Solar-assisted tri-generation system with LCPV‑CPC and small-scale gas turbine for year-round clean energy in hot-dry climates

Abstract

This study develops, dynamically simulates, and optimizes an integrated tri‑generation system for year-round electricity, heating, and cooling supply under the hot-dry climatic conditions of Baghdad, Iraq. The proposed configuration couples a low‑concentration hybrid PV–compound parabolic concentrator (LCPV-CPC) with dual small‑scale gas turbines, high- and low-grade water-source heat pumps, and an ammonia-water absorption chiller, coordinated through a following-electric-load (FEL) strategy. The primary objectives are to maximize primary energy savings, annual cost reduction, CO₂ emissions mitigation, and exergy efficiency by exploiting multi‑grade thermal integration and dispatch optimization. A methodological novelty lies in applying a Reference Vector Guided Evolutionary Algorithm (RVEA) with entropy‑weighted VIKOR analysis to achieve balanced trade‑offs among energy, economic, environmental, and thermodynamic criteria. Dynamic co‑simulation through Aspen HYSYS-MATLAB, validated against high‑quality experimental data, ensures predictive reliability. Results confirm substantial performance gains compared with a separate production facility: primary energy savings up to ~ 33%, annual cost savings exceeding 10% at favorable solar conditions, and CO₂ emission reduction approaching 50%. Parametric analysis shows that increased solar irradiance significantly improves environmental and economic outcomes, with economic feasibility achieved beyond ~ 472 W/m² average radiation. Exergy efficiency remains stable or slightly declines at high irradiance due to intensified off‑design irreversibilities. Optimal inlet water temperatures to the LCPV-CPC further enhance renewable contribution without notable thermodynamic penalties. The findings demonstrate a technically and economically viable pathway for sustainable tri‑generation in climates with strong solar resources and high cooling demand, offering a transferable optimization framework for future hybrid renewable–fossil energy applications in urban buildings.

Introduction

The transition toward renewable and clean energy systems is imperative for mitigating greenhouse gas emissions, enhancing energy security, and ensuring long-term environmental sustainability^1,2. Advancing these technologies supports decarbonization pathways, accelerates climate resilience, and drives the integration of low‑carbon solutions within global energy infrastructures^3,4. Among various renewable energy resources, solar energy holds exceptional importance and popularity due to its global abundance, scalability, and suitability for both centralized and decentralized power generation^5,6. Its versatility, low operational costs, and rapid technological advancements make it a cornerstone of sustainable energy transition strategies worldwide^7,8. Despite its advantages, solar energy is inherently constrained by intermittency and seasonal variability, which can limit its reliability as a standalone supply source⁹. Integrating solar systems with natural gas—the cleanest fossil fuel in terms of specific CO₂ emissions—offers a synergistic solution that enhances overall energy security, operational flexibility, and dispatchability^10,11. Such hybrid configurations maximize renewable penetration while ensuring stable output, improved load‑matching, and reduced lifecycle greenhouse gas emissions¹². They can be effectively deployed in multi‑output energy infrastructures, such as tri‑generation facilities, to simultaneously produce electricity, heating, and cooling with enhanced efficiency and reduced environmental impact¹³.

Among various solar energy technologies, photovoltaic/thermal (PVT) systems are of particular importance due to their simultaneous generation of electricity and useful thermal energy, enabling higher overall conversion efficiency, improved land‑use performance, and the capability to provide heating for residential, industrial, or district energy applications¹⁴. These systems can be integrated with natural gas‑based technologies—such as small‑scale gas turbine generators or NG‑heat generators—to create a stable, dispatchable hybrid energy supply. From a technical perspective, this coupling allows excess thermal output from the PVT unit to preheat feedwater, process fluids, or space‑heating circuits in the gas‑based system, thereby reducing the fuel input required for the same energy output and increasing the combined system’s overall efficiency¹⁵. Additional benefits include enhanced load‑matching flexibility, reduced greenhouse gas emissions per unit of energy, and greater operational resilience under variable solar irradiance conditions.

In integrated PVT–natural gas configurations, small‑scale gas turbine generators offer high power‑to‑heat ratios, rapid start‑up capabilities, and the ability to utilize preheated working fluids from the solar subsystem, thereby enhancing overall electrical efficiency¹⁶. NG‑heat generators provide precise thermal load control, high reliability, and seamless operation during periods of low solar irradiance, ensuring continuous heating supply with reduced specific fuel consumption¹⁷. Among photovoltaic/thermal technologies, the LCPV-CPC thermal system is particularly significant due to its enhanced optical concentration ratio, higher overall conversion efficiency, and effective utilization of both direct and diffuse solar radiation¹⁸. When integrated with small‑scale gas turbine generators, the system’s thermal output can be employed to preheat the turbine’s working fluid, thereby reducing the fuel requirement and increasing electrical efficiency. This hybridization not only improves part‑load performance and operational flexibility but also reduces specific greenhouse gas emissions, leading to a more sustainable and resilient energy supply. In complex hybrid systems, control precision and dynamic adaptability are crucial. As noted by Kong et al.¹⁹, modulation-assisted diagnostics improve system stability under nonstationary conditions. Similarly, recent advances in PWM schemes (Zeng & Goetz²⁰ enable better control of power electronics in multi-source systems.

In integrated solar and small‑scale gas turbine generator systems, applying the FEL (following electric load) or the FTL (following thermal load) operational strategies directly influences energy dispatch balance, fuel utilization, and overall efficiency. While FTL prioritizes meeting thermal demand, FEL can offer superior performance in scenarios with variable solar input by optimizing turbine operation for electrical efficiency, enhancing grid stability, and reducing excess electricity curtailment, thereby improving both economic returns and renewable penetration. For these reasons, we intend to implement the FEL strategy in an integrated tri‑generation system, aiming to maximize electrical efficiency, enhance operational flexibility, and leverage solar–gas synergies for simultaneous electricity, heating, and cooling production.

The primary objective of optimization in such integrated tri‑generation systems is to maximize overall energy efficiency, minimize fuel consumption, and reduce lifecycle environmental impacts while ensuring stable multi‑output energy delivery. Recent advancements have focused on multi‑objective optimization frameworks that simultaneously address thermodynamic performance, economic viability, and emissions reduction through advanced algorithms and hybrid metaheuristics. Furthermore, the integration of high‑fidelity modeling with real‑time operational data has enabled adaptive control strategies, significantly improving both system responsiveness and part‑load performance. Multiple studies have employed evolutionary optimization algorithms, along with multi‑criteria decision‑making methods, to improve economic, environmental, energy, and exergy indicators in integrated and tri/multi-generation systems, achieving outcomes such as reduced annual costs, lower CO₂ emissions, and enhanced thermal and electrical efficiencies. Additionally, some research has utilized stochastic simulations and bi‑level modeling to assess the impact of load and solar irradiance uncertainty as well as decision variables on system performance, providing solutions to improve efficiency, seasonal performance, and internal rate of return.

Chen et al.²¹ presented a tri-generation system that harnesses solar and wind energy, incorporating solar PVs, wind turbines, and a solar cooling/heating subsystem to achieve net-zero carbon emissions through renewable energy sources and carbon trading strategies. An enhanced multi-objective algorithm was employed to optimize the configurations of the energy system across various scenarios. Sensitivity analysis revealed that an increase in power grid coverage and microgrid penetration rates leads to a reduction in total costs, whereas elevated building demands negatively impact economic performance. Zoghi et al.²² advanced the theoretical efficiency of a 500 kW gas turbine cycle based on a combustion chamber by substituting the natural gas combustion chamber with a solar power tower, thereby transforming it into a multi-generation system. The total cost rate and unit cost for the solar-based configuration were recorded at 142.1 $/h and 15.14 $/GJ, respectively, compared to 145.5 $/h and 31.58 $/GJ for the combustion chamber-based configuration. Mei et al.²³ introduced an innovative poly-generation system that utilizes solar, biogas, and geothermal heat sources. They conducted exergy-economic-environmental analyses through parametric studies and optimization techniques. The solar power tower exhibited the highest rates of exergy destruction and cost. The optimization yielded an exergy efficiency of 18.36% and a unit cost of 32.2 $/GJ.

