Optimization of a novel polygeneration system integrating photovoltaic/thermal collectors, solar assisted heat pump, adsorption chiller and electrical energy storage

In this paper a model for the dynamic simulation and the optimization of a novel solar polygeneration system is presented. The system is based on a flat-plate photovoltaic/thermal collector solar field, coupled with water-to-water electric heat pump/chiller, adsorption chiller and electrical energy storage technologies. The system is modelled to supply space heating or cooling, domestic hot water and electrical energy. The produced electrical energy is self-consumed by both user and system auxiliary equipment, stored and/or supplied to the grid. For the simulation purpose, a detailed building model and a comprehensive electrical energy model, taking into account the electrical energy storage and exchange with the grid, are implemented. This paper is a further development of a recent work previously presented by the authors, where measured electrical demands of real users are used in the simulation and a comprehensive energy-economic analysis is performed. The present paper deals with a comprehensive sensitivity analysis and an optimization of the polygenerative system under investigation. In particular, energy and economic objective functions are used and the optimal set of design parameters are calculated, using the computer-based Design of Experiment procedure and the Generalized Search Method. The main effects plots and contour plots are discussed for the selected objective functions, while the optimum values of selected parameters, obtained with both optimization methods, are compared.


Introduction
In the last decades, issues regarding the climate change, depletion of fossil fuels and pollution caused by the use of conventional energy sources caused a radical change of the energetic world scenario. Concepts regarding sustainable development, energy saving, greenhouse gas emissions reduction and the use of renewable energy sources become important for the modern society. From the point of view of energy production and consumption, different sectors have been influenced by this aspects: industry, transport, buildings, etc. In particular, the building heating and cooling sector is subject of significant attention of international organizations and government policymakers like the International Energy Agency (IEA) [1] and the European Union (EU) [2]. In particular, several European Directives dealing with reduction of electrical/thermal energy consumption and with the use of renewable energy sources have been launched [3,4]. In this framework, technical solutions regarding solar collectors and heat pump technologies are interesting alternatives in order to match the goals of renewable energy use and energy saving [5]. These solutions, namely Solar Assisted Heat Pumps (SAHP), are extensively investigated in literature. For example, an optimum configuration of PhotoVoltaic (PV) and solar thermal collectors coupled with air to air or ground water heat pumps was studied by Ochs et al. [6]. The authors found that a small solar thermal system is better from the energy point of view with respect to a PV one. The analysis also revealed that the seasonal coefficient of performance of the ground water heat pump ranges from 4.0 to 5.7 when the share of solar thermal energy and the number of floors are varied. Chow et al. [7] studied the coupling of PhotoVoltaic/Thermal (PVT) collectors and heat pumps developing a simulation model. Under the climatic conditions of Hong Kong, the results showed that a conventional heat pump plus PV "side-by-side" system achieves a lower performance than a PVT-heat pump coupled system. For the last configuration, a year average Coefficient Of Performance (COP) of 5.93 and a PV efficiency of 12.1% were achieved. Other interesting studies were developed by Hazi and Hazi [8] and Bellos et al. [9]. In both papers, comparisons of different SAHP systems were carried out.
The possible energy saving measures in buildings sector include also the electrical energy management/consumption strategy coupled with storage systems. Energy and economic criteria are used by Chabaud at al. [10] to evaluate a novel energy resources management approach in a residential microgrid. The authors determined that shifting some domestic loads from on-peak to off-peak periods using an electricity storage impacts on the performance of the system. Koh and Lim [11] used an electrical load measured in a building to evaluate the viability of energy storage systems. The analyzes highlighted that the installation of an energy storage system determines a reduction of the overall cost of the system. A system consisting of six apartments, solar thermal and photovoltaic collectors, a geothermal heat pump, a tank and two electrical energy storages was investigated by Comodi at al. [12]. The results outlined that the self-consumed energy was about 60% of the produced one, and 3000 hours of microgrid self-sufficient operation are achieved.
