Net Zero Agrivoltaic Arrays for Agrotunnel Vertical Growing Systems: Energy Analysis and System Sizing

1. Introduction

Agriculture has enormous negative impacts on the natural environment (22% of 2019 global greenhouse gas emissions) [1], but indoor growing can significantly reduce the environmental impact of agriculture, especially by minimizing transportation emissions [2,3]. Moreover, indoor growing can drastically reduce water usage compared to traditional farming methods [4]. Indoor farming also allows increased crop productivity per unit area and reduces the time required to reach plant maturity [4]. Indoor growing can reduce and in some cases eliminate the use of harmful herbicides or pesticides promoting healthier produce [5]. Unlike traditional outdoor farming, indoor growing enables year-round production, ensuring a consistent food supply regardless of seasonal changes or weather conditions [6,7]. The technology also provides spatial efficiency and land use optimization [7]. With advancements in LED lighting technology and optimized envelope, indoor growing operations can minimize energy consumption, mitigating their carbon footprint [8,9]. Closed-loop systems in indoor growing can minimize waste production by recycling water, nutrients, and organic matter, contributing to a circular economy model [10,11]. Indoor growing also helps preserve biodiversity by allowing for more diverse and resilient ecosystems in agricultural regions [12]. Unfortunately, indoor growing in general has a major problem: increased energy costs have forced many indoor growing operations into bankruptcy [3], which hits vertical growers particularly hard [13]. High energy costs and energy price volatility have made even startups with hundreds of millions of dollars of funding go bankrupt [14].

To overcome electrical costs for indoor farming, the agrivoltaics agrotunnel introduced here uses four approaches: 1) high insulation for a building dedicated to vertical growing, 2) high efficiency light emitting diodes (LEDs) for lighting, 3) the use of heat pumps (HPs), and 4) to control the volatility and reduce the electricity costs, solar photovoltaics (PV) provide for a known LCOE and a 25-year lifetime. All these approaches have been combined in an agrivoltaics agrotunnel where agrivoltaics arrays on the outside provide power for the grow lights and water pumps and other electrical equipment on the inside. The core concept involves either an earth and vegetation-covered tunnel (Figure 1a) or a mobile unit (Figure 1b) housing high-density vertical aeroponic-hydroponic hybrid systems illuminated by high-efficiency LED grow lights. Next to the agrotunnel fixed/variable tilt agrivoltaics PV arrays [15] are shown, which provide all of the power necessary to operate the agrotunnel.

PV technology has declined in price for decades [16,17], making it the lowest-cost electricity generation technology [18,19]. This provides an opportunity to control the costs of indoor growing. Already because of this cost advantage, PV is the most rapidly-expanding electricity source [20,21] and dominates new sources of power [22]. With the growth of PV, which demands large surface areas to provide large amounts of energy there have been land-use conflict associated with installing PV plants on farmland [23,24,25,26]. Fortunately, this can be rectified with agrivoltaics, which refers to the dual use of land for clean electricity generation with PV and agriculture [27,28,29,30,31]. This increases land efficiency [32,33] and agrivoltaic systems have proven to be economically viable as they provide farmers with dual stream of revenue – one through generation of electricity and one through the produce/crop yield [30,34,35,36,37,38]. To push this concept further this paper investigates the potential of using agrivoltaics to power the even more land use efficient indoor growing inside an agrotunnel.

In order to size the net-zero agrivoltaics array that is necessary to support an agrotunnel, this study first develops a thermal model for load calculations in agrotunnel, which has been validated using the results of a commercial building’s load calculation with the Hourly Analysis Program (HAP). Using measured data, the effect of plants’ evapotranspiration is included subsequently as it is not incorporated in HAP software. The size of heat pumps (HPs) needed to maintain a constant temperature in the agrotunnel is determined in the next step. Next, plug loads (i.e., water pump energy needed to provide for the hybrid aeroponics/hydroponics system, DC power running the LEDs hung on the grow walls, and dehumidifier assisting in moisture condensation in summer) are measured/modeled. Ultimately, all models are combined to establish an annual load profile for an agrotunnel (also verified based on two month performance) that is then used to model the necessary PV to power the system throughout the year. The results are discussed, and future work is outlined to completely solarize agrivoltaics agrotunnels.

