Set2 Transformer - Lecture notes 1,3-7,19 PDF

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TRANSFORMERS

Dr. Abdul Khaliq

Chapter Topics to be Covered 1. Introduction 2. Types and Construction of Transformers. 3. The Ideal Transformer 4. Theory of Operation of Real Single Phase Transformer 5. The Equivalent Circuit of a Transformer 6. The Per Unit System of Measurements 7. Transformer Voltage Regulation and Efficiency 8. Transformer Taps and Voltage Regulation 9. The Autotransformer 10. Three Phase Transformers

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2.1: Why Transformers are Important •

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The first power distribution system in U.S. was 120V dc system invented by Thomas A. Edison to supply power for incandescent light bulbs. Edison’s first central power station went into operation in New York city in 1882. The power was transmitted at very low voltage level, thus requiring a very large current to supply significant amount of power resulting in high power losses. To avoid this problem central power stations were located every few blocks of the city. The invention of transformer and concurrent development of ac power sources eliminated these restrictions forever.

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Introduction to Transformers •

A transformer is a device that changes ac electric power from one voltage level to another voltage level through the action of magnetic field. The transformer has two windings: i. Primary winding: The winding connected to the power source is called the primary winding. ii. Secondary winding: The winding connected to the load is called secondary winding.

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2.2: Types of Transformers w. r. t. Core Design Core Type Transformer

Shell Type Transformer

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2.2: Types of Transformers w.r.t. Core Design •

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With respect to the core of the transformer there are two types of the transformers: i. Core type transformer: Winding wrapped around two sides of the core. ii. Shell type transformer: This is three legged laminated core, with the winding wrapped around the center leg. Core is made up of laminations with the High voltage winding outside & Low voltage winding inside. Advantages: i. Easy to insulate H.V. winding from core ii. Less leakage than if they are at distance from each other.

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Transformer Types w.r.t. its Applications 1. 2. 3. 4. 5.

Unit transformer: To step up the voltage at generation. Substation transformer: To step down voltage from transmission to distribution level. Distribution transformer: Takes distribution voltage and steps it down to final voltage at which the power is used. Potential transformer: Is used to change the high voltage to low voltage, but can handle very small current. Current transformer: Is used to change the primary current to much smaller secondary current but the current is directly proportional to the primary current. Types 4 and 5 are used for instrumentation.

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Ideal Transformer Ideal transformer is a lossless device Np: no of turns on primary side Ns: no of turns on the secondary side Then Voltage eq. is:

Where a is the turn ratio, and the Current eq. is:

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Ideal Transformer Phasor

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Vp. & Vs have same phase angle Ip & Is have same phase angle Turn ratio just effects only the magnitude of voltage & current.

1. If Vp is +ve @ dotted end w.r.t un-dotted end then Vs will be also +ve @ dotted end. 2. If Ip flows into the dotted end of primary then Is it will flow out of dotted end of secondary.

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Power in Ideal Transformer  Primary side: Where θp is the angle between Vp and Ip  Secondary side: Where θs is angle between Vs and Is  Since voltage and current angles are unaffected for an ideal transformer Power factor on primary and secondary side is the same 10

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Power in Ideal Transformer For an Ideal Transformer Output power =Input power Likewise

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Impedance Transformation Through a Transformer •

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With a transformer it is possible to match the magnitude of the load impedance to a source simply by picking the proper turn ratio. To analyze the circuit replace the portion of circuit on one side of the transformer by an equivalent circuit with the same terminal characteristics. This process is known as referring the first to the second side.

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Class Activity 1: Effect of Transformer on the losses  Example 2-1: A single phase power system consists of a 480V 60 Hz generator supplying a load Zload=4+j3Ω through a transmission line of impedance Zline=0.18+j0.24Ω. Answer the following questions about this system. a) If the power system is exactly as described above what will the line losses be. b) Suppose a 1:10 step up transformer is placed at the generator end of transmission line and 10:1 step down transformer is placed at the load end of the line, What will the load voltage be now? what will the transmission line losses be now?

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Class Activity 1: Effect of Transformer on the losses

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Class Activity 1: Effect of Transformer on the losses

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Real Single Phase Transformer • • •

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Primary connected to an AC source and secondary is open circuited λ is the flux linkage in the coil across which voltage is being induced. Total flux linkage is the sum of the flux passing through each turn in the coil added over all turns of the coil. However, average flux can be given by:

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The Voltage Ratio Across a Real Transformer •

When the voltage is applied on the primary side of the transformer then the flux produced by this voltage is:

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The Voltage Ratio Across a Real Transformer •

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Some of this flux produced in the primary links with the secondary winding and some goes into the leakage. There is similar division of flux in the secondary side: Thus the Faraday’s law for the primary winding can be written as:

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The Voltage Ratio Across a Real Transformer Like wise for secondary side:

• From eqs. above the primary and secondary voltages due to mutual flux are given by: • The ratio of the primary voltage producing the mutual flux to the secondary voltage induced by the mutual flux is equal to the turn ratio of the transformer.

