# Per Unit System Calculation Method in Power System

In this article, we will explore the concept of the per unit system in power systems. We will understand why the per unit system is used, how to convert actual values to per unit values, and the formulas associated with it.

## Introduction

During a fault in an electrical system, abnormal currents flow through the system. To protect the equipment and ensure their optimal performance, it is crucial to understand and analyze these currents. This knowledge helps in selecting the appropriate rating of circuit breakers, designing components, and setting up relays. However, dealing with actual values can be complex and requires lengthy calculations. To simplify this process, electrical quantities are often represented in their base units or per units.

## Understanding the Per Unit System

The per unit value of a quantity is calculated as the ratio of its actual value to the corresponding base value. Moreover, percentage value can be obtained by multiplying the per unit value by 100. Let’s look at the relevant formulas:

• Per unit value of voltage: Actual value of voltage / Base value of voltage
• Percentage value of voltage: Per unit value x 100
• Base current: Base KVA / Base Voltage (Amperes)
• Base Impedance: Base Voltage (Volts) / Base Current (Amperes) (Ohms)
• Base Impedance: (Base KV)² x 1000 / Base KVA (Ohms)
• Per unit impedance: Actual impedance / Base impedance (Ohms)
• Per Unit current: Actual current / Base Current

For three-phase systems, the formula for calculating base current is given by:

Base current = Base KVA / √3 x Base voltage in KV (Amperes)

## How does Per Unit System Work?

The Per Unit (PU) system is a method used in power systems to simplify calculations and analysis. It’s particularly useful when dealing with transformers, generators, transmission lines, and other components with varying voltage and power ratings. The PU system normalizes quantities to a common base, making it easier to compare and perform calculations regardless of the actual physical values.

Here’s how the Per Unit system works and how calculations are performed:

1. Base Values: In the PU system, you choose a set of base values for voltage (Vbase) and apparent power (Sbase). These values are typically selected to match the nominal values of a specific component, such as a generator or a transformer. The choice of base values depends on the specific application and the components under consideration.
2. Normalization: All quantities are then normalized to their respective base values using the following equations:
• Voltage PU (Vpu) = Actual Voltage (V) / Vbase
• Current PU (Ipu) = Actual Current (I) / Ibase
• Apparent Power PU (Spu) = Actual Apparent Power (S) / Sbase
3. Per Unit Quantities: After normalization, all quantities are expressed in per unit. This means that quantities are represented as a decimal or fractional value relative to their base values.
4. Per Unit Impedance: For components like transformers, reactors, and transmission lines, impedance is an important parameter. The per unit impedance (Zpu) is calculated as:
• Impedance PU (Zpu) = Actual Impedance (Z) / Zbase
5. Per Unit Power: Power can be expressed in per unit as well. For power components like generators and loads, the per unit power (Ppu) is calculated as:
• Power PU (Ppu) = Actual Power (P) / Pbase
6. Per Unit Admittance: Admittance (the reciprocal of impedance) can also be expressed in per unit:
7. Calculation and Comparison: With quantities normalized to per unit values, you can perform calculations, such as power flow, fault analysis, and stability studies, more easily. You can compare per unit values across different components regardless of their actual ratings.
8. Voltage Drop and Losses: Voltage drop and losses can also be calculated in per unit, helping to analyze the system’s efficiency.

By using the per unit system, engineers and analysts can simplify complex power system calculations and focus on the relative relationships between components. It’s important to note that while per unit values are dimensionless, they still retain the proportions and relationships between quantities. When presenting results or making decisions, the engineer can convert back to the actual units if necessary.

Keep in mind that the choice of base values is important for accurate representation. Common base values for voltage are the nominal line-to-line voltage of a system, while for apparent power, the base power is often the rated capacity of a major component like a generator or transformer.

## Advantages of the Per Unit System

The per unit and percentage systems offer several advantages:

1. Simpler calculations: Working with per unit values simplifies complex calculations in power systems.
2. Easy equipment comparison: Manufacturers often mention per unit values, making it easier to compare different equipment.
3. Equivalent pu impedance: Regardless of the transformer connections, the equivalent per unit impedance remains consistent in a three-phase system.
4. Easy research: Micro machines that represent actual power system machines have the same per unit values, facilitating research and analysis.
5. Reduced chances of error: In a three-phase system, using per unit values for both lines and phase quantities minimizes the chances of calculation errors.
6. Uniform representation of transformers: In a three-phase transformer, whether in a star or delta connection, the equivalent per unit values remain the same.
7. Simplified transformer representation: Transformers are commonly represented by R+jX, neglecting the magnetizing current. This simplifies calculations, as the per unit current values remain the same on both sides of the transformer.

By utilizing the per unit system, power system engineers can perform efficient calculations and analyses, leading to improved reliability and optimal performance of electrical systems.