2. Agrivoltaic Agrotunnel

The agrotunnel (Food Security Structures Canada (FSSC) [39], London, ON) presents a solution to combat food insecurity by offering an easily assembled, scalable, and sustainable indoor vertical farming structure. It is designed to withstand extreme climate conditions and can be adapted to various locations. FSSC uses fiber reinforced polymer (FRP) construction to enhance portability, strength, and lightweight design to reduce the embodied energy and emissions for transportation. This innovative growing chamber enables precise control of light, humidity, and temperature, facilitating year-round cultivation of hybrid-aeroponic fruits and vegetables in harsh environments. Assembling the 1.2 m × 2.4 m panels allows for easy transportation of components. The detailed dimensions and thermal resistances of the agrotunnel envelope are illustrated in Figure 2.

The agrotunnel under study is located at the Western Innovation for Renewable Energy Deployment (WIRED) in London, Ontario (Figure 3a). As shown in Figure 3b, the design is composed of two sections (grow room and monitoring room). 8 grow walls, each with two sides and two mini walls for each side are installed in the growing room in addition to 6 grow bins. Utilizing the same growing technology as the grow walls featuring adjustable lighting brackets, the grow bins offer an ideal growing setting for root vegetables and other plants that demand greater space.

All the growing facilities are fed by low wattage and low voltage LED lights produced by Better Grow Lights [40]. These commercial lights are specifically designed for high density plant spacing and come with three 180 ° (BGL180A), 180 ° (BGL180C), and 360 ° (BGL360A) designs. BGL180A lights are hung on the side aisles as well as top of the grow bins, and BGL360A are hung on the center aisles, as shown in Figure 4. BGL180C are horizontally hung on top of the grow bins. In the agrotunnel, there are 28 BGL180A each with 75 W, 42 BGL360A each with 100 W, and 12 BGL180C each with 30 W wattage (11 in grow room and 1 in monitoring room).

3. Methodology

The agrotunnel’s load is made up of four sub systems: lights, water pumps, heat pump (HP), and a dehumidifier. A dehumidifier is operated to assist HPs in maintaining the relative humidity (RH) at a desired level. The HP is the major component in meeting the thermal (sensitive and latent) loads of the system. Artificial lighting also has a major contribution to increasing the temperature of the agrotunnel’s microclimate. All these loads are characterized as shown in Figure 5. Sizing all the thermal and electrical equipment would be done based on the loads as the results of the structure’s specifications and the circumstances the plants will grow under.

3.1. Thermal Model

The load calculations of the agrotunnel are estimated using the following thermal model developed. It is assumed that all the lights are on and planted crops are mature enough. Meanwhile, one person is doing some non-strenuous work such as planting, harvesting, watering, etc. in the building. The following sub-models are developed based on the load calculation principles [41].

3.1.1. External Loads

CLTD/CLF method, described in the 1997 AHSRAE Fundamentals [42], is used to calculate the transmission load of the agrotunnel, which is the most practical method for sizing the HVAC equipment while being simple.

Equation (1) is used for calculating the heat gains through the walls, the roof, and the floor. Cooling load temperature difference (CLTD) considers the collective impact of variations in indoor and outdoor temperatures, daily temperature fluctuations, solar radiation, and heat retention within the building structure. The values are determined using the tables provided in Chapter 28^th of ASHRAE Fundamentals Handbook [42].

$${\dot{Q}}_{cc}=\sum \frac{A_k}{R_{tot,k}}CLTD+\frac{A_{floor}}{R_{tot,floor}}(T_o-T_i),$$

(1)

where, ${\dot{Q}}_{cc}$ represents the heat losses due to the conduction and convection transmission through the envelope. $A_k$ is the surface area of each part of the envelope (m² or ft²) except for the floor and $A_{floor}$ stands for the surface area of the floor. $R_{tot,k}$ corresponds to the conduction and convection thermal resistance of each part of the envelope (m².K/W or hr. ft².F/Btu), which can be calculated by Equation (2) [43]:

$$R_{tot,k}=R_{conv,o}+R_{cond}+R_{conv,i},$$

(2)

$T_i$ and $T_o$ are the indoor design temperature and the outdoor temperature (°C or °F), respectively. As the ASHRAE tables offer hourly CLTD values based on a standard scenario, such as an outdoor maximum temperature of 95 °F, mean temperature of 85 °F, and a daily temperature range of 21 °F, Equation (1) is modified through Equations (3-5) to accommodate correction factors for situations deviating from this base case. CLTD values of the base case for the material used in the envelope are tabulated in Table 1.

$${\dot{Q}}_{cc}=\sum \frac{A_k}{R_{tot,k}}{CLTD}_{corrected}+\frac{A_{floor}}{R_{tot,floor}}(T_o-T_i),$$

(3)

$${CLTD}_{corrected}=CLTD+\left(78-T_i\right)+(T_{o,mean}-85),$$

(4)

$$T_{o,mean}=T_{o,max}-\frac{DRT}{2},$$

(5)

the daily range of temperature (DRT) indicates the difference between the maximum and the minimum temperature within 24 hours. For the floor transmission, ($T_o-T_i$) will be simply used.

