Influence of Photovoltaic Shading on Rooftop Heat Transfer, Building Energy Loads, and Photovoltaic Power Output

Alasadi, Habeeb; Choi, Jun-Ki; Mulford, Rydge B.

doi:10.1115/1.4054710

Abstract

Photovoltaic (PV) modules on building rooftops provide shade from summer heating, leading to a reduction in cooling load during hot seasons. However, PV shading also reduces passive solar heating during winter months, leading to an increase in the building heating load during cold seasons. In this study, the heat transfer performance of an enclosure formed by adjacent PV modules is analyzed for three locations in the United States, comparing the daily heat flux through rooftops for the case of a PV-shaded rooftop as well as an unshaded roof. Several result metrics are developed as part of this work, including the saved energy load (SEL), or the energy conserved by adding PV-shading to the rooftop, and the additional energy load (AEL), or the supplemental building energy required to replace shaded solar heating. Finally, this work calculates the utility factor, being the ratio of SEL and PV power output to AEL as a metric of PV effectiveness. SELs are 5.2, 6.2, and 11.7 kWh/m² · year for Dayton, Boise, and Phoenix, respectively, while the AELs for the same locations are 1.6, 1.5, and 2.1 kWh/m² · year. The utility factors for the same three locations are 61, 71, and 79. In general, locations with hot, non-cloudy summers and clear skies in winter see the largest utility factor. Further, it is shown that PV shading can conserve building energy during the winter months by preventing radiative losses to cold winter skies.

Introduction

Buildings account for over 40% of primary U.S. energy consumption [1]. As such, reducing building energy consumption is an essential component of global energy reduction strategies. During the summer months, a building cooling load can be reduced by shading the building rooftop using roof-mounted photovoltaic (PV) arrays. However, rooftop shading prevents passive solar heat gain during winter months, increasing heating loads [2]. PV-shaded rooftop performance depends on PV array design parameters, such as the tilt angle of the PV panels and the distance between one PV to the next PV, as well as local weather conditions.

Several papers have been published that consider PV-shading to enhance buildings’ roof performance and reduce the energy consumption of buildings [3–6]. One study [7] examines the impact of PV-augmented rooftops on building energy consumption located in Western Greece. The simulation result showed that seasonal heating loads increased by 6.7%, and cooling loads declined by 17.8% for the top floor. A separate study [8] developed a simplified physical and corresponding mathematical model. The results showed that the heat gain and cooling load were minimized by 77.4% and 69.4%, while the system comprehensive energy efficiency of flat and tilted PV on roofs was 63.35% and 62.73%, respectively. Experimental work completed by Liu et al. [9] investigated the influence of a distributed PV array on a flat roof’s cooling load in July and August on low bracket and high bracket systems. The research results of high bracket installation show that the cooling load of a shadowed roof declined about 27.5% in a whole day and decreased about 37.4% between 08:00 and 17:00 compared to the unshaded roof on a sunny day. On the other hand, the cooling load of a shadowed roof with a low bracket PV installation minimizes the cooling load by 18.8% over the course of a full day, while the cooling load is reduced by 27.2% between 08:00 and 17:00 compared to unshaded rooftops for a sunny day. Additional works had found that cooling loads could be reduced by between 14% and 23% for hot or warm weather [10,11].

Other researchers have investigated different simulation approaches for predicting the performance of PV-shaded rooftops. Eftychios et al. used trnsys to examine temperatures, heat flux, and the cooling load of a single cooling zone affected by PV-shading [12]. The simulated results of the research indicate that summertime PV-shading has a high impact on the roof temperature located directly under PV panels that the roof temperature could be reduced by 16 °C around noon. Likewise, PV shading can reduce the heat flux of the roof by 37%. The energy plus simulation environment was used in other research to investigate the effect of PV shading on rooftop temperature [13]. This work examines the roof temperature for three cases: with and without PV panels, with and without exposure to sunlight, and using roof materials with different thermal conductivities and for different climatic zones. Another work investigates the use of phase change materials (PCMs) and different cell positions on the facade. By applying PCMs to the shading system, the building demand was reduced about 44%, while the building thermal comfort increased by about 34% [14]. Additional research shows that solar cells on the facade and roof decrease the annual energy consumption inside the facility by approximately 15% and 40%, respectively [15].

