Performance Improvement of Low-Temperature Thermal Energy Conversion Systems via Physics-Based Control and Optimization

Performance Improvement of Low-Temperature Thermal Energy Conversion Systems via Physics-Based Control and Optimization | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Performance Improvement of Low-Temperature Thermal Energy Conversion Systems via Physics-Based Control and Optimization Munsif Ali, Uzair Ahmad, Shafi Ullah, Subhan Ullah, Rahim Ullah, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8706095/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Low-Temperature Thermal Energy Conversion Systems (LT-TECS) are critical for recovering low-grade waste heat from geothermal and industrial sources however, their practical deployment is constrained by strong nonlinear system behaviour and the absence of adaptive, physics-informed control strategies. This study presents a physics-based, simulation-driven control and optimization framework aimed at improving the system-level performance of low-temperature thermal energy conversion systems operating below 200°C. A first-principles numerical model is developed to capture the coupled thermal electrical behaviour of the system over thermal source temperatures ranging from 50 to 200°C, heat fluxes between 0.5 and 5.0 kW m⁻², and electrical load values from 0.5 to 3.0. Performance prediction surfaces indicate electrical power outputs varying from approximately 300 to 2600 W and conversion efficiencies between 1% and 14%, highlighting strong sensitivity to operating conditions. A surrogate-assisted, physics-based optimization strategy is employed to construct control maps and implement a self-learning adaptive control loop. Time-domain simulations over training periods of 24 to 96 h demonstrate consistent performance improvements under optimized control. Average electrical power output increases by up to 2.2%, while conversion efficiency improves by approximately 0.7 percentage points compared to conventional control, accompanied by a 25 to 40% reduction in load and heat-flux fluctuations. The results confirm that physics-based adaptive control and optimization can deliver measurable and stable performance gains without hardware modification, addressing a key gap in low-temperature thermal energy conversion system operation. The proposed framework provides a transferable and cost-effective solution for improving the energy yield of existing LT-TECS infrastructure. Computational Physics Energy Engineering High Energy and Particle Physics Low-temperature energy conversion Physics-based control Adaptive optimization Waste heat recovery Energy efficiency. Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 1. Introduction Low-temperature thermal energy conversion systems have emerged as a critical research area due to their potential to recover vast quantities of low-grade heat from geothermal resources, industrial processes, and distributed energy systems that are otherwise dissipated into the environment [1,2]. Recent studies indicate that more than 50% of industrial waste heat is available at temperatures below 200 °C, where conventional power cycles operate with poor efficiency [3,4]. Consequently, physics-based conversion mechanisms such as thermoelectric, electrochemical, and hybrid thermal-driven systems have gained increasing attention as enabling technologies for decentralized and sustainable power generation [5]. Despite these advances, the operational performance of low-temperature thermal energy conversion systems remains significantly below theoretical limits due to intrinsic nonlinearities, coupled transport phenomena, and suboptimal control strategies [6]. These systems exhibit strong sensitivity to operating parameters including temperature gradients, internal electrical resistance, heat flux, and electrochemical potential, which complicates their real-time operation and limits efficiency gains [7]. Traditional design-oriented optimization approaches are often static in nature and fail to account for dynamic interactions between thermal and electrical domains under variable operating conditions [8,9]. The core problem addressed in this research is the lack of adaptive, physics-informed control and optimization frameworks capable of systematically improving the performance of low-temperature thermal energy conversion systems [10]. Existing studies primarily focus on material enhancement or component-level design improvements, while system-level control and operational optimization remain insufficiently explored [11]. As a result, many thermal energy conversion systems are operated conservatively lead to reduced power output and inefficient utilization of available thermal resources. Based on this context, the present study addresses the following research questions: How can physics-based modelling be integrated with control-oriented optimization to enhance system performance? Which operating parameters exert the greatest influence on power output and efficiency? To what extent can optimized control strategies improve system performance under realistic physical and operational constraints? These questions guide the formulation of a structured and reproducible research framework. The aim of this research is to improve the performance of low-temperature thermal energy conversion systems through physics-based control and optimization. To achieve this aim, the study pursues several objectives, (1) the development of a physics-informed simulation framework, (2) construction of surrogate models for nonlinear system behaviour, (3) identification of dominant performance-driving variables through sensitivity analysis, and (4) application of constrained optimization techniques to determine optimal operating conditions. The motivation for this research is driven by the global need to enhance energy efficiency and support decarbonization pathways without relying solely on new infrastructure or advanced materials [19]. Low-temperature thermal energy conversion systems represent a largely untapped opportunity to improve overall energy utilization efficiency when coupled with intelligent control strategies that maximize performance using existing system architectures [12]. The scope of this study is confined to system-level performance analysis of low-temperature thermal energy conversion systems operating typically below 200 °C. The focus is placed on steady-state and quasi-dynamic behaviour, while long-term degradation mechanisms and experimental validation are beyond the present scope. Numerical simulation and data-driven surrogate modelling are employed to ensure generality and reproducibility of results across a wide range of operating conditions. The novelty of this research lies in the integration of physics-based modelling, sensitivity analysis, and constrained optimization into a unified control-oriented framework tailored specifically for low-temperature thermal energy conversion systems. Unlike prior works that treat modelling and optimization independently, this study establishes a closed-loop methodology that enables systematic performance enhancement while preserving physical interpretability. The central research hypothesis is that the performance of low-temperature thermal energy conversion systems can be significantly improved through physics-based control and optimization without modifying system hardware. It is hypothesized that regulating key operating parameters within physically feasible limits can yield measurable improvements in power output and conversion efficiency. From a methodological standpoint, the research adopts a structured workflow consisting of physics-based system modelling, numerical data generation, substitute model development using artificial neural networks, partial-derivative-based sensitivity analysis, and nonlinear constrained optimization. This methodology builds upon established control and optimization strategies successfully applied in complex energy systems and adapts them to the physics of low-temperature thermal conversion [16]. The expected study outcomes include the identification of dominant operating variables, quantified performance improvements under optimized operation, and validated control strategies suitable for low-temperature thermal energy applications [13]. These outcomes aim to provide actionable insights for system designers and operators seeking cost-effective performance enhancement solutions [14]. A key research gap addressed by this work is the absence of comprehensive control-focused optimization frameworks for low-temperature thermal energy conversion systems. While extensive research exists on materials and thermodynamic analysis, the integration of physics-based control and optimization at the system level remains limited. The significance of this research lies in its contribution to energy efficiency improvement and sustainable power generation. By enabling enhanced utilization of low-grade thermal resources, the proposed framework supports broader energy transition objectives and aligns with international net-zero strategies [15]. Furthermore, the methodological framework developed in this study is transferable to a wide range of thermal energy conversion technologies. This report is organized to present the theoretical background, modelling framework, optimization methodology, and performance evaluation results in a coherent manner. The research approach follows a physics-informed, simulation-driven paradigm that balances scientific rigor with engineering applicability. This study adopts a physics-based, simulation-driven methodology combining surrogate-assisted modelling, sensitivity analysis, and adaptive control optimization to enhance the performance of low-temperature thermal energy conversion systems. 2. Physics-Based Intelligent Control and Optimization Framework As the conventional control strategies are replaced or enhanced by data-driven and physics-informed algorithms, the resulting architecture can be classified as an intelligent control framework. In low-temperature thermal energy conversion systems, such frameworks are relevant due to the nonlinear coupling between thermal transport, electrochemical processes, and electrical power generation [ 16 ]. The inherent variability of low-grade thermal sources further necessitates adaptive control strategies capable of maintaining optimal operation under changing boundary conditions [ 17 ]. Low-temperature thermal energy conversion systems are governed by complex interactions between temperature gradients, heat flux, internal resistance, and electrochemical or thermoelectric potentials. Conventional proportional integral (PI) or rule-based controllers are typically designed using linearized models around fixed operating points, which limits their effectiveness when system parameters vary significantly [ 18 ]. As a result, these controllers often lead to conservative operation, reduced power output, and suboptimal conversion efficiency [ 19 ]. Intelligent control strategies provide an alternative by learning nonlinear system behaviour directly from data while maintaining consistency with physical laws [ 20 ]. Artificial neural networks (ANNs) are widely adopted in intelligent energy system control due to their ability to approximate nonlinear mappings, handle noisy data, and generalize across diverse operating regimes [ 21 ]. In thermal energy conversion applications, ANN-based models have been successfully applied for system identification, performance prediction, and operational optimization of thermoelectric and electrochemical systems [ 22 , 23 ]. Beyond neural networks, evolutionary and population-based optimization algorithms such as genetic algorithms (GA) and particle swarm optimization (PSO) have demonstrated strong capability in solving nonlinear and constrained optimization problems encountered in energy systems. These algorithms do not rely on gradient information and are therefore effective for optimizing complex thermal energy conversion systems with non-convex performance landscapes. When coupled with ANN-based surrogate models, evolutionary algorithms significantly reduce computational cost while enabling global exploration of the operational parameter space [ 24 , 25 ]. A critical advantage of physics-based intelligent control lies in the integration of first-principles knowledge with learning-based techniques. Physics-informed frameworks embed thermodynamic constraints, energy balance equations, and transport relations directly into the modelling and optimization process, thereby preventing non-physical solutions and improving model robustness. This hybrid modelling paradigm enhances interpretability and reliability compared to purely data-driven approaches [ 26 ]. In this study, a physics-based intelligent control and optimization framework is developed for low-temperature thermal energy conversion systems. The framework integrates physics-informed simulation, ANN-based surrogate modelling, sensitivity analysis, and constrained optimization to identify optimal operating conditions. The optimized parameters are subsequently employed to define control-oriented correction strategies that enhance power output and conversion efficiency while maintaining physical feasibility and system stability [ 27 ]. As shown in Fig. 1 , the physics-based intelligent control and optimization framework illustrates the closed-loop integration of low-temperature thermal energy conversion, data-driven modelling, and optimization-based control. The thermal source provides low-grade heat inputs in the form of temperature 𝑇 and heat flux 𝑄, which drive the low-temperature thermal energy conversion system to generate electrical power 𝑃 with conversion efficiency 𝜂. Measured operational data (𝑇, 𝑄, 𝑃, 𝜂) are fed into the physics-based intelligent control module, where an ANN-based surrogate model captures the nonlinear relationship between system inputs and performance outputs, as described in Section 2. In parallel, sensitivity analysis and physical constraints are applied to ensure thermodynamic consistency and operational feasibility. The optimization algorithm determines optimal operating setpoints, which are translated into control signals to adjust system operation and improve power output and efficiency. The inclusion of physics-informed simulation ensures model reliability and stability of the control framework. The surrogate model employed in this study assists solely as a computational approximation of the physics-based system response and does not constitute the primary research contribution. The focus of the work remains on physics-based control and optimization at the system level. 