On-site solar PV generation and use: Self-consumption and self-sufficiency

As energy storage systems are typically not installed with residential solar photovoltaic (PV) systems, any “excess” solar energy exceeding the house load remains unharvested or is exported to the grid. This paper introduces an approach towards a system design for improved PV self-consumption and self-sufficiency. As a result, a polyvalent heat pump, offering heating, cooling and domestic hot water, is considered alongside water storage tanks and batteries. Our method of system analysis begins with annual hourly thermal loads for heating and cooling a typical Australian house in Geelong, Victoria. These hourly heating and cooling loads are determined using Transient System Simulation (TRNSYS) software. The house’s annual hourly electricity consumption is analysed using smart meter data downloaded from the power supplier and PV generation data measured with a PV system controller. The results reveal that the proposed system could increase PV self-consumption and self-sufficiency to 41.96% and 86.34%, respectively, resulting in the annual imported energy being reduced by about 74%. The paper also provides sensitivity analyses for the hot and cold storage tank sizes, the coefficient of performance of the heat pump, solar PV and battery sizes. After establishing the limits of thermal storage size, a significant impact on self-efficiency can be realised through battery storage. This study demonstrates the feasibility of using a polyvalent heat pump together with water storage tanks and, ultimately, batteries to increase PV self-consumption and self-sufficiency. Future work will concentrate on determining a best-fit approach to system sizing embedded within the TRNSYS simulation tool.


Introduction
Rooftop solar photovoltaic (PV) systems are increasingly being installed in Australian households.Over 30% of Australian houses are reported to have rooftop solar PV systems (Australian Renewable Energy Agency 2022).Reasons for the widespread use of PV technology include the desire of r esidents to re duce their electricity bills ( Li et al. 2021), low equipment prices (Khezri et al. 2020), and government policies and incentives (Chapman et al. 2016).For example, under the Solar Homes prog ram, Victorian residents can claim a rebate of up to AUD 1,400 for th e purchase of solar PV panels, plus the option of interest-free loans (Solar Victoria 2022).Similarly, a zero-interest loan of from AUD 2,000 to 15,000 can be used by Canberra residents to purchase rooftop solar panels, household battery storag e systems, hot water heat pumps, etc., under the Sustainable Household Scheme (ACT Government 2022).It is expected that the installation of rooftop solar PV systems into Australian homes will continue to increa se while government subsidies for renewable energy system installations continue.
However, the widespread installation of rooftop solar PV systems has created many problems.Firstly, the mismatch between peak PV generation and peak electricity consumption leads to a large excess PV generation being delivered to the electrical grid, which raises concerns tha t high reverse energy flows can lead to overvoltage on lo w-voltage lines, transformer fault currents, and substation transformer damage (Byrne et al. 2018).Secondly, Feed-in tariffs (FiTs) in Australia c ontinue to de crease each year, because the electricity grid, designed to supply energy rather than receive it, is becoming overburdened.Electricity suppliers are beginning to restrict t he export of PV-generated electricity to the grid by lowering feed-in tariffs or prohibiting feed-in entirely.As a result, h ouseholds with rooftop PV s ystems may be unable to sell the ele ctricity to the grid in the future.Thirdly, be cause PV generation and house electrical loads are not often simultaneous, PV self-consumption, which mea sures the proportion of total PV generation consumed locally, is relatively low (Bee et al. 2019;Horan et al. 2021).Therefore, finding strategies to increase PV self-consumption is increasingly important for households with rooftop PV systems.
Using electric batteries is a possible method to increase the self-consumption of roo ftop PV systems (Ren et al . 2016).Integrating electric batteries into PV systems stores the excess PV-generated electricity during the day (Ke et al. 2015), and consumes it during periods with peak demand (Saez-de-Ibarra et al. 2016).However, a study conducted by Khezri et al. (2020) found that integrating electric batteries in solar PV houses is unattra ctive in NSW, Australia until the battery price decreases to $190/kWh, a quarter of th e current market price.However, a heat pump couple d with water storage tanks is a promising approa ch to increase PV self-consumption (Wang et a l. 2021).Co mbining rooftop PV systems w ith air-to-water heat pumps coupled with water storage tanks allows residential heating and cooling needs to b e met by consuming PV-gene rated electricity, thereby increasing the self-consumption of rooftop PV and reducing the residential grid energy consumption (Battaglia et al. 2017).Arteconi et al. (2017) analysed the performance of industrial b uildings using heat pum ps in combination with a water storage tank for space cooling in a simulation, and the results showed that incorporating PV into this combined system can make thermal energy storage economically viable, regardless of the electricity tariffs.
Although thermal energy storage is less expensive, its stored energy can only me et residential thermal energy needs.Although electric batteries are expensive, combining thermal energy storage and electric batteries may be a better solution, as it will provide PV houses with a higher l evel of electrical and thermal energy self-sufficiency (Langer and Volling 2020).Many stud ies have examined the feasibility of using electric batteries or heat pumps coupled with water storage tanks in grid-connected solar PV houses to increase the PV self-consumption as well as to partially meet residential energy requirements.However, there are currently no studies that report the effectiveness of us ing an electric battery and heat pumps coupled with water storage tanks to increase rooftop PV self-consumption and PV self-consumption while fulfilling the heating, cooling, DHW and electrical demand of houses.Therefor e, this paper aims to integrat e electric batteries, a polyvalen t heat pump with two wate r storage tanks, and a grid-connected solar PV house to meet the electrical and thermal energy needs of the house, while investigating the impact of such system integration on PV self-consumption and sel f-sufficiency.In this context, PV self-sufficiency refers to the pro portion of the house load met by PV generation (Wang et al. 2022).

