Thermodynamic Modeling and Energy Efficiency Optimization of Energy Systems in Tourist Attractions

Driven by the global “dual carbon” goals [1, 2] and the pursuit of high-quality tourism development [3, 4], tourist attractions—characterized as high-energy-consuming, multi-sectoral composite service systems—have reached a critical juncture in transforming their energy consumption structures and enhancing energy efficiency, both of which are essential for sustainable development [5]. In recent years, the tourism industry in China has continued to expand, resulting in a rigid increase in energy demand within tourist attractions [6]. However, traditional energy systems generally suffer from issues such as a single energy supply structure, delayed load response, and mismatched energy grades [7, 8]. During peak tourist seasons, heavy reliance on fossil fuels to meet high loads has led to surges in carbon emissions, whereas in off-peak periods, low-load operation has caused difficulties in the utilization of renewable energy. Moreover, the direct use of high-grade electrical energy to meet low-grade thermal and cooling demands has resulted in severe exergy losses. These contradictions not only increase the operational costs of tourist attractions but also impede their transition toward green and low-carbon development [9]. At the same time, energy loads in tourist attractions exhibit pronounced spatiotemporal nonuniformity, as they are strongly influenced by visitor activity patterns, seasonal variations, and weather conditions [10]. When combined with the stochastic output characteristics of renewable energy sources such as PV and wind power, the operational complexity of the energy system is further intensified, posing significant challenges to conventional planning and optimization methodologies [11].

Extensive research has been conducted domestically and internationally to address the optimization of integrated energy systems. Regarding load characteristic analysis, most existing studies have focused on scenarios such as industrial parks and urban communities [12-14], emphasizing macroscopic statistical descriptions of load features. However, insufficient attention has been paid to the unique operational characteristics of tourist attractions, which exhibit intense fluctuations in service-oriented loads and the coexistence of multi-grade energy demands. Fine-grained analyses that elucidate the coupling mechanisms between thermal/cooling loads and visitor behavior remain lacking. In terms of thermodynamic modeling, many studies have relied solely on the first law of thermodynamics to construct energy balance models [15-17], neglecting the quantification of exergy losses arising from differences in energy grades. Consequently, such models fail to accurately reflect the intrinsic nature of system energy efficiency. Regarding optimization algorithms, traditional multi-objective optimization methods [18-26] often suffer from imbalanced convergence and distribution when addressing high-dimensional objectives. Furthermore, these algorithms have not been adapted to accommodate the coupled characteristics of discrete on/off variables and continuous output variables that are prevalent in tourist attractions, thereby limiting the engineering feasibility of their optimization results. Overall, existing research has yet to establish a comprehensive technical framework tailored to the operational characteristics of tourist attractions that integrates thermodynamic fundamentals with advanced optimization algorithms. As a result, current approaches remain insufficient to meet the practical demands of achieving low-carbon, high-efficiency, and economically coordinated optimization in tourist attraction energy systems.

To address the aforementioned research gap, a systematic study was conducted on the integrated energy systems of tourist attractions, following the core logical framework of characteristic analysis–thermodynamic modeling–multi-objective optimization. First, multi-scale system boundaries were defined, and the fluctuation patterns of electrical, thermal, and cooling loads were analyzed from spatiotemporal dimensions. High- and low-grade energy demands were distinguished to establish a foundation for subsequent modeling and optimization. Second, based on the first and second laws of thermodynamics, a refined model of key components—such as PV panels, wind turbines, and heat pumps—was developed. By coupling energy and material flows, a system-level steady-state and dynamic simulation model was constructed, enabling precise depiction of energy conversion processes and exergy losses. Finally, considering the multi-objective conflict, nonlinearity, and high dimensionality inherent in the optimization problem of tourist attractions, an improved NSGA-III algorithm was selected and modified. A three-dimensional objective function encompassing economic, environmental, and energy-efficiency objectives was formulated, and global optimization of system operation strategies was achieved under constraints such as energy balance and equipment operating limits.

