Fuzzy Logic Energy Management Strategy of a Multiple Latent Heat Thermal Storage in a Small-Scale Concentrated Solar Power Plant

: Latent heat thermal energy storage (LHTES) systems allow us to e ﬀ ectively store and release the collected thermal energy from solar thermodynamic plants; however, room for improvements exists to increase their e ﬃ ciency when in operation. For this reason, in this work, a smart management strategy of an innovative LHTES in a micro-scale concentrated solar combined heat and power plant is proposed and numerically investigated. The novel thermal storage system, as designed and built by the partners within the EU funded Innova MicroSolar project, is subdivided into six modules and consists of 3.8 tons of nitrate solar salt kNO 3 / NaNO 3 , whose melting temperature is in the range 216 ÷ 223 ◦ C. In this study, the partitioning of the storage system on the performance of the integrated plant is evaluated by applying a smart energy management strategy based on a fuzzy logic approach. Compared to the single thermal energy storage (TES) conﬁguration, the proposed strategy allows a reduction in storage thermal losses and improving of the plant’s overall e ﬃ ciency especially in periods with limited solar irradiance. The yearly dynamic simulations carried out show that the electricity produced by the combined heat and power plant is increased by about 5%, while the defocus thermal losses in the solar plant are reduced by 30%.


Introduction
The building sector accounts for about 40% of the final energy consumption and 36% of CO 2 emissions in Europe [1]. In order to curb the share of the sector on the final energy consumption and the related environmental impact, the European Union is pushing towards an improvement in the energy efficiency of buildings and an increase in renewable energy technologies' penetration into the grid [2]. Among the different renewable energy technologies, Concentrated Solar Power (CSP) plants in combination with Combined Heat and Power (CHP) systems [3] are foreseen as a valuable alternative to substitute thermal and electric power generation from fossil fuels. So far, a good contribution in this direction has been given by the introduction of concentrated evacuated tube collectors due to their optimal compromise between cost and conversion efficiency, promoted by recent progress in manufacturing [4]. One way to convert low and mid-temperature energy sources into power may be represented by the adoption of Organic Rankine Cycle (ORC) systems that can be also easily inserted in fuzzy logic controller, which manages the thermal storage connections, has been considered for the micro solar plant already modeled by the authors in previous studies [16,22,23]. It consists of a 2 kWe concentrated solar ORC system coupled with a LHTES equipped with reversible heat pipes [24], which is going to be tested in the city of Almatret, Spain, under the framework of the H2020 Innova MicroSolar project [25], made up of a consortium of three EU Universities and six EU companies, coordinated by Northumbria University. With reference to the LHTES, it consists of 3.8 tons of Solar Salt, whose melting temperature is in the range 216-223 • C [26].
To the best of the authors' knowledge, some studies in the literature already addressed the influence of TES subdivision [14,27], as described above, but none of them referred to subdivided LHTES (sub-LHTES) operated with fuzzy logic control. Therefore, in this paper, the authors apply this logic to investigate the effects of the storage subdivision and its smart management on the performance of the overall plant. Hence, the main novelties of the work rely on: (i) the development of a fuzzy logic approach to sub-LHTES systems; (ii) the assessment of the influence of the smart management of the sub-LHTES on the performance of the small-scale integrated plant and its comparison with the system in its standard configuration.
Hence, after the introduction, Section 2 briefly reports the methodology of the work, Section 2.1 describes the global system where the new control logic is tested, Section 2.2 illustrates the sub-LHTES model on which this study is based and Section 2.3, the fuzzy logic control in detail. In Section 3, the effects of the sub-LHTES smart management on the performance of the integrated system are reported and eventually, in Section 4, the main conclusions are drawn.

Methodology
A dynamic model of the Innova MicroSolar plant was developed in Matlab/Simulink [28] and the performance of the integrated system assessed in terms of electric and thermal efficiency and energy production. The control logic implemented into the model aims at producing electricity at its maximum, whilst the thermal load is considered as a by-product, which can be usefully collected by final users. In particular, the cascade fuzzy logic controller has been implemented to improve the operational management of the thermal storage with the purpose of increasing the global performance of the plant. Eventually, the obtained performance of the integrated system is compared with that of the plant operating at the same ambient conditions, but with a single LHTES without a smart control management.

The Micro Solar CHP Model
The following main components have been included into the model: (i) the LFR solar field; (ii) the micro ORC plant; and (iii) the Phase Change Material (PCM) thermal energy storage tank equipped with reversible heat pipes. Specific subroutines for the LFR solar field, the ORC unit and the PCM storage tank equipped with heat pipes have been developed by the authors in Matlab as extensively discussed in reference [16]. In particular, the LFR and ORC subsystems are quasi-steady state models, whilst the thermal storage is a purely dynamic model. In order to take into account the thermal losses of the tubes connecting the different subsystems and the influence of their thermal inertia, a 1D longitudinal model of the pipelines has also been included, as further explored in reference [29]. The different subroutines were validated with available performance data from the manufacturers, as better discussed in reference [16].
