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3.1 What is magnetic material and give difference between magnetic and
non magnetic material.
- The magnetic material are define as material in which a state of magnetism can be induced. Magnetic materials, when magnetized create a magnetic field. Magnetic material Nonmagnetic material
- Magnetic materials are materials having a magnetic domain and are attracted to an external magnetic field.
- Non-magnetic materials are materials that are not attracted to an external magnetic field.
- The magnetic domains of magnetic materials are aligned either parallel or anti parallel arrangements thus they can respond to a magnetic field when they are under the influence of an external magnetic field.
- The magnetic domains of non-magnetic materials are arranged in a random manner in such a way that the magnetic moments of these domains are cancelled out. Thus, they do not respond to a magnetic field.
- Magnetic materials are used to make permanent magnets are the parts of operating systems where magnetic properties are required.
- Magnetic materials are used to make permanent magnets are the parts of operating systems where magnetic properties are required.
3.2 Explain the different types of magnetic material
- Classification of magnetic material as below: ✓ Paramagnetic material ✓ Diamagnetic material ✓ Ferromagnetic material
Paramagnetic Diamagnetic Ferromagnetic Figure 2. 1 Types of magnetic materials
(1) Paramagnetic material
- If a bar of paramagnetic material is suspended in between the pole pieces of an electromagnet, it sets itself parallel to the lines of force.
- When a bar of paramagnetic material is placed in a magnetic filed the lines of force tend to accumulate in it.
- If a paramagnetic liquid is placed in a watch glass resting on the pole pieces of an electromagnet then it accumulates in the middle.
- It is because in the central region the field is the strongest. If the pole pieces are not close together the field is strongest near the poles and the liquid moves away from the
- center giving an almost opposite effect.
- If one end of a narrow u-tube containing a paramagnetic liquid is placed within the pole pieces of an electromagnet in such a manner that the level of the liquid is in the lie with the field, then on applying the field the level of the liquid rises.
- The rises in proportional to the susceptibility of the liquid.
- When a paramagnetic gas is allowed to ascend between the poles pieces of an electromagnet it spreads along the direction of the field.
- Example of paramagnetic material aluminum, manganese platinum, crown glass solution of salts of iron and oxygen (2) Diamagnetic material
- When a diamagnetic substance is placed in a magnetic field it sets itself at right angles to the direction of the lines of force.
- When a diamagnetic material is placed within a magnetic field the lines of force tend to go away from the material.
- When a diamagnetic substance is placed in a watch glass on the pole pieces of a magnet the liquid accumulates on the sides causing a depression at the center which is the strongest part of the field.
- When the distance between the pole pieces is larger, the effect is reversed.
- A diamagnetic liquid in a u-tube placed in a magnetic field shows as depression. When a diamagnetic gas is allowed to ascend between, the poles piece of an electromagnet it spreads across the field.
- Example of diamagnetic material bismuth, phosphorus ,antimony, copper, water, alcohol, ,hydrogen (3) Ferromagnetic material
- Ferromagnetic substance shows the properties of the paramagnetic substance to a much greater degree.
- The susceptibility has a positive value and the permeability is also very large.
- The intensity of magnetization I is proportional to the magnetizing field H for small value.
- Example of Ferromagnetic material Iron nickel, cobalt and their alloys
- Comparison of difference types of magnetic material
Properties Paramagnetic Materials Diamagnetic Material Ferromagnetic Materials State They can be solid, liquid or gas.
They can be solid, liquid or gas.
They are solid.
Effect of Magnet Weakly attracted by a magnet.
Weakly repelled by a magnet.
Strongly attracted by a magnet. Behavior under non-uniform field
Tend to move from low to high field region.
Tend to move from high to low region.
Tend to move from low to high field region. Behavior under external field
They do not preserve the magnetic properties once the external field
They do not preserve the magnetic properties once the external field
They preserve the magnetic properties after the external field is removed.