The innovations of this study are reflected in three main aspects: (a) A spatiotemporal coupling and energy-grade stratification framework for load characteristic analysis in tourist attractions was proposed, quantifying the coupling mechanisms among visitor behavior, seasonal rhythms, and energy demand, while establishing energy-grade matching criteria for various service types. (b) A full-chain thermodynamic model incorporating exergy efficiency was constructed, overcoming the limitations of conventional energy balance models and achieving a dual characterization of both the quantity and quality of energy. (c) A load-coupling-based population initialization and hierarchical constraint-handling strategy was introduced to improve the NSGA-III algorithm, enabling adaptation to the multi-variable coupling characteristics of tourist attractions and enhancing convergence and engineering feasibility in high-dimensional optimization problems.

The research outcomes are expected to provide theoretical and technical support for the planning, design, and operational optimization of integrated energy systems in tourist attractions. These results possess significant engineering application value in promoting the transformation of energy consumption structures, reducing carbon emissions, and improving operational efficiency within tourist attractions. The structure of the study is as follows: Section 2 presents the characteristic analysis and thermodynamic modeling of the tourist attraction energy system; Section 3 constructs the multi-objective optimization model and applies the improved algorithm for solution; the subsequent sections validate the effectiveness of the proposed model and algorithm through case studies and provide optimization strategies and recommendations.

Based on the preceding analysis of the physical boundaries, load characteristics, and system architecture of energy systems in tourist attractions, the thermodynamic modeling was established on the fundamental principles of the law of energy conservation and the law of entropy increase. A hierarchical modeling framework was adopted, combining component-level refined modeling with system-level coupled modeling, to construct a mathematical model capable of accurately representing the mechanisms of energy conversion, transfer, and dissipation within the system. The developed model is required to comprehensively account for the spatiotemporal fluctuations of energy loads, the stochastic nature of renewable energy outputs, and the multi-energy complementary characteristics of the system. This provides a robust quantitative analytical tool for energy efficiency optimization and operational strategy formulation in subsequent research and practical applications. Several key assumptions were established during the modeling process: (a) The effect of pressure loss in the transmission and distribution network on energy grade is neglected, and only temperature-induced exergy losses are considered. (b) All components are assumed to operate under quasi-steady-state conditions, where dynamic responses are simplified as steady-state superpositions within each time step. (c) During the charging and discharging processes of energy storage devices, parameters such as temperature and pressure are assumed to be uniformly distributed, thereby avoiding the additional complexity caused by local thermodynamic nonequilibrium.

3.1 Component-level thermodynamic model

The component-level model serves as the foundation of the entire system model. It was established for the key equipment within the tourist attraction energy system—including PV modules, wind turbines, heat pumps, energy storage units, and boilers—to quantify the relationships between their input–output characteristics and critical operating parameters. Moreover, exergy analysis indicators were incorporated to evaluate and quantify energy utilization efficiency, ensuring the thermodynamic consistency of the overall modeling framework.

3.1.1 PV system model

The core function of the PV system is to convert solar irradiance into electrical energy, with its output characteristics primarily influenced by solar radiation intensity, ambient temperature, and the aging condition of the PV modules. Based on the law of energy conservation, the output power model of the PV system can be expressed as:

${{P}_{pv}}\left( t \right)={{P}_{stc}}\cdot \frac{G\left( t \right)}{{{G}_{stc}}}\cdot \left[ 1+k\left( {{T}_{c}}\left( t \right)-{{T}_{stc}} \right) \right]\cdot {{\eta }_{pv}}$                   (1)

The temperature model of the PV cell is given by:

${{T}_{c}}\left( t \right)={{T}_{a}}\left( t \right)+\frac{NOCT-20}{800}\cdot G\left( t \right)$ (2)                       

where, P_pv(t) denotes the PV output power at time t (kW); P_stc represents the rated output power under standard test conditions (STC) (kW); G(t) is the total solar irradiance at time t (W/m²); G_stc is the standard irradiance under STC, equal to 1000 W/m²; T_c(t) denotes the PV cell temperature (℃); T_a(t) represents the ambient temperature (℃); T_stc is the standard cell temperature, set at 25℃; k is the power temperature coefficient, equal to −0.0045/℃; η_pv denotes the combined efficiency of the inverter and electrical wiring, typically ranging between 0.92 and 0.96; and NOCT is the nominal operating cell temperature, ranging from 45℃ to 48℃.