Depending on the solar radiation and the state of charge of the LHTES, the integrated plant works according to different operation modes (OM), which are detailed in Table 1. Indeed, the diathermic oil from the solar field flows to the LHTES and/or directly to the ORC, based on its temperature and on the amount of power collected at the receiver. In the following, the different operation modes are described: • OM1: the oil flow rate through the LFR is adjusted to maintain 210 • C as the outlet temperature when the collected solar power is greater than 15 kWth.
• OM3: if the solar power is below 15 kWth, the ORC does not operate, while the thermal storage (if not fully charged, T TES,av < 215 • C) is charged and the LFR outlet temperature set-point is kept 10 • C higher than the LHTES temperature to contrast the thermal losses. • OM4: if the solar radiation is even higher than the power needed by the ORC, the thermal storage is also recharged and when it goes above the limit of 280 • C, defocus occurs to reduce the collected thermal power (OM1). • OM5 and OM6: when the power produced by the solar field is low or zero but the average TES temperature is within a given operating range (hysteresis cycle between T ORC,on = 217 • C and T ORC,off = 215 • C), the thermal energy of the TES can be used to run the ORC unit together with energy from the LFR (OM6) or even with no sun (OM5) for a maximum of 4 h. In this work, the LHTES is modelled as subdivided into six modules (sub-LHTES), as reported in Figure 1, and each of them may have a distinct operation and temperature level. The TES control unit monitors their state of charge and sends signals to the main control system to choose the number of modules in operation, according to a fuzzy logic approach. OM4: if the solar radiation is even higher than the power needed by the ORC, the thermal storage is also recharged and when it goes above the limit of 280 °C, defocus occurs to reduce the collected thermal power (OM1). • OM5 and OM6: when the power produced by the solar field is low or zero but the average TES temperature is within a given operating range (hysteresis cycle between TORC,on = 217 °C and TORC,off = 215 °C), the thermal energy of the TES can be used to run the ORC unit together with energy from the LFR (OM6) or even with no sun (OM5) for a maximum of 4 h. In this work, the LHTES is modelled as subdivided into six modules (sub-LHTES), as reported in Figure 1, and each of them may have a distinct operation and temperature level. The TES control unit monitors their state of charge and sends signals to the main control system to choose the number of modules in operation, according to a fuzzy logic approach. The dynamic performance of the integrated system is simulated in Matlab/Simulink for a whole year. Weather data in terms of solar radiation and ambient temperature have been taken from Meteonorm database for the city of Lerida, Spain, since it is close to the location where the prototype plant is installed. The dynamic performance of the integrated system is simulated in Matlab/Simulink for a whole year. Weather data in terms of solar radiation and ambient temperature have been taken from Meteonorm database for the city of Lerida, Spain, since it is close to the location where the prototype plant is installed.

The Thermal Storage Model
The thermal storage has been designed to guarantee 4 h of ORC unit operation with a nominal input power of 25 kW, thus a total of 100 kWh. This thermal energy storage system, as designed by Northumbria University and Aavid Thermacore [30] and investigated by the team at Lleida University [31], consists of 3.8 tons of nitrate solar salt kNO 3 (40 wt.%)/NaNO 3 (60 wt.%), whose melting temperature is in the range 216 ÷ 223 • C [32]. Reversible heat pipes, developed by Aavid Thermacore, enhance the heat transfer between the PCM and the heat transfer fluid. The mathematical model follows the guidelines described in the International Energy Agency IEA Task 32 report on advanced storage concepts [33], where a detailed description of Type 185 for the Trnsys simulation tool [34] is provided. The model is based on the following main assumptions: (i) material isotropic and isothermal in each internal time-step; (ii) no hysteresis and subcooling effects; and (iii) charging and discharging are not simultaneous. The presence of heat pipes is modelled by both limiting the maximum power exchanged to 40 kW and fixing a minimum temperature difference between the oil and the PCM equal to 5 • C (asymptotic condition).
