1. Introduction
In the last 20 years, climate change has become a relevant issue in the global scenario [
1]. As a matter of fact, the global average temperature is constantly increasing, and the effects of greenhouse gas (GHG) emissions in the atmosphere are dramatic [
2]. EU countries have established several strategies to face the climate change issue by increasing the usage of renewables in their systems [
3]. The ever-increasing primary energy consumption in all the energy sectors has led to the necessity of exploiting alternative renewable sources [
4]. Polygeneration systems based on renewable energy sources (RESs) can replace traditional machinery and supply several energy demands, consequently reducing CO
2 emissions and increasing primary energy saving, as renewables are renewed by the environment and release little or even no carbon dioxide [
5]. The concept of the polygeneration system is to exploit one or more renewable sources to simultaneously provide electricity, heating, cooling, and fuels [
6]. In the case of residential applications, instead of producing fuels, these systems are used to produce freshwater [
7]. The adoption of innovative renewable-based systems for residential applications is becoming increasingly proposed in the scientific literature [
8]. Moreover, the study of innovative control strategies to optimize building heating and cooling systems performances is increasingly developing [
9].
Several technologies may be adopted for polygeneration systems, based on the different energy source that is supposed to be exploited [
10]. The most commonly adopted source in the case of residential applications is the solar one. In recent work, Alqaed et al. [
11] proposed a comparative analysis of three polygeneration systems combining in different configurations a desiccant cooling system, an organic Rankine cycle, and a humidification–dehumidification desalination device. N-octane was used as an organic fluid for the ORC cycle. Results for the optimal configuration showed a production of 102 kW for electricity (all systems), 214.7 kg/h of freshwater (System 2), 29.94 kW of heating (System 2), 225.6 kW of cooling (System 1), and an overall energy efficiency of 0.6303 (System 1). In a more recent study [
12], the n-octane solution was compared with other organic fluids such as R245fa, R113, isopentane, and toluene. R113 showed the best result in terms of the energy efficiency of the system.
The polygeneration structure can vary widely to be suitable for different types of buildings and be assessed based on three main indicators, i.e., technical, economic, and environmental [
13]. In particular, Chabaud et al. [
14] evaluated a novel energy resource management approach in a residential microgrid, using energy and economic criteria. A grid-connected building equipped with energy production and storage systems was modeled and simulated. The authors outlined that the combination of photovoltaic (PV) and wind turbine (WT) systems is an interesting energy mix option for residential buildings. Figaj et al. [
15] investigated the energy performance and economic feasibility of polygeneration systems based on biomass, wind turbine, and solar energy for small isolated districts. The polygeneration system also includes thermal and electrical energy storage, an adsorption chiller, and a reverse-osmosis water desalination unit. The proposed system is modeled and simulated through TRNSYS software to dynamically analyze space heating and cooling, electrical energy, and fresh and domestic hot water demands of 10 households located on Pantelleria Island, Italy. Economic results showed that without considering any incentive fee, the simple payback (SPB) of the system proposed ranges between 7 and 12 years. Ceglia et al. [
16] recently presented an environmental, energy, and economic analysis of a polygeneration plant based on a geothermal source for district heating and cooling. The residential district is located in Naples, Italy, and the dynamic energy demand is simulated in TRNSYS. Parametric analyses were performed by ranging the depth of the geothermal well and the usage time of the district. The SPB and the net present value are 7 years and EUR 6.11 M, respectively. From the energy point of view, the yearly saved primary energy is 27.2 GWh, with 5490 tons of carbon dioxide emissions avoided.
Buonomano et al. [
17] showed a thermoeconomic analysis of a polygeneration system consisting of PV and WT (190 kW and 10 kW, respectively), connected to an energy storage system (ESS) (400 kWh). The plant was modeled in TRNSYS to maximize economic benefits. It was considered time-dependent tariffs applied to the electricity exchanged with the grid and the possibility to store electricity. Results presented a remarkable reduction in operating costs. Calise et al. [
18] investigated a thermoeconomic simulation of a polygeneration plant consisting of a solar-assisted heat pump, photovoltaic/thermal collectors (PVT), an adsorption chiller, and an ESS. The system provides domestic hot water (DHW), space cooling and heating, and electricity. Comodi et al. [
19] presented the operational results of a residential microgrid system, consisting of a photovoltaic and solar thermal energy plant, a geothermal heat pump, a tank, and an ESS. The results showed that the self-consumption of photovoltaic energy is maximized by the operation of the ESS, with a reduction of electricity fed back to the grid.
