Per Unit Value Concept

The per unit value system is a standardized method used extensively in electrical engineering, particularly in the analysis of power systems. It involves expressing electrical quantities such as voltage, current, impedance, and power as fractions or multiples of a chosen reference quantity, known as the base value. This system simplifies complex calculations by converting various values into a common, dimensionless representation, making it easier to compare and analyze system components across different voltage levels.

The fundamental relationship for calculating the per unit value for any given quantity is defined by a simple division:

$$ \text{Per unit value} = \frac{\text{Actual value}}{\text{Base value}} $$

This formula demonstrates that to determine the per unit value of an electrical quantity, you must divide its actual measured or specified value by a predetermined base value of the same quantity. This normalization process provides a unified scale for all system parameters.

Understanding Components of Per Unit Calculation

• Actual Value: This refers to the real, measured, or calculated value of the electrical quantity in its standard units. For example, if you are working with voltage, the actual value would be in Volts (V) or Kilovolts (kV). Similarly, for current, it would be in Amperes (A); for impedance, in Ohms ($\Omega$); and for power, in Watts (W), Kilowatts (kW), Megawatts (MW), or Volt-Amperes (VA), Kilovolt-Amperes (kVA), Megavolt-Amperes (MVA).
• Base Value: This is a carefully selected reference value for a particular electrical quantity. In power system analysis, base values are typically chosen for power (e.g., a system MVA base) and voltage (e.g., a bus voltage base). Once these two base values are established, the base values for other quantities like current and impedance can be derived using fundamental electrical formulas such as Ohm's Law and power equations. The selection of appropriate base values is crucial for consistent per unit calculations throughout the system.

Benefits of Per Unit System in Power System Analysis

The adoption of the per unit system offers several significant advantages, which contribute to its widespread use in power system studies:

• It simplifies calculations by eliminating the need to explicitly refer values across different voltage levels through transformers. All quantities are expressed on a common base, regardless of the physical voltage.
• Equipment manufacturers often provide the impedance values of components (like transformers, generators, and motors) directly in per unit, which streamlines their integration into system models.
• The per unit values of impedances for various types of electrical machines and transformers tend to fall within a relatively narrow and predictable range, making it easier for engineers to identify potential errors in calculations or data input.
• It standardizes fault calculations and overall system analysis, making it more efficient and less prone to numerical errors, especially in large and complex power networks.

Formula Derivation for Per Unit Value

The concept of per unit value is a form of normalization. If we have an actual quantity $Q_{\text{actual}}$ and we define a base quantity $Q_{\text{base}}$ (both in the same units), then the per unit representation $Q_{\text{p.u.}}$ is simply the ratio:

$$ Q_{\text{p.u.}} = \frac{Q_{\text{actual}}}{Q_{\text{base}}} $$

This universal formula applies uniformly across all electrical quantities, ensuring a consistent and dimensionless representation that greatly aids in power system modeling and analysis.

Therefore, the per unit value for any quantity is calculated by dividing its actual value by its chosen base value.