Applying Faraday s law to both the primary and the secondary (noting the possibility of sources applied to either winding), yields


 Phoebe Taylor
 1 years ago
 Views:
Transcription
1 TRANSFORMERS Transformers are key elements in power systems. In order to effectively transmit power over long distances without prohibitive line losses, the voltage from the generator (a maximum of output voltage of approximately kv) must be increased to a significantly higher level (from approximately 150 kv up to 750 kv). Transformers must also be utilized on the distribution end of the line to step the voltage down (in stages) to the voltage levels required by the consumer. Transformers also have a very wide range of applications outside the power area. Transformers are essential components in the design of DC power supplies. They can provide DC isolation between two parts of a circuit. Transformers can be used for impedance matching between sources and loads or sources and transmission lines. They can also be used to physically insulate one circuit from another for safety. Fundamentally, the transformer consists of two or more windings that are magnetically coupled using a ferromagnetic core. For a twowinding transformer, the winding connected to the AC supply is typically referred to as the primary while the winding connected to the load is referred to as the secondary. A timevarying current passing through the primary coil produces a timevarying magnetic flux density within the core. According to Faraday s law, the timechanging flux passing through the secondary induces a voltage in the secondary terminals.
2 IDEAL TRANSFORMER The basic twowinding (singlephase) transformer is shown below. To simplify the initial analysis, the transformer will be assumed to be ideal. The following assumptions are made in the analysis of an ideal transformer: (1) The transformer windings are perfect conductors (zero winding resistance). (2) The core permeability is infinite (the reluctance of the core is zero). (3) All magnetic flux is confined to the transformer core (no leakage flux). (4) Core losses are assumed to be zero. The figure above shows the common convention for the primary and secondary voltage polarities and current directions. The voltage polarities and current directions shown above yield positive input power on the primary and positive output power on the secondary. The actual polarity relationship between the primary voltage and the secondary voltage is dictated by the orientation of the primary and the secondary coils. The transformer voltage relationship is obtained by applying Faraday s law.
3 Applying Faraday s law to both the primary and the secondary (noting the possibility of sources applied to either winding), yields where the line integrals of the electric fields are along the primary and secondary windings from the! terminal to the + terminal, and the corresponding surface integrals of the magnetic flux densities are over the crosssections of the primary and secondary coils. The directions of the differential lengths and differential surfaces are related by the righthand rule. The total magnetic flux passing through the primary coil also passes through the secondary coil, assuming an ideal transformer (all of the flux is confined to the transformer core). Note that the orientations of the given coils yield differential surface vectors that point in the same direction around the magnetic circuit, such that
4 Dividing the equations for v 1 and v 2 gives where the ratio of the primary turns to the secondary turns (defined as the turns ratio a) is equal to the ratio of the primary and secondary voltages. According to the turns ratio equation, a transformer with more secondary turns than primary turns yields a secondary voltage that is larger than the primary voltage (stepup transformer) while a transformer with fewer secondary turns than primary turns yields a secondary voltage that is smaller than the primary voltage (stepdown transformer). If the orientation of one of the transformer coils is reversed, then the differential surface vectors for the primary and secondary would be in opposite directions yielding If we apply Ampere s law around the transformer core (clockwise, on the centerline of the core), we find Note that with L clockwise, the normal to the surface S is inward, so that currents inward are positive and currents outward are negative. The total enclosed current is then
5 Assuming an ideal transformer core (: r = 4), the magnetic field inside the core is zero (similar to the fact that the electric field is zero inside a perfect conductor with F = 4, but carries a current on the surface of the conductor). Thus, The conservation of power relationship for the ideal transformer (power in equals power out, given no losses) can be stated by multiplying the voltage ratio by the current ratio: Assuming sinusoidal excitation, the ideal transformer can be analyzed using phasor techniques. The ratios of the phasor voltages and phasor currents satisfy the same turns ratio relationships as the timedomain values.
6 Note that the complex power relationship is also valid for the ideal transformer.
7 Polarity of Transformer Windings The operation of the transformer depends on the relative orientation of the primary and secondary coils. We mark one of the terminals on the primary and secondary coils with a dot to denote that currents entering these two terminals produce magnetic flux in the same direction within the transformer core. The equivalent circuit diagram and phasor equations for this ideal transformer are If either coil orientation is reversed, the dot positions are reversed and the current and voltage equations must include a minus sign.
8 Input Impedance (Ideal Transformer) Consider an arbitrary load (Z 2 ) connected to the secondary terminals of the ideal transformer as shown below. The impedance seen looking into the primary winding is given by input Thus, the input impedance seen looking into the primary of the ideal transformer is the load impedance times a 2. Using this property, the secondary impedance of the ideal transformer can be reflected to the primary.