The sensible and latent loads caused by infiltration can be calculated using Equations (6) & (7), respectively.

$${\dot{Q}}_{sens,inf}=n_{ACH}{V}_{AT}{\rho }_a{Cp}_a\left(T_o-T_i\right),$$

(6)

$${\dot{Q}}_{lat,inf}=n_{ACH}{V}_{AT}{\rho }_a\left({\omega }_o-{\omega }_i\right)h_{fg},$$

(7)

here, $V_{AT}$ is the total volume of the agrotunnel (m³ or ft³). ${\rho }_a$ and ${Cp}_a$ are the air density (kg/m³ or lb_m/ft³) and specific heat capacity (kJ/kg.K or Btu/lb_m.F), respectively. $n_{ACH}$ indicates the infiltration rate in ACH (hr^-1), which usually is 0.25 for a newly constructed and well-insulated building [44]; for this specific building without any windows and completely sealed walls, however, 0.1 will be a rational assumption. Also, ${\omega }_i$ and ${\omega }_o$ denote the indoor and outdoor humidity ratio in (kg_w/kg_da or lb_m,w/lb_m,da), respectively, and $h_{fg}$ corresponds to the enthalpy of vaporization of water in (kJ/kg or Btu/lb_m).

3.1.2. Lights

The waste heat dissipated by the LED lights mainly depends on their power and the cooling load factor ($F_{CLF,light}$), which can vary within a day based on the operating schedule of lights. $F_{CLF,light}$ would be 1 for the case lights are on for 24 hours. Otherwise, Table 2 will be used for one story building [42].

Equation (8) gives the waste heat dissipated by lights in (W or Btu/hr). $n_{lights}$, $P_{lights}$, $F_{lu}$, and $F_a$ are the number of lights used, the power of lights used in (W), the lights use factor, which can be assumed to be 1, and the ballast allowance factor, which can be assumed 1 for LED lights [45].

$${\dot{Q}}_{lights}=n_{lights}{P}_{lights}{F}_{lu}{F}_a{F}_{CLF,light},$$

(8)

3.1.3. People

Each person working in agrotunnel brings in both sensible and latent loads. Sensible and latent heat gained by a person who is doing sedentary (standing or walking slowly) or some light works are 92.4 W (315 Btu/hr) and 95.3 W (325 Btu/hr), respectively [42]. Total cooling load caused by the presence of the people in agrotunnel can be calculated using Equation (9):

$${\dot{Q}}_{people}={\dot{Q}}_{sens,people}+{\dot{Q}}_{lat,people}=n_{people}\times (315\times F_{CLF,people}+325\times F_{CLF,lat,people}),$$

(9)

where, $n_{people}$ represents the total number of people who are working in agrotunnel, and $F_{CLF,people}$ stands for the cooling load factor of people, based on the number of hours they work each day. In the basic scenario in the present study, it is assumed that one person is working 8 hours 7 days of week from 9 AM to 5 PM. Therefore, using Table 3, the $F_{CLF,people}$ will be extracted. $F_{CLF,lat,people}$ includes either 0 or 1 to consider the effect of the grower’s presence.

3.1.4. Evapotranspiration of Plants

There are many models of evapotranspiration [46,47], which incorporate the effect of various parameters, interpretation of which is beyond the scope of this study. In this case 8 walls each with 720 pots for a total of 5,760 all of which are being watered aeroponically at potentially different stages of growth and different species present an enormously complicated system. A more straightforward way to estimate the evapotranspiration load in a grow room involves calculating the net water consumption of plants. This entails measuring the volume of irrigation water introduced into the agrotunnel and subtracting the volume of water drained away [48]. The average amount of water consumed (${\dot{m}}_{water}$) can be estimated in (kg/s or lb_m/hr). Hence, the heat of vaporization will be calculated using Equation (10):

$${\dot{Q}}_{evap}={\dot{m}}_{water}{h}_{fg}$$

(10)

