Single-Phase. Three-Phase

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Single-Phase. Three-Phase"

Transcription

1

2 Three-Phase Transformers When more power is needed - three transformers can be tied together. This is called three-phase. Here s a simple way of comparing single-phase to threephase power. Single-Phase Three-Phase Think of single-phase as one guy driving a stake into the ground; Three-phase as three guys, working together, driving the same stake into the ground. 25

3 Generating Three-Phase Three-phase power is delivered from a generator with three separate windings. These windings are equally spaced around a rotating cylinder (rotor) with each winding occupying one-third of the rotor circumference. Three-phase generator windings are spaced 120 apart for a total of Because the three source voltages timed at three different intervals, they can be transmitted over just three conductors (rather than the six conductors needed to transmit three separate single-phase loads) A three-phase system can produce 173% higher effective voltage than a single-phase system. This is very useful for higher power loads such as large motors. 26

4 We calculate the total voltage (of all three lines of a three-phase transformer) by multiplying the voltage of each single winding (phase) by the square root of 3 (!3). The reason for this is the angles of each phase are always 120 apart By using this trigonomic formula (don t get scared) we can see where we derive the square root of three. sin = =!3 sin Wye Connection One way of tying three transformers together is in parallel (+ to +) and (- to -). This is called a Wye connection. Here s how a Wye connection is wired: Line Phase eutral 27

5 We call each of the single-phase transformer windings Phases.The combination (hooked together) of the three single-phase transformers (-- ) is called the Line. We really only draw three-phase from the Line side. Also, Line Amps on a Wye connected transformer equals Phase Amps. It would seem that current would not remain the same in a parallel circuit. But, three transformers wired in parallel are not like three resistors in parallel. Transformers produce, instead of consume voltages, so the opposite rules would would apply in this case. A more simplified representation of a Wye looks like this: A B C If we tie together three single-phase, olt, transformers in a Wye configuration our output voltage would look like this: 208 v 3Ø Why do we get 208 volts, three-phase on the Line side (--)? Just multiply olts times the square root of 3 (!3). Remember phase angles of three olt sources. olts x (!3) = 208 volts 28

6 We can also get 208 volts, single-phase on the Line side of this transformer by connecting (-); "A" 208 v 1Ø "C" "B" As you see, we are connecting only two of the three single-phase transformers available. We still only get 208 volts (120 x!3) from this connection, and it is just single-phase. But, we have the capability of using two transformers ( A & B ) to help share the load. Also, we can use two other possible connections (-) and (-) to feed other 208 volt, single-phase loads. Guess what! Yes, it s even possible to get olts, single-phase out of the same transformer. "A" "C" "B" 1Ø Remember, we have the benefit of a neutral conductor and, by connecting (-) we can feed olt, single-phase loads. And, seeing that we are only using one single-phase transformer ( B ), that leaves two other possibilities (- ) and (-) for serving other olt circuits. What s also very useful is that we can balance three olt circuits on just one neutral. In other words, A 208/olt (Wye configured) transformer could supply olt, single-phase equipment (like fluorescent lights), 208 volt, single-phase 29

7 equipment (like range or oven), and 208 volt, three-phase equipment (like heavy machinery). This is what makes three-phase so great! Delta Connections Another way of tying three transformers together is in series (+ to -). This is called a Delta connection. Here s how a Delta connection is wired: Line Phase A more simplified representation of a Delta configuration looks like this: A B C 30

8 By connecting three (240 volt) single-phase transformers (Delta) we get 240 volts, three-phase. We don t multiply by!3 because Line volts equals Phase volts on Delta transformers. It would seem that voltage, would not remain the same in a series type circuit. But, three transformers wired in series are not like three resistors in series. Transformers produce, (instead of consume) voltages, so the opposite rules would would apply in this case. 240 v 240 v 240 v 240 v 3Ø Connect (-) and you ll get 240 volts, single-phase. Connecting (-) or (-) will also give us 240 volts, single-phase. otice how three different 240 volt (1Ø) loads utilize three different transformers. 240 v 240 v 240 v 240 v 1Ø We can still get olts, (single-phase) out of a 240 volt Delta system, but it s going to take some additional work. We are going to have to center-tap one of the 240 volt, single-phase transformers. It s customary to center-tap transformer C... "C" 240 v, 1Ø, 1Ø 31

9 As you can see, we can get olts, (single-phase) from a Delta configuration (-) (-). Unfortunately, all olt loads must be carried on transformer C. Types Of Three-Phase Transformers With the possibility of wiring both the primary and secondary of threephase transformers, there are four possible configurations: (1) Wye/Wye is commonly used for interior wiring systems. (2) Wye/Delta is used to step-down utilities high line voltages. (3) Delta/Delta is often used for industrial applications. (4) Delta/Wye is popular for stepping down transmission lines to fourwire services when neutrals are needed. The most commonly used three-phase transformer is a Delta/Wye configuration. It s used primarily for power distribution from utilities to residential and commercial services. 480 v 3Ø Primary 480 v 480 v 480 v Secondary 208 v 1Ø 208 v 3Ø 1Ø The given voltage designations for a Delta/Wye three-phase transformer is: Primary-Line/Secondary-Line/Secondary-Phase Or in this case: Delta/Wye (480/208/120) 32

10 Phase-To-Phase Let s not forget that three-phase is a product of three individual singlephase transformers. When calculating the Phase-To-Phase relationship the same rules apply as any single-phase transformer. In other words, Our Phase-To- Phase voltage below is 480 to 120 which is a ratio of 4:1. Line Phase Phase Line "A" 480 v "A" "B" 480 v R A T I O "A" eutral "C" 480 v "A" We can also use the the same ladder chart we used for a typical single-phase transformer. Primary Phase Secondary Phase x VA R 480 A 120 T I O x Don t forget that this is just one of three single-phase transformers. There may be efficiency or power factor losses between the primary and secondary phases. But, we ll assume that this transformer is 100% efficient with no power factor loss so the Primary va will equal the Secondary Watts. 33