Hence, the temperature variation of the PCM due to the heat exchanged can be obtained by: where f is a function of both PCM and oil thermal properties. Then, from the temperature variation of the PCM, it is possible to calculate the heat exchanged as: During the LHTES operation, the power released or acquired is affected by the heat exchange characteristics among diathermic oil, heat pipes and PCM material. This aspect is crucial on the performance of the whole plant, e.g., a slow or ineffective heat extraction from the thermal storage could cause LFR defocusing or low inlet temperature into the ORC inlet. For a better understanding of the power amount available at different oil temperatures, Figure 2a

The Thermal Storage Model
The thermal storage has been designed to guarantee 4 h of ORC unit operation with a nominal input power of 25 kW, thus a total of 100 kWh. This thermal energy storage system, as designed by Northumbria University and Aavid Thermacore [30] and investigated by the team at Lleida University [31], consists of 3.8 tons of nitrate solar salt kNO3 (40wt.%)/NaNO3 (60wt.%), whose melting temperature is in the range 216 ÷ 223 °C [32]. Reversible heat pipes, developed by Aavid Thermacore, enhance the heat transfer between the PCM and the heat transfer fluid. The mathematical model follows the guidelines described in the International Energy Agency IEA Task 32 report on advanced storage concepts [33], where a detailed description of Type 185 for the Trnsys simulation tool [34] is provided. The model is based on the following main assumptions: (i) material isotropic and isothermal in each internal time-step; (ii) no hysteresis and subcooling effects; and (iii) charging and discharging are not simultaneous. The presence of heat pipes is modelled by both limiting the maximum power exchanged to 40 kW and fixing a minimum temperature difference between the oil and the PCM equal to 5 °C (asymptotic condition).
Hence, the temperature variation of the PCM due to the heat exchanged can be obtained by: where f is a function of both PCM and oil thermal properties. Then, from the temperature variation of the PCM, it is possible to calculate the heat exchanged as: During the LHTES operation, the power released or acquired is affected by the heat exchange characteristics among diathermic oil, heat pipes and PCM material. This aspect is crucial on the performance of the whole plant, e.g., a slow or ineffective heat extraction from the thermal storage could cause LFR defocusing or low inlet temperature into the ORC inlet. For a better understanding of the power amount available at different oil temperatures, Figure 2   From the figures above, it is evident the power gain available within the melting region and this is the reason why the ORC is set to operate between 215 and 217 °C (TORC,off, TORC,on, respectively). The represented charging phase refers to 3 kg/s of inlet oil flow rate at 280 °C. Similarly, during the discharging phase, PCM is initially at the maximum temperature of 280 °C and heat is removed by oil from the ORC at design conditions (oil temperature 150 °C and oil flow rate 0.22 kg/s).  From the figures above, it is evident the power gain available within the melting region and this is the reason why the ORC is set to operate between 215 and 217 • C (T ORC,off , T ORC,on , respectively). The represented charging phase refers to 3 kg/s of inlet oil flow rate at 280 • C. Similarly, during the discharging phase, PCM is initially at the maximum temperature of 280 • C and heat is removed by oil from the ORC at design conditions (oil temperature 150 • C and oil flow rate 0.22 kg/s).

The Fuzzy Logic Controller
The fuzzy logic controller has been implemented based on the following assumptions [23]. First of all, to ensure an effective charging of the thermal storage, the LFR plant must supply oil at a temperature higher than the storage temperature to cover the thermal loss in the piping system (10 • C is the temperature difference assumed). Due to the different temperature of each module, the control system checks the maximum temperature of the current connected sub-LHTES module and supplies all the connected modules with a temperature higher than that. Secondly, during the discharging phase, corresponding to OM5 and OM6 (Table 1), the connected sub-LHTES must have a temperature suitable for the ORC supply, thereby the control system of the storage allows the connection only of the modules with a temperature higher than the temperature of the ORC inlet oil. Third, the oil flow rate is split equally among the sub-LHTES both in the charging and discharging phase.
The fuzzy logic controller has been designed according to a cascade approach to accomplish the following tasks: (i) select the number of modules to be connected with the plant; and (ii) manage each module based on a priority scale set out by the previous decision. In general, the performance of the plant can benefit from the subdivision of the LHTES. For example, when the solar radiation is high and the sub-LHTES is not fully charged, connecting a high number of modules allows mitigating of the temperature overheating of the LFR solar field, thus avoiding the inefficient defocusing of some mirrors [14]. On the contrary, when the solar radiation is low, it is convenient to connect and charge as few modules as possible so that the temperature of the storage medium is higher. Therefore, a close relationship exists between the outlet temperature of the diathermic oil from the LFR solar field and the number of modules to be connected. For this reason, a logarithmic function, shown in Figure 3, has been chosen to correlate the diathermic oil outlet temperature from the solar field with the number of modules to be connected. The LFR outlet oil temperature ranges between 210 • C, corresponding to operation mode OM1, and 305 • C, i.e., the maximum allowed temperature before defocusing. The logarithmic function was preferred since it leads to a low number of modules to be connected at low temperatures, whilst the number increases quickly at high temperatures to prevent the risk of defocusing.

