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A Scott-connected transformer takes power from a 11000 V (line-to-line) 3-phase supply and delivers power to two single-phase 75 V furnaces with power factor = 0.8 (agging) as shown below Furnace-1 is consuming 250 kW and Furnace-2 is consuming 250 kW power The phase sequence is A-C-B. Estimate the RMS value of the current Ia,Ib and Ic (in Amp) (Please enter a positive number)?
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A Scott-connected transformer takes power from a 11000 V (line-to-line...
To determine the RMS values of the currents Ia, Ib, and Ic in the Scott-connected transformer, we need to follow a step-by-step process. Here's how you can calculate the values:
1. Calculate the power consumed by each furnace:
- Furnace-1: 250 kW
- Furnace-2: 250 kW
2. Calculate the apparent power consumed by each furnace:
- Apparent power (S) = Active power (P) / Power factor (pf)
- Apparent power of Furnace-1 = 250 kW / 0.8 = 312.5 kVA
- Apparent power of Furnace-2 = 250 kW / 0.8 = 312.5 kVA
3. Calculate the apparent power consumed by the Scott-connected transformer:
- Total apparent power = Apparent power of Furnace-1 + Apparent power of Furnace-2 = 625 kVA
4. Calculate the line current (Iline) of the 3-phase supply:
- Line current (Iline) = Total apparent power / (sqrt(3) x Line-to-line voltage)
- Line current (Iline) = 625 kVA / (sqrt(3) x 11,000 V)
- Line current (Iline) ≈ 32.17 A
5. Calculate the phase currents Ia, Ib, and Ic:
- The phase currents can be calculated using the Scott connection formula:
- Ia = Iline / sqrt(3)
- Ib = Iline / sqrt(3)
- Ic = -2 * Iline / sqrt(3)
6. Substitute the values and calculate the RMS values of the currents:
- Ia = 32.17 A / sqrt(3) ≈ 18.59 A
- Ib = 32.17 A / sqrt(3) ≈ 18.59 A
- Ic = -2 * (32.17 A / sqrt(3)) ≈ -37.18 A (Note: The negative sign represents a lagging phase)
Therefore, the estimated RMS values of the currents Ia, Ib, and Ic are approximately:
- Ia ≈ 18.59 A
- Ib ≈ 18.59 A
- Ic ≈ -37.18 A
1. Calculate the power consumed by each furnace:
- Furnace-1: 250 kW
- Furnace-2: 250 kW
2. Calculate the apparent power consumed by each furnace:
- Apparent power (S) = Active power (P) / Power factor (pf)
- Apparent power of Furnace-1 = 250 kW / 0.8 = 312.5 kVA
- Apparent power of Furnace-2 = 250 kW / 0.8 = 312.5 kVA
3. Calculate the apparent power consumed by the Scott-connected transformer:
- Total apparent power = Apparent power of Furnace-1 + Apparent power of Furnace-2 = 625 kVA
4. Calculate the line current (Iline) of the 3-phase supply:
- Line current (Iline) = Total apparent power / (sqrt(3) x Line-to-line voltage)
- Line current (Iline) = 625 kVA / (sqrt(3) x 11,000 V)
- Line current (Iline) ≈ 32.17 A
5. Calculate the phase currents Ia, Ib, and Ic:
- The phase currents can be calculated using the Scott connection formula:
- Ia = Iline / sqrt(3)
- Ib = Iline / sqrt(3)
- Ic = -2 * Iline / sqrt(3)
6. Substitute the values and calculate the RMS values of the currents:
- Ia = 32.17 A / sqrt(3) ≈ 18.59 A
- Ib = 32.17 A / sqrt(3) ≈ 18.59 A
- Ic = -2 * (32.17 A / sqrt(3)) ≈ -37.18 A (Note: The negative sign represents a lagging phase)
Therefore, the estimated RMS values of the currents Ia, Ib, and Ic are approximately:
- Ia ≈ 18.59 A
- Ib ≈ 18.59 A
- Ic ≈ -37.18 A
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A Scott-connected transformer takes power from a 11000 V (line-to-line) 3-phase supply and delivers power to two single-phase 75 V furnaces with power factor = 0.8 (agging) as shown below Furnace-1 is consuming 250 kW and Furnace-2 is consuming 250 kW power The phase sequence is A-C-B. Estimate the RMS value of the current Ia,Ib and Ic (in Amp) (Please enter a positive number)?
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A Scott-connected transformer takes power from a 11000 V (line-to-line) 3-phase supply and delivers power to two single-phase 75 V furnaces with power factor = 0.8 (agging) as shown below Furnace-1 is consuming 250 kW and Furnace-2 is consuming 250 kW power The phase sequence is A-C-B. Estimate the RMS value of the current Ia,Ib and Ic (in Amp) (Please enter a positive number)? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about A Scott-connected transformer takes power from a 11000 V (line-to-line) 3-phase supply and delivers power to two single-phase 75 V furnaces with power factor = 0.8 (agging) as shown below Furnace-1 is consuming 250 kW and Furnace-2 is consuming 250 kW power The phase sequence is A-C-B. Estimate the RMS value of the current Ia,Ib and Ic (in Amp) (Please enter a positive number)? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A Scott-connected transformer takes power from a 11000 V (line-to-line) 3-phase supply and delivers power to two single-phase 75 V furnaces with power factor = 0.8 (agging) as shown below Furnace-1 is consuming 250 kW and Furnace-2 is consuming 250 kW power The phase sequence is A-C-B. Estimate the RMS value of the current Ia,Ib and Ic (in Amp) (Please enter a positive number)?.
A Scott-connected transformer takes power from a 11000 V (line-to-line) 3-phase supply and delivers power to two single-phase 75 V furnaces with power factor = 0.8 (agging) as shown below Furnace-1 is consuming 250 kW and Furnace-2 is consuming 250 kW power The phase sequence is A-C-B. Estimate the RMS value of the current Ia,Ib and Ic (in Amp) (Please enter a positive number)? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about A Scott-connected transformer takes power from a 11000 V (line-to-line) 3-phase supply and delivers power to two single-phase 75 V furnaces with power factor = 0.8 (agging) as shown below Furnace-1 is consuming 250 kW and Furnace-2 is consuming 250 kW power The phase sequence is A-C-B. Estimate the RMS value of the current Ia,Ib and Ic (in Amp) (Please enter a positive number)? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A Scott-connected transformer takes power from a 11000 V (line-to-line) 3-phase supply and delivers power to two single-phase 75 V furnaces with power factor = 0.8 (agging) as shown below Furnace-1 is consuming 250 kW and Furnace-2 is consuming 250 kW power The phase sequence is A-C-B. Estimate the RMS value of the current Ia,Ib and Ic (in Amp) (Please enter a positive number)?.
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