9 In a similar fashion, a load on the primary side of the ideal transformer can be reflected to the secondary.
10 Example (Ideal transformer) Determine the primary and secondary currents for the ideal transformer below if Z s = (18!j4) S and Z 2 = (2+j1) S. The load impedance reflected to the primary of the transformer is The primary current is then The primary voltage is The secondary voltage is The secondary current is
11 TRANSFORMER RATING Transformers carry ratings related to the primary and secondary windings. The ratings refer to the power in kva and primary/secondary voltages. A rating of 10 kva, 1100/110 V means that the primary is rated for 1100 V while the secondary is rated for 110 V (a =10). The kva rating gives the power information. With a kva rating of 10 kva and a voltage rating of 1100 V, the rated current for the primary is 10,000/1100 = 9.09 A while the secondary rated current is 10,000/110 = 90.9 A. NONIDEAL TRANSFORMER EQUIVALENT CIRCUITS The nonideal transformer equivalent circuit below accounts for all of the loss terms that are neglected in the ideal transformer model. The individual loss terms in the equivalent circuit are: R w1, R w2  primary and secondary winding resistances (losses in the windings due to the resistance of the wires) X l1, X l2  primary and secondary leakage reactances (losses due to flux leakage out of the transformer core) R c1  core resistance (core losses due to hysteresis loss and eddy current loss) X m1  magnetizing reactance (magnetizing current necessary to establish magnetic flux in the transformer core)
12 Using the impedance reflection technique, all the quantities on the secondary side of the transformer can be reflected back to the primary side of the circuit. The resulting equivalent circuit is shown below. The primed quantities represent those values that equal the original secondary quantity multiplied by a (voltages), divided by a (currents) or multiplied by a 2 (impedance components). Approximate Transformer Equivalent Circuits Given that the voltage drops across the primary winding resistance and the primary leakage reactance are typically quite small, the shunt branch of the core loss resistance and the magnetizing reactance (excitation branch) can be shifted to the primary input terminal. The primary voltage is then applied directly across the this shunt impedance and allows for the winding resistances and leakage reactances to be combined.
13 A further approximation to the transformer equivalent circuit can be made by eliminating the excitation branch. This approximation removes the core losses and the magnetizing current from the transformer model. The resulting equivalent circuit is shown below. Note that this equivalent circuit is referred to the primary side of the transformer (V 1 and VN 2 ). This circuit can easily be modified so that it is referred to the secondary side of the transformer (VN 1 and V 2 ).
14 DETERMINATION OF EQUIVALENT CIRCUIT PARAMETERS In order to utilize the complete transformer equivalent circuit, the values of R w1, R w2, X l1, X l2, R c1, X m1 and a must be known. These values can be computed given the complete design data for the transformer including dimensions and material properties. The equivalent circuit parameters can also be determined by performing two simple test measurements. These measurements are the noload (or opencircuit) test and the shortcircuit test. NoLoad Test  ShortCircuit Test  The rated voltage at rated frequency is applied to the highvoltage (HV) or lowvoltage (LV) winding with the opposite winding opencircuited. Measurements of current, voltage and real power are made on the input winding (most often the LV winding, for convenience). Either the LV or HV winding is shortcircuited and a voltage at rated frequency is applied to the opposite winding such that the rated current results. Measurements of current, voltage and real power are made on the input winding (most often the HV winding, for convenience, since a relatively low voltage is necessary to obtain rated current under shortcircuit conditions).
15 Example (Equivalent circuit parameters / noload / shortcircuit tests) The approximate equivalent circuit parameters for a singlephase 10kVA, 2200/220, 60 Hz transformer are required. The rated currents and voltages for the transformer windings are: V H,rated = 2200 V I H,rated = 10000/2200 = 4.55 A V L,rated = 220 V I L,rated = 10000/220 = 45.5 A Noload and shortcircuit tests are performed on the transformer with the following results: Noload test (HV winding open, V L = V L,rated = 220 V) I L = 2.5 A, P L = 100 W Shortcircuit test (LV winding shorted, I H = I H,rated = 4.55 A) V H = 150 V, P H = 215 W (a.) Determine the approximate equivalent circuit parameters from the test data (use the approximate equivalent circuit that includes core losses). Draw the equivalent circuit for this transformer referred to the LV side. (b.) Draw the equivalent circuit for this transformer referred to the HV side. (c.) From the noload test results, express the excitation current as a percentage of the rated current in the LV winding. (d.) Determine the power factor for the noload and shortcircuit tests. Referred to LV side Referred to HV side
16 Equivalent circuit for noload test (determine R cl and X ml )
17 Equivalent circuit for shortcircuit test (determine R eqh and X eqh ) The values measured on the HV winding (primary) in the shortcircuit test need to be referred to the LV side. Note that our turns ratio is given by
18 (a.) Referred to LV side (b.) To obtain the same equivalent circuit referred to the HV side (primary), we simply multiply all impedances by a 2 (100). The resulting equivalent circuit is Referred to HV side (c.) From the noload test results, the total excitation current is 2.5 A while the rated current in the LV winding is 45.5 A. Thus the excitation current is (2.5/45.5) or 5.5% of the rated current.
19 (d.) The power factor is defined as For the noload test, the power factor is For the shortcircuit test, the power factor is
20 TRANSFORMER VOLTAGE REGULATION For a given input (primary) voltage, the output (secondary) voltage of an ideal transformer is independent of the load attached to the secondary. As seen in the transformer equivalent circuit, the output voltage of a realistic transformer depends on the load current. Assuming that the current through the excitation branch of the transformer equivalent circuit is small in comparison to the current that flows through the winding loss and leakage reactance components, the transformer approximate equivalent circuit referred to the primary is shown below. Note that the load on the secondary (Z 2 ) and the resulting load current (I 2 ) have been reflected to the primary (ZN 2, IN 2 ). The percentage voltage regulation (VR) is defined as the percentage change in the magnitude of the secondary voltage as the load current changes from the noload to the loaded condition. The transformer equivalent circuit above gives only the reflected secondary voltage. The actual loaded and noload secondary voltages are equal to the loaded and noloaded refelcted secondary values divided by the turns ratio.