Despite the body of excellent literature published on this subject, there is still additional work required. The presented published papers consider only a single PV panel interacting with the building rooftop and do not consider the entire enclosure produced by PV arrays. Different regions located in Europe, the Middle East, Asia, and part of the U.S. were considered in these published papers, however, a variety of different climate zones in the United States are not considered yet. Likewise, a metric quantifying the utility of PV shading remains to be proposed.

This work examines the impact of PV shading on roof temperature and defines and calculates metrics to quantify the utility of PV shading on energy building performance for three different locations in the U.S., considering the influence of the entire PV array enclosure.

Methods

Energy Balance.

The energy balances for both unshaded and PV-augmented rooftops are presented in Figs. 1(a) and 1(b), respectively. For an unshaded roof, diffuse and beam solar irradiation is absorbed by the roof while heat is exchanged between the roof and the surroundings via convection, radiative interchange with the night sky, and conduction into the building through the rooftop. For a PV-augmented rooftop, solar energy is absorbed by the rooftop directly from diffuse and beam solar irradiation streaming in through the gap between panels as well as radiative exchange with the back of the PV. As with the unshaded rooftop, heat is exchanged between the roof and the surroundings via convection, radiative exchange with the atmosphere, and heat conduction into the building.

Fig. 1

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(a) Energy balance on the unshaded roof and (b) energy balance on the PV-shaded roof

The energy balance for the unshaded case is given in Eq. , with terms expanded as shown in Eqs. and to obtain Eq. . The energy entering the system is the solar heat flux

(q_{s u n}^{″})

⁠, consisting of beam irradiation (I_b) and diffuse irradiation (I_d) multiplied by the roof absorptivity

(α_{r} = 50 %)

[16]. The energy leaving the system is the summation of the heat flux through the roof

(q_{r}^{″})

⁠, the heat loss to the surroundings by convection

(q_{c o n}^{″})

⁠, and radiation heat flux into the surroundings

(q_{r a d, s k y}^{″})

⁠.

\begin{matrix} q_{s u n}^{″} = q_{r}^{″} + q_{c o n}^{″} + q_{r a d, s k y}^{″} \end{matrix}

(1)

The heat conduction into the building from the rooftop is calculated in Eqs. (2) and (3) for rooftops without PV-shading $(q_{r}^{″})$ and with PV-shading $(q_{r, PV}^{″})$ ⁠. The heat transfer is a function of the roof temperature, which is calculated with and without PV shading (T_r,PV, T_r), and internal building temperature (T_in = 21.11 °C) [17], the overall heat coefficient and convection coefficient of the roof (U = 0.19 W/m² · K for Dayton and Boise and 0.23 W/m² · K for Phoenix, h_in = h_r = W/m² · K) [18,19]. The roof emissivity (ɛ_r) used in work is 0.5 [20]. The overall heat coefficient values are recommended by ASHRAE for a roof of a medium-sized building located in the three locations.

\begin{matrix} q_{r}^{″} = \frac{T_{r_{}} - T_{i n}}{\frac{1}{U} + \frac{1}{h_{i n}}} \end{matrix}

(2)

\begin{matrix} q_{r, PV}^{″} = \frac{T_{r, PV} - T_{i n}}{\frac{1}{U} + \frac{1}{h_{i n}}} \end{matrix}

(3)

\begin{matrix} α_{r} \cdot (I_{b} + I_{d}) = \frac{T_{r} - T_{i n}}{\frac{1}{U} + \frac{1}{h_{i n}}} + h_{r} \cdot (T_{r} - T_{o}) + ε_{r} \cdot σ \cdot \leq (T_{r}^{4} - T_{s k y}^{4}) \end{matrix}

(4)

