Fundamentals Of Electricity
Simple DC
Series
Circuit,
Rt = R1+R2+R3
Simple DC
Parallel
Circuit,
Rt = (R1.R2.R3 )
/(R2.R1+R3.R2+R1 .R3)
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Fundamentals Of Electricity
Simple AC
Series
Circuit,
Simple AC
Parallel
Circuit,
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Fundamentals Of Electricity
Three Phase
(AC)
Transformer
Configurations
Note:
a = Turns Ratio
= Np/Ns
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Fundamentals Of Electricity
Impedance :
z
Definition : Impedance is the current
resisting and impeding characteristic of
load or conductor in an AC Circuit.
z
Symbol for Impedance: Z
Z = R + jXl - jXc
Where, jXl = Zl and, -jXc = Zc
z
Unit for Impedance: Ohms or Ωs.
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Fundamentals Of Electricity
Ohms Law:
z
Mathematical Statement of the Ohm’s
Law:
V = I R for DC circuits
V = I Z for AC Circuits
Note: BOLD letters, in general, represent
Vectoral quantities
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Impedance
Calculation:
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Fundamentals Of Electricity
Power :
z
Definition: Power is defined as the capacity of a system
to perform work or Rate of work performed by a system.
z
Symbols and Types of Power:
z
Pdc= V.I , in watts. Note: Pdc= Preal
Papparent = S = Apparent Power (kVA) or Total AC
Power
Preal = P = Real Power Comp. of Apparent Power, in kW
Preactive = Q = Reactive Comp. of App. Power in kVAR
z ⏐ Pappent⏐ = (Preal)2 + (Preactive)2 or⏐S⏐ = (P)2 +(Q)2
z Magnitude of Total (3 ∅ ) Power = ⏐S⏐= √3. VL.IL
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Fundamentals Of Electricity
Power Factor :
z
Definition: Power Factor is defined as the Ratio
of Real Power (kW) to Apparent Power (kVA). It
is also defined as the quantity cos(θ - φ).
PF = ⏐P⏐/⏐S⏐ or
PF = cos(θ - φ),
where θ is the angle of voltage V, where V =
VRMS ∠ θ
z φ is the angle of current i = I RMS ∠ φ
Note: Detailed discussion on the topic of Power
Factor is covered under the Power Factor
segment of this seminar.
z
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Fundamentals Of Electricity
Voltage Regulation:
Definition: Real voltage sources are unable
to hold the voltage constant as they assume
a significant amount of load (Resistance or
Impedance). This results in the difference
between Vno load and Vfull load.
The formula for Voltage Regulation is as
follows:
Voltage Reg. = (Vno load - Vfull load)/ Vfull load x 100%
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Fundamentals Of Electricity
Service Factor of a Motor:
Definition: Service factor of a motor is the
ratio of safe to standard (nameplate) loads.
Service factor is expressed in decimal. The
formula for Service Factor is as follows:
Service Factor = Safe Load / Nameplate Load
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Fundamentals Of Electricity
Classifications of Motors:
¾
Motor categorization by NEMA, National
Electrical Manufacturers Association:
¾ Speed:
¾
¾
¾
¾
Constant Speed
Adjustable Speed
Multispeed
Varying Speed
¾ Service Classification:
¾
¾
¾
¾
General
Definite
Special Purpose
Varying Speed
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Fundamentals Of Electricity
Classifications of Motors, contd.:
¾Motor Class is determined by the maximum
allowable operating temperature of the motor,
which is dependant on the type/grade of
insulation used in the motor.
Class A: 105° C
¾ Class B: 130° C
¾ Class F: 155° C
¾ Class H: 180° C
¾
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Fundamentals Of Electricity
Kirchhoff’s Voltage Law (KVL):
Algebraic sum of voltage drops around
any closed path, within a circuit, is
equal to the sum of voltages presented
by all of the voltage sources. The
mathematical representation of KVL
is as follows:
Σ VDrops = Σ VSource
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Fundamentals Of Electricity
Kirchhoff’s Current Law (KCL):
Total current flowing into a node is
equal to the total current that flows
out of the node. The mathematical
representation of KCL is as follows:
Σ iin = Σ iout
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Fundamentals Of Electricity
Motor Speed Calculation:
z
Given:
Number of Poles = P = 4
Frequency of AC Power Supply to the Motor, in Hertz = f = 60
Hz
Speed, in RPM = S = ?
– Formula: S x P = 120 x f
• S = (120 x f ) / P
• S = (120 x 60) / 4 = 1800 RPM
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Fundamentals Of Electricity
Motor Slip:
Slip is usually expressed in percent and can be computed as follows:
Percent slip = (Synchronous speed - Actual speed ) x 100
Synchronous Speed
z Induction motors are made with slip ranging from less than 5% up to
20%.
z A motor with a slip of 5% or less is known as a normal-slip motor. A
normal-slip motor is sometimes referred to as a 'constant speed'
motor because the speed changes very little from no-load to full-load
conditions. A common four-pole motor with a synchronous speed of
1,800 rpm may have a no-load speed of 1,795 rpm and a full-load
speed of 1,750 rpm. The rate-of-change of slip is approximately linear
from 10% to 110% load, when all other factors such as temperature
and voltage are held constant. Motors with slip over 5% are used for
hard to start applications.
The direction of rotation of a polyphase ac induction motor depends on
the connection of the stator leads to the power lines. Interchanging
any two input leads reverses rotation.
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Fundamentals Of Electricity
Motor Torque, Power and Horsepower:
z
Torque is equivalent to the amount of work performed.
