SIDDAGANGA INSTITUTE OF TECHNOLOGY, TUMAKURU-572103

(An Autonomous Institute under Visvesvaraya Technological University, Belagavi)

DEPARTMENT OF ELECTRICAL & ELECTRONICS ENGINEERING

MAR 2025- JUL 2025, 6th semester

POWER SYSTEMS - I
Report on
Representation of Power Systems

Submitted by
NAME USN
ANANYA N 1SI22EE002
 Representation of Power System
Introduction
A power system is a critical infrastructure that enables the
generation, transmission, and distribution of electrical energy from
producers to consumers. The structure of a power system is
hierarchical and interconnected, comprising three primary sections:
generating stations, transmission lines, and distribution systems.
Each segment plays an essential role in the seamless delivery of
electrical energy.
Generating stations are responsible for producing electrical energy
from various sources such as thermal energy, hydro energy, nuclear
energy, and increasingly, renewable sources like solar and wind.
This generated power needs to be delivered to consumers, which
involves transporting it over long distances. To achieve this
efficiently, the voltage is stepped up using transformers and
transmitted via high-voltage transmission lines.
The transmission lines carry bulk electrical energy to load centers
where it is stepped down in substations and further distributed
through distribution systems. These systems ensure that electricity
reaches end-users—residences, industries, and commercial
establishments—at usable voltage levels. In interconnected systems,
transmission lines also play a vital role in connecting different power
system grids, allowing power exchange between regions and
enhancing system reliability and stability.
Equivalent Circuit of a Two-Winding Transformer &
Transmission Line
In power system analysis, understanding the internal behaviour and
interactions of components is crucial. Therefore, engineers use
equivalent circuits to model the electrical characteristics of devices
like transformers and transmission lines.
Two-Winding Transformer
A two-winding transformer consists of a primary winding and a
secondary winding wound on a common magnetic core. In its
equivalent circuit, the transformer can be represented by a
combination of resistances and reactances that model:
• Winding resistance (R₁ and R₂): Accounts for the copper
losses in primary and secondary windings.
• Leakage reactance (X₁ and X₂): Represents the leakage flux
that does not link both windings.
• Core loss resistance (R₀) and magnetizing reactance (X₀):
Model core losses due to hysteresis and eddy currents and the
magnetizing current needed for core excitation.
By transferring all parameters to one side (usually primary), the
transformer can be modeled as a simple circuit, facilitating easier
analysis during power flow and fault studies.

Transmission Line
Transmission lines, used for carrying electricity over long distances,
are also represented by equivalent circuits. Depending on their
length, they are classified as short, medium, or long lines. The
simplified model usually includes:
• Series impedance (R + jX): Represents resistance and
inductive reactance of the conductors.
• Shunt admittance (Y): Models the capacitive effects between
conductors and between conductors and the ground.
Such modeling is essential for calculating voltage drops, power
losses, and efficiency, and for ensuring the safe and reliable
operation of the transmission network.

One-Line Diagram
A one-line diagram (also known as a single-line diagram) is a
simplified schematic representation used in the analysis and design
of three-phase power systems. Although actual power systems are
three-phase, representing all three phases would make the diagram
complex and difficult to interpret. Hence, the single-line diagram
uses standardized symbols to show only one phase of the system,
assuming that the system is symmetrical and balanced.

This type of diagram includes components like generators,

transformers, buses, circuit breakers, loads, and transmission lines.
These are all depicted using unique symbols and connected by a
single line, which conceptually represents the three-phase
conductors. It enables engineers to visualize the structure of the
power system, trace power flows, and plan switching operations
without getting into phase-by-phase details.
For example, a typical one-line diagram of a substation will show
how incoming transmission lines connect to transformers and how
the transformed voltage is distributed to different feeder lines serving
loads.

Representations in Power Systems

For effective analysis of power systems, it is necessary to simplify
the representation of the system. This is achieved using two types of
diagrams:
Impedance Diagram

The impedance diagram is a step ahead of the one-line diagram. It

replaces each component in the system with its single-phase
equivalent impedance, including the resistive and reactive elements.
Generators are represented by their internal impedance and voltage
source, transformers by their equivalent impedance, and transmission
lines by their series impedance and shunt admittance if necessary.
This representation is particularly useful when analyzing power
flow, load flow, and short-circuit conditions in the system.
Reactance Diagram

The reactance diagram is a further simplified version of the

impedance diagram. It only includes the reactive elements of the
power system components, omitting resistive components. This is
possible because, in most practical power systems, the resistance of
elements is much smaller than their reactance and can be neglected
for many types of analysis, especially fault studies.
The use of reactance diagrams significantly reduces the complexity
of calculations while still providing accurate insights into system
behaviour under balanced fault conditions.
Per Unit (P.U) System
The Per Unit System is a method of normalization that expresses
system quantities as fractions of a defined base unit. This approach is
widely used in power system studies because it simplifies the
mathematical analysis and comparison of different components in
the system.
Definition

The per unit value of any quantity is given by:

Per Unit Value=Actual Value/Base Value

This means that a quantity like current, voltage, power, or impedance

is divided by a predefined base value (chosen for each system or
zone), converting it into a unitless number that is easier to handle in
calculations.
Example

If the base current is 50 A and the actual current in the circuit is 30

A, then the per unit value is:
P.U. Current=30/50=0.6

Advantages of Per Unit Computations

Using the per unit system offers several advantages in simplifying

power system calculations:
1. Uniformity Across Components: Per unit normalization
eliminates the need to refer parameters like impedance from one
voltage level to another, especially when dealing with
transformers.
2. Simplified Transformer Calculations: Transformer
impedances remain the same on both the primary and secondary
sides in per unit, avoiding cumbersome conversions.
3. Normalized Values: It eliminates extremely large or small
numbers, improving the readability and stability of calculations.
4. Consistency: When all quantities are expressed in per unit,
power system equations become dimensionally consistent and
simpler to solve.
 5. Ease of Fault Analysis: In fault studies, per unit quantities
facilitate quick fault current calculations and the coordination of
protection devices.
6. Scalability: It helps in designing and scaling power systems
from small networks to large interconnection grids using a
consistent analytical framework.

Conclusion
In conclusion, the representation of power systems using equivalent
circuits, one-line diagrams, impedance and reactance diagrams, and
the per unit system is foundational to the understanding and analysis
of electrical networks. These methods help engineers and technicians
model real-world components in simplified forms that are suitable
for both manual and computational analysis.
The one-line diagram provides a bird’s eye view of the system’s
structure, while impedance and reactance diagrams delve deeper into
electrical behaviour. The per unit system ensures that these analyses
are not bogged down by scale differences, making it an
indispensable tool in the design, planning, and operation of modern
power systems.
Through these representations, engineers can simulate, troubleshoot,
and optimize the performance of power systems, ensuring that
electricity is delivered efficiently, reliably, and safely from
generation to consumption.