Electrotechnics
N5
Module 1: DC machines
CONSTRUCTION
The general construction of a four-pole dc generator or motor is shown
below:
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Module 1: DC machines (continued)
GENERATOR AND MOTOR PRINCIPLES
There is no real difference between an electric generator and an electric
motor. Consider a conductor lying in a magnetic field as shown in the figure.
If the conductor is moved downwards, the emf is in such a
direction that the current produced, sets up an upward
force. In maintaining the motion against this force, work is
done. Mechanical energy is converted into electrical energy
and the apparatus is essentially an electric generator.
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Module 1: DC machines (continued)
THE COMMUTATOR
A commutator is a cylinder at one end of the armature
formed by a large number of copper segments. The
segments are insulated from each other and from the
shaft by thin mica or micanite sheets and clamped
together by insulated end rings. A sectioned view is
illustrated.
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Module 1: DC machines (continued)
ARMATURE WINDINGS
Armature windings are distributed in slots over the circumference of the
armature core. Armature windings can be divided into two groups depending
on the manner in which the windings are connected to the commutator. The
two groups are lap windings and wave windings.
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Module 1: DC machines (continued)
FIELD COILS
Direct current (dc) machines are named according to the method used to
connect the field coils. A separately-excited machine is one in which the dc
supply to the field coils is completely separate from the connections to the
armature.
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Module 1: DC machines (continued)
ARMATURE REACTION
Armature reaction is the distortion of the main flux entering and leaving the
armature, caused by the flux set up by armature conductors when they carry
current.
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Module 1: DC machines (continued)
CALCULATION OF DEMAGNITISING AND CROSS AMPERE-TURNS
For every 360 electrical degrees there are 4𝜃 electrical degrees containing
conductors that are responsible for the demagnetising of ampere-turns.
∴ Demagnetising ampere-turns per pole = (𝑡𝑜𝑡𝑎𝑙 𝑎𝑚𝑝𝑒𝑟𝑒 − 𝑡𝑢𝑟𝑛𝑠/𝑝𝑜𝑙𝑒) ×
1
=
2
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1
𝑐
× ×
𝑍
2𝑝
×
4𝜃
360
4𝜃
360
Module 1: DC machines (continued)
ARMATURE REACTION IN A DC MOTOR
The direction of the armature current in a dc motor is opposite to that of the
generated emf. It follows that in a dc motor, the flux is distorted backwards,
and the brushes have to be shifted backwards if they are to be on the
magnetic neutral axis when the machine is loaded.
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Module 1: DC machines (continued)
COMPENSATING WINDING
Ampere-turns per pole for compensating winding =
1 𝐼 𝑍
𝑎𝑟𝑐
× ×
× 𝑝𝑜𝑙𝑒
2 𝑐 2𝑝
𝑝𝑜𝑙𝑒 𝑝𝑖𝑡𝑐ℎ
𝑎𝑚𝑝𝑒𝑟𝑒
≈ 0,7 × 𝑎𝑟𝑚𝑎𝑡𝑢𝑟𝑒
𝑡𝑢𝑟𝑛𝑠/𝑝𝑜𝑙𝑒
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Module 1: DC machines (continued)
COMMUTATION
Commutation is the reversal of the emf and current in the short-circuited coil
during its transfer from one commutator segment to the next. Up to the
instant of short-circuit, the coil has been carrying full-circuit current in one
direction. The moment it leaves short-circuit, it must carry full-circuit current
in the opposite direction. If the current has just reached its fully reversed
value at the end of the short-circuit period, commutation is ideal.
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Module 1: DC machines (continued)
TORQUE OF AN ELECTRIC MOTOR
In a practical motor, the commutator and brushes ensure that the current
through the armature conductor windings are always in such a direction,
relative to the field set up by the field coils, that continuous, unidirectional
forces are exerted on the armature conductors. The resulting unidirectional
forces cause the armature to rotate. The magnitude of the resulting rotational
force is referred to as the torque of the motor.
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Module 1: DC machines (continued)
STARTING TORQUE AND ACCELERATION
The value of the starting torque required, will depend largely on its duty. At
the instant of starting there is no back emf as the rotor is at standstill and
only the armature circuit resistance is there to limit the armature current. The
current drawn at the instant of starting would be excessive. In order to limit
the starting current, a reduced voltage must be supplied to the armature.
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Module 1: DC machines (continued)
GRADING OF STARTING RESISTORS
A common method of grading the resistance is based on a current-time
diagram as in the figure below. Notching up is presumed to take place
always when the current has fallen to a certain minimum value 12 , and the
maximum current on each notch is taken to be 11 .