Hassani et al.²⁴ established a 7.2 MWe gas power facility that incorporates solar preheating. The optimization techniques NSGA-III and MOGOA were employed for the adjustment of critical parameters. The Fuzzy AHP-TOPSIS method facilitates the selection of the optimal design. The outcome indicates a 13.8% reduction in gas consumption and a decrease in emissions. This study presents a low-carbon solution for the energy transition in the MENA region. Zhou et al.²⁵ enhanced a solar cooling-power system utilizing AI and the Grey Wolf algorithm. The transient performance of the proposed system was assessed under optimal conditions. A modification involving five turbines was suggested to address the issue of sunlight intermittence. At a constant power output of 100 kW, an optimized cooling capacity of 161 kW and a life cycle cost of 2.91 m$ were achieved. The transient performance results validated the reliability of the five-turbine modification.

As hybrid energy systems evolve, incorporating hydrogen as a flexible carrier can enhance resilience. Recent studies such as Song et al.²⁶ offer valuable frameworks for integrating hydrogen energy in uncertain renewable conditions. Moreover, system reliability under external stressors, as analyzed by Wu et al.²⁷, is critical to long-term performance. A comprehensive literature review was conducted to identify and compare relevant works on solar-assisted hybrid, tri‑generation, and polygeneration systems. Table 1 summarises the main objectives, system configurations, solar technologies employed, and applied optimization algorithms with their respective objectives for the reviewed studies. This structured comparison facilitates identifying research gaps, assessing technological evolution, and positioning the present work within the existing body of knowledge.

Table 1.

Technical summary of reviewed solar-based hybrid and polygeneration systems.

Ref.	Main Objectives & Significance with System Description	Solar System Type	Optimization Algorithm & Objective	Key Results
28	To comprehensively assess and multi-criteria optimize a novel solar-geothermal-based polygeneration system integrating CPVT, flat plate collectors, geothermal wells, ORC, ERC, SOEC, and multiple output units. The study emphasizes multi-source thermal recovery and advanced exergy, exergoeconomic, and energetic investigation in polygeneration.	Concentrated-PVT and Flat Plate Solar Collectors	Multi-objective optimization employing NSGA-II, fuzzy TOPSIS, and fuzzy VIKOR, targeting minimization of unit product cost and maximization of exergy efficiency.	VIKOR selection: 4.06% exergy efficiency/1.07 $/GJ unit cost; TOPSIS: 4.29%/1.13 $/GJ; system performance highly sensitive to geothermal punch temperature gradient; renewable integration maximizes energy utilization.
29	To analyze and optimize an integrated polygeneration arrangement for electricity, cooling, potable water, hydrogen, and sodium hypochlorite, focusing on detailed energy, exergy, economic, environmental, and risk-based assessments (4E, 5E, safety). The system couples SOFC, gas turbines, ORC, hydrogen and desalination subsystems.	Hybrid: Photovoltaic/thermal and solar-driven hydrogen generation (details from reference list suggest integration of PV/PEC)	Multiple references apply multi-objective evolutionary optimization (e.g., NSGA-II) and risk-based methods, but the primary paper focuses on multi-criteria assessment rather than explicit optimization within the core text.	Achieved energy and exergy efficiencies up to 65%; integrated system demonstrates superior polygeneration capability; risk-based optimization improves operational safety and reliability; notable reduction in environmental impact and total costs.
30	To propose a novel ORC-VCR-CCHP solar system with integrated ternary refrigerant screening, maximizing exergoeconomic efficiency and system sustainability for campus-scale energy demand. Detailed modeling and selection of optimal refrigerants are central.	Solar-driven Organic Rankine Cycle (ORC) coupled with Vapor Compression Refrigeration within a CCHP architecture	Mixed-Integer Nonlinear Programming optimizing refrigerant composition and associated process parameters, with exergoeconomic efficiency as target metric.	Optimal exergoeconomic efficiency reported at 42.49%; best ORC mixture: R245fa/R41/R1336mzz(z); best VCR mixture: R1234ze/R1234yf/R32; advanced refrigerant selection reduces environmental impact and improves thermodynamic stability.
5	To develop and thermodynamically model a solar PVT system equipped with a novel coaxial condensing heat pipe, targeting enhanced energy exploitation in built environments and improved heat transfer performance.	PVT system using Coaxial Condensing Heat Pipe (CCHP)	No explicit optimization algorithm is employed; the study focuses on parametric analysis and performance assessment.	CCHP/PVT system achieves 14.4% (thermal) and 5.2% (electrical) efficiency enhancements over conventional heat pipe systems; PV panel temperature reduction: 30.3% (vs. natural cooling), 16.3% (vs. standard heat pipe); average error from previous studies < 10%.
31	To review hybrid combined cooling, heating, and power systems, particularly highlighting the integration of renewables (solar) and advanced fuel cell-gas turbine hybrids (SOFC/MGT/ORC), focusing on improved efficiency, ROI, and fossil fuel reduction via case study comparisons.	Solar energy as a supplementary/primary source in multi-generation, often paired with SOFC, MGT, and ORC subcomponents	No system-level optimization algorithm featured; emphasis is placed on techno-economic and exergy comparisons of system configurations.	Power saving of up to 9.1%; ROI period approx. 14.6 years; peak SOFC electrical efficiency: 66.3%; peak energy/exergy efficiencies: 88.4%/62.3%; solar integration demonstrably reduces fossil fuel dependency and emissions.
24	To conduct a 4E (energy, exergy, exergoeconomic, environmental) and sustainability assessment of hybrid solar gas turbine configurations, including integration of CSP towers/heliostats with Brayton cycles, sometimes complemented by ORC or steam bottoming, aimed at multigeneration performance enhancement.	Concentrated Solar Power with integrated gas turbine systems and potential ORC/bottoming cycles	Multiple metaheuristic and evolutionary optimization algorithms referenced for heliostat field design (e.g., hybrid GA-GOA), but the main presented model emphasizes performance mapping rather than direct optimization of the plant case.	Seasonal thermodynamic predictions show improved Brayton cycle efficiencies; hybrid solar-gas concepts enhance capacity factors and reduce CO2 intensity; heliostat optimization yields higher annual optical efficiencies; 4E benefits demonstrated with significant environmental advantage over conventional gas-only operation.
32	To evaluate a hybrid solar–biogas polygeneration system for rural dairy applications, emphasizing techno-economic feasibility, CO2 mitigation, and optimization of component sizing using open-source modeling frameworks. Includes simultaneous supply of electricity, refrigeration, cooking fuel, and biofertilizers.	Solar Photovoltaic integrated with biogas-fueled CHP and absorption refrigeration	Python-based open-source optimization framework (MicroGridsPy-CHP); objective: minimize Net Present Cost while satisfying all electrical and thermal demands.	Aggregated cost of electricity and heat: 0.044–0.070 USD/kWh; solar penetration up to 32%; annual CO2 savings: 109–127 t CO2; optimal sizing reduces both capital and operating costs while increasing renewable share in the mix.
33	To design and techno-economically optimize a hybrid solar–biogas polygeneration plant in Bolivia, servicing an association of small dairy farms, integrating PV, biogas CHP, batteries, and thermal use for milk cooling and fertilizer drying.	Solar Photovoltaic with biogas-based CHP in polygeneration mode	Modified MicroGridsPy model; objective: minimize NPC and assess LCOE/LCOH under varying scenario constraints.	LCOE: 0.044–0.070 USD/kWh; renewable fraction up to 32%; biogas demand and solar sizing optimized for reliability; potential CO2 emissions reduction: 109–127 t/year; system meets all service demands sustainably with improved financial viability over fossil alternatives.
Current work	To develop, dynamically simulate, and multi-objective optimize an integrated tri‑generation system for year‑round clean energy supply in hot‑dry climates, combining LCPV‑CPC, dual small‑scale gas turbine generators, HP‑LG, HP‑HG, and an ammonia–water absorption chiller. The focus is on maximizing primary energy savings, cost reduction, CO2 mitigation, and exergy efficiency through coordinated multi‑grade thermal utilization and FEL operation.	LCPV‑CPC system integrated with small-scale gas turbines and dual-grade heat pumps	RVEA with entropy‑weighted VIKOR for balanced multi‑criteria optimisation; objectives: maximise SPEC, SATCR, RRCO2, and exergy efficiency.	Substantial performance gains compared with a separate production facility: primary energy savings up to ~ 33%, annual cost savings exceeding 10% at favorable solar conditions, and CO2 emission reduction approaching 50%.

