Per Unit System in Power System Analysis

Per Unit System in Power System Analysis (Complete Guide with Applications)

In modern electrical power system engineering, it is often necessary to simplify complex calculations involving voltage, current, impedance, and power. One of the most efficient and widely used methods to achieve this is the Per Unit (PU) System. This method plays a critical role in power system analysis, electrical design, load flow studies, and fault calculations.

Originally, the per-unit system was developed to simplify manual calculations. However, even in today’s era of advanced electrical engineering software and simulation tools, this method remains indispensable due to its accuracy, consistency, and practical benefits.

Per unit system formula and advantages in power system analysis showing normalization, impedance calculation, and relay settings example

What is the Per Unit System?

The Per Unit System is a normalization technique in which electrical quantities are expressed as a ratio of a defined base value. Instead of dealing with large numbers in kilovolts, amperes, or ohms, engineers work with simplified, dimensionless values.

Basic Per Unit Formula:

Percentage Value (%) = Per Unit Value × 100Per Unit (PU) = Actual Value / Base Value

Where:

Actual Value = The real measured value (Volts, Amperes, Ohms, etc.)
Base Value = A selected reference value with the same unit
PU Value = Dimensionless number used for easier analysis

Why Use the Per Unit System in Power Systems?

The per-unit system offers several advantages that make it essential in high voltage power systems, transmission line analysis, and transformer design.

Key Advantages:

✅ Simplified Calculations
Electrical quantities become easier to compare and compute, especially in load flow analysis and short circuit calculations.

✅ Error Detection
Device parameters fall within a narrow range. This helps engineers quickly identify incorrect data or abnormal values.

✅ Uniform Representation
All values are expressed as ratios, enabling easy comparison across different voltage levels and ratings.

✅ Transformer Impedance Consistency
The per unit impedance of a transformer remains the same when referred to either primary or secondary side.

✅ Independent of Transformer Connections
Whether a transformer is connected in wye-delta, delta-wye, delta-delta, or wye-wye, its per-unit impedance remains unchanged.

✅ Voltage-Level Independence
The system is unaffected by voltage transformation or phase shifts, making it ideal for multi-voltage power system networks.

Per Unit vs Percentage System

The per-unit system is closely related to the percentage method used in electrical engineering.

Relationship:

Percentage Value (%) = Per Unit Value × 100

Industry Usage and Manufacturer Standards

Most electrical equipment manufacturers provide data like impedance, reactance, and resistance in per unit or percentage form. These values are usually based on:

Rated Power (kVA or MVA)
Rated Voltage (V or kV)

This standardization allows engineers to quickly integrate equipment into power system design, electrical protection systems, and fault analysis models.

Application of Per Unit System in Power Engineering

The per-unit system is extensively used in:

Power System Stability Analysis
Short Circuit Studies
Load Flow Analysis
Electrical Protection Systems
Relay Coordination

Practical Application: Relay Settings in Transmission Lines

A common real-world application of the per-unit system is in distance protection relays for transmission lines.

Zone Settings Example:

🔹 Zone 1 (Primary Protection):

Typically set to 85% of the transmission line impedance
Provides fast and reliable protection without overreaching

🔹 Zone 2 (Backup Protection):

Set to at least 125% of the line impedance
Must be carefully coordinated to avoid overlapping with adjacent line protection zones

Proper relay coordination is essential for maintaining power system reliability, grid stability, and fault isolation.

Importance in Modern Power System Engineering

Even with advanced tools like ETAP, DIgSILENT PowerFactory, and MATLAB simulations, the per-unit system remains fundamental because it:

Reduces complexity in large interconnected power grids
Improves accuracy in power system modeling
Enables consistent analysis across different voltage levels
Supports efficient electrical design and optimization

Conclusion

The Per Unit System is a powerful and essential tool in electrical power engineering. It simplifies analysis, improves consistency, and enhances accuracy in everything from transformer design to transmission line protection.

For engineers working in power generation, transmission, or distribution systems, mastering the per-unit method is crucial for efficient system analysis and reliable operation.

Comments

Anurag Segekar said…

explain the per unit system for DC quantities.

Wednesday, 16 May, 2018

Auto Transformer Tap Changing

Auto Transformer Tap Changing: Working Principle, Switching Sequence and Applications Auto transformer tap changing is a practical method of adjusting transformer output voltage without unnecessarily interrupting the electrical supply. In power transmission and distribution networks, the load does not remain constant throughout the day. As load current changes, voltage drops across transformers, cables, feeders, and transmission lines also change. A tap-changing arrangement compensates for these variations by modifying the effective number of turns in the transformer winding. A reactor-type on-load tap changer uses a center-tapped reactor, selector switches, and a bypass or short-circuiting switch to transfer the load from one tap to the next. The reactor limits the circulating current during the transition, allowing the tap position to change while the transformer continues supplying the connected load. This article explains the auto transformer tap-changing working principle , switch...