Many of the works presented have been proposed for residential applications in warm countries where the large availability of solar energy allows one to make the polygeneration system more profitable. Many interesting works have been proposed in Spain for polygeneration applied to residential buildings analyzing energy and exergy performances [
20]. Sigarchian et al. [
21] proposed instead a comparative analysis of polygeneration systems in several weather conditions in Iran to analyze the optimal configuration for each case. The analysis shows that in the case of the coldest climate the CO
2 emissions avoided are by 27%, whereas in the warmest case, this value rises to 41%. Unfortunately, the economic feasibility is still far since incentives are needed from the Government to make the systems proposed profitable.
Solar-based systems, namely PV and PVT, are thus widely exploited as renewable energy technologies for the refurbishment of the residential sector. Because of their relevance in this framework, many experimental studies were recently developed to improve their performance. Praveenkumar et al. [
22] recently proposed an experimental study on the optimization of a PV module employing thermos-electric cooling. According to their study, a reduction of roughly 12 ℃ of the PV module temperature, from about 45 ℃ to 33 ℃, lead to an increase in the cell efficiency of 5%. The drawback of the system is the higher capital cost of the technology than the conventional one. Conversely, the levelized cost of electricity (LCE) is almost the same, around 0.41 USD/kWh, for 8760 hours/year of functioning. The reason is the high power generated thanks to the increase in performance. Ultimately, the same author proposed a 5E analysis of a PV module cooled using a fanless central processing unit (CPU) heat pipe [
23]. In this case, the module temperature reduction is 6.7 ℃, with a consequent increase in the average power of 1.66 W. The increase in the electric efficiency is 2.98% for the cooled panel, and the embodied energy recorded is 438.52 kWh. The main findings of the LCE analysis show that in the case of a cooled panel, the cost may range from 0.277 to 0.964 USD/kWh, depending on the hours of functioning. Results for the uncooled panel are close, with an LCE from 0.205 to 0.698 USD/kWh, confirming the relevance of the results obtained.
Furthermore, optimization techniques can be used in polygeneration systems to find their best configuration or to improve performance parameters. Stadler et al. [
24] examined 139 different commercial buildings in California, performing an analysis of the economic and environmental benefits. A mixed-integer linear algorithm was developed to evaluate the building energy costs and CO
2 emissions. Singh et al. [
25] built up a PV–wind system, including biomass and electrical storage. The system matched the electrical load demand of a small-scale zone. In the work, the ideal sizing of components was defined through an artificial bee colony and particle swarm algorithms. The results highlighted the robustness of the algorithm in terms of good-quality results. Destro et al. [
26] investigated the ideal design and management strategy of a trigeneration plant for an isolated hotel in the North of Italy consisting of a PV field, a thermal energy storage (TES), a diesel combined heat and power (CHP) engine, and two ESSs, namely, a pumped hydro and a lead–acid battery. The configuration and operation strategies were defined by applying a particle swarm optimization algorithm to reduce costs and meet the hotel’s consumption of electricity, heating, cooling, and freshwater.
A large number of papers present polygeneration schemes for cooling, heating, electricity, DHW, and desalinated water production. However, to the best of the authors’ knowledge, none of the papers already published include a detailed dynamic thermoeconomic optimization of a polygeneration system based on a solar-assisted desiccant air conditioning (DAC) to supply five demands for the residential sector. To cover such a lack of literature, the present study aims to perform a Hooke–Jeeves optimization to minimize the SPB of a polygeneration system. Furthermore, a sensitivity analysis was performed to investigate the system’s behavior according to the electricity and natural gas prices.
3. Results
The case study is reported by Gesteira et al. [
48]. It consists of a single family dwelling based in Almería, Spain. Meteonorm weather data for Almería (36°50′17″ N, 2°27′35″ W) were used during the simulation. It is worth noting that polygeneration systems applied to European Mediterranean countries can reach up to 80% of energy savings with a suitable level of energy mixture [
49].