3.1.2 Wind power generation system model

In tourist attractions, small-scale distributed wind turbines are predominantly employed, and their output power exhibits a nonlinear dependence on wind speed. To accurately describe this relationship, the power characteristic model was developed based on the law of energy conservation, incorporating the operational constraints of cut-in, rated, and cut-out wind speeds. The output power of the wind turbine can be expressed as:

${{P}_{wt}}\left( t \right)=\left\{ \begin{align}  & 0,v\left( t \right)\le {{v}_{ci}}\text{ or }v\left( t \right)\ge {{v}_{co}} \\ & \frac{1}{2}\rho Av{{\left( t \right)}^{3}}{{C}_{p}}{{\eta }_{wt}},{{v}_{ci}}<v\left( t \right)<{{v}_{r}} \\ & {{P}_{rated}},{{v}_{r}}<v\left( t \right)<{{v}_{co}} \\ \end{align} \right.$                 (3)

where, P_wt(t) denotes the wind turbine output power at time t (kW); v(t) represents the wind speed at hub height (m/s); v_ci is the cut-in wind speed, typically between 3–4 m/s; v_co is the cut-out wind speed, typically 25 m/s; v_r is the rated wind speed, generally between 12–15 m/s; ρ represents the air density, equal to 1.225 kg/m³; A denotes the swept area of the wind turbine rotor (m²); C_p is the power coefficient, typically ranging from 0.35 to 0.45; η_wt represents the generator efficiency, within 0.90–0.95; and P_rated denotes the rated power output of the turbine (kW).

3.1.3 Heat pump system model

The heat pump system serves as the core component for supplying low-grade heating and cooling loads in tourist attractions. Its performance is directly influenced by the evaporation temperature and condensation temperature. Based on the first law of thermodynamics, the performance model under heating and cooling conditions was formulated below. The heating COP is expressed as:

$CO{{P}_{h}}\left( t \right)={{\eta }_{carnot}}\cdot \frac{{{T}_{cond}}\left( t \right)}{{{T}_{cond}}\left( t \right)-{{T}_{evap}}\left( t \right)}$                        (4)

The cooling COP is expressed as:

$CO{{P}_{c}}\left( t \right)={{\eta }_{carnot}}\cdot \frac{{{T}_{evap}}\left( t \right)}{{{T}_{cond}}\left( t \right)-{{T}_{evap}}\left( t \right)}$                    (5)

The power balance relationship of the heat pump system is given by:

${{P}_{hp}}\left( t \right)=\frac{{{Q}_{heating}}\left( t \right)}{CO{{P}_{h}}\left( t \right)}=\frac{{{Q}_{cooling}}\left( t \right)}{CO{{P}_{c}}\left( t \right)}$                (6)

where, COP_h(t) represents the heating COP; COP_c(t) denotes the cooling COP; T_cond(t) and T_evap(t) are the condensation and evaporation temperatures, respectively (K); η_carnot is the Carnot efficiency factor, typically ranging from 0.5 to 0.7; P_hp(t) denotes the input electrical power of the heat pump (kW); and Q_heating(t) and Q_cooling(t) represent the heating power and cooling power, respectively (kW).

3.1.4 Energy storage system models

The energy storage system in tourist attractions encompasses electrical, thermal, and cooling storage subsystems. Separate charge–discharge characteristic models were established for each, with emphasis placed on efficiency degradation, self-discharge, and state constraints. The electrical energy storage model was developed based on the law of energy conservation, describing the relationship between charging/discharging power and the state of charge (SOC), while incorporating charge–discharge efficiency and self-discharge rate corrections. The expression is formulated as:

$\frac{dSO{{C}_{bat}}\left( t \right)}{dt}=\frac{{{\eta }_{ch}}{{P}_{ch}}\left( t \right)-\frac{{{P}_{dis}}\left( t \right)}{{{\eta }_{dis}}}}{E_{bat}^{\max }}$                     (7)

The thermal energy storage model accounts for both latent and sensible heat storage in phase change materials, establishing the relationship between temperature and stored thermal energy under energy conservation principles:

$\frac{dSO{{C}_{tes}}\left( t \right)}{dt}=\frac{{{Q}_{ch}}\left( t \right)-{{Q}_{dis}}\left( t \right)}{E_{bat}^{\max }}\cdot {{\eta }_{tes}}$                (8)

