refresher course on electrical fundamentals 090310
TRANSCRIPT
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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 Voltage
3. Series RL circuit
4. Types of power and energy in ac circuits, powertriangle
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 withsinusoidal voltages and currents
All loads may be represented as series/ parallel combination
ofresistance, inductance and capacitance. We want to obtain the steady state performance of the circuit.
Simplest method of calculation is to use notations ofPhasorAlgebra.
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VOLTAGE / CURRENT SINE WAVE
The equation of instantaneous value isv = Vm sinv =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 givesthe 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 timeProduce the same heat as produced by the alternating current whenFlowing through same circuit for the same duration.
RMS current
I = Im / 2
PEAK current
Im
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 byThat of AC
Avg. currentIav= 2Im /
PEAK currentIm
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Scalar
A scalar is a quantity with magnitude only. Ithas 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 hasboth
magnitude
and direction.
E.g.
Displacement
, Velocity,
force,acceleration
etc.
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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= vi
Vm Im= - ---------- sin 2t2
The shaded areas in this diagramshow how poweris absorbed and
returned 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= vi
Vm Im= ---------- sin 2t2
The shaded areas in this diagram showhow poweris absorbed and returned 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 = 0
V
I
900
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Expression for a sinusoidal voltagesource:
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 +=
222 LRZ +=
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= 0R
The voltage and currentphasors are in phase.
pure Inductive element:Impedance=
90L
the current lags the voltage by 90o
pure Capacitive element:Impedance=
901
C
the 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
PowerApparent
PowerActive
S
PCos ==
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 UnitApparent VI volt-ampere or VA
Active VI Cos watt or W
Reactive VI Sin reactive volt-ampereor 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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Power Flow Quadrants: IEC62053-23
Export Reactive Power
V
Import Active Power
Import Reactive Power
Export Active Power
Q1PF: lagging /
Inductive
Q2PF: Leading /
capacitive
Q3PF: lagging
/Inductive
Q4PF: Leading
/capacitive
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Power Flow
Power System Power System
Electricity
Interconnected system of generation and load centers
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Measurement Reference
Power flow to Voltage bus is taken positive (import) Current transformer connection polarity (p2 to bus side)
Utility A
A B
Utility B
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EHV BUS
P1 P2
HV BUS
P2 P1
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Power Components
Quadrature component
In phase component
V ( reference)
I
00
900
1800
2700
I Sin
I Cos
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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 byPhasor 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