The energy balance for the PV shaded case presented in Fig. 1(b) is given in Eq. and is the summation of the energy entering the control volume, including the radiation heat flux from the PV to the roof

(q_{r a d_PV}^{″})

and the solar heat flux

(q_{s u n}^{″})

⁠. The energy leaving the system is the summation of the convection

(q_{c o n}^{″})

⁠, the radiation heat flux into the surroundings

(q_{r a d_s k y}^{″})

⁠, and the heat flux through the roof

(q_{r, PV}^{″})

⁠. As before, the energy balance is written in terms of temperature, as shown in Eq. .

\begin{matrix} q_{s u n}^{″} + q_{r a d, PV}^{″} = q_{r, PV}^{″} + q_{c o n}^{″} + q_{r a d, s k y}^{″} \end{matrix}

(5)

α_{r} \cdot (I_{b} \cdot \frac{A_{b}}{A_{r}} + I_{d} \cdot F) + ε_{r} \cdot σ \cdot F_{PV} \cdot (T_{k}^{4} - T_{r, P V}^{4}) = \frac{T_{r, PV} - T_{i n}}{\frac{1}{U} + \frac{1}{h_{i n}}} + h_{r} \cdot (T_{r, PV} - T_{o}) + ε_{r} \cdot σ \cdot F \cdot (T_{r, PV}^{4} - T_{s k y}^{4})

(6)

The solar heat flux $(q_{s u n}^{″})$ is the summation of the beam and diffuse irradiation hitting the roof surface located between adjacent PV modules multiplied by the roof’s absorptivity (α_r). The beam irradiation reaching the roof surface is equivalent to the beam irradiation multiplied by the ratio of roof area on which the beam is incident divided by the total roof area (Fig. 2). The diffuse irradiation reaching the roof surface is equivalent to the diffuse sky irradiation multiplied by the view factor between the roof surface and the sky (F), which is found using Hottel’s crossed strings method [21]. F_PV is the view factor between the PV and the roof while A_b is the roof area projected to the beam radiation.

Fig. 2

Geometry terms used to calculate the distance exposed to beam irradiation between adjacent PV panels (D3)

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Geometry terms used to calculate the distance exposed to beam irradiation between adjacent PV panels (D₃)

The sky temperature (T_sky ) and the temperature of the back of the PV (T_k) are found using equations from the literature [22,23] and are illustrated in Eqs. and . The term ws is the wind speed while “a” and “b” found in Eq. are “−3.473” and “−0.0595”, respectively, for an open rack of glass/cell/glass [22,23], while I_T is the total irradiation incident on the PV surface.

\begin{matrix} T_{sky} = 0.0552 * T_{o}^{1.5} \end{matrix}

(7)

\begin{matrix} T_{k} = T_{o} + I_{T} \cdot \exp (a + b \cdot w s) \end{matrix}

(8)

The area illuminated by beam irradiation is calculated using values given in Eqs. –. The vertical distance between the roof and the top of the PV panel (H) and the horizontal distance between the bottom and top of the right PV panel (D₁) are presented in Eqs. and . The horizontal distance between the top of the right PV and the bottom of the left PV (D₂), and the total distance between the bottom point of the right PV and the left PV (D_t) are calculated in Eqs. and , respectively. The roof area between adjacent PV panels, A_r, is given by multiplying D_t by the depth of the roof.

\begin{matrix} H = \sin (Φ) * 1 m \end{matrix}

(9)

\begin{matrix} D_{1} = \cos (Φ) * 1 m \end{matrix}

(10)

\begin{matrix} D_{2} = \frac{H}{\tan (θ)} \end{matrix}

(11)

\begin{matrix} D_{t} = D_{1} + D_{2} \end{matrix}

(12)

A_b as found in Eq. is given by multiplying D₃ (Fig. 2) by the depth of the roof. D₃ is calculated in Eq. , where θ_b is the sun elevation angle. Equation does not account for the “skew” of the shadow when the sun is not at solar noon. However, it is assumed that a large number of adjacent panels will cause the skew to have little impact on the total shaded area of the building rooftop.