11 Calculate the Primary va, Primary Amps and Secondary Watts assuming that our Secondary Amps = 100. Primary Phase Secondary Phase x 480 VA R A T I O x Did you get 12,000 Primary va? Multiplying 12,000 by 3 (three transformers) will give us 36 kva (36,000 va). We ll call this our Line kva, which is the sum total of all three-phases. In other words, our transformer rating is 36 kva. It s important to understand the difference between Phase and Line. Phase is the single-phase transformer relationship. Line is the result of the combination of all three transformers hooked together. Line-To-Line There are a few of rules we must remember. (1) Line Watts = Phase Watts x 3 (or) Phase Watts = Line Watts 3 (2) Delta Phase Volts = Delta Line Volts (3) Wye Phase Amps = Wye Line Amps Yes, we can use the ladder Line-To-Line on three-phase transformers Check this out... Primary Secondary! 3 VA 36, ! 3 36, x! 3 x! 3 34

12 For example, knowing the values of Secondary Line Amps (100) and Secondary Line Volts (208) we would multiply going up the ladder to find Secondary Line Watts. In this case, because we are dealing with three-phase, we ll multiply our answer by!3 (1.732). Here s what it looks like... Line Amps (100) x Line Volts (208) x!3 (1.732) = Line Watts (36,000) I know! You get 36, watts. The problem is that 208 volts (3Ø) is not exactly 208 volts. olts x = So we round up! Remember, whenever we see 3Ø, the square root of three!3 must be involved. On the Primary side. stepping down the ladder... Primary va (36,000) Primary Volts (480)!3 (1.732) = Primary Amps (43.3) The key to using the ladder in three-phase is multiplying the answer by!3 going up the ladder, and divide the answer by!3 going down the ladder. Here s a chart that may be useful.!3 va e i x!3 delta line line volts=phase volts amps phase to phase va e i line phase!3 watts line phase 3 w e i volts line phase!3 wye line w e i line amps=phase amps!3 x!3 On the bottom of this chart are a few helpful tools: For the Delta side Amps... line amps phase amps x!3 For the Wye side Amps... line volts phase volts x!3 For the Watts... line watts phase watts x 3 Just cover the value you need to know. For example: line amps = phase amps x!3 (or) phase amps = line amps/!3 35

13 Here s one for you to try; Primary Secondary! 3 VA ! x! 3 x! 3 Delta/Delta A Delta/Delta connected transformer looks like this... Primary Secondary! 3 VA! 3 x! 3 x! 3 There are the rules we must remember. (1) Line Watts = Phase Watts x 3 (or) Phase Watts = Line Watts 3 (2) Delta Phase Volts = Delta Line Volts Phase-To-Phase Although our transformer is connected Delta/Delta the Phase-To-Phase situation has not changed. We still have three single-phase transformers. Let s do some calculations for a Delta/Delta 480/240/120 transformer. First we must find the Secondary Watts, then the Primary va and Primary Amps... 36

14 Primary Phase Secondary Phase x 480 VA R A T I O x Then, we can calculate the values for Line... Primary Secondary! 3 VA 480! 3 7, x! 3 x! 3 3Ø Transformer Size Chart Full-Load Current In Amps At The Line Voltages Listed Below kva Rating olts 240 volts 480 volts 600 volts 2400 volts 4160 volts kva = ( full load current x voltage x!3) 1,000 37

15 Wye Transformer Balancing We might have forgotten the real purpose of a three-phase transformer which is to serve loads. Wye connected 208/olt secondaries can feed loads at three different levels: (1) 208 volts, 3Ø (--) (2) 208 volts, 1Ø (-) or (-) or (-) (3) olts, 1Ø (-) or (-) or (-) "A" "B" "C" A 208 volt (3Ø) load would be distributed on all three Phases... 1/3 on Phase A 1/3 on Phase B 1/3 on Phase C A 208 volt (1Ø) load would be distributed on two Phases... 1/2 on one Phase 1/2 on one Phase A olt (1Ø) load would be distributed on one Phase % on any one Phase For example, Let s balance the following loads Ø, 208 volt, Motor at 9,000 watts 3-1Ø, 208 volt, Ovens at 6,000 watts each 3-1Ø, olt, Light Circuits at 1,800 watts each 38

16 The 208 volt (3Ø) Motor can be distributed on all three Phases... Load Phase A Phase B Phase C Motor (3Ø) 3,000 w (1/3) 3,000 w (1/3) 3,000 w (1/3) The three 208 volt (1Ø) Ovens can be distributed on two Phases each... Load Phase A Phase B Phase C Oven (1Ø) 3,000 w (1/2) 3,000 w (1/2) - Oven (1Ø) 3,000 w (1/2) 3,000 w (1/2) Oven (1Ø) 3,000 w (1/2) 3,000 w (1/2) The three olt (1Ø) Light Circuits can be distributed on one Phases each... Load Phase A Phase B Phase C Light Ckt (1Ø) 1,800 w (100%) - - Light Ckt (1Ø) - 1,800 w (100%) - Light Ckt (1Ø) - - 1,800 w (100%) Totals 10,800 w 10,800 w 10,800 w So, our total demand is 32,400 watts (10,800 x 3). We re lucky, our loads balanced evenly, otherwise, we would have to multiply our largest Phase by three. Looks like we need a 45 kva (standard size) Wye/Wye or Delta/Wye connected transformer. Delta Transformer Balancing What if we had a Delta connected (240/) secondary Delta connected 240/olt secondaries can also feed loads at three different levels: (1) 240 volts, 3Ø (--) (2) 240 volts, 1Ø (-) or (-) or (-) (3) olts, 1Ø (-) or (-) A 240 volt (3Ø) load would be distributed on all three Phases... 1/3 on Phase A 1/3 on Phase B 1/3 on Phase C A 240 volt (1Ø) load would be distributed 100% on one Phase only... 39