Literature review
This section reviews the existing literature related to the application of heat pumps with energy s torage systems in solar PV houses, as they are the most prominent and effective approaches to increasing PV self-consumption and self-sufficiency.

PV-battery system
Several papers have presented the energy and cost performance of using electric batteries in grid-connected solar PV houses.For example, Ren et al. ( 2016) analysed the effect of using PV and batteries in houses on reducing peak electricity demand and annual grid electricity consumption.They also pres ented the bills savings of case study houses under different tariff structures.Horan et al. (2021) examined the energy and cost performance of applying PV battery systems in three case study ho uses.The authors discovered that a battery, regardless of size, requires a significantly large PV system to charge during wintertime.Beck et al. (2016 ) developed a mixed-integer linear optimization model to investigate how the PV self-consumption is affected by the temporal resolution of electrical load and PV generation profiles.The results demonstrated that the temporal resolution of l oad profile may cont ribute more than the resolution of PV generation for accuratel y estimating th e PV self-consumption rate.Li et al. (2018) investigated the impact of battery storage on increasing PV self-consumption and peak shaving in grid-connected households in Kyushu, Japan.The authors con cluded that increasing the battery size can raise t he PV self-consumption, b ut the rate of its increase varies significantly across months and is greatly influenced by home loads and PV generation profiles.
Furthermore, the sizing of residential PV-battery system has gained a great deal of res earch attention.For example, Weniger et al. (2014) developed a simulation model with one-minute time intervals to analyse the sizing of residential PV battery sys tems.The study found that small-scale PV systems accompanied by a high self-consumption rate are considered the best, as reven ues from feed-in tariffs will become less and less in the future.In or der to reduce the total annual electr icity bill of houses equipped with PV battery systems, a genetic algorithm-based method for optimal sizing of PV batteries was proposed and validated using the collected data (Li 2 019).The auth or discovered that the house energy use pattern and, electricity and battery prices have a significant impact on the optimal sizing of PV battery systems.
This paper focuses on t he use of e nergy storage systems in grid-connected solar PV houses.In addition to the previously mentioned electric energy storage through batteries, hydrogen-based energy storage is now emergin g as a new form of energ y storage.While hydrogen energ y storage may n ot currently be used in a single residentia l building, it is already widely used in the commercial sector or at the community level in combination with renewable energy generation.Therefore, it is necessary to review the literature related to the use of hydrogen energy storage in solar PV systems.Electrolysis of water through electricity generated from renewable sources, such as solar PV is an option for producing carbon-free and e nvironmentally friendly hydrogen, which al so promises to address the demand and supply imbalance associated with the intermittent or unstable nature of most renewable energy sources (Ozturk and Dincer 2 021).Mobasseri et al. (2022) presented a schematic diagram of the multi-energy microgrids, showing the integration of facilities such as electricity grid, solar PV, battery storage, hydrogen en ergy storage, natural gas fuel cell and co mbined heat and power, etc.In particular, the gaseous hydrogen produced from water electrolys is can be compressed under high pressure and sto red directly in storage tanks for use in fuel cell electric v ehicles.While hydrogen energy storage is promising, its use in the commercial sector or at the community level may be more feasible.Izadi et al. (2022) in vestigated the impact of using hydrogen energy storage on reducing the carbon emissions of an off-grid office building with PV panels and wind turbines.The results show that the use of hydrogen storage can provide 39% of the electricity demand of the office building, thus increasing the total power supply fro m renewable sources from 49% to 88%.An energy management framework considering flexible demand, battery energy storage, and electric vehicles was developed aiming to achieve the maximum collective benefit of the ener gy community for prosumers (Tostado-Véliz et al. 2022b), which paves the way for the development of hydrogen energy storage in energy communities.

