Contributions to System Integration of PV and PVT Collectors with Heat Pumps in Buildings

A common approach to improve self-consumption of photovoltaic (PV) generation in buildings with heat pumps (HP) is to overload the thermal storage capacities during times with surplus PV generation (hereinafter referred to as thermal overloading). The impact of battery capacity and domestic hot water (DHW) consumption on the effectiveness of this method in a single-family home (SFH) is evaluated through numerical simulations. Increased battery capacity is shown to decrease the effectiveness of thermal overloading. Regarding DHW consumption, temporal concentration is shown to have a stronger influence on the effectiveness of thermal overloading than total energy. Furthermore, the potential of photovoltaic-thermal collectors (PVT) as heat exchangers for air/brine/water heat pumps (ABWHP) is estimated. The results show that the properties of PVT collectors with high thermal conductivity are in the feasible range for application in a well-insulated SFH in Central European climate.


Introduction
Recent years have seen an increase in rooftop PV and heat pumps for residential heating [1] [2]. In addition to optimizing these components individually, the interactions between them should be examined, in order to derive guidelines for the design of building energy systems combining both. In this study, two contributions to this goal are made: Firstly, numerical simulations are used to evaluate the effectiveness of improving self-consumption of PV generation in a SFH through thermal overloading in dependence of battery capacity and DHW consumption. Along with the increasing share of solar power in electricity generation [3], the question of electricity storage grows in significance [4] [5]. Heat pumps with control systems maximizing self-consumption of PV generation have the potential to use the thermal masses of DHW storage and the building itself to alleviate this problem, especially in buildings with underfloor heating or thermally activated building systems. This potential however depends on many parameters and boundary conditions. A realistic selection thereof is crucial for the validity of the evaluation.
Secondly, the feasibility of using PVT collectors as heat exchangers for ABWHP is estimated by comparing their thermal properties to those of dedicated heat exchangers and solar-thermal collectors. PVT collectors offer the potential to maximize energy gains from a given roof area. Compared to dedicated solar-thermal collectors, their return temperatures are often too low to be used for DHW directly. However, due to their large area, they may serve as primarily convective heat exchangers for ABWHP. If functional, this approach offers several advantages over air-source HP: The external fans of airsource HP are noisy and consume substantial amounts of electric energy. Since the PVT approach requires no fans, it emits no noise and might be more energy efficient. The first point is particularly relevant regarding the increasingly strict noise regulations in residential areas [6]. The intermediate brine cycle also allows bypassing the heat pump to recover a ground source or latent heat storage in summer.

Simulation Models
The simulations are conducted using Matlab/Simulink R2016b with the CARNOT Blockset Toolbox, Version 6.2. All simulations start with one month of settling time, then cover one year. For the analysis, the state of the components is sampled every minute. Fig. 1 and Fig. 2 show the hydraulic and electric schematics of the examined system, consisting of photovoltaics, battery, heat pump, space heating (SH), DHW storage and domestic appliances. The following sections detail the individual components.

Building
The SFH45 building as defined by IEA HPT Annex 38 SHC Task 44 [7] is used, which corresponds to a SFH meeting minimum efficiency requirements for modern buildings. The floor area is 140 m 2 with a space heating demand of 45 kWh/m 2 a. The building has an underfloor heating system as well as temperature dependent ventilation and window shading, though no heat recovery for the ventilation. The internal load from occupants and household appliances is set to a constant 322 W. The implementation of the model neglects all spatial aspects and consists of two thermal masses: The heating system with 40 MJ/K and the remaining building mass with 70 MJ/K.

Heat Pump
The building has an air/water HP with a thermal power of 6 kW at the operation point A-7/W35. The auxiliary electric heater also has a power of 6 kW. The implementation uses power maps, based on input air temperature and output water temperature. The power for defrosting the external heat exchanger is integrated into the power maps.

Domestic Hot Water Storage
The DHW storage has a capacity of 390 l and is well insulated. The heat pump is connected to a heat exchanger coil. The DHW is drawn directly from the storage. Stratification is taken into account by discretizing the storage into 10 vertical nodes.

Photovoltaics, Inverter and Battery
The building has a rooftop photovoltaic system with a peak power of 5 kW. The roof is facing south with a 30° inclination. The implementation calculates the power as an algebraic function of solar irradiance, taking cell temperature into account. The inverter is implemented as a simple power-efficiency-curve. The battery has a usable capacity of 5.9 kWh and an efficiency of 95% each way, which corresponds to the data sheet of the battery installed in the institute's laboratory. Charging the battery is always prioritized over grid feed-in and thermal overloading. Discharging the battery is always prioritized over grid draw.

