Curso sobre sistemas trifsicos

Manandes SCCI calle 10 #1004 y Av. 10 Manta- Ecuador

Formacin Tcnica Div. Tele/fax 624078 626652 email: manandes@ecua.net.ec

E = Voltage / I = Amps /W = Watts / PF = Power Factor / Eff = Efficiency / HP = HorsepowerAC/DC Formulas

To FindDirect CurrentAC / 1phase 115v or 120vAC / 1phase208,230, or 240vAC 3 phaseAll Voltages

Amps whenHorsepower is KnownHP x 746E x EffHP x 746E x Eff X PFHP x 746E x Eff x PFHP x 7461.73 x E x Eff x PF

Amps whenKilowatts is knownkW x 1000EkW x 1000E x PFkW x 1000E x PFkW x 10001.73 x E x PF

Amps whenkVA is knownkVA x 1000EkVA x 1000EkVA x 10001.73 x E

KilowattsI x E1000I x E x PF1000I x E x PF1000I x E x 1.73 PF1000

Kilovolt-AmpsI x E1000I x E1000I x E x 1.731000

Horsepower(output)I x E x Eff746I x E x Eff x PF746I x E x Eff x PF746I x E x Eff x 1.73 x PF746

Three Phase Values

For 208 volts x 1.732, use 360For 230 volts x 1.732, use 398For 240 volts x 1.732, use 416For 440 volts x 1.732, use 762For 460 volts x 1.732, use 797For 480 Volts x 1.732, use 831

E = Voltage / I = Amps /W = Watts / PF = Power Factor / Eff = Efficiency / HP = HorsepowerAC Efficiency and Power Factor Formulas

To FindSingle PhaseThree Phase

Efficiency746 x HPE x I x PF746 x HPE x I x PF x 1.732

Power FactorInput WattsV x AInput WattsE x I x 1.732

Power - DC Circuits

Watts = E xI

Amps = W / E

Ohm's Law / Power Formulas

P = watts

I = ampsR = ohmsE = Volts

Voltage Drop Formulas

Single Phase(2 or 3 wire)VD =2 x K x I x LCMK = ohms per mil foot

(Copper = 12.9 at 75)

(Alum = 21.2 at 75)

Note:K value changes with temperature. See Code chapter 9, Table 8L = Length of conductor in feet

I = Current in conductor (amperes)

CM = Circular mil area of conductor

CM=2K x L x IVD

Three PhaseVD=1.73 x K x I x LCM

CM=1.73 x K x L x IVD

Calculating Motor Speed:A squirrel cage induction motor is a constant speed device. It cannot operate for any length of time at speeds below those shown on the nameplate without danger of burning out.

To Calculate the speed of a induction motor, apply this formula:Srpm = 120 x F PSrpm = synchronous revolutions per minute.120 = constantF = supply frequency (in cycles/sec)P = number of motor winding poles

Example: What is the synchronous of a motor having 4 poles connected to a 60 hz power supply?

Srpm = 120 x F PSrpm = 120 x 60 4Srpm = 7200 4Srpm = 1800 rpm

Calculating Braking Torque:Full-load motor torque is calculated to determine the required braking torque of a motor.To Determine braking torque of a motor, apply this formula:T = 5252 x HP rpmT = full-load motor torque (in lb-ft)5252 = constant (33,000 divided by 3.14 x 2 = 5252)HP = motor horsepowerrpm = speed of motor shaft

Example: What is the braking torque of a 60 HP, 240V motor rotating at 1725 rpm?

T = 5252 x HP rpmT = 5252 x 60 1725T = 315,120 1725T = 182.7 lb-ft

Calculating Work:Work is applying a force over a distance. Force is any cause that changes the position, motion, direction, or shape of an object. Work is done when a force overcomes a resistance. Resistance is any force that tends to hinder the movement of an object.If an applied force does not cause motion the no work is produced.

To calculate the amount of work produced, apply this formula:

W = F x DW = work (in lb-ft)F = force (in lb)D = distance (in ft)

Example: How much work is required to carry a 25 lb bag of groceries vertically from street level to the 4th floor of a building 30' above street level?