17 100% on Phase A 100% on Phase B 100% on Phase C A olt (1Ø) load would be distributed on Phase C only % on Phase C only Let s balance the same loads on a Delta Ø, 208 volt, Motor at 9,000 watts 3-1Ø, 208 volt, Ovens at 6,000 watts each 3-1Ø, olt, Light Circuits at 1,800 watts each The 240 volt (3Ø) Motor can be distributed on all three Phases... Load Phase A Phase B Phase C Motor (3Ø) 3,000 w (1/3) 3,000 w (1/3) 3,000 w (1/3) The three 240 volt (1Ø) Ovens can be distributed on one Phase each... Load Phase A Phase B Phase C Oven (1Ø) 6,000 w (100%) - - Oven (1Ø) - 6,000 w (100%) - Oven (1Ø) - - 6,000 w (100%) The three olt (1Ø) Light Circuits can be distributed on Phase C only... Load Phase A Phase B Phase C Light Ckt (1Ø) - - 1,800 w (100%) Light Ckt (1Ø) - - 1,800 w (100%) Light Ckt (1Ø) - - 1,800 w (100%) Totals 9,000 w 9,000 w 14,400 w Poor old Phase C has to carry 1/3 of all three-phase loads, 100% of any 240 volt (1Ø) loads that distributed on it, and 100% of all olt loads. Our total demand is 43,200 watts (14,400 x 3). This time we re not so lucky, our loads did not balanced evenly. But, we can still use a 45 kva (standard size) Wye/Delta or Delta/Delta connected transformer. 40

18 Open Delta One benefit of a Delta three-phase configuration is that it can still work with just two single-phase transformers. An Open-Delta or V-connected transformer can be used in a emergency or temporary situation.the only problem is that there is a power reduction to just 57.7% of full power. Primary Secondary A third single-phase transformer can be added later if needed. Or, if one original transformer should fail, it can be removed temporarily for repair. In this situation, partial service can be maintained temporarily. Three-Phase Transformer Sample Problem Problem: Calculate the three-phase 480/208/olt transformer required to feed the following loads: one 10 hp, 208 volt, 3Ø Motor (11,096 w) three 3 kw, 208 volt, 1Ø Heaters three 1 kw, olt, 1Ø Light Banks Solution: Loads Balanced: Phase A Phase B Phase C 3Ø Motor (1/3 per phase) 3,699 w 3,699 w 3,699 w 1Ø Heaters (1/2 per phase) 1,500 w 1,500 w - - 1,500 w 1,500 w 1,500 w - 1,500 w 1Ø Light Banks (100% per phase) 1,000 w ,000 w w 7,699 w 7,699 w 7,699 w 41

19 !3 va e i x!3 delta line line volts=phase volts amps phase to phase va e i line phase!3 watts line phase 3 w e i volts line phase!3 wye line w e i line amps=phase amps!3 x!3 Voltages: Primary Line = 480 volts Secondary Line = 208 volts Primary Phase = 480 volts Secondary Phase = olts Amps: Primary Line = 27.7 amps Secondary Line = 64 amps Primary Phase = 16 amps Secondary Phase = 64 amps Wattage: Primary Line = 23,096 watts Secondary Line = 23,096 watts Primary Phase = 7,699 watts Secondary Phase = 7,699 watts Use (25 kva) rated, 3Ø, 480/208/olt transformer. 42

20 Transformer Problems (1) The phase current of a fully loaded 36 kva, 208/olt, three-phase transformer would be amps. (a) 300 (b) 175 (c) 100 (d) 75 (2) If ten single phase 208 volt, 5000 watt office machines were on the same transformer, the total current with all the machines operating would be amps. (a) 120 (b) 208 (c) 240 (d) 416 (3) With a three-phase, delta-wye transformer bank having a 480 volt primary and a 208/olt secondary, the line current of the secondary is 120 amps. The primary line current will be amps. (a) 480 (b) 208 (c) 52 (d) 30 (4) The voltage from either leg, excluding the hi-leg, to neutral of a threephase, delta-delta hi-leg transformer system with a secondary of 240/120 volts is volts. (a) 120 (b) 190 (c) 208 (d) 240 (5) If all the load on a three-phase 480/208/olt transformer is single-phase olt, the size of the neutral on a 24 kva transformer would have a load current rating of amps. (a) 24 (b) 67 (c) 75 (d) 100 (6) If a three-phase wattmeter reads 12,970 watts on a three-phase 208/120 volt system and each ammeter reads 36 amps, the power factor would be. (a) 1 (b).96 (c).62 (d) none of these (7) With a three-phase delta-delta, hi-leg transformer system, the primary is 480 volts, and the secondary is 240/olts, the turns ratio for the transformer is. (a) 2 to 1 (b) 4 to 1 (c) 1 to 4 (d) 1 to 2 43

21 (8) If three 115 volt, 1,800 watt lighting circuits and two 2 H.P. single-phase 115 volt pumps are balanced as closely as possible on a three-wire 230 volt system. The conductor amp rating will be approximately amps. (a) 15 (b) 45 (c) 48 (d) 54 (9) The secondary load of a three-phase 480/208/olt includes; 1- Motor (3 hp, 3Ø, 208 volt) 4- Heat Strips (2500 va, 3Ø, 208 volt) 1- Induction Heater (2000 va, 1Ø, 208 volt) 3- Light Banks (1500 va, 1Ø, olt) Calculate- Primary Feeder? Secondary Phase Current? Transformer Size Required? (10) Determine the three-phase transformer requirements based on the following loads: (voltages are 480/208/olts connected Delta-Wye) 1- Motor (15 hp, 3Ø, 208 volt) 5- Water Heaters (2500 va, 1Ø, 208 volt) 2- Dryers (1500 va, 1Ø, 208 volt) 1- Cooktop (1600 va, 1Ø, 208 volt) 4- Light Circuits (3000 va, 1Ø, olt) Calculate- Primary Feeder? Secondary Phase Current? Transformer Size Required (kva)? 44

Module 19 Units 1-3 Three-Phase Transformers

Module 19 Units 1-3 Three-Phase Transformers Module 19 Units 1-3 Three-Phase Transformers 1. What is the difference between a three-phase transformer and a bank of singlephase transformers? Windings from all three phases are wound on the same core

More information

Chapter 24. Three-Phase Voltage Generation

Chapter 24. Three-Phase Voltage Generation Chapter 24 Three-Phase Systems Three-Phase Voltage Generation Three-phase generators Three sets of windings and produce three ac voltages Windings are placed 120 apart Voltages are three identical sinusoidal

