1. Introduction
Energy is pivotal to the economic growth of any country and its increased demand/production in recent times, triggered by increasing population, has led to the extreme usage of fossil fuels such as petroleum, natural gas, coal, etc. The utilization of fossil fuels as prime sources has drawbacks, especially in the area of global warming caused by greenhouse gas emission. This is in addition to the cost-intensiveness and depletion of its reserves [
1,
2]. Environmental deterioration caused by these greenhouse gas emissions from power plants is seen as a significant threat to societies that are concerned by the consequences of global warming. According to an IEA 2022 report [
3], CO
2 emission increased by 0.9% in 2022, peaking to an all-time high value of about 36.8GT. Spahni et al. [
4] have reported that electricity generation accounts for about 32% of CO
2 emissions followed by heating and cooling sources, which account for 33%, and transportation media, which account for 35%. This demonstrates that about 65% of CO
2 emission are due to power generation, heating and cooling, which are necessities for human survival. It justifies the need for efficient systems to manage and improve energy conservation as well as renewable energy sources that could complement or replace fossil fuels.
An energy management system that has gained research interest due to its fuel efficiency and reduced greenhouse emission rate is the combined cooling, heating and power (CCHP) system. The CCHP system involves the integration of various thermodynamic systems to produce two or more forms of energy in such a way that a ‘top system’ can be employed to drive a ‘bottom system’. A ‘top system’ in this context refers to systems such as gas turbines that require a high degree of energy for their operation while a ‘bottom system’ such as the Rankine cycle, Kalina cycle, absorption chiller, etc., require a lower amount of energy [
5]. Wu and Wang conducted an analysis to compare a usual energy system with the CCHP system [
6]. Their study established that efficiency improved by about 33%, owing to the cascade energy application of the CCHP system.
The inclusion of renewable energy, either as an adjunct to or as a replacement, for fossil fuels is another energy management idea that is under consideration. According to the 2023 BP Energy Outlook [
7], wind and solar power would account for about two-thirds of the global power generation by 2050 and their rapid adoption would be fuelled by a fall in their costs. The solar energy source is predominately employed in CCHP systems—though, due to its variability and the volatility of its radiation, not necessarily as a standalone energy source—to decrease the amount of fossil fuel expended. In CCHP systems, thermal energy is generated from the sun via solar thermal collectors which are either concentrating or non-concentrating. Several pieces of literature have discussed the CCHP systems integrated with solar energy for multiple applications. The effectiveness of a solar energy-integrated CCHP system over one powered by an internal combustion engine has been confirmed by Yousefi et al. [
8], who configured a solar-assisted CCHP system. Similarly, Zhang et al. [
9] have proposed a hybrid CCHP system that yielded a 30.4% fuel saving with a 26% solar energy input.
CCHP systems offer a sustainable solution to improve energy conservation by reducing greenhouse emissions, heat loss and operation cost, and by improving the overall energy efficiency while ensuring the presence and reliability of several energy generation options [
10]. However, the search for more optimal thermodynamic performance indicators is on-going. The CCHP system’s performance can be enhanced through optimization [
11]. Optimization advancements in the 1960 and 1970s saw the advent of a meta-heuristic approach, known as evolutionary algorithms. A predominant example of this approach is the genetic algorithm optimization proposed by Holland [
12]. This approach is inspired by Charles Darwin’s principles of mutation, crossover and survival of the fittest. Another fundamental metaheuristic method that came into the limelight in the 1990s was the swarm intelligence algorithm spearheaded by Dorigo et al. [
13], while Kennedy and Eberhart [
14] proposed the ant colony optimization (ACO) and the particle swarm optimization techniques, respectively. Real engineering problems are typically multi-objective in nature, and this implies that the mathematical formulation involves more than one objective function in general [
15]. Multi-objective functions are solved by arbitrarily assigning weights in a weighted-sum problem formulation and were employed by Zeng et al. [
16] and Song et al. [
17] to effectively improve the objectives of a CCHP system. The weight-based optimization or a priori method, however, has the drawback of requiring multiple runs and the need to always seek counsel from an expert/decision maker [
18]. These can also be solved using the posteriori method, which involves retaining the multi-objective formulation and obtaining the Pareto optimal solutions in a single run. However, these are computationally intensive. There are a handful of optimization techniques in the literature, namely the response surface method (RSM) [
19], non-dominated sorting genetic algorithm-II (NSGA-II) [
20], particle swarm optimization (PSO) [
21], Harris hawk optimization (HHO) [
22], grasshopper optimization (GOA) [
23], ant-lion optimization [
24], moth flame optimization (MFO) [
25], and greywolf optimization(GWO) [
26], etc. This research illustrates how GWO could be used to formulate and solve a problem related to a solar-assisted combined cooling, heating and power system. A breakdown of the optimization algorithms is displayed in
Figure 1.