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The Voltage Ratio Across a Real Transformer •

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In a good design ØM >> ØLP and ØM >> ØLS. Therefore, Ratio of the total voltage on the primary of transformer to the ratio of the total voltage on the secondary of a transformer is approximately. Which was the case for the ideal transformer. The smaller the leakage flux, the closer the transformer will be to the ideal one.

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The Magnetization Current in Real Transformer •

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When AC power is connected to the transformer a current flows even when secondary is open circuited. This is the current required to produce the flux in real ferromagnetic material and it consists of two components: 1. Magnetization current iM, Current required to produce the flux in the core of transformer. 2. Core losses current ih+e, current required for hystersis and eddy current losses.

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The Magnetization Current in Real Transformer

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The Magnetization Current in Real Transformer •

If the value of the current required to produce a given flux is known then it is possible to construct the sketch of magnetizing current in the winding of the core.  Observations: 1) im is not sinusoidal 2) Øm reaches max; a small increase in Ø requires very large increase in im. 3) im lags voltage applied by 90˚.

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The Hysteresis and Eddy Current in Real Transformer •

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This is the current required to supply power to make up the hysteresis and eddy current losses in the core, known as core loss current. since the eddy current are proportional to the rate of change of flux. Therefore, the eddy current are largest when the flux is passing through the 0 wb.

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The Total No Load (Excitation) Current in Real Transformer •

Total no load current is called excitation current which is sum of magnetization and core loss current.

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The Current Ratio & Dot Convention • •

Connect a load on the secondary side of the transformer. A current flowing into the dotted end of the transformer produces a positive mmf.

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The Current Ratio & Dot Convention •

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A current flowing into the dotted end produces +ve mmf, while a current flowing into the undotted end produce a –ve mmf. If both currents are entering the dotted end then the mmf will add to each other. If one current enters and the other one leaves then the mmf will subtract from each other. For a good designed transform, R should be very small nearly zero, as long as the core is operating in unsaturated region. In order for mmf to be zero, current must flow in to the one dotted end and out of the other dotted end.

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The Current Ratio & Dot Convention  Assumptions to convert a real transformer into an ideal transformer. 1. The core must have no hysteresis or eddy current. 2. The Magnetization curve must be an ideal one. 3. The leakage flux in the core must be zero, implying that all the flux in the core couples both windings. 4. The resistance of the transformer winding must be zero.

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2.5: The Equivalent Circuit of a Transformer 

An accurate model of the transformer, have to account for all the losses of the transformer. 1. Copper Losses( ): The resistive heating losses in the primary and secondary winding of the transformer. They are proportional to the square of the current in the winding. 2. Leakage Flux( ): The flux which escapes the core and pass only through one of the transformer winding. These escaped fluxes produce a self inductance in the primary and secondary coil. 3. Eddy Current Losses: These are resistive heating losses in the core and are proportional to the square of the voltage applied to the transformer. 4. Hysteresis loses: These are associated with the rearrangement of the magnetic domains in the core during each half cycle and are nonlinear function of 29 applied voltage.

Driving The Equivalent Circuit Model 1. Copper Losses: The resistive copper losses are modeled by placing the a resistance RP in the primary and RS in the secondary winding of the transformer. 2. Leakage Flux: which escapes the core and pass only through one of the transformer winding. • LP: self inductance of primary coil • LS: self inductance of secondary coil Therefore, Leakage flux will be modeled by primary and secondary inductances.

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Driving The Equivalent Circuit Model 3.

4.

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(Eddy Current +Hysteresis Losses): The core loss current, ih+e, is proportional to voltage applied to the core and is in phase with voltage. Therefore, can be modeled by Rc across primary. The Magnetization Current: Is proportional to the voltage applied to the core (in unsaturated region) and is lagging the applied voltage by 90o. So it can be modeled by a reactance connected across the winding, represented by XM. The XM & RC represent the excitation effect which includes the core loss current (eddy+hysteresis) and the magnetization current. The XM & RC are placed inside, after LP and RP, because the voltage applied to the core is input voltage.

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The Final Equivalent Circuit Model •

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To analyze practical circuits containing transformers, it is important to convert the entire circuit to a single voltage level. Therefore the circuit must be referred either to primary or to its secondary side.

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The Final Equivalent Circuit Model Referred to One Side of Transformer

I.

Referred to Primary Side

II.

Referred to Secondary Side

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Approximate Equivalent Circuit of a Transformer • •

Excitation branch adds complexity. However, current through this branch is very small, as compared to the load current. It causes negligible voltage drop in the Rp and Xp and hence can be neglected.

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The Open Circuit Test •

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Rp & Xp are too small as compared to Rc and Xm. Therefore, significant voltage drops in Rc and Xm, approximately all the voltage drop across the excitation impedance Easy to look at the admittance and conductance to calculate Rc and Xm. [Parallel equivalent of Gc and BM].

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The Open Circuit Test • •

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Magnitude of YE referred to primary side. The P.F. for real transformer is always lagging. Therefore: I lags V by θ Finally , compare (i) and (ii) and you can obtain the values of RC and XM directly.