More information

Three-phase AC circuits

Three-phase AC circuits Three-phase AC circuits 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 information

A fter studying this unit, you should be able to:

A fter studying this unit, you should be able to: Unit 12 Three-Phase Circuits objectives A fter studying this unit, you should be able to: Discuss the differences between three-phase and single-phase voltages. Discuss the characteristics of delta and

More information

Transformer Calculations

Transformer 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 alternating-current

More information

Figure. 1 - Split Phase 240/120V circuit (180 phase shift)

Figure. 1 - Split Phase 240/120V circuit (180 phase shift) This technical note describes the option of connecting the 60Hz XW Inverter/Charger to a three-phase source by using a transformer to convert the AC source to split-phase 240/120V. INTRODUCTION: Split-phase

More information

Definition AC Power Distribution

Definition AC Power Distribution COMMON AC POWER DISTRIBUTION CONFIGURATIONS The input voltage needed to power electronic equipment is provided by the manufacture in the product specifications. Matching this requirement to the facility

More information

Chapter 5 TRANSFORMERS

Chapter 5 TRANSFORMERS Chapter 5 TRANSFORMERS Objective Understand the transformer nameplate Describe the basic construction features of a transformer. Explain the relationship between voltage, current, impedance, and power

More information

Three phase circuits

Three phase circuits Three phase circuits THREE PHASE CIRCUITS THREE-PHASE ADVANTAGES 1. The horsepower rating of three-phase motors and the kva rating of three-phase transformers are 150% greater than single-phase motors

More information

Lecture Notes ELE A6

Lecture Notes ELE A6 ecture Notes EE A6 Ramadan El-Shatshat Three Phase circuits 9/12/2006 EE A6 Three-phase Circuits 1 Three-phase Circuits 9/12/2006 EE A6 Three-phase Circuits 2 Advantages of Three-phase Circuits Smooth

More information

BALANCED THREE-PHASE CIRCUITS

BALANCED THREE-PHASE CIRCUITS BALANCED THREE-PHASE CIRCUITS The voltages in the three-phase power system are produced by a synchronous generator (Chapter 6). In a balanced system, each of the three instantaneous voltages have equal

More information

GENERATOR SELECTION. a. Three phase - 120/208V, 3 phase, 4W wye; 277/408, 3 phase, 4W wye; * 120/240V 3 phase, 4W Delta

GENERATOR SELECTION. a. Three phase - 120/208V, 3 phase, 4W wye; 277/408, 3 phase, 4W wye; * 120/240V 3 phase, 4W Delta GENERATOR SELECTION Generators must be sized to handle their load based on the continuous KW, kilowatt load, and KVA, kilovoltamp load, and the worst case starting load KW + KVA. They must be derated for

More information

Alternating current three-phase circuits

Alternating current three-phase circuits Unit. C HEE-PHE CCU lternating current three-phase circuits Unit. C HEE-PHE CCU COE: hree-phase systems characteristics Generation of three-phase voltages hree-phase loads -Y and Y- transformation nstantaneous

More information

USE OF A SINGLE ELEMENT WATTMETER OR WATT TRANSDUCER ON A BALANCED THREE-PHASE THREE-WIRE LOAD WILL NOT WORK. HERE'S WHY.

USE OF A SINGLE ELEMENT WATTMETER OR WATT TRANSDUCER ON A BALANCED THREE-PHASE THREE-WIRE LOAD WILL NOT WORK. HERE'S WHY. USE OF A SINGLE ELEMENT WATTMETER OR WATT TRANSDUCER ON A BALANCED THREE-PHASE THREE-WIRE LOAD WILL NOT WORK. HERE'S WHY. INTRODUCTION Frequently customers wish to save money by monitoring a three-phase,

More information

Series and Parallel Circuits

Series and Parallel Circuits Series and Parallel Circuits Components in a circuit can be connected in series or parallel. A series arrangement of components is where they are inline with each other, i.e. connected end-to-end. A parallel

More information

Equipment: Power Supply, DAI, Variable resistance (8311), Variable inductance (8321)

Equipment: Power Supply, DAI, Variable resistance (8311), Variable inductance (8321) Lab 4: 3-phase circuits. Objective: to study voltage-current relationships in 3-phase circuits; to learn to make delta and Y connections; to calculate and measure real, apparent, and reactive powers. Equipment:

More information

Unit 33 Three-Phase Motors

Unit 33 Three-Phase Motors Unit 33 Three-Phase 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 information

3-Phase AC Calculations Revisited

3-Phase AC Calculations Revisited AN110 Dataforth Corporation Page 1 of 6 DID YOU KNOW? Nikola Tesla (1856-1943) came to the United States in 1884 from Yugosiavia. He arrived during the battle of the currents between Thomas Edison, who

More information

Understanding Power Factor and How it Affects Your Electric Bill. Presented by Scott Peele PE

Understanding Power Factor and How it Affects Your Electric Bill. Presented by Scott Peele PE Understanding Power Factor and How it Affects Your Electric Bill Presented by Scott Peele PE Understanding Power Factor Definitions kva, kvar, kw, Apparent Power vs. True Power Calculations Measurements

More information

Ground Fault Protection

Ground Fault Protection GE Energy Industrial Solutions Ground Fault Protection Digital Specification Program Latin America Ground Fault. I. Introduction In the electrical systems always exists the possibility of having shutdowns

More information

codeissues APPLYING DEMAND FACTOR AND DIVERSITY FACTOR PER THE NEC By James Stallcup Sr., NEC/OSHA Consultant

codeissues APPLYING DEMAND FACTOR AND DIVERSITY FACTOR PER THE NEC By James Stallcup Sr., NEC/OSHA Consultant By James Stallcup Sr., NEC/OSHA Consultant APPLYING DEMAND FACTOR AND DIVERSITY FACTOR PER THE NEC Don t be confused by these terms! There are two terms used in calculating loads in electrical systems

More information

Application guide for power factor testing of power & distribution transformers

Application guide for power factor testing of power & distribution transformers Application guide for power factor testing of power & distribution transformers Introduction The transformer is probably one of the most useful electrical devices ever invented. It can raise or lower the

More information

Transformer Basics Information Guide

Transformer Basics Information Guide Property of Motion Laboratories, Inc. Transformer Basics Information Guide 2014 Motion Laboratories, Inc. Created By: Jim Herrick / Michael Shaw Approved By: Peter Herrmann Page: 1 Transformer Definition

More information

The generation and supply of electricity within the U.K is achieved through the use of a 3-phase system.