Figure 2.3 Circuit diagram form Magnetic hysteresis
Figure 2.4 magnetic hysteresis loop
- When current is increased from zero value to a certain value, magnetizing force and flux density both are set up and increased following the path o to a.
- For a certain value of current, flux density becomes maximum (Bm). The point indicates the magnetic saturation or maximum flux density of this core material. All element of core material get aligned perfectly.
- When the value of current is decreased from its value of magnetic flux saturation, H is decreased along with decrement of B not following the previous path rather following the curve a to b.
- The point b indicates H = 0 for I = 0 with a certain value of B. This lagging of B behind H is called hysteresis.
- The point b explains that after removing of magnetizing force (H), magnetism property with little value remains in this magnetic material and it is known as residual magnetism (Br) or residual flux density.
- If the direction of the current I is reversed, the direction of H also gets reversed. The increment of H in reverses direction following path b – c decreases the value of residual magnetism that gets zero at point c with certain negative value of H. This negative value of H is called coercive force (Hc)
Magnetic core
V
Magnetic Flux
I
-H H
+Bm
B
o
a
b
c
d
e
f Hc
Br
Br - Residual magnetism Hc - Coercivity
-Bm -B
-Hm +Hm
- Now B gets reverses following path c to d. At point‘d’, again magnetic saturation takes place but in opposite direction with respect to previous case. At point‘d’, B and H get maximum values in reverse direction.
- If decrease the value of H in this direction, again B decreases following the path d. At point e, H gets zero valued but B is with finite value.
- The point e stands for residual magnetism (-Br) of the magnetic core material in opposite direction with respect to previous case.
- If the direction of H again reversed by reversing the current I, then residual magnetism or residual flux density (-Br) again decreases and gets zero at point ‘f’ following the path e to f.
- Again further increment of H, the value of B increases from zero to its maximum value or saturation level at point a following path f to a.
- Hard and soft material hysteresis loop are given below.
H
B Soft
Hard
Figure 2.5 Types of hysteresis loop
3.4 What is requirement of transformer?
- A transformer is defined as a static device converts the electric power from one electrical circuit to another electrical circuit without change of frequency. It can also up and down the voltage level.
- In our country usually electrical power is generated at 11kV. For economical reason a.c. power is transmitted at very high voltage (220kV or 400 kV) over long distance, therefore, a step up transformer is applied at the generating station.
- To feed different area, voltage is step down to different levels by transformer at various substations.
- Ultimately for utilization of electrical power, the voltage is step down to 400/230 V for safety reasons.
- By effectively laminating the core, the eddy-current losses can be reduced. The lamination can be done with the help of a light coat of core plate varnish or lay an oxide layer on the surface. The thickness of the lamination varies from 0.35mm to 0.5mm.
- The types of transformers differ in the manner in which the primary and secondary coils are provided around the laminated steel core. According to the design, transformers can be classified into two: (1) Core type of transformer (2) Shell type of transformer
Breather
Core
Terminal
Bushings Oil conservator
Figure 2.8 Transformer inside view
(1) Core type of transformer
- In core-type transformer, the windings are given to a considerable part of the core. The coils used for this transformer are form-wound and are of cylindrical type.
- Such type of transformer can be applicable for small sized and large sized transformers.
- In the small sized type, the core will be rectangular in shape and the coils used are cylindrical.
- Round or cylindrical coils are wound in such a way as to fit over a cruciform core section is shown in figure.
- In case of circular cylindrical coils, they have a fair advantage of having good mechanical strength. The cylindrical coils will have different layers and each layer will be insulated from the other with the help of materials like paper, cloth, mica board and so on.
- The general arrangement of the core-type transformer with respect to the core is shown in figure. Both low-voltage (LV) and high voltage (HV) windings are shown. The low voltage windings are placed nearer to the core as it is the easiest to insulate.