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Module 1: DC machines (continued)
SPEED CHARACTERISTICS OF ELECTRIC MOTORS
The speed characteristic of a motor represents the variation of speed with
current. Its shape can be derived from:
𝑉 − 𝐼𝑎 𝑅𝑎
𝑁=
𝑘∅
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Module 1: DC machines (continued)
TORQUE CHARACTERISTICS OF ELECTRIC MOTORS
The torque of a shunt motor is α armature current:
Curves A, B and C in the figure show the relative shapes of
torque curves for shunt series and compound motors which
have the same full-load torque OQ with the same full-load
armature current OP, the exact shape of curve C depending on
the relative value of the shunt and series ampere-turns at full
load.
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Module 1: DC machines (continued)
SPEED CONTROL
The speed of series motors may be controlled by varying the exciting current,
but in this, the regulating resistance must be connected in parallel with the
field winding. By these means, a varying amount of the total current can be
diverted and the field winding can carry any desired fraction of the main
current.
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Module 2: AC circuit theory
ALTERNATING CURRENT
In the case of alternating current the current reverses its direction at a
constant rate. This occurs as a result of the constant reversal of polarity at
the output terminals of the power supply.
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Module 2: AC circuit theory (continued)
GENERATION OF A SINGLE-PHASE ALTERNATING EMF
The emf can be represented by a sine wave, which represents a two pole
generator with the armature rotating in an anticlockwise direction through a
uniform magnetic field.
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Module 2: AC circuit theory (continued)
AVERAGE AND EFFECTIVE OR RMS VALUE OF AN ALTERNATING
QUANTITY
The effective value of an alternating current is that value of alternating
current, which produces the same amount of heat energy, at the same rate,
as a direct current would, if passed through an identical resistance.
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Module 2: AC circuit theory (continued)
NON-SINUSOIDAL WAVEFORM
To find the average and/or effective value of a non-sinusoidal waveform, use
is made of the midordinate rule.
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Module 2: AC circuit theory (continued)
RESISTANCE IN AC CIRCUITS
The current flowing through a pure resistor is governed by Ohm’s law for
every instant of time, i.e. 1 = e/R for every point on the cycle. This means
that the current waveform for a purely resistive circuit is exactly the same
shape as the waveform of the applied pd and is in phase with it.
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Module 2: AC circuit theory (continued)
INDUCTANCE IN AC CIRCUITS
A self-induced emf is produced in an inductor whenever the current through it
changes. When an alternating current flows through a pure inductor, the
value of the current is continually changing and so produces a self-induced
emf at every instant.
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Module 2: AC circuit theory (continued)
CAPACITANCE IN AC CIRCUITS
A capacitor is a device for storing electric charge. The charge on the plates is
always proportional to the pd between them, thus, as this pd varies, current
must flow either into or out of the capacitor in order to maintain the correct
charge. The greater the rate of change of the pd, the greater will be the rate
of change of current.
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Module 2: AC circuit theory (continued)
THE SERIES CIRCUIT
Consider a series circuit comprising a resistor R, an inductance L with an
inductive reactance of XL , and a capacitor C with a capacitive reactance XC ,
connected across a supply voltage, V. The resulting current I will be common
to all the components.
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Module 2: AC circuit theory (continued)
SERIES PARALLEL CIRCUITS
If circuits with impedances of Z1 , Z2 , etc, are connected in parallel:
1
1
1
=
+
𝑍 𝑍1 𝑍2
𝑍1 𝑍2
∴𝑍=
𝑍1 + 𝑍2
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Module 2: AC circuit theory (continued)
THREE-PHASE AC SYSTEMS
When compared to single-phase systems, three-phase distribution has the
following advantages:
• Two voltage are available, and
• For the same power rating, three-phase motors are smaller, cheaper, more
efficient, operate at a better power factor, and are self-starting.
• Only 87% of the amount of copper is required for the same output.
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Module 3: Transformers
PRINCIPLES OF OPERATION OF A TRANSFORMER
Transformers are used for raising or lowering the voltage in an ac circuit with
a corresponding decrease or increase in the current. Essentially, a
transformer is made up of a primary and secondary winding, electrically
separate from each other, but magnetically coupled by means of an iron
core.
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Module 3: Transformers (continued)
CONSTRUCTION
The construction of transformers is the simplest of all ac machines. The
principal elements of a transformer are;
• The magnetic circuit,
• The windings,
• the cooling system, and in larger transformers,
• The oil tanks, and
• Protection devices.