The cooling energy storage model utilizes the latent heat of ice melting to store cold energy. Its mathematical formulation is analogous to that of the thermal energy storage model, with the principal difference lying in the exergy computation of cold energy and the phase change parameters. The phase change temperature was set at 0℃, and the latent heat of the phase change was taken as 334 kJ/kg. The operational constraints corresponding to the aforementioned models are expressed as:

$\left\{ \begin{align}  & SO{{C}_{\min }}\le SOC\left( t \right)\le SO{{C}_{\max }} \\ & 0\le {{P}_{ch}}\left( t \right)\le P_{ch}^{\max } \\ & 0\le {{P}_{dis}}\left( t \right)\le P_{dis}^{\max } \\ & {{P}_{ch}}\left( t \right)\cdot {{P}_{dis}}\left( t \right)=0 \\\end{align} \right.$                (9)

where, SOC(t) denotes the state of charge, ranging from 0 to 1; η_ch and η_dis represent the charging and discharging efficiencies, respectively, typically within 0.92–0.98; P_ch(t) and P_dis(t) denote the charging power and discharging power (kW); E^max_bat is the maximum capacity of the battery storage system (kWh); E^max_tes represents the maximum capacity of the thermal storage tank (kWh); η_tes denotes the thermal storage efficiency, generally ranging between 0.85 and 0.95; and δ_sd refers to the self-discharge rate (%/day).

3.1.5 Gas boiler model

The gas boiler functions as a backup heat source in tourist attractions, with its primary purpose being the conversion of the chemical energy of natural gas into thermal energy. Based on the first law of thermodynamics, the energy balance equation for the boiler system is established as follows:

${{Q}_{boiler}}\left( t \right)={{\eta }_{boiler}}\cdot {{\dot{m}}_{fuel}}\left( t \right)\cdot LH{{V}_{fuel}}$                (10)

The exergy efficiency of the boiler is calculated according to the following expression:

${{\eta }_{ex,boiler}}=\frac{\dot{E}{{x}_{out}}}{\dot{E}{{x}_{in}}}=\frac{\dot{Q}\left( 1-\frac{{{T}_{0}}}{{{T}_{steam}}} \right)}{{{{\dot{m}}}_{fuel}}\cdot e{{x}_{fuel}}}$                     (11)

where, Q_boiler(t) denotes the boiler thermal output power (kW); η_boiler represents the boiler thermal efficiency, typically ranging from 0.85 to 0.95; ${{\dot{m}}_{fuel}}$(t) is the mass flow rate of the fuel (kg/s); LHV_fuel denotes the lower heating value of the fuel (kJ/kg); η_ex,boiler represents the exergy efficiency of the boiler; T_steam is the steam temperature (K); T₀ denotes the ambient temperature (K); and ex_fuel represents the specific exergy of the fuel (kJ/kg).

3.2 System-level coupling model

At the system level, the aforementioned component models were coupled through energy flow, mass flow, and information flow, thereby forming a comprehensive thermodynamic model that encompasses the entire “energy supply–transmission and distribution–consumption–storage” chain. The system-level model is classified into steady-state and dynamic categories, corresponding respectively to the planning and design and operational optimization phases of the energy system in tourist attractions.

(a) Steady-state model

The system energy balance equations were formulated based on the law of energy conservation, with their primary objective being the matching between total energy supply and total energy demand, while ensuring that the operational constraints of all components are satisfied. Taking a typical day under steady operating conditions in a tourist attraction as an example, the system energy balance equations are expressed below. The electricity balance, thermal energy balance, cooling energy balance, and exergy balance equations, respectively, are expressed as follows:

$\begin{align}  & {{P}_{grid}}\left( t \right)+{{P}_{pv}}\left( t \right)+{{P}_{wt}}\left( t \right)+P_{dis}^{bat}\left( t \right) \\ & =P_{load}^{elec}\left( t \right)+P_{ch}^{bat}\left( t \right)+{{P}_{hp}}\left( t \right)+{{P}_{other}}\left( t \right) \\ \end{align}$                      (12)

$\begin{align}  & {{Q}_{boiler}}\left( t \right)+CO{{P}_{h}}\left( t \right)\cdot {{P}_{hp}}\left( t \right)+Q_{dis}^{tes}\left( t \right) \\ & ={{H}_{load}}\left( t \right)+Q_{ch}^{tes}\left( t \right)+{{H}_{loss}}\left( t \right) \\ \end{align}$                    (13)

