Optimal Planning and Operation of an Integrated Energy System Based on a Compression-Assisted Double-Effect Absorption Refrigeration Cycle

Abstract

Integrated energy systems (IESs) have gained significant attention for their ability to enhance energy efficiency and reduce carbon emissions through multi-energy coupling and complementary coordination. Absorption refrigeration technology plays a key role in IESs by utilizing low-grade waste heat for cooling supply. However, conventional working fluid pairs such as NH₃/H₂O and LiBr/H₂O face limitations related to safety, stability, and environmental impact. This study proposes a novel low-pressure-side compression-assisted double-effect absorption refrigeration system (LC-DARS) using the environmentally friendly refrigerant R-1233zd(E) paired with the phosphonium-based ionic liquid [P₆₆₆₁₄][TMPP]. A bi-level optimization model is developed for the LC-DARS-based IES, incorporating equipment modeling and economic evaluation. The unit capacity investment cost of the LC-DARS is calculated to be 255.61 $/kW. A case study of an industrial park in Luoyang, China, demonstrates that the proposed system achieves significant improvements in economic (29.6%), energy efficiency (47.0%), and environmental (59.8%) performance compared to a conventional separate supply system. Optimal dispatch strategies for typical summer, transition season, and winter days are further analyzed, highlighting the system’s ability to operate with high autonomy and efficiency. The results validate the practical potential of the LC-DARS in enhancing IES performance and promoting sustainable energy utilization.

1. Introduction

Under the global energy transition background, improving energy utilization efficiency and reducing carbon emissions have become key research directions in the energy field. Traditional energy supply systems are typically planned and operated separately, with limited coupling between energy supply devices. Consequently, these systems suffer from low energy utilization rates and high carbon emissions. Integrated energy systems (IESs) integrate multiple energy forms and plan and optimize the processes of energy generation, conversion, transmission, consumption, and storage. This enables cascaded utilization and complementary coordination of energy, enhances energy utilization efficiency, promotes renewable energy consumption, and achieves low carbon emissions [1,2]. Within IESs, diverse energy applications are prominent, particularly concerning the use of low-grade heat sources (such as industrial waste heat, solar thermal energy, and gas turbine flue gas waste heat). These sources can be used for direct heating or converted via energy equipment, for example, for power generation or cooling. The application of absorption refrigeration technology enables low-grade heat to drive the refrigeration cycle, supplying cooling energy to users. Basu and Ganguly [3] validated the technical and economic feasibility of solar-driven absorption refrigeration technology through a 3.5 kW system, which achieved an average daily surplus of 17.4 kWh and payback periods of under four years. Wei et al. [4] optimized a biogas-driven micro-CCHP system with hybrid absorption and electric chillers using NSGA-II on a TRNSYS-Matlab platform. It obtains Pareto-optimal strategies to maximize energy savings and minimize costs, revealing internal energy coupling. The study highlights absorption refrigeration as key to recovering waste heat for cooling, reinforcing its role as a core technology for thermal–cooling coupling in integrated energy systems. Zhang et al. [5] proposed a shipborne ammonia absorption refrigeration-ice storage system driven by waste heat. By integrating ice storage, the system balances cooling supply and demand, overcoming the poor adjustability of absorption refrigeration. Multi-objective optimization shows significant reductions in energy consumption, operating costs, and lifecycle costs compared to conventional systems. Therefore, absorption refrigeration technology has become one of the key technologies for thermal–cooling coupling and a core technology for cooling supply in IESs.

Traditional absorption chillers typically employ NH₃/H₂O or LiBr/H₂O solutions as the working fluid pair for the refrigeration cycle. The use of these conventional working pairs has certain limitations, constraining their safety and applicability. The limitations of the NH₃/H₂O solution include: ammonia toxicity, explosion risk, corrosiveness to copper metals, and the requirement of an additional rectification device [6]. The limitations of the LiBr/H₂O solution include: susceptibility to crystallization phase change, corrosiveness, and operation under negative pressure conditions [7]. Therefore, the development of alternative working fluid pairs is crucial to overcoming the limitations of conventional pairs. Ionic liquids (ILs) have attracted widespread attention from researchers worldwide due to their outstanding physicochemical properties (such as near-zero vapor pressure, non-flammability, absence of pungent odor, and compatibility with most metals). They are regarded as highly promising absorbents [8,9].

In research related to ILs as absorbents, the common refrigerants studied include H₂O, NH₃, CO₂, and HFC [9,10,11]. However, with the evolution of refrigerants, more researchers are focusing on HFO (Hydrofluoroolefin) refrigerants. Due to the carbon–carbon double bond in their molecular structure, HFO refrigerants have a significantly shortened atmospheric lifetime, resulting in an extremely low Global Warming Potential (GWP). These environmentally friendly refrigerants not only meet the urgent global demand for low-carbon refrigerants but also provide new avenues for the development of working fluids for absorption refrigeration systems. Sujatha and Venkatarathnam [12] investigated the performance of low-GWP HFO refrigerants R-1234ze(E) and R-1234yf with the ionic liquid [hmim][Tf₂N] in vapor absorption refrigeration systems, highlighting their potential as environmentally friendly working fluids for absorption refrigeration applications. Wu et al. [13] thermodynamically investigated and compared absorption cycles using HFO refrigerants R-1234yf and R-1234ze(E) with ionic liquid [hmim][Tf₂N], demonstrating their feasibility as novel environmentally friendly working pairs for absorption refrigeration. Liu et al. [14] proposed and evaluated two absorption–compression hybrid refrigeration systems using R-1234yf with various ionic liquids, showing improved cooling performance and expanded operating ranges, which provides new working fluid options for absorption cycles. Sun et al. [15] analyzed the performance of six R-1234yf/ionic liquid working pairs in both single-effect and compression-assisted absorption refrigeration systems, highlighting their potential as alternative low-GWP working fluids. Jiang et al. [16] experimentally measured the solubility of R-1234ze(E) and R-1233zd(E) in the phosphonium ionic liquid [P₆₆₆₁₄][Cl] and confirmed their suitability as promising working pairs for absorption refrigeration applications. Asensio-Delgado et al. [17] performed a comprehensive thermodynamic analysis of 16 low-GWP HFC and HFO refrigerants combined with low-viscosity ionic liquids in single-effect and compression-assisted absorption cycles, identifying high-performance working pairs that open new avenues for absorption refrigeration technology.