W = F x DW = 25 x 30W = 750 -lb

Calculating Torque:Torque is the force that produces rotation. It causes an object to rotate. Torque consist of a force acting on distance. Torque, like work, is measured is pound-feet (lb-ft). However, torque, unlike work, may exist even though no movement occurs.

To calculate torque, apply this formula:T = F x DT = torque (in lb-ft)F = force (in lb)D = distance (in ft)Example: What is the torque produced by a 60 lb force pushing on a 3' lever arm?

T = F x DT = 60 x 3T = 180 lb ft

Calculating Full-load Torque:Full-load torque is the torque to produce the rated power at full speed of the motor. The amount of torque a motor produces at rated power and full speed can be found by using a horsepower-to-torque conversion chart. When using the conversion chart, place a straight edge along the two known quantities and read the unknown quantity on the third line.

To calculate motor full-load torque, apply this formula:T = HP x 5252 rpmT = torque (in lb-ft)HP = horsepower5252 = constantrpm = revolutions per minuteExample: What is the FLT (Full-load torque) of a 30HP motor operating at 1725 rpm?

T = HP x 5252 rpmT = 30 x 5252 1725T = 157,560 1725T = 91.34 lb-ft

Calculating Horsepower:Electrical power is rated in horsepower or watts. A horsepower is a unit of power equal to 746 watts or 33,0000 lb-ft per minute (550 lb-ft per second). A watt is a unit of measure equal to the power produced by a current of 1 amp across the potential difference of 1 volt. It is 1/746 of 1 horsepower. The watt is the base unit of electrical power. Motor power is rated in horsepower and watts.Horsepower is used to measure the energy produced by an electric motor while doing work.

To calculate the horsepower of a motor when current and efficiency, and voltage are known, apply this formula:HP = V x I x Eff 746HP = horsepowerV = voltageI = curent (amps)Eff. = efficiencyExample: What is the horsepower of a 230v motor pulling 4 amps and having 82% efficiency?HP = V x I x Eff 746HP = 230 x 4 x .82 746HP = 754.4 746HP = 1 Hp

Eff = efficiency / HP = horsepower / V = volts / A = amps / PF = power factor

Horsepower Formulas

To FindUse FormulaExample

GivenFindSolution

HPHP = I X E X Eff. 746240V, 20A, 85% Eff.HPHP = 240V x 20A x 85% 746HP=5.5

II = HP x 746 E X Eff x PF10HP, 240V, 90% Eff., 88% PFII = 10HP x 746 240V x 90% x 88%I = 39 A

To calculate the horsepower of a motor when the speed and torque are known, apply this formula:HP = rpm x T(torque) 5252(constant)Example: What is the horsepower of a 1725 rpm motor with a FLT 3.1 lb-ft?HP = rpm x T 5252HP = 1725 x 3.1 5252HP = 5347.5 5252HP = 1 hp

Calculating Synchronous Speed:AC motors are considered constant speed motors. This is because the synchronous speed of an induction motor is based on the supply frequency and the number of poles in the motor winding. Motor are designed for 60 hz use have synchronous speeds of 3600, 1800, 1200, 900, 720, 600, 514, and 450 rpm.

To calculate synchronous speed of an induction motor, apply this formula:rpmsyn = 120 x f Nprpmsyn = synchronous speed (in rpm)f = supply frequency in (cycles/sec)Np = number of motor polesExample: What is the synchronous speed of a four pole motor operating at 50 hz.?

rpmsyn = 120 x f Nprpmsyn = 120 x 50 4rpmsyn = 6000 4rpmsyn = 1500 rpm

Options: - Useful Formulas- Motor Formulas

To better understand the following formulas review the rule of transposition in equations.A multiplier may be removed from one side of an equation by making it a division on the other side, or a division may be removed from one side of an equation by making it a multiplier on the other side.

