HV transformer loss

What this step does

The loss of a high-voltage step-up transformer at the substation: the no-load loss drawn while it is connected and the load loss that grows with the square of the power through it. It is computed once for the system, on the sum of the inverter outputs or, with the Cascade reference, on the power leaving the MV line.

The math

1. Running total
2. Loss at a timestep

$$E_{after} = E_{before} - E_{row},\qquad E_{row} = \frac{\Delta t}{1000\,P_{DC}}\sum_i L_i \tag{1}$$ $$L_i = f_{HV,Fe}\,N_{inv}\,P_{ref}\,[\text{connected}] + \frac{f_{HV,Cu}}{N_{inv}\,P_{ref}\,\text{PF}^2}\,P_{c,i}^2 \tag{2}$$

where

Symbol	Meaning	Unit
$E_{before}$	the running total of the loss diagram before this row	kWh/kWp
$E_{after}$	the running total after this row	kWh/kWp
$E_{row}$	the row taken as a loss	kWh/kWp
$\Delta t$	the length of one timestep	hours
$P_{DC}$	the DC nameplate of the system	kWp
$L_i$	the power lost at timestep $i$ over the whole system	W
$f_{HV,Fe}$	the no-load loss, as a fraction of the reference power	—
$N_{inv}$	the number of inverters	—
$P_{ref}$	the AC power reference of one inverter: its AC nameplate, or its share of the array's STC reference power, the DC nameplate reduced by the module and string mismatch derates (the Model tab's AC power reference step sets which)	W
$[\text{connected}]$	1 while the transformer is connected; 0 on a timestep without export when the night disconnect is on	—
$f_{HV,Cu}$	the load loss at the reference power and unit power factor, as a fraction of the reference power	—
$\text{PF}$	the power factor	—
$P_{c,i}$	the power the load loss is computed on: the sum of the inverter outputs; when the Model tab's AC resistive reference step is set to Cascade, the power leaving the MV line	W

Reading the number

A loss, negative. A few tenths of a percent over a year on a utility system that has one; zero on every system that connects at medium or low voltage, rooftop systems included. The no-load loss runs whenever the transformer is connected, so disconnecting it at night (Losses tab) lowers the row.

References

1. IEC 60076-1:2011, Power transformers, Part 1: general (no-load and load losses)

API

loss.hv_transformer

Symbols follow the symbol registry.