As outlined by the available literature, solar heating/cooling and electrical energy storage systems based on renewable energy sources are extensively investigated as technical solutions in buildings. Conversely, the investigation of complex polygenerative systems based on the mutual integration of these technologies is scarce. Hence, in order to reduce the lack of information regarding the coupled integration of solar heating/cooling and electrical energy storage solutions, the authors present a dynamic simulation of a novel polygenerative system. In particular, the system is based on PVT collectors, reversible heat pump, adsorption chiller and battery storage. The developed system was investigated by the authors in a previous work [13], where the dynamic operation of the system, weekly energy flows, energy and economic performance and sensitivity analyzes were performed with Transient System Simulation (TRNSYS) software. The analyzes were carried out under different Italian climatic conditions, for office and fitness center user, with and without electric energy storage and with two different modes for the electrical energy exchange (net metering and simplified purchase/resale arrangement contracts). Conversely in this study, the energy and economic optimization of the novel polygeneration system under the climatic condition of Naples, Italy, is presented. This climatic condition is typical of the Mediterranean region, with moderate winters and warm summers. The yearly solar radiation of Naples is about 1.6 -1.7 MWh/m 2 , which is significantly higher to center Europe countries as Germany and Poland, where the solar energy availability is about 1.0 to 1.2 MWh/m 2 [14].
In particular, the case study achieving the best economic performance is optimized, consisting of fitness center user and net metering contract. Moreover, in order to perform a comprehensive analysis, the system with electrical energy storage is considered in the optimization procedure. Both computerbased Design of Experiment (DoE) analysis and Generalized Search Method were used to perform the optimization. It is worth noting that the radiation characteristic of specific locality determine the performance of PV/PVT panel [15], however the effect of different climatic conditions (solar 2. System layout and operating principle The proposed system is designed to match the space heating/cooling demand of the user during the heating/cooling season and the Domestic Hot Water (DHW) one all year long. The system produces also electrical energy that consumed by the user, stored or supplied to the electrical grid. In Figure 1 [13], the layout and the main components of the polygeneration system are shown. The system layout is based on several fluid loops and electrical flows. The system integrates several main components: photovoltaic/thermal collector field (PVT), solar thermal storage (TK1), two tanks (TK2, TK3), solar loop heat exchanger (HE), auxiliary boiler (GB), reversible heat pump/chiller (HP), adsorption chiller (ADS), well (WE), fan-coil units (FC), electrical energy control device (R/I), electrical energy storage, (BATT), variable and fixed speed pumps (P) and valves managing the fluid loops (M,D). The layout is also completed with other mandatory components (not reported in Figure 1 for sake of clarity) included in order to monitor and control the system. A comprehensive operating and control strategy of the system is reported in ref. [13], thus, here only a brief description is provided. During winter, the PVT field produces thermal energy that is supplied to the evaporator of the heat pump by means of the solar tank. The space heating demand is matched by the thermal energy provided by the heat pump condenser and hydronic system. DHW is produced only the solar tank is thermally loaded. The heat pump is activated in order to ensure the hydronic tank temperature within a fixed range (45 -48°C), allowing a propped operation of the fancoil system. During summer, the PVT field supplies thermal energy to the generator side of the adsorption chiller, which absorber side provides the cooling effect needed to ensure a proper temperature of the hydronic tank (12 -14°C) for space cooling operation. DHW is produced in case of a surplus of produced solar thermal energy. The reversible heat pump is activated when the adsorption chiller driving temperature is not ensured (at least 55°C) and/or the hydronic tank temperature is too high (16°C). The surface aquifer is used to dissipate the heat rejected by the absorption chiller and heat pump.
The produced electrical energy is firstly consumed by the user. If the power output is higher than the demand, the energy is used to charge the battery if it is not fully charged. In case of charged battery, the excess electrical energy is supplied to the grid. Moreover, in case of low or no solar radiation and charged battery, this one supplies the user in order to match the demand, conversely the electrical grid is used. Moreover, the user is supplied by the electric grid also when the battery power output is lower than the electrical energy demand.