1. Voltage and Current: Primary (p) secondary (s)Power(p) = power (s) or Ep x Ip = Es x IsA.Ep =Es x IsIpB.Ip =Es x IsEp

C.Is =Ep x IpEsD.Es =Ep x IpIs

2. Voltage and Turns in Coil:Voltage (p) x Turns (s) = Voltage (s) x Turns (p)or Ep x Ts = Es x IpA.Ep =Es x IpTsB.Ts =Es x TpEp

C.Tp =Ep x TsEsD.Es =Ep x TsTp

3. Amperes and Turns in Coil:Amperes (p) x Turns (p) = Amperes (s) x Turns (s)or Ip x Tp = Is x TsA.Ip =Is x TsTpB.Tp =Is x TsIp

C.Ts =Ip x TpIsD.Is =Ip x TpTs

FLA Motor Chart Options:

DC motors

AC Single Phase AC 2 Phase (4 wire) Induction Type Squirrel Cage and Wound Rotor

AC 3 Phase Induction Type Squirrel Cage and Wound Rotor

AC 3 Phase Synchronous Type Unity Power Factor

DC Motors

Horse-power90v120v180v240v500v550v

Amperes

1/44.03.12.01.6----

1/35.24.12.62.0----

1/26.85.43.42.7----

3/49.67.64.83.8----

112.29.56.14.7----

1-1/2--13.28.36.6----

2--1710.88.5----

3--251612.2----

5--402720----

7-1/2--58--2913.612.2

Horse-power90v120v180v240v500v550v

Amperes

10--76--381816

15------381816

20------552724

25------894338

30------1065146

40------1406761

Horse-power90v120v180v240v500v550v

Amperes

50------1738375

60------2069990

75------255123111

100------341164148

125------425205185

150------506246222

200------675330294

AC Single Phase Motors

Horse-power115v200v208v230v

Amperes

1/64.42.52.42.2

1/45.83.33.22.9

1/37.24.14.03.6

1/29.85.65.44.9

3/413.87.97.66.9

1169.28.88.0

1-1/22011.51110

22413.813.212

33419.618.717

55632.230.828

7-1/280464440

1010057.55550

Horse-power115v200v208v230v

2 Phase (4 wire) AC Induction TypeSquirrel Cage and Wound Rotor

Horse-power115v230v460v575v2300v

Amperes

1/24.02.01.00.8--

3/44.82.41.21.0--

16.43.21.61.3--

1-1/29.04.52.31.8--

211.85.93.02.4--

3--8.34.23.3--

5--13.26.65.3--

10--241210--

15--361814--

20--472319--

25--592924--

30--693528--

40--904536--

Horse-power115v230v460v575v2300v

Amperes

50--1135645--

60--133675314

75--166836618

100--2181098723

125--27013510828

150--31215612532

200--41620816743

AC 3 Phase Induction Type Squirrel Cage and Wound Rotor

Horse-power115V200V208V230V460V575V2300V

Amperes

1/24.42.52.42.21.10.9--

3/46.43.73.53.21.61.3--

18.44.84.64.22.11.7--

1-1/212.06.96.66.03.02.4--

213.67.87.56.83.42.7--

3--11.010.69.64.83.9--

5--17.516.715.27.66.1--

7-1/2--25.324.222119--

Horse-power115v200v208v230v460v575v2300v

10--32.230.8281411--

15--48.346.2422117--

20--62.159.4542722--

25--78.274.8683427--

30--9288804032--

40--1201141045241--

Horse-power115v200v208v230v460v575v2300v

50--1501431306552--

60--177169154776216

75--221211192967720

100--2852732481249926

125--35934331215612531

150--41439636018014437

200--55252848024019249

Horse-power115v200v208v230v460v575v2300v

Amperes

250--------30224260

300--------36128972

350--------41433683

400--------47738295

450--------515412103

500--------590472118

AC 3 Phase Synchronous Type Unity Power Factor

Horse-power230v460v575v2300v

Amperes

25532621--

30633226--

40834133--

501045242--

60123614912

75155786215

1002021018120

12525312610125

15030215112130

20040020116140

Horse-power230v460v575v2300v

Formato base

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