\begin{matrix} D_{3} = D_{2} - \frac{H}{\tan (θ_{b})} \end{matrix}

(13)

PV power output (Eq. ) is a function of the total irradiation hitting the PV (I_T), PV surface area (A_PV), PV temperature (T_PV), and PV efficiency

(η_{PV} = 20 %)

at standard test conditions and temperature coefficient

(T_{COP} = 0.45 % /^{\circ} C)

⁠. The efficiency used in this work is an average efficiency of crystalline Si cells. Equation depicts that the PV temperature depends on ambient temperature (T_o) and total irradiation, the absorptivity (α) and the efficiency of the PV (η_PV), the solar transmittance of the cover over the PV (τ), and standard testing conditions, including the nominal operating cell temperature (NOCT) (T_C,NOCT ) (50 °C), the ambient temperature at NOCT (T_o,NOCT) (50 °C), and the solar irradiation at NOCT (G_T,NOCT 800 W/m²).

\begin{matrix} P_{PV} = I_{T} * A_{PV} * η_{PV} * [1 - ((T_{PV} - 25) * T_{COP})] \end{matrix}

(14)

\begin{matrix} T_{PV} = T_{o} + I_{T} [\frac{T_{C, NOCT} - T_{o, NOCT}}{G_{T, NOCT}}] [1 - \frac{η_{PV}}{τ α}] \end{matrix}

(15)

The annual saved energy load (SEL) and the annual additional energy load (AEL) are presented in Eqs. and , respectively. The SEL is obtained by subtracting the net heat flux through the unshaded roof from the net heat flux through the shaded roof, reducing the cooling load due to PV shading. This value is then divided by the coefficient of performance (COP) of the cooling system to determine the electrical energy saved due to PV shading. Similarly, the AEL is determined by subtracting the roof heat flux for the shaded and unshaded terms and then dividing by the efficiency of the heating system (assumed to be a furnace) to determine the additional energy required due to PV shading. SEL is calculated when the heat flux flows from the rooftop into the building interior, while AEL is calculated when the heat flux flows from the interior to the outside.

SEL = (Σ q_{r}^{″} - Σ q_{r, PV}^{″}) / COP \to Where q_{r}^{″} and q_{r, PV}^{″} > 0

(16)

AEL = (Σ q_{r, PV}^{″} - Σ q_{r}^{″}) / η \to Where q_{r}^{″} and q_{r, PV}^{″} < 0

(17)

Equations through give a complete analysis framework by which the roof heat flux, roof temperature, total saved cooling loads, and additional energy load of a PV-augmented roof are determined. In this study, hourly calculations are used to compute daily average roof temperature, roof heat flux, saved, and additional energy loads of a PV array on an identical rooftop located in three different U.S. cities. Finally, the power produced by the PV arrays was calculated and compared against the AEL in order to quantify the utility of the PV array. The utility factor presented in Eq. , is a ratio of energy benefits resulting from roof-mounted PV arrays (reduction in energy and electricity generation) to the negative effects of roof-mounted PV arrays (increase in building energy load). Larger utility factor values indicate a greater energy benefit resulting from roof-mounted PV arrays.

\begin{matrix} ψ = \frac{SEL + P_{PV}}{AEL} \end{matrix}

(18)

The program used to obtain the results and to evaluate the model using the Eqs. (1)–(18) is matlab R2020a.

Locations.

This study examines three locations in different states of the United States: (1) Dayton and Ohio, (2) Boise and Idaho, and (3) Phoenix and Arizona, where each location is situated in a unique climate zone [18]. Table 1 presents the ambient temperature, beam irradiation, and cloud percentage averaged over three winter months (December, January, and February) and three summer months (June, July, and August) for each city. The typical meteorological year data (TMY3) provided by EU Science Hub were utilized on an hourly basis to determine the typical weather and incident solar irradiation on the PV and the roof, as given in Table 1 [24].