The main advantages and contributions of this paper are as:.

Innovative multi‑source integration, LCPV‑CPC array, dual small‑scale gas turbine generators, dual heat pumps (HP‑LG, HP‑HG), and an ammonia–water absorption chiller into a single tri‑generation plant, enabling coordinated utilisation of multi‑grade thermal outputs rarely addressed in prior works.

Operational strategy advancement – Implements a FEL dispatch control to optimise turbine loading and grid interaction, minimizing curtailment and enhancing renewable penetration under fluctuating solar conditions, an aspect often overlooked in earlier designs.

Methodological novelty in optimisation– Employs a RVEA combined with entropy‑weighted VIKOR for balanced multi‑criteria optimisation, delivering a rigorous decision‑making framework that simultaneously targets energy, economic, environmental, and exergy objectives.

Proven performance gains– Achieves significant improvements compared with a conventional separate production facility, including primary energy savings, annual cost reduction, CO₂ emissions mitigation, and an increase in exergy efficiency, validated through dynamic Aspen HYSYS–MATLAB co‑simulation and subsystem‑level experimental benchmarks.

In this work, a novel integrated tri‑generation configuration—comprising a low‑concentration hybrid PV–compound parabolic concentrator thermal system (LCPV‑CPC), dual small‑scale gas turbine generators, a heat pump supplied by a low‑grade water source (HP‑LG), a heat pump supplied by a high‑grade water source (HP‑HG), and an ammonia–water absorption chiller—is developed, modelled, and comprehensively optimised for application in a university building under the hot‑dry climatic conditions of Baghdad, Iraq. The proposed system embodies a carefully engineered synergy between dispatchable natural gas technologies and variable renewable input, thereby maximising renewable penetration while preserving operational stability and flexibility in meeting simultaneous electricity, heating, and cooling demands. A key innovation lies in the coordinated exploitation of multi‑grade thermal sources from both the LCPV‑CPC and the waste‑heat recovery generator to drive high‑ and low‑temperature heat pump cycles, enabling improved exergy utilisation and effective seasonal matching of heating and cooling loads. Unlike conventional micro‑gas turbine or simple PVT‑based designs, the incorporation of LCPV‑CPC collectors enhances conversion efficiency through optical concentration while effectively harvesting both direct and diffuse solar irradiance, whereas the use of dual turbine units improves part‑load performance and redundancy.

Furthermore, the thermal and electrical dispatch logic is implemented under a FEL operational strategy, which was selected for its capacity to optimise turbine loading, minimise electricity curtailment, and enhance system–grid interactions in conditions of fluctuating solar availability. From a methodological perspective, the study advances the field by adopting a Reference Vector Guided Evolutionary Algorithm (RVEA) within a multi‑objective optimisation framework to simultaneously improve primary energy consumption savings, annualised cost savings, CO₂ emissions reduction, and exergy efficiency—criteria weighted objectively via entropy‑based analysis and synthesised through a VIKOR decision‑making approach. This integration of a modern angle‑based many‑objective evolutionary search with rigorous multi‑criteria decision assessment represents a methodological contribution applicable to a wide range of coupled renewable–fossil energy systems. The developed mathematical model is implemented through a dynamic co‑simulation environment coupling Aspen HYSYS with MATLAB, supported by separate subsystem validations against high‑quality experimental benchmarks to ensure predictive robustness and minimise error propagation. Consequently, the research contributes both a technically viable pathway for high‑efficiency, low‑emission tri‑generation in climates with strong solar resources and pronounced cooling demand, and an optimised operational framework that can guide the design of future hybridised small‑scale power and thermal systems for urban buildings. By addressing the interplay between renewable intermittency, thermodynamic efficiency, and economic feasibility within a unified modelling and optimisation structure, this study offers transferable insights for energy system designers, policy makers, and researchers seeking integrated solutions for sustainable building energy supply.

Section 2 details the system configuration, thermodynamic modelling, and control strategies for the proposed LCPV‑CPC‑assisted tri‑generation plant, along with the baseline separate production facility for comparison. Section 3 presents the multi‑objective optimisation framework, employing the RVEA and VIKOR‑based decision analysis to balance energy, economic, environmental, and exergy objectives. Sections 4–6 encompass model validation against experimental benchmarks, a comprehensive results and discussion of the Baghdad case study, and concluding recommendations for performance enhancement and broader applicability.

Methodology

Configuration principle

The SPF (separate production facility) shown in Fig. 1, represents the conventional baseline in which the energy demands for heating and cooling are satisfied by independent, non‑integrated units. Electrical power is drawn exclusively from the utility grid and used to operate the cooling cycle of an ammonia–water absorption chiller, which rejects heat through a cooling tower. The main advantage of an ammonia–water absorption chiller over a lithium bromide–water type is its ability to achieve sub‑zero cooling temperatures, making it suitable for both air‑conditioning and refrigeration applications. Chilled water produced by the chiller is stored in a dedicated thermal tank before being circulated to the thermal conditioning units for space conditioning. The heating demand is met by an NG‑heat generator, which directly converts the chemical energy of natural gas into hot water supplied to a separate storage tank and then pumped to the thermal conditioning units. In this arrangement, there is no exchange or recovery of waste heat between subsystems, and each energy service operates in isolation. While technically straightforward, this lack of integration results in higher fuel consumption, reduced overall efficiency, and a complete dependence on fossil‑based heat generation and grid‑supplied electricity. The schematic underlines the inherent operational limitation of SPFs: the inability to harness synergies between heating and cooling processes or to incorporate renewable resources into the main energy supply chain.

Fig. 1.

The operating schematics and energy flows of the SPF configuration.

The integrated tri‑generation facility with LCPV-CPC in Fig. 2 illustrates a fully integrated approach where electricity, heating, and cooling are produced in a coordinated manner, maximising the utilisation of both renewable and fossil fuel resources. At the core, two small-scale gas turbine generators generate electricity for on‑site loads, with their high‑temperature exhaust routed through a WHRG to produce thermal energy. This output, supplemented when necessary by the NG‑heat generator, is directed to a heat pump supplied by a HP-LG for driving the ammonia–water absorption chiller. The cooling subsystem stores chilled water in dedicated tanks and maintains thermal balance via the cooling tower. On the low‑temperature side, the LCPV-CPC array contributes both electrical and low‑grade thermal energy; the latter is routed to the low‑temperature heat pump for heating services or stored for later use. Multiple stratified water tanks handle distinct temperature levels, enabling temporal decoupling of generation and demand. Electricity from the LCPV-CPC is first utilised locally and then exported to the grid through an inverter when in surplus. The schematic demonstrates the synergistic operation that allows waste heat from power generation to reduce fossil fuel consumption, enabling higher overall efficiencies, reduced CO₂ emissions, and enhanced flexibility in meeting the fluctuating cooling and heating demands characteristic of Baghdad’s hot‑dry climate.

Fig. 2.

The operating schematics and energy flows of the tri-generation configuration.

