Keywords

1 Introduction

Solar energy is the most accessible decentralized energy source to enhance building power generation and reduce carbon emissions. Hybrid photovoltaic/thermal (PV/T) collectors have significant advantages compared to typical photovoltaic (PV) panels and thermal collectors by combining their power generation for the same surface area. PV/T uses a heat exchanger to capture the solar energy not converted into electricity from the PV cells. In this way, PV/T can achieve significantly greater efficiencies near 80% total efficiency depending on designs [1]. The added thermal energy generation is especially beneficial for buildings that are in heating-dominant climates such as in Canada.

Building-integrated energy generation can significantly reduce the building's net energy consumption as well as increase the building's resiliency. The potential for self-generation reduces dependency to utilities and, when combined with energy storage, can enable buildings to significantly reduce power outages. However, solar energy intermittent and unpredictable nature can make the design of these systems to meet building energy demands complex. In this way, multiple studies have evaluated the ideal sizing of battery storage systems to enhance renewable energy generation [2]. Intuitive methodologies are often utilized to approximately size PV systems based on the monthly solar energy, while other studies favor artificial intelligence methodologies to find an appropriate solution without guaranteeing perfect sizing [3]. Mathematical programming models are also utilized to find optimal PV-battery sizing for their applied case study building [5].

Similarly, thermal storage solutions for solar thermal systems have also been studied broadly [6]. Water thermal storages are often used for solar applications since they are an effective and affordable solution achieving good performance for low-temperature applications [7], such as building heating. Thermal storage adequate sizing has shown that it can significantly improve solar thermal collector performance [8], with tank stratification improving the efficiency [9]. Studies have also investigated the ideal sizing for PV/T collectors to maximize their performance [15], however thermal storage sizing remains the most common difficulty of PV/T system implementation [12].

Solar-energy storage systems’ appropriate sizing can enhance building performance as well as increase building resiliency by mitigating power outages. In the United States, electricity consumers averaged 7 h of power interruption in 2021, with power outages from major events going as high as 8 h on average in recent years [13]. Some studies have investigated the potential of PV-battery systems to minimize these power outages by utilizing optimal sizing for the designed systems [14] as well as developing stochastic methods to incorporate solar variability to maximize resiliency [15]. In this way, PV/T combined with batteries and thermal storage has the potential to enhance typical PV-battery systems for building performance as well as resiliency to power outages.

The aim of this study is the optimization of PV/T collector, batteries, and thermal storage sizing through a sensitivity analysis to maximize system performance as well as increase building resiliency to power outages for cold climate building heating.

2 Methodology

This study consists of a sensitivity analysis to optimize the sizing of a PV/T-battery-thermal storage system applied as a case study on the offices of a school building in Sainte-Marthe-sur-le-Lac, near Montreal, Canada. The system is optimized to increase building resiliency to power outages for a minimum of 8 h of self-sufficiency. The self-sufficiency duration is calculated based on the duration where the stored total energy can meet the totality of the load starting when the PV/T electrical generation cannot meet the entirety of the load. The studied system is to be dimensioned to meet the heating load of the school offices’ radiant hydronic loop during winter operation. The initial system dimensions are based on an existing operational retrofitted PV/T-thermal storage system on a research building. The studied system components are modeled with Python (Fig. 1).

Fig. 1.
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Studied school building, Horizon-du-Lac (near Montreal, Canada) [16].

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The school building is located near Montreal, Canada with a back façade facing 37° South-East where the PV/T collectors would be installed in the façade at a 90° slope to maximize solar gains for winter operation. The solar radiation, ambient temperature, wind speed, and direction, weather data for the school location were taken from Solcast database at the school coordinate [14] and are utilized by the model. The performance of the system is evaluated for 3 days in January with mixed conditions, a sunny day, and 2 partly sunny/cloudy days with exterior temperature varying from −20 ℃ to 0 ℃ with an average 10 ℃ temperature (Fig. 2).

Fig. 2.
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PV/T-battery-thermal storage system configuration.