During this process, the moist of soil and plants’ leaves absorb heat from the environment, causing a temperature drop (sensible heating load), then evaporate. The energy absorbed is converted to latent heat of vapor in the air, which causes an increase in the humidity level of the microclimate (the latent cooling load). This transfer in energy leads to a constant enthalpy process, which is shown in Figure 6. Since the evapotranspiration of mature plants in a fully planted agrotunnel can be significant, it is assumed that the sensible heating load caused by the evapotranspiration of plants on the warmest day of the year will be met by the HP and the latent part is met by the dehumidifier. This is a rational assumption according to the experience of growers in similar facilities [49].

Total sensible and latent thermal loads of the agrotunnel will be calculated using Equations (11) & (12), respectively.

$${\dot{Q}}_{tot,sens}={\dot{Q}}_{cc}+{\dot{Q}}_{sens,inf}+{\dot{Q}}_{lights}+{\dot{Q}}_{sens,people}-{\dot{Q}}_{sens,evap}$$

(11)

$${\dot{Q}}_{tot,lat}={\dot{Q}}_{lat,inf}+{\dot{Q}}_{lat,people}+{\dot{Q}}_{lat,evap}$$

(12)

The following assumptions are taken into account to run the simulation:

• It is assumed that the growing room and the monitoring room are at the same temperature such that no heat transmission occurs between them.
• It is assumed that the air inside the agrotunnel is uniformly mixed, which is appropriate as the HP locations and clearance over the grow walls ensure paths of airflow.
• The design conditions of agrotunnel are the temperature of 22 °C, and the relative humidity (RH) of 68%.
• The thermal resistance of the still air ($R_{conv,i}$) on the vertical walls is 0.12 m².K/W [44].
• The thermal resistance of the still air ($R_{conv,i}$) on the ceiling is 0.11 m².K/W whenever the indoor temperature is higher than the outdoor temperature, and is 0.16 m².K/W when the indoor temperature is lower than the outdoor temperature [44].
• The thermal resistance of the still air ($R_{conv,i}$) on the floor is 0.16 m².K/W whenever the indoor temperature is higher than the outdoor temperature, and is 0.11 m².K/W when the indoor temperature is lower than the outdoor temperature [44].
• The thermal resistance of the outdoor moving air ($R_{conv,o}$) is 0.029 m².K/W [44].

3.1.5. Maximum Heating Load Model

In order to size HP, the maximum cooling load obtained by CLTD method will be compared to the maximum heating load under the worst-case scenario. The worst-case scenario for heating load estimations is defined for an evacuated agrotunnel, where conduction and convection heat transfer along with the infiltration losses are the only factors included. Total sensible heat loss from the agrotunnel is calculated by Equation (13) in (W or Btu/hr) [44]:

$${\dot{Q}}_{sens,heat}={\dot{Q}}_{cc,heat}+{\dot{Q}}_{sens,inf,heat}=\sum \frac{A_k}{R_{tot,k}}\left(T_i-T_o\right)+n_{ACH}{V}_{AT}{\rho }_a{Cp}_a\left(T_i-T_o\right),$$

(13)

Total latent heat loss through infiltration is calculated using Equation (7). Accordingly, the maximum total heating load will be calculated by Equation (14):

$${\dot{Q}}_{tot,heat}={\dot{Q}}_{cc,heat}+{\dot{Q}}_{sens,inf,heat}+{\dot{Q}}_{lat,inf,heat}$$

(14)

3.1.6. Heat Pump Model

The black box heat pump model is created by utilizing the performance datasheet of GSZ16 Goodman Air-Air Split heat pump (16 SEER and 9 HSPF) for both heating and cooling functions [50]. A supervised regression approach is implemented in Python to derive mathematical functions for the COP (Coefficient of Performance) of heat pumps within a nominal capacity range of 18,000-60,000 BTU/hr. Drawing from Li et al.'s correlations for load demand and COP of an air-conditioning heat pump [51], it is anticipated that the COP regressions would follow a second-degree polynomial pattern based on indoor and ambient temperatures.

3.1.6.1. Heating Mode

The correlation of COP is dependent on the ambient temperature (T_o) in (°C) as Equation (15):

$${COP}_{heating}=b_0+b_1{T}_o+b_2{T}_o^2,$$

(15)

the coefficients $b_0-b_2$ are extracted using the polynomial curve fitting technique and are shown for all rated capacities of GSZ16 Goodman Heat Pumps in Table 4 for heating mode. The fitting curve of heating COP for 18,000 BTU/hr heat pump is shown in Figure 7a.