The Fuzzy Logic Controller
The fuzzy logic controller has been implemented based on the following assumptions [23]. First of all, to ensure an effective charging of the thermal storage, the LFR plant must supply oil at a temperature higher than the storage temperature to cover the thermal loss in the piping system (10 °C is the temperature difference assumed). Due to the different temperature of each module, the control system checks the maximum temperature of the current connected sub-LHTES module and supplies all the connected modules with a temperature higher than that. Secondly, during the discharging phase, corresponding to OM5 and OM6 (Table 1), the connected sub-LHTES must have a temperature suitable for the ORC supply, thereby the control system of the storage allows the connection only of the modules with a temperature higher than the temperature of the ORC inlet oil. Third, the oil flow rate is split equally among the sub-LHTES both in the charging and discharging phase.
The fuzzy logic controller has been designed according to a cascade approach to accomplish the following tasks: (i) select the number of modules to be connected with the plant; and (ii) manage each module based on a priority scale set out by the previous decision. In general, the performance of the plant can benefit from the subdivision of the LHTES. For example, when the solar radiation is high and the sub-LHTES is not fully charged, connecting a high number of modules allows mitigating of the temperature overheating of the LFR solar field, thus avoiding the inefficient defocusing of some mirrors [14]. On the contrary, when the solar radiation is low, it is convenient to connect and charge as few modules as possible so that the temperature of the storage medium is higher. Therefore, a close relationship exists between the outlet temperature of the diathermic oil from the LFR solar field and the number of modules to be connected. For this reason, a logarithmic function, shown in Figure  3, has been chosen to correlate the diathermic oil outlet temperature from the solar field with the number of modules to be connected. The LFR outlet oil temperature ranges between 210 °C, corresponding to operation mode OM1, and 305 °C, i.e., the maximum allowed temperature before defocusing. The logarithmic function was preferred since it leads to a low number of modules to be connected at low temperatures, whilst the number increases quickly at high temperatures to prevent the risk of defocusing. The fuzzy logic decision criteria are based on the above-mentioned logarithmic function, used to define the membership functions (related in this case with the number of modules), as presented in Figure 4; it provides as output a non-integer value correlated with the final number of modules by varying the oil temperature. The fuzzy logic decision criteria are based on the above-mentioned logarithmic function, used to define the membership functions (related in this case with the number of modules), as presented in Figure 4; it provides as output a non-integer value correlated with the final number of modules by varying the oil temperature. Energies 2020, 13, x FOR PEER REVIEW 7 of 17 Furthermore, in order to consider more accurately the changes in the diathermic oil temperature, a second parameter, i.e., its derivative with time, is included in the fuzzy logic. Therefore, the relative membership function of the controller adds a module if the derivative is positive (T_LFR derivative greater than 0.1 °C/min) or keeps the same number of modules if the derivative is zero, and finally, it reduces the number of modules in case it is negative, according to Figure 5. Once the number of modules to be connected with the plant is assessed by the first fuzzy logic controller, a second fuzzy logic controller in cascade is applied in order to establish the working priority on the basis of the storage state of charge. The priority of charging has been chosen on the basis of the melting temperature range of the selected PCM, but also on the ORC turn on/off set points (OM5) and on the heat exchange between heat pipes and modules of the sub-LHTES.
The criteria for priority are as follows: (i) Charging the thermal storage at low temperature is not convenient, even if the corresponding thermal losses are negligible, and at the same time, the high difference in temperature between the PCM and the LFR outlet temperature facilitates the thermal exchange (preventing the defocusing). Indeed, rarely the received energy increases to the point that the sub-LHTES temperature is suitable for the ORC supply, and as consequence it is often lost. Thus, a low priority for this occurrence has been chosen. The low priority also occurs when the sub-LHTES is at high temperature, since the thermal losses are high, whilst the ORC unit does not benefit from this increase in temperature (there is a limit of the inlet temperature for preventing its damage). Moreover, the sub-LHTES is less prone to receive thermal energy at high temperatures, Furthermore, in order to consider more accurately the changes in the diathermic oil temperature, a second parameter, i.e., its derivative with time, is included in the fuzzy logic. Therefore, the relative membership function of the controller adds a module if the derivative is positive (T_LFR derivative greater than 0.1 • C/min) or keeps the same number of modules if the derivative is zero, and finally, it reduces the number of modules in case it is negative, according to Figure 5.  Furthermore, in order to consider more accurately the changes in the diathermic oil temperature, a second parameter, i.e., its derivative with time, is included in the fuzzy logic. Therefore, the relative membership function of the controller adds a module if the derivative is positive (T_LFR derivative greater than 0.1 °C/min) or keeps the same number of modules if the derivative is zero, and finally, it reduces the number of modules in case it is negative, according to Figure 5. Once the number of modules to be connected with the plant is assessed by the first fuzzy logic controller, a second fuzzy logic controller in cascade is applied in order to establish the working priority on the basis of the storage state of charge. The priority of charging has been chosen on the basis of the melting temperature range of the selected PCM, but also on the ORC turn on/off set points (OM5) and on the heat exchange between heat pipes and modules of the sub-LHTES.
