2.1. Theoretical Background of PV Modules
PVWatts is a standalone PV simulator that is available as an application programming interface (API) as well as on the web [
24]. It was developed in the National Renewable Energy Laboratory (NREL) in the US in 1998, and the newest version, 8.1, was developed in early 2023. The newest EnergyPlus version 22 adopted PVWatts version 5, which was developed in 2014 [
26].
In general, PV electricity generation is calculated by multiplying the voltage and current at maximum power point tracking (MPPT) as follows: .
The TRNSYS model is based on an equivalent one-diode model that generates the I–V (current and volt) curve and identifies the maximum point. The current is calculated by subtracting the diode current (I
d) from the light current (I
L).
The diode current (
Id) is determined from the Shockley equation:
The diode reverse saturation current (
Io) is determined from the reference temperature, and the light current (
IL) is linearly calculated from the incident radiation:
Three conditions, namely the open-circuit, short circuit, and maximum power, are considered to determine IL,ref, Io,erf, γ, and Rs in Equation (2). The current (Imp) and voltage (Vmp) are then iteratively determined from the MPPT along the I–V curve.
The Sandia model was developed in Sandia National Lab [
27]. Similar to the TRNSYS model, it can generate the I–V curve from the short circuit current (
Isc), current and voltage at MPPT (
Imp,
Vmp), open-circuit voltage (
Voc), half of the open-circuit voltage (
Ix), and the average of open-circuit voltage and MPPT (
Ixx). The current at the short circuit (
Isc) is calculated from the polynomial functions (
f1,
f2) of the solar spectrum through the airmass (
AMa) and the solar angle from the nominal (
AOI) portion (
fd) of diffuse solar radiation (
Ediff) and the difference between the reference outdoor (
T0) and inside cell (
Tc) temperatures by applying a multiplier (
αISC). The PV module temperature is calculated from the wind, and the cell inside temperature (
Tc) can then be calculated.
The remaining variables are defined based on the empirical coefficients relating the effective solar radiation (
Ee) and temperature (
Tc,
To) to the current (
Imp,
Ix,
Ixx) and voltage (
Vmp,
Voc). Detailed information on the mathematical formulation can be found in the work of King et al. [
27].
Unlike the TRNSYS and Sandia models, the PVWatts model is based on a simpler formulation. The module DC power (
Pdc) is computed by multiplying the transmitted plane-of-array (POA) irradiance (
Itr) by the nameplate DC rating (
Pdc0) of the module and the temperature difference between the reference (
Tref) and cell temperatures (
Tcell).
The transmitted POA irradiance (
Itr) is calculated by multiplying the POA irradiance (
Ipoa), which consists of the beam and diffuse (sky and ground-reflected) components, by the transmittance through the antireflective (AR) coating and glass (
τAR and
τglass). The angle between the solar rays and the panel is calculated from the aforementioned transmittance coefficients. A detailed explanation can be obtained from the manual [
25] and its source [
28,
29].
2.2. Model Validation
PVWatts was adopted in EnergyPlus, which has a biaxial tracking feature, unlike existing PV modules, including the Sandia and TRNSYS models. Therefore, we calibrated the PVWatts module against the existing models. Notably, the Simple model, which is too simple, was excluded from the calibration. PV angles from 0 to 90° with 15° increments were considered. To simulate the tilted PV with the Simple, Sandia, and TRNSYS models in EnergyPlus, we built a dummy structure based on the X, Y, and Z coordinates by calculating the angle of the surface on which the PV models was installed.
The capacity of the PV module for all models was set to approximately 5 kW. Detailed properties of Sandia and TRNSYS models were set based on the default value from their original model in EnergyPlus. For example, Isc and Imp were set to 4.75 A and 4.45 A, and Voc and Vmp were set to 21.4 V, and 17 V, respectively. Example files including “Generator_PVWatts” and “GeneratorswithPV” were used as references to configure the validation models.
In the initial comparison of the total and monthly electricity generation, consistent over-generation was observed in PVWatts compared to the two existing modules. This trend was observed in a daily and hourly comparison, which will be discussed later. Therefore, the constant of PV efficiency was manually calibrated with daily data. Accordingly, “system losses” of Generator:PVWatts in EnergyPlus was calibrated. The default value was 0.24, which denotes an efficiency of 0.76 (i.e., 76%). The initial comparison revealed that approximately 83% and 84% of the electricity was generated in the TRNSYS and Sandia models, respectively. Therefore, the efficiency of PVWatts needs to be reduced to similar proportions. The default efficiency of 0.76 decreased by 0.72 (0.76 × 0.835). Finally, the calibrated system losses were 0.28. The initial and calibrated PVWatts models are compared with the two models in
Figure 2. Compared to the initial PVWatts model, the final model exhibited a good match with the detailed models in EnergyPlus.