Simulation model
The proposed system was modelled and dynamically simulated with TRNSYS software [16]. In order to develop the simulation model of the system both built-in validated components and user defined ones have been used. In particular, control system, electrical energy management, energy and economic models have been developed by the authors. The software features allowed to calculate the dynamic operation of the system in terms of temperature and power profiles, while the integration capability was used to determine the system energy and economic performance on a weekly and yearly time basis [13]. All the simulations were carried out for a one year period (for 0 to 8760 h) and with a 0.05 h time step.
The models of the build-in components used in the simulation are available the software reference [16], while the ones developed by the authors are available in the previous paper dealing with the investigated system [13], thus are omitted for sake of brevity In particular, the energy and economic model was developed in order to evaluate the performance of the proposed system. This model calculates the primary energy and economic saving, along with the Simple Pay Back (SPB) period, assuming a reference system consisting of a natural gas boiler for DHW, a reversible air-to-air conditioning unit and the public grid for matching the electric demand of the building. Obviously, the model assumes that the same amount of energy (heating, cooling, power and DHW) is supplied by both reference and proposed systems. As concerns the operating costs of the reference system (RS), they are due to natural gas consumption and the operation of electrical devices, while the possible economic savings achieved by the proposed system (PS) with respect to RS are due to: -PVT field production of thermal energy, supplied in part to the evaporator of the heat pump and for the remaining one used to produce DHW; -electric energy output of the PVT field, which is in part self-consumed by the user and in the remaining part remunerated by the electric grid contracts, Net-Metering (NM) or simplified Purchase/Resale arrangement (PR); -lower electrical energy consumption of the water-to-water heat pump with respect to the air-to-air one, due to a higher COP; -electrical energy consumption avoided due to the operation of the adsorption chiller instead of the electric chiller.
Furthermore, 2% of the cost of the solar field was assumed for the maintenance cost of the PVT system. The operating cost of PS were calculated taking into account of the two possible electric energy contracts. The annual operating costs for PS with MN contract are expressed as follows , , , where PPS,buy,grid is the power supplied by the grid (kW), jel,buy,NM is the electrical energy tariff for NM contract (€/kWh), Eth,DHW,GB thermal energy consumed by GB (kWh), LHVNG is the lower heating value of natural gas (kWh/Sm 3 ), ηRS,DHW is the thermal efficiency of GB (-), jNG is the natural gas price (€/Sm 3 ), CPVT is the cost of the solar field (€), Ctariff,NM is the tax for NM contract (€), PPS,sell,grid is the power supplied to the grid (kW), jel,sell,NM is the sell tariff of electrical energy for NM contract (€/kWh), Cnet,NM is the adjustment of the annual saving concerning the sold electrical energy (€) and Csell,batt is the revenue due to the sale of sale of the eventual electrical energy stored by the battery at the end of the year (€). For PR contract the same calculation was performed.
Detailed information about the implemented model of the whole system is available in ref. [13].

Case study
In the previous paper of the authors [13], fitness centre and office users were investigated, conversely here only the first one was selected as case study in order to perform the optimization analysis. The previous analyses showed that the energy and economic profitability of the system in case of office user is scarce for any investigated configuration, thus, the fitness centre user was selected. In order to perform the simulation, Meteonorm weather data of Naples, South of Italy, was used. The case study building (Figure 2), consisted of a one-floor structure, with 5 zones and a flat roof. Both roof and floor were assumed of 600 m 2 and the floor height was 3.00 m. The space heating or cooling thermal was provided with an independent fan coil system per each zone of the building, operating from 16 th November to 31 st March (space heating) and from 1 st April to 15 th November (space cooling). Different operating hours for week and weekend days were considered [13].
The Google SketchUP tool and TRNSYS3d plug-in were used to develop and implement the building 3D model, respectively. The thermal model of the building was completed with building envelope components (wall, roof and floor) data and dynamic internal thermal loads.
The electrical demand of the user has been determined on the basis of measured data, and a realistic user profile of DHW demand was implemented. The system design and operation parameters were selected in order to match the user demand and to achieve a proper operation of the system.
A measured electrical demand of real fitness center user was used to simulate the electrical demand of the case study ( Figure 3). The thermal demand, calculated on the basis of dynamic simulation, is shown in Figure 4.   In ref. [13], the main parameters are reported. It is important to note that a parametric design approach was used, allowing to select automatically the capacities of the components on the basis of the main design parameters.

Optimization procedures
In this paper, computer-based Design of Experiment (DoE) analysis and the Generalized Search Method (GSM) were used to perform the optimization procedure. The DoE analysis is a repetition of experiments performed in order to analyse the effect of variables and parameters on the wanted results/output parameters. In the performed DoE analysis, the conventional experiments were replaced with simulations of the developed system model. In particular, the DoE analysis has been used in order to: evaluate the effect of design variables on the selected objective functions, determine the relative interaction plots, obtain the optimal response surface for the objective function and determine the optimum configuration. The optimization performed with GSM was carried out by means of the TRNOPT plug-in tool, available in the TRNSYS software package [16]. In particular the Hooke-Jeeves modified algorithm [17] included in the GENOPT package developed by Lawrence Berkeley National Laboratory [18]. was used. This algorithm uses the TRNSYS solving method for the objective function calculation and avoids the achievement of local minimum points. For both DoE and GSM procedures the following design variables have been considered: PVT collector field area (APVT), number of batteries (Ncell), specific volume of the solar tank (vTK1), winter and summer PVT collectors set-point temperature when the solar tank is supplied (TPVT,wint, TPVT,sum). In particular, in the DoE analysis, 4 levels for each design variable have been taken in to account (Table 1), determining the run of 1024 different simulations. It is important to note that the ranges of the design variables were accurately selected, taking into account the technical constrains (especially temperatures) needed to ensure proper operation of the system components.