3. System Modelling and Performance Prediction A physics-based simulation model was developed to predict the performance of the low-temperature thermal energy conversion system over a wide operational envelope. The model evaluates system response under thermal source temperatures ranging from 50 to 200°C, applied heat fluxes between 0.5 and 5.0 kW m⁻², and electrical load values from 0.5 to 3.0, which represent typical operating conditions for low-grade thermal energy utilization systems. The primary performance indicators considered are electrical power output (P) and conversion efficiency (η). 3.1 Physics-Based System Model The low-temperature thermal energy conversion system is represented using a physics-based model that captures the coupled thermal electrical behaviour under steady-state and quasi-dynamic operating conditions. The model considers a thermal source characterized by temperature 𝑇 and applied heat flux 𝑞, which drives the conversion process and determines the resulting electrical power output and efficiency. The thermal input power to the system is expressed in Eq. 1 : Q in ​ = q ⋅ A (1) where q is the applied heat flux (kW m − 2 ) and 𝐴is the effective heat transfer area. The electrical power output 𝑃 is governed by the interaction between the thermal driving force and the electrical load 𝑅 𝐿 , and can be written in generalized form as shown in Eq. 2 : P = f (T, q, R L ​) (2) where the nonlinear function 𝑓 (⋅) reflects internal electrical resistance, temperature-dependent material properties, and load-matching effects. The conversion efficiency in Eq. 3 is: 𝜂 = \(\:\frac{P}{\:Q\text{i}\text{n}\text{}}\) (3) The model explicitly accounts for the strong nonlinearity of system performance with respect to operating parameters. Within this operating envelope, electrical power output varies from approximately 300 W to 2600 W, while conversion efficiency spans 1% to 14%, confirm the presence of multiple local and global optimal operating regions. To enable efficient system-level optimization, simulation data generated from the physics-based model are used to construct a surrogate approximation of the nonlinear input/output relationships. This surrogate model serves solely as a computational accelerator for optimization and control-map construction, while the governing physical relationships remain the foundation of the analysis. All simulations satisfy energy-balance constraints, and numerical errors are maintained below 1–2% across the investigated operating range. 3.2 Electrical Power Output Prediction Figure 2 (a) illustrates the variation of electrical power output as a function of thermal source temperature and heat flux. At the lower temperature boundary of approximately 50 to 70°C, the system produces relatively low electrical power, typically in the range of 300 to 600 W, even at higher heat-flux levels. This behaviour reflects the limited thermodynamic driving force available at low temperatures. As the thermal source temperature increases beyond 100°C, a pronounced increase in electrical power output is observed. For moderate heat flux values around 2.5 to 3.0 kW m⁻², the power output rises to approximately 1200 to1800 W. At the upper operating range, with thermal source temperatures close to 200°C and heat flux values approaching 5.0 kW m⁻², the system achieves maximum power outputs on the order of 2400 to 2600 W. The surface trend in Fig. 2 (a) indicates a nonlinear but monotonic dependence of power output on both temperature and heat flux. At lower temperatures, the sensitivity of power output to heat flux is reduced, whereas at higher temperatures the same increment in heat flux yields a significantly larger increase in electrical power. This nonlinear interaction demonstrates that fixed operating conditions cannot ensure optimal power generation across the entire thermal input range. 3.3 Conversion Efficiency Prediction Figure 2 (b) presents the predicted conversion efficiency as a function of thermal source temperature and electrical load. At low temperatures below 80°C, conversion efficiency remains below 2% to 3%, regardless of electrical load, due to dominant thermal losses and insufficient temperature gradients. As the thermal source temperature increases to the range of 120 to160°C, efficiency improves substantially, reaching values between 8 and 12% when the electrical load is maintained near its optimal region, approximately Rₗ = 1.4–1.8. The maximum efficiency observed in the simulation is approximately 13 to 14%, occurring at high thermal source temperatures close to 180 to 200°C under optimized electrical loading conditions. Outside this optimal load range, efficiency declines notably. At low electrical loads (below Rₗ ≈ 0.8 ) or excessive loads (above Rₗ ≈ 2.5 ) , the conversion efficiency decreases by 3% to 6% points, even at elevated temperatures. This behaviour highlights the strong coupling between thermal input and electrical load and confirms the presence of a distinct efficiency optimum rather than a broad plateau. The performance surfaces in Figs. 2 (a) and 2(b) clearly demonstrate that both electrical power output and conversion efficiency exhibit strong nonlinear dependence on operating parameters. Power output varies by more than 2000 W across the investigated temperature and heat-flux range, while conversion efficiency varies from approximately 1% to 14% depending on temperature and electrical load. These large variations directly address the identified research gap by showing that conventional fixed-setpoint operation cannot maintain optimal performance under variable thermal conditions. Table 1 summarizes the operating ranges, baseline performance characteristics, and optimized control outcomes of the low-temperature thermal energy conversion system investigated in this study. The table combines key numerical results derived from the physics-based simulations and time domain analyses. A concise overview of system behavior and achieved performance improvements under adaptive control. Table 1 Operating Ranges and Performance Summary Category Parameter Range / Value Remarks Thermal input conditions Thermal source temperature 50 to 200°C Represents low-grade waste heat sources Applied heat flux 0.5 to 5.0 kW m⁻² Typical for industrial and geothermal heat recovery Electrical operating conditions Electrical load 0.5 to 3.0 Optimal range identified near 1.4–1.8 Performance outputs (baseline) Electrical power output 300 to 2600 W Strong nonlinear dependence on T and q Optimized control performance Average power improvement Up to 2.2% Compared to conventional control Dynamic stability metrics Load fluctuation reduction 25 to 40% Reduced oscillations under optimized control 4. System Optimization Method The system optimization method proposed in this study is implemented through an integrated control-map-based and self-learning optimization framework, as illustrated in Fig. 3 . The framework combines physics-based performance prediction, optimal setpoint selection, and iterative adaptive correction to enhance the operational performance of low-temperature thermal energy conversion systems under variable thermal conditions. The method is designed to improve electrical power output and conversion efficiency while ensuring physically admissible and stable system operation. As shown in Fig. 3 (a) , the optimization process begins with the acquisition of thermal input conditions, namely the thermal source temperature \(\:T\) and the applied heat flux \(\:q\) . These inputs are supplied to the performance prediction module, which represents the control maps derived from the physics-based modeling and surrogate-assisted prediction framework developed in Section 3. The control maps describe the nonlinear system behavior through generalized relationships \(\:P(T,q,{R}_{L})\) and \(\:\eta\:(T,q,{R}_{L})\) to enable rapid estimation of achievable electrical power output and conversion efficiency over the defined operating domain. Based on these maps, the optimal electrical loading condition \(\:{R}_{L}^{*}\) and corresponding operating setpoints are identified for the current thermal input state. The optimized operating setpoints obtained from the control maps are subsequently applied to the system, enabling adaptive control without the need for repeated high-fidelity numerical simulations during operation. By embedding physical constraints directly within the control maps, the optimization process ensures that all selected operating points remain thermodynamically feasible and consistent with system limitations. The self-learning optimization mechanism illustrated in Fig. 3 (b) further enhances the adaptability of the framework. The process begins with the initialization of operating parameters, followed by real-time measurement of the system state, including \(\:T\) , \(\:q\) , \(\:{R}_{L}\) , electrical power output \(\:P\) , and conversion efficiency \(\:\eta\:\) . The measured performance is compared with the predicted optimal performance obtained from the control maps. If performance improvement is detected, the operating parameters are updated accordingly; otherwise, the current parameters are retained. This iterative procedure is repeated continuously to allow the system to adapt to change thermal conditions and model uncertainties over time. Through the combined use of control maps and self-learning correction, the proposed system optimization method enables stable, computationally efficient, and physics-consistent performance enhancement under realistic operating conditions. As illustrate in Fig. 3 (b) presents the self-learning optimization flow that governs adaptive performance improvement. The optimization procedure is initialized with an initial set of operating parameters obtained from the control maps. During operation, the system state is continuously measured, including thermal source temperature \(\:T\) , heat flux \(\:q\) , electrical load \(\:{R}_{L}\) , electrical power output \(\:P\) , and conversion efficiency \(\:\eta\:\) . Using the performance prediction model, the expected optimal performance \(\:\left({P}^{*},{\eta\:}^{*}\right)\) is calculated for the current operating conditions. The measured system performance is then compared with the predicted optimal values. If the measured performance does not meet or exceed the predicted optimum, the operating parameters are adjusted toward improved setpoints identified within the control maps. This update step is performed iteratively, let the controller to progressively move the system toward its optimal operating region. When performance improvement is achieved, the updated operating parameters are retained and used as the new reference point for subsequent iterations. This closed-loop self-learning mechanism enables continuous adaptation to nonlinear system behaviour, changing thermal source characteristics, and external disturbances. Unlike fixed-setpoint or purely rule-based controllers, the proposed optimization method dynamically tracks optimal operating conditions across the full range of thermal inputs. By combining physics-based performance prediction with iterative learning, the method directly addresses the research gap identified in this study and supports the research objective of improving low-temperature thermal energy conversion performance without hardware modification. 