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Module 3: Transformers (continued)
TRANSFORMER ON OPEN-CIRCUIT
When connected to an ac supply with the secondary winding open-circuited,
it acts simply as a highly inductive coil, and the current drawn is just sufficient
to set up a flux which makes the emf of self inductance (neglecting the small
resistance drop) equal and opposite to the supply pd.
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Module 3: Transformers (continued)
USEFUL AND LEAKAGE FLUXES IN A TRANSFORMER
The effect of leakage flux can be considered as being equivalent to two
inductive reactances 𝑋1 and 𝑋2 in series with a transformer which has no
leakage flux.
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Module 3: Transformers (continued)
EQUIVALENT CIRCUIT OF A TRANSFORMER
The behaviour of a transformer may be considered by assuming it to be
equivalent to a transformer which has no losses and no magnetic leakage
and an iron core, thus requiring no magnetising current, and then allowing for
the imperfections of the transformer by means of additional impedances.
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Module 3: Transformers (continued)
THREE-PHASE, CORE-TYPE TRANSFORMERS
Modern large transformers are usually of the three-phase core-type shown
below. Three similar limbs are connected by top and bottom yokes, each limb
has the primary and secondary windings arranged concentrically.
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Module 3: Transformers (continued)
PARALLEL OPERATION
When operating two or more transformers in parallel, their satisfactory
performance requires that they have:
• The same voltage-ratio,
• The same per-unit impedance,
• The same polarity, and
• The same phase-sequence and zero relative phase-displacement.
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Module 4: Measuring instruments
CONSTRUCTION
Essentially, most measuring instruments comprise:
• A fixed field system,
• A controlling system,
• A damping system, and
• A pointer attached to a moving system and pivoted in jewelled bearings.
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Module 4: Measuring instruments (continued)
TYPES OF MEASURING INSTRUMENTS
Ammeters and voltmeters are the most common and well-known of all
measuring instruments. Power is measured by means of a wattmeter. A
frequency meter is used to measure the frequency of ac cycles per second
in an alternating current circuit. Power factor meters are used to measure
the power factor of an alternating current circuit.
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Module 4: Measuring instruments (continued)
MEASUREMENT OF POWER IN THREE-PHASE SYSTEMS
Measuring power in three-phase systems is similar to measuring power in
single-phase systems. Consider a star-connected, balanced load, with an
accessible, neutral connection. The total power can be measured with a
single wattmeter.
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Module 4: Measuring instruments (continued)
RANGE EXTENSION
Measuring instruments are mostly required to be connected to measure
currents or voltages of values higher than their construction is able to allow
them. In ac circuits, instrument transformers are invaluable in fulfilling this
function.
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Module 5: AC machines
INDUCTION MOTOR
In an induction motor, there are no electrical connections between the stator
and the rotor. The energy is transferred entirely magnetically, as in the case
of a transformer, by means of the emf induced in the rotor conductors, by the
rotating field set up by the stator windings. This principle of operation
enables the motor to be manufactured as a simple, robust and efficient
machine.
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Module 5: AC machines (continued)
EXPRESSION FOR THE EMF OF AN ALTERNATOR
Magnetic flux cutting a conductor in 1 revolution
= Ф × 2𝑝
Magnetic flux cutting a conductor in 1 second
= 2𝑝𝑛Ф × 𝑛
Average emf generated in 1 conductor
= 2𝑝𝑛Ф volts
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Module 5: AC machines (continued)
EFFECT OF DISTRIBUTING THE WINDING (DISTRIBUTOR FACTOR)
By distributing the winding in two or more slots per pole per phase, the
number of conductors per slot is reduced and the emf waveform is improved.
emf with a distributed winding
The ratio =
emf with a concentrated winding
is termed the distribution factor of the winding and may be represented by
the symbol 𝐾𝑑 .
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Module 5: AC machines (continued)
SHORT-PITCH WINDING: PITCH FACTOR
The waveform of the resultant emf generated in an alternator may be
improved by making the coil pitch less than a pole pitch. With a full-pitch coil,
the emf 's generated in the two sides are in phase with each other. When the
coil is short-pitched by an angle ‘a’ electrical degrees, as shown below, the
emf's generated in coil sides A and B differ in phase by an angle ‘a’.