Results and discussion
The main effect plots for SPB value are reported in Figure 5. The main effects plots are used to show how each design parameter affects the selected objective function trend and to outline the mean value of the selected objective function for each level of the considered design parameter.
As expected, the most significant parameters affecting the value of SPB are the capacities of PVT solar field, solar storage tank and electrical energy storage. Conversely, the set point temperatures of the solar collectors scarcely affect the economic performance of the system. In particular, the SPB value increases almost linearly when the electrical storage and tank capacities vary. Lower are the value of capacities of such components, better is the economic profitability of the proposed system. However, the effect of TK1 volume value is more significant compared to the electrical energy storage capacity. Apart from the different costs of both components, this is due to the fact that the thermal storage scarcely affects the thermal energy production and thus the economic saving of the system. As a consequence, the increase of the tank volume (cost) leads only to an increase of total investment cost without any saving benefits. Conversely, the electrical storage capacity determines the amount of electrical energy self-consumed and supplied from/to the grid, therefore it definitively affects the economic saving. Moreover, it is worth noting that the main effect for the PVT area is not a monotone function, thus an optimum value can be identified.
Furthermore, the main effects plot for PES (not reported for sake of brevity) show that the trends are almost linear in case of the PVT area and TK and BATT capacities parameters, while the set point temperatures do not affect the value of PES. As expected, higher are the PVT area and the number of battery cell, higher is PES. Conversely, increasing the solar tank volume, PES decreases due to the higher thermal losses and higher charging times.
The contour plots of SPB optimal response surfaces are showed in Figure 6. Here, also the information available from the interaction plots (where only one parameter per time is varied, fixing the remaining ones) is included.    In Figure 6, ten subplots showing all the possible combinations of the five considered design parameters are reported. In particular, each subplot refers to the product of the two considered independent variables when all the remaining variables are kept constant (see hold values). In such figure, it is clearly shown that the best economic profitably of the proposed system is achieved when the minimum capacity of the solar tank and electrical storage capacity are selected. Moreover, the results also outline that for each system design configuration there is a value of the PVT field area that allows to achieve a minimum SPB. As outlined by the main affects plot, the variation of the PVT set point temperatures during winter/summer slightly affects the profitability of the system, since the lowest gradients are achieved for such parameters. As expected, the contour plots achieved for PES (not reported for brevity) highlight that the maximum primary energy is achieved the maximum PVT area and electrical storage capacity along with the lowest solar tank capacity are considered.

Mean of SPB
Finally, the selected objective functions have been optimized by means of the optimum response surface results achieved in the DoE analysis. In particular, the set of selected design parameters minimizing and maximizing the SPB and PES values, respectively, was determined. The optimal solutions for the objective functions and the reference values achieved in Ref. [13] are reported in Table 2. The results show the same values of selected design parameters except the one for PVT field are achieved for the optimization of SPB and PES objective functions. According to the previous results, maximum PES is achieved of the maximum PVT area, conversely, the optimal area value from the economic point of view is lower (about 244 m 2 ). The optimal economic configuration of the system allows one to reduce the SPB of about 2 years compared to the initial value, while only a slight increase can be achieved in case of PES optimization.  The different optimal results are achieved because the GSM incurred in a local minimum value. This condition is extremely probable with a GSM approach since the complexity and not linearity of considered system model is high. Therefore, according to this result, a repetition of the GSM optimization was performed successively. The second optimization run (    10

Conclusions
In the presented paper, a comprehensive sensitivity analysis and an optimization of a polygenerative based on photovoltaic/thermal collectors, electric heat pump/chiller, adsorption chiller and electrical energy storage technologies was performed. Both computer-based Design of Experiment procedure and the Generalized Search Method were used. The results show that: -the most significant parameters affecting the value of SPB and PES are the capacities of PVT solar field, solar storage tank and electrical energy storage, while the effect of winter/summer PVT set point temperatures variation is scarce; -the optimum set of design parameters reduces SPB of about 2 years, with respect to 16.6 years; -different optimal results are achieved because performing the GSM incurred in a local minimum value, due to the complexity and not linearity of considered system model, thus particular attention must be paid when performing such optimization procedure.