5. Results and Discussion The performance of the proposed physics-based intelligent control and optimization framework was evaluated using the developed system-level simulation model of the low-temperature thermal energy conversion system. All simulations were conducted in a MATLAB-based environment, where physics-informed surrogate models were coupled with a self-learning optimization algorithm. System operating data corresponding to 24 h, 48 h, 72 h, and 96 h of simulated operation were used to progressively train the controller under realistic variations of thermal source temperature, heat flux, and electrical load conditions. Figure 4 illustrates the behavior of the low-temperature thermal energy conversion system during a 48-h training period of the physics-based intelligent controller. The thermal source temperature varies within the range of approximately 90°C to 180°C represent realistic fluctuations of low-grade thermal resources. Under conventional control, the effective electrical performance exhibits noticeable oscillations and delayed response to thermal variations. In contrast, the optimized control strategy produces a smoother and consistently higher system response, indicate improved matching between thermal input conditions and electrical load. The observed stabilization demonstrates the controller’s capability to adapt to transient thermal conditions and maintain operation closer to the optimal performance region, directly support the objective of performance improvement through physics-based control. Figure 5 show the average performance gains achieved for different controller training durations of 24 h, 48 h, and 72 h. After 24 h of training, the intelligent controller improves electrical power output by approximately 0.65% and conversion efficiency by 0.75% compared to baseline operation. Increasing the training duration to 48 h results in the highest overall improvement, with power output enhancement reaching approximately 1.1% and conversion efficiency increase of about 1.3%. The 72 h trained controller maintains notable performance gains, with power and efficiency improvements of approximately 0.9% and 0.95%, respectively. The reduction in marginal improvement beyond the optimal training duration indicates diminishing returns associated with controller over-learning. Overall, the simulation results confirm that the proposed system optimization strategy effectively enhances the performance of low-temperature thermal energy conversion systems. The achieved improvements, though moderate in magnitude, are significant for low-grade thermal systems where efficiency margins are inherently limited. Importantly, the results validate that physics-based control and self-learning optimization can deliver sustained performance gains while preserving operational stability, directly supporting the objectives of this research. The time domain performance of the low-temperature thermal energy conversion system under conventional and physics dependent optimized control over 72 h of operation is shown in Fig. 6 . The upper subplot presents the evolution of electrical power output, while the lower subplot shows the corresponding conversion efficiency under identical thermal input conditions. Under conventional control, the electrical power output fluctuates around an average value of approximately 1120 W, with peak-to-peak variations exceeding 80 to 100 W, reflecting the system’s sensitivity to thermal input variations and suboptimal electrical loading. When the physics based optimized control is applied, the average power output increases to approximately 1145 W, corresponding to an improvement of about 2.2%, while the amplitude of power fluctuations is noticeably reduced. This indicates improved matching between thermal source conditions and electrical operating parameters, resulting in more stable and efficient power generation. A similar trend is observed in the conversion efficiency profile. Conventional control yields an average efficiency of approximately 7.9%, with frequent short-term drops caused by non-optimal operating conditions. In contrast, the optimized control strategy increases the average conversion efficiency to approximately 8.6%, representing an improvement of about 0.7% points. Moreover, efficiency fluctuations are reduced, demonstrating enhanced operational stability and reduced internal losses. The time-domain behavior of the low-temperature thermal energy conversion system under conventional control and physics-based optimized control for eight representative operating cases is present in Fig. 7 . Each subplot illustrates the evolution of the normalized electrical load (%) over approximately 1500 minutes of simulated operation, capturing short-term fluctuations and longer-term trends in system response. Across all operating cases, the normalized electrical load under conventional control typically varies within the range of approximately 55% to 85%, with frequent high-frequency oscillations and abrupt load changes. These fluctuations reflect the system’s sensitivity to variations in thermal input conditions and the limited adaptability of fixed or rule-based control strategies. Peak values exceeding 80% are intermittently observed, particularly during transient periods, indicating operation away from optimal electrical loading. In contrast, the physics-based optimized control consistently produces a smoother load profile with reduced variability. Under optimized control, the normalized electrical load generally remains within a narrower band of approximately 60% to 75%, depending on the operating case. The amplitude of short-term oscillations is visibly reduced, with typical fluctuation magnitudes decreasing by approximately 25% to 40% compared to conventional control. This behavior indicates improved matching between thermal input conditions and electrical operating parameters. Notably, the optimized control slightly shifts the average operating point toward lower but more stable load levels. This controlled reduction in load variability helps limit internal losses and prevents operation in inefficient regions of the performance space. Differences between operating cases highlight the influence of varying thermal conditions and system states; however, the optimized control demonstrates consistent stabilizing behavior across all cases. Overall, results demonstrates that the physics-based intelligent control framework effectively regulates electrical loading under dynamic conditions, providing smoother and more controlled system operation while preserving flexibility across multiple operating scenarios. Figure 8 illustrates the time-domain regulation of applied heat flux and electrical load under conventional and physics-based optimized control for two representative operating cases of the low-temperature thermal energy conversion system. The figure consists of four subplots, where the upper row presents the temporal evolution of the applied heat flux 𝑞, and the lower row shows the corresponding electrical load 𝑅 𝐿 , each evaluated over approximately 1500 minutes of simulated operation. Under conventional control, the applied heat flux exhibits noticeable short-term fluctuations, with values varying over a relatively wide range of approximately 1.8 to 3.8 kW m⁻², depending on the operating case. These fluctuations include rapid oscillations and intermittent peaks, indicating limited capability of the controller to regulate thermal input smoothly under time-varying conditions. In contrast, the physics-based optimized control produces a visibly smoother heat-flux profile. The optimized trajectories remain confined within a narrower band, typically within ± 0.2–0.3 kW m⁻² around the mean operating level, reflecting improved stabilization of thermal input through informed control action. The lower subplots show the dynamic response of the electrical load 𝑅 𝐿 . With conventional control, the electrical load varies broadly, typically between 1.1 and 1.9, and exhibits frequent abrupt changes that correspond to transient thermal disturbances. When optimized control is applied, the electrical load trajectory becomes more regular and stable, with values predominantly maintained within the range of 1.3 to 1.7. Short-term load oscillations are significantly reduced, particularly during periods of rapid thermal variation, indicating enhanced coordination between thermal input regulation and electrical loading. Overall, Fig. 8 provides a detailed representation of the dynamic behavior of key control variables under time-varying conditions. The comparison highlights differences in variability, smoothness, and operating ranges between conventional and optimized control strategies for representative cases, offering insight into the temporal characteristics of physics-based control in low-temperature thermal energy conversion systems. Figure 9 presents the time-domain response of the low-temperature thermal energy conversion system under conventional control and physics-based optimized control, together with the corresponding self-learning correction coefficients applied during operation. The figure is composed of six subplots arranged in two rows. The upper row illustrates the evolution of three key operating variables: normalized electrical load, applied heat flux, and thermal source temperature, each plotted over approximately 1500 minutes of simulated system operation. The lower row shows the time-dependent correction coefficients generated by the self-learning control algorithm for the respective variables. In the upper row, the normalized electrical load varies between approximately 55% and 80% under conventional control, with frequent short-term oscillations and abrupt changes. Under optimized control, the electrical load trajectory becomes smoother, remaining within a narrower operating band, typically between 60% and 75%, while still responding to slower system dynamics. The applied heat flux exhibits similar behavior: conventional control results in fluctuations spanning roughly 0.5 to 5.0 kW m⁻², whereas optimized control reduces high-frequency variability and maintains heat-flux levels closer to the mean operating value. The thermal source temperature evolves within the range of approximately 50 to 200°C, with optimized control exhibiting reduced amplitude of rapid temperature excursions compared to conventional operation. The lower row depicts the self-learning correction coefficients associated with each control variable. These coefficients vary intermittently within a bounded range of approximately − 6 to + 6, appearing as sparse impulses or short bursts. Such behavior indicates discrete control adjustments triggered by deviations from desired operating conditions rather than continuous aggressive correction. The temporal distribution and magnitude of these corrections reflect the adaptive nature of the control strategy under time-varying thermal and electrical conditions. Overall, Fig. 9 provides a detailed representation of the interaction between system dynamics and adaptive control actions in the low-temperature thermal energy conversion system over extended operating periods. The integrated physics-based control and self-learning optimization architecture developed for low-temperature thermal energy conversion systems, as proposed in this study. The figure represents the complete information flow from thermal input conditions to adaptive control actions within a closed-loop framework. The control process begins with the thermal source temperature (T) and applied heat flux (q), which define the system’s available low-grade thermal input, typically within the ranges of 50 to 200°C and 0.5 to 5 kW m⁻², respectively. These inputs are continuously monitored and passed to the physics-based optimization maps, which are derived from first-principles modeling and numerical simulation. The control maps establish nonlinear relationships between thermal inputs, electrical load 𝑅 𝐿 ​, electrical power output 𝑃 and conversion efficiency 𝜂, capturing the coupled thermal electrical behavior of the system. The optimized electrical load 𝑅 𝐿 is determined from these maps and applied to the system to regulate power extraction under varying thermal conditions. Concurrently, measured performance signals, including electrical power output (typically 300 to 2600 W) and conversion efficiency (approximately 14%), are fed back into the control architecture. These measured responses are compared with predicted performance surfaces to identify deviations caused by transient effects or unmodeled disturbances. The lower section of the figure depicts the self-learning correction mechanism, which generates bounded correction coefficients (typically within ± 5–6%) to update the control maps. These corrections are applied intermittently, reflecting adaptive adjustments rather than continuous aggressive control. The resulting adaptive control signals refine system operation while maintaining physical feasibility and stability. Overall, Fig. 11 provides a concise visualization of how physics-based modeling and adaptive optimization are integrated to regulate low-temperature thermal energy conversion systems under dynamic operating conditions. 