Controls
The conventional control system keeps the DHW storage temperature in a defined band. The space heating supply temperature is kept in a defined band around a set point in function of the averaged ambient temperature (Tamb), while the room temperature is used to control the mass flow to the heating system. If the surplus PV generation is below 1500 W, the thermal overloading control is identical to the conventional control. Above this threshold, the temperature set points are elevated by 1 K for the room temperature and 7.5 K for the DHW storage. The parameters for both control strategies are listed in Table 1. The surplus PV generation is processed through a first order low-pass filter with a time constant of 600 s.

Hydraulics
The hydraulic are highly simplified. Pipes and valves have neither dynamics nor friction. The circulation pumps feed a constant mass flow at a constant electric power when running. The power consumption of these pumps can be thought of as a representation of the hydraulic resistance.

Boundary Conditions
The following boundary conditions are used for the simulations. Since the results are expected to depend strongly on the synchronicity of the conditions, they all have a one-minute resolution.

Weather
A weather data set for the city of Strasbourg, France is used. The average temperature is 11 °C and the annual solar irradiance 1102 kWh/m 2 .

Domestic Electricity Consumption
A stochastic domestic electricity consumption profile with a total annual energy of 3385 kWh is used. While 90% of all loads are below 1 kW, the peak load is at 7.1 kW [8].

Domestic Hot Water Consumption
Three stochastic annual profiles and three repetitive daily profiles are used, shown in Table 2. The stochastic profiles are mostly scaled versions of each other with small differences in individual drawings. The basic repetitive profile is the "Tapping Cycle M" from the EN 13203 standard. This profile has one large drawing each in the morning and evening. Two modifications thereof are used, in which these drawings are concentrated in the morning ("M-mor") or the evening ("M-eve").

Variation of Battery Capacity
Three battery capacities are compared. The 5.9 kWh battery corresponding to the real one is complemented by a 3.0 kWh battery and a simulation without battery (0.0 kWh). As a baseline, Table 3 shows the key performance indicators for varying battery capacity with the conventional control system. Increasing battery capacity has a significant impact on the KPI, though with a quickly diminishing marginal benefit.  Table 4 shows the relative change in KPI when switching from the conventional control system to thermal overloading. In general, the expected effects are observed. The SG and SC are increased, the GFI and GD are reduced. For the SG and SC, the impact of thermal overloading quickly diminishes with increased battery capacity. For the GFI and GD, the picture is less clear. However, all reductions in GFI are consistently larger than the reductions in GD. In general, varying the battery capacity has a far greater impact than changing the control system.  Table 5 shows the KPI for DHW profiles with varying total energy. The impact on all KPI is rather small. Table  6 shows the relative changes in KPI when switching from the conventional control system to thermal overloading. Similar to the varying battery capacity, all KPI change in the expected direction. SG and SC increase, GFI and GD decrease. The degree of change is similar for all DHW profiles.   Table 7 shows the KPI for varying daily timing of DHW consumption. Similar to the variation of total energy, the impact of DHW timing is rather small. Table 8 shows the relative changes in KPI when switching from the conventional control system to thermal overloading.

Variation of DHW Timing
While the values are similar for the profiles with DHW consumption concentrated on the morning or evening, thermal overloading shows greater impact for the distributed DHW consumption profile "M".  The results for the grid interaction are summed up in Fig.  4. It can be seen that varying the timing of DHW consumption has a stronger influence on the impact of thermal overloading than varying the total energy. To examine the observed effects in detail, the daily surplus PV generation (Pel,surplus = PPV -Pel,domestic) and the electric power of the heat pump with both control strategies (Pel,HP,conventional, Pel,HP,overloading) are shown in the figures below. Fig. 5 shows the results for the distributed repetitive DHW profile "M". Compared to the conventional control, the HP power with thermal overloading is clearly shifted to the midday hours with high electric surplus. The effect is most pronounced for the DHW peaks in the morning and evening.

