the transmission of electric energy

21 April 2023

DelftUniversity ofTechnology

Electrical Power System Essentials

ET2105 Electrical Power System Essentials

Prof. Lou van der Sluis

The Transmission of Electric Energy

23. The Transmission of Electric Energy | 39

Electrical Power System Essentials ET2105

Introduction (1)

• Transmission and Distribution• Advantages of interconnected systems

• Better reliability• Smaller frequency deviations• Better overall system efficiency• Facilitates power exchange

• Disadvantages of interconnected systems• Limitations to interconnection transport capacity• Power losses because of energy exchange• Unwanted parallel power flows• More complex system operation



Introduction (2)Rated voltage for AC – power system



Introduction (3)Voltage levels in the Dutch Power System



The Dutch High-Voltage Network

Introduction (4)



Network Structures

Radial structure Loop structure Multi-loop structure



Substations (1)Open-air substation

Courtesy of TenneT TSO B.V.



Substations (2)High-Voltage Circuit Breakers and Pantograph Disconnector




Substations (3)SF6-insulated substation

Courtesy of Eaton Holec



Substations (4)Bus system

Single bus system

Double bus system



The TransformerThe ideal transformer



The Transformer Model (1)

• Not ideal• Permeability is not infinity

• Finite self inductance

• Leakage flux• Winding losses (copper losses)• Core losses

• Hysteresis

• Eddy-current losses



The Transformer Model (2)

Copper lossesLeakage reactance

Iron losses (core) Magnetizing susceptance

Efficiency = Pout / Pin = 1 – Ploss / Pin



Three-Phase Transformer (1)

• Three single-phase transformers

• Three phase transformer

• Complex turns ratio 1 : a*ej

• Amplitude• Phase shift: multiple of 30°



Three-Phase Transformer (2)Single-phase equivalent



Three-Phase Transformer (3)Out of the tank




The Yy-4 Transformer



The Yd-11 Transformer



The Magnetization CurrentThe magnetization current contains a third harmonic



Overhead Transmission Lines (1)380 kV River crossing




Overhead Transmission Lines (2)The power carriers in the Dutch power system



Overhead Transmission Lines (3)150kV transmission line tower



Transmission Line Conductors (1)

• Material• Al• Cu

• ACSR (Aluminum Conductor Steel Reinforced)



Transmission Line Conductors (2)




Transmission Line Conductors (3)Advantages and disadvantages of bundled conductors



Galloping Lines

• Counter measures



Shield Wires



Transposition (1)

• Unbalanced system

• Solution: transposition



Transposition (2)



High-Voltage Cable

Courtesy of Prysmian Cable Holding B.V.

• 6/10 kV cable • 220/380 kV cable



Transmission of PowerPoynting Vector: S = E x H

VV

HH

HH

HHEE

EE

EE

SS

SS

SS

EE

SS

SS

HH

HHEE

SS

SS



Conductor Modeling

• L : H-field• C : E-field• R : Ohmic losses• G : Insulator and corona losses

RL

G C



Line / Cable

• Line, 150 kV• R = 0.125 /km• XL = 0.425 /km

• C = 7.7 nF/km• Sth = 130 MVA

• Cable, 150 kV• R = 0.12 /km• XL = 0.166 /km

• C = 210 nF/km• Sth = 135 MVA



1 km Line / Cable

• Line, 132 kV• R = 0.178 • XL = j0.40 • XC = -j350 k• I = 450 A

• Cable, 400 kV• R = 9 m• L = 0.4 mH• C = 0.38 µF• I = 1.9 kA



Line Models

• Short(<80 km)

• Medium(80 km..240 km)

• Long(>240 km)

VR

IRIS

VS

Z

IRIS

VS Y/2Y/2 VR

Z

IRIS

VS VR

/kmH/kmF/km



Short Line

VR

IRIS

VS

R+jX

Vr

Vs

jIrX

IrIrR

Vr

VsjIrX

IrIrR

Vr

Vs jIrX

Ir

IrR



Series-Compensation

• Z = R + jX = R + j (L - 1/C)

Hydro-Quebec / 735 kV



Long Line: Distributed Elements

zx

yx V(x)

x

V(x+x)

I(x)I(x+x)



Equivalent Circuits of Lines

• Short

• Medium

• Long

VR

IRIS

VS

Z

IRIS

VS

Z

Y/2

Y/2 VR

IRIS

VS

Z'

Y'/2

Y'/2 VR

the transmission of electric energy

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