Table 1

Seasonal average of temperature, beam irradiation, and cloud percentage [25]

	Winter			Summer
	Temperature (°C)	Beam irradiation (Wh/m²)	Cloud (%)	Temperature (°C)	Beam irradiation (Wh/m²)	Cloud (%)
Dayton	0.68	70.47	77.95	22.84	230.42	61.29
Boise	0.91	76.68	73.01	21.87	302.66	27.58
Phoenix	13.39	145.18	36.93	34.46	320.00	33.22

	Winter			Summer
	Temperature (°C)	Beam irradiation (Wh/m²)	Cloud (%)	Temperature (°C)	Beam irradiation (Wh/m²)	Cloud (%)
Dayton	0.68	70.47	77.95	22.84	230.42	61.29
Boise	0.91	76.68	73.01	21.87	302.66	27.58
Phoenix	13.39	145.18	36.93	34.46	320.00	33.22

The dimension of the PV is 1 m while the tilt angles of the PV (ϕ) are 33 deg, 36 deg, and 28 deg for Dayton, Boise, and Phoenix, respectively. The tilt angles are not equivalent to the location latitudes, but instead were determined based on results from Naraghi [26] who used optimization techniques to determine the best-performing tilt angle for locations across the United States. The distance between PV panels (Dt in Fig. 2) is set in order to avoid shading at solar noon between adjacent PV panels, as depicted in Fig. 2. The required distance between PV panels is a function of the tilt of the PV panels and the sun elevation at solar noon, which varies with location.

A demonstration building, with and without PV shading on the rooftop, is analyzed in each of the three locations to explore the intersection of PV roof shading and climate. The total surface area of the demonstration building’s roof is 1800 m² (30 m in width and 60 m in length). The same total area is investigated in the three locations in the U.S. The total PV area installed on the roof varies with location due to the variation in ideal PV tilt angle, with the distance between PV panels and the total PV area given in Table 2. The COP of the cooling used in the study is 3.5 [27], while the heater efficiency is 95% [28]. These values are used to determine the variation in building primary energy consumption as a result of PV shading.

Table 2

Photovoltaic, roof, and air conditioning specifications

	Dayton	Boise	Phoenix
Roof area (m²)	1800	1800	1800
PV tilt angle	33	36	28
Distance between PV panels (Dt)	2.87	3	2.17
PV area (m²)	626	599	828
COP	3.5	3.5	3.5
Heating and inverter efficiency	0.95	0.95	0.95

Results

Figures 3(a)–5(a) depict the daily average ambient temperature and the roof temperature for both a PV-augmented roof and an unshaded roof for three different locations in the U.S.: Dayton, Phoenix, and Boise. Figures 3(b)–5(b) illustrate the daily average heat flux through a PV-augmented and an unshaded roof for the three locations. The positive values indicate heat flux that passes into the building, while negative values present heat flux passing out of the building. Figures 3(c)–5(c) present daily PV power output, and Fig. 6 indicates the five steps average of daily saved energy and additive energy of the three cities as a function of time. The total annual SEL per each meter square of roof area are 5.2, 6.2, and 11.7 kWh/m² · year for Dayton, Boise, and Phoenix, respectively, while the total annual AEL per each square meter of roof area are 1.6, 1.5, and 2.1 kWh/m² · year for Dayton, Boise, and Phoenix, respectively.

Fig. 3

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Results for Dayton, Ohio, including: (a) daily average ambient temperature and roof temperature without (T_r) and with (T_r_,PV) PV panel shading and (b) roof heat flux without $(q_{r}^{″})$ and with $(q_{r, PV}^{″})$ PV panel shading, and (c) PV panel power output

Fig. 4

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Results for Boise, Idaho, including: (a) daily average ambient temperature and roof temperature without (T_r) and with (T_r_,PV) PV panel shading, (b) roof heat flux without $(q_{r}^{″})$ and with $(q_{r, PV}^{″})$ PV panel shading, and (c) PV panel power output

Fig. 5

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Results for Phoenix, Arizona, including: (a) daily average ambient temperature and roof temperature without (T_r) and with (T_r_,PV) PV panel shading, (b) roof heat flux without $(q_{r}^{″})$ and with $(q_{r, PV}^{″})$ PV panel shading, and (c) PV panel power output

Fig. 6

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Five-point daily average of energy savings and additional energy loads of three cities. A positive value indicates a decrease in building energy load when compared with an unshaded rooftop.