The current research on HFO refrigerants paired with ILs primarily focuses on system-level studies like performance simulations of single-effect absorption refrigeration systems. The existing improvement schemes enhance the coefficient of performance (COP) by adding electrically driven compressors for assistance, but they remain confined to single-effect systems, making it difficult to achieve higher COPs. Notably, double-effect absorption refrigeration systems achieve cascaded utilization of thermal energy through two stages of generators. Furthermore, the introduction of an auxiliary compressor transforms the absorption refrigeration system from purely thermally driven to a hybrid thermo-electrically driven system. These characteristics of such absorption refrigeration technologies demonstrate unique advantages in the optimal operation of IESs, enhancing the dynamic coupling capability of cooling, heating, and electricity multi-energy flows.

Research on optimal operation in IESs still lacks comprehensive modeling of key cooling supply equipment. While the modeling of energy supply equipment within systems has received considerable attention, studies have primarily focused on renewable energy utilization, variable operating conditions of equipment, and multi-energy storage, with little detailed research on absorption chiller units within the system. Currently, the efficiency of absorption chiller units in IESs is often simplified as a constant or considered only in terms of load rate impact, with thermal energy being the sole input form. Introducing compressor assistance in absorption refrigeration systems using HFO/IL pairs not only improves system performance but also transforms the refrigeration system from purely thermally driven to hybrid thermo-electrically driven. The characteristic exhibits unique advantages within IESs, strengthening the dynamic coupling capability of cooling, heating, and electricity. Our previous work [18] identified the optimal cycle configuration (low-pressure-side compression-assisted double-effect absorption refrigeration system, LC-DARS) and its corresponding refrigerant–absorbent pair (R-1233zd(E)/[P₆₆₆₁₄][TMPP]) and compression ratio. To deeply investigate the application of the LC-DARS using the new working pair in the optimal operation of IESs, this paper constructs an IES framework based on the LC-DARS, develops equipment models and a bi-level optimization model, and calculates the unit capacity investment cost of the LC-DARS. Then, taking an industrial park in Luoyang, China, as a case study, the performance improvements brought by the application of the LC-DARS to IES optimal operation are evaluated. Finally, aiming for the lowest annual operating cost, the optimal operation strategies for the industrial park on typical days in summer, transition seasons, and winter are presented.

2. System Framework and Equipment Model

2.1. System Framework

IESs achieve cascading utilization and complementary coordination of energy through the planning and optimization of various processes, including energy production, conversion, transmission, consumption, and storage. Consequently, such systems exhibit diverse configurations. Within the LC-DARS-based IES, energy conversion equipment includes solar photovoltaic panels, electric chillers, gas turbines, organic Rankine cycle units, gas boilers, and absorption chillers. Energy storage is implemented through thermal storage and electrical storage (batteries), with the system interconnected to the electrical grid. Figure 1 illustrates the energy flow diagram of the LC-DARS-based IES.

2.2. Equipment Models

(1) Photovoltaic (PV) Panels

The model for calculating the electrical output power of PV panels is as follows:

$$E_{\mathrm{PV}}=A_{\mathrm{PV}}G{\eta }_{\mathrm{ref}}\left[1-\beta \left(T_{\mathrm{cell}}-T_{\mathrm{ref}}\right)+\delta LogG\right]$$

(1)

E_PV is the electrical output power of the PV panels (kW). A_PV is the area of the PV panels (m²). G is the solar radiation intensity (W·m⁻²). η_ref is the reference module efficiency. β is the temperature coefficient (°C⁻¹). T_ref is the reference temperature (°C). δ is the irradiance coefficient. T_cell is the temperature of the PV panels (°C), which depends on ambient conditions and is calculated as follows:

$$T_{\mathrm{cell}}=T_{\mathrm{a}}+{\displaystyle \frac{G(T_{\mathrm{NOCT}}-20)}{800}}$$

(2)

T_a is the ambient temperature (°C). T_NOCT is the nominal operating cell temperature of the PV panels (°C).

(2) Combined Heat and Power (CHP) Unit

The CHP unit consists of a gas turbine (GT) and an organic Rankine cycle (ORC) unit. The ORC unit recovers waste heat from the GT exhaust flue gas. The relationship between the electrical output power and fuel consumption power of the GT is

$$E_{\mathrm{GT}}=F_{\mathrm{GT}}{\eta }_{\mathrm{GT},\mathrm{E}}$$

(3)

E_GT is the electrical output power of the GT (kW). F_GT is the fuel consumption power of the GT (kW). η_GT,E is the electrical generation efficiency of the GT. The relationship between the thermal output power and electrical output power of the GT is

$$Q_{\mathrm{GT}}={\displaystyle \frac{1-{\eta }_{\mathrm{GT},\mathrm{E}}-{\eta }_{\mathrm{GT},\mathrm{loss}}}{{\eta }_{\mathrm{GT},\mathrm{E}}}}{\eta }_{\mathrm{GT},\mathrm{Q}}{E}_{\mathrm{GT}}$$

(4)

Q_GT is the thermal output power of the GT (kW). η_GT,loss is the heat loss rate of the GT. η_GT,Q is the thermal production efficiency of the GT. The ORC unit is a high-temperature back-pressure-type ORC, offering advantages of low investment cost and the potential for further utilization of condensation heat. Its electrical output power is given by

$$E_{\mathrm{ORC}}=Q_{\mathrm{ORC},\mathrm{in}}{\eta }_{\mathrm{ORC},\mathrm{E}}$$

(5)

E_ORC is the electrical output power of the ORC unit (kW). Q_ORC,in is the thermal energy input to the ORC unit (kW). η_ORC,E is the electrical generation efficiency of the ORC unit.

The thermal output power of the ORC unit is given by

$$Q_{\mathrm{ORC},\mathrm{out}}=Q_{\mathrm{ORC},\mathrm{in}}\left(1-{\eta }_{\mathrm{ORC},\mathrm{E}}\right){\eta }_{\mathrm{ORC},\mathrm{Q}}$$

(6)

Q_ORC,out is the thermal output power of the ORC unit (kW). η_ORC,Q is the thermal production efficiency of the ORC unit.

