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In a three phase balanced,delta connected system each phase voktage contains a fundamental,a third harmonic and a fifth harmonic of RMS values:100v,30v,20v resp. what is the RMS value of the line to line voltage?
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Calculation of Line to Line Voltage in a Balanced Delta Connected System
To calculate the line to line voltage in a balanced delta connected system with harmonics, we need to consider the phase voltages and their harmonic components.
Given Data:
- Fundamental RMS phase voltage (V1) = 100V
- Third harmonic RMS phase voltage (V3) = 30V
- Fifth harmonic RMS phase voltage (V5) = 20V
Calculation:
1. Line to Line Voltage (VL-LL) in a Delta Connection:
In a delta connected system, the line to line voltage is given by:
VL-LL = √3 * Vph
2. Total Phase Voltage with Harmonics:
The total phase voltage can be calculated by adding the RMS values of fundamental and harmonic components:
Vph = √(V1^2 + V3^2 + V5^2)
Vph = √(100^2 + 30^2 + 20^2)
Vph = √(10000 + 900 + 400)
Vph = √11300 ≈ 106.3V
3. Line to Line Voltage Calculation:
VL-LL = √3 * Vph
VL-LL = √3 * 106.3
VL-LL ≈ 184.1V
Result:
The RMS value of the line to line voltage in the balanced delta connected system with harmonics is approximately 184.1V.
To calculate the line to line voltage in a balanced delta connected system with harmonics, we need to consider the phase voltages and their harmonic components.
Given Data:
- Fundamental RMS phase voltage (V1) = 100V
- Third harmonic RMS phase voltage (V3) = 30V
- Fifth harmonic RMS phase voltage (V5) = 20V
Calculation:
1. Line to Line Voltage (VL-LL) in a Delta Connection:
In a delta connected system, the line to line voltage is given by:
VL-LL = √3 * Vph
2. Total Phase Voltage with Harmonics:
The total phase voltage can be calculated by adding the RMS values of fundamental and harmonic components:
Vph = √(V1^2 + V3^2 + V5^2)
Vph = √(100^2 + 30^2 + 20^2)
Vph = √(10000 + 900 + 400)
Vph = √11300 ≈ 106.3V
3. Line to Line Voltage Calculation:
VL-LL = √3 * Vph
VL-LL = √3 * 106.3
VL-LL ≈ 184.1V
Result:
The RMS value of the line to line voltage in the balanced delta connected system with harmonics is approximately 184.1V.
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