System electronics

The system electronics stage takes the DC electrical output calculated for individual PV modules and determines the system-level DC and AC performance.

Modules from the simulated unit-system are series-connected to form strings, which can be defined in various configurations. These strings are then connected in parallel to the DC input of an inverter. At each timestep, the inverter parameters determine the DC operating point of the combined strings and the resulting AC power output. DC wiring losses are calculated based on an ohmic resistance and the operating point current.

The outputs from this stage include the AC power delivered at each timestep, the DC power output of each string, and the DC power at the inverter input, along with associated losses from mismatch, wiring, constraints, and conversion efficiency. Those losses are described in more detail on the waterfall loss chart page.

Strings and arrays

Strings are defined as containing a certain number of series connected modules. Each module in the string is linked to a single specific module from within the unit-system and assumes that module’s IV curve. The modules within the unit-system may be linked to as many times as needed.¹ There is no wiring loss defined specifically within the string (other than what is already included within the module). This is defined at the array level. Multiple string definitions can be created, with the output of each string calculated independently.

Arrays are composed of (i) parallel strings of modules, (ii) an inverter, and (iii) associated wiring (including combiner boxes, connectors and other DC components).² The array also defines solving options, such as the model to use for inverter temperature.

String IV curve calculation

The DC electrical output of each string is calculated by combining the IV curves of all modules within the string. Note that these IV curves assume the module is at its calculated operating temperature and already includes losses due to cell-to-cell mismatch.

The algorithm to combine the IV curves in series is as follows:

1. The maximum current ($I_{max}$) at 0 V that occurs in any module IV curve from within the string is determined.

2. A uniform current step ($I_{step}$) is calculated as $I_{limit}$ divided by the number of positive IV steps (an advanced user input set to 300 by default).

3. Loop from a target current ($I_{target}$) of $-10 \cdot I_{step}$ to $I_{limit}$ incrementing by $I_{step}$. At each step, calculate the DC voltage from each module that would result from a module current of $I_{target}$. Module voltage is determined from the discrete IV points of each module IV curve using linear interpolation. If the target is outside the recorded IV points, then it is projected based on the closest two points. Note that this results in 310 total points.

4. The string voltage ($V_{string}$) at each $I_{target}$ is calculated as the sum of all module voltages determined in (3). A string IV curve is constructed from the pairs $[I_{target}, V_{string}]$.

5. The maximum power point of the string IV curve is calculated by fitting with a second order polynomial.

Note that it is possible to define multiple string definitions. In this case the output of each string is calculated as described above and the output recorded. At this point in the solving there is no connection between different string definitions, that is defined at the array level (see next section).

Array IV curve and AC output

Calculation of the array IV curve

The algorithm to combine the string IV curves in parallel is as follows:

1. The maximum voltage ($V_{max}$) that occurs in any of the parallel string IV curves is determined.

2. A uniform voltage step ($V_{step}$) is calculated as $V_{max}$ divided by the number of positive IV steps (an advanced user input set to 300 by default).

3. Loop from a target voltage ($V_{target}$) of 0 V to $V_{max}$ incrementing by $V_{step}$. At each step, calculate the DC current from each parallel string that would result from a string voltage of $V_{target}$. String current is determined from the discrete IV points of each string IV curve using linear interpolation. If the target is outside the recorded IV points, then it is projected based on the closest two points.

4. The array current ($I_{array}$) at each $V_{target}$ is calculated as the sum of all string currents determined in step (3). An array IV curve is constructed from the pairs $[I_{array}, V_{target}]$.

5. The maximum power point of the array IV curve is calculated by fitting the resulting curve with a second order polynomial.

Calculation of the AC output of the array

The calculation of AC output involves several steps that account for DC wiring losses, inverter input constraints, and power limiting. For a step-by-step breakdown of how these calculations appear in simulation outputs, see Electrical energy waterfall.

The overall workflow is:

1. Combine string IV curves in parallel to determine array IV curve
2. Calculate DC operating point and wiring losses
3. Apply inverter input constraints (voltage, current, power thresholds)
4. Calculate AC output with inverter efficiency
5. Apply AC power limiting and calculate clipping losses
6. Recalculate final losses at actual operating point

DC operating point and wiring losses

The initial DC operating point is determined at the array maximum power point (MPP):

1. The string IV curves are combined in parallel to determine the array IV curve as described above.

2. The DC ohmic wiring loss at the array MPP is calculated:

   $$\Delta P_{DC \ wiring, \ MPP} = I_{array,MPP}^2 \times R_{DC,wiring}$$

3. The current, voltage and power at the inverter DC input are calculated, accounting for voltage drop across the DC wiring resistance:

   $$I_{DC,in} = I_{array,MPP}$$ $$V_{DC,in} = V_{array,MPP} - I_{array,MPP} \times R_{DC,wiring}$$ $$P_{DC,in} = I_{DC,in} \times V_{DC,in}$$

Inverter input constraints

The inverter operating temperature is determined (see Inverter operating temperature section below), then the DC input values are compared to inverter limits and adjusted if necessary:

1. The following limits are applied in order:

   • $P_{DC, thr}$ – minimum threshold power
   • $V_{MPPT, min}$ – minimum input voltage for maximum power point tracking
   • $V_{MPPT, max}$ – maximum input voltage for MPPT
   • $I_{PNOM, max}$ – maximum input current limit

2. After each constraint is applied, the current, voltage and power at the inverter DC input are updated using the array IV curve adjusted for DC wiring resistance.³ In some cases, previous constraints must be reimposed (particularly ensuring power remains above the threshold). The array voltage is bounded between zero and the array open-circuit voltage.