Using the total roof area (1800 m²), Table 3 presents the total annual SEL, AEL, PV power output, and utility factor of SEL and PV power output to AEL for Dayton, Boise, and Phoenix. The yearly power output of the PV shading system located in Phoenix 309,150 kWh/yr is higher than the yearly power output of the same system in Boise 193,932 kWh/yr or Dayton 181,710 kWh/yr, while it is higher in Boise than in Dayton. The annual SEL is 2654, 3189, and 5991 kWh/yr for Dayton, Boise, and Phoenix. The annual AEL for each location is 3032, 2785, and 4017 kWh/yr. The utility factor is 61, 71, and 79 for Dayton, Boise, and Phoenix.

Table 3

Annual cooling, heating, power output, and utility factor for three locations

	Dayton	Boise	Phoenix
Energy savings (kWh/yr)	2654	3189	5991
Additional energy (kWh/yr)	3032	2785	4017
PV power output (kWh/yr)	181,710	193,932	309,150
Utility factor	61	711	79

In the discussion with aid of the results provided (Figs. 3–6), the influence of PV shading on the building rooftop temperature, heat flux, and PV power production for the three different locations are compared. Then, the variation in building energy loads between unshaded and shaded rooftops and interpretation of the utility factor is provided.

Rooftop Temperature.

Figures 3(a)–5(a) illustrate that the daily average unshaded roof temperature is higher than the daily average PV-shaded roof temperature and outdoor air temperature for the three locations owing to the direct exposure of the full unshaded roof to passive solar heating. For the three locations, the daily average PV-shaded roof temperature is larger than the daily average outdoor temperature during summer hours and less during some winter hours. The PV-shaded roof is completely shielded from beam solar radiation by the PV module when the sun elevation angle is small, such as in mid-winter and during morning and evening hours. At other times, in which the sun elevation angle is high, the PV-shaded roof is partly exposed to beam radiation.

A close comparison of summer and winter rooftop temperatures in Dayton and Phoenix illustrates an interesting and unexpected benefit of PV shading during the winter months. Figures 7(a)–7(d) focuses on the comparison between the daily ambient and shaded and unshaded roof temperatures during the summer and winter months in Dayton and Phoenix. Figures 7(a) and 7(b) depict the temperature data during July for Dayton and Phoenix, respectively. As expected, the unshaded roof temperature is higher than the PV shaded roof temperature due to shading from the summer sun in both locations. In contrast, Figs. 7(c) and 7(d) present the ambient temperature and shaded and unshaded roof temperature during December in Dayton and Phoenix, respectively. In Phoenix, the result is as expected, where shading of the solar load in winter prevents passive solar gain, causing the shaded roof temperature to decrease, which increases the building heating energy load. In Dayton, however, the PV shaded roof temperature is higher than the shaded temperature on almost all days in December, decreasing the building heating energy load and resulting in energy savings. Unlike in Phoenix, significant winter cloud cover in Dayton (77% coverage during December) prevents the PV panels from shading the passive solar load as the solar load has already been shaded by cloud cover. However, the PV panels do protect the relatively cold winter sky, preventing radiative losses from the roof, which yields a net increase in rooftop temperature. This surprising behavior is an unforeseen benefit of PV shading in colder environments dominated by cloud cover in the winter months.

Fig. 7

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Results for Dayton, Ohio, and Phoenix, Arizona, including daily average ambient temperature and roof temperature without (T_r) and with (T_r_,PV) PV panel shading: (a) and (b) during July, and (c) and (d) December. Figures 7(a) and 7(c) are for Dayton, Ohio, and Figs. 7(b)–7(d) are for Phoenix, Arizona.