The criteria for priority are as follows: (i) Charging the thermal storage at low temperature is not convenient, even if the corresponding thermal losses are negligible, and at the same time, the high difference in temperature between the PCM and the LFR outlet temperature facilitates the thermal exchange (preventing the defocusing). Indeed, rarely the received energy increases to the point that the sub-LHTES temperature is suitable for the ORC supply, and as consequence it is often lost. Thus, a low priority for this occurrence has been chosen. The low priority also occurs when the sub-LHTES is at high temperature, since the thermal losses are high, whilst the ORC unit does not benefit from this increase in temperature (there is a limit of the inlet temperature for preventing its damage). Moreover, the sub-LHTES is less prone to receive thermal energy at high temperatures, Once the number of modules to be connected with the plant is assessed by the first fuzzy logic controller, a second fuzzy logic controller in cascade is applied in order to establish the working priority on the basis of the storage state of charge. The priority of charging has been chosen on the basis of the melting temperature range of the selected PCM, but also on the ORC turn on/off set points (OM5) and on the heat exchange between heat pipes and modules of the sub-LHTES.
The criteria for priority are as follows: (i) Charging the thermal storage at low temperature is not convenient, even if the corresponding thermal losses are negligible, and at the same time, the high difference in temperature between the PCM and the LFR outlet temperature facilitates the thermal exchange (preventing the defocusing). Indeed, rarely the received energy increases to the point that the sub-LHTES temperature is suitable for the ORC supply, and as consequence it is often lost. Thus, a low priority for this occurrence has been chosen. The low priority also occurs when the sub-LHTES is at high temperature, since the thermal losses are high, whilst the ORC unit does not benefit from this increase in temperature (there is a limit of the inlet temperature for preventing its damage). Moreover, the sub-LHTES is less prone to receive thermal energy at high temperatures, because of the low temperature difference between the PCM and the oil and, therefore, a serious risk of LFR defocusing exists. (ii) The highest priority occurs whenever the sub-LHTES module has a temperature close to the melting temperature range of the PCM. In this case, indeed, the thermal energy input can be exploited to run the ORC unit in OM5 and OM6. (iii) When the sub-LHTES is at mid-high temperature, although the storage is near the melting phase with good thermal exchange properties, thermal losses are significant and the temperature difference between the PCM and the outlet temperature of the diathermic oil from the LFR is quite low; then, it is not very convenient to charge the sub-LHTES. Therefore, a mid-priority is assigned to this condition.
The membership functions of the second fuzzy logic controller depend on the above criteria and the charging of the sub-LHTES modules occurs with the priority shown in Figure 6.
Energies 2020, 13, x FOR PEER REVIEW 8 of 17 because of the low temperature difference between the PCM and the oil and, therefore, a serious risk of LFR defocusing exists. (ii) The highest priority occurs whenever the sub-LHTES module has a temperature close to the melting temperature range of the PCM. In this case, indeed, the thermal energy input can be exploited to run the ORC unit in OM5 and OM6. (iii) When the sub-LHTES is at mid-high temperature, although the storage is near the melting phase with good thermal exchange properties, thermal losses are significant and the temperature difference between the PCM and the outlet temperature of the diathermic oil from the LFR is quite low; then, it is not very convenient to charge the sub-LHTES. Therefore, a mid-priority is assigned to this condition.
The membership functions of the second fuzzy logic controller depend on the above criteria and the charging of the sub-LHTES modules occurs with the priority shown in Figure 6. Therefore, according to the two fuzzy logic controllers in cascade described above, a matrix of identification of the modules to be connected with the plant and their priority is defined. All the identification codes are managed by an ad hoc routine, which sorts the six outputs coming from the respective fuzzy logic controllers and acts on the oil flow rate by directing it into the selected modules of the sub-LHTES.

Results and Discussion
In this section, the performance of the system when the fuzzy logic controller is applied is investigated. The TES subdivided in modules (sub-LHTES) with the fuzzy logic controller is compared with the standard system, where the single TES is operated following only the rules described in Table 1. Firstly, the performance of the two systems is analyzed during typical days of different seasons, i.e., summer, winter and mid-season, then the monthly and yearly behavior is evaluated.