21 Thus, the percentage voltage regulation may be written in terms of the reflected secondary voltages. According to the approximate transformer equivalent circuit, the reflected secondary voltage under noload conditions is equal to the primary voltage, so that The secondary voltage for the loaded condition is taken as the rated voltage. Inserting the previous two equations into the percentage voltage regulation equation gives Note that this equation is defined in terms of the voltages given in the transformer approximate equivalent circuit. Also note that the rated secondary voltage reflected to the primary is the rated primary voltage. To determine the percentage voltage regulation, we may use the reflected secondary voltage as the voltage reference, and determine the corresponding value of *V 1 * from the approximate equivalent circuit.
22 The voltages V 1 and VN 2 in the approximate equivalent circuit are related by where The reflected secondary current can be written as The expression for V 1 becomes We can draw the phasor diagram relating the voltages V 1 and VN 2 to determine how the phase angles of the load and the transformer impedance affect the percentage voltage regulation. Note that the percentage voltage regulation can be positive or negative and the sign of VR is affected by the phase angle in the expression above. Thus, the power factor of the load will affect the voltage regulation of the transformer.
23 The percentage voltage regulation is positive if *V 1 * > V 1,rated and negative if *V 1 * < V 1,rated. Note that with the limits on the angles of the worst case scenario for the percentage voltage regulation occurs when or when the load has a lagging power factor with the power factor angle equal to the transformer impedance angle of Z eq1.
24 Example (Transformer voltage regulation) Using the transformer for which the approximate equivalent circuits were found based on noload and shortcircuit test results, determine the percentage voltage regulation for (a.) a load drawing 75% of rated current at a power factor of 0.6 lagging (b.) a load drawing 75% of rated current at a power factor of 0.6 leading. The approximate equivalent circuit for the transformer (10kVA, 2200/220, 60 Hz) referred to the high voltage winding was found to be (neglecting the excitation branch of the model) Assume: Primary = HV winding Secondary = LV winding a = N 1 /N 2 = 10 V H,rated = 2200 V I H,rated = 10000/2200 = 4.55 A V L,rated = 220 V I L,rated = 10000/220 = 45.5 A (a.) The reflected voltage V L N on the HV side is given by so that the circuit to be analyzed becomes
25 Based on the information provided in the problem statement, the magnitude of the load current (and thus the current I L N) is 0.75 times that of the rated value. The phase angle of I L N is given by the load power factor. so that the phasor current I L N is The voltage V H and V L N are related by The percentage voltage regulation is thus (b.) For the leading power of 0.6, 2 i = o so that the phasor current I L N is and V H is given by
26 The voltage regulation is The percentage voltage regulation results for these two cases shows that if this transformer is providing 75% of rated current (3.41 Arms) to a load with a power factor of 0.6 lagging, and the load is suddenly removed, the load voltage magnitude rises from 220 V to V. For the load with a power factor of 0.6 leading, the load voltage magnitude drops from 220 V to V.
27 TRANSFORMER EFFICIENCY The efficiency (0) of a transformer is defined as the ratio of the output power (P out ) to the input power (P in ). The output power is equal to the input power minus the losses (P loss ) in the transformer. The transformer loss power has two components: core loss (P core ) and socalled copper loss (P cu ) associated with the winding resistances. The transformer efficiency in percent is given by Assuming a relatively constant voltage source on the primary of the transformer, the core loss can be assumed to be constant and equal to power dissipated in the core loss resistance (R c1 ) of the equivalent circuit for the noload test. The copper loss in a transformer may be written in terms of both the primary and secondary currents, or in terms of only one of these currents based on the relationship I 2 = ai 1. The output power of the transformer can be written in terms of the secondary voltage and current (real part of output complex power).
28 The transformer efficiency, written in terms of secondary values, is It can be shown that the maximum transformer efficiency occurs when the core losses equal the copper losses and the power factor is unity. Example (Transformer efficiency) Using the transformer for which the approximate equivalent circuits were found based on noload and shortcircuit test results, determine (a.) the transformer efficiency at 75% of rated output power with a power factor of 0.6 lagging (b.) the output power at maximum efficiency, the value of maximum efficiency, and at the percentage of full load power where maximum efficiency occurs. (a.) The rated power for this transformer is 10 kw at a power factor of unity. If P out is 75% of the rated value at a power factor of 0.6, then From the noload test, the core losses were P core = 100 W. The copper losses for this transformer are The transformer efficiency is
29 (b.) At maximum efficiency Y P Cu = I L 2 R eql = P core = 100 W, PF = 1 The maximum efficiency is The maximum efficiency occurs at
THE PERUNIT SYSTEM. (2) The perunit values for various components lie within a narrow range regardless of the equipment rating.