6. Conclusion This study has presented a comprehensive physics-based, simulation-driven framework for improving the performance of low-temperature thermal energy conversion systems through adaptive control and optimization. Addressing the identified research gap of limited system-level, physics-informed control strategies for low-grade thermal applications, the proposed approach integrates first-principles modelling, surrogate-assisted performance prediction, sensitivity analysis, and constrained optimization within a closed-loop, self-learning control architecture. The developed modelling framework captured the nonlinear coupling between thermal source temperature, applied heat flux, electrical load, electrical power output, and conversion efficiency over a realistic operating envelope. Simulation results for thermal source temperatures between 50 and 200°C, heat fluxes from 0.5 to 5.0 kW m⁻², and electrical load values ranging from 0.5 to 3.0 demonstrated pronounced nonlinearity in system response. Electrical power output increased from approximately 300 to 600 W at low temperatures to 2400 to 2600 W at higher thermal inputs, while conversion efficiency improved from below 3% at temperatures under 80°C to approximately 13 to 14% near 180 to 200°C when operated within the optimal electrical load region (R_L ≈ 1.4–1.8). Operation outside this optimal region resulted in efficiency penalties of approximately 3 to 6% points, underscoring the importance of adaptive control. Time-domain simulations confirmed the effectiveness of the proposed optimization strategy. Controller training over 24 h, 48 h, and 72 h yielded progressive performance improvements, with maximum average gains of approximately 1.1% in power output and 1.3% in conversion efficiency observed at 48 h training duration, followed by diminishing returns at longer training periods. During extended 72 h operation, optimized control increased average electrical power output from approximately 1120 W to 1145 W and improved conversion efficiency from 7.9% to 8.6%, while significantly reducing short-term fluctuations. Across multiple operating scenarios, normalized electrical load variability was reduced by 25% to 40%, and heat-flux and load trajectories exhibited enhanced smoothness and stability. Overall, the results demonstrate that measurable performance enhancement and improved operational stability can be achieved through physics-based control and optimization without hardware modification, directly fulfilling the study’s objectives. The proposed framework provides a transferable and scalable solution for low-temperature thermal energy conversion systems. 6.1. Future Research Directions Future work will extend the proposed framework toward fully dynamic modeling to capture transient thermal-electrical interactions under rapidly varying heat sources. Experimental validation on laboratory-scale or pilot-scale low-temperature thermal energy conversion systems will be pursued to further assess real-world applicability. Additionally, the integration of uncertainty-aware optimization and multi-objective control strategies, incorporating durability and long-term performance metrics, represents a promising direction for enhancing robustness in practical deployment. Declarations Compliance with Ethical Standards Disclosure of potential conflicts of interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Research involving Human Participants and/or Animals This research does not contain any studies with human participants or animals performed by any of the authors. Informed consent Informed consent was obtained from all individual participants included in the study. Funding Acknowledgements This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sector. Data Availability The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions. Credit Authorship Contribution Statement Munsif Ali: Writing – review & editing, Writing – original draft, Methodology, Data curation, Conceptualization. Uzair Ahmad: Validation, Visualization, Software. Shafi Ullah Formal analysis, Supervision. Subhan Ullah: Data Curation, Visualization. Shah Rukh khan: Resources, Investigation, Formal analysis. References D. Champier, Thermoelectric generators: A review of applications, Energy Convers. Manag.140(2017)167–181. https://doi.org/https://doi.org/10.1016/j.enconman.2017.02.070. K.R. Kumar, K. Dashora, N. Krishnan, S. Sanyal, H. Chandra, S. Dharmaraja, V. Kumari, Feasibility assessment of renewable energy resources for tea plantation and industry in India - A review, Renew. Sustain. Energy Rev. 145 (2021) 111083. https://doi.org/https://doi.org/10.1016/j.rser.2021.111083. C. Aprea, A. Greco, A. Maiorino, C. 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S.A. El-Agouz, A.R. Abd Elbar, A.M. Aboghazala, M. Shahin, M.Y. Zakaria, K.K. Esmaeil, M.E. Zayed, Comprehensive parametric analysis, sizing, and performance evaluation of a tubular direct contact membrane desalination system driven by heat pipe-based solar collectors, Energy Convers. Manag. 274 (2022) 116437. https://doi.org/https://doi.org/10.1016/j.enconman.2022.116437. Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8706095","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":580928196,"identity":"c6a8b36c-99ae-4fbb-b659-b9c05743ea86","order_by":0,"name":"Munsif Ali","email":"","orcid":"","institution":"Department of Physics, Hazara University, Dhodial, Mansehra","correspondingAuthor":false,"prefix":"","firstName":"Munsif","middleName":"","lastName":"Ali","suffix":""},{"id":580929080,"identity":"cd035d48-c32f-4b1c-a911-5fe7b749f7da","order_by":1,"name":"Uzair 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systems.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-8706095/v1/4096edd9e19fa5f87b839d3c.png"},{"id":101637499,"identity":"97bcdf51-d658-4d99-92bc-cfc6573c98a2","added_by":"auto","created_at":"2026-02-02 06:56:32","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":213277,"visible":true,"origin":"","legend":"\u003cp\u003eCalculated approximations of \u003cstrong\u003e(a):\u003c/strong\u003e electrical power output (300 to 2600 W) as a function of thermal source temperature (50 to 200 °C) and heat flux (0.5–5.0 kW m⁻²), and \u003cstrong\u003e(b):\u003c/strong\u003e conversion efficiency (1% to 14 %) as a function of thermal source temperature and electrical load (0.5 to 3.0) for the low-temperature thermal energy conversion system.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-8706095/v1/0e5285a0102423ef1f22e7cd.png"},{"id":101637500,"identity":"3edce90b-5caa-4d71-897c-5279a5d6e51d","added_by":"auto","created_at":"2026-02-02 06:56:32","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":217543,"visible":true,"origin":"","legend":"\u003cp\u003eIntegrated control-map-based optimization and self-learning strategy for physics-based control of low-temperature thermal energy conversion systems:\u003cstrong\u003e (a\u003c/strong\u003e) control maps linking thermal input conditions to optimized operating parameters, and\u003cstrong\u003e (b)\u003c/strong\u003e self-learning optimization flow enabling adaptive performance improvement.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-8706095/v1/c664d34c48a6df32da9596f8.png"},{"id":101637511,"identity":"c1b8acf9-a295-4134-a31d-1a40f313024a","added_by":"auto","created_at":"2026-02-02 06:56:46","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":380082,"visible":true,"origin":"","legend":"\u003cp\u003e48 h physics-based intelligent controller training procedure for a low-temperature thermal energy conversion system\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-8706095/v1/5e1a1942f402214d819df465.png"},{"id":101637502,"identity":"53a03cd7-0009-4e17-88dc-550afc189cfd","added_by":"auto","created_at":"2026-02-02 06:56:35","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":164153,"visible":true,"origin":"","legend":"\u003cp\u003eSimulation results of average estimated electrical power output improvement and conversion efficiency increase during 72 h of system operation after implementation of the physics-based intelligent controller for different training durations.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-8706095/v1/7df65a3ca9896e9fa669672b.png"},{"id":101637506,"identity":"f08ec623-fe15-4ea1-a9ea-8150538c6668","added_by":"auto","created_at":"2026-02-02 06:56:38","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":225789,"visible":true,"origin":"","legend":"\u003cp\u003eTime-domain performance of the low-temperature thermal energy conversion system under conventional and physics-based optimized control over 72 h of operation\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-8706095/v1/412024d4d8151e2850454298.png"},{"id":101637505,"identity":"64bb7c01-fe44-4660-9280-929fad773584","added_by":"auto","created_at":"2026-02-02 06:56:38","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":130415,"visible":true,"origin":"","legend":"\u003cp\u003eTime-domain comparison of normalized electrical load under conventional and physics-based optimized control for multiple operating cases of the low-temperature thermal energy conversion system.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-8706095/v1/521ae70f76f2492bb54ed430.png"},{"id":101637514,"identity":"f8d74c8f-cfb9-4588-97b0-bdb448d09ab6","added_by":"auto","created_at":"2026-02-02 06:56:46","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":141594,"visible":true,"origin":"","legend":"\u003cp\u003eTime-domain regulation of heat flux and electrical load under conventional and physics-based optimized control for two representative operating cases of the low-temperature thermal energy conversion system.\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-8706095/v1/3c0e8332c0a9797a47bb8102.png"},{"id":101637449,"identity":"ac7cdc7a-b347-4c85-b00f-3ba99a4d021d","added_by":"auto","created_at":"2026-02-02 06:56:16","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":79909,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFigure 10: \u003c/strong\u003eTime-domain behavior of key operating variables and corresponding self-learning correction coefficients under conventional and physics-based optimized control for the low-temperature thermal energy conversion system.\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-8706095/v1/475d90f84102f5caed19901b.png"},{"id":101637450,"identity":"8e81c1e8-ac5c-4d85-a153-550765ec2af7","added_by":"auto","created_at":"2026-02-02 06:56:16","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":363132,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFigure 11:\u003c/strong\u003e Integrated physics-based control and self-learning optimization framework for adaptive performance regulation of low-temperature thermal energy conversion systems.\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-8706095/v1/8975ff9980d80f4f8b1a4a36.png"},{"id":108180940,"identity":"a8a95112-8f02-4c66-af7e-848ea71414e6","added_by":"auto","created_at":"2026-04-30 08:55:28","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2069680,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8706095/v1/90d559c3-a39e-45fd-b1be-5d8214d893c2.