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Module 5: AC machines (continued)
GENERAL EXPRESSION FOR THE EMF OF AN ALTERNATOR
If 𝐾𝑑 = distribution factor of the winding, and
𝐾𝑝 = pitch factor of the winding,
then rms value of emf/phase = 2,22 𝐾𝑑 𝐾𝑝 𝑍𝑓Ф.
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Module 5: AC machines (continued)
SYNCHRONISING OF ALTERNATORS
A represents an alternator connected to the bus-bars, and B is an alternator
to be connected in parallel. To enable this to be done, the following
conditions must be fulfilled:
• The frequency of B must be the same as that of A.
• The emf generated in B must be equal to the busbar voltage.
• The emf of B must be in phase with the busbar voltage.
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Module 5: AC machines (continued)
PARALLEL OPERATION OF ALTERNATORS
Consider two similar single-phase alternators, A and B, connected in parallel
to the busbars, and assume that there is no external load connected across
the bus-bars:
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Module 5: AC machines (continued)
THREE-PHASE MOTORS
The operation of an induction motor is dependent on a rotating magnetic field
which is established in the air gap of the motor by the stator currents. The
manner in which the rotating magnetic field is established by a three-phase
stator winding of a three-phase induction motor, may be illustrated by
considering the direction of current flow through the three phases, at several
successive instants.
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Module 5: AC machines (continued)
PRINCIPLE OF OPERATION OF A THREE-PHASE INDUCTION MOTOR
When the stator winding is energised from a three-phase supply, a rotating
magnetic field is established, which rotates at synchronous speed. As the
field sweeps across the rotor conductors, an emf is induced in them. Since
the rotor circuit is completed, either through end rings, or slip-rings and
external resistors, the induced emf causes a current to flow in the rotor
conductors. The rotor conductors carrying current in the stator field thus have
a force exerted upon them.
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Module 5: AC machines (continued)
SPEED CONTROL BY POLE-CHANGING
Two economical speeds can be obtained, one double the other, by arranging
the stator windings so that the number of poles can be changed at will in
some simple ratio, such as eight to four.
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Module 6: Generation and supply of AC power
TRANSMISSION AND SUPPLY
Power stations are often situated considerable distances from centres of
power consumption. One of the main reasons that makes it practical and
economically viable for power stations to be built far from consumers, is that
it is relatively cheap and easy to transport the final product, in this case,
electrical power.
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Module 6: Generation and supply of AC power (continued)
RESISTANCE OF OVERHEAD LINES
The resistance of a conductor is directly proportional to the length (ℓ) of the
conductor. Another factor which affects the resistance is the type of material
(ρ) from which the conductor is manufactured. It can be said:
𝜌
𝑅=
𝑎
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Module 6: Generation and supply of AC power (continued)
INDUCTANCE OF A SINGLE-PHASE OVERHEAD LINE
An alternating current results in inductance in any conductor. Since
transmission lines run for great distances, the inductance becomes
problematic.
L of conductor B only
= 0,05 + 0,2 log 𝑒 (𝑑/𝑟) 𝑚𝐻/𝑘𝑚
The total inductance of the line
= 0,1 + 0,4 log 𝑒 (𝑑/𝑟) 𝑚𝐻/𝑟𝑜𝑢𝑡𝑒 𝑘𝑚
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Module 6: Generation and supply of AC power (continued)
INDUCTANCE OF A THREE-PHASE, THREE-WIRE OVERHEAD LINE
The three conductors are said to be symmetrically spaced when their centres
lie on the corners of an equilateral triangle. Let each side of the triangle be d
metres long and the radius of each conductor, be r metres, then:
𝐿
𝑝ℎ
= 0,05 + 0,5log e (d/r)mH/km
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Module 6: Generation and supply of AC power (continued)
CAPACITANCE OF A SINGLE-PHASE OVERHEAD LINE
Capacitance is directly proportional to the area between two parallel
conductors and inversely proportional to the distance between them.
Because of the length of the conductors, the effective area is very large,
which counteracts the large distance between the conductors.
𝐶=
1
F/m,
36×109 ×log𝑒 [(𝑑−𝑟)/𝑟]
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line to line.
Module 6: Generation and supply of AC power (continued)
CAPACITANCE OF A SINGLE-PHASE, THREE-WIRE OVERHEAD LINE
The total charging current between any conductor and the neutral plane is
the phasor sum of two equal charging currents 120 degrees apart. The total
equivalent capacitance between any conductor and the neutral plane is
𝑑
𝐶𝑁 = 1/18. log 𝑒 [( )/𝑟]μF/km
𝑟
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