THE PERUNIT SYSTEM An interconnected power system typically consists of many different voltage levels given a system containing several transformers and/or rotating machines. The perunit system simplifies
More informationElectrical Machines II. Week 1: Construction and theory of operation of single phase transformer
Electrical Machines II Week 1: Construction and theory of operation of single phase transformer Transformers Overview A transformer changes ac electric power at one frequency and voltage level to ac electric
More informationCoupled Inductors. Introducing Coupled Inductors
Coupled Inductors From power distribution across large distances to radio transmissions, coupled inductors are used extensively in electrical applications. Their properties allow for increasing or decreasing
More informationModule 7. Transformer. Version 2 EE IIT, Kharagpur
Module 7 Transformer Version EE IIT, Kharagpur Lesson 4 Practical Transformer Version EE IIT, Kharagpur Contents 4 Practical Transformer 4 4. Goals of the lesson. 4 4. Practical transformer. 4 4.. Core
More informationEE 221 Circuits II. Chapter 13 Magnetically Coupled Circuits
EE Circuits II Chapter 3 Magnetically Coupled Circuits Magnetically Coupled Circuits 3. What is a transformer? 3. Mutual Inductance 3.3 Energy in a Coupled Circuit 3.4 inear Transformers 3.5 Ideal Transformers
More informationDigital Energy ITI. Instrument Transformer Basic Technical Information and Application
g Digital Energy ITI Instrument Transformer Basic Technical Information and Application Table of Contents DEFINITIONS AND FUNCTIONS CONSTRUCTION FEATURES MAGNETIC CIRCUITS RATING AND RATIO CURRENT TRANSFORMER
More informationSYNCHRONOUS MACHINES
SYNCHRONOUS MACHINES The geometry of a synchronous machine is quite similar to that of the induction machine. The stator core and windings of a threephase synchronous machine are practically identical
More informationChapter 4. Magnetic Materials and Circuits
Chapter 4 Magnetic Materials and Circuits Objectives List six characteristics of magnetic field. Understand the righthand rule for current and magnetic fluxes. Define magnetic flux, flux density, magnetomotive
More information7.1 POWER IN AC CIRCUITS
C H A P T E R 7 AC POWER he aim of this chapter is to introduce the student to simple AC power calculations and to the generation and distribution of electric power. The chapter builds on the material
More informationDHANALAKSHMI COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING EE2302  ELECTRICAL MACHINES II UNITI SYNCHRONOUS GENERATOR
1 DHANALAKSHMI COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING Constructional details Types of rotors EE2302  ELECTRICAL MACHINES II UNITI SYNCHRONOUS GENERATOR PART A 1.
More informationThe Ideal Transformer. Description and Circuit Symbol
The Ideal Transformer Description and Circuit Symbol As with all the other circuit elements, there is a physical transformer commonly used in circuits whose behavior can be discussed in great detail. However,
More information2. A conductor of length 2m moves at 4m/s at 30 to a uniform magnetic field of 0.1T. Which one of the following gives the e.m.f. generated?
Extra Questions  2 1. A straight length of wire moves through a uniform magnetic field. The e.m.f. produced across the ends of the wire will be maximum if it moves: a) along the lines of magnetic flux
More informationExtra Questions  1. 1. What current will flow in a 20Ω resistor when it is connected to a 50V supply? a) 0.4A b) 1.6A c) 2.5A
Extra Questions  1 1. What current will flow in a 20Ω resistor when it is connected to a 50V supply? a) 0.4A b) 1.6A c) 2.5A 2. A current of 500mA flows in a resistance of 12Ω. What power is dissipated
More informationOutline. Systems and Signals 214 / 244 & Energy Systems 244 / 344. Ideal Inductor. Ideal Inductor (cont... )
Outline Systems and Signals 214 / 244 & Energy Systems 244 / 344 Inductance, Leakage Inductance, Mutual Inductance & Transformers 1 Inductor revision Ideal Inductor NonIdeal Inductor Dr. P.J. Randewijk
More informationTransformer circuit calculations
Transformer circuit calculations This worksheet and all related files are licensed under the Creative Commons Attribution License, version 1.0. To view a copy of this license, visit http://creativecommons.org/licenses/by/1.0/,
More information13 ELECTRIC MOTORS. 13.1 Basic Relations
13 ELECTRIC MOTORS Modern underwater vehicles and surface vessels are making increased use of electrical actuators, for all range of tasks including weaponry, control surfaces, and main propulsion. This
More informationPower Technology Issue 104. Modeling of TwoWinding Voltage Regulating Transformers for Positive Sequence Load Flow Analysis in PSS E
SIEMENS Siemens Energy, Inc. Power Technology Issue 104 Modeling of TwoWinding Voltage Regulating Transformers for Positive Sequence Load Flow Analysis in PSS E Carlos GrandeMoran, Ph.D. Principal Consultant
More informationChapter 16. Current Transformer Design. Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
Chapter 16 Current Transformer Design Table of Contents 1. Introduction 2. Analysis of the Input Current Component 3. Unique to a Current Transformer 4. Current Transformer Circuit Applications 5. Current
More informationThree phase circuits
Three phase circuits THREE PHASE CIRCUITS THREEPHASE ADVANTAGES 1. The horsepower rating of threephase motors and the kva rating of threephase transformers are 150% greater than singlephase motors
More informationThe purposes of this experiment are to test Faraday's Law qualitatively and to test Lenz's Law.