Figure 2 displays the building’s 3D view and its floor plan.
The simulation was performed from 0 h to 8760 h (1 year) with a 5 min time step. Firstly, to investigate the system’s best configuration, a parametric study was carried out. Then, a thermoeconomic optimization was used to determine the set of parameters that minimize the simple payback period. For that reason, the number of PV panels, PVT collectors, and primary and secondary TES volumes was optimized. The yearly results of the optimal structure are presented for the main parameters. Finally, a sensitivity analysis was performed to investigate the system’s behavior according to the electricity and natural gas prices.
3.1. Parametric Study
A parametric study was carried out to investigate the most significant design variables when all other parameters remain fixed. The top temperature of the secondary TES (TTES2,top) and the boiler outlet temperature (Tboiler,out) were analyzed as they affect the thermal demand coverages. Furthermore, the study was also performed to define the minimum boiler power capacity (Pboiler). TTES2,top and Tboiler,out were both varied from 45 ℃ to 55 ℃, while Pboiler ranged from 8 to 20 kW.
3.1.1. Parametric Study: Secondary TES Top Temperature
Increasing the T
TES2,top leads to an increase in the DHW coverage, as this temperature ensures the achievement of the hot water setpoint defined for the house. As seen in
Figure 3, the coverage is almost constant for T
TES2,top higher than 49 ℃. Thus, it is not convenient to increase T
TES2,top over 49 ℃, as the maximum DHW coverage is already achieved.
3.1.2. Parametric Study: Boiler Outlet Temperature
The boiler outlet temperature affects all thermal demands. The minimum T
boiler,out is equal to T
TES2,top, which was already defined in the previous analysis. T
TES2,top of 49 ℃ ensures the maximum DHW coverage. However, the maximum HVAC coverage was not achieved yet. The increase in the T
boiler,out provides a higher temperature for the heating fan coil and the DAC regenerator.
Figure 4 shows that the coverages are directly proportional to the boiler outlet temperature. The heating and cooling coverages increased from 96% to 102% and from 97% to 104%, respectively. Therefore, there is no energy convenience to increase T
boiler,out to values higher than 51 ℃. This temperature was selected as a setpoint for the boiler as it provided the maximum coverage for both cooling and heating demands.
3.1.3. Parametric Study: Boiler Power Capacity
The BB adds heat to the flow stream at its power capacity (P
boiler) whenever the boiler outlet temperature (T
boiler,out) is less than a setpoint. It performs like an auxiliary heater with an internal control to maintain T
boiler,out fixed. The boiler power is related to the capacity of providing an outlet temperature whenever it is required during the simulation. The minimum power capacity commercially available was considered 8 kW.
Figure 5 shows the correlation between the P
boiler and the thermal coverages. The DHW coverage can be satisfied for all capacities due to its lower temperature requirement. Lower power capacities affect cooling, which achieves 100% at 9 kW. Heating shows the same trend as the others’ demands; however, it only meets full coverage at 12 kW. Thus, the power capacity of 12 kW was selected for the boiler as it provided 100% coverage for all house thermal demands.
3.2. Thermoeconomic Optimization
A thermoeconomic optimization was implemented using the TRNOPT tool included in the TRNSYS simulation studio. TRNOPT is designed to link the optimization algorithm and the dynamic simulation. A complex mathematical algorithm is performed by the GENOPT package developed by Lawrence Berkeley National Laboratory [
50]. In particular, the Generalized Search Method was used in the optimization by the Hooke–Jeeves [
51] modified algorithm. The optimization was performed considering the main design variables, namely: the number of PVT collectors (N
coll), number of PV panels (N
pan), primary TES volume (V
TES1), and secondary TES volume (V
TES2). Moreover, the SPB was selected as the optimization objective function.
Table 4 shows the details of the main variables. The optimization range is defined by its minimum and maximum values. The first attempt starts with the initial value and proceeds with the iterations according to the step size.