Existing optimization studies have revealed that there are typical evaluation criteria that informs CCHP systems optimization and these are the exergetic, economic and environmental factors [
27]. The exergetic factors comprise the exergy efficiency, energy efficiency, primary energy saving ratio, etc. The economic factors include, the product unit cost, total cost saving, net present value, etc. while the environmental factors are CO
2 emission and integrated performance. This manuscript is structured as follows:
Section 2 presents the literature review;
Section 3 describes the tri-generation system to be optimized, the greywolf optimization technique and the mathematical formulation of the problem; and
Section 4 reports and discusses the results obtained from the optimization and sensitivity analysis. In the light of the above, the proposed research sets out to achieve the following objectives:
to propose a new approach for the optimization of a solar-assisted CCHP system;
to maximize the net power and exergy efficiency while minimizing the CO2 emission of a solar energy-integrated CCHP system using the multi-objective greywolf optimization technique;
to perform an analysis to ascertain the effect that the decision variables have on the objective functions.
2. Literature Review
The struggle to continuously improve CCHP systems with various optimization techniques represents a progressive research trend in the domain of energy conservation/management. Therefore, this section reviews the relevant pieces of literature that seek to optimize certain performance criteria of the solar-based CCHP system.
An extensive review revealed that a greater number of researchers employed the genetic algorithm for optimization applications in solar-assisted CCHP systems. Cao et al. [
28] proposed a modified solar-integrated CCHP system and optimized the amount of electricity it generated, its exergy efficiency, and its total cost per unit exergy via the genetic algorithm approach. They also carried out a parametric study to ascertain how their decision variables (oil mass ratio, Rankine inlet pressure, temperature, etc.) affect the objective functions. The proposed approach improved results in terms of the above mentioned performance criteria thus outperforming conventional methods. The thermodynamic analysis and performance optimization of a solar energy- and natural-gas-integrated CCHP system has been presented by Wang et al. [
29]. They employed the genetic optimization algorithm with the purpose of maximizing the energetic and exergetic capacities of the CCHP system. Furthermore, a multi-objective optimization model via a genetic algorithm has been developed by Wang et al. [
30], who proposed an operational flexibility approach determined by the sizes of the photovoltaic (PV) solar panels and gas turbine to improve the CCHP system’s energy savings, cost savings, CO
2 emission and grid integration level. The results obtained illustrate that, although the operational flexibility, as selected by the entropy weighting method, improved the system’s ability to adjust to variable conditions, corresponding decreases in grid interaction level and exergetic, economic and environmental factors were recorded. Song, Liu and Lin [
31] employed the NSGA-II for the multi-objective optimization of a solar-based CCHP system modelled on three operational modes. Utilizing the gas turbine capacity, PV area and solar collector area as decision variables, an optimal solution that maximized the cost saving and energy saving ratio was obtained. The study confirmed that the CCHP system was significantly affected by energy prices and by the efficiencies of the PV, solar collector and gas turbine. The NSGA-II optimization approach was presented by Yousefi, Ghodusinejad and Kasaeian [
8], with the aim of achieving the best microgrid capacities necessary to provide the needed tri-generation loads for a specified structure. They compared the results obtained from an internal combustion engine-based CCHP system and a solar energy-integrated CCHP system. This revealed that the latter had a better performance in terms of primary energy saving and CO
2 emission, though at the expense of a slightly increased net present cost.