(3) Gas Boiler (GB)

The thermal output power of the GB is given by

$$Q_{\mathrm{GB}}=F_{\mathrm{GB}}{\eta }_{\mathrm{GB},\mathrm{Q}}$$

(7)

Q_GB is the thermal output power of the GB (kW). F_GB is the fuel consumption power of the GB (kW). η_GB,Q is the thermal production efficiency of the GB.

(4) Electric Chiller (EC)

The cooling output power of the EC is given by

$$C_{\mathrm{EC}}=E_{\mathrm{EC}}{\mathrm{COP}}_{\mathrm{EC}}$$

(8)

C_EC is the cooling output power of the EC (kW). E_EC is the electrical power consumption of the EC (kW). COP_EC is the coefficient of performance of the EC.

(5) Absorption Chiller (AC)

The cooling output power of the AC is related to its thermal and electrical input power as follows:

$$Q_{\mathrm{AC}}=C_{\mathrm{AC}}{\mathrm{TECR}}_{\mathrm{AC}}$$

(9)

$$E_{\mathrm{AC}}=C_{\mathrm{AC}}{\mathrm{EECR}}_{\mathrm{AC}}$$

(10)

C_AC is the cooling output power of the AC (kW). Q_AC is the thermal energy consumption power of the AC (kW). E_AC is the electrical power consumption of the AC (kW). TECR_AC is the thermal energy consumption ratio of the AC system (kWth/kWcool). EECR_AC is the electrical energy consumption ratio of the AC system (kWe/kWcool). It is important to note that the current model assumes constant TECR and EECR values under all operating conditions, which neglects part-load behavior, start-up transients, and performance degradation over time. This simplification may lead to optimistic estimates of cooling output and energy efficiency, particularly during low-load periods or frequent on–off cycles. Incorporating dynamic characteristics of absorption chillers into IES operation optimization remains a nontrivial challenge and will be addressed in our future work using empirical part-load models and degradation curves.

(6) Grid Interaction

The electrical power exchanged with the grid and the corresponding fuel consumption power are related as follows:

$$E_{\mathrm{Grid}}=F_{\mathrm{Grid}}{\eta }_{\mathrm{Grid},\mathrm{p}}{\eta }_{\mathrm{Grid},\mathrm{t}}$$

(11)

E_Grid is the electrical power exchanged with the grid (kW, positive for import, negative for export). F_Grid is the corresponding fuel consumption power (kW). η_Grid,p is the average power generation efficiency of the grid. η_Grid,t is the average power transmission efficiency of the grid.

(7) Thermal Energy Storage (TES) Device

The TES device operates in one of three modes at time t: charging, discharging, or idle (where neither charging nor discharging occurs, considered as zero storage activity). The stored thermal energy in the TES device relates to the charging/discharging power as follows:

$$Q_{\mathrm{TES}}^t=Q_{TES}^{t-1}(1-{\eta }_{\mathrm{TES}})+Q_{\mathrm{TES},\mathrm{ch}}^t{\eta }_{\mathrm{TES},\mathrm{ch}}\Delta t$$

(12)

$$Q_{\mathrm{TES}}^t=Q_{\mathrm{TES}}^{t-1}(1-{\eta }_{\mathrm{TES}})-{\displaystyle \frac{Q_{\mathrm{TES},\mathrm{dis}}^t}{{\eta }_{\mathrm{TES},\mathrm{dis}}}}\Delta t$$

(13)

$Q_{\mathrm{TES}}^t$ is the thermal energy stored in the TES device at time period t (kWh). η_TES is the hourly self-discharge (heat loss) rate (e.g., per hour). $Q_{\mathrm{TES},\mathrm{ch}}^t$ and $Q_{\mathrm{TES},\mathrm{dis}}^t$ are the charging power and discharging power of the TES device during time period t (kW). η_TES,ch and η_TES,dis are the charging efficiency and discharging efficiency of the TES device, respectively. Δt is the duration of the time period (hours).

(8) Electrical Energy Storage (EES) Device

The EES device operates in one of three modes at time t: charging, discharging, or idle (where neither charging nor discharging occurs, considered as zero storage activity). The stored electrical energy in the EES device relates to the charging/discharging power as follows:

$$E_{\mathrm{EES}}^t=E_{\mathrm{EES}}^{t-1}(1-{\eta }_{\mathrm{EES}})+E_{\mathrm{EES},\mathrm{ch}}^t{\eta }_{\mathrm{EES},\mathrm{ch}}\Delta t$$

(14)

$$E_{\mathrm{EES}}^t=E_{\mathrm{EES}}^{t-1}(1-{\eta }_{\mathrm{EES}})-{\displaystyle \frac{E_{\mathrm{EES},\mathrm{dis}}^t}{{\eta }_{\mathrm{EES},\mathrm{dis}}}}\Delta t$$

(15)

$E_{\mathrm{EES}}^t$ is the electrical energy stored in the EES device at time period t (kWh). η_EES is the hourly self-discharge (energy loss) rate (e.g., per hour). $E_{\mathrm{EES},\mathrm{ch}}^t$ and $E_{\mathrm{EES},\mathrm{dis}}^t$ are the charging power and discharging power of the EES device during time period t (kW). η_EES,ch and η_EES,dis are the charging efficiency and discharging efficiency of the EES device, respectively.

3. Bi-Level Optimization Model

3.1. Upper-Level Planning Model

(1) Decision Variables

In the upper-level planning model, the decision variables are the installation area of the PV panels, the capacities of the energy equipment, and the grid interaction power limit, expressed as

$$X=[A_{\mathrm{PV}},N_{\mathrm{GT}},N_{\mathrm{GB}},N_{\mathrm{EC}},N_{\mathrm{AC}},N_{\mathrm{Grid}},N_{\mathrm{TES}},N_{\mathrm{ES}}]$$

(16)

A_PV is the installation area of PV panels (m²). N_GT, N_GB, N_EC, N_AC are the rated capacities of the GT, GB, EC, and AC, respectively (kW). N_TES and N_ES are the rated capacities of the TES and EES devices, respectively (kWh). N_Grid is the upper limit for grid interaction power (kW).

