## 2 Materials and Methods
### Financial Feasibility Study  
The financial feasibility of simulated energy production and energy load demand for a complex of four poultry houses was evaluated using Excel. Electricity consumption, \(E\), of the farm in each month, in kWh, is given by the following:  
\[E=\sum_{j=1}^{m}\sum_{i=1}^{n}E_{ij}=\sum_{j=1}^{m}\sum_{i=1}^{n}P_{Lij} \tag{1}\]  
where \(P_{L}\) is the hourly farm electricity load in kW, where \(i=1,2,3,\ldots,n\) tracks the hour in a day \(j=1,2,3,\ldots,m\) for each month, and \(m\) tracks the day in a month (i.e., for January, \(m=31\)). The electricity generation by the PV system of each month, \(G_{PV}\), in kWh, is the accumulated hourly production that varies by time of day and month as given by the following:  
\[G_{PV}=\sum_{j=1}^{m}\sum_{i=1}^{n}G_{PVij} \tag{2}\]  
In the case of NEM, _net_ electricity, \(N\), in kWh, is the monthly difference between energy consumption, \(E\), and the PV generation, \(G_{PV}\). \[N=\sum_{j=i}^{m}\sum_{i=1}^{n}N_{ij}=\sum_{j=1}^{m}\sum_{i=1}^{n}E_{ij}-\sum_{ j=1}^{m}\sum_{i=1}^{n}G_{PVij} \tag{3}\]  
The electricity cost C\({}_{\rm E}\) without any PV production, in USD, is given by the following:  
\[C_{E}=\sum_{j=1}^{m}\sum_{i=1}^{n}E_{ij}Z_{Rij} \tag{4}\]  
where \(Z_{R}\) is the electricity retail cost rate in USD/kWh. Therefore, with an on-site PV production and under NEM, _net_ electricity cost, in USD, is given by the following:  
\[C_{NEM}=\sum_{j=1}^{m}\sum_{i=1}^{n}N_{ij}Z_{Rij} \tag{5}\]  
The net electricity cost with NEB, in USD, is considered separately during hours when consumption is higher than PV production (\(N_{ij}>0\)) and when consumption is smaller than PV production (\(N_{ij}<0\)) and given by the following:  
\[C_{ij}=N_{ij}Z_{Rij}\;if\;N_{ij}>0\;or\;N_{ij}Z_{Aij}\;if\;N_{ij}<0 \tag{6}\]  
\[C_{NEB}=\sum_{j=1}^{m}\sum_{i=1}^{n}C_{ij} \tag{7}\]  
where \(Z_{A}\) is the electricity avoided cost rate in USD/kWh. The self-consumption ratio, \(s\), is calculated as the fraction of the self-consumed portion of PV generation over the total PV generation. \[s=\frac{G_{DU}}{G_{PV}} \tag{8}\]  
where \(G_{DU}\) is the sum of the electricity consumed that is either equal to the simultaneous PV production at each hour (when \(P_{Lij}<G_{PVij}\)) or the PV production (when \(P_{Lij}>G_{PVij}\)). Electricity production and consumption are held constant over the useful life of the PV system. We used the net present value (NPV) of cash flow and internal rate of return to investigate the feasibility of the solar PV project on the model poultry farm. The NPV is given as follows:  
\[NPV(i_{d},T_{tt})=\sum_{t=1}^{T_{tt}}\frac{R_{t}}{\left(1+i_{d}\right)^{t}} \tag{9}\]where \(t=\) time of the cash flow (for example one year), \(T_{lt}=\) lifetime of the PV technology in years (\(T_{lt}=25\)), \(i_{d}=\) discount rate (the rate of return that could be earned on an investment in financial markets with a similar risk), and \(R_{t}\)--net cash flow, i.e., cash inflow and cash outflow at time, \(t\), in USD. Investments during the initial design to the system start-up (assumed to occur in the first year) are summed up with a negative cash flow. Parameters used for the financial analysis are listed in Table 2. A capital expenditure of USD 2000/kW for the PV systems is used, and a value of USD 7.5/kW-year is assumed for the annual operation and maintenance [22]. The economic life of the PV system is assumed at 25 years with a discount rate of 5% and an average annual inflation rate of 5%. Note that all simulations were conducted using a 30% federal investment tax credit that could be realized in the first year with the passage of the Inflation Reduction Act. As such, the project cost was credited USD 0.30 for each dollar invested in the PV system. The annual bill savings were defined as the difference between the cost of energy without any PV system (\(C_{E}\)) installed and the cost of energy using PV (\(C_{NEM}\) or \(C_{NEB}\)). Besides the NPV, we considered the payback period (PP) of each scenario as well.