refresher course basics of electrical circuits

7/28/2019 Refresher Course Basics of Electrical Circuits

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Copy right :- YMPL, Udaipur11/10/2010 1

Refresher course on Electrical fundamentals

(Basics of A.C. Circuits)

by B.M.Vyas

A specifically designed programme for

Da Afghanistan Breshna Sherkat (DABS)Afghanistan


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2

Areas Covered Under this Module

1. Sinusoidal AC waveform

2. Instantaneous current and Voltage3. Series RL circuit

4. Types of power and energy in ac circuits, power

triangle

5. Vector diagrams as a analysis tool

6. Power flow principles


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Components of A.C. Circuits

Generation, transmission and distribution, all deal with

sinusoidal voltages and currents

All loads may be represented as series/ parallel combinationofresistance, inductance and capacitance.

We want to obtain the steady state performance of the circuit. Simplest method of calculation is to use notations ofPhasor

Algebra.


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VOLTAGE / CURRENT SINE WAVE

The equation of instantaneous value isv = Vm sin

v =Vm sint

v = instantaneous voltageVm = maximum /peak voltage

= angle in degrees or radians= 2 f

What about ac sine current waveform?


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Phase Shift

Red is Leading

Red is lagging

This gap gives

the amount ofphase shift


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How much is Phase Shift of B with respect to A ?


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The RMS value of an alternating current is given by the steady (DC)Current which when flowing through a given circuit for a given time

Produce the same heat as produced by the alternating current whenFlowing through same circuit for the same duration.

RMS current

I = Im / 2

PEAK currentIm

RMS CURRENT


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AVERAGE CURRENT

The average value of an AC is expressed by that steady current (DC)Which transfers across any circuit, the same charge as is transferred by

That of AC

Avg. current

Iav= 2Im /

PEAK current

Im


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Scalar A scalar is a quantity with magnitude only. It

has no direction.

Example of scalar quantities are Length Area Volume

Speed Mass Energy Work Power Temperature Pressure


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Vector or phasorA vector

quantity has

both

magnitude

and direction.

E.g.

Displacement

, Velocity,

force,

accelerationetc.


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Addition & Subtraction of two Vectors


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A

B

A-B


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PURE RESISTIVE CIRCUIT

AC Power Waveform

v = Vm sint

i = Im sint

Power P= V I

Both V and I areRMS values

Power is positive inboth half cycles

VI


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INDUCTIVE CIRCUIT

AC Power Waveform

v = Vm sint

i = Im sin (t /2)

Power P= viVm Im

= - ---------- sin 2t2

The shaded areas in this diagramshow how poweris absorbed andreturned to the circuit.

The shaded areas above the baseline( + levels) represent power that isabsorbed by the inductor.

The shaded areas below the baseline

(- levels) representpower that isreturned to the circuit.

P (over the cycle) = 0

V

I

900


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CAPACITIVE CIRCUIT

AC Power Waveform

v = Vm sint

i = Im sin (t +/2)

Power P= viVm Im

= ---------- sin 2t2

The shaded areas in this diagram showhow poweris absorbed and returned tothe circuit.

The shaded areas above the baseline( + levels) represent power that isabsorbed by the inductor.

The shaded areas below the baseline

(- levels) representpower that isreturned to the circuit.

P = 0

V

I

900


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Expression for a sinusoidal voltage

source:

For a linearcircuit, in thesteady state, the current is alsosinusoidal and can beexpressed as:

R-L circuit

i = Im sin (t - )

v = Vm sint

V

I


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Is the phase difference.

+= sincos IjII

Impedance Triangle

LjRZ +=

222LRZ +=

R

L 1tan =

R

Z

XL

RIZIVIPav22

coscos ===

Thus, all the power consumedin the R-L circuit is actually thepower dissipated in theresistance


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Phase Relationship:pure resistive element: Impedance=

o

0R

The voltage and currentphasors are in phase.

pure Inductive element:

Impedance=o

90Lthe current lags the voltage by 90o

pure Capacitive element:

Impedance=o

90

1

Cthe current leads the voltage by 90o


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Power Factor

The power factorin the circuit is a factor by which V.I(Apparent Power) should be multiplied to get the Active

(or real) power

PowerApparentPowerActive

SPCos ==

By convention, it is assumed, that if the circuit is inductive,

the reactive power is positive,and for capacitive circuit, the reactive power is negative.


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Three Types of Power

V

I

I cos

ISin

P - Active

QR

eactive

Power Triangle

Type Formula Unit

Apparent VI volt-ampere or VA

Active VI Cos watt or W

Reactive VI Sin reactive volt-ampere or VAR


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Copy right :- YMPL, Udaipur

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The reactive power is the power thattravels back and forth between thesupply and the circuit due to thepresence of reactive elements(inductance and capacitance).

Over a cycle, its average is zero.

By convention, it is assumed, that ifthe circuit is

inductive, the reactive power ispositive, and for

capacitive circuit, the reactivepower is negative.

Reactive Power

AC Power Waveform for

pure capacitance

v = Vm sint

i = Im sin (t +/2)


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Three phase system

1200

1200

1200

1

23

12

23

31

1,2,3 phase voltages

12,23,31 Line voltages


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Three phase system

1200

1200

1200

1

23

23

31

1,2,3 phase voltages

12,23,31 Line voltages

How to getphase voltages by

Phasor additions?

V12= V1-V2=V1+(-V2) 12

23

31

30

30

30

12

-V2

Using Law ofParallelogram


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Three-phase Y configurations


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Three-phase Y and configurations


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Phasor representation of a 3 phase load

Er,Ey, Eb voltages. Ir,Iy,Ib currents.

1,2,3 phaseangles (lagging)

er

eyeb

ir

iy

ib

1

23


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Thank you

refresher course basics of electrical circuits

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