(2) Objective Functions

The economic, energy efficiency, and environmental objective functions in the upper-level planning model are as follows:

$$f_1=f_{\mathrm{Invest}}+f_{\mathrm{Main}}+f_{\mathrm{Gas}}+f_{\mathrm{Grid}}$$

(17)

$$f_{\mathrm{Invest}}+f_{\mathrm{Main}}=\left(1+{\mu }_{\mathrm{Main}}\right){\displaystyle \sum _{m=1}^M\frac{r{(1+r)}^{l_m}}{{(1+r)}^{l_m}-1}}{\kappa }_m{N}_m$$

(18)

$$f_{\mathrm{Gas}}={\displaystyle \sum _{s=1}^k\left(365P_s{\displaystyle \sum _{t=1}^{24}\left[F_{\mathrm{GT}}(t,s)+F_{\mathrm{GB}}(t,s)\right]}{\theta }_{\mathrm{f}}\right)}$$

(19)

$$f_{\mathrm{Grid}}={\displaystyle \sum _{s=1}^k\left(365P_s{\displaystyle \sum _{t=1}^{24}\left[E_{\mathrm{Grid},\mathrm{in}}(t,s){\theta }_{\mathrm{e}}(t,s)-0.5E_{\mathrm{Grid},\mathrm{out}}(t,s){\theta }_{\mathrm{e}}(t,s)\right]}\right)}$$

(20)

$$f_2={\displaystyle \sum _{s=1}^k\left(365P_s{\displaystyle \sum _{t=1}^{24}\left[F_{\mathrm{GT}}(t,s)+F_{\mathrm{GB}}(t,s)+F_{\mathrm{Grid},\mathrm{out}}(t,s)\right]}\right)}$$

(21)

$$f_3={\displaystyle \sum _{s=1}^k\left(365P_s{\displaystyle \sum _{t=1}^{24}\left[\left(F_{\mathrm{GT}}(t,s)+F_{\mathrm{GB}}(t,s)\right){\lambda }_{\mathrm{f}}+E_{\mathrm{Grid},\mathrm{in}}(t,s){\lambda }_{\mathrm{e}}\right]}\right)}$$

(22)

f₁, f₂, and f₃ represent the economic, energy efficiency, and environmental objective functions, respectively. f_Invest is the annualized investment cost of the system ($). f_Main is the annual maintenance cost of the system ($). f_Gas is the annual fuel cost for gas consumption ($). f_Grid is the annual electricity cost for grid interaction ($). μ_Main is the system maintenance cost coefficient. r is the interest rate. l_m is the service life of the m-th piece of equipment (years). κ_m is the investment cost per unit capacity for the m-th piece of equipment ($/kW or $/kWh for storage). N_m is the rated capacity of the m-th piece of equipment (kW or kWh for storage). P_s is the proportion of time that season s represents relative to the whole year. F_GT(t,s) and F_GB(t,s) represent the fuel consumption of the GT and GB during hour t of the typical day in season s, respectively (kWh). E_Grid,in(t,s) and E_Grid,out(t,s) represent the electricity purchased from and sold to the grid during hour t of the typical day in season s, respectively (kWh). F_Grid,in(t,s) is the fuel consumption corresponding to purchased grid electricity (kWh). θ_f and θ_e are the natural gas price and electricity price, respectively ($/kWh). λ_f and λ_e are the equivalent carbon emission factors for natural gas and grid electricity, respectively (kg CO₂/kWh). The constraints involved in the upper-level planning model are listed in

Table 1. The constraints involved in the upper-level planning model.

Variable	Unit	Constraint
APV	m2	[0, Amax]
NGT	kW	[0, 5·Max(ELoad)]
NGB	kW	[0, 5·Max(QLoad)]
NORC	kW	NORC = QGTηORC,E
NEC	kW	[0, 5·Max(CLoad)]
NAC	kW	[0, 5·Max(CLoad)]
NGrid	kW	[0, 5·Max(ELoad)]
NTES	kWh	[0, 5·Max(QLoad)·1 h]
NES	kWh	[0, 5·Max(ELoad)·1 h]

.

3.2. Lower-Level Dispatch Model

(1) Decision Variables

The decision variables in the lower-level dispatch model mainly include the output power of each device, expressed as

$$X=[E_{\mathrm{PV}},E_{\mathrm{GT}},Q_{\mathrm{GB}},C_{\mathrm{EC}},C_{\mathrm{AC}},E_{\mathrm{Grid},\mathrm{in}},E_{\mathrm{Grid},\mathrm{out}},Q_{\mathrm{TES},\mathrm{ch}},Q_{\mathrm{TES},\mathrm{dis}},E_{\mathrm{EES},\mathrm{ch}},E_{\mathrm{EES},\mathrm{dis}}]$$

(23)

(2) Objective Function

The objective function of the lower-level dispatch model is to minimize the system’s annual operating cost, calculated as follows:

$$f_4=f_{\mathrm{Main}}+f_{\mathrm{Gas}}+f_{\mathrm{Grid}}$$

(24)

(3) Constraints

The constraints in the lower-level dispatch model primarily include energy balance constraints. The electrical, thermal, and cooling power balance constraints are as follows:

$$E_{\mathrm{PV}}^t+E_{\mathrm{GT}}^t+E_{\mathrm{ORC}}^t+E_{\mathrm{Grid},\mathrm{in}}^t+E_{\mathrm{EES},\mathrm{dis}}^t=E_{\mathrm{Load}}^t+E_{\mathrm{EC}}^t+E_{\mathrm{AC}}^t+E_{\mathrm{Grid},\mathrm{out}}^t+E_{\mathrm{EES},\mathrm{ch}}^t$$

(25)

$$Q_{\mathrm{GT}}^t+Q_{\mathrm{GB}}^t+Q_{\mathrm{ORC},\mathrm{out}}^t+Q_{\mathrm{TES},\mathrm{dis}}^t=Q_{\mathrm{Load}}^t+Q_{\mathrm{AC}}^t+Q_{\mathrm{TES},\mathrm{ch}}^t+Q_{\mathrm{ORC},\mathrm{in}}^t$$

(26)

$$C_{\mathrm{AC}}^t+C_{\mathrm{EC}}^t=C_{\mathrm{Load}}^t$$

(27)