Heat Flux and Photovoltaic Power Production.

For the three locations, the daily heat flux passing through the PV-shaded roof is below the daily heat flux passing through the unshaded roof as presented in Figs. 3(b)–5(b). This can also be determined using the temperature data, as the daily average PV-shaded roof temperature is most of the time below the unshaded roof temperature.

Daily PV power output, in Figs. 3(c)–5(c), is slightly higher during spring and fall due to the slope of the PV panel; in all three locations. The results show that the PV power output of the roof area (1800 m²) in Dayton is lower than the PV power output in Boise and Phoenix. The Phoenix total annual PV power output 309,150 kWh/yr is higher than both Boise’s 193,932 kWh/yr and Dayton’s total annual PV power output of 181,710 kWh/yr owing to the difference in the cloud percentages and average irradiation values as found in Table 1. It is important to note that, owing to the smaller spacing between panels, the Phoenix rooftop contains more PV panels (total PV area of 828 m²) than either the Boise (599 m²) or Dayton (626 m²) rooftops. This assists the Phoenix rooftop in producing more power than the Boise or Dayton locations.

Shaded and Unshaded Comparison.

The SEL for a PV-shaded roof located in Phoenix SEL = 5991 kWh/yr is nearly double the SEL of the same roof located in Boise SEL = 3189 kWh/yr or Dayton SEL = 2654 kWh/yr, which are roughly equivalent. Of the three locations, the shading provided by the Phoenix PV panels is the most effective owing to the large solar irradiation found in Phoenix. In addition, the annual AEL of a PV-shaded roof in Dayton AEL = 3032 kWh/yr is nearly equivalent to the annual AEL value in Boise AEL = 2785 kWh/yr and 24% less than the annual value in Phoenix AEL = 4017 kWh/yr, a pattern which corresponds with the average winter temperatures of each region, where Dayton and Boise have similar average winter temperatures and Phoenix is 13 °C hotter than both locations in the winter months. The AEL annual value in Phoenix is higher than in Dayton and Boise because the roof area shaded by PV in Phoenix during the winter is higher than the shaded area roof in Dayton and Boise, as illustrated in Fig. 8. This is due to the smaller distance between panels for the Phoenix building compared to Dayton and Boise. Limiting passive solar heating via PV shading is, therefore, more detrimental in colder climates. These results indicate that PV-shading of a rooftop is more effective at limiting building energy consumption (by reducing cooling load and requiring little additional energy) in hot climates with clear skies.

Fig. 8

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Shaded roof area percentage of the total roof area for the three cities

The utility factor, being the sum of PV power and saved energy load divided by the additional energy load, quantifies the performance of a roof-mounted photovoltaic panel, factoring in the influence of the panel on the building additive and saved loads. A large value indicates that the building saved energy and electricity produced by the panel far exceeds the additional energy required due to the shading of the building rooftop. A small ratio that is greater than unity indicates that the PV panel results in a net positive energy influence but is less useful at generating/conserving energy. Finally, a value below unity indicates that the panel consumes more power (as additional required energy) than the power it creates/conserves. This utility factor is presented in Table 3 for all three locations. Phoenix features the largest utility factor, being 79, which is within range but higher than the ratio of 61 found in Dayton, which produced less PV power and required less additional energy than Phoenix. Boise, on the other hand, features a ratio of 71, nearly 10% less than the ratio in Phoenix. This ratio can easily be attributed to the smaller SEL in Boise. However, the AEL alone does not give the full picture. The combination of extreme ambient summer temperatures and large solar irradiation in Phoenix increases the value of the shade provided by the PV panels, severely decreasing the cooling load on the building. Likewise, the temperate winter conditions devalue passive solar heating in the winter, and therefore shading in the winter causes very little change in building heating loads. In summary, PV panels on rooftops are utilized most effectively in sunny, hot summer conditions and temperate winter conditions. Conversely, locations with limited solar resources as well as cold winter temperatures will find the lowest utility factor, indicating that the overall impact of PV panel installation will be poor. However, the PV panels provide an unexpected benefit by shielding the rooftop from radiative losses to the cold night air, which is most advantageous if the solar resource is already limited by excessive cloud cover in the winter.