The application of the multi-objective greywolf technique has been employed for the optimization of various multi-generation systems. Shakibi et al. [
32] proposed a new solar-assisted CCHP system utilizing the heliostat generation unit and employed the RSM and the greywolf optimizer for the multi-objective optimization of exergy performance and unit cost via six selected decision variables. They utilized the three weight-based methods to determine the optimal exergy efficiency, unit cost and performance coefficient. Asgari et al. [
33] proposed a heliostat solar-based CCHP system incorporated with a phase change material to regulate the heat rate, thus ensuring a constant temperature input to the gas turbine. They employed the multi-objective greywolf optimization in a bid to further increase the exergy efficiency and power generated while reducing the unit product cost. The optimization results show an increase in exergy efficiency, exergy and environmental impact index as well as a decrease in the unit cost and cooling loads when compared with a similar study. Haghghi et al. [
34] employed the greywolf multi-objective technique, coupled with an ANN-based procedure for the optimization of a geothermal-operated poly-generation system. Based on the energy, exergy and economic point of views, the study made use of four distinct approaches that involved the optimization of energy efficiency, investment cost, exergy efficiency and levelized cost. The study achieved its optimization objective of maximizing the energy efficiency and exergy efficiency while minimizing the investment and levelized costs. Habibollahzade and Houshfar [
35] remodelled an ORC-based power generation system in a bid to reduce the emission of CO
2. This was achieved by incorporating a membrane separator to harness an appreciable amount of the CO
2 into a gasifier. Utilizing the greywolf optimizer, the proposed model yielded relatively lower CO
2 emission rates and higher exergy efficiency and cost when compared with a similar study. Furthermore, Zhang and Sobhani [
36] proposed the analysis and multi-objective optimization of a power and freshwater generation system based on the geothermal and gas turbine cycles. The greywolf optimizer was employed to maximize the net power, freshwater production, exergy efficiency and total emission while minimizing the payback period. The conducted sensitivity analysis confirmed that the air-preheater effectiveness on the system performance criteria is predominant. A solar-based system that produces power, cooling capacity, freshwater and hydrogen has been presented by Azizi, Nedaei and Yari [
37]. A thermodynamic analysis of the proposed model was carried out to ascertain the base conditions of the generated electricity, drinking water, cooling capacity and hydrogen. Thereafter, the greywolf optimizer was applied, using two different scenarios, to optimize the unit cost, exergy efficiency and rate of freshwater production. Chen Huang and Shahabi [
26] developed a hybrid CCHP system to reduce the primary energy consumption, CO
2 emission and cost. The study employed a modified version of the greywolf optimizer that is based on the non-dominated sorting theory, variable detection, memory-based strategy selection and fuzzy theory. The obtained optimization results were validated using the multi-objective particle swarm optimization technique.
Behzadi et al. [
38] presented a methanol-fuelled co-generation system consisting of a solid oxide fuel cell (SOFC), heat recovery unit and absorption power cycle (APC). The greywolf multi-objective technique was used to optimize the exergy efficiency and total cost implemented on three different systems, the SOFC, SOFC-ORC and SOFC-APC. The optimization results indicate a better optimal result from the SOFC-APC due to its non-thermal evaporator, condensation process and temperature glide matching. Zhang et al. [
39] conducted an investigation on the feasibility of a biomass-based co-generation system. The investigations were carried out using four biomass fuels, with the best fuel—municipal solid waste—subsequently becoming the subject of the multi-objective optimization and parametric analysis of the system. Optimum results were generated and these maximized the total cost and minimized the CO
2 emissions. Nedaei, Azizi and Farshi [
40] developed a heliostat solar-based multi-generation system comprising the Brayton cycle, absorption refrigeration cycle, humidification, dehumidification, etc. In addition to the conducted thermodynamic exergetic and economic analysis, the greywolf technique was used to compute optimum values for the exergy efficiency, freshwater production rate and unit product cost. Finally, Mahdavi et al. [
5] developed a new, solar-based CCHP system and utilized the RSM for the multi-objective optimization of its net power, CO
2 emission and exergy efficiency. In the developed system, waste heat between the compressors was harnessed by an intercooler to power an absorption chiller. By means of interaction effects between the four decision variables, six optimal solutions were obtained and the technique for order preferences by similarity to ideal solution (TOPSIS) method was used to determine the best solution. Optimal results corresponding to the net power, CO
2 emission and exergy efficiency were obtained.
Table 1 gives a summary of some of the reviewed pieces of literature.
The GWO has been applied successfully in many studies. However, no existing study has used this approach for the CCHP system. Hence, this paper illustrates how the greywolf optimizer could be employed to improve the performance of a solar-based CCHP system.