3.1.6.2. Cooling Mode

The manufacturer's datasheet for cooling mode were created considering fluctuations in 3 variables (ambient temperature, indoor dry bulb temperature, and indoor wet bulb temperature) [50]. Hence, the regression is carried out in two steps: first, fitting a 2D curve as a function of indoor dry bulb and wet bulb temperatures, second, fitting a 3D surface as a function of first formulation and the outdoor temperature. Figure 6b depicts the fitting surface for the COP of an 18,000 Btu/hr HP in cooling mode. The COP for the cooling mode is determined using Equation (16).

$${COP}_{cooling}=b_o+b_1{T}_i+b_2{T}_{iwb}+b_3{T}_o+b_4{T}_i{T}_{iwb}+b_5{T}_i{T}_o+b_6{T}_{iwb}{T}_o+b_7{T}_i^2+b_8{T}_{iwb}^2+b_9{T}_o^2+b_{10}{T}_i^2{T}_o+b_{11}{T}_{iwb}^2{T}_o+b_{12}{T_i{T}_{iwb}T}_o$$

(16)

Table 5. Coefficients of polynomial correlations of COP in cooling mode.

		Rated Capacity (Btu/hr)
		18,000	24,000	30,000	36,000	42,000	48,000	60000
Coefficients of COP	b0	10.45648	9.14469	10.80332	10.66776	11.1678	10.7799	10.48214
	b1	-0.11064	0.012049	-0.13687	-0.12536	-0.14811	-0.12931	-0.12989
	b2	-0.21069	-0.21788	-0.18697	-0.19849	-0.208	-0.1978	-0.18888
	b3	-0.17693	-0.15915	-0.18717	-0.18142	-0.19111	-0.18515	-0.18156
	b4	-0.00038	-5E-05	-0.00024	-0.00012	8.46E-05	-0.00013	-0.00014
	b5	0.001363	-0.00014	0.001632	0.001463	0.001723	0.001535	0.001532
	b6	0.002596	0.002523	0.002229	0.002317	0.002419	0.002348	0.002227
	b7	0.002739	-0.0001	0.003153	0.002864	0.003197	0.002939	0.00295
	b8	0.008582	0.008251	0.007745	0.007893	0.00789	0.00791	0.007562
	b9	0.000623	0.000609	0.000722	0.000671	0.000727	0.000694	0.000706
	b10	-3.4E-05	1.16E-06	-3.8E-05	-3.3E-05	-3.7E-05	-3.5E-05	-3.5E-05
	b11	-0.00011	-9.6E-05	-9.2E-05	-9.2E-05	-9.2E-05	-9.4E-05	-8.9E-05
	b12	7.73E-06	9.2E-07	4.63E-06	2.34E-06	-1.6E-06	2.54E-06	2.61E-06
	R2	99.96	99.98	99.97	99.98	99.98	99.98	99.98

Table 5. Coefficients of polynomial correlations of COP in cooling mode.

		Rated Capacity (Btu/hr)
		18,000	24,000	30,000	36,000	42,000	48,000	60000
Coefficients of COP	b0	10.45648	9.14469	10.80332	10.66776	11.1678	10.7799	10.48214
	b1	-0.11064	0.012049	-0.13687	-0.12536	-0.14811	-0.12931	-0.12989
	b2	-0.21069	-0.21788	-0.18697	-0.19849	-0.208	-0.1978	-0.18888
	b3	-0.17693	-0.15915	-0.18717	-0.18142	-0.19111	-0.18515	-0.18156
	b4	-0.00038	-5E-05	-0.00024	-0.00012	8.46E-05	-0.00013	-0.00014
	b5	0.001363	-0.00014	0.001632	0.001463	0.001723	0.001535	0.001532
	b6	0.002596	0.002523	0.002229	0.002317	0.002419	0.002348	0.002227
	b7	0.002739	-0.0001	0.003153	0.002864	0.003197	0.002939	0.00295
	b8	0.008582	0.008251	0.007745	0.007893	0.00789	0.00791	0.007562
	b9	0.000623	0.000609	0.000722	0.000671	0.000727	0.000694	0.000706
	b10	-3.4E-05	1.16E-06	-3.8E-05	-3.3E-05	-3.7E-05	-3.5E-05	-3.5E-05
	b11	-0.00011	-9.6E-05	-9.2E-05	-9.2E-05	-9.2E-05	-9.4E-05	-8.9E-05
	b12	7.73E-06	9.2E-07	4.63E-06	2.34E-06	-1.6E-06	2.54E-06	2.61E-06
	R2	99.96	99.98	99.97	99.98	99.98	99.98	99.98

When the maximum heating and cooling load of the agrotunnel on the coldest/warmest day of the year is calculated, the size of HP can be determined. After selecting the HP, its COP correlation is used to calculate the power consumption in kW.