PV and heat pumps with water storage tanks
Numerous studies have looked into the impacts of combining heat pumps with water st orage tanks t o enhance th e self-consumption and grid compatibility of rooftop P V systems, in addition to employing batteries to increase the PV self-consumption rate of houses.For instance, Sánchez et al. (2019) presented a h euristic control algorithm for operating a 1 kW input air-to-water heat pump with a 600 litre hot water storage tank in a typical Swiss house with the a im of increasing PV self-use and minimizin g the cost of pur chasing electricity and running the heat pump.Results demonstrated that the developed control program yielded a 49% cheaper o perating cost and 5% higher PV self-consumption in the short term compared to other nonlinear programming solvers.Beck et al. (2017 ) created a mixed-integer lin ear programming model to determine the optimal operation, setup, a nd sizing of a cost-effective residential heat pump system in the context of PV self-consumption.The authors found that demand is the primary determinant of heat pump sizing.FiT s typically promote lower PV self-consu mption, and small demanddriven PV systems can boost high self-consumption levels when FiTs are unavailable.Fischer et al. (2016) studied the impact of increased residential PV system installations and variable electricity prices on the o ptimal system sizin g operation of heat pumps and th ermal energy storage.They discovered that the residential thermal load profile strongly influences the system sizing.The existing sizing procedures are sufficient for sizing the he at pumps and thermal energy storage, except for some extreme cases such as the capacity of the PV system be ing too large or when the price of electricity fluctuates significan tly.In these cases, a larger energy storage is required.By integrating heat pumps, water storage tanks, and PV with domestic heating and coolin g systems, Li et al. (2021) proposed a rule-based control strategies using TRNSYS simulation and analysed the effect of this combined system on lowering house grid-based power demand and raising PV self-cons umption.The authors discovered that in comparison with a trad itional non-thermal storage system, the combined system red uces annual grid el ectricity usage by a bout 76% by including a 5 kW solar PV system.Moreover, the use of thermal energy storage raises the PV self-consumption from 27% to 56%.However, the heat pump used could only provide heating or cooling modes but not both at once.Nor did the authors consider using electric batteries to store excess PV energy.

PV, heat pumps with water storage tanks and batteries
Numerous studies have also focused on a pplying electric batteries and heat pumps in combination with water storage tanks in grid-connected solar PV houses.Battaglia et al. (2017) in vestigated the potential to increase PV selfconsumption by applying electric batteries and heat pumps with water storage tanks in houses, but it only focused on the use of energy storage for residential electricity consumption, space heating, and domestic hot wate r (DHW) production, and neglected space cooling.Similarly, Williams et al. (2012) demonstrated the effectiveness of using electric batte ry storage and heat pumps with water storage tanks to enhance PV self-consumption of houses, but the energy storage systems were used only to meet residential electrical and heating needs, without considering the use of heat pumps and thermal storage for DHW and cooling.Psimopo ulos et al. ( 2016) showed how electric battery storage and heat pumps coupled with thermal energy storage have the potential to increase PV self-consumption and decrease grid-based energy consumption in residential PV systems.They discovered that for PV sizes ranging from 3.1 to 9 .3kW, using existing thermal ene rgy storage could reduce fin al energy by 279 to 573 kWh annually.For the setups and module sizes studied, the g rid-based energy red uctions from utilizing electric batteries are s ignificantly greater than those from adopting thermal storage.However, again, the energy storage systems in this study were only used for household electricity, s pace heating, and DHW use, but were not considered for space cooling.
The literature review shows that the use of electric batteries or he at pumps co upled with water storage tanks in grid-connected solar PV houses to increase PV selfconsumption and manage residential energy requirements has been stud ied extensively.In this pape r, a combined system is st udied in which an elec tric battery and a polyvalent heat pump co mbined with wate r storage tanks buffer electrical and therma l energy by consuming PV power for providing electricity and DHW, heating and cooling for the house.A polyvalent heat pump can offer three modes: heating only, cooling only, or simultaneo us heating and cooling in one system.In addition, the polyvalent heat pump is built with a DC compressor, so it can operate by directly consuming PV-generated electricity and battery storage.

System configuration
The schematic of the propos ed combined system is shown in Figure 1.This system includes a rooftop solar PV system, a hybrid inverter, a battery, a polyvalent h eat pump, two water storage tanks, and some other a uxiliary components such as water pumps, a fan coil unit, and hydronic conditioning systems etc.The detailed ex planations for each component are as follows.
A hybrid inverter is one of the most important components in this design as it connects to the g rid, the battery, and the household appliances and provides control.On the one hand, it can convert the DC o utput from th e battery or the solar PV to AC and suppl y it to home appliances or t he grid.On the other hand, it can conver t the AC supply to 48V DC, charging the battery or operating DC appliances, such as the proposed polyvalent heat pump.The rooftop solar PV system is used to provide electricity for operating home appliances and the polyvalent heat pump as well as charging the battery.
Conventional heat pumps can offer heating only or cooling only mode, but ca nnot offer both simultaneous heating and cooling.As such, the idea of considering both thermodynamic outputs of heat pumps, namely, heating on the condenser side and cooling on the evaporator side, leads to a co-generation system, implying th at both heating and cooling processes are achieved with th e same energ y input.This type of heat pump can be called the polyvalent heat pump, or a 3-in-1 heat pump.The polyvalent heat pump can achieve both heating and cooling simultane ously, or it can provide only heating or only cooling.It is important to note that when the pol yvalent heat pump initially operates in b oth heating and cooling mo des, it works as a water-to-water heat pump system to produce both hot and cold water.Eventually, when the water temperature in one of the tanks reaches the preset point, the polyvalent heat pump a utomatically switches to an air-to-water or a water-to-air heat pump system to continue heating the hot water or cooling the cold water.In addition, the polyvalent heat pump used in th is work is designed and bu ilt with a 48V DC co mpressor, so it can operate directly from PV-generated electricity or b attery storage.Hot and cold water are produced during the operation of the polyvalent heat pump an d is stored into two storage tanks.The hot water can then be used for DHW or heating, while the cold water is used for cooling t hrough a fan coil unit or a hydronic conditioning system.