By utilizing the system’s schematics (Figs. 1 and 2), Aspen HYSYS is utilized to create the configurations simulations. In addition, for the mathematical modelling of the LCPV-CPC system as well as the configuration optimization, MATLAB software was integrated with Aspen HYSYS software. Further, Tables 2 and 3 explains the supervision techniques in FEL mode. Investigation is conducted in an office building. It is essential to analyze the effect of important choice variables on the objective functions. This study investigates the effect of these variables on the SPEC (saving of primary energy consumption), SATCR (saving of annual total cost rate), RRCO₂, and the exergy efficiency of the system. By incorporating solar power supply, the NG utilization and the pollutants emissions can be diminished. Heating capacities of the system are greatly affected by components such as the heat pump supplied by a low‑grade water source (HP-LG), HP-HG, NG-heat generator, and WHRG.

Table 2.

Electricity management description under following electric load method.

No.	Operating condition	Electricity management
#1	LCPV-CPC output is below demand; small-scale gas turbine generator is operating and fully covers the shortfall.	Local generation meets the entire demand with no electricity imported from or exported to the grid.
#2	LCPV-CPC output is below demand; small-scale gas turbine generator is operating but cannot fully meet the load.	Part of the demand is met by the small-scale gas turbine generator and the remainder is purchased from the utility grid.
#3	Output from the low-concentration LCPV-CPC subsystem exceeds instantaneous electrical demand; small-scale gas turbine generatoris off.	Surplus electricity is directed to the utility grid after satisfying the local load.
#4	LCPV-CPC output is below demand; small-scale gas turbine generator is off.	Entire electrical shortfall is supplied by the utility grid.

Table 3.

Thermal management description under following electric load method (winter& summer).

Condition	No.	Operating condition	Thermal management
Winter – Outlet temp ≥ 55.7 °C	#1	LCPV-CPC heat is insufficient; small-scale gas turbine generator off; NG‑heat generator off.	Stored heat is discharged from the water storage tank to meet demand.
	#2	LCPV-CPC heat is insufficient; small-scale gas turbine generator on; NG‑heat generator off.	Waste heat from small-scale gas turbine generator is used directly for the load while the storage discharges.
	#3	LCPV-CPC heat output exceeds demand; small-scale gas turbine generator off; NG‑heat generator off.	Excess thermal energy charges the water storage tank.
	#4	LCPV-CPC heat is insufficient; small-scale gas turbine generator on; NG‑heat generator off.	Waste heat from small-scale gas turbine generator is used to charge the water storage tank.
	#5	LCPV-CPC heat output exceeds demand; small-scale gas turbine generator on; NG‑heat generator off.	Surplus thermal energy is used to charge the water storage tank.
	#6	LCPV-CPC heat is insufficient; small-scale gas turbine generator on; NG‑heat generator on.	Heat from both small-scale gas turbine generator and NG‑heat generator supports the load, with storage discharging.
Winter – Outlet temp < 55.7 °C	#1	LCPV-CPC heat is insufficient; small-scale gas turbine generator off; NG‑heat generator off.	Stored heat is discharged from the tank to meet demand.
	#2	LCPV-CPC heat is insufficient; small-scale gas turbine generator on; NG‑heat generator off.	Waste heat from small-scale gas turbine generator is used directly and the tank discharges.
	#3	LCPV-CPC heat output exceeds demand; small-scale gas turbine generator off; NG‑heat generator off.	Excess thermal energy charges the water storage tank.
	#4	LCPV-CPC heat is insufficient; small-scale gas turbine generator on; NG‑heat generator off.	Waste heat from small-scale gas turbine generator charges the storage tank.
	#5	LCPV-CPC heat output exceeds demand; small-scale gas turbine generator on; NG‑heat generator off.	Surplus heat (including from small-scale gas turbine generator) is stored in the water tank.
	#6	LCPV-CPC heat is insufficient; small-scale gas turbine generator on; NG‑heat generator on.	Both small-scale gas turbine generator and NG‑heat generator supply heat while the tank discharges.
Summer	#1	LCPV-CPC heat is insufficient; small-scale gas turbine generator off; NG‑heat generator off.	Stored heat is discharged from the tank for the load.
	#2	LCPV-CPC heat is insufficient; small-scale gas turbine generator on; NG‑heat generator off.	Waste heat from small-scale gas turbine generator goes to the load while the storage discharges.
	#3	LCPV-CPC heat output exceeds demand; small-scale gas turbine generator off; NG‑heat generator off.	Excess thermal energy charges the storage tank.
	#4	LCPV-CPC heat is insufficient; small-scale gas turbine generator on; NG‑heat generator off.	Waste heat from small-scale gas turbine generator charges the storage tank.
	#5	LCPV-CPC heat output exceeds demand; small-scale gas turbine generator on; NG‑heat generator off.	Surplus thermal energy (including from small-scale gas turbine generator) charges the storage tank.
	#6	LCPV-CPC heat is insufficient; small-scale gas turbine generator on; NG‑heat generator on.	Both small-scale gas turbine generator waste heat and NG‑heat generator output support the load while the tank discharges.

Note that, while short-term solar variability and real-time grid signals can affect instantaneous dispatch, these effects typically have a marginal impact on the annual performance metrics used in our multi-objective framework, given the thermal and electrical storage capacities inherent in integrated systems. As such, the steady-state FEL assumption is not a simplification that undermines the validity of our conclusions, but rather a modelling choice appropriate for the study’s scope and for comparability with existing literature. Further, to model future high-fidelity scenarios, the impact of transient conditions such as pulsed loads (Mi et al.³⁴ and inrush currents in MMC-HVDC systems (Wang et al.³⁵ should be considered, especially for grid-tied tri-generation configurations.

The CO₂ objective is to include upstream NG supply-chain emissions and LCPV-CPC embodied emissions amortized over the project lifetime. Let denote operational emissions, upstream NG emissions, and amortized embodied LCPV-CPC emissions. The total life-cycle emissions are:

1

The life-cycle reduction rate is then,

2

We model upstream NG emissions as a multiplicative factor of combustion emissions, i.e.,

3

and amortize LCPV-CPC embodied emissions over lifetime (years) using the annual electricity/thermal production:

4

where, reported per system size and normalized per year. We report RRCO₂ both operational-only and life-cycle aware ().

Optimization framework

In the present study, RVEA was used to optimize the tri-generation system. The RVEA is a multi objective optimization method introduced to address the challenge of maintaining both convergence (moving towards the Pareto front) and diversity (well spread solutions) in problems with two or more conflicting objectives. It is particularly useful for many-objective optimization problems (MaOPs) but has proven effective for 2–3 objective cases as well. RVEA uses a set of reference vectors that span the normalized objective space. Each candidate solution is associated with one reference vector, guiding the search towards a well-distributed Pareto front. The reference vectors themselves can adapt over iterations, focusing more on promising regions.

Mathematical formulation

Let:

Decision vector in the search space ;

Objective vector for objectives;

Reference vector , normalized such that ;

Normalized objective vector;

Step 1 – Normalization of objectives

5

where, and ​ are the minimum and maximum values of objective iii in the current population.

Step 2 – Association with reference vectors

For each solution , determine the acute angle to each :

6

Assign to the vector with the smallest .

Step 3 – Scalar projection for selection

Within each reference vector’s niche, select individuals based on the scaled perpendicular distance:

7

Smaller indicates better convergence.

Step 4 – Adaptive reference vectors

Every tadapttadapt​ iterations, update:

8

where, is a representative solution in the niche and is the ideal point. Pseudocode of the RVEA is shown as:

The present study aims to optimize the system configuration through the simultaneous enhancement of SPEC, SATCR, RRCO₂, and exergy efficiency, formulated as:

9

Here, the SPEC is determined by:

10

where,

11

The SATCR can be articulated as follows:

12

Further, the RRCO₂ value is formulated by:

13

Here, : CO₂ emission rate.

Moreover, the following formula expresses the exergy efficiency ():

14

EX: Exergy, elec: electrical, H: Heating, and C: Cooling.

The model range restrictions for system variables are outlined in Table 4. Further, Fig. 3 presents the step-by-step process for resolving the optimization model.

Table 4.

The model range restrictions for system variables.

Parameter	Lower bound	Upper bound
Capacity of HP-HG, kW	230	400
Capacity of HP-LG, kW	72	182
Capacity of NG-heat generator, kW	380	530
Area of LCPV-CPC, m2	40	250
Efficiency of WHRG, %	45%	95%

Fig. 3.