3.2. Electrical Loads

The power demanded by the lighting system and the HPs can be calculated as mentioned in the previous section. The load imposed by the water pumps and dehumidifier is included in this section.

3.2.1. Water Pump

Water pumps are integrated into the grow walls, and they operate 2-4 times per day (1 minute each time) based on the requirements of the plants according to their stage (seedlings or mature). Therefore, the average power consumption of water pumps is reported based on the data recorded by clamp meter [52]. The average power demand by the water pumps is 0.038 kWh, as reported in the data logger (Figure 8).

3.2.2. Dehumidifier

A commercial 23.7 L/day (50 pits/day) refrigerant dehumidifier with the integrated energy efficiency (IEF) of 1.9 L/kWh is being used in cases the heat pump cannot meet the latent load inside the agrotunnel [53]. Based on previous work it is assumed that if the latent load of the agrotunnel is higher than one third (which can be usually provided by HPs) of the maximum sensible load, the rest will be met by dehumidifier [54]. To be conservative, it is considered that all the grow walls are filled with mature plants. Table 6 reports the average water added to each pot of a mature plant during a week, which is measured in the agrotunnel under study. In the basic scenario, it is assumed that all pots are equally allocated for planting four types of crops.

3.3. Solar PV Sizing

PV system sizing was carried out by determining the 1-kW PV potential using the open-source System Advisor Model (SAM) [55] for each of the six locations: Albany, Edmonton, Houston, London, Montreal and San Francisco. Using the total annual electrical energy required for agrotunnel operation (E_{Annual load} in (kWh)) in each location and the annual energy potential of 1-kW PV system determined from SAM (E_{Annual load, 1kW} in (kWh)), the total PV system size (PV_Sys.Capacity) required to meet the annual electrical load is ascertained. The formula for the determining the PV size in (kW) is given by Equation (17):

$${PV}_{Sys.Capacity}=\frac{E_{AnnualLoad}}{E_{AnnualLoad,1kW}}$$

(17)

The PV system capacity determined through the estimate calculation is then used as input in SAM to run a detailed simulation at the appropriate scale. The simulations are run for each location and double checked if they meet the annual electrical load of the agrotunnel. Additionally, the land area required for PV systems, considering their modules’ transparency levels ranging from 0% (conventional silicon modules) to 69% (semi-transparent modules) will be reported. Table 7 details the assumptions used to perform the final modelling in SAM. A novel fixed-tilt racking design, adaptable into a variable-tilt racking system [15], is considered for use in this research. Soiling losses, DC power losses and AC power losses are kept as default.

Self-consumption (SC) and self-sufficiency (SS) are important metrics for assessing the energy performance of distributed energy systems at the local level [56]. SC measures the proportion of locally produced energy that is consumed locally, calculated as the energy generated by the PV system (E_PV) minus the energy sent to the grid (E_togrid), divided by the total energy generated by the PV system (E_PV) as seen in Equation 18. SS, on the other hand, indicates the extent to which local energy production meets local energy demand, calculated as the energy generated by the PV system minus the energy sent to the grid, divided by the local energy consumption (E_load) (Equation 19). Both metrics exclude nighttime hours when the PV system is not operational, and all energy is sourced from the grid, thus SC and SS are set to zero during these times. These metrics can be formulated through Equations (18) & (19) [57,58].

$$SC=\frac{E_{PV}-E_{togrid}}{E_{PV}}\times 100$$

(18)

$$SS=\frac{E_{PV}-E_{togrid}}{E_{Load}}\times 100$$

(19)

Table 7. Input parameter for SAM for PV system sizing for the agrotunnel.