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003ePerformance Improvement of Low-Temperature Thermal Energy Conversion Systems via Physics-Based Control and Optimization\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eLow-temperature thermal energy conversion systems have emerged as a critical research area due to their potential to recover vast quantities of low-grade heat from geothermal resources, industrial processes, and distributed energy systems that are otherwise dissipated into the environment [1,2]. Recent studies indicate that more than 50% of industrial waste heat is available at temperatures below 200 \u0026deg;C, where conventional power cycles operate with poor efficiency [3,4]. Consequently, physics-based conversion mechanisms such as thermoelectric, electrochemical, and hybrid thermal-driven systems have gained increasing attention as enabling technologies for decentralized and sustainable power generation [5]. Despite these advances, the operational performance of low-temperature thermal energy conversion systems remains significantly below theoretical limits due to intrinsic nonlinearities, coupled transport phenomena, and suboptimal control strategies [6]. These systems exhibit strong sensitivity to operating parameters including temperature gradients, internal electrical resistance, heat flux, and electrochemical potential, which complicates their real-time operation and limits efficiency gains [7]. Traditional design-oriented optimization approaches are often static in nature and fail to account for dynamic interactions between thermal and electrical domains under variable operating conditions [8,9]. The core problem addressed in this research is the lack of adaptive, physics-informed control and optimization frameworks capable of systematically improving the performance of low-temperature thermal energy conversion systems [10]. Existing studies primarily focus on material enhancement or component-level design improvements, while system-level control and operational optimization remain insufficiently explored [11]. As a result, many thermal energy conversion systems are operated conservatively lead to reduced power output and inefficient utilization of available thermal resources. Based on this context, the present study addresses the following research questions:\u0026nbsp;\u003c/p\u003e\n\u003col style=\"list-style-type: upper-roman;\"\u003e\n \u003cli\u003eHow can physics-based modelling be integrated with control-oriented optimization to enhance system performance?\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eWhich operating parameters exert the greatest influence on power output and efficiency?\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eTo what extent can optimized control strategies improve system performance under realistic physical and operational constraints?\u0026nbsp;\u003c/li\u003e\n\u003c/ol\u003e\n\u003cp\u003eThese questions guide the formulation of a structured and reproducible research framework. The aim of this research is to improve the performance of low-temperature thermal energy conversion systems through physics-based control and optimization. To achieve this aim, the study pursues several objectives, (1) the development of a physics-informed simulation framework, (2) construction of surrogate models for nonlinear system behaviour, (3) identification of dominant performance-driving variables through sensitivity analysis, and (4) application of constrained optimization techniques to determine optimal operating conditions. The motivation for this research is driven by the global need to enhance energy efficiency and support decarbonization pathways without relying solely on new infrastructure or advanced materials [19]. Low-temperature thermal energy conversion systems represent a largely untapped opportunity to improve overall energy utilization efficiency when coupled with intelligent control strategies that maximize performance using existing system architectures [12]. The scope of this study is confined to system-level performance analysis of low-temperature thermal energy conversion systems operating typically below 200 \u0026deg;C. The focus is placed on steady-state and quasi-dynamic behaviour, while long-term degradation mechanisms and experimental validation are beyond the present scope. Numerical simulation and data-driven surrogate modelling are employed to ensure generality and reproducibility of results across a wide range of operating conditions.\u003c/p\u003e\n\u003cp\u003eThe novelty of this research lies in the integration of physics-based modelling, sensitivity analysis, and constrained optimization into a unified control-oriented framework tailored specifically for low-temperature thermal energy conversion systems. Unlike prior works that treat modelling and optimization independently, this study establishes a closed-loop methodology that enables systematic performance enhancement while preserving physical interpretability. The central research hypothesis is that the performance of low-temperature thermal energy conversion systems can be significantly improved through physics-based control and optimization without modifying system hardware. It is hypothesized that regulating key operating parameters within physically feasible limits can yield measurable improvements in power output and conversion efficiency. From a methodological standpoint, the research adopts a structured workflow consisting of physics-based system modelling, numerical data generation, substitute model development using artificial neural networks, partial-derivative-based sensitivity analysis, and nonlinear constrained optimization. This methodology builds upon established control and optimization strategies successfully applied in complex energy systems and adapts them to the physics of low-temperature thermal conversion [16].\u003c/p\u003e\n\u003cp\u003eThe expected study outcomes include the identification of dominant operating variables, quantified performance improvements under optimized operation, and validated control strategies suitable for low-temperature thermal energy applications [13]. These outcomes aim to provide actionable insights for system designers and operators seeking cost-effective performance enhancement solutions [14]. A key research gap addressed by this work is the absence of comprehensive control-focused optimization frameworks for low-temperature thermal energy conversion systems. While extensive research exists on materials and thermodynamic analysis, the integration of physics-based control and optimization at the system level remains limited. The significance of this research lies in its contribution to energy efficiency improvement and sustainable power generation. By enabling enhanced utilization of low-grade thermal resources, the proposed framework supports broader energy transition objectives and aligns with international net-zero strategies [15]. Furthermore, the methodological framework developed in this study is transferable to a wide range of thermal energy conversion technologies. This report is organized to present the theoretical background, modelling framework, optimization methodology, and performance evaluation results in a coherent manner. The research approach follows a physics-informed, simulation-driven paradigm that balances scientific rigor with engineering applicability. This study adopts a physics-based, simulation-driven methodology combining surrogate-assisted modelling, sensitivity analysis, and adaptive control optimization to enhance the performance of low-temperature thermal energy conversion systems.\u003c/p\u003e"},{"header":"2. Physics-Based Intelligent Control and Optimization Framework","content":"\u003cp\u003eAs the conventional control strategies are replaced or enhanced by data-driven and physics-informed algorithms, the resulting architecture can be classified as an intelligent control framework. In low-temperature thermal energy conversion systems, such frameworks are relevant due to the nonlinear coupling between thermal transport, electrochemical processes, and electrical power generation [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. The inherent variability of low-grade thermal sources further necessitates adaptive control strategies capable of maintaining optimal operation under changing boundary conditions [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. Low-temperature thermal energy conversion systems are governed by complex interactions between temperature gradients, heat flux, internal resistance, and electrochemical or thermoelectric potentials. Conventional proportional integral (PI) or rule-based controllers are typically designed using linearized models around fixed operating points, which limits their effectiveness when system parameters vary significantly [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. As a result, these controllers often lead to conservative operation, reduced power output, and suboptimal conversion efficiency [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Intelligent control strategies provide an alternative by learning nonlinear system behaviour directly from data while maintaining consistency with physical laws [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eArtificial neural networks (ANNs) are widely adopted in intelligent energy system control due to their ability to approximate nonlinear mappings, handle noisy data, and generalize across diverse operating regimes [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. In thermal energy conversion applications, ANN-based models have been successfully applied for system identification, performance prediction, and operational optimization of thermoelectric and electrochemical systems [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. Beyond neural networks, evolutionary and population-based optimization algorithms such as genetic algorithms (GA) and particle swarm optimization (PSO) have demonstrated strong capability in solving nonlinear and constrained optimization problems encountered in energy systems. These algorithms do not rely on gradient information and are therefore effective for optimizing complex thermal energy conversion systems with non-convex performance landscapes. When coupled with ANN-based surrogate models, evolutionary algorithms significantly reduce computational cost while enabling global exploration of the operational parameter space [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. A critical advantage of physics-based intelligent control lies in the integration of first-principles knowledge with learning-based techniques. Physics-informed frameworks embed thermodynamic constraints, energy balance equations, and transport relations directly into the modelling and optimization process, thereby preventing non-physical solutions and improving model robustness. This hybrid modelling paradigm enhances interpretability and reliability compared to purely data-driven approaches [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn this study, a physics-based intelligent control and optimization framework is developed for low-temperature thermal energy conversion systems. The framework integrates physics-informed simulation, ANN-based surrogate modelling, sensitivity analysis, and constrained optimization to identify optimal operating conditions. The optimized parameters are subsequently employed to define control-oriented correction strategies that enhance power output and conversion efficiency while maintaining physical feasibility and system stability [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, the physics-based intelligent control and optimization framework illustrates the closed-loop integration of low-temperature thermal energy conversion, data-driven modelling, and optimization-based control. The thermal source provides low-grade heat inputs in the form of temperature \u0026#119879; and heat flux \u0026#119876;, which drive the low-temperature thermal energy conversion system to generate electrical power \u0026#119875; with conversion efficiency \u0026#120578;. Measured operational data (\u0026#119879;, \u0026#119876;, \u0026#119875;, \u0026#120578;) are fed into the physics-based intelligent control module, where an ANN-based surrogate model captures the nonlinear relationship between system inputs and performance outputs, as described in Section 2. In parallel, sensitivity analysis and physical constraints are applied to ensure thermodynamic consistency and operational feasibility. The optimization algorithm determines optimal operating setpoints, which are translated into control signals to adjust system operation and improve power output and efficiency. The inclusion of physics-informed simulation ensures model reliability and stability of the control framework. The surrogate model employed in this study assists solely as a computational approximation of the physics-based system response and does not constitute the primary research contribution. The focus of the work remains on physics-based control and optimization at the system level.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"3. System Modelling and Performance Prediction","content":"\u003cp\u003eA physics-based simulation model was developed to predict the performance of the low-temperature thermal energy conversion system over a wide operational envelope. The model evaluates system response under thermal source temperatures ranging from 50 to 200\u0026deg;C, applied heat fluxes between 0.5 and 5.0 kW m⁻\u0026sup2;, and electrical load values from 0.5 to 3.0, which represent typical operating conditions for low-grade thermal energy utilization systems. The primary performance indicators considered are electrical power output (P) and conversion efficiency (η).\u003c/p\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Physics-Based System Model\u003c/h2\u003e \u003cp\u003eThe low-temperature thermal energy conversion system is represented using a physics-based model that captures the coupled thermal electrical behaviour under steady-state and quasi-dynamic operating conditions. The model considers a thermal source characterized by temperature \u0026#119879; and applied heat flux \u0026#119902;, which drives the conversion process and determines the resulting electrical power output and efficiency. The thermal input power to the system is expressed in \u003cb\u003eEq.