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The building loads are taken from historical 2020 measured data of the radiant slab floor heating of 5 offices in the school with a total floor area of approximately 144 m2. The average daily heating load of the offices during January and February was 81 kWh (0.5625 kWh/m2) and the average peak load was 7.5 kW. The studied system consists of liquid-based PV/T collectors with parallel thermal hydronic connections that directly feed a large liquid thermal storage tank. The PV/T and storage tank have a mixture of 50/50 glycol water to minimize freezing. The tank is connected to a heat pump that heat radiant slabs in the school offices. An auxiliary heating source is used if the tank-stored heat is insufficient. The PV/T electrical generation can be used directly to power auxiliary heating, charge the battery, or sent to the grid. It is assumed that the excess electrical generation cannot be used for other building loads to recreate a self-reliant building.

The PV/T collector panels, the tank dimension, and the battery maximal capacity are varied with the sensitivity analysis as shown in Table 1 to evaluate the impact on the building load and the PV/T performance. The PV/T and thermal storage costs are based on the component cost of an existing system in Quebec, Canada, while the battery costs are based on the commonly used residential Tesla PowerWall.

Table 1. Sensitivity analysis evaluated varied parameters and costs
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2.1 PV/T Collector

The PV/T collectors are modelled with a grey-box 1st-order thermal network approach that was developed for control application in a previous study and experimentally validated with a less than 5% error [18]. The model is calibrated utilizing experimental data to improve its accuracy for real-world operation. The electrical model of the PV/T is based on the manufacturer’s performance specifications and the PV cell temperature that is calibrated with a set coefficient of \({\alpha }_{corr}=0.86\) based on experimental measurements. The thermal model is based on energy balance equations of each of the thermal nodes of the thermal network of Fig. 3 with an effective capacitance located at the thermal heat exchanger.

Fig. 3.
figure 3

PV/T thermal network [18].

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The calibration is based on a single day of data from real-world operation from identical PV/T collectors installed on the façade of an institutional building in Quebec. The quantity of PV/T collected is evaluated in this study from 18 panels up to 54. It is assumed that the hydronic circuits of the collectors are connected in parallel. The solar PV/T control pumps are set to operate when the temperature of the tank top node is below 1.5 ℃ the temperature of the PV/T outlet fluid temperature and stop when the difference is below 0.5 ℃. The pump flow rate is based on the quantity of PV/T collectors set at 100 kg/h per panel based on the manufacturer’s recommendations.

2.2 Thermal Storage

The thermal storage tank is directly connected to the PV/T hydronic thermal loop and is filled with a 50/50 glycol-water mix. The tank is modelled with 5 control volumes to evaluate the stratification between the different tank layers. Since the flow rate is dependent on the number of solar collectors, depending on the studied configuration stratification could be minimal or have a large impact on performance. The tank heat loss coefficient was calibrated utilizing experimental measurements to 3.25 W/m2-K. The tank nodes are modelled with energy balance equations from Klein and al [19].

$${C}_{i}\frac{{dT}_{i}}{dt}={\dot{m}}_{1}{c}_{p}\left({T}_{i-1}-{T}_{i}\right)-{\dot{m}}_{2}{c}_{p}\left({T}_{i+1}-{T}_{i}\right)+{U}_{i}{A}_{i}\left({T}_{amb}-{T}_{i}\right)$$
(1)

where C is the thermal capacitance, \({\dot{m}}_{1}\) and \({\dot{m}}_{2}\) are the source/load mass flowrate, U is the heat loss coefficient, cp is the specific heat, \({T}_{i-1}{, T}_{i }, {T}_{i+1}\) are the above, current, and below control volume source/load temperature, and Tamb is the ambient temperature.