The generation and supply of electricity within the U.K is achieved through the use of a 3-phase system. Three Phase Electricity Supplies and Systems The generation and supply of electricity within the U.K is achieved through the use of a 3-phase system. This consists of 3 separate phase conductors along

More information

Single and Three Phase Transformer Testing Using Static Motor Circuit Analysis Techniques

Single 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 ALL-TEST Pro, LLC Old Saybrook, CT Introduction Field and shop testing of

More information

September, Rectifier Duty Transformers

September, Rectifier Duty Transformers September, 2013 Rectifier Duty Transformers Transformers play an important role in industrial applications, especially in metallurgical plants and processes. Very high currents need to be supplied for

More information

Three-Phase Electric Power Distribution for Computer Data Centers

Three-Phase Electric Power Distribution for Computer Data Centers Three-hase Electric ower Distribution for Computer Data Centers WHITE AER E901 Geist January 008 Summary This paper will describe the characteristics of three-phase power and outline the advantages of

More information

1 Introduction. 2 The Symmetrical Component Transformation. J.L. Kirtley Jr.

1 Introduction. 2 The Symmetrical Component Transformation. J.L. Kirtley Jr. Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.06 Introduction to Power Systems Class Notes Chapter 4 Introduction To Symmetrical Components J.L. Kirtley

More information

(3 )Three Phase Alternating Voltage and Current

(3 )Three Phase Alternating Voltage and Current EEE 2015 EECTRCS (3) Monophase 1 Three phase Three phase electric power is a common method of alternating current electric power generation, transmission, and distribution. t is a type of polyphase system

More information

Delta and Wye 3-phase circuits

Delta and Wye 3-phase circuits Delta and Wye 3-phase circuits 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 information

The Fundamentals of Three-Phase Power Measurements. Application Note

The Fundamentals of Three-Phase Power Measurements. Application Note The Fundamentals of - Power Measurements pplication ote pplication ote 0 120 240 360 Figure 1. -phase voltage wavefm. Figure 2. -phase voltage vects. 100Ω 100Ω Figure 4. -phase supply, balanced load -

More information

Module Overview. This module presents the following topics: Principle of Operation Types of Transformers Operating Considerations and Limitations

Module Overview. This module presents the following topics: Principle of Operation Types of Transformers Operating Considerations and Limitations Course Outline 1. Introduction to WECC 2. Fundamentals of Electricity 3. Power System Overview 4. Principles of Generation 5. Substation Overview 6. Transformers 7. Power Transmission 8. System Protection

More information

Lecture 5: Transformers(continued)

Lecture 5: Transformers(continued) Lecture 5: Transformers(continued) Equivalent circuit of a transformer Figure (1) shows an equivalent circuit of a transformer. R 1 and R 2 represent the resistances of the primary and secondary windings

More information

Three Phase Circuits. Three Phase Circuits

Three Phase Circuits. Three Phase Circuits Three Phase Circuits 1 Three Phase Circuits Chater Objectives: Be familiar with different three-hase configurations and how to analyze them. Know the difference between balanced and unbalanced circuits

More information

Technical Reference. Introduction. Capstone MicroTurbine Electrical Installation

Technical Reference. Introduction. Capstone MicroTurbine Electrical Installation Capstone Capstone Turbine Corporation 21211 ordhoff Street Chatsworth CA 91311 USA Telephone: (818) 734-5300 Facsimile: (818) 734-5320 Website: www.microturbine.com Technical Reference Capstone MicroTurbine

More information

TRANSFORMER: THREE PHASE

TRANSFORMER: THREE PHASE CONTENTS Transformer : Three Phase 1211 C H A P T E R 33 Learning Objectives Three-phase Transformers Three-phase Transformer Connections Star/Star or Y/Y Connection Delta-Delta or Connection Wye/Delta

More information

Induction Motor (No-Load Test) Induction Motor (Blocked Rotor Test) Example (No-Load/Blocked Rotor Tests) The results of the no-load and blocked rotor tests on a three-phase, 60 hp, 2200 V, six-pole, 60

More information

Introduction to Transformer Rated Meters

Introduction to Transformer Rated Meters Introduction to Transformer Rated Meters Module 141 87 rd Annual Short Course and Conference Southeastern Electricity Metering Association November, 2012 Orlando, FL Larry Waters General Electric Company

More information

ACCURACY OF POTENTIALTRANSFORMERS

ACCURACY OF POTENTIALTRANSFORMERS 8 VOLTAGE TRANSFORMERS Two types of voltage transformer are used for protective-relaying purposes, as follows: (1) the "instrument potential transformer," hereafter to be called simply "potential transformer,"

More information

Transformer / Line Loss Calculations

Transformer / Line Loss Calculations 70072-0153-07 TECHNICAL NOVEMBER 2006 Transformer / Line Loss Calculations This document gives a brief overview of transformer loss and line loss calculations and describes how these calculations are implemented

More information

Voltage Drop (Single-Phase)

Voltage Drop (Single-Phase) Voltage Drop (Single-Phase) To Find: To Find Voltage Drop Formula: 2 x K x L x I V.D. = ------------------- C.M. Variables: C.M. = Circular Mill Area (Chapter 9, Table 8) To Find Voltage Drop Percentage

More information

615xx, 616xx, 617xxx, 646x, 64xx, 65xx Series Programmable AC source

615xx, 616xx, 617xxx, 646x, 64xx, 65xx Series Programmable AC source Chroma Systems Solutions, Inc. AC Power Definitions 615xx, 616xx, 617xxx, 646x, 64xx, 65xx Series Programmable AC source Keywords: Peak, RMS, Phase, Inrush Current, Power Factor, Crest Factor, Apparent

More information

Rule 5.500 Fast Track Analysis for National Life Insurance Co.