Rules of energy flows for the solar PV house wit h a polyvalent heat pump, water storage tanks and batteries
It is assumed that the pol yvalent heat pump can heat ho t water to a maximum of 65 °C, and there is no available hot water storage when the hot water temperature falls below 40 °C.Once th e hot water te mperature drops below 55 °C , the polyvalent heat pump will be activated to heat the water to 60 °C.Here, PV energy is first to be consumed to operate the heat pump, followed by battery storage and grid power when PV out put is insufficient.If th ere is still excess PV production after that, the polyvalent heat pump will continue to heat the hot water to 65 °C.Similarly, assuming that cold water can be cooled to a minimum of 5 °C by the polyvalent heat pump, there is no availab le cold water storage when the cold water temperature is above 25 °C.When the cold water te mperature exceeds 15 °C, th e polyvalent heat pump will begin to cool the water to 10 °C.Again, PV ene rgy is first to be consumed to operate the heat pump, fo llowed by battery storage and grid power when PV output is insufficient.If there is still excess PV output after that, the heat pump will continue to bring the cold water down to 5 °C.The set-point t emperatures of the two water storage tanks are shown in Table 1.Controls of a grid-connected solar PV house with an electric battery and a polyvalen t heat pump with two water storage tanks are illustrated in Figure 2.This flowchart considers: (1) When the secondary thermostats for the hot or cold-water tank are triggered, the polyvalent heat pump will operate until the secondary thermostats stops triggering.(2) When the PV energy is greater than the house electrical load, the excess energy is used to operate the polyvalent heat pump to store heating and cooling energy into two water storage tanks.(3) When there is excess PV energy during the operation of the polyvalent heat pump o r after two wate r tanks are fully charged, it is used to charge the battery.(4) When there is excess PV energy after the battery is fully charged, it is exported to the grid.(5) If the PV energy is smaller than the house electrical load, the remaining required electricity is drawn from the battery.(6) If there is still an electricity requirement after the battery is discharged, it will be met by importing the electricity from the grid.

Additional insights on the development of control program
The control program described in Section 3.2 was constructed in Excel Visual Basic for Applications with the expectation of obtaining a basic understanding of how energy flows between solar PV generation and a polyvalent heat pump together with th ermal storage and a battery might be realized in acco mmodating the hourly energy loads of the house selected.The program allows the user to select and alter the solar PV array, heat pump, thermal storage, and battery sizes to explore interaction between these factors.It was decided, for learnin g purposes not necessarily accuracy, that a flexible yet quick tool be designed for a n hourly ann ual analysis, yet allowing for solar PV, heat pump, thermal storage and battery size to be altered and studied in pursuit of meeting the hourly and peak loads of the particular house studied.
To achieve th ese goals, some assumptions have to be considered.It is well known that heat pumps have different COP values at different stag es of their input and output temperatures under different environmental conditions.However, due to the limitations of developing the control program in Excel Visual Basic for Applications, the COP o f the polyvalent heat pump in the three modes was assumed to be a constant value of 4. This cause d the results to deviate from the actual operation of the heat pump.
To address this issue, an analys is of showing how the heat pump COP affects the PV self-consumption, self-sufficiency and the annual imported energy is conducted and illustrated in Section 6.2.

Case study
A grid-connected solar PV house, located in Geelong, Australia, is used as a case study house in this paper.The house is a single storey building with three bedrooms.It is well insulated and double glazed, and the eaves are used to control sunlight exposure.The space heating is provided by a gas ducted system, and th ere is no equipment used for cooling.A hot water heat pump was installed in the home in June 2022 to supply DHW.Prior to that, a gas-boosted solar hot water system was used to meet home hot water demand.

TRNSYS simulation
First of all, the thermal demand for heating and cooling of the case study house needs to be obta ined for this work.There are a few methods available to achieve this.For example, Tostado-Véliz et al. ( 2021) derived a thermostatic model of a building, including the equivalent thermal resistance of the house and the ai r mass inside, by linearizing the differential equations and assuming a rectangular geometry of the building.T he parameters considered in the model in clude the index for build ing elements, such as walls and windows, thickness, area, an d thermal coefficient of each building element, the density of air, the d imension of the building and the roof angle of the building.However, some non-geometric para meters are not mentioned, such as the profiles of infiltration, ventilation, internal gains, h eating, cooling, comfort and humidity of different building zones.
In this study, the Transient System Simulation (TRNSYS) program is used to simulate the house's annual hourly heating and cooling demand.TRNSYS is a dynamic simulation tool that is frequ ently utilized in the area of thermal processes, and it has the ability to model th e heating and cooling of many types of buildings (Laxmi and KesavaRao 2020).It in cludes the weather data files for various specific locations that are required for the simulation, including temperature, pressure, wind speed, humidity, and solar intensity (Jani e t al. 2020).In addition, TRNBuild, serving as an interface to th e TRNSYS application, enables editing data pertaining to n on-geometric features, such as infiltration, ventilation, int ernal gains, heating, cooling, comfort, and humidity profiles for various building zones.
First, the case study house model is drawn in TRNSYS3D, which is a plugin for SketchUp.The finished geometry can be found in Figure 3.This geometry is then sent directly to TRNSYS in which the materials properties of walls, floors, and windows and the regime types, such as profiles of infiltration, ventilation, cooling and heating, gain and loss, and humidity for each zon e of the ho use is edited in TRNBuild.
The house model is divided into seven zones, including three bedrooms, lounge, living room, sitting room and study.Therefore, the total volume to be cooled or heated in the   As mentioned above, a ho t water heat pump was installed in the house in June 2022 to meet the hot water demand.The electricity consumption of the heat pump has been monitored every minut e since its installation by a Yokogawa power meter and recorded on a Secure Digital (SD) card.W e extended the four months of power data collected to one year as the a nnual power consumption for the hot water heat pump.Additionally, a COP of 4 is assumed for this hot water heat pump.Therefore, the hourly DHW demand can be calculated based on the electricity consumption and the COP of the heat pump water heater.