PVT Collector as Heat Exchanger
With a given brine/water HP, mass flows and operating temperatures, the thermal power of the system is proportional to the UA value of the heat exchanger on the air/brine side. Three heat exchange systems on the air/brine side are compared here: Forced-air heat exchangers, PVT collectors and uncovered solar-thermal collectors. Fig. 7 shows the simplified hydraulics of an air/brine/water PVT-HP system. In a series of measurements, the UA value of an air/brine heat exchanger supplying a brine/water HP with a thermal power of 6 kW at the operating point A-7/W35 is determined to be 1500 W/K, corresponding to 250 W/K per kW of heating power. This value is compared to the wind-dependent UA values for PVT collectors, according to equation (1), where u is the wind speed and A is the heat exchanger area. Solar irradiance is neglected, since it is considered a minor factor during the critical winter months [12]. Table 9 shows the corresponding parameters for a PVT collector with high thermal conductivity, a PVT collector with average thermal conductivity and a purely solarthermal air/brine pipe heat exchanger, consisting of two rows of parallel uncovered plastic pipes.
(1)  [11] 21.5 3.66 ISFH PVT-A [11] 10.2 1.15 Pipe heat exchanger [12] 27.5 47.1 Assuming a required thermal conductivity of 250 W/K per kW of heating power, the required PVT collector area is calculated using equation (1) and shown in Fig. 8. A significant difference between the three components can be seen, especially at higher wind speeds. The average wind speed from the weather data for Strasbourg is approx. 3 m/s for all seasons. The wind speed at the roof of a SFH in a built environment is estimated to be half the unimpeded speed, i.e. 1.5 m/s. With this assumption, the highly conductive PVT collectors would require an area of approx. 10 m 2 per kW of heating power. This value is in the feasible range for application in a SFH with state-of-the-art thermal insulation. E.g. 5 kW of heating power with 50 m 2 of south-facing roof area.    [12]. With these areas and the assumed wind speed of 1.5 m/s, the HP heat exchanger has the highest UA value, followed by the highly conductive PVT collectors and the pipe heat exchanger. At wind speeds above 3 m/s, this relationship is inverted.

Discussion
While the results for varying battery capacity yield no surprises, the parameters correspond to new batteries in good condition. As capacity and efficiency decrease with age, the results may change. DHW consumption patterns have many characteristics: Total energy, repetitiveness, daily timing, concentration respectively distribution of drawings, etc. The significance of the results may be improved by using additional DHW profiles covering all these aspects. Varying the DHW storage capacity may also yield additional insights. For both evaluations, it should be noted that the parameters for the thermal overloading have not been varied or optimized.
While the application of PVT collectors as heat exchangers for heat pumps is deemed feasible, the impact of snowfall and frosting is neglected at this point. An extended evaluation would also include a comparison of cost and efficiency with a more conventional combination of pure photovoltaics and an air-source HP.

Conclusions
The simulation results indicate that the potential for improving SC through thermal overloading in a SFH is rather limited. In comparison, the impact of a medium capacity battery is much higher. The addition of a battery also further lowers the benefits of thermal overloading. The variation of DHW consumption patterns are of comparable significance to the potential of thermal overloading. However, temporal concentration respectively distribution of DHW consumption has a greater impact than its total energy. This effect may be even stronger with lower DHW storage capacity. The relationship between optimal SC of PV generation and DHW storage capacity should be kept in mind when applying legionella counter-measures, which often involve minimizing the volume of standing hot water.
The application of PVT collectors as heat exchangers for heat pumps appears to be feasible for a well-insulated SFH with a relatively large usable roof area. It is however crucial to use PVT collectors designed for high thermal conductivity, since solar-thermal systems used as source for a heat pump gain most heat from convection, not solar irradiance [12].

Outlook
The evaluation of the influence of DHW consumption patterns may be extended with additional DHW profiles and different DHW storage capacities. An experimental evaluation of an energy management system (EMS) to complement the simulations is currently in progress. Fig.  11 shows a preliminary measurement. The regular temperature band for the DHW storage is 40-50 °C. During the afternoon hours with surplus PV generation (Pel,surplus = PPV -Pel,domestic -Pbattery -Pel,HP,DHW), the EMS triggers a DHW charging cycle (Pel,HP,DHW) before the lower temperature limit is reached and overloads the storage to approx. 54 °C (TDHW). The temperature dip before the charging is the result of turbulences stirring up the stratified layers of water. Compared to the identical test without the EMS, the SC and SG are significantly increased while the GFI and GD are significantly decreased. Extended results may be published in a few months.
The evaluation of PVT collectors yields positive indicators and may be continued with simulations and experiments. In addition to the heating application, PVT collectors could also be used for cooling. Their large upward facing surface and high infrared emissivity makes them suitable for nocturnal radiative cooling. While this approach is already being investigated, the cooling power per surface area is usually rather low [13] [14]. A heat pump elevating the collector temperature during cooling operation could counter this limitation.