and 3 achieve a higher energy output of approximately 4.30 GWh, significantly more than Cases 2 and 4, which produce around 2.95 GWh. This increase is attributed to the additional energy supplied by the PV system in Cases 1 and 3.

Incorporating a PV system and recuperator in the ORC system, as seen in Case 1, results in high investment costs, reaching up to 2.57 million EUR. In contrast, Case 4, excluding both the PV system and the recuperator, offers a low investment cost of approximately 0.87 million EUR. However, investment cost alone is insufficient for a comprehensive economic evaluation; thus, SIC is used to provide a more balanced assessment, as it accounts for both investment cost and power production. The SIC results show that Case 4 achieves low SIC, around 1.83 thousand EUR/kW, reflecting its cost efficiency despite the lower power output. In contrast, Case 2, without a PV system, but including a recuperator, has a high SIC, at approximately 2.08 thousand EUR/kW. Although Case 1 has the highest upfront investment, its SIC remains relatively competitive and is notably lower than that of Case 2.

In terms of NPV and PBP, Case 4 presents a high NPV of approximately 1.33 million EUR, while Case 2 has a slightly low NPV of around 1.21 million EUR. Interestingly, cases that incorporate a PV system, such as Case 1 and Case 3, tend to have low NPVs, with values of about 0.65 million EUR and 0.77 million EUR, respectively. This suggests that, despite increasing power production, the PV system reduces profitability when measured by NPV. The impact of PV on economic performance is further evident in the PBP results. Cases with PV systems, such as Case 1 and Case 3, have longer PBPs, extending beyond thirteen years, making them slower to recover their investment costs.

In contrast, cases without PV, like Case 2 and Case 4, demonstrate more competitive PBPs, ranging from 6–8 years. Case 4, in particular, stands out with an attractive PBP of approximately 6.2 years, indicating a quicker ROI. This study highlights that, while adding a PV system increases energy production, it may result in a longer PBP and reduced NPV, making cases without PV potentially more attractive from a financial perspective.

In this study, all cases demonstrate favourable economic assessment with low LCOE ranging from 0.037 to 0.064 EUR/kWh and ROI above 25%. These low LCOE values suggest that each case is cost-effective in terms of energy production, making them economically attractive options for sustainable power generation and waste heat recovery. It is important to mention that Cases 2 and 4 indicate high ROI above 100%, making them attractive from an economical point of view. The high ROI indicates that the initial investments in each configuration are expected to result in significant financial returns over their operational lifetimes, underscoring the viability of the systems analysed.

This study demonstrates that the proposed system is economically competitive, as illustrated in Figure 1 and represented by Case 1. Case 1 achieves an SIC of 1.96 thousand EUR/kW, an NPV of approximately 654,541 EUR, a PBP of 14.06 years, an LCOE of 0.064 EUR/kWh, and an ROI of 25.48%. This system can generate around 1.31 MW, with an estimated annual energy production of 4.30 GWh, indicating both high output and efficient energy costs. As an alternative, Case 4 (the configuration without PV and without a recuperator) demonstrates greater economic attractiveness in terms of SIC, NPV, and PBP. However, this comes at the cost of a significant reduction in power generation, producing approximately 63.59% less energy than the proposed Case 1. The electricity from the grid can power the heat pump and ORC system pump. Therefore, while Case 4 is economically favourable, its lower power output may limit its application where higher energy demands are required. It is also proven that Case 4, which can be referred to as a Carnot battery without a recuperator in ORC, offers competitiveness in waste heat recovery in this study.

The proposed system can be designed with a modular approach, allowing the system to scale proportionally with the size of the manufacturing facility. In that situation, the size of the system will influence the area used for installation. Also, Cases 1 and 3 consider PV systems in the installation. The PV system is likely to occupy approximately 5% of the available rooftop area in the automotive manufacturing plant.

5. Future Directions

For future research, exploring scenarios with potential government interventions, such as feed-in tariffs and subsidies, could make the proposed system even more financially viable. A feed-in tariff [41], for instance, could enhance the revenue stream, while subsidies on PV installation costs might reduce the upfront investment burden, improving NPV, PBP, and other economic assessments for Case 1, the proposed system illustrated in Figure 1. Such incentives could position the system as an attractive choice for both investors and policymakers committed to renewable energy expansion and sustainable infrastructure.

In addition to these potential incentives, a thorough economic assessment that considers the depreciation of assets, in this case, each individual automotive unit, would add valuable practical depth to the financial modelling. Given the limited and often confidential data, incorporating depreciation would offer a more comprehensive understanding of long-term costs and residual value, supporting more resilient economic evaluations. Integrating these elements into future studies could result in valuable insights into lifecycle costs and enhance the accuracy of financial forecasts, which would be particularly beneficial for assessing viability in sensitive and high-stakes investments.

