Short Answer

The per unit system is a method used in power systems to express electrical quantities like voltage, current, power, and impedance as a fraction of a chosen base value. Instead of using actual values, quantities are represented in a simplified form, which makes calculations easier.

It is widely used in electrical engineering because it reduces complexity, avoids unit conversion problems, and helps in comparing different system values easily.

Detailed Explanation:

Per unit system

The per unit (p.u.) system is a method of expressing electrical quantities as a ratio of their actual value to a selected base value. It is commonly used in power system analysis to simplify calculations and make comparisons easier.

In this system, every quantity such as voltage, current, power, and impedance is divided by a corresponding base value. The result is a dimensionless number, which means it has no unit.

For example, if the actual voltage is equal to the base voltage, then its per unit value will be 1. If the actual value is half of the base value, the per unit value will be 0.5.

Mathematically, it can be written as:

Per unit value = Actual value / Base value

This simple formula helps in converting any electrical quantity into per unit form.

Base values in per unit system

To use the per unit system, we must first choose base values. Usually, base power (S_base) and base voltage (V_base) are selected.

From these, other base values can be calculated:

Base current is derived from base power and base voltage.
Base impedance is calculated using base voltage and base power.

Once base values are selected, all other quantities in the system are converted into per unit values using the same base.

This standardization helps in analyzing different parts of the power system easily.

Advantages of per unit system

The per unit system offers many advantages in power system analysis.

It simplifies calculations by reducing large and complex numbers into smaller values, usually close to 1. This makes mathematical operations easier.

It eliminates the need for unit conversions. Since all values are expressed in per unit, there is no confusion between different units like volts, kilovolts, or megavolts.

It makes comparison of different system components easy. For example, transformers of different ratings can be compared directly using per unit values.

It also reduces errors in calculations and improves accuracy in system analysis.

Application in power system

The per unit system is widely used in analyzing transmission lines, transformers, generators, and loads.

It is especially useful in load flow studies, fault analysis, and stability studies. Engineers prefer this system because it makes complex network calculations simple and uniform.

In transformers, per unit values remain the same on both primary and secondary sides if the same base is used. This is a major advantage in system analysis.

Conclusion

The per unit system is an important method used in electrical engineering to simplify calculations and analysis of power systems. By expressing quantities as a ratio of base values, it reduces complexity and improves understanding. It is widely used for efficient and accurate analysis of electrical networks.