Rule 5.500 Fast Track Analysis for National Life Insurance Co. Rule 5.500 Fast Track Analysis for National Life Insurance Co. For a 500 kw Solar array to be located at 155 Northfield Street in Montpelier, Vermont Green Mountain Power Pam Allen Date: 5/31/13 SECTION

More information

Ohm s Law. George Simon Ohm

Ohm s Law. George Simon Ohm Ohm s Law George Simon Ohm The law which governs most simple and many complex electrical phenomena is known as Ohm s Law. It is the most important law in electricity. In 1827, a German locksmith and mathematician

More information

6/14/02 Chapter 2: Basic Electrical Power Fundamentals 1/6

6/14/02 Chapter 2: Basic Electrical Power Fundamentals 1/6 Basic Electrical Power Fundamentals LOAD REFERENCE Kilowatts Kilovolt amps Power Factor PF Motors KW KVA USE NEC 430-148 KW < KVA.6-.95 and 430-150 to find current for given HP Indancescant Lighting USE

More information

Effective: September 10, 2006 Vermont Attachment 1 to Rule 5.500 Public Service Board Page 1 of 6

Effective: September 10, 2006 Vermont Attachment 1 to Rule 5.500 Public Service Board Page 1 of 6 Public Service Board Page 1 of 6 STANDARD APPLICATION FOR INTERCONNECTION OF GENERATION RESOURCES IN PARALLEL TO THE ELECTRIC SYSTEM OF: (Interconnecting Utility) Preamble and Instructions: An owner of

More information

Power System Harmonics

Power System Harmonics Pacific Gas and Electric Company Power System Harmonics What are power system harmonics? Ideally, voltage and current waveforms are perfect sinusoids. However, because of the increased popularity of electronic

More information

AC Generators. Basic Generator

AC 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 information

THREE PHASE CIRCUITS

THREE PHASE CIRCUITS THREE PHASE CIRCUITS A. PREPARATION 1. Three Phase Voltages and Systems 2. The Determination of Phase Sequence 3. Blondel's Theorem and Its Consequences 4. References B. EXPERIMENT 1. Equipment List 2.

More information

1 Introduction. 2 Two Phases. J.L. Kirtley Jr.

1 Introduction. 2 Two Phases. J.L. Kirtley Jr. Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.061 Introduction to Power Systems Class otes Chapter 3 Polyphase etworks J.L. Kirtley Jr. 1 Introduction

More information

Pre-certificati on V oltali!e Drop Calculations

Pre-certificati on V oltali!e Drop Calculations 7 Pre-certificati on V oltali!e Drop Calculations Rule 8-102 governs the maximum amount of voltage drop for an electrical installation (this includes service, feeder and branch circuit conductors). Subrule

More information

Lab 6: Transformers in parallel and 3-phase transformers.

Lab 6: Transformers in parallel and 3-phase transformers. Lab 6: Transformers in parallel and 3-phase transformers. Objective: to learn how to connect transformers in parallel; to determine the efficiency of parallel connected transformers; to connect transformers

More information

Basic Electrical Theory

Basic Electrical Theory Basic Electrical Theory Power Principles and Phase Angle PJM State & Member Training Dept. PJM 2014 10/24/2013 Objectives At the end of this presentation the learner will be able to; Identify the characteristics

More information

Buck and Boost Transformer

Buck and Boost Transformer Buck and Boost Transformer Class 7414 CONTENTS Description Page Product Description.................................................. 2 Specifications.......................................................

More information

Radial Distribution Test Feeders

Radial Distribution Test Feeders Radial Distribution Test Feeders Distribution System Analysis Subcommittee Report Abstract: Many computer programs are available for the analysis of radial distribution feeders. In 1992 a paper was published

More information

2013 ElectriCities Electric Utility Webinar Series

2013 ElectriCities Electric Utility Webinar Series 2013 ElectriCities Electric Utility Webinar Series Sizing of Transformers Calculation of Loads Demand and Demand Factor Demand The value of electrical power required for a particular load. Expressed in

More information

TRANSFORMERS. Unit 14 OBJECTIVES

TRANSFORMERS. Unit 14 OBJECTIVES Unit 14 TRANSFORMERS OBJECTIVES After studying this unit, the student will be able to state the purpose of a transformer. explain the principle of mutual induction. determine the output voltage of a transformer

More information

4.5 Transformer Connections

4.5 Transformer Connections ELECTRIC POWER SYSTEMS IN COMMERCIAL BUILDINGS IEEE Std 241-1990 5) Flat Billing Ñ Certain applications involve service to the load of a Þxed characteristic. For such loads, the supplying utility may offer

More information

1. The type of service available at any particular location should be determined by inquiry at PG&E's local office.

1. The type of service available at any particular location should be determined by inquiry at PG&E's local office. Revised Cal. P.U.C. Sheet No. 11257-E Cancelling Revised Cal. P.U.C. Sheet No. 6925-E ELECTRIC RULE NO. 2 Sheet 1 A. GENERAL 1. The type of service available at any particular location should be determined

More information

101 BASICS SERIES LEARNING MODULE 4: TRANSFORMERS. Cutler-Hammer

101 BASICS SERIES LEARNING MODULE 4: TRANSFORMERS. Cutler-Hammer 101 BASICS SERIES LEARNING MODULE 4: TRANSFORMERS Cutler-Hammer WELCOME Welcome to Module 4, which is about the transformer. In this module you will begin to appreciate how the topics discussed in previous

More information

SECTION 26 09 13 - POWER MONITOR FOR ELECTRICAL, STEAM CONDENSATE, AND WATER PART I - GENERAL

SECTION 26 09 13 - POWER MONITOR FOR ELECTRICAL, STEAM CONDENSATE, AND WATER PART I - GENERAL SECTION 26 09 13 - POWER MONITOR FOR ELECTRICAL, STEAM CONDENSATE, AND WATER PART I - GENERAL 1.1 SUMMARY A. This section describes the requirements for the installation of Power Monitors and associated