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Short Circuit Test • • •

In this test the secondary terminals of the transformer are short circuited. Apply a fairly low voltage to primary side, till current in short circuited winding is equal to rated current. Caution: Make sure to keep the primary voltage low, otherwise you could burn the transformer’s winding.

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Short Circuit Test •

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In this test the input voltage is so low. Therefore, no current flows though the excitation branch.=> All the voltage drop is in the series elements in the circuit. The magnitude and angle of the series impedance referred to primary side are given by:

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Class Activity 2: Determining Transformer Model’s Parameters  Example 2-2: The equivalent circuit impedance of a 2-kVA, 8000/240 V. 60 HZ transformer are to be determined. The open circuit test and short circuit test were performed on the primary side of the transformer, and the following data were taken. Find the impedance of the approximate equivalent circuit referred to primary side, and sketch the circuit. Open-circuit test (on primary)

Short-circuit test (on primary)

Voc=8000 V

Vsc=489 V

Ioc=0.214 A

Isc=2.5 A

Poc= 400 W

Psc= 240 W 39

2.7: Transformer Voltage Regulation and Efficiency •

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Due to series impedance in the transformer, the output voltage of the transformer varies with the load even if input voltage remains constant. The voltage regulation can be calculated at any load. However, we define full load voltage regulation as a quantity which compares the output voltage of transformer at no load with the output voltage at full load to conveniently compare various transformers.

Since at no load:

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Transformer Voltage Regulation • Low voltage regulation means less impedance of the winding. So is mostly desirable. • However, some times high impedances are used to reduce the short circuit current. •

Figure 2-18(b) and 2-18(d)

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VR with Lagging P.F.

The voltage regulation of a transformer with lagging loads must be greater than zero. 42

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VR with Unity P.F.

The voltage regulation of a transformer with unity loads must be greater than zero. However, it is a smaller number compared to lagging P.F. load. 43

VR with Leading P.F.

If the secondary current is leading , the secondary voltage can be actually higher than the referred primary voltage. Which means a -ve voltage regulation. 44

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Simplified Voltage Regulation •

Considering a lagging p.f. because this is the practical case mostly, we will drive an approximate equation for calculating the primary voltage.

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Transformer Efficiency In general:

From equivalent circuit we can calculate  easily. 1. Copper losses -in series resistance, Rp and Rs 2. Hystersis losses -accounted for by Rc 3. Eddy current -accounted for by Rc Therefore, at any given load efficiency can be calculated as:

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2.8: Transformer Taps •

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So far we considered turn ratio to be fixed. Practically, almost all the distribution transformers have taps in the winding which allows small changes in transformer’s turns ratio in the field. Typically 4 taps are designed, in addition to nominal setting with spacing of ± 2.5 percent of full load voltage between them. Taps accommodate the variations in local voltages. These taps normally can not be changed while the power system is operating and power is being supplied to the load. Tap Changing Transformer Under Load (TCUL): It is transformer which has the ability to change taps while power is connected to it.

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Class Activity 4: Transformer Taps Example 2-6: A 500 KVA, 13,200/480 V distribution transformer has four 2.5% taps on the primary winding. What are the voltage ratios of transformer at each tap setting. + 5.0% taps

13,860/480

+2.5% taps

13,530/480

Nominal rating

13,200/480

-2.5% taps

12,870/480

-5.0% taps

12,540/480 48

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Class Activity 3:  Example 2-5: A 15 kVA, 2300/230-V transformer is to be tested to determine its excitation branch components, its series impedance and its voltage regulation. The following test data have been taken from the primary side of the transformer. a) Eq ckt. Referred to HV. b) Eq ckt. Referred to LV. c) Full load VR at 0.8 pf Lagging, 1.0, and 0.8 leading. d) Perform the above using approximate Eq. e) Plot VR versus load from no load to full load at 0.8 pf Lagging, 1.0, and 0.8 leading. f) Efficiency at full load and 0.8 pf.

Open-circuit test (on primary) Voc=2300 V

Short-circuit test (on primary) Vsc=47 V

Ioc=0.21 A

Isc=6.0 A

Poc= 50 W

Psc= 160 W 49

2.9: The Auto Transformer •

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Some times it is desirable to change voltage levels by only small amount. For example from 110 V to 120 V or 13.2 kv to 13.8 kv. In this case it is wasteful and excessively expensive to wind a transformer with two full windings each rated at about the same voltage and a special purpose transformer called Autotransformer is used. The voltage at the output of the whole transformer is the sum of the voltage on the first winding and voltage on the second winding. The winding across which both the primary and secondary voltages appear is called Common Winding and the smaller winding which is connected in series with the common winding and across which only one voltage (primary/secondary) appears is called Series Winding. 50

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The Auto Transformer

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A Step-down Auto Transformer

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The Auto Transformer Voltage Relationship between two sides of the transformer

Current Relationship between two sides of the transformer

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Application of Auto Transformers •

Autotransformer is used when the turn ratio is nearly equal to 1 and where there is no objection to electrical connection between the primary and secondary winding. Hence such transformers are used: 1) To give small boost to a distribution cable to correct the voltage drop. 2) As autotransformer to give ...