Parameters	London	Albany	Edmonton	Houston	Montreal	San Francisco
PV module	Heliene 144HC-460 Bifacial [59]
Module type	Mono Crystalline Silicon - Bifacial
Tilt angle	34o [60]	34o [61]	53o [62]	27o [63]	30o [64]	32o [65]
Azimuth	180o
Soiling losses	5%
DC Power losses	4.44%
AC Power losses	1%

Table 7. Input parameter for SAM for PV system sizing for the agrotunnel.

Parameters	London	Albany	Edmonton	Houston	Montreal	San Francisco
PV module	Heliene 144HC-460 Bifacial [59]
Module type	Mono Crystalline Silicon - Bifacial
Tilt angle	34o [60]	34o [61]	53o [62]	27o [63]	30o [64]	32o [65]
Azimuth	180o
Soiling losses	5%
DC Power losses	4.44%
AC Power losses	1%

3.4. PV System Sizing

The annual electrical energy requirements of the agrotunnel for the six locations are given in Table 9. According to Table 9, colder regions have lower energy requirements compared to warmer regions. This is because the excess heat generated by lights compensates for the heating needs imposed by the outdoor environment.

The SAM results including the PV system size and the annual electrical energy generation for the six locations are detailed in Table 10.

The bar graph in Figure 20 depicts the annual electrical energy required and produced by the associated PV systems for all the six locations. The chart clearly indicates that the net-zero approach has been achieved for all locations. The similar sizes of PV systems confirm that the agrotunnel's performance is not sensitive to its location, particularly in northern climates. The smallest PV system size is needed in San Francisco (41.42 kW). Interestingly, the annual electrical output from the system in San Francisco comes out to be higher than London, Montreal, Edmonton and Albany since the electrical energy generation potential is higher in San Francisco (1641.5 kWh/kW) due to the higher level of solar irradiation there.

Figure 21 illustrates how the total land area used for PV installations changes with increasing module transparency. The data obtained from SAM for all locations are detailed in Table 11. A notable point in Figure 21 concerns the land required for PV system installations in Edmonton. Due to the high interrow spacing necessary to avoid shading, the total land area used for the PV system in Edmonton is considerably larger compared to other locations.

Table 12 presents the SC and SS values for the six locations under study. Despite the higher electrical energy demand in warmer regions, such as Houston, the PV system capacity required to supply the agrotunnel is smaller. This results in higher SC and SS values due to the adequate solar irradiation levels. Among the cold regions, London, ON exhibits the highest SC and SS values.

Figure 22 illustrates the monthly variations in SC and SS values over 12 months in London, ON. Figure 22 shows that SC and SS values exhibit opposite behaviors: SC increases when the electrical load exceeds the generation capacity of the PV system (e.g., in winter), whereas SS rises when the electrical demand is below the PV system's total energy capacity (e.g., in summer).

Figure 23 demonstrates that the electrical energy demand of the agrotunnel remains relatively consistent throughout the year, while the energy generated by the PV system fluctuates with variations in solar irradiation. To improve the compatibility between the load and the generated energy, and thereby increase the SS of the system, the use of electrical or thermal batteries can be considered.

4. Discussion

This study provides valuable insights into the feasibility of agrivoltaic agrotunnels. The PV sizes, ranging from 41.42 kW to 48.32 kW across locations with significantly different climates, indicate that the agrotunnel is not highly sensitive to location and climatic conditions. For conventional opaque PV modules, the required installation land area is 373 m² in San Francisco, 453 m² in Houston, 631 m² in Albany, 637 m² in London, 654 m² in Montreal, and 1,226 m² in Edmonton. For an agrotunnel with a total surface area of 117 m², the PV land index (total land area required by PV system to the total surface area of agrotunnel) is as follows: 3.2 m²/m² for San Francisco, 3.87 m²/m² for Houston, 5.39 m²/m² for Albany, 5.44 m²/m² for London, 5.59 m²/m² for Montreal, and 10.48 m²/m² for Edmonton. The solar flux level, commercial availability of PV moules and the interrow spacing alter the values for each location. The land requirements increase for systems with semi-transparent modules with transparencies of 8%, 44%, and 69%.

