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Component Efficiency

In an electrical or photovoltaic circuit, no component is perfect. Some of the received power is lost (heat, friction, magnetic losses, etc.), and only a portion is actually useful at the output. Efficiency quantifies this "quality" of conversion.

Definition of Efficiency

The efficiency of a component is defined by the ratio:

\[ \eta = \frac{P_{\mathsf{output}}}{P_{\mathsf{input}}} \]
  • \(P_{\mathsf{input}}\): received (or absorbed) power
  • \(P_{\mathsf{output}}\): useful power supplied

Efficiency is a dimensionless number (often expressed as a percentage).

  • If \(\eta = 1\) (or 100%), the component would be perfect: no loss.
  • In practice, \(\eta\) is always less than 1 (or 100%).

We can also write:

\[ \eta\ \% = 100 \times \frac{P_{\mathsf{output}}}{P_{\mathsf{input}}} \]

Losses

Losses correspond to the power that is not transmitted to the output:

\[ P_{\mathsf{losses}} = P_{\mathsf{input}} - P_{\mathsf{output}} \]

They can also be expressed as a percentage of the input power.

Example:

If \(\eta = 90\ \%\), this means that 10% of the received power is lost.

Practical Examples

1. Transformer or Power Supply

  • A converter receives \(1000\ \mathrm{W}\) at the input.
  • It delivers \(920\ \mathrm{W}\) at the output.
  • Efficiency:
\[ \eta = \frac{920}{1000} = 0.92 = 92\ \% \]
  • Losses: \(80\ \mathrm{W}\) dissipated (mainly as heat).

2. Photovoltaic inverter

  • The inverter receives \(5000\ \mathrm{W}\) of DC power from the modules.
  • It supplies \(4750\ \mathrm{W}\) of AC power to the grid.
  • Efficiency:
\[ \eta = \frac{4750}{5000} = 0{,}95 = 95\ \% \]

3. Photovoltaic module (viewed as a radiation-to-electricity converter)

  • The module receives solar power of \(1000\ \mathrm{W/m^2}\) over a given surface area.
  • It supplies, for example, \(200\ \mathrm{W}\) of electrical power.
  • Conversion efficiency: 20%.

Key points

  • The efficiency \(\eta\) of a component is:

    • \(\eta = \frac{P_{\mathsf{output}}}{P_{\mathsf{input}}}\)
    • often expressed as a percentage: \(100 \times \frac{P_{\mathsf{output}}}{P_{\mathsf{input}}}\)

  • Losses are:

    • \(P_{\mathsf{losses}} = P_{\mathsf{input}} - P_{\mathsf{output}}\)
  • An efficiency of 95% means that 5% of the received power is lost (often as heat).
  • In a photovoltaic system, each component (modules, cables, inverter, etc.) has an efficiency < 100%, which reduces the usable power available at the end of the chain.

Efficiency Calculator

Enter the input power and output power of a component.
The calculator displays the efficiency and power loss.

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