1. Power in AC Circuits ELEC 308 Elements of Electrical Engineering
Dr. Ron Hayne
Images Courtesy of Allan Hambley and Prentice-Hall
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2. Power Delivered to a Load
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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 = ______
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5. CAPACITIVE Load Pure Capacitance Current Leads Voltage
Reactive power flows from source to load; Pavg = ______
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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
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7. Real Power
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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.
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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)
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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:
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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
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12. Power Triangle Demonstrates relationships between Real power, P
Reactive power, Q
Apparent power VrmsIrms
Power angle, θ
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13. Additional Power Relationships
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14. Using Power Triangles
Find the power, reactive power, and power factor for the source in the circuit below.
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15. Using Power Triangles
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16. Using Power Triangles
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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
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18. Thévenin and Norton
Use same techniques for circuits with impedances as we did for resistive circuits
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19. Maximum Power Transfer
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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
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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
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22. Summary AC Power Thevenin and Norton Real Power Reactive Power
Apparent Power
Power Factor
Thevenin and Norton
Maximum Power Transfer
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