Future work will include adding reflectors onto rooftops between adjacent PV modules, increasing PV power output while providing additional rooftop shading. However, the increased temperature of the panels and the influence of the reflectors on rooftop temperatures must be considered. Further, an economic study of PV-shaded rooftops, as well as PV-reflector-shaded rooftops, will be pursued to determine the cost savings related to PV-shading on rooftops. Finally, experimental validation of these results will also be pursued.

Conclusion

Roof thermal performance may be improved by adding PV panels to the rooftops, resulting in shading, which decreases the building cooling load, although this approach causes the building heating load to increase during winter months. Results from an energy balance on a shaded and unshaded roof show that the daily average temperature of a PV-shaded roof is lower than the daily average unshaded roof temperature and higher than the ambient temperature most of the time. Likewise, the daily average heat flux through an unshaded roof is less than the daily average heat flux of a PV-augmented roof during the summer months. The SEL and AEL of PV-augmented roofs depend on the weather conditions of the system locations and shaded roof area. For hot, dry weather like Phoenix, Arizona, the SEL is more than the SEL of the same system located in colder weather like in Boise or in a location with greater cloud cover like Dayton. Likewise, hot locations experience less AEL. The utility ratio varies significantly from one city to another, with hot, sunny climates like Phoenix exhibiting ratios that are roughly 24% greater than the ratio in colder, cloudier climates like Dayton or Boise. During winter months, obstruction from PV panels limits radiative losses to the cold night sky, sometimes decreasing building energy loads in winter months if the solar resource is already limited due to cloud cover. In conclusion, a PV-augmented roof located in hot weather is more effective at generating power and reducing energy consumed by cooling equipment than a PV-shaded roof located in warm or cold weather.

Acknowledgment

The authors would like to acknowledge the contributions of Dr. Robert Gilbert for initial discussion regarding this work.

Funding Data

We appreciate the US Department of Energy for supporting this work through its funding of the Industrial Assessment Center program (DE-EE0007710).

Conflict of Interest

There are no conflicts of interest.

Nomenclature

h =: convection coefficient (W/ (m² · K))
A =: area (m²)
D =: width (m)
F =: view factor
H =: PV edge height (m)
I =: irradiation (w/m²)
T =: temperature (K)
U =: overall heating thermal coefficient (W/ (m² K))
q″ =: heat flux (w/m²)
α =: absorptivity
ɛ =: emissivity
η =: efficiency
θ =: sun elevation (deg)
σ =: Stefan–Boltzmann constant (W/ (m² · K⁴))
ϕ =: PV tilt angle (deg)
ψ =: utility factor

Subscripts

b =: beam radiation
d =: diffuse
k =: back of PV panel
o =: outside
r =: roof
t =: total
in =: inside
con =: convection
rad =: radiation
PV =: PV panel

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Influence of Photovoltaic Shading on Rooftop Heat Transfer, Building Energy Loads, and Photovoltaic Power Output

Abstract

Introduction

Methods

Energy Balance.

Locations.

Results

Rooftop Temperature.

Heat Flux and Photovoltaic Power Production.

Shaded and Unshaded Comparison.

Conclusion

Acknowledgment

Funding Data

Conflict of Interest

Nomenclature

Subscripts

References

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Influence of Photovoltaic Shading on Rooftop Heat Transfer, Building Energy Loads, and Photovoltaic Power Output

Abstract

Introduction

Methods

Energy Balance.

Locations.

Results

Rooftop Temperature.

Heat Flux and Photovoltaic Power Production.

Shaded and Unshaded Comparison.

Conclusion

Acknowledgment

Funding Data

Conflict of Interest

Nomenclature

Subscripts

References

Get Email Alerts

Cited By

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