The Figure 7 shows temperature and power trends for a typical summer day. In this case, because of the intense solar radiation when the storage reaches the maximum allowed temperature of 280 °C, the system is forced to defocus and it alternates the operation mode OM1 with OM4 to maintain the storage temperature level. It is evident that the sub-LHTES involves progressively the different modules on the basis of the thermal power coming from the LFR (Figure 7c-d). At the beginning, only two modules (modules 2 and 3, chosen on the basis of the priority set by their initial temperature linked to the system dynamic the previous day) are connected to the LFR and only later, the whole storage is activated (Figure 7c). This causes a longer time for the overall storage to reach the maximum temperature in comparison with the single TES (Figure 7a), but on the other side, a better management of the LFR power is possible. Indeed, the availability of some modules at lower temperature when the solar radiation rises allows a reduction in the defocus, as demonstrated by the Therefore, according to the two fuzzy logic controllers in cascade described above, a matrix of identification of the modules to be connected with the plant and their priority is defined. All the identification codes are managed by an ad hoc routine, which sorts the six outputs coming from the respective fuzzy logic controllers and acts on the oil flow rate by directing it into the selected modules of the sub-LHTES.

Results and Discussion
In this section, the performance of the system when the fuzzy logic controller is applied is investigated. The TES subdivided in modules (sub-LHTES) with the fuzzy logic controller is compared with the standard system, where the single TES is operated following only the rules described in Table 1. Firstly, the performance of the two systems is analyzed during typical days of different seasons, i.e., summer, winter and mid-season, then the monthly and yearly behavior is evaluated.
The Figure 7 shows temperature and power trends for a typical summer day. In this case, because of the intense solar radiation when the storage reaches the maximum allowed temperature of 280 • C, the system is forced to defocus and it alternates the operation mode OM1 with OM4 to maintain the storage temperature level. It is evident that the sub-LHTES involves progressively the different modules on the basis of the thermal power coming from the LFR (Figure 7c,d). At the beginning, only two modules (modules 2 and 3, chosen on the basis of the priority set by their initial temperature linked to the system dynamic the previous day) are connected to the LFR and only later, the whole storage is activated (Figure 7c). This causes a longer time for the overall storage to reach the maximum temperature in comparison with the single TES (Figure 7a), but on the other side, a better management of the LFR power is possible. Indeed, the availability of some modules at lower temperature when the solar radiation rises allows a reduction in the defocus, as demonstrated by the trend of LFR losses in Figure 7d compared to Figure 7b. Nevertheless, the overall ORC performance in summer is similar with the two TES configuration, due to the huge amount of solar energy available that brings both storages into fully charged mode.  The graphs represent also the operating mode (OM) of the plant, as specified in Table 1.
In Figure 8, a typical mid-season day is illustrated. In this case, due to the limited solar energy available, the sub-LHTES activates only two modules, which can reach a temperature slightly higher than the single-TES. Thanks to this small increase, the heated modules reach the melting stage and the TES can contribute to supply the ORC (the plant works in OM5 and OM6 between 4:30 p.m. and 6:00 p.m.). This behavior explains the longer duration of operating modes 5 and 6 in the presence of sub-LHTES, as described later in the discussion on yearly results reported in Table 2. In Figure 8, a typical mid-season day is illustrated. In this case, due to the limited solar energy available, the sub-LHTES activates only two modules, which can reach a temperature slightly higher than the single-TES. Thanks to this small increase, the heated modules reach the melting stage and the TES can contribute to supply the ORC (the plant works in OM5 and OM6 between 4:30 p.m. and 6:00 p.m.). This behavior explains the longer duration of operating modes 5 and 6 in the presence of sub-LHTES, as described later in the discussion on yearly results reported in Table 2.
Eventually, in Figure 9a typical winter day is shown. Even in this case it is possible to see that the sub-LHTES involves in the charging phase only two modules, which can increase significantly their temperature rather than the single TES, while the other modules remain cold (<50 • C, Figure 9c). This effect causes the reduction in the heat stored in the thermal storage (see P_TESin in Figure 9b,d). Nevertheless, the warm modules have a pretty high temperature, almost close to the melting condition. Thus, in case a bit more solar radiation would be available, the graphs demonstrate how easily the sub-LHTES could reach a sufficient temperature level to supply the ORC (switching on OM5 and OM6). This effect influences the better performance of the sub-LHTES in winter in comparison with the single TES, which experiences often too low temperature levels to discharge the stored heat towards the ORC. The graphs represent also the operating mode (OM) of the plant, as specified in Table 1.