Smart meter and solar PV data processing
In 2013, a smart meter was installed at the house, which records the a mount of electricity importe d from and fe d into the grid in half-hourly intervals.A CSV file containing the last two years of smart meter data, re corded every 30 minutes, can be downloaded from the elect ricity provider (Powercor 2022).This house also has a 10-kW rooftop solar PV system, and a PV system controller records PV generation data every fifteen minutes.
The smart me ter data meas ures imported energy as house electrical load minus harvested sol ar energy, and measures exported energy as harvested solar energy minus house electrical load.Since the imported and exporte d energy flow on the same wire, when one is positive, the other has a va lue of zero.The PV generation and smart meter data of the house in 2021 is used for the analysis in this work.The time interval used in this work is one ho ur.Thus, in each hour of the year, the electrical energy loads of the house can be calculated as follows: where: This calculated h i E reflects the distinctive electricity consumption patterns of household appliances, because in this house, space heating is provided b y a gas ducted system, and DHW is provided by a gas-boosted solar water heating system.This calculated h i E is taken as the base electrical load of the house.

A System sizing approach: key parameters
After importing the obtained annual hourly cooling, heating, DHW loads and PV generation data into Excel Visual Basic for Applications and ru nning the proposed control program, several key parameters can be calculated, separately, using the following equations.h h p total 0 0 where: t represents a given period such as a day, a month or a year.L total is the total ele ctrical load of th e house ove r a given period t, including the total base electrical load and the total electrical load for operating the polyvalent heat pump.PV c is the total amount of PV energy consumed on site over a given period t.PV total is the total amount of PV generation over a given time period t.SC is the PV self-consumption rate, and SS is the PV self-sufficiency rate.