The step-by-step process for resolving the optimization model.

Table 5 gives the input parameters for the RVEA in multi-objective energy system optimization. The parameter configuration for the RVEA was selected based on documented best practices for many-objective optimization in energy systems. A population size of 120 ensures adequate Pareto front coverage without excessive computational cost, consistent with the guidance of Deb & Jain³⁶ and recent RVEA applications in energy optimization. The crossover probability of 0.85 promotes exploration in early stages, while a mutation probability of 0.10 preserves diversity in later generations—settings widely adopted in frameworks such as PlatEMO. The reference vector adaptation frequency () follows Cheng et al.³⁷, ensuring that reference vectors adapt gradually without destabilizing convergence. The number of reference vectors equals the population size, enabling uniform distribution in normalized objective space and robust diversity via angle-based selection. These choices have been validated in multi-objective energy design studies, demonstrating strong performance in balancing convergence speed and solution diversity. Note that, the crossover probability was set to 0.80 to promote genetic material exchange and rapid exploration in the early generations, while mutation probability was fixed at 0.10 to ensure diversity retention in later generations without excessive randomness. These settings were adopted following best-practice guidelines for RVEA in multi-objective energy optimisation.

Table 5.

The input parameters for the RVEA in multi-objective energy system optimization.

Parameter	Value	Parameter	Value
Population size	120	Mutation probability	10%
Crossover probability	80%	Maximum generation number	250
Reference vector adaptation frequency (tadapt)	Every 20 generations	Number of reference vectors	Equal to population size
Distribution of reference vectors	Uniformly spread in normalized objective space	Selection method	Angle-based association with perpendicular distance minimization
Crossover method	SBX (Simulated Binary Crossover, η = 20)	Mutation method	Polynomial mutation (η = 20)

To select the most appropriate solution from the Pareto front generated by the RVEA, the VIKOR method was employed. In comparison with conventional decision-making approaches, which often measure performance based solely on proximity to an ideal point, VIKOR places greater emphasis on identifying a balanced compromise among conflicting objectives. This method simultaneously considers overall performance across all objectives (group utility) and the largest shortfall in any single objective (individual regret). By combining these measures with equal emphasis, VIKOR determines the alternative that best reconciles trade‑offs between energy efficiency, economic benefits, environmental sustainability, and exergy efficiency. Entropy weighting was applied to objectively determine the relative importance of each criterion, avoiding subjective bias. This combination of RVEA for generating diverse optimal solutions and VIKOR for systematic selection provides a robust framework for integrated energy system optimization, particularly where balanced performance across multiple objectives is essential.

Model validation

To ensure the predictive reliability and technical soundness of the developed simulation framework, a systematic validation procedure was performed for the two key subsystems of the proposed tri‑generation configuration: LCPV-CPC and the ammonia–water absorption chiller. The validation was conducted separately for each subsystem to: isolate performance deviations attributable to specific thermodynamic processes, prevent compounded error masking when assessing the integrated system, and ensure that each model meets acceptable accuracy thresholds before being coupled within the overall simulation environment.

For the LCPV-CPC, performance predictions were benchmarked against the experimental results reported by Yang et al.³⁸, with detailed comparisons presented in Table 6(a). They presented a low-concentrating PV/T triple-generation system to demonstrate the feasibility of the triple-generation system in the experiment. For validation purposes, all input data and design conditions were matched precisely to those reported in the corresponding reference study. The selected validation metrics included outlet water temperature, electrical power generation, and overall thermal‑electrical efficiency under identical inlet fluid temperatures and flow rates. The maximum observed deviations across all operating hours were 1.88% for outlet temperature, 2.76% for electrical output, and 2.05% for overall efficiency, with most differences remaining well below 2%. Such close agreement confirms the model’s ability to capture both the optical‑thermal conversion characteristics of the CPC geometry and the electro‑thermal coupling effects inherent in hybrid concentrator systems.

Table 6.

Model validation results. (a): model validation of the low-concentration hybrid PV–compound parabolic concentrator thermal system vs. work of Yang et al.³⁸. (b): model validation of the ammonia–water absorption chiller vs. work of Palacios-Lorenzo and Marcos³⁹.

Parameter	Time
	11.30	12.30	13.30	14.30	15.30	16.30
Inlet temperature	32.57 °C	33.22 °C	33.86 °C	34.05 °C	33.38 °C	32.51 °C
Outlet temperature-Literature	52.09 °C	52.68 °C	53.52 °C	54.18 °C	53.47 °C	50.06 °C
Outlet temperature-Model	52.18 °C	53.67 °C	54.35 °C	54.61 °C	53.53 °C	50.44 °C
Deviation	0.18%	1.88%	1.55%	0.79%	0.12%	0.76%
Power generation-Literature	2.268 kW	2.174 kW	2.061 kW	2.096 kW	2.021 kW	1.798 kW
Power generation-Model	2.310 kW	2.210 kW	2.118 kW	2.140 kW	2.055 kW	1.818 kW
Deviation	1.85%	1.65%	2.76%	2.1%	1.68%	1.12%
Overall efficiency-Literature	70.16%	70.86%	70.91%	73.3%	76.61%	76.92%
Overall efficiency-Model	71.13%	71.95%	72.02%	74.72%	78.18%	78.07%
Deviation	1.38%	1.54%	1.56%	1.94%	2.05%	1.49%
Parameter	Ambient temperature
	15 °C	30 °C	35 °C	39 °C
Cooling capacity-Literature	9.13 kW	7.22 kW	5.93 kW	4.89 kW
Cooling capacity-Model	8.97 kW	7.07 kW	5.81 kW	4.80 kW
Deviation	1.78%	2.12%	2.06%	1.87%
COP-Literature	0.586	0.525	0.482	0.416
COP-Model	0.572	0.516	0.471	0.408
Deviation	2.45%	1.74%	2.33%	1.96%

For the ammonia–water absorption chiller, validation relied on the performance dataset published by Palacios‑Lorenzo and Marcos³⁹. They developed a modular mathematical model to simulate an indirectly fired, air-cooled ammonia-water absorption refrigeration system. This model incorporated governing equations that were based on mass, species, and energy balances, which were applied to the primary components of the system. Similarly, for validation purposes, all input data and design conditions were matched precisely to those reported in the corresponding reference study. As summarised in Table 6(b), cooling capacity and coefficient of performance were evaluated at four distinct ambient temperatures (15 °C, 30 °C, 35 °C, and 39 °C), representing a realistic operational envelope. The largest deviations between simulated and experimental values were 2.12% for cooling capacity and 2.45% for COP, with all other cases demonstrating even smaller discrepancies. These results indicate that the thermodynamic representation of the ammonia–water working pair, together with the absorber, generator, condenser, and evaporator interactions, is reproduced with high precision under varying driving and sink temperature conditions.

The decision to validate each subsystem independently ensures that the integrated system results are built upon rigorously verified component models, thus minimising uncertainty propagation in the combined simulation. The consistently low error margins across Table 6 demonstrate that the developed models can be confidently applied to optimisation and scenario analyses without compromising technical credibility or decision‑making robustness. Note that, although thermal performance is validated, incorporating emission morphology studies such as those by Chen et al.⁴⁰ could enhance environmental analysis, especially under variable heat load operations.

Results and discussion

Case study: an university building in Baghdad, Iraq

Baghdad, the capital of Iraq, is located in a hot‑dry subtropical climate distinguished by extremely hot, arid summers, mild winters, and a high annual solar resource. These climatic conditions present both operational challenges and opportunities for the deployment of solar‑assisted tri-generation facilities. Figure 4 depicts the climatic and load characteristics for Baghdad, Iraq. Long‑term meteorological assessment using NASA‑POWER and Meteonorm datasets for the period 2000–2020 shows that global horizontal irradiance (GHI) reaches approximately 880 W/m² in midsummer, with values above 700 W/m² persisting for over six consecutive months, while direct normal irradiance (DNI) peaks above 900 W/m² during June and July. Ambient temperature exhibits pronounced seasonal variation, exceeding 37 °C in July–August and decreasing to 10–12 °C in winter months. The coincidence of high solar irradiation and elevated ambient temperatures during the cooling season offers substantial potential for solar‑driven electricity and thermal production in tri-generation applications.