By utilizing single-axis tracking PV systems on just 1% of the total agricultural lands in Ontario, Quebec, and Alberta [68], it is possible to establish 231,167, 220,944, and 534,334 agrotunnels in these regions, respectively. This demonstrates the potential of this technology to enhance food security, especially in areas with harsh climates where local food production is challenging and energy, operation, and transportation costs are high [69]. In grid-tied conventional formats, the high capital costs of indoor farming facilities and the vertical farming industry [70] have deterred many investors [71], leading to farm closures, asset sales, loan defaults, and company bankruptcies [72,73,74,75,76,77,78,79,80,81]. Some industry giants, operating multiple industrial-scale farms with significant funding, have gone bankrupt after 20 years [82], and many startups have failed due to high operational costs and lower-than-expected crop yields [83,84]. In this context, becoming less dependent from/on the electricity grid by using affordable renewable energy sources, such as PV technology, can help many companies survive. For this, an open-source thermal-electrical model has been developed in the current study for predicting the energy demands of a semi-commercial scale indoor vertical farming facility, the agrotunnel. The model has been validated using commercial software, industrial datasheets, and real-time data from the agrotunnel, making it reliable and applicable to various locations. Investors and farmers can use this model and the findings of this research to evaluate the energy requirements of indoor farming, thereby investing in such technologies with greater confidence. With the PV systems sized appropriately as shown here agrivoltaics agrotunnel investors are completely insulated from electricity price fluctuations. Similarly, when compared to competitors that use natural gas for heating, the agrivoltaics agrotunnel economics are not impacted by natural gas fluctuations. An upfront cost in solar PV, means that all operational energy for 25 years on the agrivoltaics agrotunnel is known and paid for via financing.

The open-source model provided in this study is available for researchers worldwide to assess, modify, and upgrade to address its limitations. Currently, the model only considers the plug loads in the agrotunnel. Safety factors must be incorporated for future potential loads. The heat pump model can be enhanced from a black-box model to a thermodynamic model, increasing compatibility with various conditions and environmental limitations. Additionally, a comprehensive economic model should be developed to compare capital, labor, and energy costs. Future economic investigations will offer more valuable insights for farmers and investors.

5. Conclusions

This study developed and validated a thermal-electrical model to size a net-zero agrivoltaics array for an agrotunnel. It incorporated wall transmission, infiltrations, and plant evapotranspiration, sized heat pumps for temperature control, and measured plug loads such as water pumps, LED lighting, and dehumidifiers. Thermal analysis showed that in an agrotunnel in London, ON, lights contributed 40% of the thermal load, while plant evapotranspiration added 32%. Sensible infiltration and wall transmission together accounted for about 25% of the load, and the presence of people had a negligible impact on the thermal load.

The choice of crop in an agrotunnel significantly impacts water usage and building load due to varying evapotranspiration rates. Although the thermal load remains consistent because evapotranspiration is isenthalpic, power demand decreases as dehumidifier electricity consumption drops with reduced latent load. For example, growing kale, which requires frequent watering, increased annual electricity demand by 25.53% compared to herbs (Basil, Parsley, Oregano, and Mint), and by 32.26% and 34.32% compared to vegetables and fruits (tomatoes, beans, and strawberries) and lettuce, respectively. Reducing the photoperiod from 24 to 14 hours per day significantly decreased the annual electrical load of an agrotunnel from 65,658 kWh to 37,711 kWh, primarily due to reduced lighting power. In colder climates, extended photoperiods helped offset heating demands due to lights' dissipated energy. Hence, optimizing photoperiods is crucial, especially when conventional non-electrical sources supply thermal demands. Moreover, the design temperature was a crucial parameter, strongly influencing both thermal (63.26% sensitivity) and electrical (19.05% sensitivity) loads.

The agrotunnels located in colder regions have lower annual electrical energy requirements compared to those in warmer regions. This is because the excess heat generated by the lights offsets the heating needs caused by the outdoor environment. According to the results, the net-zero approach was achieved for the annual electrical energy requirements and production from PV systems across six locations (London, Montreal, Edmonton, Albany, San Francisco, and Houston). Albany required the largest PV capacity at 48.32 kW to meet its annual energy demand of 67,497 kWh. Conversely, San Francisco needed the smallest system size at 41.42 kW. Notably, San Francisco's PV system generates more electricity annually than London, Montreal, Edmonton, and Albany due to its higher solar irradiation, yielding 1641.5 kWh/kW. The PV system capacity for an agrotunnel in warmer regions such as Houston was smaller due to ample solar irradiation. Consequently, these regions showed higher SC and SS values. London, ON, among the colder regions, exhibited the highest SC and SS values overall. Evaluating the monthly trend of SC and SS values proved that they behave oppositely: SC increased during months when electrical demand surpassed PV system generation capacity (e.g., winter), while SS rose when demand fell below the PV system's energy capacity (e.g., summer).