Three different system sizing scenarios
The coordination of the proposed system considers th e off-grid electrification of the house load through solar PV.
Next, is th e importance of utilising self-generated energy for thermal load requirements.This is achieved first by the polyvalent heat pump and w ater storage tanks, resulting in all DHW, heating and cooling loads being accommodated by conditioned water stored in tanks.Finally, the ther mal load shift prov ides for electrical appliances to be o perated primarily through battery storage.B uilding operation, including space heating, cooling and DHW heating, accounts for 65% of the total energy consum ption of Australian households (Energy Consult 2022).Therefore, by considering thermal storage in the first place, the size of the battery can be significantly red uced.In addition, water storage tank s are cheaper and can last many more years than batteries .The concept of improved thermostatically controlled devices, such as proposed by Tostado-Véliz et al. (2022a) would add value to the above system being controlled effectively.Three different scenarios are designed in this paper to analyse the impact of us ing electric batteries and a polyvalent heat pump with water storage tanks on the PV self-consumption, self-sufficiency, and grid energy consumption of the house.Scenario 1 ref ers to a house with a 10 kW solar PV system and a polyvalent heat pump that produces cold and hot water for space heating, cooling, and DHW.It is worth noting that no storage system is used in Scenario 1. Scenario 2 refers to a house with a 10 kW solar PV system, a polyvalen t heat pump, and two water storage tanks.Scenario 3 refe rs to the house with a 10 kW solar PV system, a polyvalent heat pump coupled with two water storage tanks, and a 5 kWh bat tery.The battery technology considered in this paper is a lithium-ion battery and it is assumed that the battery can reach a 100% state of charge and 0% state of c omplete discharge.The input capacity of the polyvalent heat pump for the three scenarios is determined based on the peak hourly heating, cooling, and DHW load of the house, and the size of two wate r tanks in Scenarios 2 and 3 are determined based on the peak daily hea ting, cooling and DHW load of the house.Additionally, the two water tanks and the batt ery are assumed to be fully charged at the initial stage.The capacities of relevant systems in th e three scenarios are listed in Table 3.In order to show the difference in the con sumption of the house on t he grid and P V energy, the annual imported energy, annual PV self-consu mption and annual PV selfsufficiency for the three scenarios were collected after running the control program and plotted in Figure 4.It can be seen that us ing a polyvalent heat pump in combination with water sto rage tanks red uces annual imported energy by around 28%, from 3380 kWh in Scenario 1 to 2429 kWh in Scenario 2. After adding a 5 kWh battery in Scenario 3 , this value is decreased to 892 kWh, whi ch is around 74% less than the value in Scenario 1.Moreover, Figure 4 shows that the annual PV self-co nsumption, which measures the proportion of total yearly PV output consumed by house loads, rises from 23.25% in Scenario 1 to 29.56% in Scenario 2 and finally to 40.24% in S cenario 3. On the other hand, annual PV self-sufficiency, w hich refers to the percentage of the annual house load met by PV en ergy, rises fro m 49.70% in Scenario 1 to 63.6 1% in Scenario 2 and then to 86.63% in Scenario 3. The significant change in these values can be a ttributed to the fact that mo re PV energy is consumed through a battery and the polyvalent heat pump coupled with water storage tanks.
It has been found that the annual PV self-consumption and self-sufficiency can be increased by using batteries and heat pumps with water st orage tanks.To figure out how the use of thermal and electric battery storage affects the Fig. 4 Annual imported energy, PV se and self-sufficiency with different service system scenarios consumption of PV and gr id energy of t he house each month, we pl ot the monthl y PV self-consumption and self-sufficiency for the three scenarios in Figure 5. Scenario 3 has the highes t PV self-consu mption and self-sufficiency every month of the year.This is because the use of batteries and water storage tanks allows more PV energy to be stored during the day and used at night o r during peak load periods.Furthermore, in each scenario, monthly P V self-sufficiency is high er in summer than in winter, whil e the opposite is true for monthly PV self-consumption, with higher values in winter than in summer.This is because PV generation is greater in summer than in winter.In summer, more of the house load can be met by PV energy, leading to higher PV self-sufficiency, whil e in winter, higher PV selfconsumption is due to the fact that most of the limited PV energy is consumed during daylight hours.
These facts can also be supported by the results shown in Figure 6, which depicts the monthly imported and exported energy for the three scenarios.It is obvious that for each of the three scenarios, the monthly energy imports from spring to autumn are larger than those in winter, while the monthly energy ex ports are lower than those in winter.This effect can be explained by several reasons, including high nighttime ene rgy demand and the limited PV generation in winter.Furthermore, it is evident that in Scenario 2 with thermal energy storage, monthly grid energy imports are lower than in Scenario 1.When a 5 kWh battery is included, Scenario 3 imports less energy t han Scenario 2 does for each month of the year.These effects are due to the battery and the polyvalent heat pump coupled with water storage tanks that enable excess PV output during the day to be stored a s electrical or thermal energy, reducing th e amount of PV output to the grid and partially offsetting the household's grid energy demand.Therefore, it can be argued that using a battery and a polyvalent heat pump coupled with water storage tanks has a substantial impact on reducing the house gr id energy de mand as well as minimizing th e burden of exporting PV energy to the grid.
To figure out how the daily PV self-consumption and self-sufficiency are distributed, we use the data for the three scenarios in February 2021 as an example of a month, and the results are plotted in Figure 7.It can b e noticed that Scenario 3 has the highest da ily PV self-consumption and self-sufficiency rates due to t he use of wate r storage tanks and batteries, allowing excess PV energy to be stored during the day and consumed during peak hours.In ad dition, Fig. 5 Monthly PV self-consumption and self-sufficiency for the three scenarios Fig. 6 Monthly imported and exported energy for the three scenarios the batteries have a greater impact on increasing PV self-consumption and self-sufficiency rates for several days than using a polyvalent heat pump with water storage tanks.This can be ex plained by the fact that the t hermal energy stored in the t wo storage tanks can only be used for space heating, cooling or DHW use, while the electricity stored in the batteries can be consumed by all house hold appliances as well as by heat pumps to produce hot and cold water.
To further illustrate the effects of using a battery and a polyvalent heat pump coupled with water storage tanks on the red uction of house g rid energy consumption, the annual hourly imported energy for the thre e scenarios was collected and presented in Figure 8.It is discovered that the large portion of the imported energy that occurs from late afternoon to early morning in Scenario 1 is greatly reduced in Scenarios 2 and 3.In addition, the peak h ourly imported energy occurring at 19:00 in Scenario 1 is greatly diminished and shifted to 8: 00 a.m. in Scenario 3. Additionally, Scenario 3 has a sm oother imported energy curve than Scenarios 1 and 2. These s ignificant effects result from the load shifting caused b y the battery and the polyvalent heat pump with water storage tanks to match the home energy demand with PV output.The sizes of several system components, in cluding hot and cold tanks, sol ar PV arrays, electric batteries and the hea t pump COP, are varied to analyse their impact on annual PV self-consumption and self-sufficiency as well as the annual grid energy consumption of the house.

