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Pharos University EE-385

Pharos University EE-385. Electrical Power & Machines “Electrical Engineering Dept” Prepared By: Dr. Sahar Abd El Moneim Moussa. Single Phase System. Review on AC Circuit. Basic Principles:

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Pharos University EE-385

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  1. Pharos UniversityEE-385 Electrical Power & Machines “Electrical Engineering Dept” Prepared By: Dr. SaharAbd El MoneimMoussa Dr. Sahar Abd El Moneim Moussa

  2. Single Phase System Dr. Sahar Abd El Moneim Moussa

  3. Review on AC Circuit • Basic Principles: • Sinusoidal voltage source: it is a source that produces voltage that varies with time as sine wave • Waveform: Where: T: periodic time: the time of one complete cycle. f: number of cycles per second = 1/T Hz ω: angular frequency of the sine wave = 2πf rad/sec T Dr. Sahar Abd El Moneim Moussa

  4. Equation: V(instantaneous)= Vm sin ωt Where: Vm : The maximum voltage value & it is knows as the amplitude Vrms : Root mean square of the voltage = • Symbol: ~ V(t)= Vm sin ωt Dr. Sahar Abd El Moneim Moussa

  5. V(t)= Vm sin ωt • Resistive Circuit • Circuit diagram: • Equation: • V= Vm sin ωt , I= Imsin ωt • Waveform: “in terms of the time domain” • Phasor diagram: ∴The Resistive current is in phase with the voltage Im Vm Dr. Sahar Abd El Moneim Moussa

  6. Xc = 1/ωc Ω • Capacitive Circuit • Circuit diagram: • Equation: • V= Vm sin ωt , I= Imsin (ωt+90) • Waveform: • Phasor Diagram: Where θ is the angle between the voltage and the current ( cosθ is called the power factor ) ∴The Capacitive current leads the voltage by 90o Im θ Vm Dr. SaharAbd El MoneimMoussa

  7. XL = ωL Ω • Inductive Circuit • Circuit diagram: • Equation:V= Vm sin ωt , I= Imsin (ωt-90) • Waveform: • Phasor Diagram: Where θ is the angle between the voltage and the current ( cosθ is called the power factor ) ∴The Inductive current lags its voltage by 90o Vm θ Im Dr. SaharAbd El MoneimMoussa

  8. Dr. Sahar Abd El Moneim Moussa

  9. Power in a Single-Phase System • Active Power, P, Watt: The electric energy per second consumed by the resistive loads in the circuit which can be withdrawn outside the circuit as thermal, mechanical, light or another forms of energy P= VrmsIrms Cos θ watt • Reactive Power, Q, VAR: This type of power is the source of the energy stored in the circuit & used to maintain the magnetic field in case of the inductor ORthe electric field in case of the capacitor P= VrmsIrms Sin θ VAR This type of energy cannot be withdrawn outside the circuit Dr. Sahar Abd El Moneim Moussa

  10. Apparent Power, S, VA: The resultant of the active & reactive power S= Vrms I*rms  S= Vrms Irms ∠ -θ VA Q Q P S Q Source Load θ P P V Dr. SaharAbd El MoneimMoussa

  11. Itotal IL IC IR NOTE: • Circuit diagram: • Equations: v(t)= Vm sinωt iR (t)= IRm sin ωt iL (t)= ILm sin(ωt-90) iC (t)= ICm sin(ωt+90) • Phasor diagram of the current: I IC IR V Ѳ IL - IC Itotal IL Dr. SaharAbd El MoneimMoussa

  12. I • Phasor diagram of the power: P=S Cos θ = I2 R V Ѳ Q=S Sin θ = I2 X S=VrmsIrms Dr. SaharAbd El MoneimMoussa

  13. Therefore, the power triangle will be P Ѳ Q S Dr. Sahar Abd El Moneim Moussa

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