1. Kazi Md. Shahiduzzamna, EEE, NUB
Power System 1 EEE 3231 One line Diagram, Impedance and Reactance Diagram and Per unit concept
Kazi Md. Shahiduzzamna, EEE, NUB

2. Outline of this chapter
The One-line Diagram
The Impedance and Reactance Diagram
The per unit concept and its advantages
Base selection

3. One line diagram Definition:
Often any diagram is simplified by omitting the completed circuit
through the neutral and by indicating the component parts by standard
symbols rather than by their equivalent circuits. Such a simplified
diagram of an electric system is called a one-line diagram.

4. Example of one line diagram:
#1 Generator-20,000 kva, 6.6 kv, X" = ohms
#2 Generator-10,000 kva, 6.6 kv, X" = 1.31 ohms
#3 Generator-30,000 kva, 3.81 kv, XI! = ohrns
T l and T 2 -each transformer in each 3-phase bank-10,000 kva, kv,
X = ohms referred to the high-tension side
Reactance of the transmission line = 17.4 ohms
Load A = 15,000 kw, 6.6 kv, pJ. = 0.9 lag
Load B = 30,000 kw, 3.81 kv, pJ. = 0.9 lag

5. The Impedance and Reactance Diagrams
Definition:
When the components of the one line diagram is represented by there
corresponding impedance and reactance is known as Impedance and Reactance
Diagram of that one line diagram.
Need for The Impedance and Reactance Diagrams:
To calculate the performance of a system under load conditions
To calculate the performance of a system upon the occurrence of a short circuit
Point should be noted that The impedance diagram does not include the
current-limiting impedances shown in the one-line diagram.

6. The Impedance and Reactance Diagram of the given example of one line diagram is shown
below:
Point should be noted
As the magnetizing current of a transformer is usually insignificant compared
to the full-load current, the shunt admittance is usually omitted in the
equivalent circuit of the transformer.
the inductive reactance of a system is much larger than its resistance. So resistance is
omitted from the impedance diagram.

7. So the impedance diagram is reduce to the following figure where only reactance
is existed,
This figure is called reactance diagram of the system.

8. Per Unit Concept:
The per-unit value of any quantity is defined as the ratio of the quantity to its base value
expressed as a decimal.
The ratio in per cent is 100 times the value in per unit.
The per-unit method has an advantage over the per cent method because the product of
two quantities expressed in per unit is expressed in per unit itself, but the product of two
quantities expressed in per cent must be divided by 100 to obtain the result in per cent.
Important points regarding Per unit Quantity:
three-phase circuits are solved as a single line with a neutral return, the bases for
quantities in the impedance diagram are kVA per phase and kV from line to neutral.
For single-phase systems, or three-phase systems where the term current refers to
line current, the term voltage refers to voltage to neutral, and the term kVA refers to kVA
per phase.
But Data are usually given as total three-phase kVA and line-to-line kV.
So The base voltage to neutral is the base voltage from line to line divided by √3.
And the per-unit value of the kVA per phase on the kVA-per-phase base is the per-unit
value of the three-phase kVA on the three-phase kVA base divided by three .

9. Formulas related various Quantities:
For phase base voltage
and single phase base
kVA.
For line to line base
voltage and total three
phase base kVA.

10. to change from per-unit impedance on a given base to per- unit impedance on a new base, the following formula applies:
The Advantages of Per-unit Computations:
Manufacturers usually specify the impedance of a piece of apparatus
in per cent or per unit on the base of the name-plate rating.
The per-unit impedances of machines of the same type and widely
different rating usually lie within a narrow range, although the ohmic values differ
materially for machines of different ratings.
The way in which transformers are connected in three-phase circuits does not affect
the per-unit impedances of the equivalent circuit.
Example related this topics are 6.10 and 6.11 from the book and 8.2 in the soft copy
of the book.

11. Reference Book
Elements of Power System Analysis by Willaim D. Stevenson, Jr.