Fig. 4.

Climatic and load characteristics for Baghdad, Iraq: (a) monthly average GHI, DNI, and ambient temperature; (b) monthly average cooling load, heating load, and total electrical load. Data derived from NASA‑POWER and Meteonorm sources for the 2000–2020 period and building load simulations under local climatic conditions^41,42.

The reference building is a university facility operating on a 12‑hour daily schedule under typical occupancy and internal load conditions. Cooling and heating loads were determined through degree‑hour analysis, incorporating local climatic parameters, envelope thermal characteristics, internal heat gains, and HVAC performance coefficients. Results indicate that cooling demand dominates the annual profile, with a peak monthly average of approximately 158 kWh/h in July and sustained high demand from May to September. Heating requirements are concentrated in winter, with a peak of about 78 kWh/h in January and negligible values during warmer months. Total electrical demand (Power Load), calculated as the sum of non‑HVAC base consumption and chiller power input, remains around 400 kWh/h in the shoulder and heating seasons, rising to approximately 460 kWh/h during peak summer due to the added cooling load. These combined solar resource and demand characteristics create favorable conditions for full electric load operational strategies, where a considerable share of electrical demand can be met directly from LCPV-CPC generation during summer, reducing reliance on small-scale gas turbine generators and grid import. In winter, LCPV-CPC thermal output contributes to space heating via water‑source heat pumps, supplemented by recovered waste heat from the small-scale gas turbine generator exhaust and auxiliary NG-heat generators. The climatological and load profiles of Baghdad therefore provide a representative and technically demanding environment for evaluating the energy, exergy, and techno‑economic performance of optimized solar–natural gas tri-generation configurations operating in hot‑dry regions.

Table 7 presents the key technical and economic parameters employed in modelling the proposed hybrid energy system for the university building in Baghdad, Iraq (base year 2021). The adjusted values reflect cost data updated to 2024 USD by applying an overall inflation factor of 1.262.

Table 7.

Technical and economic parameters applied in modelling the proposed system for a university Building in Baghdad, Iraq.

Parameter	Value	Adjusted Value (2024, under inflation factor of 1.262)
Thermal efficiency of small-scale gas turbine generator	10%	10%
COP of HP-LG	4.72	4.72
Electrical efficiency of small-scale gas turbine generator	25%	25%
COP of HP-HG	4.55	4.55
Efficiency of power grid	92%	92%
CO₂ emission factor for grid	0.94 kg/kWh (Iraq grid mix 2024)	0.94
CO₂ emission factor of NG	0.202 kg/kWh (Middle East NG average)	0.202
Efficiency of LCPV-CPC	18.7%	18.7%
Efficiency of WHRG	68%	68%
Electrical efficiency of grid	36%	36%
Lifetime	25 years	25 years
Interest rate	6.6%	6.6%
LCPV-CPC cost	300 USD/kW (+ 20–40% BOS)	378.6 USD/kW
NG-heat generator cost	116 USD/kW	146.392 USD/kW
Cost of hot water generator	20 USD/kW	25.24 USD/kW
Heat pump cost	272 USD/kW	343.26 USD/kW
Absorption chiller cost	210 USD/kW	265.02 USD/kW
Electric chiller cost	128 USD/kW	161.53 USD/kW
Small-scale gas turbine generator cost	1072 USD/kW	1352.86 USD/kW
Water storage tank cost	326.7 USD/kW	412.29 USD/kW
Pump cost	56 USD/kW	70.67 USD/kW
Cooling tower cost	120 USD/kW	151.4 USD/kW
Unit price of electricity	0.055–0.21 USD/kWh	0.055–0.21 USD/kWh
Unit price of NG	0.345 USD/m³ (Iraq 2024 adjusted)	0.345 USD/m³
Feed-in tariff for LCPV-CPC production	0.1050 USD/kWh	0.1050 USD/kWh
Feed-in tariff for NG	0.096 USD/kWh (LCOE-based)	0.096 USD/kWh

Parametric analysis results

Solar irradiation impact

Figure 5 illustrates the variation of key performance and sustainability metrics for the integrated Baghdad‑based energy system—comprising the LP‑LG, the HP‑HG, the small‑scale gas turbine generator, the LCPV‑CPC subsystem, and the ammonia–water absorption chiller—under different levels of solar radiation. As solar radiation increases from 300 to 1000 W/m², the saving of primary energy consumption rises steadily from approximately 18% to over 33%, reflecting the enhanced solar‑driven contribution of the LCPV‑CPC in supporting both thermal and electrical outputs. The reduction rate of CO₂ emissions follows a similar yet more pronounced upward trend, ranging from 37% to nearly 50%, which indicates the substantial displacement of fossil‑fuel‑based generation when renewable input grows. Conversely, the saving of annual total cost rate begins in a slightly negative range due to capital recovery and operational expenses at lower radiation levels but crosses into a positive domain beyond roughly 472 W/m², demonstrating improved economic competitiveness with greater solar availability. In contrast, exergy efficiency exhibits a gradual decline from about 22.5% to 17%, suggesting that although the absolute quantity of useful energy increases, thermodynamic irreversibilities within coupled subsystems—particularly in hybrid thermal loops—are amplified under high‑radiation, off‑design conditions. This multidimensional response highlights that, for Baghdad’s climatic conditions, operational optimization must aim to maximize environmental and economic benefits without excessive compromise in exergy performance, with mid-to-high solar radiation regimes emerging as the most favorable operating window.

Fig. 5.

The variation of key performance and sustainability metrics for the integrated Baghdad‑based energy system under different levels of solar radiation.

Inlet fluid temperature of LCPV-CPC impact

Figure 6 presents the influence of inlet water temperature to the LCPV‑CPC subsystem on the integrated Baghdad‑based configuration. As inlet water temperature rises, the saving of primary energy consumption improves progressively before stabilizing, indicating that hotter water enhances the thermal output contribution of the LCPV‑CPC but only up to a practical limit. A similar trend is observed for CO₂ emission reduction, reflecting the increasing role of renewable heat in displacing fossil‑based input. The saving of annual total cost rate shows a gradual movement toward break‑even, suggesting that economic feasibility strengthens as the subsystem approaches optimum thermal matching conditions. Exergy efficiency remains relatively stable across most of the temperature range, with slight improvement near the optimal inlet temperature, implying that the thermodynamic quality of energy conversion is less sensitive to inlet water variations compared with resource‑driven changes, such as solar radiation. Overall, the results highlight that tuning inlet water temperature is an effective operational lever to improve environmental and economic indicators without introducing notable penalties to system exergy performance.

Fig. 6.

The influence of inlet water temperature to the LCPV‑CPC subsystem on the integrated Baghdad‑based configuration.

LCPV-CPC’s area impact

Figure 7 shows how variations in the LCPV-CPC collector area affect key performance and sustainability indicators. Increasing the collector surface leads to continuous gains in primary energy savings and CO₂ emission reductions, demonstrating the direct link between solar collection capacity and renewable contribution. The emission reduction curve, in particular, maintains a steady upward trend even at higher areas, suggesting that environmental performance benefits persist beyond moderate sizing. In contrast, the saving of annual total cost rate remains slightly negative across the entire range, indicating that the capital costs for larger solar fields are not fully offset by operational savings within the studied boundary. Exergy efficiency exhibits only a mild decline, implying that thermodynamic quality is largely preserved, though some marginal increase in irreversibilities may arise from oversizing relative to downstream subsystem capacities. Overall, the results suggest that maximizing collector area is highly effective for environmental objectives, yet economic optimization for Baghdad’s conditions necessitates balancing size with cost recovery, potentially favoring a mid‑range configuration that retains strong emission reductions without substantial financial drawbacks.