Eventually, in Figure 9 a typical winter day is shown. Even in this case it is possible to see that the sub-LHTES involves in the charging phase only two modules, which can increase significantly their temperature rather than the single TES, while the other modules remain cold (< 50 °C, Figure9 c). This effect causes the reduction in the heat stored in the thermal storage (see P_TESin in 9b and 9d). Nevertheless, the warm modules have a pretty high temperature, almost close to the melting condition. Thus, in case a bit more solar radiation would be available, the graphs demonstrate how easily the sub-LHTES could reach a sufficient temperature level to supply the ORC (switching on OM5 and OM6). This effect influences the better performance of the sub-LHTES in winter in comparison with the single TES, which experiences often too low temperature levels to discharge the stored heat towards the ORC. The graphs represent also the operating mode (OM) of the plant, as specified in Table 1. On the basis of the priority schedule previously described in Figure 6, the module of the sub-LHTES with the highest priority should work more hours than the second one; the same behavior can be expected by the second module with respect to the third one and so on. Running a yearly dynamic simulation and recording the hours in which there is heat exchange between the n-th module and the transfer fluid, it is possible to draw the normalized histogram of Figure 10a: only three modules are used most of the time. It is confirmed by the mean temperature level of the different modules of the sub-LHTES, as shown in Figure 10b. It is also possible to observe that during wintertime, only a few modules work with a temperature above the average temperature of the single LHTES, while the others are cold and not involved in the charging phase, as already commented above. (c) (d) Figure 9. Daily temperatures (a) and power trends (b) of the LHTES compared with the daily temperature (c) and power trends (d) of the sub-LHTES for a typical winter day (30 January). The graphs represent also the operating mode (OM) of the plant, as specified in Table 1.
On the basis of the priority schedule previously described in Figure 6, the module of the sub-LHTES with the highest priority should work more hours than the second one; the same behavior can be expected by the second module with respect to the third one and so on. Running a yearly dynamic simulation and recording the hours in which there is heat exchange between the n-th module and the transfer fluid, it is possible to draw the normalized histogram of Figure 10a: only three modules are used most of the time. It is confirmed by the mean temperature level of the different modules of the sub-LHTES, as shown in Figure 10b. It is also possible to observe that during wintertime, only a few modules work with a temperature above the average temperature of the single LHTES, while the others are cold and not involved in the charging phase, as already commented above. Figure 9. Daily temperatures (a) and power trends (b) of the LHTES compared with the daily temperature (c) and power trends (d) of the sub-LHTES for a typical winter day (30 January). The graphs represent also the operating mode (OM) of the plant, as specified in Table 1. With the purpose of showing the influence of the developed cascade fuzzy logic control on the global performance of the plant, all the parameters of interest have been compared based on a yearly simulation with and without the smart storage management ( Table 2). It is evident that, thanks to a better management of the TES, its average temperature (considering the working modules) is increased in the sub-LHTES. Furthermore, even if less energy enters in the subdivided thermal storage, a higher amount of the stored energy is discharged to the ORC (TES efficiency increases of about 13%). These two aspects contribute to increase slightly the electric energy produced in the overall year (+4.7%) and also the ORC electric efficiency (+1.8%). This result is confirmed by the  (Table 2). It is evident that, thanks to a better management of the TES, its average temperature (considering the working modules) is increased in the sub-LHTES. Furthermore, even if less energy enters in the subdivided thermal storage, a higher amount of the stored energy is discharged to the ORC (TES efficiency increases of about 13%). These two aspects contribute to increase slightly the electric energy produced in the overall year (+4.7%) and also the ORC electric efficiency (+1.8%). This result is confirmed by the duration of operation mode OM5 and OM6 (i.e., when the TES discharges to the ORC, see Table 1), that are 11% longer than for the single storage. Considering both the thermal losses due to the TES and to the pipelines, they compensate each other in the sub-LHTES configuration. Indeed, the TES thermal losses are decreased due to the fact that less modules are involved in charging/discharging phases in cases of limited energy being available (thus, less mass of the storage medium), while the pipelines thermal losses are bigger because the average oil temperature is higher (with less modules involved, the charging phase is slower and the oil temperature tends to increase). Therefore, also the wasted energy through pipelines is crucial for the whole plant performance, and a good estimation of it, using accurate models, is paramount, as shown in reference [29].
Furthermore, the subdivision of the storage in the modules allows a reduction in the solar plant defocusing (about −30%): the thermal storage is better managed and more volume at lower temperature is available to store the surplus of solar energy. In Figure 11a, it is interesting to observe that the sub-LHTES causes often defocusing at low LFR power generation compared to the single LHTES, because at low solar power, less modules are connected to the plant. However, the single TES produces much more defocusing at higher LFR power generation and this causes the higher defocusing during the overall year. This behavior is supported by Figure 11b, where it is evident that modules 4, 5 and 6 work only at a high power rate compared with the others (they are colder and work only when the LFR temperature is particularly high, i.e., in cases of high temperature difference between the heat transfer fluid and the phase change material).