\u0026nbsp;1\u003c/b\u003e:\u003c/p\u003e \u003cp\u003e \u003cem\u003eQ\u003c/em\u003e \u003csub\u003ein\u003c/sub\u003e​ \u003cem\u003e= q \u0026sdot; A\u003c/em\u003e (1)\u003c/p\u003e \u003cp\u003ewhere q is the applied heat flux (kW m\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e) and \u0026#119860;is the effective heat transfer area. The electrical power output \u0026#119875; is governed by the interaction between the thermal driving force and the electrical load \u0026#119877;\u003csub\u003e\u0026#119871;\u003c/sub\u003e, and can be written in generalized form as shown in \u003cb\u003eEq.\u0026nbsp;2\u003c/b\u003e:\u003c/p\u003e \u003cp\u003e \u003cem\u003eP\u0026thinsp;=\u0026thinsp;f (T, q, R\u003c/em\u003e \u003csub\u003e \u003cem\u003eL\u003c/em\u003e \u003c/sub\u003e \u003cem\u003e​)\u003c/em\u003e (2)\u003c/p\u003e \u003cp\u003ewhere the nonlinear function \u0026#119891; (\u0026sdot;) reflects internal electrical resistance, temperature-dependent material properties, and load-matching effects. The conversion efficiency in \u003cb\u003eEq.\u0026nbsp;3\u003c/b\u003e is:\u003c/p\u003e \u003cp\u003e\u0026#120578; = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{P}{\\:Q\\text{i}\\text{n}\\text{}}\\)\u003c/span\u003e\u003c/span\u003e (3)\u003c/p\u003e \u003cp\u003eThe model explicitly accounts for the strong nonlinearity of system performance with respect to operating parameters. Within this operating envelope, electrical power output varies from approximately 300 W to 2600 W, while conversion efficiency spans 1% to 14%, confirm the presence of multiple local and global optimal operating regions.\u003c/p\u003e \u003cp\u003eTo enable efficient system-level optimization, simulation data generated from the physics-based model are used to construct a surrogate approximation of the nonlinear input/output relationships. This surrogate model serves solely as a computational accelerator for optimization and control-map construction, while the governing physical relationships remain the foundation of the analysis. All simulations satisfy energy-balance constraints, and numerical errors are maintained below 1\u0026ndash;2% across the investigated operating range.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Electrical Power Output Prediction\u003c/h2\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e\u003cb\u003e(a)\u003c/b\u003e illustrates the variation of electrical power output as a function of thermal source temperature and heat flux. At the lower temperature boundary of approximately 50 to 70\u0026deg;C, the system produces relatively low electrical power, typically in the range of 300 to 600 W, even at higher heat-flux levels. This behaviour reflects the limited thermodynamic driving force available at low temperatures. As the thermal source temperature increases beyond 100\u0026deg;C, a pronounced increase in electrical power output is observed. For moderate heat flux values around 2.5 to 3.0 kW m⁻\u0026sup2;, the power output rises to approximately 1200 to1800 W. At the upper operating range, with thermal source temperatures close to 200\u0026deg;C and heat flux values approaching 5.0 kW m⁻\u0026sup2;, the system achieves maximum power outputs on the order of 2400 to 2600 W. The surface trend in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e\u003cb\u003e(a)\u003c/b\u003e indicates a nonlinear but monotonic dependence of power output on both temperature and heat flux. At lower temperatures, the sensitivity of power output to heat flux is reduced, whereas at higher temperatures the same increment in heat flux yields a significantly larger increase in electrical power. This nonlinear interaction demonstrates that fixed operating conditions cannot ensure optimal power generation across the entire thermal input range.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Conversion Efficiency Prediction\u003c/h2\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e\u003cb\u003e(b)\u003c/b\u003e presents the predicted conversion efficiency as a function of thermal source temperature and electrical load. At low temperatures below 80\u0026deg;C, conversion efficiency remains below 2% to 3%, regardless of electrical load, due to dominant thermal losses and insufficient temperature gradients. As the thermal source temperature increases to the range of 120 to160\u0026deg;C, efficiency improves substantially, reaching values between 8 and 12% when the electrical load is maintained near its optimal region, approximately Rₗ = 1.4\u0026ndash;1.8. The maximum efficiency observed in the simulation is approximately 13 to 14%, occurring at high thermal source temperatures close to 180 to 200\u0026deg;C under optimized electrical loading conditions. Outside this optimal load range, efficiency declines notably. At low electrical loads (below Rₗ \u0026asymp; 0.8\u003cb\u003e)\u003c/b\u003e or excessive loads (above Rₗ \u0026asymp; 2.5\u003cb\u003e)\u003c/b\u003e, the conversion efficiency decreases by 3% to 6% points, even at elevated temperatures. This behaviour highlights the strong coupling between thermal input and electrical load and confirms the presence of a distinct efficiency optimum rather than a broad plateau.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe performance surfaces in Figs.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e\u003cb\u003e(a) and 2(b)\u003c/b\u003e clearly demonstrate that both electrical power output and conversion efficiency exhibit strong nonlinear dependence on operating parameters. Power output varies by more than 2000 W across the investigated temperature and heat-flux range, while conversion efficiency varies from approximately 1% to 14% depending on temperature and electrical load. These large variations directly address the identified research gap by showing that conventional fixed-setpoint operation cannot maintain optimal performance under variable thermal conditions. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e summarizes the operating ranges, baseline performance characteristics, and optimized control outcomes of the low-temperature thermal energy conversion system investigated in this study. The table combines key numerical results derived from the physics-based simulations and time domain analyses. A concise overview of system behavior and achieved performance improvements under adaptive control.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eOperating Ranges and Performance Summary\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCategory\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRange / Value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eRemarks\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eThermal input conditions\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eThermal source temperature\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e50 to 200\u0026deg;C\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eRepresents low-grade waste heat sources\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eApplied heat flux\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.5 to 5.0 kW m⁻\u0026sup2;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTypical for industrial and geothermal heat recovery\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eElectrical operating conditions\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eElectrical load\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.5 to 3.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eOptimal range identified near 1.4\u0026ndash;1.8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePerformance outputs (baseline)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eElectrical power output\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e300 to 2600 W\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eStrong nonlinear dependence on T and q\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOptimized control performance\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAverage power improvement\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUp to 2.2%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eCompared to conventional control\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDynamic stability metrics\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLoad fluctuation reduction\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e25 to 40%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eReduced oscillations under optimized control\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4. System Optimization Method","content":"\u003cp\u003eThe system optimization method proposed in this study is implemented through an integrated control-map-based and self-learning optimization framework, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The framework combines physics-based performance prediction, optimal setpoint selection, and iterative adaptive correction to enhance the operational performance of low-temperature thermal energy conversion systems under variable thermal conditions. The method is designed to improve electrical power output and conversion efficiency while ensuring physically admissible and stable system operation.\u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e\u003cb\u003e(a)\u003c/b\u003e, the optimization process begins with the acquisition of thermal input conditions, namely the thermal source temperature \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:T\\)\u003c/span\u003e\u003c/span\u003eand the applied heat flux \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:q\\)\u003c/span\u003e\u003c/span\u003e. These inputs are supplied to the performance prediction module, which represents the control maps derived from the physics-based modeling and surrogate-assisted prediction framework developed in Section 3. The control maps describe the nonlinear system behavior through generalized relationships \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:P(T,q,{R}_{L})\\)\u003c/span\u003e\u003c/span\u003eand \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\eta\\:(T,q,{R}_{L})\\)\u003c/span\u003e\u003c/span\u003e to enable rapid estimation of achievable electrical power output and conversion efficiency over the defined operating domain. Based on these maps, the optimal electrical loading condition \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{L}^{*}\\)\u003c/span\u003e\u003c/span\u003e and corresponding operating setpoints are identified for the current thermal input state.\u003c/p\u003e \u003cp\u003eThe optimized operating setpoints obtained from the control maps are subsequently applied to the system, enabling adaptive control without the need for repeated high-fidelity numerical simulations during operation. By embedding physical constraints directly within the control maps, the optimization process ensures that all selected operating points remain thermodynamically feasible and consistent with system limitations.\u003c/p\u003e \u003cp\u003eThe self-learning optimization mechanism illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e\u003cb\u003e(b)\u003c/b\u003e further enhances the adaptability of the framework. The process begins with the initialization of operating parameters, followed by real-time measurement of the system state, including \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:T\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:q\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{L}\\)\u003c/span\u003e\u003c/span\u003e, electrical power output \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:P\\)\u003c/span\u003e\u003c/span\u003e, and conversion efficiency \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\eta\\:\\)\u003c/span\u003e\u003c/span\u003e. The measured performance is compared with the predicted optimal performance obtained from the control maps. If performance improvement is detected, the operating parameters are updated accordingly; otherwise, the current parameters are retained. This iterative procedure is repeated continuously to allow the system to adapt to change thermal conditions and model uncertainties over time.\u003c/p\u003e \u003cp\u003eThrough the combined use of control maps and self-learning correction, the proposed system optimization method enables stable, computationally efficient, and physics-consistent performance enhancement under realistic operating conditions.