Hot and cold water size
The sizes of the hot and cold tanks are varied to analyse their effects on the annual PV s elf-consumption, annual PV self-sufficiency, and annual energy impo rts of the house , and the results are shown in Figure 9.When the hot tank size is fixed, the annual PV self-consumption and annual PV self-sufficiency, as well as the annual i mported energy, remain almost stable when increasing the cold tank size.This is because the cooling load only oc curs in su mmer.Due to the da ily demand for DHW, the polyvalent heat pump can operate in simul taneous heating and cooling modes, producing hot and cold wate r with the same electrical input.Therefore, increasing the size of the cold water tank does not really affect the grid or the PV energy consumption.The figure also shows that increasing the hot tank size leads to more ann ual PV self-consumption and self-sufficiency, and results in a decrease in annual imported energy, but the increase or de crease is not significant.This is because th e COP of the polyvalent heat pump is considered to be a constant value of 4, which enables th e heat pump to operate effectively at all times and res ults in its relatively low power consumption.Another reason is that when t he size of the hot tank incr eases, the store d heating energy is not used efficiently and becomes redundant.
Figure 10, which depicts the temperature of the hot and cold water tanks in relation to th e hot water tank size, Fig. 7 Daily PV and daily PV self-sufficiency for the three scenarios in February 2021 Fig. 9 Annual PV self-consumption, annual PV self-sufficiency, and annual imported energy as functions of hot and cold tank sizes (PV system size = 10 kW, battery capacity = 5 kWh, and polyvalent heat pump input capacity = 2.8 kW) Fig. 10 Hot and cold tank temperature as a function of hot tank size (PV system size = 10 kW, battery capacity = 5 kWh, polyvalent heat pump input capacity = 2.8 kW, cold tank size = 2.0 m 3 ) illustrates similar results.As seen in the graph, the frequency with which the hot water tank tem perature approaches the maximum temperature of 65 °C increases as the size of the hot water tank increases.This indicates tha t a continuo us increase in the size of the hot water tank to consume PV energy becomes less useful, i.e., the increase in annual PV self-consumption and self-sufficiency becomes progressively slower as the size of the hot water tank increases.It can also be observed t hat the hot ta nk temperature drops below 60 °C far more frequently in the winter than at other times of the year for the four various tank sizes.This is attributed to the house having higher heating and DHW demand in winter, which causes hot water consumption to be higher than in other seasons.Additionally, the limited PV generation in winter restricts the operating time of the polyvalent heat pump.According to the co ntrol strategy, when the PV generation is insufficient in winter, the polyvalent heat pump will only be t urned on whe n the hot tan k temperature drops below 55 °C and heat s the hot water to 60 °C by consuming grid energy.Therefore, in summary, the size of the tank shoul d take into account both the home cooling, heating, and domestic hot water loads, as well as the seasonal characteristics of PV power generation.

Heat pump COP
The polyvalent heat pump in this w ork can provide three modes, i.e., heating only, cooling only, and both simultaneous heating and cooling modes.The COP of the heat pump is varied with changes in the ambient con ditions and the temperature of the heat source and sink .Due to the limitations of developing control programs in Excel Vis ual Basic for Applications, th e COP value of the polyvalent heat pump in all three modes is assumed to be a constant value of 4. In order to reduce the impact of the assumption of the heat pump C OP on the final results of this work, we analysed how the annual PV self-consumption, annual PV self-sufficiency, and annual en ergy imports vary with the change of the heat pump COP, and the results are illustrated in Figure 11.As the COP value decreases from the initially assumed value of 4, ther e is a gradually increasing trend of annual PV self-consumption and annual imported energy.This is due to the fact that as the heat pump's COP decreases, it needs to operate for longer periods to maintain the same level of thermal output.As a result, the heat pump consumes more PV power during the day, contributing to the increased annual PV sel f-consumption.Similarly, the heat pump must draw more energy from batteries or th e electricity grid at night or during periods of low PV power to maintain t he same ther mal output, re sulting in mo re annual grid energy consumption.On the other hand, the graph shows that the annual PV self-sufficiency remains almost constant when the COP value of the heat pump is higher than 2.4, and only when its value continues to decrease from 2.4, the annual PV self-sufficiency slowly decrea ses.This is be cause when th e COP value of the heat pump is very low, the hot or cold water produced by the heat pump through the consumption of PV energy during the day is not enough to meet the house energy demand.The heat pump has to by consuming more grid energ y during night time, resulting in reduced annual PV self-sufficien cy.In addition, it is important to note that based on the input power of the heat pump and the existing size of the wat er storage tanks, the COP of the heat pump needs to be at least as shown in the figur e, to meet the annual heating, cooling DHW loads of the house.Thus, it can be found th at the heat pump COP does h ave an impact on annual PV self-consumption and self-sufficiency as well as on the annual grid energy consumption of the house.Future research will focus on simulating the polyvalent heat pump in TRNSYS to explore more precisely the impact of changes in hea t pump performance on PV and grid energy consumption at different ambient temperat ures, heat sources, and sink temperatures.

PV-battery system capacity
Figure 12 illustrates the a nnual PV self-consumption , annual self-sufficiency, and annual imported energy of the house as functions of PV and battery sizes.Four different PV system sizes, including 2.5 kW, 5 kW, 7.5 kW, and 10 kW, are studied, and the PV generation rises proportionally to its size.It has been dis covered that, for ev ery PV s ystem size, the annual amount of energy imported falls as battery capacity rises, and the annu al PV self-co nsumption and self-sufficiency rise.However, the incre asing trend is constrained by PV generation because the amount of electricity generated by PV is influenced by the seasons.In particular, PV generation is adequate in the summer, and any excess energy can be used to charge the battery.The PV generation is not sufficient to satisfy the daily househol d load during the winter due to shorter da ys, lower solar altitude and g reater night-time energ y demand, so the battery cannot be charged effectively.It can also be found that under a fixed battery capacity, such as 5 kWh, increasing the PV system size leads to an increase in annual PV self-sufficiency, from 52.25% for 2.5 kW PV to 86.63% for 10 kW PV, b ut the annual P V self-consumption de crease dramatically, from 96.09% for 2.5 kW PV system to 40.24% for 10 kW PV system.Th is is because the increase in PV system size can reduce the amount of en ergy imported from the grid, but it is smal l compared to the increased amount of en ergy exported to the gr id.Therefore, it is noted that wh en installing PV systems and batteries, it is necessary to consider the characteristics of PV generatio n and house electricity demand in o rder to determine th e best size combination of PV and battery systems.

