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POWER SYSTEM ANALYSIS

TADP 641

ELECTRICAL CIRCUIT FUNDAMENTALS

Juan Manuel Gers, PhD

Electrical Circuit Laws

The most important concepts of electrical circuits are treated inthis chapter. The three basic laws of electrical circuits are:

• Ohm’s Law

• Kirchhoff’s Voltage Law

• Kirchhoff’s Current Law

Ohm’s Law

Ohm’s Law establishes the relationship between voltage, current and impedance in electrical circuits, as follows:

Kirchhoff’s Voltage Law

For any closed path in a network, Kirchhoff voltage law (KVL)

states that the algebraic sum of the voltages is zero.

Some of the voltages will be sources, while other will result

from current in passive elements creating a voltage, which is

sometimes referred to as a voltage drop.

The law applies equally well to circuits driven by constant

sources, DC, time variable sources, v(t) and i(t), and to

circuits driven by sources.

Example of KVL

Write the KVL equation for the circuit shown in the

following figure.

Example of KVL

Starting at the lower left corner of the circuit, for the current

direction as shown, we have

)(

0

0

321

321

321

RRRivv

iRiRviRv

vvvvv

ba

ba

ba

Find V3 and its polarity if the current I in the circuit of fig. is

0.40 A.

Example

Assume that V3 has the same polarity as V1. Applying KVLand starting from the lower left corner

Find V3 and its polarity if the current I in the circuit of fig. is

0.40 A.

Example

VV

V

VIVIV

0.30

00.80.100.20.50

0)0.20()0.5(

3

3

321

Terminal a is positive with respect to terminal b

Kirchhoff’s Current Law

The connection of two or more circuit elements creates a

junction called a node. The junction between two elements is

called a simple node and no division of current results.

The junction of three of more elements is called a principal

node, and here current division does take place. Kirchhoff’s

current law (KCL) states that the algebraic sum of the currents

at a node is zero.

It may be stated alternatively that the sum of the currents

entering a node is equal to the sum of the currents leaving that

node. The basis for the law is the conservation of electric

charge.

Example of KCL

Write the KCL equation for the principal node shown in the

following figure.

Circuit Theorems

Circuit Theorems are derived from the circuit laws. The three mostcommonly used for system analysis are :

• Thevenin Theorem

• Star/Delta Transform

• Superposition Theorem

Thevenin’s Theorem

This is useful for replacing part of a network which is not of particular interest.

Any active network viewed from any 2 terminals can be replaced by a singledriving voltage in series with a single impedance where:

Driving voltage = Open circuit voltage between terminals

Impedance = Impedance of the network as viewed from the two

terminals with all driving voltages short circuited.

/Y and Y/ Transform Theorem

3 23 2

Z30 Z20

Z10Z31 Z12

Z23

𝑍12 = 𝑍10 + 𝑍20 + 𝑍10 ∗ 𝑍20

𝑍30

𝑍10 = 𝑍12 ∗ 𝑍31

𝑍12 + 𝑍23 + 𝑍31

Superposition Theorem

In any linear network the current in any branch due to thesimultaneous action of several different driving voltages is equal tothe vector sum of the currents caused by each driving voltage actingalone with the others short circuited.

Z1 Z2

Z3

E1 E2

I 3

Superposition Theorem

Z1 Z2

Z3E1 E2

Z1 Z2

I31

Z3

I32

I3 = I31 + I32

Questions?