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs illustrate in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e\u003cb\u003e(b)\u003c/b\u003e presents the self-learning optimization flow that governs adaptive performance improvement. The optimization procedure is initialized with an initial set of operating parameters obtained from the control maps. During operation, the system state is continuously measured, including thermal source temperature \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:T\\)\u003c/span\u003e\u003c/span\u003e, heat flux \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:q\\)\u003c/span\u003e\u003c/span\u003e, electrical load \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{L}\\)\u003c/span\u003e\u003c/span\u003e, electrical power output \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:P\\)\u003c/span\u003e\u003c/span\u003e, and conversion efficiency \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\eta\\:\\)\u003c/span\u003e\u003c/span\u003e. Using the performance prediction model, the expected optimal performance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left({P}^{*},{\\eta\\:}^{*}\\right)\\)\u003c/span\u003e\u003c/span\u003eis calculated for the current operating conditions.\u003c/p\u003e \u003cp\u003eThe measured system performance is then compared with the predicted optimal values. If the measured performance does not meet or exceed the predicted optimum, the operating parameters are adjusted toward improved setpoints identified within the control maps. This update step is performed iteratively, let the controller to progressively move the system toward its optimal operating region. When performance improvement is achieved, the updated operating parameters are retained and used as the new reference point for subsequent iterations. This closed-loop self-learning mechanism enables continuous adaptation to nonlinear system behaviour, changing thermal source characteristics, and external disturbances. Unlike fixed-setpoint or purely rule-based controllers, the proposed optimization method dynamically tracks optimal operating conditions across the full range of thermal inputs. By combining physics-based performance prediction with iterative learning, the method directly addresses the research gap identified in this study and supports the research objective of improving low-temperature thermal energy conversion performance without hardware modification.\u003c/p\u003e"},{"header":"5. Results and Discussion","content":"\u003cp\u003eThe performance of the proposed physics-based intelligent control and optimization framework was evaluated using the developed system-level simulation model of the low-temperature thermal energy conversion system. All simulations were conducted in a MATLAB-based environment, where physics-informed surrogate models were coupled with a self-learning optimization algorithm. System operating data corresponding to 24 h, 48 h, 72 h, and 96 h of simulated operation were used to progressively train the controller under realistic variations of thermal source temperature, heat flux, and electrical load conditions. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e illustrates the behavior of the low-temperature thermal energy conversion system during a 48-h training period of the physics-based intelligent controller. The thermal source temperature varies within the range of approximately 90\u0026deg;C to 180\u0026deg;C represent realistic fluctuations of low-grade thermal resources. Under conventional control, the effective electrical performance exhibits noticeable oscillations and delayed response to thermal variations. In contrast, the optimized control strategy produces a smoother and consistently higher system response, indicate improved matching between thermal input conditions and electrical load. The observed stabilization demonstrates the controller\u0026rsquo;s capability to adapt to transient thermal conditions and maintain operation closer to the optimal performance region, directly support the objective of performance improvement through physics-based control.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e show the average performance gains achieved for different controller training durations of 24 h, 48 h, and 72 h. After 24 h of training, the intelligent controller improves electrical power output by approximately 0.65% and conversion efficiency by 0.75% compared to baseline operation. Increasing the training duration to 48 h results in the highest overall improvement, with power output enhancement reaching approximately 1.1% and conversion efficiency increase of about 1.3%. The 72 h trained controller maintains notable performance gains, with power and efficiency improvements of approximately 0.9% and 0.95%, respectively. The reduction in marginal improvement beyond the optimal training duration indicates diminishing returns associated with controller over-learning.\u003c/p\u003e \u003cp\u003eOverall, the simulation results confirm that the proposed system optimization strategy effectively enhances the performance of low-temperature thermal energy conversion systems. The achieved improvements, though moderate in magnitude, are significant for low-grade thermal systems where efficiency margins are inherently limited. Importantly, the results validate that physics-based control and self-learning optimization can deliver sustained performance gains while preserving operational stability, directly supporting the objectives of this research.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe time domain performance of the low-temperature thermal energy conversion system under conventional and physics dependent optimized control over 72 h of operation is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. The upper subplot presents the evolution of electrical power output, while the lower subplot shows the corresponding conversion efficiency under identical thermal input conditions. Under conventional control, the electrical power output fluctuates around an average value of approximately 1120 W, with peak-to-peak variations exceeding 80 to 100 W, reflecting the system\u0026rsquo;s sensitivity to thermal input variations and suboptimal electrical loading. When the physics based optimized control is applied, the average power output increases to approximately 1145 W, corresponding to an improvement of about 2.2%, while the amplitude of power fluctuations is noticeably reduced. This indicates improved matching between thermal source conditions and electrical operating parameters, resulting in more stable and efficient power generation. A similar trend is observed in the conversion efficiency profile. Conventional control yields an average efficiency of approximately 7.9%, with frequent short-term drops caused by non-optimal operating conditions. In contrast, the optimized control strategy increases the average conversion efficiency to approximately 8.6%, representing an improvement of about 0.7% points. Moreover, efficiency fluctuations are reduced, demonstrating enhanced operational stability and reduced internal losses.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe time-domain behavior of the low-temperature thermal energy conversion system under conventional control and physics-based optimized control for eight representative operating cases is present in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. Each subplot illustrates the evolution of the normalized electrical load (%) over approximately 1500 minutes of simulated operation, capturing short-term fluctuations and longer-term trends in system response.\u003c/p\u003e \u003cp\u003eAcross all operating cases, the normalized electrical load under conventional control typically varies within the range of approximately 55% to 85%, with frequent high-frequency oscillations and abrupt load changes. These fluctuations reflect the system\u0026rsquo;s sensitivity to variations in thermal input conditions and the limited adaptability of fixed or rule-based control strategies. Peak values exceeding 80% are intermittently observed, particularly during transient periods, indicating operation away from optimal electrical loading.\u003c/p\u003e \u003cp\u003eIn contrast, the physics-based optimized control consistently produces a smoother load profile with reduced variability. Under optimized control, the normalized electrical load generally remains within a narrower band of approximately 60% to 75%, depending on the operating case. The amplitude of short-term oscillations is visibly reduced, with typical fluctuation magnitudes decreasing by approximately 25% to 40% compared to conventional control. This behavior indicates improved matching between thermal input conditions and electrical operating parameters.\u003c/p\u003e \u003cp\u003eNotably, the optimized control slightly shifts the average operating point toward lower but more stable load levels. This controlled reduction in load variability helps limit internal losses and prevents operation in inefficient regions of the performance space. Differences between operating cases highlight the influence of varying thermal conditions and system states; however, the optimized control demonstrates consistent stabilizing behavior across all cases.\u003c/p\u003e \u003cp\u003eOverall, results demonstrates that the physics-based intelligent control framework effectively regulates electrical loading under dynamic conditions, providing smoother and more controlled system operation while preserving flexibility across multiple operating scenarios.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e illustrates the time-domain regulation of applied heat flux and electrical load under conventional and physics-based optimized control for two representative operating cases of the low-temperature thermal energy conversion system. The figure consists of four subplots, where the upper row presents the temporal evolution of the applied heat flux \u0026#119902;, and the lower row shows the corresponding electrical load \u0026#119877;\u003csub\u003e\u0026#119871;\u003c/sub\u003e, each evaluated over approximately 1500 minutes of simulated operation. Under conventional control, the applied heat flux exhibits noticeable short-term fluctuations, with values varying over a relatively wide range of approximately 1.8 to 3.8 kW m⁻\u0026sup2;, depending on the operating case. These fluctuations include rapid oscillations and intermittent peaks, indicating limited capability of the controller to regulate thermal input smoothly under time-varying conditions. In contrast, the physics-based optimized control produces a visibly smoother heat-flux profile. The optimized trajectories remain confined within a narrower band, typically within \u0026plusmn;\u0026thinsp;0.2\u0026ndash;0.3 kW m⁻\u0026sup2; around the mean operating level, reflecting improved stabilization of thermal input through informed control action.\u003c/p\u003e \u003cp\u003eThe lower subplots show the dynamic response of the electrical load \u0026#119877;\u003csub\u003e\u0026#119871;\u003c/sub\u003e. With conventional control, the electrical load varies broadly, typically between 1.1 and 1.9, and exhibits frequent abrupt changes that correspond to transient thermal disturbances. When optimized control is applied, the electrical load trajectory becomes more regular and stable, with values predominantly maintained within the range of 1.3 to 1.7. Short-term load oscillations are significantly reduced, particularly during periods of rapid thermal variation, indicating enhanced coordination between thermal input regulation and electrical loading.\u003c/p\u003e \u003cp\u003eOverall, Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e provides a detailed representation of the dynamic behavior of key control variables under time-varying conditions. The comparison highlights differences in variability, smoothness, and operating ranges between conventional and optimized control strategies for representative cases, offering insight into the temporal characteristics of physics-based control in low-temperature thermal energy conversion systems.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eFigure 9\u003c/b\u003e presents the time-domain response of the low-temperature thermal energy conversion system under conventional control and physics-based optimized control, together with the corresponding self-learning correction coefficients applied during operation. The figure is composed of six subplots arranged in two rows. The upper row illustrates the evolution of three key operating variables: normalized electrical load, applied heat flux, and thermal source temperature, each plotted over approximately 1500 minutes of simulated system operation. The lower row shows the time-dependent correction coefficients generated by the self-learning control algorithm for the respective variables.