Energies 2020, 13, x FOR PEER REVIEW 13 of 17 Furthermore, the subdivision of the storage in the modules allows a reduction in the solar plant defocusing (about −30%): the thermal storage is better managed and more volume at lower temperature is available to store the surplus of solar energy. In Figure 11a, it is interesting to observe that the sub-LHTES causes often defocusing at low LFR power generation compared to the single LHTES, because at low solar power, less modules are connected to the plant. However, the single TES produces much more defocusing at higher LFR power generation and this causes the higher defocusing during the overall year. This behavior is supported by Figure 11b, where it is evident that modules 4, 5 and 6 work only at a high power rate compared with the others (they are colder and work only when the LFR temperature is particularly high, i.e., in cases of high temperature difference between the heat transfer fluid and the phase change material). The analysis based on the yearly averaged values does not clearly show the exact influence of the developed fuzzy control logic on the whole performance of the plant. Therefore, the monthly trends of the main performance parameters for the LHTES are shown in Figure 12 and Table 3. The analysis based on the yearly averaged values does not clearly show the exact influence of the developed fuzzy control logic on the whole performance of the plant. Therefore, the monthly trends of the main performance parameters for the LHTES are shown in Figure 12 and Table 3. Figure 12 shows the monthly variation in percentage of the TES performance parameters in the case of smart management compared to the standard control without fuzzy logic. During the winter period, the TES subdivision enables the LFR to produce oil at higher temperature, because it stores heat in a smaller amount of PCM. The low solar radiation entails a frequent operation in OM1 and OM3, the latter one occurs with an augmented temperature which, in turn, raises the pipeline thermal losses, as clearly shown in Figure 12. The mid-season is a particular period, in fact, the temperature of several modules of the sub-LHTES is still higher than the single module, but the latter one has a stored energy reservoir not exploited (temperature below the melting point), accumulated during the past weeks. At this time, the exceeding solar energy can be easily stored and immediately released, while the sub-LHTES version uses this extra energy also to recharge the other modules that are not still in the right temperature range to run the ORC. The behavior described above affects the ORC efficiency and electricity production: a light decrease in the electricity production is observed especially in the mid-season months of March and October, while the system performs better in winter and as good as the plant with the single TES in summer. The analysis based on the yearly averaged values does not clearly show the exact influence of the developed fuzzy control logic on the whole performance of the plant. Therefore, the monthly trends of the main performance parameters for the LHTES are shown in Figure 12 and Table 3.  Figure 12 shows the monthly variation in percentage of the TES performance parameters in the case of smart management compared to the standard control without fuzzy logic. During the winter period, the TES subdivision enables the LFR to produce oil at higher temperature, because it stores

Conclusions
This paper aims at evaluating the benefits provided in terms of thermal efficiency of a plant equipped with a thermal storage subdivided in several modules, while managing their operation by means of a smart fuzzy logic controller. In this case, the storage subdivision has been applied to an innovative micro solar CHP plant used in residential applications. Six sub-LHTES modules have been used and their operation has been managed according to cascade fuzzy logic control. While the main control system of the plant is designed to maximize the annual electric energy production, this further control aims at managing the sub-LHTES system only, but, as a consequence, it affects the thermal and electric energy production of the whole plant over the year. Hence, the performance of the integrated plant has been evaluated on a monthly and yearly basis and compared to that of the plant with a single LHTES (without subdivision into modules and smart management). The main findings of the comparison highlight that the proposed smart management of the sub-LHTES contributes to: • a significant increase in the storage efficiency during the winter season, allowing a longer duration of the discharging phase of the storage towards the ORC, while the two TES configuration behaves in a similar way in the other seasons (overall annual TES efficiency increase of 13%); • an electric efficiency of the ORC unit, as well as the operating time, is higher in winter, which results in an increased yearly electric energy production (about 5%); • 30% less thermal losses of the LFR solar field are due to defocus.
Conversely, it causes more than 9% additional thermal losses due to the higher pipeline working temperature (compensated by the increased TES efficiency mentioned above).
Concluding, the adoption of a smart control management of the sub-LHTES allows increasing the performance of an integrated micro CHP unit powered by solar energy when the plant works in part load conditions. Furthermore, it is not expected an increase in investment costs for the proposed system because the modular design of the TES is a more effective technical solution envisaged also for the standard system, thus, the real cost difference would be related mainly to some valves while the cost of the control algorithm implementation can be considered negligible. Nevertheless, further investigation is required to better estimate the exact potential of the proposed approach changing the priority ranges, and a validation of the control strategy is desirable during the forthcoming experimental tests campaign.

Conflicts of Interest:
The authors declare no conflict of interest.