EEPW 2251
ELECTRICAL POWER TECHNOLOGY
SEM 1 /2022-2023
Premanand K.P.
Lecturer-EE, Engg Dept
UTAS-Al Musannah
1
Faraday's Law
• A voltage is induced in a conductor when
that conductor is moved through a
magnetic field. or
• A voltage is induced in a conductor when
the magnetic field moves through the
conductor.
• That means, the requirement for producing
the voltage are:
1- A conductor
2- A magnetic field
3- Relative motion between the conductor
and the magnetic field
AC GENERATOR
Position A- the magnetic flux does not cut a coil conductor, therefore an induced voltage is zero.
Position B- the coil cuts across the field to produce maximum EMF or Voltage.
PositionC- the magnetic flux does not cut a coil conductor; therefore an induced voltage is zero.
Position D- the loop cuts across the flux again for maximum voltage, but here the flux is cutin the
opposite direction, thus the polarity at D is negative.
The coil completes the last quarter turn in the cycle where it returns to position A, the point
where it started. The cycle of voltage values is repeated itselfas the coil continues to rotate.
EQUATION OF ALTERNATING QUANTITY
✓Expression of Alternating emf, v(t) = Vm Sin(ωt ± ),
Where,
V - the instantaneous value of alternating emf,
Vm - The maximum value or peak value of the alternating emf
in Volts
ω - Angular velocity of the coil or angular frequency in
rad/sec
ϴ – Phase angle in degree or in radians
✓In generator, Since the rotating coil moves through an angle
of 2 radians in one cycle, the angular velocity, ω = 2f (radians)
V(t) = Vm. Sin (2f.t ± )
where,
f = number of cycles completed per second or frequency
in hertz
t= Time Period in seconds
PROPERTIES OF ELECTRICAL SIGNALS
TERMS IN A.C. CIRCUIT
•Maximum value
•Instantaneous value
•Cycle
•Frequency
•Time period
•Phase
•RMS Value
AMPLITUDE (V MAX)
•Unit: Volt
• It is the maximum voltage reached by the
signal.
•Peak voltage is another name for amplitude.
PEAK-PEAK VOLTAGE ( VPP )
✓It is twice the peak voltage
(Amplitude).
✓V pp =2Vp
✓Time period (T):
Unit: second
✓ It is the time taken for the
signal to complete one
cycle.
FREQUENCY ( F )
Unit: Hertz (Hz)
• It is the number of cycles per second.
• The frequencies tend to be high so kiloHertz
(kHz) and MegaHertz (MHz) are often used.
1kHz = 1000Hz = 103 Hz
1MHz = 1000000Hz = 106 Hz.
WAVEFORM
It is the path traced by a quantity, such as voltage as a
function of some variable such as time, position, degrees,
temperature and so on.
Voltage Peak Voltage
RMS Voltage
0
Time
CYCLE
Complete set of positive and negative values
Half cycle : Portion of waveform
Voltage
ROOT MEAN SQUARE (RMS) VALUES
𝟏
•VRMS = × Vpeak
√(𝟐)
•VRMS = 0.707 × Vpeak and
• Vpeak = 1.4 × VRMS
PHASE RELATION
RESISTIVE LOAD CAPACITIVE LOAD INDUCTIVE LOAD
SINGLE-PHASE AC CIRCUITS
Circuit Parameters or Passive elements:
✓ Resistance - R
✓ Inductance - L
✓ Capacitance - C.
1.PURELY RESISTIVE CIRCUIT
Voltage v = VmSinωt , Current iR = = Im Sinωt
( The current and voltage are in phase )
Average power = Vm Im / 2
VOLTAGE & CURRENT WAVEFORM
WITH RESPECT TO TIME PERIOD
CIRCUIT DIAGRAM PHASOR DIAGRAM
j
2.PURELY INDUCTIVE CIRCUIT
Average power consumed in Inductance=0.
VOLTAGE & CURRENT WAVEFORM
PHASOR DIAGRAM
CIRCUIT DIAGRAM WITH RESPECT TO TIME PERIOD
INDUCTIVE REACTANCE (XL) CONTD.
