Short Answer

Per unit values are calculated by dividing the actual value of a quantity by its selected base value. This method is used to express electrical quantities like voltage, current, power, and impedance in a simple and uniform form.

To convert into per unit, first base values are chosen, and then all system quantities are divided by these base values. This makes calculations easier and helps in comparing different parts of the power system.

Detailed Explanation:

Conversion into per unit values

The per unit system is widely used in electrical engineering to simplify calculations in power systems. In this system, all electrical quantities are expressed as a fraction of their respective base values. Converting quantities into per unit values is a simple and systematic process.

The basic formula used for conversion is:

Per unit value = Actual value / Base value

This formula applies to all electrical quantities such as voltage, current, power, and impedance. The key step in this process is selecting appropriate base values.

Steps for conversion

To convert any electrical quantity into per unit value, the following steps are followed:

Selection of base values

First, base values must be selected. Usually, base power (S_base) and base voltage (V_base) are chosen. These values are selected based on the system under study.

The base values should be consistent throughout the system. Once these are selected, other base quantities can be calculated.

Calculation of base current

Base current is calculated using base power and base voltage. It helps in converting actual current into per unit form.

Base current depends on whether the system is single-phase or three-phase, but the concept remains the same.

Calculation of base impedance

Base impedance is calculated using base voltage and base power. It is used to convert actual impedance into per unit value.

Base impedance plays an important role in analyzing transmission lines and transformers.

Conversion of quantities

After determining base values, actual values are divided by their corresponding base values.

For example:
Per unit voltage = Actual voltage / Base voltage
Per unit current = Actual current / Base current
Per unit impedance = Actual impedance / Base impedance
Per unit power = Actual power / Base power

This gives the per unit values, which are dimensionless and easy to handle.

Importance of proper base selection

Choosing correct base values is very important. If base values are not selected properly, the per unit values may not be meaningful.

In large power systems, a common base is used for all components to maintain consistency. This helps in comparing different parts of the system easily.

Application in power system

Conversion into per unit values is used in various power system studies such as load flow analysis, fault analysis, and stability analysis.

It is especially useful in transformer calculations. When the same base is used, the per unit impedance remains the same on both sides of the transformer. This simplifies analysis.

Engineers use per unit values to create simplified models of complex systems, making calculations faster and more accurate.

Advantages of conversion

Converting quantities into per unit values reduces the size of numbers, making them easier to work with.

It eliminates the need for unit conversions and reduces chances of errors. It also provides a uniform system for analyzing electrical networks.

Conclusion

Conversion into per unit values is a simple process of dividing actual values by base values. It helps in simplifying calculations, improving accuracy, and making power system analysis easier. Proper selection of base values ensures effective use of the per unit system.