What is the per-unit system in power system analysis?

Short Answer:

The per-unit system in power system analysis is a method used to express electrical quantities like voltage, current, power, and impedance as fractions (or multiples) of a chosen base value. It simplifies calculations by converting different values across transformers and voltage levels into a common reference.

This system makes it easier to compare, analyze, and model various parts of the power system, especially when components operate at different ratings and voltage levels. It also helps reduce errors and improves clarity in large-scale system analysis.

Detailed Explanation:

Per-unit system in power system analysis

In a large power system, equipment such as generators, transformers, transmission lines, and loads operate at different voltage levels, ratings, and impedances. Comparing or analyzing their values directly in real units (ohms, volts, amps) can be confusing and complex.

To simplify this, engineers use the per-unit (pu) system, where all quantities are expressed as a ratio of their actual value to a selected base value. This process converts different values into dimensionless numbers, making it easier to work across varying voltage levels and equipment types.

How the per-unit system works

To apply the per-unit system, two base values are chosen:

  • Base power (S_base) in MVA or kVA
  • Base voltage (V_base) in kV

From these, other base values are calculated:

  • Base current (I_base) = S_base / (√3 × V_base) for three-phase systems
  • Base impedance (Z_base) = (V_base)² / S_base

Then, the actual value of a quantity is divided by its corresponding base value to get its per-unit value:

Per-unit value=Actual valueBase value\text{Per-unit value} = \frac{\text{Actual value}}{\text{Base value}}Per-unit value=Base valueActual value​

Example:
If a transformer’s actual impedance is 4 ohms and its base impedance is 20 ohms, then its per-unit impedance is:

Zpu=420=0.2 puZ_{pu} = \frac{4}{20} = 0.2 \text{ pu}Zpu​=204​=0.2 pu

Advantages of using the per-unit system

  1. Simplifies complex calculations:
    • No need to change units for different equipment.
    • Impedances become more manageable and similar in range.
  2. Easy comparison:
    • Per-unit values allow easy comparison of components regardless of their size or voltage rating.
  3. Transformer analysis made easy:
    • Transformer ratios are automatically handled, and impedance values remain consistent across different voltage sides.
  4. Reduces calculation errors:
    • Working in per-unit avoids large or small numbers, minimizing mistakes.
  5. Common ground for software and modeling:
    • Most power system simulation tools like ETAP, PSS®E, and PowerWorld use the per-unit system for internal calculations.

Typical applications

  • Short circuit analysis: Helps express fault levels in per-unit.
  • Load flow studies: All voltages, powers, and impedances are converted into per-unit for uniformity.
  • Transformer modeling: Impedance values are easily transferred across windings.
  • System planning and comparison: Engineers can evaluate performance without dealing with mixed units.
Conclusion:

The per-unit system in power system analysis is a simplified method to represent electrical quantities as fractions of base values. It is especially useful in dealing with systems that include different voltage levels and component ratings. The per-unit system reduces complexity, standardizes analysis, and is widely used in designing and modeling reliable electrical power networks.