2.3 Heat Pump

The heat generated during the winter months for unglazed PV/T collectors can be significantly affected by the exterior temperature and wind speed causing significant thermal losses. The heat quality is significantly affected which often necessitates a heat pump to increase the temperature for building heating purposes. In this way, a heat pump was selected from Nordic GHP which has a large high-temperature range that is suitable for winter solar applications. The selected heat pump can operate between tank temperatures from 7 ℃ to 32 ℃ with an output temperature of at least 47 ℃, ideal for radiant floor heating. Experimental measurements have shown that an 18 PV/T configuration with a 454 L thermal storage tank could achieve a maximal temperature of up to 31 ℃ during winter operation – which is ideal for the selected heat pump. The heat pump model is based on performance curves from the manufacturer’s available data [20] where the \({\text{COP}}\) is the coefficient of performance.

$${\text{COP}}=0.12578*{{\text{T}}}_{{\text{ELT}}}+0.91531$$
(2)

The controls for heating the school offices are rule-based, where the heat pump is used for heating if the temperature of the tank is greater than 10 ℃ and the PV/T electrical generation with the auxiliary heating is not enough to meet the load. The heat pump operation stops if the tank temperature in the tank reaches 7.5 ℃.

2.4 Battery

The batteries are utilized to store the excess electrical energy generated by the PV/T collectors. The stored energy is then utilized to meet the electrical load that is not met by the heat pump, including the heat pump's electricity consumption, to reduce the heating load until it reaches zero. The battery's State-of-Charge (SoC) is based on the electrical load provided by the PV/T and the discharge to meet the office's heating load. The SoC is limited to a range of 20 to 80% to minimize the battery degradation effects by operating in a linear portion of the nominal discharge curve [21]. In this way, the battery SoC was modelled based on the battery's maximal capacity \({C}_{bat}\), the time \(\Delta t\), and the charge/discharge power rate \(P\left(t\right)\) that was limited to a C-rate of 0.5 to minimize long-term battery degradation.

$$SoC \left(t\right)=SoC\left(t-1\right)+\frac{P\left(t\right)*\Delta t}{{C}_{bat}}$$
(3)

3 Results

The three studied parameters were varied in a sensitivity analysis to determine their impact on the performance of the system to maximize the number of hours the system can be self-sufficient after a fully sunny day in winter. The largest difference in system performance is caused by the variation in the number of PV/T collectors and the thermal storage tank, which directly affect the potential heat gains. Figure 4 shows the number of self-sufficient hours with a fixed battery capacity of 10 kWh and variations of PV/T collectors and tank volume. There is significantly reduced performance at 18 PV/T compared to other configurations. Increasing the tank storage does improve its performance at a tank volume of 908 L with a decrease in performance when it further increases. Larger tanks have higher stratification and lower temperatures, improving collector efficiency.

Fig. 4.
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Maximum self-sufficient hours based on PV/T quantity and tank size with a fixed 10 kWh battery capacity.

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However, when the tank volume is too large for the generated collectors’ thermal energy, the temperature quality is too poor to be utilized by the heat pump. At 27 panels and larger, there are significant performance gains, but the number of self-sufficient hours is mostly below 8 h without increasing tank size, significantly improving performance up to 1362 L. Similarly, if we observe the impact of varying the thermal storage and battery size with a fixed number of PV/T collectors, we have a significant difference in performance.

Figure 5a shows these effects with a 27 PV/T configuration. The increase in battery capacity significantly improves the number of self-sufficient hours until it is maximized at 30 kWh and there is not enough excess PV electricity generated to charge the battery.

Fig. 5.
figure 5

Maximum self-sufficient hours based on tank size and battery capacity. 5a (Left); For 27 PV/T collectors. 5b (Right); For 54 PV/T collectors

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However, if we have 54 PV/T collectors (Fig. 5b), there are important increase in the number of hours from the greater storage capacity since the system can better utilize the excess generated electricity, improving self-sufficiency until the next day's sunny conditions – significantly inflating results. Additionally, increasing the storage tank volume seems to also significantly improve the hours of self-sufficiency when the battery capacity size is large enough to meet the heat pump electrical generation, which seems sufficient near 20 to 30 kWh with 36 panels. Figures 6a and 6b, respectively shows the effects of the variation of the three parameters on the number of self-sufficient hours and the component costs.

Fig. 6.
figure 6

Thermal storage, PV/T quantity, and battery capacity effects on: 6a (Left); the maximum self-sufficiency. 6b (Right); the component cost.