The RMSE and cvRMSE of PVWatts and the existing models (Sandia and TRNSYS) are shown in
Figure 3. For a fine scale, hourly data were layered on the daily comparison without further calibration. In both comparisons with Sandia and TRNSYS models, the daily evaluation exhibited a good match in the middle angle range (i.e., 30–45°), whereas the hourly evaluation exhibited the reverse trend. In the hourly comparison, the cvRMSE increases but is largely less than 10%, which is acceptable for the simulation case study.
2.4. Building Load Coverage Analysis
For simulating the reference commercial building, we considered a typical office schedule, namely 9 a.m.–6 p.m. The heating, ventilation, and air-conditioning (HVAC) system was assumed as an ideal system, with only the pure heating and cooling load being calculated: ZoneHVAC:IdealLoadsAirSystem was applied in EnergyPlus. The COPs of the heating and cooling systems were set to 2.27 and 3.97, respectively, which are typical for HVAC systems, to calculate the electricity consumption.
The annual cooling and heating loads were 57,849 kWh and 23,577 kWh, and the corresponding electricity consumption levels were 14,572 kWh and 10,386 kWh, respectively. The electricity consumption levels of the lighting and equipment were 16,481 kWh and 18,341 kWh, respectively. The total building electricity requirement was 59,780 kWh, whereas the generation of one tracking PV was 8594 kWh. The HVAC took up 34% and 14% of the entire building load, as shown in
Figure 5. As previously stated, six PV arrays could be installed, considering the roof area, which could produce 86% of the entire building load. However, seven PV arrays were required to satisfy the building requirement for net-zero energy. Therefore, further analysis is required, including an hourly load comparison because of time variations. However, the required load of the typical office building is expected to be well-matched with daytime electricity generation.
Figure 6 shows the monthly load requirement and generation from one tracking PV.
Figure 7 shows the electricity load coverage of the PV generation per HVAC and the total electricity load of the building. When considering the electricity load of the entire building, the coverage is stable—from 15% to 20%. However, if only the thermal electricity load is considered, this exceeds 100% (green shade) during the intermediate season, during which the thermal load is insignificant compared to that during the warm and cool seasons.
2.5. Life Cycle Cost Analysis
For the LCC analysis, we assumed arrays ranging from one to six, which covered approximately 94% of the entire roof area. The 2023 electricity cost structure of S. Korea was applied [
30]. The demand charge was applied: for each month, 6610 ₩/kW was multiplied by the maximum electricity usage, including the HVAC, lighting, and equipment load. The seasonal prices applied for the summer, intermediate, and winter seasons were 124.4 ₩/kWh, 83.9 ₩/kWh, and 111 ₩/kWh, respectively. The net present value method was utilized to convert the future value into the current value, considering the inflation rate and increase rate in electricity cost. The average values from 2011 to 2022 were utilized. The average inflation rate was 1.867%, whereas the average electricity cost increase rate was 1.396%. Detailed rate information is presented in
Appendix A (
Table A1,
Table A2,
Table A3,
Table A4 and
Table A5).
The entire building electricity load, including the HVAC, lighting, and equipment, was calculated from the reference building model and summarized in
Table 1. The annual electricity requirement was the same for all cases. However, the base utility cost was calculated with the peak demand for each month, which varies depending on the number of PVs. For this evaluation, hourly data of the building electricity load and PV electricity generation were used to estimate the peak electricity usage. Specifically, the electricity generation was extracted from the building electricity load. The annual net electricity cost was then calculated and used for the LCC analysis. The TMY3 weather file for the target region (Incheon, S. Korea) was repeatedly applied for 15 years for the LCC analysis.
Figure 8 shows the LCC analysis results for 15 years. The accumulated cost was calculated from the initial investment, including the product and installation costs. We identified between six and seven products with product and installation information, and their averaged values were used, that is, 3,570,000 ₩ and 3,520,000 ₩, respectively. For the fixed PV, the initial cost was approximately half that of the tracking PV. Therefore, the payback period was relatively short, that is, 5.3 years. The tracking PV with two, four, and six arrays required payback periods of 8.0 years, 8.3 years, and 8.4 years, respectively. However, in the 15-year evaluation, the total accumulated costs of fixed and tracking PV assuming two PV arrays were similar, namely 10.7% and 10.1% compared to that in the case without PV, respectively. Those with four and six arrays exhibited 18.7% and 26.8% savings, respectively.