260 171 I. THEORY EXPERIMENT 17 QUALITATIVE STUDY OF INDUCED EMF Along the extended central axis of a bar magnet, the magnetic field vector B r, on the side nearer the North pole, points away from this
More informationChapter 14 Magnets and
Chapter 14 Magnets and Electromagnetism How do magnets work? What is the Earth s magnetic field? Is the magnetic force similar to the electrostatic force? Magnets and the Magnetic Force! We are generally
More informationFull representation of the real transformer
TRASFORMERS EQVALET CRCT OF TWOWDG TRASFORMER TR Dots show the points of higher potential. There are applied following conventions of arrow directions: for primary circuit the passive sign convention
More informationDIRECT CURRENT GENERATORS
DIRECT CURRENT GENERATORS Revision 12:50 14 Nov 05 INTRODUCTION A generator is a machine that converts mechanical energy into electrical energy by using the principle of magnetic induction. This principle
More informationQuestion Bank. 1. Electromagnetism 2. Magnetic Effects of an Electric Current 3. Electromagnetic Induction
1. Electromagnetism 2. Magnetic Effects of an Electric Current 3. Electromagnetic Induction 1. Diagram below shows a freely suspended magnetic needle. A copper wire is held parallel to the axis of magnetic
More informationEdmund Li. Where is defined as the mutual inductance between and and has the SI units of Henries (H).
INDUCTANCE MUTUAL INDUCTANCE If we consider two neighbouring closed loops and with bounding surfaces respectively then a current through will create a magnetic field which will link with as the flux passes
More informationModeling of Transmission Lines
Modeling of Transmission Lines Electric Power Transmission The electric energy produced at generating stations is transported over highvoltage transmission lines to utilization points. The trend toward
More information3Phase AC Calculations Revisited
AN110 Dataforth Corporation Page 1 of 6 DID YOU KNOW? Nikola Tesla (18561943) came to the United States in 1884 from Yugosiavia. He arrived during the battle of the currents between Thomas Edison, who
More informationTRANSFORMER: THREE PHASE
CONTENTS Transformer : Three Phase 1211 C H A P T E R 33 Learning Objectives Threephase Transformers Threephase Transformer Connections Star/Star or Y/Y Connection DeltaDelta or Connection Wye/Delta
More informationLab 14: 3phase alternator.
Lab 14: 3phase alternator. Objective: to obtain the noload saturation curve of the alternator; to determine the voltage regulation characteristic of the alternator with resistive, capacitive, and inductive
More information3 Synchronous Generator Operation
3 Synchronous Generator Operation 3.1 Cylindrical Rotor Machine xa xl ra xa E xl ra E Load A (a) (b)phasor diagram for R load xs ra Zs Xs Zs Load (c) φ (d)phasor diagram for RL load Ι Figure 30: Equivalent
More informationTutorial One: Calculation of leakage inductance of transformer using FEM. 31.5 MVA, 132 kv/33kv, Y/, Ampereturns: 135024, No.
Tutorial One: Calculation of leakage inductance of transformer using FEM Consider a transformer with the following rating: 31.5 MVA, 132 kv/33kv, Y/, Ampereturns: 135024, No. of HV turns = 980 Although
More informationCircuits with inductors and alternating currents. Chapter 20 #45, 46, 47, 49
Circuits with inductors and alternating currents Chapter 20 #45, 46, 47, 49 RL circuits Ch. 20 (last section) Symbol for inductor looks like a spring. An inductor is a circuit element that has a large
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5  ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3. OUTCOME 3  MAGNETISM and INDUCTION
EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5  ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 3  MAGNETISM and INDUCTION 3 Understand the principles and properties of magnetism Magnetic field:
More informationDOE FUNDAMENTALS HANDBOOK ELECTRICAL SCIENCE Volume 4 of 4
DOEHDBK1011/492 JUNE 1992 DOE FUNDAMENTALS HANDBOOK ELECTRICAL SCIENCE Volume 4 of 4 U.S. Department of Energy Washington, D.C. 20585 FSC6910 Distribution Statement A. Approved for public release;
More informationEEL303: Power Engineering I  Tutorial 4
1. Determine the voltage at the generating station and the efficiency of the following system (Figure 1): Both transformers have ratio of 2kV/11kV. The resistance on LV side of both Figure 1: transformers
More informationMutual Inductance and Transformers F3 3. r L = ω o
utual Inductance and Transformers F3 1 utual Inductance & Transformers If a current, i 1, flows in a coil or circuit then it produces a magnetic field. Some of the magnetic flux may link a second coil
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5  ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 4  ALTERNATING CURRENT
EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5  ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 4  ALTERNATING CURRENT 4 Understand singlephase alternating current (ac) theory Single phase AC
More informationChapter 14: Inductor design
Chapter 14 Inductor Design 14.1 Filter inductor design constraints 14.2 A stepbystep design procedure 14.3 Multiplewinding magnetics design using the K g method 14.4 Examples 14.5 Summary of key points
More informationVOLTAGE REGULATOR AND PARALLEL OPERATION
VOLTAGE REGULATOR AND PARALLEL OPERATION Generator sets are operated in parallel to improve fuel economy and reliability of the power supply. Economy is improved with multiple paralleled generators by
More informationFunctions, variations and application areas of magnetic components
Westring 18 3314 Büren Germany T +49 951 60 01 0 F +49 951 60 01 3 www.schaffner.com energy efficiency and reliability 1.1 Transformers The transformer is one of the traditional components of electrical
More informationChapter 12: Three Phase Circuits
Chapter 12: Three Phase Circuits 12.1 What Is a Three Phase Circuit? 12.2 Balance Three Phase Voltages 12.3 Balance Three Phase Y to Y Connection 12.4 Other Balance Three Phase Connections 12.5 Power in
More informationTransformer Calculations
Transformer Calculations Transformers Transformers are one of the most basic yet practical devices used today. No matter where you are there is always a transformer nearby. They are used throughout alternatingcurrent
More information6 J  vector electric current density (A/m2 )
Determination of Antenna Radiation Fields Using Potential Functions Sources of Antenna Radiation Fields 6 J  vector electric current density (A/m2 ) M  vector magnetic current density (V/m 2 ) Some problems
More informationApplication Note. So You Need to Measure Some Inductors?