$E_{\mathrm{Load}}^t$, $Q_{\mathrm{Load}}^t$, and $C_{\mathrm{Load}}^t$ are the electrical, thermal, and cooling loads during hour t of the typical day in season s, respectively (kW). Furthermore, the output power of each component must be constrained by the rated capacities determined in the upper-level planning model and the grid interaction power limit. Additional constraints are required for TES and EES devices: TES has charging/discharging rate limits and state-of-charge (SOC) range limits; EES has charging/discharging rate limits and SOC range limits. The output power constraints for each component are as follows:

$$\mathrm{TES}\left\{\begin{array}{l}0\le Q_{\mathrm{TES},\mathrm{dis}}^t\le 0.4N_{\mathrm{TES}}\hfill \\ 0\le Q_{\mathrm{TES},\mathrm{ch}}^t\le 0.4N_{\mathrm{TES}}\hfill \\ 0.1N_{\mathrm{TES}}\le Q_{\mathrm{TES}}^t\le 0.9N_{\mathrm{TES}}\hfill \end{array}\right.\mathrm{EES}\left\{\begin{array}{l}0\le E_{\mathrm{ES},\mathrm{dis}}^t\le 0.4N_{\mathrm{ES}}\hfill \\ 0\le E_{\mathrm{ES},\mathrm{ch}}^t\le 0.4N_{\mathrm{ES}}\hfill \\ 0.1N_{\mathrm{ES}}\le E_{\mathrm{ES}}^t\le 0.9N_{\mathrm{ES}}\hfill \end{array}\right.$$

(28)

$$\left\{\begin{array}{l}0\le E_{\mathrm{GT}}^t\le N_{\mathrm{GT}}\\ 0\le Q_{\mathrm{GB}}^t\le N_{\mathrm{GB}}\\ 0\le E_{\mathrm{ORC}}^t\le N_{\mathrm{ORC}}\\ 0\le C_{\mathrm{EC}}^t\le N_{\mathrm{EC}}\\ 0\le C_{\mathrm{AC}}^t\le N_{\mathrm{AC}}\\ 0\le E_{\mathrm{Grid},\mathrm{in}}^t\le N_{\mathrm{Grid}}\\ 0\le E_{\mathrm{Grid},\mathrm{out}}^t\le N_{\mathrm{Grid}}\end{array}\right.$$

(29)

In the current model, the grid is assumed to be an unlimited source/sink with constant efficiency and emission factors. Practical constraints such as export caps, time-of-use demand charges, and time-varying carbon intensity are not considered. These simplifications may lead to an overestimation of grid flexibility and underestimation of operational carbon footprints.

3.3. Bi-Level Optimization Procedure

(1) Upper-level Planning Method

The planning and configuration process of the LC-DARS-based IES involves algorithm selection and decision-making method application. The upper-level planning model has three objective functions evaluating economic, energy efficiency, and environmental performance indicators. This planning problem involving three conflicting and mutually constraining objectives belongs to multi-objective optimization. Given the nonlinear and non-convex nature of the integrated energy system planning model, intelligent optimization algorithms are commonly employed, such as Multi-Objective Particle Swarm Optimization (MOPSO), Genetic Algorithms (GAs), and Simulated Annealing (SA). MOPSO’s inertia weight and velocity update mechanisms enable it to effectively escape local optima during the solving process, discovering higher-quality Pareto front solutions compared to GA. Therefore, this study employs the MOPSO algorithm based on the aforementioned optimization model to obtain a set of Pareto front solutions, all of which are optimal solutions to this planning problem.

However, among the set of Pareto solutions, no single solution simultaneously achieves the best values for all three objectives (economic, energy efficiency, and environmental). An optimal compromise solution must be selected. Consequently, this study applies the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) to process the Pareto front solutions (including normalization, standardization, weight assignment, defining ideal/anti-ideal solutions, calculating distances to these solutions, and ranking based on relative closeness). This process yields the system’s optimal compromise solution.

(2) Lower-Level Dispatch Method

The lower-level dispatch optimization of the integrated energy system is essentially a Mixed-Integer Linear Programming (MILP) problem. Common optimization software for solving such problems includes LINGO, CPLEX, Gurobi, and GAMS. CPLEX and GAMS can solve complex problems, guaranteeing the accuracy of finding optimal or feasible solutions. Moreover, the CPLEX solver provides interfaces for various programming languages, such as Python, MATLAB, and Java. CPLEX demonstrates advantages in reliability, speed, and flexibility for energy dispatch optimization. Therefore, this study employs the CPLEX solver for lower-level energy dispatch optimization.

(3) Optimization Procedure

An interaction exists between the upper-level planning model and the lower-level dispatch model. The planning solutions obtained from the upper level serve as input parameters for the lower-level dispatch optimization. The dispatch solutions obtained from the lower level are used to calculate the fitness values for the upper-level planning model. The specific optimization procedure and decision-making method are illustrated in Figure 2. Stopping criterion for MOPSO: The algorithm stops when the Pareto front stabilizes (i.e., no significant improvement in hypervolume or spread over 50 consecutive generations) or when the maximum number of iterations (200) is reached. Convergence check: The algorithm uses an archive of non-dominated solutions and updates it each iteration; convergence is monitored via changes in archive size and diversity. Fitness calculation: The fitness for each particle in MOPSO is evaluated by running the lower-level CPLEX dispatch model for the given planning configuration; the resulting annual operating cost, energy consumption, and emissions are used to compute the three objective functions (f₁, f₂, f₃). Interaction between levels: The planning solution from MOPSO is passed to CPLEX for dispatch optimization, and the dispatch results are fed back to evaluate the objectives in MOPSO. To ensure the feasibility of the bi-level optimization, the operational optimization results from the literature [19] were verified. By importing the basic data from the reference, the final output values for the three performance parameters and their relative errors are shown in

Table 2. Feasibility verification results of bi-level optimization.

Parameter	This Work	Literature [19]	MRE
f1	264,144 $	263,230 $	0.35%
f2	4,065,120 kWh	4,164,315 kWh	−2.38%
f3	89,4691 kg	917,240.6368 kg	−2.46%

. The maximum relative error was only −2.46%, validating the reliability of the proposed bi-level optimization model.