Reactance – X:
➢ It is a form of opposition that electronic components exhibit to the passage
of alternating current (alternating current) because of capacitance or
inductance.
➢ It is like an AC counterpart of DC (direct current) resistance.
3. PURELY CAPACITIVE CIRCUIT
VOLTAGE & CURRENT WAVEFORM
CIRCUIT DIAGRAM WITH RESPECT TO TIME PERIOD PHASOR DIAGRAM
CAPACITIVE REACTANCE (XC) CONTD.
The ratio of Vm to Im is defined as Capacitive Reactance Xc ,
Sl.No. INDUCTIVE REACTANCE (XL) CAPACITIVE REACTANCE (XC)
1. The opposition to the flow of The opposition to the flow of
alternating current due to alternating current due to
inductance is called “inductive capacitance is called "capacitive
reactance.“ reactance."
𝟏
2. It is denoted as XL & 𝑋𝐿 = 2𝜋𝑓𝐿 It is denoted as XC & XC =
𝟐𝜋𝑓𝑪
It is measured in ohms It is measured in ohms
3. If the reactance releases if the reactance releases energy in the
energy in the form of a form of an electric field, it is called
magnetic field, it is called capacitive reactance
inductive reactance
4. Inductive reactance (in ohms) Capacitive reactance (in ohms)
increases with increasing AC decreases with increasing AC
frequency. frequency
EXAMPLES - PURE INDUCTIVE CIRCUIT
PROBLEM - 1:
Calculate the reactance of a coil of inductance 0.32 H when
it is connected to a 50 Hz supply.
SOLUTION:
PROBLEM - 2:
A coil has a reactance of 124 Ω, in a circuit with a supply of
frequency 5 kHz. Determine the inductance of the coil.
SOLUTION:
PROBLEM - 3:
A coil has an inductance of 40 mH and negligible resistance.
Calculate its inductive reactance and the resulting current if
connected to:
(a)A 240 V, 50 Hz supply, and
(b) a 100 V, 1 kHz supply.
SOLUTION:
PROBLEM - 4:
Determine the capacitive reactance of a capacitor of
10 µF when connected to a circuit of frequency
(a) 50 Hz,
(b) 20 kHz.
PROBLEM - 5:
Calculate the current taken by a 23 microFarad
capacitor when connected to a 240V, 50Hz supply.
Single phase R-L series AC Circuit
For RL circuit 90 > Ø > 0
Impedance - Z:
✓ It is the property of an electronic component, circuit, or system that opposes
the flow of AC or DC current.
✓ Impedance is a vector (two-dimensional)quantity having resistance and
reactance.
SINGLE PHASE R-C SERIES AC CIRCUIT
For RC circuit 0 > Ø > -90
SINGLE PHASE R-L-C SERIES CIRCUIT
1. If XL>XC ,the circuit will be Inductive, then I lags V.
2. If XL=XC, the circuit will be Resistive, then I in phase
with V. (Resonance condition…’I’ will be maximum).
3. If XL<XC, the circuit will be Capacitive I leads V.
ELECTRIC POWER IN SINGLE PHASE AC CIRCUIT
Instantaneous power, P = V(t).I(t), Watt
S – Apparent power (VA) =VI
The total power drawn from the source
P – Active power (Watt) =VI CosØ = I2R
P is also called Useful Power
Ø – Phase angle between V and I
Q – Reactive power (VAR) =VI SinØ
or Power loss = I2 XL or I2 XC
Power factor - Cos Ø
Power factor = = = kW
kVA
= Cos Ø =
For Purely Resistive circuit,
Power factor = 1 (unity power factor – UPF circuit).
For Purely Inductive and Capacitive circuits,
Power factor = 0 (ZPF circuit).
The Power Factors of a Typical Motor: (1 HP =745.7 W or 0.746 kW)
Power Factor - Inductive Load
Problem 1 : RL series circuit pg.12
PROBLEM 2: pg.11
PROBLEM 3: pg12
Example: pg.16
A series RCL consist of R = 148 Ω, C = 150 µF, and L = 35.7 mH, connected to 25V, 512 Hz
AC power supply. Find the:
a) The voltage across each circuit element
b) The electric power delivered by the power supply
THANK YOU
