At the injection point

Method

The limit holds at the injection point. Before the timesteps run, the ceiling of the inverters is found as the output that leaves exactly the limit for the grid once the losses after the inverters are taken: the AC wiring, the transformers, the lines, the flat fractions and the auxiliaries, each counted only while it is modelled. The losses of (2) are taken on the inverter output under both resistive references. Equation 3 is a quadratic in the ceiling; its smaller root is kept, and the ceiling never falls below the limit itself. Each inverter gets an equal share, and its own AC limit still applies. On a timestep where the array could deliver more, the inverter brings its output down to the ceiling by the rules of the Inverter operating limits step. The energy not produced counts in the Inverter Loss over nominal inv. power row, or in the Unused energy (grid limitation) row when the limit is accounted as a separate loss (Losses tab).

The math

1. Loss coefficient
2. Losses after the inverters
3. Ceiling of the inverters
4. Ceiling of each inverter

$$k_R = \frac{f_{AC} + f_{Cu} + f_{MVL} + f_{HV,Cu} + f_{HVL}}{P_{ref,sys}\,\text{PF}^2} \tag{1}$$ $$L(P_{inv,sum}) = k_R\,P_{inv,sum}^2 + \left(f_T + f_O + \frac{a_{aux}}{1000}\right)P_{inv,sum} + (f_{Fe} + f_{HV,Fe})\,P_{ref,sys} + A_{day} \tag{2}$$ $$P_{inv,sum}^* - L(P_{inv,sum}^*) = P_{grid,lim} \tag{3}$$ $$P_{max} = \min\!\left(P_{ac}(T_{amb}),\ \frac{\max(P_{inv,sum}^*,\ P_{grid,lim})}{N_{inv}}\right) \tag{4}$$

where

Symbol	Meaning	Unit
$k_R$	the combined coefficient of the resistive losses	1/W
$f_{AC},\ f_{Cu},\ f_{MVL},\ f_{HV,Cu},\ f_{HVL}$	the losses of the AC wiring, the MV transformer copper, the MV line, the HV transformer copper and the HV line at the reference power and unit power factor, each as a fraction of the reference power	—
$P_{ref,sys}$	the AC power reference of the system: the sum of the inverters' AC nameplates, or the STC reference power (AC power reference step)	W
$\text{PF}$	the power factor	—
$L(P_{inv,sum})$	the losses after the inverters when they deliver $P_{inv,sum}$	W
$P_{inv,sum}$	the sum of the inverter outputs	W
$f_T$	the fixed transmission loss fraction	—
$f_O$	the other AC loss fraction	—
$a_{aux}$	the auxiliary draw proportional to the output	W/kW
$f_{Fe}$	the MV transformer iron loss as a fraction of the reference power	—
$f_{HV,Fe}$	the HV transformer iron loss as a fraction of the reference power	—
$A_{day}$	the constant day draw of the auxiliaries	W
$P_{inv,sum}^*$	the ceiling of the inverters together	W
$P_{grid,lim}$	the grid power limitation as active power: a limit in kVA is multiplied by the power factor	W
$P_{max}$	the AC ceiling of one inverter	W
$P_{ac}(T_{amb})$	the inverter's own AC limit at the ambient temperature $T_{amb}$	W
$N_{inv}$	the number of inverters	—

References

1. PVsyst 8 help, Grid power limitation
2. Analysis of PVsyst 8.1.5 outputs shows this convention in its results.

API

ac_losses.use_grid_limit = true, ac_losses.grid_limit_at = injection

Symbols follow the symbol registry.