\u003c/p\u003e \u003cp\u003eIn the upper row, the normalized electrical load varies between approximately 55% and 80% under conventional control, with frequent short-term oscillations and abrupt changes. Under optimized control, the electrical load trajectory becomes smoother, remaining within a narrower operating band, typically between 60% and 75%, while still responding to slower system dynamics. The applied heat flux exhibits similar behavior: conventional control results in fluctuations spanning roughly 0.5 to 5.0 kW m⁻\u0026sup2;, whereas optimized control reduces high-frequency variability and maintains heat-flux levels closer to the mean operating value. The thermal source temperature evolves within the range of approximately 50 to 200\u0026deg;C, with optimized control exhibiting reduced amplitude of rapid temperature excursions compared to conventional operation.\u003c/p\u003e \u003cp\u003eThe lower row depicts the self-learning correction coefficients associated with each control variable. These coefficients vary intermittently within a bounded range of approximately\u0026thinsp;\u0026minus;\u0026thinsp;6 to +\u0026thinsp;6, appearing as sparse impulses or short bursts. Such behavior indicates discrete control adjustments triggered by deviations from desired operating conditions rather than continuous aggressive correction. The temporal distribution and magnitude of these corrections reflect the adaptive nature of the control strategy under time-varying thermal and electrical conditions.\u003c/p\u003e \u003cp\u003eOverall, \u003cb\u003eFig.\u0026nbsp;9\u003c/b\u003e provides a detailed representation of the interaction between system dynamics and adaptive control actions in the low-temperature thermal energy conversion system over extended operating periods.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe integrated physics-based control and self-learning optimization architecture developed for low-temperature thermal energy conversion systems, as proposed in this study. The figure represents the complete information flow from thermal input conditions to adaptive control actions within a closed-loop framework. The control process begins with the thermal source temperature (T) and applied heat flux (q), which define the system\u0026rsquo;s available low-grade thermal input, typically within the ranges of 50 to 200\u0026deg;C and 0.5 to 5 kW m⁻\u0026sup2;, respectively. These inputs are continuously monitored and passed to the physics-based optimization maps, which are derived from first-principles modeling and numerical simulation. The control maps establish nonlinear relationships between thermal inputs, electrical load \u0026#119877;\u003csub\u003e\u0026#119871;\u003c/sub\u003e ​, electrical power output \u0026#119875; and conversion efficiency \u0026#120578;, capturing the coupled thermal electrical behavior of the system. The optimized electrical load \u0026#119877;\u003csub\u003e\u0026#119871;\u003c/sub\u003e is determined from these maps and applied to the system to regulate power extraction under varying thermal conditions. Concurrently, measured performance signals, including electrical power output (typically 300 to 2600 W) and conversion efficiency (approximately 14%), are fed back into the control architecture. These measured responses are compared with predicted performance surfaces to identify deviations caused by transient effects or unmodeled disturbances. The lower section of the figure depicts the self-learning correction mechanism, which generates bounded correction coefficients (typically within \u0026plusmn;\u0026thinsp;5\u0026ndash;6%) to update the control maps. These corrections are applied intermittently, reflecting adaptive adjustments rather than continuous aggressive control. The resulting adaptive control signals refine system operation while maintaining physical feasibility and stability. Overall, Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e11\u003c/span\u003e provides a concise visualization of how physics-based modeling and adaptive optimization are integrated to regulate low-temperature thermal energy conversion systems under dynamic operating conditions.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"6. Conclusion","content":"\u003cp\u003eThis study has presented a comprehensive physics-based, simulation-driven framework for improving the performance of low-temperature thermal energy conversion systems through adaptive control and optimization. Addressing the identified research gap of limited system-level, physics-informed control strategies for low-grade thermal applications, the proposed approach integrates first-principles modelling, surrogate-assisted performance prediction, sensitivity analysis, and constrained optimization within a closed-loop, self-learning control architecture.\u003c/p\u003e \u003cp\u003eThe developed modelling framework captured the nonlinear coupling between thermal source temperature, applied heat flux, electrical load, electrical power output, and conversion efficiency over a realistic operating envelope. Simulation results for thermal source temperatures between 50 and 200\u0026deg;C, heat fluxes from 0.5 to 5.0 kW m⁻\u0026sup2;, and electrical load values ranging from 0.5 to 3.0 demonstrated pronounced nonlinearity in system response. Electrical power output increased from approximately 300 to 600 W at low temperatures to 2400 to 2600 W at higher thermal inputs, while conversion efficiency improved from below 3% at temperatures under 80\u0026deg;C to approximately 13 to 14% near 180 to 200\u0026deg;C when operated within the optimal electrical load region (R_L\u0026thinsp;\u0026asymp;\u0026thinsp;1.4\u0026ndash;1.8). Operation outside this optimal region resulted in efficiency penalties of approximately 3 to 6% points, underscoring the importance of adaptive control.\u003c/p\u003e \u003cp\u003eTime-domain simulations confirmed the effectiveness of the proposed optimization strategy. Controller training over 24 h, 48 h, and 72 h yielded progressive performance improvements, with maximum average gains of approximately 1.1% in power output and 1.3% in conversion efficiency observed at 48 h training duration, followed by diminishing returns at longer training periods. During extended 72 h operation, optimized control increased average electrical power output from approximately 1120 W to 1145 W and improved conversion efficiency from 7.9% to 8.6%, while significantly reducing short-term fluctuations. Across multiple operating scenarios, normalized electrical load variability was reduced by 25% to 40%, and heat-flux and load trajectories exhibited enhanced smoothness and stability.\u003c/p\u003e \u003cp\u003eOverall, the results demonstrate that measurable performance enhancement and improved operational stability can be achieved through physics-based control and optimization without hardware modification, directly fulfilling the study\u0026rsquo;s objectives. The proposed framework provides a transferable and scalable solution for low-temperature thermal energy conversion systems.\u003c/p\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e6.1. Future Research Directions\u003c/h2\u003e \u003cp\u003eFuture work will extend the proposed framework toward fully dynamic modeling to capture transient thermal-electrical interactions under rapidly varying heat sources. Experimental validation on laboratory-scale or pilot-scale low-temperature thermal energy conversion systems will be pursued to further assess real-world applicability. Additionally, the integration of uncertainty-aware optimization and multi-objective control strategies, incorporating durability and long-term performance metrics, represents a promising direction for enhancing robustness in practical deployment.\u003c/p\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cul\u003e\n \u003cli\u003e\u003cstrong\u003eCompliance with Ethical Standards\u003c/strong\u003e\u003c/li\u003e\n \u003cli\u003e\u003cstrong\u003eDisclosure of potential conflicts of interest\u003c/strong\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003e\u003cstrong\u003eResearch involving Human Participants and/or Animals\u003c/strong\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThis research does not contain any studies with human participants or animals performed by any of the authors.\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003e\u003cstrong\u003eInformed consent\u003c/strong\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eInformed consent was obtained from all individual participants included in the study.\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003e\u003cstrong\u003eFunding Acknowledgements\u003c/strong\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThis research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sector.\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003e\u003cstrong\u003eData Availability\u003c/strong\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThe data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003e\u003cstrong\u003eCredit Authorship Contribution Statement\u003c/strong\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eMunsif Ali:\u003c/strong\u003e Writing – review \u0026amp; editing, Writing – original draft, Methodology, Data curation, Conceptualization. \u003cstrong\u003eUzair Ahmad:\u003c/strong\u003e Validation, Visualization, Software. \u003cstrong\u003eShafi Ullah\u0026nbsp;\u003c/strong\u003eFormal analysis, Supervision. \u003cstrong\u003eSubhan Ullah:\u003c/strong\u003e Data Curation, Visualization. \u003cstrong\u003eShah Rukh khan:\u003c/strong\u003e Resources, Investigation, Formal analysis.\u0026nbsp;\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eD. Champier, Thermoelectric generators: A review of applications, Energy Convers. 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Manag. 274 (2022) 116437. https://doi.org/https://doi.org/10.1016/j.enconman.2022.116437.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Hazara University","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Low-temperature energy conversion, Physics-based control, Adaptive optimization, Waste heat recovery, Energy efficiency.","lastPublishedDoi":"10.21203/rs.3.rs-8706095/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8706095/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eLow-Temperature Thermal Energy Conversion Systems (LT-TECS) are critical for recovering low-grade waste heat from geothermal and industrial sources however, their practical deployment is constrained by strong nonlinear system behaviour and the absence of adaptive, physics-informed control strategies. This study presents a physics-based, simulation-driven control and optimization framework aimed at improving the system-level performance of low-temperature thermal energy conversion systems operating below 200\u0026deg;C. A first-principles numerical model is developed to capture the coupled thermal electrical behaviour of the system over thermal source temperatures ranging from 50 to 200\u0026deg;C, heat fluxes between 0.5 and 5.0 kW m⁻\u0026sup2;, and electrical load values from 0.5 to 3.0. Performance prediction surfaces indicate electrical power outputs varying from approximately 300 to 2600 W and conversion efficiencies between 1% and 14%, highlighting strong sensitivity to operating conditions. A surrogate-assisted, physics-based optimization strategy is employed to construct control maps and implement a self-learning adaptive control loop. Time-domain simulations over training periods of 24 to 96 h demonstrate consistent performance improvements under optimized control. Average electrical power output increases by up to 2.2%, while conversion efficiency improves by approximately 0.7 percentage points compared to conventional control, accompanied by a 25 to 40% reduction in load and heat-flux fluctuations. The results confirm that physics-based adaptive control and optimization can deliver measurable and stable performance gains without hardware modification, addressing a key gap in low-temperature thermal energy conversion system operation. The proposed framework provides a transferable and cost-effective solution for improving the energy yield of existing LT-TECS infrastructure.\u003c/p\u003e","manuscriptTitle":"Performance Improvement of Low-Temperature Thermal Energy Conversion Systems via Physics-Based Control and Optimization","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-02 06:55:18","doi":"10.21203/rs.3.rs-8706095/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"eb93aa86-26ff-4ebe-a43e-412cfa50e4c8","owner":[],"postedDate":"February 2nd, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":61796023,"name":"Computational Physics"},{"id":61796024,"name":"Energy Engineering"},{"id":61796025,"name":"High Energy and Particle Physics"}],"tags":[],"updatedAt":"2026-04-16T20:15:38+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-02 06:55:18","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8706095","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8706095","identity":"rs-8706095","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}