1. Electrical Power & Machines “Electrical Engineering Dept” Prepared By: Dr. Sahar Abd El Moneim Moussa 1

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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 Moussa3

4.  Equation: V(instantaneous)= V m sin ωt Where: V m : The maximum voltage value & it is knows as the amplitude V rms : Root mean square of the voltage =  Symbol: ~ V(t)= V m sin ωt Dr. Sahar Abd El Moneim Moussa4

5. Resistive Circuit  Circuit diagram:  Equation:  V= V m sin ωt,I= I m sin ωt  Waveform: “in terms of the time domain”  Phasor diagram: ∴ The Resistive current is in phase with the voltage VmVm ImIm Dr. Sahar Abd El Moneim Moussa5 V(t)= V m sin ωt

6. Capacitive Circuit  Circuit diagram:  Equation:  V= V m sin ωt,I= I m sin (ωt+90)  Waveform:  Phasor Diagram: Where θ is the angle between the voltage and the current ( cos θ is called the power factor ) ∴ The Capacitive current leads the voltage by 90 o VmVm ImIm X c = 1/ωc Ω θ Dr. Sahar Abd El Moneim Moussa6

7. Inductive Circuit  Circuit diagram:  Equation:V= V m sin ωt,I= I m sin (ωt-90)  Waveform:  Phasor Diagram: Where θ is the angle between the voltage and the current ( cos θ is called the power factor ) ∴ The Inductive current lags its voltage by 90 o X L = ωL Ω VmVm ImIm θ 7Dr. Sahar Abd El Moneim Moussa

8. Power in a single-phase system Active Power P Watt Reactive Power Q VAR Apparent Power S VA Dr. Sahar Abd El Moneim Moussa8

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 Active Power, P, Watt: The electric energy per second consumed by the resistive loads in the circuit which can be withdrawn outside the circuit as thermal, mechanical, light or another forms of energy P= V rms I rms Cos θ watt  Reactive Power, Q, VAR: This type of power is the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of the inductor OR the electric field in case of the capacitor P= V rms I rms Sin θ VAR This type of energy cannot be withdrawn outside the circuit Dr. Sahar Abd El Moneim Moussa9

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

11. NOTE:  Circuit diagram:  Equations: v(t)= V m sinωt i R (t)= I Rm sin ωt i L (t)= I Lm sin (ωt-90) i C (t)= I Cm sin (ωt+90)  Phasor diagram of the current: 11 V I IRIR ICIC ILIL I L - I C I total Ѳ IRIR ICIC ILIL Dr. Sahar Abd El Moneim Moussa

12.  Phasor diagram of the power: 12 V I P=S Cos θ = I 2 R Q=S Sin θ = I 2 X S=V rms I rms Ѳ Dr. Sahar Abd El Moneim Moussa

13. Therefore, the power triangle will be Dr. Sahar Abd El Moneim Moussa13 Ѳ Q S P