Torque can be considered as turning effort. For example,
suppose a wheel with a crank arm one-foot long takes a
force of one pound to turn at steady rate. The torque
required would be one pound times one foot or one footpound.
z
Horsepower, i .e. Power, is defined as the rate at which
work is performed or rate at which torque is produced.
z
In the wheel cranking example above, if one were to crank
the wheel twice as fast, the torque remains the same but
the power and horsepower delivered would double,
regardless of how fast the crank is turned, as long as the
crank is turned at a steady speed.
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Fundamentals Of Electricity
Motor Torque and Horsepower,
contd.:
z
Power, Horsepower and Torque Relationship:
Torque(ft-lbf) = 5250 x P (horsepower)
Speed (rpm)
Torque(N-m) = 9549 x P (kW)
Speed (rpm)
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Fundamentals Of Electricity in Industrial and Commercial Environment
Motor Power – Line Current Calculation:
z
Motor Nameplate Information:
Power rating, in HP (Horse Power) = P = 10 HP
Voltage Rating = 480 VAC
No. of Phases = 3; also stated as 3 ∅
Power Factor = PF = 0.8
Efficiency = Eff. = 0.9
Magnitude of Line Current = FLA, Full Load Current = ⏐ I ⏐ = I = ?
Note: 1 HP = 746 Watts = 746 W = 0.746 kW
Formula:
I = Power in Watts / PF / Eff./ (√3 x VL)
• I = 10HP x 746 W/HP/0.8/0.9/(√3 x480VAC)
• I = 12.46 Amps
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Fundamentals Of Electricity
Miscellaneous:
z Demand: This term means the highest average
power (kW) in a given interval, or demand
interval. Electric utilities charge commercial and
industrial customers for the peak demand set
each month.
z Peak demand: This is the maximum demand
used in any demand interval for a given month.
z Load factor: The load factor is the ratio of
average power to peak demand. Utility
customers are sometimes penalized for low load
factor that can occur when large amounts of
power are used in short periods of time, instead
of at a steady rate for long periods of time.
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Electronics
Semiconductor
Diode:
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Electronics
Outputs From Simple
Diode Circuits:
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Electronics
Outputs From Simple Diode Circuits:
Special Types of Diodes:
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Electronics
Bipolar Junction
Transistors:
Bipolar Junction Transistor
Operating Regions
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Standards
z
NEMA: National Electrical Manufacturers
Association; www.nema.org
– NEMA, created in the fall of 1926 by the merger of the Electric Power
Club and the Associated Manufacturers of Electrical Supplies, provides
a forum for the standardization of electrical equipment, enabling
consumers to select from a range of safe, effective, and compatible
electrical products.
z
ANSI: American National Standards Institute;
www.ansi.org
– The American National Standards Institute (ANSI) is a private,
non-profit organization that administers and coordinates the U.S.
voluntary standardization and conformity assessment system
z
IEC: International Electrotechnical Commission.
– IEC is the authoritative worldwide body responsible for
developing consensus global standards in the electrotechnical
field
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Standards
z
IEEE: Institute of Electrical and Electronic
Engineers; www.ieee.org
– The IEEE is a non-profit, technical professional association
for Electrical and Electronics Engineers.
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Power Distribution Systems
Power Distribution Systems Consist of:
z
z
z
z
z
z
z
z
z
z
MCC or Motor Control Centers
Loop Switches
Transformers
Voltage Regulators
Capacitor Banks
Circuit Breakers
– OCB’s, Oil Circuit Breakers
– Air Circuit Breakers
Disconnect Switches
Fuses
Starters and Combination Starters
Power Monitoring and Control Systems
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Power Factor Correction
Bobby Rauf ©
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Topics
z Power
Factor, Definition, Concept
and Formulas
z Power Factor Correction /
Improvement Example
z Additional Comments /
Discussion on Power Factor
z Power Factor and Loss
Calculation Example
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Fundamentals Of Electricity
Power Factor, Definition, Concept and
Formula:
z
Definition: Power Factor is defined as the Ratio
of Real Power (kW) to Apparent Power (kVA). It
is also defined as the quantity cos(θ - φ).
PF = ⏐P⏐/⏐S⏐ or
PF = cos(θ - φ),
z
z
z
where θ is the angle of voltage V, where V =
VRMS ∠ θ
φ is the angle of current i = I RMS ∠ φ
% PF = (PF) x 100
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Fundamentals Of Electricity
Power Factor, contd.:Zc= Xc ∠ -90=-j Xc
z
I
V
θ-φ
Leading Power Factor:
¾ Power factor is said to be leading when, φ
the angle of the current, exceeds θ, the angle
of the voltage.
¾In other words, (θ - φ) is negative.
¾Impedance, Zc, due to pure capacitance
reactance, Xc, has a negative angle. Or, Zc =
Xc ∠ -90
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Fundamentals Of Electricity
Power Factor, contd.:
z
V
Zl = Xl ∠ +90=+j Xl
I
Pf Angle
=θ-φ
Lagging Power Factor:
¾ Power factor is said to be lagging when, φ the angle
of the current, is less than θ, the angle of the voltage.
¾ In other words, (θ - φ) is positive.
¾ Impedance, Zl, due to pure inductive reactance, Xl,
has a positive angle. Or, Zl = Xl ∠ 90
z
In Inductive Circuits, add Capacitance, or
Capacitive Reactance, Xc, to offset the Inductive
Reactance, Xl, and to Increase the PF. V
90 Deg.
I
V
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Fundamentals Of Electricity
Power Factor, contd :
C =
( Q1 - Q2 )
2 π f V2
Where,
C = Capacitance (F) required to reduce the
Reactive or Imaginary Power from Q1 to Q2
Q1 = Initial, higher Reactive Power, in VARs
Q2 = Improved, lower Reactive Power, in VARs
V = Voltage, in Volts
f = Frequency, in Hz
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