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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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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
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