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In Fig. 6a, we can observe that the increase in battery capacity has the largest impact on the system's self-sufficient hours, with thermal storage being the smallest. Nonetheless, the thermal storage sizing has a larger impact when there is enough PV/T collector for the studied case study load, necessitating at least 27 collectors. However, the effect of the components cost is the opposite, as seen in Fig. 6b. Although batteries are necessary to maximize self-sufficient hours, they increase significantly the cost compared to tank volume. In this way, the best configuration to maximize the number of self-sufficient hours for the lowest cost would have to utilize enough PV/T collectors to just meet the heating load, maximize the thermal storage tank, and reduce the battery capacity to meet the heat pump's electrical consumption. For example, a 1st configuration of 27 PV/T, 908L tank, and 10kWh battery would cost 18 861$ and achieve 8.65h of self-sufficiency while a 2nd configuration of 27 PV/T, 454 L tank, and 20 kWh battery would cost 23 856$ with 9.03h of self-sufficiency. The 1st configuration is the optimal low-cost sizing for the studied scenario shown in Fig. 7 to reach 8h of self-sufficiency.

Fig. 7.
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Net load for 3 days in January for 2 configurations: Minimum cost and most self-sufficient.

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However, if the design goal is to achieve more than 1 day of self-sufficiency during a mix of sunny and partly sunny days in winter, the minimum cost configuration that could meet the entirety of the load for 3 days was 54 PV/T, 1816L tank, and 70 kWh battery for a total component cost total of 65 422$ as shown in Fig. 7.

4 Discussion

The sensitivity analysis found that the most important parameter is to size the PV/T collector array to only just meet the base building load and optimize the thermal storage tank dimensions based on the PV/T quantity. Battery capacity should be designed based on the desired application to meet the building and the heat pump load for the required minimum number of self-sufficiency hours. In the case of this study, to minimize power outages reaching 8 h on average at the lowest component cost, 27 PV/T, a 908L tank, and 10 kWh battery capacity were found to be able to reach 8 h for all 3 days of different climatic conditions during winter. Nonetheless, depending on the applications, improving thermal storage to 1816L could slightly improve performance of 33 min, while increasing battery capacity to just 20 kWh would improve 1h 33 of self-sufficiency and both together 2h57. In this way, battery capacity has the largest impact on improving self-sufficiency if there is enough excess electricity produced.

However, these components have different impacts on the system's initial costs, with batteries and PV/T collectors’ costs being more substantial than the storage tank. In this way, the final configuration with a cost of 18 861$ would be 19 951 $ with a larger tank of 1816L, 24 401$ with a 20 kWh battery capacity, and 25 491$ with both improvements. Notably, design requirements significantly vary depending on the building, climate, and its application. In this way, for the case study, an appropriate sizing range for the case study during winter operation would be between 27 PV/T collectors (43 m2), a tank size between 900L to 2000L, and a battery capacity from 10 kWh up to 20 kWh for a building daily load of 81 kWh/day.

The study's main limitations are that the design was only optimized for a short duration in winter conditions without considering the effects of yearly changes in solar radiation and temperature, in addition to assuming the power outages were always after solar energy production in the evening. System design analysis considering a long-term approach for a full year as well as utilizing a smart predictive control methodology with probabilistic models to predict power outage events could improve real-world accuracy and reduce these limitations.

5 Conclusion

This study presented a design sensitivity analysis of a PV/T-battery-thermal storage system implemented in the offices of a school building to determine the optimal sizing to enhance building resiliency to power outages during winter. The optimal sizing to meet the office 81 kWh/day heating load was found to be around 27 PV/T (43 m2), 908L thermal storage, and 10 kWh battery to minimize cost while being self-sufficient for 8h, the average power outage length from caused external factors. The system's most cost-effective approach to improve performance was found to size the PV/T collectors based on the load without oversizing, maximize thermal storage size, and minimize battery capacity to meet the minimum heat pump electrical consumption. Nonetheless, since the system performance is highly dependent on the building load, the climate, and the system applications. The study identifies key parameters to consider for PV/T with energy storage systems to improve building performance and resiliency for winter operation while reducing component costs.