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Cable Resistance, Voltage Drop, and Ohmic Losses

Cable Resistance (Review)

A cable is not perfect: it has resistance. This resistance depends on:

  • the material (copper, aluminum, etc.),
  • the length of the cable,
  • the cross-sectional area of the conductor.

We can write it as:

\[ R = \rho \times \frac{L}{S} \]
  • \(R\): cable resistance \((\mathrm{\Omega})\)
  • \(\rho\): resistivity of the metal (depends on the material and temperature)
  • \(L\): length \((\mathrm{m})\)
  • \(S\): cross-sectional area \((\mathrm{m^2})\), typically expressed in \(\mathrm{mm^2}\)

Key points to remember:

  • the longer the cable, the higher \(R\) becomes;
  • the thinner the cable, the higher \(R\) becomes;
  • an aluminum cable has a higher resistance than a copper cable of the same length and cross-sectional area.

Ohmic losses in cables

When a current \(I\) flows through a cable with resistance \(R\), part of the power is dissipated as heat:

\[ P_{\mathsf{losses}} = R \cdot I^{2} \]

This lost power will never be available at the output (it heats up the cables). In a PV system:

  • these losses reduce the DC power reaching the inverter,
  • and also the AC power reaching the delivery point.

Voltage Drop

The presence of \(R\) also causes a voltage drop:

\[ \Delta U = R \cdot I \]

The voltage at the input is therefore:

\[ U_{\mathsf{input}} = U_{\mathsf{output}} - \Delta U \]

The relative drop is often expressed as a percentage of the output voltage:

\[ \Delta U\ \% = 100 \times \frac{\Delta U}{U_{\mathsf{output}}} \]

In practice, targets are set such as:

  • "voltage drop < 1–3% over a given cable section".

Simple example (DC)

DC power of \(1000\ \mathrm{W}\) is transmitted at \(100\ \mathrm{V}\):

  • Current: \(I = P/U = 1000/100 = 10\ \mathrm{A}\)
  • Copper cable: forward + return resistance \(R = 0{,}5\ \mathrm{\Omega}\)

Voltage drop:

\[ \Delta U = R \cdot I = 0{,}5 \times 10 = 5\ \mathrm{V} \]
  • Input: \(95\ \mathrm{V}\)
  • Relative drop: \(5 / 100 = 5\ \%\)

Power losses:

\[ P_{\mathsf{losses}} = R \cdot I^{2} = 0{,}5 \times 10^{2} = 0.5 \times 100 = 50\ \mathrm{W} \]

Key points

  • A cable’s resistance depends on the material, length, and cross-sectional area.
  • Ohmic losses are given by: \(P_{\mathsf{losses}} = R \cdot I^{2}\) \((\mathrm{W})\)
  • Voltage drop is given by: \(\Delta U = R \cdot I\) \((\mathrm{V})\), often expressed as a percentage.
  • The higher the current, the greater the losses and voltage drop.

To limit losses: shorter cables or larger cross-sections (and, if necessary, higher voltages to reduce the current).

Voltage Drop and Ohmic Loss Calculator

Calculates the resistance, voltage drop, and losses in a cable based on its characteristics.

V
A
m
mm²

Note: For a round-trip circuit, indicate the total length (2 × distance).

Results

- Ω
- V
- %
- W

In residential installations, the standard generally requires a voltage drop of ≤ 3% for lighting and ≤ 5% for other uses.