This document provides a detailed breakdown of the methodology used to estimate the expected DC power output and its subsequent conversion to AC power, incorporating degradation, thermal effects, and system losses, among other factors. Performance+ currently implements a physics-based expected-power model (ExpectedPowerPhysical); this note describes that model.

Figure 1 shows the generic modelling steps to go from input data to the physics-based expected AC power model.

Figure 1 - Generic modelling steps for the physics-based expected AC power model

Figure 1: Generic modelling steps to go from input data to the physics-based expected AC power model

The model runs per inverter. DC and AC nameplate capacities are read from each inverter's attributes, and the model is evaluated for several permutations combining the irradiance source (selected sensor vs. transposed GHI) with a degradation scenario (with vs. without degradation).

1. PV Module DC Rated Power

The rated power of PV modules is expected to be impacted by degradation. Thus, the actual DC-rated power is adapted as follows:

DC_rated_actual [kW] = P_nom_DC [kW] * f_degradation
f_degradation        = 1 - deg_rate [%/year] * time_since_start

Where:

  • deg_rate - annual degradation rate. Default: 0.5 %/year (calculated degradation rate added when available).
  • time_since_start - time in years since the degradation start date (in practice the commissioning date, cod).

The degradation factor is clipped to be non-negative. If no degradation start date is configured, degradation is skipped and the nameplate DC capacity is used directly.

2. Expected DC Power Calculation - PV Modules' output

Expected power depends primarily on Plane-of-Array (POA) irradiance. In Performance+, POA is a daily selected parameter based on the best-performing sensor for each inverter (see the Sensor Selection note). In addition, POA is corrected for interrow shading (see the Sensor Shading note) and for bifaciality on bifacial modules.

The expected DC power output without accounting for losses is calculated as follows:

P_DC [kW] = DC_rated_actual [kW] * POA [W/m^2] / G_STC [W/m^2]

Where:

  • POA [W/m^2] - plane-of-array irradiance
  • G_STC [W/m^2] - irradiance at standard test conditions, 1000 W/m^2

This equation scales the (degraded) rated DC power according to the available sunlight at the module level, and is clipped to be non-negative.

PV modules are also affected by temperature variations, which impact their efficiency. The calculation first derives the cell temperature from the measured/modelled module temperature using the SAPM cell-temperature model [1]:

T_cell [ degC] = T_mod [ degC] + (POA / G_STC) * delta T

Where delta T = 3 degC is the temperature difference between the PV cell and the module back-surface. The thermal derating factor is then defined as:

f_thermal = 1 + gamma * (T_cell - T_STC)

Where:

  • T_STC [ degC] - cell temperature at standard test conditions, 25 degC
  • gamma [%/ degC] - power-temperature coefficient. Default: -0.45 %/ degC (-0.0045)
  • f_thermal - thermal derating factor (dimensionless)
  • T_cell [ degC] - PV cell temperature

The effective DC power output considering thermal losses is:

P_DC_eff [kW] = P_DC [kW] * f_thermal

3. Expected DC Power Calculation - Inverter's input

Losses in DC cabling and system inefficiencies must be considered before converting to AC power. Rather than a single lumped factor, two DC-side losses are applied as multipliers:

P_DC_inv [kW] = P_DC_eff [kW] * ohmic_factor * mismatch_factor

Where:

  • ohmic_factor = 1 - ohmic_loss / 100 - accounts for wiring and connection (ohmic) losses. The ohmic-loss percentage scales with plant size: ohmic_loss = min(0.5 + 1.0 | (POI_limit_MW / 250), 1.0) %. If the plant capacity is unknown, the budgeted default is used.
  • mismatch_factor = 1 - mismatch_loss / 100 - accounts for module-to-module performance variation. The mismatch-loss percentage is taken from the monthly site budget, the energy-model reference, or a hard-coded default (1 %), in that priority order.

4. Expected AC Power Calculation - Inverter's output

To determine the AC power output from the inverter, we apply the PVWatts inverter efficiency model [2]. The efficiency equation is given by:

Inv_Eff = (Inv_Eff_Nom / 0.9637) * (0.9858 - 0.0162 * Load_Ratio - 0.0059 / Load_Ratio)

Where:

  • Inv_Eff - actual inverter efficiency
  • Inv_Eff_Nom - nominal inverter efficiency. Default: 0.96
  • Load_Ratio - ratio of the inverter DC input power to the rated AC power, P_DC_inv / P_nom_AC

The AC power output is then:

P_AC_inv [kW] = P_DC_inv [kW] * Inv_Eff

Finally, an inverter thermal derating is applied and the AC power is clipped to the (temperature-derated) AC capacity:

derating   = clip( 1 + gamma_inv * max(T_amb - T_ref, 0), 0.7, 1.0 )
P_AC_inv   = min( P_AC_inv, P_nom_AC * derating )

Where T_amb is the ambient temperature and T_ref = 25 degC. The resulting AC power is clipped to be non-negative. The model outputs the expected AC power together with the expected DC power (with and without DC losses) for each permutation, which then feed the downstream loss breakdown and KPIs.

References

[1] D. King et al., "Sandia Photovoltaic Array Performance Model," SAND2004-3535, Sandia National Laboratories, Albuquerque, NM, 2004.

[2] A. P. Dobos, "PVWatts Version 5 Manual," National Renewable Energy Laboratory, 2014. https://pvwatts.nrel.gov/downloads/pvwattsv5.pdf