$CO{{P}_{c}}\left( t \right)\cdot {{P}_{hp}}\left( t \right)+Q_{dis}^{tes}\left( t \right)={{C}_{load}}\left( t \right)+Q_{ch}^{ces}\left( t \right)+{{C}_{loss}}\left( t \right)$                (14)

$\sum{\dot{E}{{x}_{in}}}=\sum{\dot{E}{{x}_{out}}}+\sum{\dot{E}{{x}_{destruction}}}+\sum{\dot{E}{{x}_{loss}}}$                  (15)

where, P_grid(t) denotes the purchased power from the utility grid (kW); P^elec_load(t) represents the electrical load (kW); H_load(t) denotes the thermal load (kW); C_load(t) represents the cooling load (kW); H_loss(t) and C_loos(t) indicate the heat network loss and cooling network loss (kW), respectively; E^·x represents the exergy flow rate (kW); and E^·x_destruction denotes the exergy destruction rate (kW). The system energy performance indicators include energy utilization efficiency and exergy efficiency, defined as follows:

$EUF=\frac{\sum{\left( Useful\text{ }Output\text{ }Energy \right)}}{\sum{\left( Input\text{ }Primary\text{ }Energy \right)}}$                  (16)

${{\eta }_{ex,system}}=\frac{\sum{\left( Output\text{ }Exergy \right)}}{\sum{\left( Input\text{ }Exergy \right)}}$                 (17)

(b) Dynamic model

To account for the intra-day fluctuations in load demand and the short-term variability of renewable energy output, a dynamic simulation model was developed using a time-step method. The core of this model lies in incorporating the dynamic response characteristics of components into the steady-state framework. For example, the dynamic temperature response model of PV modules, which is influenced by thermal inertia, can be expressed as T=T+(G·α-U·(T-T))·Δt/(m·c), where α is the absorption coefficient of the PV module, U denotes the overall heat loss coefficient, m represents the mass of the PV module, and c is the specific heat capacity of the module. The dynamic model outputs include the time-dependent operational parameters of each component, the system-level energy performance indicators, and the interactive power. These simulations were typically implemented using professional platforms such as MATLAB/Simulink or TRNSYS.

The optimization problem constructed for the tourist attraction energy system exhibits pronounced characteristics of multi-objective conflict, nonlinearity, high dimensionality, and strong constraint coupling. Traditional linear optimization methods are inadequate for addressing the coupling of nonlinear and discrete variables, while low-dimensional multi-objective algorithms struggle to balance convergence and distribution performance in high-dimensional scenarios. To overcome these limitations, NSGA-III was adopted as the core algorithm. This section systematically elaborates on the algorithm selection rationale, scenario-specific adaptation strategies, end-to-end solution implementation, and performance verification, thereby establishing a closed-loop framework integrating problem formulation, algorithmic logic, and solution realization.

5.1 Algorithm selection: Adaptability analysis of NSGA-III

The selection of the algorithm is guided by four principal criteria: objective dimensional adaptability, variable type compatibility, constraint-handling capability, and computational efficiency for engineering applications. Through a comparative analysis of mainstream multi-objective intelligent optimization algorithms, NSGA-III was identified as uniquely suited to the optimization requirements of the tourist attraction energy system. Its adaptability is primarily reflected in three aspects. The first is the high-dimensional objective balancing mechanism. NSGA-III introduces a reference-point-based approach that transforms a multi-objective conflict into an association optimization between solutions and a set of uniformly distributed reference points. This design effectively mitigates the core deficiency of NSGA-II, wherein excessive non-dominated solutions under three or more objectives lead to ineffective selection. The second is the compatibility with hybrid variable types. A hybrid encoding strategy combining real-coded representation for continuous variables and binary-coded representation for discrete variables was employed. This dual-variable encoding, coupled with targeted genetic operators, enables precise adaptation to the system’s dual control requirements—continuous power regulation and discrete state switching. The third is the engineering constraint friendliness. NSGA-III incorporates a hierarchical constraint-handling mechanism, allowing direct correspondence to the system’s hard energy balance constraints and soft SOC constraints for real engineering scenarios. This approach prevents over-constraining, which may lead to feasible domain shrinkage, as well as constraint relaxation, which could otherwise yield infeasible solutions.