Conclusion
This paper is about u tilizing PV-generated solar energy through a polyvalent heat pump combined with water storage tanks and batteries.The performance of a mechanical system depends on the energy that can be stored.Conventional systems do not offer this but utilize fossil fuels and electricity during the day and nighttime hours.While we could store electrical energy in a large battery to operate mechanical systems at night, this is not economically feasible nor efficient use of electrical energy.Figure 4 Scenario 1 illustrates an instantaneous DHW and conditioning system, whi ch consumes more grid energy than the other two scenarios with thermal and battery storage.The discovery is to utilize a mechanical system (heat pump) that can provide fo r thermal storage by consuming PV energy d uring daylight hours.Thermal storage allows us to separate conditioning loads from electrical (appliance) loads.
This paper explores how the use of thermal and battery storage can increase PV self-consumption and self-sufficiency while fulfilling the house's el ectricity, heating, cooling, and DHW needs.The results revealed that by using appropriate control strategies and component sizes i.e., heat pump, storage tank capacity and battery, the proposed combined system could increase the PV self-consumption and selfsufficiency to 40.24% and 86 .63%,respectively.Compared to Scenario 1 without energy storage, the annual impor ted energy of the house is reduced by almost 74% in Scenario 3 with water storage tanks and a battery.It was also discovered that increasing the battery capacity led to an increase in PV self-sufficiency and self-consumption, but the trend is limited due to the constrained PV generation in winter.Therefore , there are limitations to costly battery sizing that depend upon solar PV array sizes.Increasing the PV system size resulted in an increase in PV self-sufficiency.Note, a decrease in PV self-consumption is due to a great deal of PV energy be ing exported to the grid.Furthermore, the increase in hot tank size could contribute to an increase in PV self-consumption and self-sufficiency, but the trend is limited as the COP of the polyvalent heat pump is assumed to be a constant value, and the amount of heating energy storage is not used effectively and becomes redundant.
Results from the control program also demonstrated that there is perhaps no such thing as "an optimum" in the selection of components to a service system of the type that we are advocating here.In other words, there may be several "best fits" of a system that are suitable to an owner's costs, the spatial accommodation of equipment, or the fact that certain factors have already been det ermined before the analysis (such as a 10 kW PV array).There is no such thing as "an optimum" for everyone, as this definition rests on the interpretation of the individual.
Another interesting point to make in this s tudy is the size of the sol ar PV array a nd the low self-consumption achieved by the project.However, it may be interesting to consider that different bat tery technologies or ele ctric vehicles may apply this excess PV power.In addition, electric vehicles may provide additional battery r equirements for our houses at night.All these considerations will be part of a much more complete sizing and energy use model for our houses in the future.
Finally, the control program and the calculation process of the house's electrical energy consumption in this study were implemented in Visual Basic for App lications.To obtain more accurate and comprehensive results, future work can be done by simulating the p roposed combined system using shorter time intervals in the TRNSYS program, in which using the cold water tank to store heating energy in winter, the water temperature stratification of the two storage tanks, the perfor mance mapping of the polyvalent heat pump can be analysed in more detail.
Open Access: This ar ticle is licensed un der a C reative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, a s long as you give appropriate credit to the original author(s) and the source, provide a link to the C reative Commons licence, a nd indicate if changes were made.
The images or other third party material in this article are included in the article' s Creative Co mmons licence, unless indicated otherwise in a credit line t o the mater ial.
If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/Funding note: Open Access funding enabled and organized by CAUL and its Member Institutions.

Fig. 1
Fig. 1 Schematic of the proposed combined system

Fig. 2
Fig. 2 Rules of energy flows for satisfying the building loads

Fig. 3
Fig. 3 (a) Southwest and (b) northeast views of the house

Fig. 8
Fig.8The annual imported energy for each hour of a year

Fig. 11
Fig. 11Annual PV self-consumption, annual PV self-sufficiency, and annual imported energy as a function of heat pump COP (PV system size = 1 0 kW, battery capacity = 5 kW h, polyvalent heat pump input capacity = 2.8 kW, hot tank size = 2.6 m 3 , cold tank size = 2.0 m 3 )

Fig.
Fig. Annual PV self-consumption, annual PV self-sufficiency, and annual imported energy as functions of PV and battery sizes (Hot tank size = 2.6 m 3 , cold tank size = 2.0 m 3 , and polyvalent heat pump input capacity = 2.8 kW)

Table 1
Setpoint temperatures of the two water storage tanks

Table 2
Operating schedule and temperature setting of different zones of the house

Table 3
Sizing of each system component in three scenarios