3. The inverter losses due to these constraints are calculated as the difference in DC power between the array maximum power point and the power at the new operating point.

AC output and power limiting

The AC output is calculated and checked against inverter AC power limits:

1. The AC output power is calculated using the DC input voltage and power, including inverter efficiency as described in the Inverter conversion efficiency section below.

2. The AC output power is compared to the AC power limit of the inverter (which may depend on inverter temperature). If the calculated power exceeds the limit:

   • The DC operating point is adjusted by increasing array voltage
   • Values of $I_{DC,in}$, $V_{DC,in}$ and $P_{DC,in}$ are recalculated to account for DC wiring loss
   • This process continues until AC output power is acceptable
   • If this causes $V_{DC,in} > V_{MPPT,max}$, the inverter switches off and output becomes 0 W$_{AC}$

3. The clipping loss occurs when the array DC power would produce AC output exceeding the inverter’s rated AC power limit. The loss is calculated as the difference between the DC power of the array at maximum power point and the DC power after adjustment to meet the power limitation. This is measured as a DC power loss. See Clipping loss for how this appears in simulation results.

4. Once the final operating point is known, the DC wiring loss is recalculated. Often this value is lower than initially calculated at the maximum power point. The difference is shown as Correction to wiring loss in the waterfall chart.

Inverter operating temperature

The inverter operating temperature may impact the maximum AC power output (affecting the clipping loss). There are three models available to determine the operating temperature of the inverter. These are the same models as used in PVSyst.

1. “External ambient” – uses the ambient temperature from the weather

   $$T_{inverter} = T_{ambient}$$

2. “External ambient with shift”

   $$T_{inverter} = T_{ambient} + T_{offset}$$

3. “Fixed temperature with linear heating”

   $$T_{inverter} = T_{base} + T_{increase} \cdot (G_{inc})$$

Where $T_{ambient}$ comes from the weather file, $G_{inc}$ is calculated using the view factor approach and $T_{offset}$, $T_{base}$, $T_{increase}$ are all user inputs.

Inverter conversion efficiency

The inverter conversion efficiency is used to convert the DC input power into AC output power. The efficiency depends on the DC operating point (DC input voltage and power). For how efficiency losses appear in simulation results, see Inverter loss during operation.

Efficiency is determined using efficiency curves defined as discrete (DC power, AC power) pairs loaded from OND (PVsyst inverter database) files. Two model variants are supported:

Single efficiency curve (voltage-independent): AC output power is calculated by linear interpolation on the AC power axis between the two surrounding DC power points in the curve. Beyond the highest DC power point, the model applies linear extrapolation based on the slope of the last two points.

Multiple efficiency curves (voltage-dependent): The model stores separate efficiency curves at different nominal DC voltages (typically 3 voltages). AC output is calculated using bi-linear interpolation: first interpolating AC power along the DC power axis for each of the two surrounding voltage curves, then interpolating between these results based on the actual DC input voltage.

Note that interpolating on AC power rather than efficiency directly produces a smooth but slightly curved efficiency profile between data points. Further details are available in [Mermoud2014].

Summary of system electronics models

Parameter	Model	Notes	Reference
String IV curve	Series combination	Combines module IV curves in series using interpolation and polynomial fitting to determine string maximum power point
Array IV curve	Parallel combination	Combines string IV curves in parallel using interpolation and polynomial fitting to determine array maximum power point
Inverter constraints	Sequential limits	Four constraints applied in order: $P_{DC,thr}$ (minimum power), $V_{MPPT,min}$, $V_{MPPT,max}$, $I_{PNOM,max}$
Inverter operating temperature	Three model options	External ambient, ambient with shift, or fixed base with linear irradiance-dependent heating
Clipping loss	AC power limiting	Occurs when DC input would produce AC output exceeding inverter rated AC power. Measured as DC loss.
Inverter efficiency		Single-curve (voltage-independent) or multi-curve (bi-linear interpolation) using OND file data	[Mermoud2014]

Footnotes

1. For example, if the unit-system represents a single-axis-tracker with a 2P configuration of 56 modules then one string can be defined to contain 28 east (upper) modules and another string to contain 28 west (lower) modules. Additionally, a third string could be defined that contains 14 east and 14 west modules. ↩

2. Currently the wiring is modelled a single resistance value that accounts for all wiring within the strings, combiner boxes and other components on the DC side. It can be understood as the total resistance seen by the inverter inputs. ↩

3. For example, if the voltage at the inverter input is lower than $V_{min,MPPT}$, then an iterative solution is used to find the array voltage that, after accounting for the voltage drop across the DC wiring resistance, gives an input voltage to the inverter of $V_{min,MPPT}$. ↩