Fig. 7.

How variations in the LCPV-CPC collector area affect key performance and sustainability indicators.

Impacts of HP-LG and HP-HG capacities

Figures 8 and 9 illustrate the influence of capacity variation for two distinct heat pump configurations on four performance indicators. In Fig. 8, increasing the HP-LG capacity from the lower to the upper bound leads to a steady, modest decline in both primary energy saving and CO₂ reduction rate. This trend suggests that enlarging the HP-LG unit gradually shifts the operational balance towards greater reliance on electricity‑driven heating, reducing the proportional contribution from solar‑assisted thermal input. The economic index declines more sharply, with the saving of annual total cost rate remaining negative across the capacity range—a clear reflection that the additional capital and running costs are not offset by equivalent operational savings. Exergy efficiency, however, remains essentially unchanged, indicating that the thermodynamic quality of energy conversion is resilient to size variation, even as environmental and economic performance deteriorates.

Fig. 8.

The influence of capacity variation for HP-LG configurations on four performance indicators.

Fig. 9.

The influence of capacity variation for HP-HG configurations on four performance indicators.

Figure 9 shows an analogous pattern for the HP-HG capacity range tested. Here, the decline in primary energy saving and CO₂ reduction is more gradual but nonetheless consistent, pointing to similar operational shifts in load coverage dynamics. The cost rate saving again worsens with size and stays negative, implying limited economic justification for larger HP-HG installations under the studied conditions. Stability in exergy efficiency is once again observed, underscoring that the fundamental quality of energy conversion is independent of unit size, although that constancy does not equate to overall system benefit.

Cross-comparison of both figures highlights that, for Baghdad’s climatic context, upsizing either HP-LG or HP-HG beyond modest levels delivers no advantage in carbon mitigation or cost performance, and progressively undermines the renewable fraction in total energy supply. From a design perspective, the results reinforce the importance of capacity optimization rather than maximization: smaller, well‑matched units not only achieve stronger gains in primary energy and CO₂ metrics but also avoid escalating investment penalties. The consistent exergy efficiency across sizes further implies that thermodynamic quality alone is insufficient as a guiding variable for sizing; instead, an integrated analysis of environmental and economic factors is essential for identifying the true optimal capacity range.

WHRG efficiency impact

Figure 10 presents the effect of varying the efficiency of the WHRG on four key performance indicators. As WHRG efficiency increases, both primary energy saving and CO₂ reduction rate exhibit steady improvements. This trend reflects the enhanced ability of the system to utilize otherwise wasted thermal energy, thereby displacing more fossil-based generation and increasing the renewable contribution to the overall energy mix. The economic indicator, the saving of annual total cost rate, remains negative across the studied efficiency range but shows modest improvement with higher WHRG performance. This partial recovery is likely due to the operational cost savings from improved energy recuperation, although the high capital costs of achieving greater WHRG efficiency still dominate the economic balance. Exergy efficiency also rises gradually, indicating that higher WHRG efficiency leads to better quality energy conversion and a reduction in irreversibilities within the thermal cycle. Overall, the results highlight the environmental and thermodynamic benefits of maximizing WHRG efficiency, while also revealing that cost competitiveness requires careful techno‐economic optimization to ensure that the financial investment aligns with long‐term performance gains.

Fig. 10.

The effect of varying the efficiency of the WHRG on four key performance indicators.

Incorporating upstream NG and LCPV-CPC embodied emissions reduces absolute RRCO₂ values while leaving the relative ranking of solutions unchanged. For the configuration that maximizes RRCO₂ under operational-only accounting (50.9%), the life-cycle aware values become 49.2% (low), 46.9% (mid), and 43.9% (high) under the bounded scenarios, as tabulated in Table 8. Figure 11 compares Baseline (operational-only) with LCA-Low/Mid/High scenarios for the top-performing solution. Values used: 50.9% (baseline), 49.2% (low), 46.9% (mid), 43.9% (high).

Table 8.

Assumptions for life-cycle CO₂ sensitivity (annualized).

Scenario	Upstream NG multiplier	LCPV-CPC embodied (annualized)	Comment
Low	0.10×NG combustion CO2	Small (e.g., aggressive lifetime/production)	Lower-bound, optimistic LCA
Mid	0.15×NG combustion CO2	Moderate	Central/best-estimate LCA
High	0.20×NG combustion CO2	Higher (e.g., conservative lifetime/production)	Upper-bound, conservative LCA

Fig. 11.

comparing Baseline (operational-only) with LCA-Low/Mid/High scenarios for the top-performing solution.

Figure 11 shows a clear decline in relative RRCO2 when upstream natural gas emissions and the embodied emissions of the LCPV‑CPC system are considered. In the baseline operational scenario, the optimised Baghdad hybrid configuration achieves a 50.9% reduction. Including low‑range life cycle assessment (LCA–Low) factors reduces RRCO₂ to 49.2%, mid‑range assumptions (LCA–Mid) to 46.9%, and high‑range estimates (LCA–High) to 43.9%. This steady decrease highlights how upstream NG supply impacts and manufacturing-related emissions erode apparent climate benefits, with the effect growing as accounting boundaries expand. In Baghdad’s context—where NG is the main fuel and year‑round heat pump use is viable—these embodied and upstream emissions meaningfully influence total performance. Neglecting them in optimisation could overstate true decarbonisation potential. The findings underscore the need for parallel strategies: lowering upstream methane leakage in small‑scale gas turbine supply chains and sourcing LCPV‑CPC components with reduced embodied carbon. Incorporating life‑cycle boundaries within multi‑objective optimisation delivers more resilient conclusions, ensuring that claimed RRCO₂ benefits remain robust under varying assumptions and guiding technology and supply‑chain decisions toward genuinely sustainable deployment.

Assessment of optimization outcomes

Figure 12 (a-d) presents the two‑dimensional kernel density distributions for the double‑objective optimization results of the proposed hybrid energy system in Baghdad optimized using the Reference Vector Guided Evolutionary Algorithm. The “Energy Saving vs. Exergy Efficiency” distribution shows a pronounced high‑density region at lower exergy efficiency values with corresponding primary energy savings between 26 and 28%, indicating that many Pareto-optimal solutions cluster in this range. This reflects the trade‑off in such systems, where boosting energy savings often brings a marginal drop in exergy efficiency due to added irreversibilities under certain operational strategies. In the “Energy Saving vs. Cost Saving” plot, the densest areas emerge at moderate energy savings and higher cost savings (about 1.3–1.5%), suggesting that economic advantages peak before maximum energy savings are reached—likely linked to the operational envelope of the HP-HG and part‑load efficiencies of auxiliary units. The “CO₂ Reduction vs. Cost Saving” density map exhibits concentrated clusters at high cost savings combined with mid‑level CO₂ reductions, implying that Baghdad’s climatic and grid‑independent operating conditions permit strong economic outputs without requiring peak emission cuts.

Fig. 12.

The two‑dimensional kernel density distributions for the double‑objective optimization results of the proposed hybrid energy system in Baghdad optimized using the Reference Vector Guided Evolutionary Algorithm.

The “CO₂ Reduction vs. Exergy Efficiency” plot mirrors these interactions, revealing dense groupings at lower exergy efficiencies with moderate CO₂ reduction, reinforcing that thermodynamic efficiency is often compromised when targeting significant carbon reductions. The overall density landscapes confirm that, within this optimization framework, there are identifiable operational “sweet spots” where environmental, economic, and thermodynamic goals intersect—though not at their individual maxima. In Baghdad’s context, these areas represent practical operating points balancing electricity generation from the small‑scale gas turbine with renewable heat and power input from the LCPV-CPC, enabling notable CO₂ reduction, cost saving, and improved energy performance without excessive system complexity or cost escalation. This alignment is particularly relevant given the city’s seasonal demand fluctuations, energy resource mix, and infrastructural constraints.