So You Need to Measure Some nductors? Take a look at the 1910 nductance Analyzer. Although specifically designed for production testing of inductors and coils, in addition to measuring inductance (L),
More informationStudent Name Instructor Name. High School or Vocational Center Grade. COMPETENCY RECORD FOR ARTICULATION Muskegon Community College Electronics
Student Name Instructor Name High School or Vocational Center Grade COMPETENCY RECORD FOR ARTICULATION Muskegon Community College Electronics Please check below each skill the student has mastered as described,
More information1. E&M induction requires change, of the intensity of a magnetic field or of motion in a magnetic field.
Chapter 25 EXERCISE key 1. E&M induction requires change, of the intensity of a magnetic field or of motion in a magnetic field. 2. Magnetic induction will not occur in nylon, since it has no magnetic
More informationThe Flyback Converter
The Flyback Converter Lecture notes ECEN4517! Derivation of the flyback converter: a transformerisolated version of the buckboost converter! Typical waveforms, and derivation of M(D) = V/! Flyback transformer
More information1. Title Electrical fundamentals II (Mechanics Repair and Maintenance)
1. Title Electrical fundamentals II (Mechanics Repair and Maintenance) 2. Code EMAMBG429A 3. Range The knowledge is needed for a wide range of aircraft repair and maintenance works,e.g. applicable to aircrafts,
More information7 Testing of Transformers
7 Testing of Transformers The structure of the circuit equivalent of a practical transformer is developed earlier. The performance parameters of interest can be obtained by solving that circuit for any
More informationRevision Calcs. 1. The flux produced by a magnet is 10mWb. Determine the flux density if the area of the pole is 250 mm 2
EMA Revision Calcs Miller College Revision Calcs Revision Calcs 1. The flux produced by a magnet is 10mWb. Determine the flux density if the area of the pole is 250 mm 2 2. For the magnet in the previous
More informationCURRENT TRANSFORMERS INSTALLATION GUIDE
CURRENT TRANSFORMERS INSTALLATION GUIDE Information contained within this document is subject to change without notice and does not represent a commitment on the part of PRI Ltd or its agents. E&OE. Copyright
More informationMotor Fundamentals. DC Motor
Motor Fundamentals Before we can examine the function of a drive, we must understand the basic operation of the motor. It is used to convert the electrical energy, supplied by the controller, to mechanical
More informationThe Synchronous Machine
Experiment No. 5 The Synchronous Machine Synchronous ac machines find application as motors in constant speed applications and, when interfaced to the power source with a variablefrequency converter system,
More informationExperiment A5. Hysteresis in Magnetic Materials
HYSTERESIS IN MAGNETIC MATERIALS A5 1 Experiment A5. Hysteresis in Magnetic Materials Objectives This experiment illustrates energy losses in a transformer by using hysteresis curves. The difference betwen
More informationFall 12 PHY 122 Homework Solutions #10
Fall 12 PHY 122 Homework Solutions #10 HW10: Ch.30 Q5, 8, 15,17, 19 P 1, 3, 9, 18, 34, 36, 42, 51, 66 Chapter 30 Question 5 If you are given a fixed length of wire, how would you shape it to obtain the
More informationSingle and Three Phase Transformer Testing Using Static Motor Circuit Analysis Techniques
Single and Three Phase Transformer Testing Using Static Motor Circuit Analysis Techniques Howard W. Penrose, Ph.D On behalf of ALLTEST Pro, LLC Old Saybrook, CT Introduction Field and shop testing of
More information5. Measurement of a magnetic field
H 5. Measurement of a magnetic field 5.1 Introduction Magnetic fields play an important role in physics and engineering. In this experiment, three different methods are examined for the measurement of
More informationChapter 35 Alternating Current Circuits
hapter 35 Alternating urrent ircuits acircuits Phasor Diagrams Resistors, apacitors and nductors in acircuits R acircuits acircuit power. Resonance Transformers ac ircuits Alternating currents and
More informationInductors & Inductance. Electronic Components
Electronic Components Induction In 1824, Oersted discovered that current passing though a coil created a magnetic field capable of shifting a compass needle. Seven years later, Faraday and Henry discovered
More informationSelecting Current Transformers Part 1 By Darrell G. Broussard, P.E.
By Darrell G. Broussard, P.E. Introduction: As engineers, we are aware that electrical power systems have grown. How much have they grown? When was the last time you specified a 2400volt system, a 4160volt
More informationPower Technology Issue 106. Modeling of ThreeWinding Voltage Regulating Transformers for Positive Sequence Load Flow Analysis in PSS E
SIEMENS Siemens Energy, Inc. Power Technology Issue 106 Modeling of ThreeWinding Voltage Regulating Transformers for Positive Sequence Load Flow Analysis in PSS E Carlos GrandeMoran, Ph.D. Principal
More informationBasics of Electricity
Basics of Electricity Generator Theory PJM State & Member Training Dept. PJM 2014 8/6/2013 Objectives The student will be able to: Describe the process of electromagnetic induction Identify the major components
More information1. The diagram below represents magnetic lines of force within a region of space.