- The effective core area of the transformer can be reduced with the use of laminations and insulation. (2) Shell type of transformer:
- In shell-type transformers, the core surrounds a considerable portion of the windings. The comparison is shown in the figure below.
- The coils are form-wound but are multi-layer disc type usually wound in the form of pancakes. Paper is used to insulate the different layers of the multi-layer discs.
- The whole winding consists of discs stacked with insulation spaces between the coils. These insulation spaces form the horizontal cooling and insulating ducts. Such a transformer may have the shape of a simple rectangle or may also have a distributed form.
- A strong rigid mechanical bracing must be given to the cores and coils of the transformers. This will help in minimizing the movement of the device and also prevents the device from getting any insulation damage.
- A transformer with good bracing will not produce any humming noise during its working and will also reduce vibration.
- Working
Transformer
Primary winding
Secondary V 1 V^2 winding
N 1 N 2
I 1 I 2
Figure 2. 9 Working of Transformer
- The main principle of operation of a transformer is mutual inductance between two circuits which is linked by a common magnetic flux.
- A basic transformer consists of two coils that are electrically separate and inductive, but are magnetically linked through a path of reluctance.
- The transformer has two windings, (1) Primary and (2) Secondary winding. Primary winding is connected with input supply side and the secondary winding is connected with output load side.
- The core laminations are joined in the form of strips in between the strips you can see that there are some narrow gaps right through the cross-section of the core. These joints are said to be ‘laminated’.
- Both the coils have high mutual inductance. A mutual electro-motive force is induced in the transformer from the alternating flux that is set up in the laminated core, due to the coil that is connected to a source of alternating voltage.
- Most of the alternating flux developed by this coil is linked with the other coil and thus produces the mutual induced electro-motive force. So the produced electro-motive force can be explained with the help of Faraday’s laws of Electromagnetic Induction as,
e = − N d dt
3.7 Explain construction and working of three phase transformer
Construction
- Three-phase transformer is effectively three interconnected single phase transformers on a single laminated core and considerable savings in cost, size and weight can be achieved by combining the three windings onto a single magnetic circuit as shown.
Primary and secondary winding
Magnetic line and flux
3 Phase,3-leg Core
Core type construction Shell type construction
Coil A
Coil B
Coil B
Coil A
Coil C
Coil C
Coil A
Coil A
Coil B
Coil B
Coil C
Coil C
3 Phase,5-leg Core
Figure 2. 11 Type of construction of 3 - phase transformer
- A three-phase transformer generally has the three magnetic circuits that are interlaced to give a uniform distribution of the dielectric flux between the high and low voltage windings.
- The exception to this rule is a three-phase shell type transformer. In the shell type of construction, even though the three cores are together, they are non-interlaced.
- The three-limb core-type three-phase transformer is the most common method of three-phase transformer construction allowing the phases to be magnetically linked.
- Flux of each limb uses the other two limbs for its return path with the three magnetic flux’s in the core generated by the line voltages differing in time-phase by 120 degrees.
- Thus the flux in the core remains nearly sinusoidal, producing a sinusoidal secondary supply voltage.
1(max) 1
1(max) 1
1(max) 1 1(max) 1 1 1 1
2 2
m
m
m m
m
E N
But f E fN RMS value is given by E E Putting the value of E in above equation we get E fN E fN Similarly we get E fN
- The shell-type five-limb type three-phase transformer construction is heavier and more expensive to build than the core-type. Five-limb cores are generally used for very large power transformers as they can be made with reduced height.
- Shell-type transformers core materials, electrical windings, steel enclosure and cooling are much the same as for the larger single-phase types. Working
- Consider the below figure in which the primary of the transformer is connected in star fashion on the cores. For simplicity, only primary winding is shown in the figure which is connected across the three phase AC supply.
- The three cores are arranged at an angle of 120 degrees to each other. The empty leg of each core is combined in such that they form center leg as shown in figure.
