DC vs. AC Ohmic Losses in a PV System

In a photovoltaic system, energy follows this simplified path:

PV modules (DC) → DC cables → inverter → AC cables → (optional AC transformer) → grid

At each stage where there are conductors (cables, transformer windings), some of the power is lost as heat: these are ohmic losses.

The basic law is the same everywhere:

• \(R\): resistance of the conductors \((\mathrm{\Omega})\)
• \(I\): current flowing \((\mathrm{A})\)
• \(P_{\mathsf{losses}}\): power lost \((\mathrm{W})\)

What differs between DC and AC are:

• the location where the losses occur,
• the voltage and current levels,
• and how they are expressed (as a % of DC losses, as a % of AC losses, etc.).

1. Ohmic losses on the DC side

On the direct current side, between the modules and the inverter, we find:

• string cables (between modules in the same string),
• busbar cables (junction boxes, DC cabinets),
• DC cables leading to the inverter inputs.

This entire network can be combined into an equivalent DC resistance \(R_{\mathsf{DC}}\), as seen from the PV array.

The instantaneous losses in this section are given by:

where \(I_{\mathsf{DC}}\) is the total current delivered by the PV array.

Important characteristics on the DC side:

• voltages are relatively high, but so are currents (especially in direct sunlight),
• cable lengths between PV arrays and the inverter can be significant,
• DC losses depend very heavily on the cross-sectional area of the cables and the number of strings in parallel.

2. Ohmic losses on the AC side

After the inverter, we move to the alternating current side:

• AC cables between the inverter and the delivery point,
• possibly one or more AC transformers (LV/MV, MV/HV).

In this AC section, there are:

a. Ohmic losses in AC cables

• the cables have a resistance \(R_{\mathsf{AC}}\),
• the losses are:

b. Copper losses in transformers

• in the windings (wire resistance),
• same law:

c. Iron losses in the transformer (non-ohmic, but worth noting)

• in the magnetic core,
• present as soon as the transformer is energized, even at low load,
• they are often modeled as "nearly constant" power.

On the AC side, voltages are generally higher (\(400\ \mathrm{V}\), \(20\ \mathrm{kV}\), etc.) than on the DC side; therefore, for the same power, currents are lower → ohmic losses can be more limited, even over long distances.

3. Comparing DC and AC losses in a PV system

We can summarize as follows:

• DC (modules → inverter)
  • generally higher currents,
  • cables sometimes long with small cross-sections (strings),
  • significant losses if cross-sections are too small or distances are long,
  • often expressed as a % of DC losses relative to the PV array’s rated power.

• AC (inverter → grid)
  • higher voltages, therefore lower currents for the same power,
  • AC cables + transformers (copper losses + iron losses),
  • ohmic losses sometimes lower in %, but at high power levels, so must be monitored,
  • often expressed as a % of AC losses at the inverter/substation’s rated power.