Figure 6 shows the SPB and the design variables as a function of the optimization iteration. The optimization process converged in a bit over 150 iterations. The optimal configuration is obtained when the SPB achieves its minimum value. The optimum SPB value of 20.68 years was obtained for 9 PVT collectors, 25 PV panels, and a primary and secondary TES volume of 1.35 m
3 and 0.25 m
3, respectively. Moreover, it is worth noting that the number of collectors and panels was limited to 50 m
2 due to the available roof area at the house.
3.3. Yearly Results
The annual results for the optimal solution are summarized in
Table 5. The table presents the yearly integrated number of electricity, heat, and water volume. Moreover, the performance parameters are also presented. The building demands were taken from Ref. [
48].
The power generation (Ptot,prod) is the PV (PPV) and PVT (PPVT) generation minus the losses (Ploss) due to the inverter’s inefficiency (10%). The excess power is injected into the grid (12.64 MWh/yr).
The total useful heat production (Qtot,prod) is the PVT heat generation (QPVT) and the BB production (Qboiler) subtracted by the energy released by the AH (QAH) and the total energy dissipated to the surroundings (Qloss). The heat released by the AH is about 12% of QPVT. Moreover, Qtot,prod is used for attending QDHW,dem, Qheat,dem, and Qcool,dem; however, as the DAC thermal COP is equal to 0.37, the heat requested by the regenerator was 4.43 MWh/yr.
3.4. Sensitivity Analysis
A sensitivity analysis investigated how electricity purchase, electricity sell-back, and natural gas prices affect the economic performance of the PS. Thus, the purchasing costs were progressively increased, and the sell-back price was reduced (
Table 6). Each parameter was evaluated for each case, and the optimization results were collected.
3.4.1. Sensitivity Analysis: Purchase Cost of Electricity
Considering that the RS is based on the consumption of electricity, the increase in the energy price worsens economic performance. Conversely, in the PS, electricity may be sold back to the grid. Thus, higher energy cost enhances its economic performance because the sell-back cost of electricity is a ratio of the electricity purchase cost. The increase in the electricity cost leads to an increase in the operational cost of the RS and improves the economic savings of the PS.
Figure 7 displays the sensitivity analysis of the electricity purchase cost.
The number of PV panels remains constant at 25 for all cases simulated. The number of PVT collectors increases from 9 to 24 between the second and third cases. At the same point, the volume of the primary TES increases, following the higher thermal energy availability, and the secondary TES volume decreases. It demonstrates that as of Case 3, the energy cost becomes very expensive; thus, the electricity sold back to the grid is more attractive, as it is proportional to the purchase cost. Therefore, electricity production increased to its maximum. The SPB decreases to 6.38 years when the purchase cost of electricity increases up to 250%.
3.4.2. Sensitivity Analysis: Purchase Cost of Natural Gas
The RS is also dependent on natural gas consumption; thus, the increase in the energy price worsens the economic performance. On the other hand, the PS is not affected by the natural gas cost. The increase in the natural gas cost leads solely to an increase in the operational cost of the RS. Therefore, the SPB decrease is slighter compared to the previous case.
Figure 8 displays the sensitivity analysis of the natural gas purchase cost.
The number of PV panels remains constant at 25 for all cases simulated. The number of PVT collectors and the primary and secondary TES volumes present a minor variation around 7, 0.8 m3, and 0.3 m3, respectively. The SPB decreases 15.81% from the base case to the last case, while the purchase cost of natural gas increases up to 250%.
3.4.3. Sensitivity Analysis: Sell-Back Cost of Electricity
In the PS, electricity may be sold back to the grid with a price defined as a ratio of the electricity purchase cost. Thus, a lower sell-back cost worsens its economic performance. The decrease in this ratio leads to an increase in the operational cost of the PS.
Figure 9 displays the sensitivity analysis of the sell-back cost of electricity.
Again, the number of PV panels remains constant at 25 for all cases simulated. The number of PVT collectors and primary and secondary TES varies between 8 to 12, 1.35 to 1.88 m3, and 0.25 to 0.28 m3, respectively. It indicates that the system design is relatively constant along the iterations. However, the SPB increases to 39.61 years when the sell-back cost of electricity decreases to 30% of the purchase cost.