- When the primary is excited with the three phase supply source, the currents IR, IY and IB are starts flowing through individual phase windings. These currents produce the magnetic fluxes ΦR, ΦY and ΦB in the respective cores.
- Since the center leg is common for all the cores, the sum of all three fluxes are carried by it. In three phase system, at any instant the vector sum of all the currents is zero.
- In turn, at the instant the sum of all the fluxes is same. Hence, the center leg doesn’t carry any flux at any instant.
Three phase supply
R Y B
IR IY IB
R Y
B
Figure 2. 12 3 - phase transformer
- So even if the center leg is removed it makes no difference in other conditions of the transformer.
- Likewise, in three phase system where any two conductors acts as return for the current in third conductor.
- Two legs act as a return path of the flux for the third leg if the center leg is removed in case of three phase transformer.
- Therefore, while designing the three phase transformer, this principle is used.
- These fluxes induce the secondary EMFs in respective phase such that they maintain their phase angle between them.
- The common terminal is indicated by suffix 1 in the figure below. If terminal with suffix 1 in both primary and secondary are used as common terminal, voltages of primary and secondary are in same phase.
- That is why this connection is called zero degree connection or 0o^ - connection. If the terminals with suffix 1 are connected together in HV side as common point and the terminals with suffix 2 in LV side are connected together as common point,
- The voltages in primary and secondary will be in opposite phase. Hence, star-star transformer connection is called 180o-connection, of three phase transformer. (2) Delta-Delta Transformer
- In delta-delta transformer, 1 suffixed terminals of each phase primary winding will be connected with 2 suffixed terminal of next phase primary winding.
- If primary is HV side, then A 1 will be connected to B 2 , B 1 will be connected to C 2 and C 1 will be connected to A 2. Similarly in LV side 1 suffixed terminals of each phase winding will be connected with 2 suffixed terminals of next phase winding.
- That means, a 1 will be connected to b 2 , b 1 will be connected to c 2 and c 1 will be connected to a 2.
- If transformer leads are taken out from primary and secondary 2 suffixed terminals of the winding, then there will be no phase difference between similar line voltages in primary and secondary.
- This delta delta transformer connection is zero degree connection or 0o-connection.
- But in LV side of transformer, if, a 2 is connected to b 1 , b 2 is connected to c 1 and c 2 is connected to a 1.
- The secondary leads of transformer are taken out from 2 suffixed terminals of LV windings, and then similar line voltages in primary and secondary will be in phase opposition. This connection is called 180o-connection, of three phase transformer. (3) Star-Delta Transformer
- Here in star-delta transformer, star connection in HV side is formed by connecting all the 1 suffixed terminals together as common point and transformer primary leads are taken out from 2 suffixed terminals of primary windings.
- The delta connection in LV side is formed by connecting 1 suffixed terminals of each phase LV winding with 2 suffixed terminal of next phase LV winding. More clearly, a 1 is connected to b 2 , b 1 is connected to c 2 and c 1 is connected to a 2.
- The secondary (here it considered as LV) leads are taken out from 2 suffixed ends of the secondary windings of transformer. The transformer connection diagram is shown in the figure beside.
- It is seen from the figure that the sum of the voltages in delta side is zero. This is a must as otherwise closed delta would mean a short circuit.
- It is also observed from the phasor diagram that, phase to neutral voltage (equivalent star basis) on the delta side lags by − 30o^ to the phase to neutral voltage on the star side; this is also the phase relationship between the respective line to line voltages.
- This star delta transformer connection is therefore known as − 30o-connection. Star- delta + 30o-connection is also possible by connecting secondary terminals in following sequence. a 2 is connected to b 1 , b 2 is connected to c 1 and c 2 is connected to a 1.