More information

Release 1.1, January 2012

Release 1.1, January 2012 THREE-PHASE TRANSFORMERS Release 1.1, January 2012 Har Hotzvim Industrial Park, 14 Hartom St., P.O.B. 45029, Jerusalem 91450, Israel Tel: 972-2-588-8222 Fax: 972-2-582-8875 Email: info@gamatronic.co.il

More information

Chapter 3: Electricity

Chapter 3: Electricity Chapter 3: Electricity Goals of Period 3 Section 3.1: To define electric charge, voltage, and energy Section 3.2: To define electricity as the flow of charge Section 3.3: To explain the generation electricity

More information

JEFFERSON ELECTRIC, INC. Buck-Boost Transformer Application Manual

JEFFERSON ELECTRIC, INC. Buck-Boost Transformer Application Manual JEFFERSON ELECTRIC, INC. Buck-Boost Transformer Application Manual Revised on February 15, 2012 Table of Contents I. Introduction... 2 II. Choosing the Proper Transformer... 2 III. Rapid Selector Charts...

More information

Objectives 316 CHAPTER 6 POWER

Objectives 316 CHAPTER 6 POWER Objectives Explain the relationship between power, current, and voltage in electrical systems. Explain the relationship between power, current, and resistance in electrical systems. Calculate energy usage

More information

TRANSFORMER LOSS COMPENSATION FOR METERMEN PRESENTED BY: MICHAEL K. BEARDEN

TRANSFORMER LOSS COMPENSATION FOR METERMEN PRESENTED BY: MICHAEL K. BEARDEN TRANSFORMER LOSS COMPENSATION FOR METERMEN PRESENTED BY: MICHAEL K. BEARDEN WHAT are transformer losses? TRANSFORMER LOSS COMPENSATION THE WHAT, WHEN, WHO, WHERE AND HOW Transformer losses can be viewed

More information

What is a transformer and how does it work?

What is a transformer and how does it work? Why is a transformer needed? A control transformer is required to supply voltage to a load which requires significantly more current when initially energized than under normal steady state operating conditions.

More information

Buck - Boost Transformers

Buck - Boost Transformers Buck - Boost Transformers Contents Buck - Boost Transformers - Terms & Definitions... 48 Buck - Boost Transformers - Sizing... 50 Quick Reference Chart - 08, 0, 40 Volts Single & Three Phase... 5 Single

More information

Motor Protection Voltage Unbalance and Single-Phasing

Motor Protection Voltage Unbalance and Single-Phasing Motor Protection Voltage Unbalance and Single-Phasing Cooper Bussmann contributes the following information, which is an excerpt from their 190-page handbook SPD Selecting Protective Devices Based on the

More information

Services. Three Phase Service

Services. Three Phase Service Services Primary Service vs Secondary Service Overhead vs Underground Common Service Types Three Phase Wye Closed Open Delta Corner Grounded Center Tapped Open Single Phase Three Phase Service Wye Delta

More information

HPS Universal. Single and Three Phase Potted. Buck-Boost Transformers. Buck-Boost Applications & Standard Specification... 80

HPS Universal. Single and Three Phase Potted. Buck-Boost Transformers. Buck-Boost Applications & Standard Specification... 80 Buck-Boost Transformers Single and Three Phase Potted Buck-Boost Transformers Buck-Boost Applications & Standard Specification... 80 Selecting Buck-Boost Transformers... 81 Single Phase Selection Tables...

More information

Electrician s Math and Basic Electrical Formulas

Electrician s Math and Basic Electrical Formulas UNIT 1 Electrician s Math and Basic Electrical Formulas INTRODUCTION TO UNIT 1 ELECTRICIAN S MATH AND BASIC ELECTRICAL FORMULAS In order to construct a building that will last into the future, a strong

More information

Three-Phase AC Power Circuits

Three-Phase AC Power Circuits Electricity and New Energy Three-Phase AC Power Circuits Student Manual 86360-F0 Order no.: 86360-00 Revision level: 10/2014 By the staff of Festo Didactic Festo Didactic Ltée/Ltd, Quebec, Canada 2010

More information

INTRODUCTION. THREE PHASE SSRs DEFINED & DESCRIBED

INTRODUCTION. THREE PHASE SSRs DEFINED & DESCRIBED pero 1 Three Phase Solid State Relays & Their Application in Three Phase Heating Circuits By Paul Bachman, Fellow Engineer, Dr. Oscar Montero, R&D Manager, and Doug Sherman, FSAE Manager, Crydom, Inc.

More information

ELECTRONIC POWER SYSTEMS

ELECTRONIC POWER SYSTEMS ELECTRONIC POWER SYSTEMS TRADEOFFS BETWEEN SINGLE-PHASE & THREE-PHASE POWER WHITE PAPER: TW0057 1 Executive Summary Modern Electronic Systems are quite often powered from a three-phase power source. While

More information

How Does a Generator Work?

How Does a Generator Work? How Does a Generator Work? Clifford Power Systems is one of the largest full service generator providers in the United States. Our generator experts specialize in equipment, service, parts and rental of

More information

THE PER-UNIT SYSTEM. (2) The per-unit values for various components lie within a narrow range regardless of the equipment rating.

THE PER-UNIT SYSTEM. (2) The per-unit values for various components lie within a narrow range regardless of the equipment rating. THE PER-UNIT SYSTEM An interconnected power system typically consists of many different voltage levels given a system containing several transformers and/or rotating machines. The per-unit system simplifies

More information

Module Title: Electrotechnology for Mech L7

Module Title: Electrotechnology for Mech L7 CORK INSTITUTE OF TECHNOLOGY INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ Autumn Examinations 2012 Module Title: Electrotechnology for Mech L7 Module Code: ELEC7007 School: School of Mechanical, Electrical and Process

More information

adjustment performs all the voltage limiting, the tapped Fig 1 SCR and Transformer transformer option lets you run with a higher power factor.

adjustment performs all the voltage limiting, the tapped Fig 1 SCR and Transformer transformer option lets you run with a higher power factor. Silicon Controlled Rectifiers and Transformers in Power Control How transformers extend the capabilities of SCRs Arthur Holland, Holland Technical Skills The most common and economical arrangement of SCR