5.2 Adaptation and improvement of NSGA-III for tourist attraction scenarios

To address the inherent limitations of the original NSGA-III when applied to tourist attraction energy systems—namely, the low proportion of feasible solutions in the initial population, weak coupling between fitness evaluation and optimization objectives, and constraint-handling operations that may induce convergence deviation—targeted adaptations were implemented across three dimensions: population initialization, fitness evaluation, and constraint handling. In terms of population initialization, instead of adopting conventional random initialization, a “typical scenario clustering + pre-constraint verification” strategy was developed. Historical load data from the tourist attraction were first clustered using the K-means algorithm, identifying three representative operating scenarios: peak, off-peak, and valley. For each scenario, key variable initial values were predefined based on scenario features and corresponding population proportions were allocated. Subsequently, all randomly generated individuals underwent pre-verification of device on/off status–output coupling constraints, and infeasible solutions were eliminated before the population was replenished to the preset scale. This approach significantly enhanced both the initial population quality and overall computational efficiency.

In terms of fitness evaluation, to ensure seamless integration between the optimization objectives and the algorithmic evaluation process, a normalized multi-objective function was directly employed as the fitness function. The Analytic Hierarchy Process–Entropy Weight Method (AHP–EWM) was applied to determine the combined weights of each objective, simultaneously accommodating subjective operational preferences of the tourist attraction and objective data-driven information entropy corrections, thereby minimizing bias in weight determination. Furthermore, a clear correspondence was established between the fitness value and the comprehensive performance of each solution, providing explicit optimization direction during algorithmic iteration. To prevent the influence of weight fluctuations on the optimization results, sensitivity analysis was subsequently conducted to verify the robustness of the obtained solutions, ensuring the algorithm’s adaptability to variations in weight assignments.

A hierarchical constraint-handling strategy combining “feasible-solution prioritization for hard constraints” and “dynamic penalty functions for soft constraints” was introduced. For hard constraints—including energy balance, device on/off–output coupling, and mutual exclusivity constraints—any violation automatically classifies the individual as a dominated solution, which is forcibly eliminated from the population. This ensures strict adherence to engineering feasibility. For soft constraints, such as SOC upper and lower limits, renewable energy utilization rate, and equipment output boundaries, dynamic penalty coefficients were designed. During early iterations, smaller penalty coefficients were used to encourage broader exploration of the feasible domain; as iterations progressed, penalty coefficients were gradually increased to drive convergence toward feasible regions. This mechanism prevented convergence stagnation due to excessive penalization while avoiding engineering infeasibility resulting from overly relaxed constraints.

5.3 Full-process solution implementation and parameter calibration

The full-process solution implementation follows the logical sequence of “data preprocessing – population initialization – genetic operations – non-dominated sorting – elite preservation – iteration termination.” Initially, equipment parameters, load profiles, meteorological data, and economic–environmental parameters of the tourist attraction were imported. Data cleaning and normalization were conducted to ensure high-quality input for the solution. Following this, the improved population initialization strategy was applied to generate a hybrid-encoded initial population. Simulated binary crossover and single-point crossover were employed for continuous and discrete variables, respectively, while polynomial and bit-flip mutations were adopted to maintain population diversity during evolution. Subsequently, parent and offspring populations were merged, and a hierarchical non-dominated sorting procedure was executed. Elite preservation was achieved through reference point association and crowding distance calculation, ensuring both solution convergence and distribution uniformity. The iterative process terminated when either the maximum number of iterations was reached or the fluctuation of fitness values satisfied the precision criterion, at which point the Pareto-optimal solution set was output.

Parameter calibration is a critical process for ensuring the performance of the algorithm. To this end, four core parameters—population size, crossover probability, mutation probability, and number of iterations—were optimized using an orthogonal experimental design. Multiple parameter combinations were tested, with convergence and distribution metrics (specifically, the spread metric, SP) adopted as evaluation criteria. Through comprehensive simulation-based testing, the optimal parameter combination was determined. Special attention was given to the interaction effects among parameters on the performance of the algorithm, ensuring that parameter combinations improve convergence efficiency without compromising the diversity or distribution quality of solutions. This establishes a highly efficient and stable computational foundation for the optimization of the tourist attraction energy system.