1. The diagram below represents magnetic lines of force within a region of space. 4. In which diagram below is the magnetic flux density at point P greatest? (1) (3) (2) (4) The magnetic field is strongest
More informationTheory of Heating by Induction
CHAPTER 2 Theory of Heating by Induction INDUCTION HEATING was first noted when it was found that heat was produced in transformer and motor windings, as mentioned in the Chapter Heat Treating of Metal
More informationMAGNETIC EFFECTS OF ELECTRIC CURRENT
CHAPTER 13 MAGNETIC EFFECT OF ELECTRIC CURRENT In this chapter, we will study the effects of electric current : 1. Hans Christian Oersted (17771851) Oersted showed that electricity and magnetism are related
More informationRLC Resonant Circuits
C esonant Circuits Andrew McHutchon April 20, 203 Capacitors and Inductors There is a lot of inconsistency when it comes to dealing with reactances of complex components. The format followed in this document
More informationKirchhoff's Rules and Applying Them
[ Assignment View ] [ Eðlisfræði 2, vor 2007 26. DC Circuits Assignment is due at 2:00am on Wednesday, February 21, 2007 Credit for problems submitted late will decrease to 0% after the deadline has passed.
More informationEMI and t Layout Fundamentals for SwitchedMode Circuits
v sg (t) (t) DT s V pp = n  1 2 V pp V g n V T s t EE core insulation primary return secondary return Supplementary notes on EMI and t Layout Fundamentals for SwitchedMode Circuits secondary primary
More informationCT Application Guide for the 489 Generator Management Relay
g GE Power Management Technical Notes CT Application Guide for the 489 Generator Management Relay GE Publication No. GET8402 Copyright 2002 GE Power Management Introduction A protection scheme operates
More informationSalman Bin Abdulaziz University College of Engineering. Electrical Engineering Department EE 3360 Electrical Machines (II)
CHAPTER # 3 SALIENTPOLE SYNCHRONOUS GENERATOR AND MOTOR 1 Introduction A cylindrical rotor synchronous machines has a uniform airgap, therefore its reactance remains the same, irrespective of the rotor
More information7CURRENT TRANSFORMERS
7CURRENT TRANSFORMERS Protective relays of the ac type are actuated by current and voltage supplied by current and voltage transformers. These transformers provide insulation against the high voltage
More informationChapter 11. Inductors ISU EE. C.Y. Lee
Chapter 11 Inductors Objectives Describe the basic structure and characteristics of an inductor Discuss various types of inductors Analyze series inductors Analyze parallel inductors Analyze inductive
More informationAC Generators and Motors
AC Generators and Motors Course No: E03008 Credit: 3 PDH A. Bhatia Continuing Education and Development, Inc. 9 Greyridge Farm Court Stony Point, NY 10980 P: (877) 3225800 F: (877) 3224774 info@cedengineering.com
More information"  angle between l and a R
Magnetostatic Fields According to Coulomb s law, any distribution of stationary charge produces a static electric field (electrostatic field). The analogous equation to Coulomb s law for electric fields
More informationAjay Kumar Garg Engineering College, Ghaziabad CLASS NOTES. Subject Name: ELECTROMECHANICAL ENERGY CONVERSIONI Subject Code: NEE 301
Ajay Kumar Garg Engineering College, Ghaziabad CLASS NOTES Subject Name: ELECTROMECHANICAL ENERGY CONVERSIONI Subject Code: NEE 301 Course: B. Tech. nd Year Branch: Electrical & Electronics Engineering
More informationOpen Phase Conditions in Transformers Analysis and Protection Algorithm
Open Phase Conditions in Transformers Analysis and Protection Algorithm Amir Norouzi GE Digital Energy Markham, ON amir.norouzi@ge.com Abstract This paper first provides an indepth analysis of open phase
More informationHPS Universal. Single and Three Phase Potted. BuckBoost Transformers. BuckBoost Applications & Standard Specification... 80
BuckBoost Transformers Single and Three Phase Potted BuckBoost Transformers BuckBoost Applications & Standard Specification... 80 Selecting BuckBoost Transformers... 81 Single Phase Selection Tables...
More informationDC GENERATOR THEORY. LIST the three conditions necessary to induce a voltage into a conductor.
DC Generators DC generators are widely used to produce a DC voltage. The amount of voltage produced depends on a variety of factors. EO 1.5 LIST the three conditions necessary to induce a voltage into
More informationEðlisfræði 2, vor 2007
[ Assignment View ] [ Print ] Eðlisfræði 2, vor 2007 30. Inductance Assignment is due at 2:00am on Wednesday, March 14, 2007 Credit for problems submitted late will decrease to 0% after the deadline has
More informationShort Circuit Current Calculations
Introduction Several sections of the National Electrical Code relate to proper overcurrent protection. Safe and reliable application of overcurrent protective devices based on these sections mandate that
More informationChapter 4: DC Generators
Chapter 4: DC Generators Creating an AC Voltage The voltage produced in a DC generator is inherently AC and only becomes DC after rectification Consider an AC generator, consisting of a coil on the rotor
More informationPhysics 1653 Exam 3  Review Questions
Physics 1653 Exam 3  Review Questions 3.0 Two uncharged conducting spheres, A and B, are suspended from insulating threads so that they touch each other. While a negatively charged rod is held near, but
More information45. The peak value of an alternating current in a 1500W device is 5.4 A. What is the rms voltage across?