Figure 13(a-d) illustrates the Pareto frontiers obtained from the tri-objective optimization of the proposed hybrid energy system in Baghdad, Iraq, considering primary energy saving, annual total cost saving, CO₂ emissions reduction, and exergy efficiency as simultaneous performance targets. The decision-making step was conducted using the VIKOR method, with the optimal compromise solution identified in each 3D objective space and marked with a red star. In the “Energy Saving–Cost Saving–CO₂ Reduction” plot, the Pareto front extends smoothly, indicating strong mutual reinforcement between the objectives. Higher primary energy savings are generally accompanied by higher cost savings and significant CO₂ emission reductions, with the VIKOR point positioned at the high-performance end. This suggests that in Baghdad’s climatic and operational context, the optimal configuration can deliver considerable fuel cost benefits while also meeting stringent environmental objectives, leveraging the synergy between renewable inputs from the LCPV-CPC and the efficiency gains of the HP-HG and LP-LG units.

Fig. 13.

The Pareto frontiers obtained from the tri-objective optimization of the proposed hybrid energy system in Baghdad using the VIKOR method.

The “Energy Saving–CO₂ Reduction–Exergy Efficiency” surface shows that while energy saving and emission reduction are well aligned, exergy efficiency exhibits diminishing returns at the upper edge. The VIKOR point corresponds to high values for all three but slightly short of the absolute maximum exergy efficiency, reflecting the thermodynamic trade-offs present when expanding renewable penetration and operating small-scale gas turbine generators closer to optimum load. Similarly, the “Energy Saving–Cost Saving–Exergy Efficiency” Pareto space reveals that high cost and energy savings are achievable alongside substantial exergy efficiency, though the density of solutions in the high‑efficiency range is lower. This distribution underlines that achieving all three objectives at their maximum levels is rare, confirming the necessity of a balanced compromise such as that identified by VIKOR.

The “CO2 Reduction–Cost Saving–Exergy Efficiency” map illustrates a more scattered frontier, indicating that the correlation between emission cuts and cost savings is strong, but the inclusion of exergy efficiency introduces greater dispersion. The VIKOR point lies within the cluster of solutions delivering top-tier results for all three metrics, validating its role as a balanced choice in multi-criteria decision-making. Collectively, these Pareto frontiers show that in Baghdad’s system context, optimal solutions occupy a narrow band where environmental, economic, and thermodynamic objectives can be concurrently satisfied without severe compromise. The VIKOR selection ensures that the chosen configuration is not only mathematically optimal within the multi-objective framework but also pragmatically relevant for policy-driven deployment, where fuel costs, emission reductions, and efficiency improvements must be weighed against real-world operational constraints.

The comparative results in Table 9 highlight the relative performance of the current study against selected literature values, offering insight into the trade‑offs achieved through the proposed optimization framework. In terms of primary energy consumption saving, the present configuration attains 35.09%, which is higher than that reported in^43,44 and only slightly lower than the 39.27% in⁴⁵. This indicates that the integration of multiple renewable and efficient conversion technologies, coupled with the applied optimization method, offers competitive energy savings within the regional constraints of Baghdad. For CO₂ emission reduction, the current study achieves 50.76%, outperforming the values in^43,44, and approaching the highest figure in⁴⁵. This improvement suggests a favourable balance between renewable contribution and low‑carbon operation. However, for annual total cost saving, the current results (1.50%) are more modest compared with the 19.69% in⁴⁴ and 5.82% in⁴³, though significantly exceeding the negative saving in⁴⁵. This outcome reflects specific cost structures and fuel price conditions in Baghdad, where environmental and energy performance gains take precedence over aggressive cost reductions, ensuring a balanced and sustainable operational strategy.

Table 9.

Comparative assessment between the current study and literature benchmarks.

Parameter	Literature [46]	Literature [44]	Literature [45]	Current article
Saving of primary energy consumption	39.27%	22.63%	34.02%	35.09%
Reduction rate of CO2 emission	55.7%	37.51%	48.58%	50.76%
Saving of annual total cost rate	−87.47%	5.82%	19.69%	1.50%

While optimizing under static conditions is valuable, real-world operation demands dynamic reconfiguration capability under fault or degradation conditions. Wang et al.⁴⁶ demonstrate how integrated networks can adapt through coordinated reconfiguration strategies. Further, integrating intelligent decision-assistance or condition-based risk detection, such as data transformation for diagnostics, may enhance the robustness of optimization strategies in future iterations.

Conclusions

This research presented the design, dynamic simulation, and multi‑objective optimization of an integrated solar–natural gas tri-generation system tailored for the hot‑dry climate of Baghdad, Iraq. The configuration combined a LCPV-CPC, dual small‑scale gas turbine generators, high- and low-grade water-source heat pumps, and an ammonia–water absorption chiller, coordinated through a following‑electric‑load operational strategy. The aim was to maximize SPEC, SATCR, RRCO₂, and exergy efficiency through coordinated utilization of multi‑grade thermal outputs and flexible dispatch scheduling. The methodological innovation of coupling the Reference Vector Guided Evolutionary Algorithm with entropy‑weighted VIKOR enabled balanced trade‑offs between energy, economic, environmental, and thermodynamic targets. Quantitatively, the optimized system achieved primary energy savings of up to ~ 33%, annual cost reductions above 10% under favorable solar availability, and CO₂ mitigation rates approaching 50% relative to a conventional separate production facility. While exergy efficiency peaked at ~ 22.5% under moderate solar radiation, a slight decline to ~ 17% was observed at very high irradiance, attributed to intensified off‑design thermal mismatches and irreversibilities in hybrid loops. Qualitatively, the FEL strategy minimized curtailment and improved renewable penetration under variable solar conditions, while multi‑grade thermal integration enhanced both system flexibility and resource utilization.

Limitations of the current work include its reliance on a single climatic dataset and case‑study building type, assumptions of constant component performance over system lifetime, and exclusion of factors such as partial shading, dust accumulation, and stochastic maintenance effects. Moreover, grid interactions were considered under simplified tariff and feed‑in structures, which may differ under evolving market regulations. Future research should extend the analysis to stochastic renewable resource modeling, adaptive control strategies for real‑time optimization, and techno‑economic assessments under variable fuel prices and policy incentives. Integration of short‑term thermal or electrical storage, demand‑side management, and emerging low-GWP working fluids could further enhance sustainability. Experimental demonstration in a pilot facility is recommended to validate long‑term operational performance, economic returns, and environmental benefits under real‑world conditions. Overall, this study demonstrates a technically robust and economically promising pathway for sustainable tri‑generation in solar‑rich, cooling‑dominated urban environments.

Abbreviations

CCHP

Combined Cooling, Heating and Power

CO₂

Carbon Dioxide

DNI

Direct Normal Irradiance

FEL

Following Electric Load

GHI

Global Horizontal Irradiance

HP-HG

Heat Pump Supplied by a High‑Grade Water Source

HP-LG

Heat Pump Supplied by a Low‑Grade Water Source

LCPV-CPC

Low‑Concentration Hybrid PV–Compound Parabolic Concentrator

MaOP

Many-Objective Optimization Problem

NG

Natural Gas

NSGA

Non-Dominated Sorting Genetic Algorithm

PVT

Photovoltaic/Thermal

RRCO₂

Reduction Rate of CO₂ Emission

RVEA

Reference Vector Guided Evolutionary Algorithm

SATCR

Saving of Annual Total Cost Rate

SPEC

Saving of Primary Energy Consumption

SPF

Separate Production Facility

WHRG

Waste Heat Recovery Generator

Author contributions

Author Statement: Mohamed Bechir Ben Hamida: Investigation, Software, Data curation, Validation, Writing – original draft.Rassol Hamed Rasheed: Investigation, Methodology, Software, Writing – original draft.Narinderjit Singh Sawaran Singh: Conceptualization, Software, Data curation, Validation, Writing – review & editing.Mohammad Taghavi: Methodology, Conceptualization, Data curation, Project administration, Writing – original draft, Software, Methodology.

Funding

This work was supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University (IMSIU) (grant number IMSIU-DDRSP2503).

Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.