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Download Three Phase Power You will notice that all of the equations that refer
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Three Phase Power You will notice that all of the equations that refer to three phase power contain the value 1.73 in the formula somewhere. The value 1.73 is the square root of 3. Intuitively, you can see how this value is applied in the formulae. (3 phases therefore 1 phase = square root of 3) Computing Watts When Volts and AMPS are Known POWER (WATTS) = VOLTS x AMPS For example, a small computer has a nameplate that shows 2.5 amps. Given a normal 120 Volt, 60 Hz power source and the ampere reading from equipment, make the following calculation: POWER (WATTS) = 2.5AMPS x 120VOLTS = 300 WATTS Generally: P=IE P= Power(WATTS) I = Current(AMPS) and E = Voltage(VOLTS). So: I = P/E and E = P/I therefore: 1 watt = 1 ampere x 1 volt Computing Volt-AMPS (VA) Same as above. VOLT-AMPS (VA) = VOLTS x AMPS = 300 VA Computing kilovolt-AMPS (KVA) KVA stands for "Thousand Volt-Amps". THREE-PHASE Example: A large disk storage system loaded with disks. The equipment documentation shows a requirement for a 50-amp 208-240 VAC power source. Do not calculate any value for the plug or receptacle. Use 220 volts for the calculation. KILOVOLT-AMPS (KVA) = VOLTS x AMPS x 1.73 / 1000 220 x 50 x 1.73 = 19,030 rounded to 19 19,030 / 1000 = 19.030 KVA This would be Computing Kilowatts Finding Kilowatts requires using a power factor in the computation. The power factor is a number that adjusts the power calculation to reflect the efficiency of the use of the electricity supplied to the system. This factor can vary widely (usually from 60% to 95%) and is never published on the equipment nameplate and is not often supplied with product information. For purposes of these calculations, we use a power factor of .85. This random number places a slight inaccuracy into the numbers. Its OK and it gets us very close for the work we need to do. Most UPS equipment will claim a power factor of 1.00. It is common for the power factor to be considered 1.0 for devices less than 3 years old. SINGLE PHASE Example: We have a medium-sized Intel server that draws 6.0 amps and the power supply has a power factor of .85. KILOWATT (KW) = VOLTS x AMPS x POWER FACTOR / 1000 120 x 6.0 = 720 VA 720 VA x .85 = 612 612 / 1000 = .612 KW 208-240 SINGLE-PHASE (2-POLE SINGLE-PHASE) Example: An enterprise server with a 4.7 amp rating and requiring a 208-240 power source. I'll use 220 volts and a power factor of .85 for our example calculations. KILOWATT (KW) = VOLTS x AMPS x POWER FACTOR x 2 / 1000 220 x 4.7 x 2 = 2068 2068 x .85 = 1757.8 1757.8 / 1000 = 1.76 KW THREE-PHASE Example: A large storage system loaded with disks. The equipment documentation shows a requirement for a 50-amp 208 VAC Power source. Do not calculate any value for the plug or receptacle. Use 220 volts for the calculation. KILOWATT (KW) = VOLTS x AMPS x POWER FACTOR x 1.73 1000 220 x 50 x .85 x 1.73 = 16,175.50 16,175.50/1000 = 16.175 KW To Convert Between KW and KVA The only difference between KW and KVA is the power factor. Once again, the power factor, unless ascertained from the manufacturer, is an approximation. For this example, we use a power factor of .85. The KVA value is always higher than the value for KW. KW to KVA KVA TO KW KW / .85 = SAME VALUE EXPRESSED IN KVA KVA x .85 = SAME VALUE EXPRESSED IN KW Here are conversions, short and sweet: To convert Watts to Volts when amps are known: Voltage = Watts / AMPS E=P/I To convert Watts to AMPS when volts are known: AMPS = Watts / Voltage I=P/E For 3 Phase power divide by 1.73 To convert AMPS to Watts when volts are known: Watts = Voltage x Amps P=ExI For 3 Phase power multiply by 1.73 To convert Horsepower to AMPS: HORSEPOWER= (E x I x EFF) / 746 EFFICIENCY= (746 x HP) / (V x A) Multiply Horsepower by 746w (1 HP = 746 Watts) Find Circuit Voltage and Phase Example: 40 HP at 480 (3 Phase) 746 multiplied by 40 = 29,840 29,840 divided by 480 (3 Phase) = 62.2 62.2 divided by 1.73 = 35.95AMPS To convert KVA to AMPS: Multiply KVA by 1000/voltage [ (KVA x 1000) / E ] For 3 Phase power divide by 1.73 [ (KVA x 1000) / E x 1.73 ] To convert KW to AMPS: Multiply KW by 1000/voltage and then by power factor [ (KW x 1000) / E x PF ] for 3 Phase power divide by 1.73 [ ( KW x 1000) / E x PF x 1.73 ] HOW TO FIND AMPS (I) Direct Current When HP, E and EFF are known: HP x 746 / E x EFF When KW and E are known: SINGLE PHASE When P, E and PF are known: When HP, E, EFF and PF are known: KW x 1000 / E P / E x PF HP x 746 / E x EFF x PF When KW, E and PF are known: KW x 1000 / E x PF When KVA and E are known: THREE PHASE When P, E and PF are known: When HP, E, EFF and PF are known: KVA x 1000 / E P / E x PF x 1.73 HP x 746 / E x EFF x PF x 1.73 When KW, E and PF are known: KW x 1000 / E x PF x 1.73 When KVA and E are known: (See abbreviations explained below) KVA x 1000 / E x 1.73 HOW TO FIND WATTS (P) When E and I are known: IxE When R and I are known: R x I2 When E and R are known: (See abbreviations explained below) E2 / R HOW TO FIND KILOWATTS (KW) Direct Current E and I must be known: SINGLE PHASE E, I and PF must be known: THREE PHASE E, I and PF must be known: (See abbreviations explained below) E x I / 1000 E x I x PF / 1000 E x I x PF x 1.73 / 1000 HOW TO FIND KILOVOLT-AMPS (KVA) SINGLE PHASE E and I must be known: E x I / 1000 THREE PHASE E and I must be known: (See abbreviations explained below) HOW TO FIND HORSEPOWER (HP) Direct Current E, I and EFF must be known: E x I x 1.73 / 1000 E x I x EFF / 746 SINGLE PHASE E, I, PF and EFF must be known: E x I x PF x EFF / 746 THREE PHASE E, I, PF and EFF must be known: E x I x PF x EFF x 1.73 / 746 WHERE: E =VOLTS P =WATTS R = OHMS I =AMPS HP = HORSEPOWER PF = POWER FACTOR KW = KILOWATTS KVA = KILOVOLT-AMPS EFF = EFFICIENCY (decimal) If you don't have all the spec's but you know the tonage, I use this rule of thumb for calc's. 1 ton = 12000 BTU 1 watt= 3.412 BTU ex. 4 tons x 12000 BTU = 48000 BTU 48000 div by 3.412 = 14068 watts 14068 div by 240v = 58.6 amps