PHYS Practice Problems hapters 8 hapter 8. 45. The peak value of an alternating current in a 5W device is 5.4 A. What is the rms voltage across? The power and current can be used to find the peak voltage,
More informationInstrument Transformers Application Guide
Instrument Transformers Application Guide Edited by ABB AB High Voltage Products Department: Marketing & Sales Text: Knut Sjövall, ABB Layout, 3D and images: Mats Findell, ABB SE771 80 LUDVIKA, Sweden
More informationProperties of electrical signals
DC Voltage Component (Average voltage) Properties of electrical signals v(t) = V DC + v ac (t) V DC is the voltage value displayed on a DC voltmeter Triangular waveform DC component Halfwave rectifier
More informationChapter 4: DC Generators. 9/8/2003 Electromechanical Dynamics 1
Chapter 4: DC Generators 9/8/2003 Electromechanical Dynamics 1 Armature Reaction Current flowing in the armature coils creates a powerful magnetomotive force that distorts and weakens the flux coming from
More informationDCDC Converter Basics
Page 1 of 16 Free Downloads / Design Tips / Java Calculators / App. Notes / Tutorials / Newsletter / Discussion / Components Database / Library / Power Links / Software / Technical Articles / OnLine Textbook
More informationBasics of Ferrite and Noise Countermeasures
TDK EMC Technology Basic Section Basics of Ferrite and Noise Countermeasures TDK Corporation Magnetics Business Group Shinichiro Ito 1 What is Ferrite? Ferrite was invented by Dr. Kato and Dr. Takei in
More informationAC Generators. Basic Generator
AC Generators Basic Generator A basic generator consists of a magnetic field, an armature, slip rings, brushes and a resistive load. The magnetic field is usually an electromagnet. An armature is any number
More informationThe Polyphase Induction Motor
Experiment No. 4 The Polyphase Induction Motor The polyphase induction motor is the most commonly used industrial motor, finding application in many situations where speed regulation is not essential.
More informationPHASOR DIAGRAMS II Fault Analysis Ron Alexander Bonneville Power Administration
PHASOR DIAGRAMS II Fault Analysis Ron Alexander Bonneville Power Administration For any technician or engineer to understand the characteristics of a power system, the use of phasors and polarity are essential.
More informationAn Introduction to the Mofied Nodal Analysis
An Introduction to the Mofied Nodal Analysis Michael Hanke May 30, 2006 1 Introduction Gilbert Strang provides an introduction to the analysis of electrical circuits in his book Introduction to Applied
More informationTransmission Line Transformers
Radio Frequency Circuit Design. W. Alan Davis, Krishna Agarwal Copyright 2001 John Wiley & Sons, Inc. Print ISBN 0471350524 Electronic ISBN 0471200689 CHAPTER SIX Transmission Line Transformers 6.1
More informationExperiment 1 The DC Machine
Experiment 1 The DC Machine ECEN 4517 R. W. Erickson and D. Maksimovic The purpose of this experiment is to become familiar with operating principles, equivalent circuit models, and basic characteristics
More informationMarch 20. Physics 272. Spring 2014 Prof. Philip von Doetinchem
Physics 272 March 20 Spring 2014 http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html Prof. Philip von Doetinchem philipvd@hawaii.edu Phys272  Spring 14  von Doetinchem  129 Summary No magnetic
More informationUnit 33 ThreePhase Motors
Unit 33 ThreePhase Motors Objectives: Discuss the operation of wound rotor motors. Discuss the operation of selsyn motors. Discuss the operation of synchronous motors. Determine the direction of rotation
More informationInduction Motor Theory
PDHonline Course E176 (3 PDH) Induction Motor Theory Instructor: Jerry R. Bednarczyk, P.E. 2012 PDH Online PDH Center 5272 Meadow Estates Drive Fairfax, VA 220306658 Phone & Fax: 7039880088 www.pdhonline.org
More informationA wave lab inside a coaxial cable
INSTITUTE OF PHYSICS PUBLISHING Eur. J. Phys. 25 (2004) 581 591 EUROPEAN JOURNAL OF PHYSICS PII: S01430807(04)76273X A wave lab inside a coaxial cable JoãoMSerra,MiguelCBrito,JMaiaAlves and A M Vallera
More informationPHASOR DIAGRAMS HANDSON RELAY SCHOOL WSU PULLMAN, WA. RON ALEXANDER  BPA
PHASOR DIAGRAMS HANDSON RELAY SCHOOL WSU PULLMAN, WA. RON ALEXANDER  BPA What are phasors??? In normal practice, the phasor represents the rms maximum value of the positive half cycle of the sinusoid
More informationSolution Derivations for Capa #11
Solution Derivations for Capa #11 Caution: The symbol E is used interchangeably for energy and EMF. 1) DATA: V b = 5.0 V, = 155 Ω, L = 8.400 10 2 H. In the diagram above, what is the voltage across the
More information