3.4. Cost Calculation for LC-DARS

Assessing the application of the LC-DARS using the R-1233zd(E)/[P₆₆₆₁₄][TMPP] pair within the IES requires inputting the techno-economic parameters of the equipment. Its technical parameters (EECR and TECR) were obtained from our previous paper [18]. Due to the lack of suitable reference values for its economic parameters arising from differences in the working fluid pair and system architecture, this study calculates the unit capacity investment cost for the absorption chiller unit. Drawing on methods from the literature for calculating the investment costs of double-effect absorption chiller units [20] and vapor compression refrigeration units [21], key components are treated as follows: (1) The high-pressure generator, low-pressure generator, generator, absorber, evaporator, and condenser are all considered heat exchangers. Their cost is a function of their heat transfer area. (2) The solution pump cost is a function of its power consumption. (3) The compressor cost is a function of its power consumption. (4) The expansion valve cost is a function of its mass flow rate. The calculation formulas are as follows:

$${\kappa }_{\mathrm{he}}={\kappa }_{\mathrm{r}\mathrm{e}\mathrm{f}}{\left({\displaystyle \frac{A_{\mathrm{he}}}{A_{\mathrm{ref}}}}\right)}^{0.6}$$

(30)

$${\kappa }_{\mathrm{p}}={\kappa }_{\mathrm{r}\mathrm{e}\mathrm{f}}{\left({\displaystyle \frac{W_{\mathrm{p}}}{W_{\mathrm{ref},\mathrm{p}}}}\right)}^{0.26}{\left({\displaystyle \frac{1-{\eta }_{\mathrm{p}}}{{\eta }_{\mathrm{p}}}}\right)}^{0.5}$$

(31)

$${\kappa }_{\mathrm{com}}={\kappa }_{\mathrm{r}\mathrm{e}\mathrm{f}}{\displaystyle \frac{W_{\mathrm{com}}}{W_{\mathrm{ref},\mathrm{com}}}}{\left({\displaystyle \frac{{\eta }_{\mathrm{c}}}{0.9-{\eta }_{\mathrm{c}}}}\right)}^{0.5}$$

(32)

$${\kappa }_{\mathrm{ev}}={\kappa }_{\mathrm{ref}}{\displaystyle \frac{{\dot{m}}_{\mathrm{ev}}}{{\dot{m}}_{\mathrm{ref}}}}$$

(33)

κ_he, κ_p, κ_com, κ_ev, κ_ref represent the costs of the heat exchanger, solution pump, compressor, expansion valve, and a reference component cost, respectively ($). A_he, A_ref represent the heat exchanger area and a reference area, respectively (m²). W_p, W_com, W_ref,p, W_ref,com represent the power consumption of the solution pump and compressor, and their respective reference power consumption values (kW). η_p, η_com represent the efficiencies of the solution pump and compressor, respectively. ṁ_ev, ṁ_ref represent the mass flow rate through the expansion valve and a reference mass flow rate, respectively (kg·s⁻¹). The parameters for the reference components used in the cost calculation process are presented in

Table 3. Investment costs and parameters of reference components.

Component	κref/$	Parameter
Compressor	12,000	Wref,com = 100 kW
Absorber	16,500	Aref = 100 m2
Solution pump	2100	Wref,p = 10 kW
Heat exchanger	12,000	Aref = 100 m2
Generator	17,500	Aref = 100 m2
Condenser	8000	Aref = 100 m2
Expansion valve	11,450	${\dot{m}}_{\mathrm{ev}}$ = 10 kg·s−1
Evaporator	16,000	Aref = 100 m2

.

This study calculated the unit capacity investment cost of the absorption chiller unit by considering the initial equipment investment cost, material cost, and installation cost. The final results are shown in

Table 4. Economic calculation results for LC-DARS.

Equipment Cost/$·kW−1	Material Cost/$·kW−1	Installation Cost/$·kW−1	Total Cost/$·kW−1
212.38	11.37	31.86	255.61

. Compared to the typical unit capacity investment cost for absorption chillers in integrated energy systems [19], the cost of the LC-DARS represents a 13.6% increase. Lifecycle perspective: Although the unit investment cost of the LC-DARS is 13.6% higher, its lower operating cost and higher efficiency lead to a payback period of approximately 4.2 years under current energy prices based on the annual operating cost savings between IES-1 and IES-2. Environmental benefit: The 59.8% reduction in CO₂ emissions compared to SSS and 2.3% improvement over IES-2 justifies the additional investment from a sustainability standpoint. Technological maturity: As a novel system using an HFO/IL working pair, LC-DARS is not yet mass-produced. The cost estimate reflects prototype-level economics. With further development and commercialization, the cost is expected to decrease.

4. Case Study

4.1. Cost Calculation for LC-DARS

This section takes an industrial park in Luoyang China as an example, utilizing the constructed model to study the optimal planning configuration and dispatch strategy for the park’s integrated energy system. The available area for solar energy utilization in this industrial park is 3000 m². Data for the cooling, heating, and electricity (C/H/E) loads of typical winter, summer, and transition season days, as well as solar radiation intensity, were obtained from the publicly available literature [22].

Table 5. Natural gas and electricity prices and equivalent carbon emission factors.

Energy Type	Price/$·kWh−1			Equivalent Carbon Emission Factor/kg·kWh−1
	8:00–11:00 18:00–23:00	7:00–8:00 11:00–18:00	0:00–7:00 23:00–24:00
Electricity	0.185	0.129	0.085	0.968
Natural gas	0.038	0.038	0.038	0.220

presents the natural gas and electricity prices, along with their equivalent carbon emission factors [19,23].

Table 6. Techno-economic parameters of the integrated energy system.

Equipment	Parameter	κm	lm	Source
PV	ηref = 0.125 Tref = 25 °C TNOCT = 45 °C δ = 0.12 β = 0.0045 °C−1	2130 $·kW−1	15 a	[19,25]
GT	ηGT,E = 0.4 ηGB,Q = 0.8 ηGT,loss = 0.05	1046 $·kW−1	20 a	[19]
GB	ηGB,Q = 0.8	25 $·kW−1	20 a	[19]
ORC	ηORC,E = 0.103 ηORC,Q = 0.718	4382 $·kW−1	20 a	[26]
EC	COPEC = 3	350 $·kW−1	20 a	[19]
AC	TECR = 0.967 EECR = 0.094	256 $·kW−1	20 a	This work
Grid	ηGrid,p = 0.35 ηGrid,t = 0.92	-	-	[19]
TES	ηTES = 0.04 ηTES,ch = 0.8 ηTES,dis = 0.8	56 $·kWh−1	20 a	[19]
EES	ηES = 0.05 ηES,ch = 0.95 ηES,dis = 0.95	145 $·kWh−1	10 a	[27]

shows the techno-economic parameters of the integrated energy system. The system maintenance cost coefficient is set to 0.02 [24], the interest rate is set to 6% [19], the number of iterations for the MOPSO algorithm is set to 200, and the particle swarm size is set to 100.