More information

IVE(TY) Department of Engineering Electrical Machines 1

IVE(TY) Department of Engineering Electrical Machines 1 Hour 8 slide 1 Introduction Transformer Transformer is a machine that has no moving parts but is able to transform alternating voltages and currents from high to low (step-up transformer ) and vice versa

More information

Rotary Phase Converters

Rotary Phase Converters FACTS from Ronk Electrical Industries, Inc. Bulletin 11981 Rotary Phase Converters ROTOVERTER Pat. No. 3,670,238 ROTO-CON Pat. No. 4,158,225 What are the ROTO-CON and ROTOVERTER power converters? The ROTO-CON

More information

Questions. Question 1

Questions. Question 1 Question 1 Questions Explain why transformers are used extensively in long-distance power distribution systems. What advantage do they lend to a power system? file 02213 Question 2 Are the transformers

More information

DISTRIBUTION SYSTEMS INDEX NOV 06 SECTION 2. Detroit...2-1-5 Ann Arbor...2-1-6 Mt. Clemens...2-1-7 Port Huron...2-1-8

DISTRIBUTION SYSTEMS INDEX NOV 06 SECTION 2. Detroit...2-1-5 Ann Arbor...2-1-6 Mt. Clemens...2-1-7 Port Huron...2-1-8 DISTRIBUTION SYSTEMS INDEX NOV 06 SECTION 2 Kinds and Uses of Service... 2-1-1 and 2-1-2 Wye Network Area Maps Detroit...2-1-5 Ann Arbor...2-1-6 Mt. Clemens...2-1-7 Port Huron...2-1-8 Transformer Connections

More information

Electrical Power. How do you calculate electrical power? 14.3

Electrical Power. How do you calculate electrical power? 14.3 . Name: Date: Electrical Power 14.3 How do you calculate electrical power? In this skill sheet you will review the relationship between electrical power and Ohm s law. As you work through the problems,

More information

Electrical Construction Technology

Electrical Construction Technology Job Ready Assessment Blueprint Electrical Construction Technology Test Code: 4130 / Version: 01 Copyright 2011. All Rights Reserved. General Assessment Information Electrical Construction Technology Blueprint

More information

Short Circuit Current Calculations

Short 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 information

Point-To-Point Method Of Short-Circuit Calculation

Point-To-Point Method Of Short-Circuit Calculation Point-To-Point Method Of Short-Circuit Calculation Calculation Of Short-Circuit Currents Point-To-Point Method. Adequate interrupting rating and protection of electrical components are two essential aspects

More information

Power Transducer User s Guide

Power Transducer User s Guide Power Transducer User s Guide Volume 1 Power Transducer User's Guide Volume 1 Applying Power Transducers Volume 1 Page I. Why Monitor Power?... 1 II. Beginning Definitions... 3 III. Basic Concepts of AC

More information

Transformer circuit calculations

Transformer 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 information

Loading Considerations When Paralleling Transformers

Loading Considerations When Paralleling Transformers Application Guide 7400DB0701 02/2007 Nashville, TN, USA Loading Considerations When Paralleling Transformers Class 7400 Retain for future use. Introduction Principles of Paralleling This application guide

More information

3. TYPES OF SERVICE AVAILABLE. 3.1 Scope

3. TYPES OF SERVICE AVAILABLE. 3.1 Scope 3. TYPES OF SERVICE AVAILABLE 3.1 Scope UI supplies 60 hertz, alternating current with different voltage and ampere ratings. Not all voltage and ampere ratings are available throughout the entire service

More information

DANGER! HIGH VOLTAGE HAZARD

DANGER! HIGH VOLTAGE HAZARD WattNode Pulse kwh Transducer Connection Instructions For use with HOBO H21, H22, U30, UX90, and UX120 series data loggers, and HOBO data nodes Applies to these WattNode Pulse kwh Transducers: Onset Part

More information

TESLA Recorder Power Metering Setup Configuration for 3 and 2 Element Watt/VAR Metering

TESLA Recorder Power Metering Setup Configuration for 3 and 2 Element Watt/VAR Metering TESLA Recorder Power Metering Setup Configuration for 3 and 2 Element Watt/VAR Metering Introduction This application note will assist the user to set up 3-phase metering to monitor Watt, VAR and VA power

More information

REVIEW QUESTIONS. A6 Test Preparation

REVIEW QUESTIONS. A6 Test Preparation A6 Test Preparation Note: The lessons, exercises and tests in this manual are great preparation for taking the ASE A6 (electrical) certification test. However, that s only for the topics we ve covered.

More information

CURRENT TRANSFORMERS INSTALLATION GUIDE

CURRENT 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 information

Electric Motor Brake Horsepower Calculations

Electric Motor Brake Horsepower Calculations Electric Motor Brake Horsepower Calculations By Norm Christopherson These motor calculations are contained here as they apply to the changing conditions of the blower motor when pulley adjustments are

More information

Power measurement in balanced 3 phase circuits and power factor improvement. 1 Power in Single Phase Circuits. Experiment no 1

Power measurement in balanced 3 phase circuits and power factor improvement. 1 Power in Single Phase Circuits. Experiment no 1 Experiment no 1 Power measurement in balanced 3 phase circuits and power factor improvement 1 Power in Single Phase Circuits Let v = m cos(ωt) = cos(ωt) is the voltage applied to a R-L circuit and i =

More information

Chapter 12: Three Phase Circuits

Chapter 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 information

S15--Physics current and Circuit PRACTICE

S15--Physics current and Circuit PRACTICE Name: Class: Date: ID: A S5--Physics current and Circuit PRACTICE Multiple Choice Identify the choice that best completes the statement or answers the question.. Three resistors, with values of 2.0, 4.0

More information

Direction of current flow. Heat produced in a resistor. Heat produced in a resistor. L 27 Electricity and Magnetism [4]

Direction of current flow. Heat produced in a resistor. Heat produced in a resistor. L 27 Electricity and Magnetism [4] L 27 Electricity and Magnetism [4] simple electrical circuits direct current DC Alternating current (AC) vs direct current (DC) electric power distribution household electricity household wiring GFIC s

More information