- The secondary leads of transformer are taken out from 2 suffixed terminals of LV windings,
A B C
A 2 A 1 B 2 B 1 C 2 C 1
Star -Delta Three phase Transformer
a b c
a 2 a 1 b 2 b 1 c 2 c 1
A B C
A 2 A 1 B 2 B 1 C 2 C 1
Delta-Star Three phase Transformer
a b c
a 2 a 1 b 2 b 1 c 2 c 1
Figure 2. 14 3 - phase transformer connections
(4) Delta-Star Transformer
- Delta-star transformer circuit diagram shown in above figure.
- Delta-star transformer connection of three phase transformer is similar to star – delta connection. If anyone interchanges HV side and LV side of star-delta transformer in diagram, it simply becomes delta – star connected 3 phase transformer.
- That means all small letters of star-delta connection should be replaced by capital letters and all small letters by capital in delta-star transformer connection
3.10 Voltage and current ratios of transformer
- Voltage and current relation of primary winding and secondary winding is given as below.
1 1 2 2
1 1 2 2 2 2 1 1
1 1 2 2 1 1 2 2 2 2 1 1 1 2
Taking ratio of eq(1) and eq(2) At no Load
At Load
Pr
m m
E fN E fN
E N (^) or E N E N E N
V E and V E V N (^) or V N V N V N V imary voltage V Secondary voltag
e
1 1 1 2 2 2 1 2 1 1 2 2 1 2 2 1 2 2 1 1 1 2 2 1 1 2
If η of transformer 100% Input power = Output power cos cos , cos cos
cos cos
V I V I
practically V I V I I V I V But V^ N K V N I N I N Power factor of primary side Power factor of S
econdary side
- Now if an alternating source voltage V 1 is applied in the primary winding of that ideal transformer, there will be a counter self emf E 1 induced in the primary winding which is purely 180 degree in phase opposition with supply voltage V 1.
- For developing counter emf E 1 across the primary winding, it draws current from the source to produce required magnetizing flux.
- As the primary winding is purely inductive, that current 90o^ lags from the supply voltage. This current is called magnetizing current of transformer Iμ.
- This alternating current Iμ produces an alternating magnetizing flux Φ which is proportional to that current and hence in phase with it.
- As this flux is also linked with secondary winding through the core of transformer, there will be another emf E 2 induced in the secondary winding, this is mutually induced emf.
- As the secondary is placed on the same core where the primary winding is placed, the emf induced in the secondary winding of transformer, E 2 is in the phase with primary emf E 1 and in phase opposition with source voltage V 1.
3.12 Explain Practical Transformer
- A practical transformer hasn’t 100% efficiency due to losses. Transformer ‘no load’ condition A transformer is on no load when its secondary winding is open circuited. So, the secondary current is zero. When AC supply is applied to primary winding, a small amount of current Io flows in the primary winding. The current Io is called the no load current of the transformer. It is made up with two components Iμ and Iw. The component Iμ is called the magnetizing component and it magnetizes the core and it is in phase with ϕm. It is also called reactive component or wattles component of no- load current. Another component is Iw, it is called active component or working component or wattful component and it is in phase with supply voltage.
V 1 Open circuitI 2 = Primary winding
Secondary winding
I 0 Transformer
Figure 2. 16 Practical transformers on no load and vector diagram
Iw Io
I
V 1
E 1
E 2
The no-load current is small of the order of 3 to 5% of the rated current of primary winding. Consider the transformer under no-load and take ϕm as a reference phasor. At no-load we have,
Since E 1 and E 2 are induced emf by the same flux ϕ and they will be in phase with each other.E 2 differs from the magnitude of E 1 , because E 2 = E 1. E 2 and E 1 are lag behind ϕ by
If the voltage drop in the primary winding are neglected E 1 will be equal and opposite to the applied voltage V 1. Iμ is in phase with ϕ and Iw is in phase with V 1 .The phasor sum of Iμ and Iw is I 0. Φ 0 is called the no-load power factor angle, so that the power factor on no load is cosΦ 0.
Also, core loss Watt. Magnetizing volt-amperes VAr Transformer on load
When an electrical load is connected to the secondary winding of a transformer, a current flows in the secondary winding.
