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Contents – Electric Power T&D
„
Introduction
„
Power in AC systems, Three Phase Systems
„
Transformers
„
P.U. System
„
Power Lines
„
Fundamentals of Power Transmission
„
Symmetrical Components
2
Voltage and current in steady state operation:
3
Definition of rms - values:
4
The instantaneous value of the power:
5
Power in AC Systems
6
Power in AC Systems
Active Power (Real Power):
Reactive Power:
Power Factor (pf):
(Wirkleistung)
(Blindleistung)
cos ϕ
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(Leistungsfaktor)
Power in AC Systems
Units
Active Power:
W, kW, MW, …
Reactive Power: Var, kVar, MVar, … (var, kvar, Mvar, …)
8
Phasor representation of a sinusoidal quantity
(Zeiger)
9
Voltage and current phasors:
Definition of the complex (apparent) power
S = P + jQ
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Power in AC Systems
The Apparent Power:
(Scheinleistung)
S = P + Q = UI
2
Unit: VA, kVA, MVA, …
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2
Power in AC Systems
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Power in AC Systems
13
Conservation of Complex Power
Figure 2.6: Conservation of complex power
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Conservation of Complex Power
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Active and Reactive Power Losses
ΔP = R I
ΔQ = X I
2
2
Inductor (reactor) consumes reactive power
Capacitor produces reactive power
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Disadvantages of single phase AC systems:
-
Pulsating instantaneous power
-
Difficulties to build “effective” electrical machines
Remedy:
-
Multi-phase AC systems
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The Three Phase System
”The Inventors” (≈ 1890):
Galileo Ferraris (1847 – 97), Italy
Nicola Tesla (1856 – 1943), USA
(G. Westinghouse)
Michael von Dolivo-Dobrowolsky (1862 – 1919), Germany
Jonas Wenström (1855 – 1893), Sweden
Charles E.L. Brown (1863 – 1924), Switzerland
…….
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Nikola Tesla’s Patent, May 1, 1888
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Nikola Tesla’s Patent, May 1, 1888
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The Three Phase System
1891: Lauffen am Neckar – Frankfurt aM, 175 km, 140 kW, 40 Hz, 25 kV
Overall electrical efficiency ≈ 75%
Brown und Dolivo - Dobrowolski
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The Three Phase System
1893: Hellsjön - Grängesberg, Sweden, 4 x 80 kW, 70 Hz, 10 kV, 15 km
Overall electrical efficiency ≈ 70%
Wenström
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Empires of Light: Edison, Tesla,
Westinghouse, and the Race to
Electrify the World
by Jill Jonnes
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Source: IEEE Power & Energy Magazine
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The three challenges of electric power engineering
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The First Challenge of Electric Power Engineering
1880 – 1920: To make it work
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The Second Challenge of Electric Power Engineering
1920 – 1980: To make it big
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The Third Challenge of Electric Power Engineering
1980 - : To make it sustainable
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Voltages in Three Phase Systems
Figure 2.7 Voltages of the phases R, S, and T in a
symmetric three phase system.
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Voltages in Three Phase Systems
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Loads in Three Phase Systems
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Symmetrical Three Phase System
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Powers in Symmetrical Three Phase Systems
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Powers in Symmetrical Three Phase Systems
The instantaneous value of the three phase power:
p(t) is constant, i.e. time independent !
34
Powers in Symmetrical Three Phase Systems
The complex (apparent) power:
Definition of the phase-to-phase voltages and currents:
35
Single phase (per phase) analysis:
36
Delta – Wye Transformation
Zy
1
=
3
Zd
Zy
Zy
1
=
3
Zd
37
Zd
Delta – Wye Transformation
Figure 2.10
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Summary
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Active, Reactive, and Apparent Power
Another definition:
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