Moreover, continued advancements in PV efficiency and recuperator design hold promise for improving overall system performance. Together, these strategies and innovations could strengthen the system’s competitiveness, making it more appealing to a range of stakeholders, from policy designers to private investors focused on renewable energy expansion.

The proposed system can be improved by utilising heat pipes to efficiently transfer thermal energy between its components. In that case, heat pipes can be used to transfer heat from the TES to the ORC, as indicated by s3 and s4 in Figure 1. They can also transfer heat from waste heat to the heat pump, as shown in s5 and s6, and from the heat pump to the TES, as represented by s7 and s8 in the same figure. By offering a highly efficient and reliable means of thermal energy transfer, heat pipes help minimize energy losses and enhance overall system performance.

6. Conclusions

This study presents a proposed system designed to recover and utilise heat from the exhaust air following the RTO process. The system integrates a Carnot battery and PV system. The Carnot battery, in this configuration, consists of three main components, including ORC, TES, and heat pump. The waste heat from exhaust air after the RTO is initially captured in TES. To further optimise heat recovery, a heat pump is employed to extract additional energy from the low-temperature waste heat. This energy is then used to raise the temperature of a secondary fluid, which is also stored in the TES. As a result, the TES is charged from two sources: directly from exhaust air and indirectly from the heat pump. The stored heat in TES can subsequently be used to produce electricity through ORC. This dual-source charging approach enables more efficient recovery and energy generation. It is worth noting that the heat pump can be considered as charging, the TES as storing, and the ORC as discharging part of the Carnot battery. In this way, the parts of the storing system—unlike most electrochemical batteries—are independent, making charging power, discharging power, and storage capacity at uncoupled quantities, giving better flexibility to fulfil the needs of consumers/users. The main results from this study are summarised as follows.

-

The proposed system demonstrates that the COP of the heat pump ranges from 2.55 to 2.87. For ORC with a recuperator, the efficiency falls between 12.5% and 15.5%, with net output power varying from 444.5 kW to 581.3 kW. As a result, the P2P of the Carnot battery system lies between 0.36 and 0.40, depending on different operating conditions.

-

The study compares the performance of the Carnot battery system with and without a recuperator in the ORC. The results indicate that the difference in efficiency between the two configurations is low, with an RMSE of 0.0075 and an MSE of 5.5947 × 10⁻⁵ for ORC efficiency. In this case, the P2P of the Carnot battery shows a slight variation, with an RMSE of 0.0202 and an MSE of 4.0907 × 10⁻⁴.

-

In addition, incorporating a recuperator in TES results in a$\zeta$ ratio between 5.86 and 6.16. Without a recuperator, however, the $\zeta$ ratio rises to a range of 6.15 to 6.54. This comparison indicates that using a recuperator reduces the PCM mass needed for TES, thereby enhancing cost-effectiveness. Also, the results indicate a difference with an MSE of 0.1121 and an RMSE of 0.3348.

-

The PV system generates between 75.35 and 145.91 MWh of AC energy, resulting in an annual energy production of approximately 1.35 GWh AC. This energy is primarily used to power the heat pump and the ORC pump. Any excess energy beyond the requirements of the system can be redirected for other uses within the manufacturing plant, enhancing overall energy efficiency and potentially lowering operational costs.

-

The Carnot battery system incorporating the PV component achieves a total annual net generation of around 4.30 GWh.

-

Four scenarios were evaluated to determine the economic viability of the project, considering configurations both with and without a PV system and a recuperator in the ORC. When operating without PV, the Carnot battery relies on electricity from the grid. The results indicate that all configurations provide strong economic performance, with the following favourable metrics across cases: a SIC below 2000 EUR/kW, an NPV over 500 thousand EUR, a PBP between 6 and 15 years, a low LCOE below 0.070 EUR/kWh, and an ROI between 25% and 160%. Among these configurations, the proposed system, which includes both PV and a recuperator, achieves a SIC of 1960 EUR/kW, an NPV of approximately 654,541 EUR, a PBP of 14.06 years, an LCOE of 0.064 EUR/kWh, and an ROI of 25.48%. This configuration provides a high output power of approximately 1.31 MW, with an estimated annual energy production of 4.30 GWh, reflecting both high energy generation and cost efficiency. As an alternative, the configuration without PV and without a recuperator demonstrates even greater economic attractiveness regarding SIC, NPV, and PBP. However, this option results in a power output approximately 63.59% lower than the proposed system with PV and a recuperator, highlighting a trade-off between lower costs and reduced energy production.

Further research directions include exploring potential government interventions, such as feed-in tariffs and subsidies, which could enhance the financial viability of the proposed system. These incentives could lower upfront costs, improve returns, and make renewable energy investments more attractive, ultimately supporting broader adoption and sustainability goals.