4.2. Planning Results and Analysis

The Pareto solution set for the optimal operation of the LC-DARS-based IES was obtained through bi-level optimization. The TOPSIS method was then applied to select the optimal compromise solution. The Pareto solution set and the planning configuration corresponding to the optimal compromise solution are presented in Figure 3 and

Table 7. Planning configuration of the optimal solution from bi-level optimization.

APV	NGT	NGB	NEC	NAC	NGrid	NTES	NES
1940 m2	910 kW	670 kW	300 kW	540 kW	1 kW	1260 kWh	330 kWh

, respectively.

The near-zero grid interaction limit (1 kW) in the optimal compromise solution reflects the multi-objective trade-off among economic, energy efficiency, and environmental objectives. Our analysis reveals the following:

Energy autonomy: The LC-DARS-based IES is designed to maximize self-sufficiency. With sufficient PV capacity, CHP generation, and storage devices (EES and TES), the system can meet most of its load without relying on the grid.

Carbon emission reduction: Purchasing grid electricity incurs a high equivalent carbon emission factor (0.968 kg CO₂/kWh), which penalizes the environmental objective. Minimizing grid import thus significantly improves f₃.

Economic trade-off: Although a higher grid interaction limit could reduce investment costs (by downsizing equipment), it increases operational costs and emissions. The TOPSIS-based compromise balances these factors, favoring a low-grid solution.

As can be seen from the figure, the economic objective function exhibits a negative correlation with the energy efficiency and environmental objective functions. This indicates a trade-off relationship between the system’s annual energy consumption, annual carbon emissions, and total annual cost. Since no single solution possesses an absolute advantage across all three aspects (economic, energy efficiency, and environmental), selecting an optimal compromise solution is necessary.

An analysis of the planning configuration corresponding to the optimal compromise solution reveals that: (1) The LC-DARS-based IES has a very low upper limit for grid interaction power, indicating that the energy system is largely independent of the grid and relies on self-sufficient operation. (2) The rated capacity of the GT accounts for approximately 80% of the peak load. The remaining load must be supplemented by electricity discharged from the EES, PV generation, and ORC generation. (3) The GB is primarily used to supplement the heating load during winter. (4) The AC unit utilizes waste heat to meet cooling demand and has a larger rated capacity than the EC unit.

Next, the performance improvement of the IESs relative to the conventional separate supply system (SSS) is analyzed. A comparison is made between Integrated Energy System 1 (IES-1), which uses the LC-DARS absorption chiller, and Integrated Energy System 2 (IES-2), which uses a conventional heat-driven absorption chiller unit. Figure 4 illustrates the schematic diagram of the traditional SSS.

Table 8. Performance improvement of IESs relative to the SSS.

Parameter	SSS	IES-2	Improvement	IES-1	Improvement
f1	1,405,284 $	948,305 $	32.52%	989,967 $	29.6%
f2	32,352,857 kWh	17,637,795 kWh	45.48%	17,139,310 kWh	47.0%
f3	9,389,142 kg	3,880,585 kg	58.67%	3,770,648 kg	59.8%

demonstrates that IES-1 and IES-2 exhibit significant improvements over the SSS in terms of economic, energy efficiency, and environmental performance. This highlights how IESs, through multi-energy coupling and complementary coordination, reduce the annualized total cost, annual primary energy consumption, and annual CO₂ emissions. Furthermore, IES-1 (LC-DARS) shows greater advantages in energy efficiency and environmental performance compared to IES-2 but is relatively weaker in economic performance.

Lower required AC capacity in IES-1: Because LC-DARS has a higher COP (due to compressor assistance), the same cooling load can be met with a smaller installed capacity (540 kW in IES-1 vs. 620 kW in IES-2 under the same optimal compromise selection).

Different EC/AC capacity split: In IES-1, the AC takes a larger share of the cooling load during surplus heat periods, reducing the need for EC capacity (300 kW vs. 350 kW in IES-2).

Tighter grid integration limit: IES-1 achieves higher self-sufficiency, leading to an even lower N_Grid (1 kW vs. 15 kW in IES-2).

Shift in operation strategy: The hybrid thermo-electric nature of the LC-DARS introduces new flexibility in dispatch, which is reflected in the optimal scheduling (e.g., AC output is adjusted according to both heat availability and electricity price).

The integration of the LC-DARS enables a more compact and self-sufficient system configuration. The higher efficiency of the LC-DARS reduces the required absorption chiller capacity, while its hybrid input characteristic allows greater operational flexibility, contributing to the near-zero grid dependency

4.3. Optimization Operation Results and Analysis

Aiming to minimize the system’s annual operating cost, the energy dispatch for the industrial park was optimized across three typical days: summer, transition season, and winter. Figure 5, Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12 and Figure 13 illustrate the optimal dispatch results for the cooling, heating, and electricity (C/H/E) loads on these three typical days.

(1) Transition Season Day

The energy demand profile on a typical transition season day can be divided into daytime (6:00–20:00) and nighttime (20:00–24:00 and 0:00–6:00). Compared to nighttime, the daytime period exhibits higher electricity and cooling load demands but lower heating load demand.

Daytime: The CHP unit generates surplus heat, accounting for 24.3% of its total heat output. This surplus heat is utilized as follows: 16.4% drives the AC, and 7.9% is stored in the TES device.

Nighttime: The CHP unit generates no surplus heat. During the period 21:00–03:00, it is insufficient to meet the heating load demand alone, requiring the TES device to discharge stored heat to cover the remaining demand.

Cooling Load: The daytime cooling demand is also high. The AC meets 45.4% of this demand, while the EC supplies the remaining 54.6%. At night, with no available heat for the AC, the EC entirely fulfills the cooling demand.

