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Power in AC Circuits ELEC 308 Elements of Electrical Engineering

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Presentation on theme: "Power in AC Circuits ELEC 308 Elements of Electrical Engineering"— Presentation transcript:

1 Power in AC Circuits ELEC 308 Elements of Electrical Engineering
Dr. Ron Hayne Images Courtesy of Allan Hambley and Prentice-Hall ELEC 308

2 Power Delivered to a Load
ELEC 308

3 RESISTIVE Load Pure Resistance Current in Phase with Voltage ELEC 308

4 INDUCTIVE Load Pure Inductance Current Lags Voltage
Reactive power flows from source to load; Pavg = ______ ELEC 308 ELEC 308

5 CAPACITIVE Load Pure Capacitance Current Leads Voltage
Reactive power flows from source to load; Pavg = ______ ELEC 308 ELEC 308

6 Importance of Reactive Power
No average power is consumed by a pure energy-storage element Reactive power still important Transmission lines, transformers, fuses, etc. must be able to withstand the current associated with reactive power Possible to have loads that draw LARGE currents, even though little average power is consumed Electric power companies STILL charge for reactive power (at a lower rate), as well as total energy delivered ELEC 308

7 Real Power ELEC 308

8 Power Factor The term cos(θ) is called the power factor:
PF = cos(θ) The power angle θ is taken as the phase of the voltage θv minus the phase of the current θi θ = θv-θi Current lags voltage = POSITIVE power angle Current leads voltage = NEGATIVE power angle Sometimes stated as a PERCENTAGE e.g. 90% lagging => cos(θ) = 0.9 and Curr. lags Volt. ELEC 308

9 Reactive Power Capacitance voltage increasing/decreasing
Energy flowing into/out of capacitance Inductance current increasing/decreasing Energy flowing into/out of inductance Instantaneous power can be VERY large Average power (and net energy) is still _________ Reactive power is peak instantaneous power associated with energy-storage elements Q = VrmsIrmssin(θ) Units are VARs (Volt Amperes Reactive) ELEC 308

10 Apparent Power Apparent power is the product of the effective voltage and effect current S = VrmsIrms Units are volt-amperes (VA) Can be determined from real and reactive powers: ELEC 308

11 Units Units indicate whether quantity is power, reactive power, or apparent power 5-kW load means that P = 5 kW 5-kVA load means that VrmsIrms = 5 kVA 5-kVAR load means that Q = 5 kVAR ELEC 308

12 Power Triangle Demonstrates relationships between Real power, P
Reactive power, Q Apparent power VrmsIrms Power angle, θ ELEC 308

13 Additional Power Relationships
ELEC 308

14 Using Power Triangles Find the power, reactive power, and power factor for the source in the circuit below. ELEC 308

15 Using Power Triangles ELEC 308

16 Using Power Triangles ELEC 308

17 Power Factor Correction
In heavy industry Many loads are partly inductive = large amounts of reactive power flow Causes higher current in transmission system Energy rates charged to industry depend on the power factor Higher charges for energy delivered at lower power factors Advantageous to choose loads that operate at near unity power factor Common approach is to place capacitors in parallel with an inductive load to increase the power factor ELEC 308

18 Thévenin and Norton Use same techniques for circuits with impedances as we did for resistive circuits ELEC 308

19 Maximum Power Transfer
ELEC 308

20 Maximum Power Transfer
Maximum power transferred achieved by maximizing the current First case: Load is complex impedance Load impedance for max. power transfer is Reactance of load CANCELS internal reactance of two-terminal circuit Second case: Load is pure resistance ELEC 308

21 Maximum Power Transfer
Determine the maximum power that can be delivered to a load by the two-terminal resistance below if The load can be any complex impedance The load must be a pure resistance ELEC 308

22 Summary AC Power Thevenin and Norton Real Power Reactive Power
Apparent Power Power Factor Thevenin and Norton Maximum Power Transfer ELEC 308


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