PRIMARY SECONDARY AND TERTIARY FREQUENCY CONTROL IN POWER SYSTEMS

Primary, Secondary and Tertiary Frequency Control in Power Systems Author: Engr. Aneel Kumar Keywords: frequency control, primary frequency control, automatic generation control (AGC), tertiary control, load-frequency control, grid stability. Frequency control keeps the power grid stable by balancing generation and load. When generation and demand drift apart, system frequency moves away from its nominal value (50 or 60 Hz). Grids rely on three hierarchical control layers — Primary , Secondary (AGC), and Tertiary — to arrest frequency deviation, restore the set-point and optimize generation dispatch. Related: Power System Stability — causes & mitigation Overview of primary, secondary and tertiary frequency control in power systems. ⚡ Primary Frequency Control (Droop Control) Primary control is a fast, local response implemented by generator governors (dro...

Advantages of Per Unit System in Power System Analysis | Electrical Engineering

Advantages of Per Unit System in Power System Analysis In electrical power engineering, the per unit (p.u.) system is one of the most widely used techniques for analyzing and modeling power systems. It is a method of expressing electrical quantities — such as voltage, current, power, and impedance — as fractions of chosen base values rather than their actual numerical magnitudes. This normalization technique provides a universal language for system calculations, minimizing errors, simplifying transformer modeling, and enabling consistency across multiple voltage levels. Because of these benefits, the per unit system is essential in fault analysis, load flow studies, transformer testing, and short-circuit calculations . ⚡ What is the Per Unit System? The per unit system is defined as: Q u a n t i t y ( p u ) = A c t u a l V a l u e B a s e V a l u e Quantity_{(pu)} = \dfrac{Actual \ Value}{Base \ Value} Q u an t i t y ( p u ) = B a se ...

Reversing the Direction of a Universal Motor: Methods and Circuit Diagram

How to Reverse the Direction of Rotation of a Universal Motor Introduction A universal motor is a high-speed electric motor that can operate on either an alternating-current or direct-current supply when designed for the applicable voltage and frequency. It is widely used in portable electric drills, grinders, vacuum cleaners, mixers, sewing machines, small machine tools, and other equipment requiring high starting torque and compact construction. The direction of rotation of a universal motor can be changed by reversing the direction of current through either the armature winding or the field winding relative to the other. The current must be reversed in only one of these windings. If the connections of both windings are reversed simultaneously, the relative direction of the field flux and armature current remains unchanged, and the motor continues rotating in the same direction. Before studying the reversing methods, readers may review the Universal Series Motors Electric Motors and...

Top 10 Transformer Manufacturers in the World

Top 10 Transformer Manufacturers in the World Transformers are among the most important and expensive assets in electrical generation, transmission, distribution, renewable-energy, industrial, infrastructure, and data-center projects. A power transformer changes voltage and current levels through electromagnetic induction while maintaining the system frequency. Generator step-up transformers increase generating-station voltage for efficient transmission, while grid and distribution transformers reduce voltage progressively before electricity reaches industrial, commercial, and residential consumers. The global transformer market continues to expand because of grid modernization, renewable-energy integration, industrial electrification, data-center development, replacement of aging equipment, and construction of new transmission infrastructure. One 2026 market assessment estimates that the global transformer market could grow from approximately USD 72.5 billion in 2026 to about USD 137....

MAIN AND PILOT EXCITER

Main Exciter The exciter (sometimes called the main exciter) is a synchronous generator that has its stator and rotor windings inverted. Its field winding is fixed in the stator, and the rotor carries the armature or AC . In addition the rotor carries the semiconductor bridge rectifier that converts the armature voltages to a two-wire DC voltage system. The AC voltages and currents in the armature are often alternating at a higher frequency than those in the main generator, e.g. 400 Hz. The higher frequency improves the speed of response of the exciter. The DC power circuit is coupled to the field of the main generator by the use of insulated conductors that pass coaxially inside the rotor of the exciter and the rotor of the main generator. This eliminates the use of slip rings, which were traditionally used before shaft mounted rectifiers were developed. A slight disadvantage of this technique is that the derivative feedback cannot be taken from the output of the exciter. Howeve...

PLUG REVERSING OF CAPACITOR START MOTORS

The capacitor start motors suffer from the disadvantage that they are not easily reversible due to the centrifugal switch connected in the auxiliary winding. The motor cannot be instantaneously reversed by simple control as the auxiliary winding remains disconnected till the motor comes near to zero speed. However, by proper design of the control circuit the motor can be made instantly reversible. This is accomplished by using an electromagnetic relay along with a special two contact centrifugal switch as shown in Figure. The circuit shown in Figure is for a small hoist using a capacitor start motor. The upper and lower limits of travel are controlled by two limit switches viz. LSU and LSD. When UP-push button is pressed, contactor U gets energized. Its contacts U 1 and U 2 energies the main winding. Closing of its contact U 3 causes relay R to get energized through the centrifugal switch contacts A—B. After the energization of relay R auxiliary winding gets ene...

ENGINEERING ARTICLES

Search This Blog