PV and GT: PV output occurs between 8:00 and 16:00. During this period, the GT generation power is correspondingly reduced to prioritize PV utilization.

EES: The EES device charges during periods of low electricity demand and discharges during peak demand periods, effectively smoothing the electricity load profile of the industrial park.

Figure 5. Optimal cooling load dispatch on a typical transition season day.

Figure 5. Optimal cooling load dispatch on a typical transition season day.

Figure 6. Optimal heating load dispatch on a typical transition season day.

Figure 6. Optimal heating load dispatch on a typical transition season day.

Figure 7. Optimal electricity load dispatch on a typical transition season day.

Figure 7. Optimal electricity load dispatch on a typical transition season day.

(2) Summer Day

The trends of the C/H/E loads on a typical summer day are similar to those in the transition season, but the magnitudes differ: the cooling and electricity load demands are relatively higher, while the heating load demand is lower.

Surplus Heat: Due to the lower heating demand, the CHP unit generates significant surplus heat (34.0% of total heat output) after meeting the heating load. This excess heat is fully utilized, supplying either the AC system or the TES device for storage.

Supplemental Heating: However, between 15:00 and 20:00, supplemental heat from either the GB or the discharging TES is required because the AC consumes a high amount of heat during this period.

Cooling Load: The AC provides cooling throughout the day. The remaining cooling demand is met by the EC. During daytime hours when heat is abundant, the AC dominates, supplying 63.1% of the cooling demand. At night, as surplus heat decreases, the AC output reduces and the EC output increases, supplying 65.0% of the nighttime cooling demand (AC: 35%).

PV and GT and EES: As PV output increases during the day, GT generation is correspondingly reduced to prioritize renewable energy utilization. The EES device charges when the electricity supply is sufficient and discharges later to supplement electricity demand.

Figure 8. Optimal cooling load dispatch on a typical summer day.

Figure 8. Optimal cooling load dispatch on a typical summer day.

Figure 9. Optimal heating load dispatch on a typical summer day.

Figure 9. Optimal heating load dispatch on a typical summer day.

Figure 10. Optimal electricity load dispatch on a typical summer day.

Figure 10. Optimal electricity load dispatch on a typical summer day.

(3) Winter Day

Compared to summer and transition season days, the heating load demand on a typical winter day surges dramatically, while the cooling and electricity load demands are relatively low. Consequently, the energy dispatch strategy differs significantly.

Heating Load: During periods of lower heating demand, the CHP unit can generally meet the park’s requirements. However, during peak heating periods, the CHP output is insufficient, requiring the GB to supplement the remaining demand. The CHP unit supplies 64.3% of the total heating load, while the GB supplies 35.7%. Crucially, no surplus heat is generated during energy dispatch. As a result, the TES device is not utilized and does not participate in the dispatch.

Cooling Load: Due to the surge in heating demand, there is no excess heat available for the AC. Furthermore, utilizing the AC would increase the park’s heating load requirement. Therefore, the AC is not deployed and does not participate in the dispatch. The entire cooling demand is met by the EC.

Electricity Load and Supply: The CHP unit, acting as the primary power supply, essentially meets the park’s electricity load demand and the power consumption of the EC. During PV generation hours (8:00–16:00), PV power is prioritized, supplying 11.0% of the electricity load demand.

Grid Interaction: Interaction with the grid is virtually non-existent, demonstrating the high degree of self-sufficiency and reliability of the LC-DARS-based IES.

Figure 11. Optimal cooling load dispatch on a typical winter day.

Figure 11. Optimal cooling load dispatch on a typical winter day.

Figure 12. Optimal heating load dispatch on a typical winter day.

Figure 12. Optimal heating load dispatch on a typical winter day.

Figure 13. Optimal electricity load dispatch on a typical winter day.

Figure 13. Optimal electricity load dispatch on a typical winter day.

5. Conclusions

This study focused on the application of an IES based on the LC-DARS using R-1233zd(E)/[P₆₆₆₁₄][TMPP]. It constructed the system framework, equipment models, and a bi-level optimization model, calculated the unit capacity investment cost for the LC-DARS, and conducted a case study using an industrial park in Luoyang, China. The key findings are summarized as follows:

• System Framework and Equipment Models: The framework of the LC-DARS-based IES was constructed, and the physical models for each key component were established. These models include: PV panels, CHP unit, AC (LC-DARS), GB, EC, grid interaction, TES, and EES devices.
• Bi-Level Optimization Model and Process: A bi-level optimization model was developed, and the optimization procedure was described. The feasibility of the optimization methodology was validated. The decision variables, objective functions, and constraints for both levels of the optimization model were introduced. An interaction exists between the levels: the upper-level model performs capacity planning optimization, while the lower-level model performs dispatch optimization. The planning solution obtained from the upper level serves as input parameters for the lower-level optimization, and the dispatch solution from the lower level is used to calculate the fitness value for the upper-level planning model. Finally, the TOPSIS was applied to the Pareto front solutions to determine the system’s optimal planning solution.
• Cost Calculation for the LC-DARS: The unit capacity investment cost for the LC-DARS was calculated. The cost is 255.61 $/kW, representing a 13.6% increase compared to typical absorption chillers used in IESs.
• Performance Comparison: Using an industrial park in Luoyang, China, as a case study, the performance improvements of the LC-DARS-based IES-1 and an IES using a conventional heat-driven AC (IES-2) were analyzed relative to a conventional SSS. The results demonstrate that integrated energy systems significantly enhance economic, energy efficiency, and environmental performance, achieving improvements of 29.6%, 47.0%, and 59.8%, respectively.
• Optimal Configuration and Dispatch Strategy: The optimal capacity configuration and dispatch strategies for three typical days (summer, transition season, and winter) in the industrial park were determined. Within the optimal configuration, the very low upper limit for grid interaction power indicates that the energy system operates largely independently of the grid, relying on self-sufficient operation. For summer and transition season typical days, the dispatch strategy can be broadly categorized into two modes: daytime and nighttime. During the daytime, the AC supplies a larger proportion of the cooling load, while the EC dominates cooling supply at night. For a winter typical day, due to the surge in heating demand, the distinct daytime/nighttime pattern disappears. The dispatch strategy utilizes the EC to meet the cooling load and the gas boiler to supplement the heating load demand.