This secondary current is due to the induced secondary voltage that is set up by the magnetic flux created in the core from the primary current. The secondary current, I 2 which is determined by the characteristics of the load this secondary current creates a self-induced secondary magnetic field Φ 2 in the transformer core which flows in the exact opposite direction to the main primary field, Φ 1. These two magnetic fields oppose each other resulting in a combined magnetic field of less magnetic strength than the single field produced by the primary winding alone when the secondary circuit was open circuited.
This combined magnetic field reduces the back EMF of the primary winding causing the primary current, I 1 to increase slightly. The Primary current continues to increase until the cores magnetic field is back at its original strength and for a transformer to operate correctly.
1 1
2 2
sin sin (^2)
sin 2
= = ^ −
= ^ −
m m
m
t e E t
e E t
0 0 0 0 0 2 2
0 0
cos sin
cos
w
w w
I I
I I
I I I
I
I
= V I 1 0 cos 0 = V I 1 w
= V 1 (^) sin 0 = V I 1
Transformer Ratio
Note that the current is inversely proportional to both the voltage and the number of turns.
This means that with a transformer loading on the secondary winding, in order to maintain a balanced power level across the transformers windings.
If the voltage is stepped up, the current must be stepped down and vice versa. In other words, “higher voltage — lower current” or “lower voltage — higher current”.
The total current drawn from the supply by the primary winding is the vector sum of the no-load current I 0 and the additional supply current I 1.
As a result of the secondary transformer loading and which lags behind the supply voltage by an angle of Φ. We can show this relationship as a phasor diagram. Transformer Equivalent Circuit
Actual real life, transformer windings have impedances of both XL and R. These impedances need to be taken into account when drawing the phasor diagrams as these internal impedances cause voltage drops to occur within the transformers windings.
The internal impedances are due to the resistance of the windings and an inductance called the leakage reactance resulting from the leakage flux. These internal impedances are given as:
V (^1) N 2
R 2 L 2
N (^1) Load
R 1 L 1
Primary Impedence Secondary Impedence
Figure 2. 19 equivalent circuit of transformer
So the primary and secondary windings of a transformer possess both resistance and reactance. Sometimes, it can be more convenient if all these impedances are on the same side of the transformer to make the calculations easier.
Pr 1 1 2 2 2 1 1 2 1 2 2 1
1 1 2 2 2 1
imary Secondary
But we know that voltage ratio turns rati
P P
V I V I
I V I
V
V I
V I
N V
o So n n I N V I
It is possible to move the primary impedances to the secondary side or the secondary impedances to the primary side. The combined values of R and L impedances are called “Referred Impedances” or “Referred Values”. The object here is to group together the impedances within the transformer and have just one value of R and XL in our calculations as shown.
3.13 Difference between Ideal transformer and actual transformer
The windings (both primary and secondary) of an ideal transformer are considered to have zero resistance, hence the transformer is lossless. There is no leakage flux in an ideal transformer. The permeability of the core material in ideal transformer is considered to be tending to infinity and hence the current needed to set up the flux in the transformer is negligible. There is zero hysteresis and eddy current losses in an ideal transformer.
3.14 Losses in Transformer
Figure 2. 20 Block diagram of types of losses As the electrical transformer is a static device, mechanical loss in transformer normally does not come into picture. We generally consider only electrical losses in transformer. Loss in any machine is broadly defined as difference between input power and output power. When input power is supplied to the primary of transformer, some portion of that power is used to compensate core losses in transformer i.e. Hysteresis loss in transformer and Eddy current loss in transformer core. some portion of the input power is lost as I^2 R loss and dissipated as heat in the primary and secondary windings, because these windings have some internal resistances in them. The first one is called core loss or iron loss in transformer and the later is known as ohmic loss or copper loss in transformer. Another loss occurs in transformer, known as Stray Loss, due to Stray fluxes link with the mechanical structure and winding conductors.
