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19 April 2023
DelftUniversity ofTechnology
Electrical Power System Essentials
ET2105 Electrical Power System EssentialsProf. Lou van der Sluis
Introduction to Power System Analysis
21. Introduction to Power System Analysis | 33
Electrical Power System Essentials ET2105
Test (1)
• The average power of the instantaneous power dissipated in an AC circuit is called
A. Complex power SB. Apparent power |S|C. Active power PD. Reactive power Q
31. Introduction to Power System Analysis | 33
Electrical Power System Essentials ET2105
Test (2)
• An inductive currentA. leadsB. lagsthe voltage
• A capacitive loadA. suppliesB. consumesreactive power
41. Introduction to Power System Analysis | 33
Electrical Power System Essentials ET2105
Electrical Power System Essentials
1. Introduction to Power System Analysis
2. The Generation of Electric Energy
3. The Transmission of Electric Energy
4. The Utilization of Electric Energy
5. Power System Control
6. Energy Management Systems
7. Electricity Markets
8. Future Power Systems
Outline
51. Introduction to Power System Analysis | 33
Electrical Power System Essentials ET2105
The energy is stored in the Electromagnetic Field
61. Introduction to Power System Analysis | 33
Electrical Power System Essentials ET2105
Why…?
• Why AC and not DC ?
• Why a sinusoidal alternating voltage ?
• Why 50 Hz (or 60 HZ) ?
• Why three-phase systems ?
71. Introduction to Power System Analysis | 33
Electrical Power System Essentials ET2105
Why AC and not DC ?Break-even distance for HVDC
81. Introduction to Power System Analysis | 33
Electrical Power System Essentials ET2105
Why a Sinusoidal Alternating Voltage ?
Triangular, sinusoidal and block
91. Introduction to Power System Analysis | 33
Electrical Power System Essentials ET2105
The choice of Frequency (1)50 Hz and 60 Hz
• Between 1885 and 1890 in the U.S.A.:• 140, 133⅓, 125, 83 ⅓, 66 ⅔, 50, 40, 33 ⅓, 30, 25 en 16⅔
Hz
• Nowadays:• 60 Hz in North America, Brazil and Japan (has also 50 Hz!)• 50 Hz in most other countries• 25 Hz Railways (Amtrak)• 16⅔ Hz Railways• 400 Hz Oil rigs, ships and airplanes
101. Introduction to Power System Analysis | 33
Electrical Power System Essentials ET2105
The choice of Frequency (2)50 Hz and 60 Hz
• A too low frequency, like 10 or 20 Hz causes flicker
• A too high frequency• Increases the hysteresis losses:
• Increases the eddy current losses:
• Increases the cable and line impedance
1.5 2.5:: hysP f
2 2::eddyP f
111. Introduction to Power System Analysis | 33
Electrical Power System Essentials ET2105
Three Phase Systems (1)Phase voltages in a balanced three-phase system (50 Hz)
121. Introduction to Power System Analysis | 33
Electrical Power System Essentials ET2105
Three Phase Systems (2)The magnetic field generated by a three-phase system is a rotating field
131. Introduction to Power System Analysis | 33
Electrical Power System Essentials ET2105
Some basics
• 3 phase systems
• Power
• Voltage levels
• Phasors
• Per unit calculation
• Power system structure
141. Introduction to Power System Analysis | 33
Electrical Power System Essentials ET2105
Three Single Phase Systems One Three Phase System
151. Introduction to Power System Analysis | 33
Electrical Power System Essentials ET2105
Balanced Three Phase System (1)
• Voltages in the 3 phases have the same amplitude, but differ 120 electrical degrees in phase
• Equal impedances in the 3 phases
Va
Vb
Vc
Ia
Ic
Ib
161. Introduction to Power System Analysis | 33
Electrical Power System Essentials ET2105
Balanced Three Phase System (2)
Va
Vb
Vc
Ia
Ic
Ib
0 n a b cI I I I
IaIc
Ib
0
171. Introduction to Power System Analysis | 33
Electrical Power System Essentials ET2105
Balanced system Single Phase calculation
Va
Ia
Vb
Ib
120º
Vc Ic
120º
181. Introduction to Power System Analysis | 33
Electrical Power System Essentials ET2105
Line-to-Line Voltage
191. Introduction to Power System Analysis | 33
Electrical Power System Essentials ET2105
Three Phase Complex Power
• 3 x 1-phase complex power
201. Introduction to Power System Analysis | 33
Electrical Power System Essentials ET2105
Power (1)
P: Active power (average value viR)Q: Reactive power (average value viX)
211. Introduction to Power System Analysis | 33
Electrical Power System Essentials ET2105
Power (2)
• Inductive load consumes reactive power (Q>0)• Current lags the supply voltage
• Capacitive load generates reactive power (Q<0)• Current leads the supply voltage
How to calculate P and Q from the voltage and current phasor ?
V
I
I*
PositivePositive
NegativeNegative
221. Introduction to Power System Analysis | 33
Electrical Power System Essentials ET2105
Power (3)
S Complex power VA
|S| Apparent power VA
P Active power
Average power
W
Q Reactive power var
231. Introduction to Power System Analysis | 33
Electrical Power System Essentials ET2105
Series / Parallel
241. Introduction to Power System Analysis | 33
Electrical Power System Essentials ET2105
Power Factor
Power factor That part of the apparent power that is related to the mean energy flow
251. Introduction to Power System Analysis | 33
Electrical Power System Essentials ET2105
System Voltage Levels
261. Introduction to Power System Analysis | 33
Electrical Power System Essentials ET2105
Steady State Analysis: f = 50 Hz
• f = 50Hz = v/f = 3e8/50 = 6000km
• Modelling with R, G, L and C
6000 km
L
C/2C/2
271. Introduction to Power System Analysis | 33
Electrical Power System Essentials ET2105
Steady State Analysis (1)
Example:
86.686.6
100100
3030°°
5500 VV
281. Introduction to Power System Analysis | 33
Electrical Power System Essentials ET2105
Steady State Analysis (2)
PowerPowerSystemSystem
291. Introduction to Power System Analysis | 33
Electrical Power System Essentials ET2105
Phasor/Vector Calculus
Real/imaginairy part:Addition/substraction
Length/angle:Multiplication/division
301. Introduction to Power System Analysis | 33
Electrical Power System Essentials ET2105
Network Elements
Element Time domain Phasor domain
Resistance v = iR V = IR
Reactor v = L (di/dt) V = jLI = jXI
Capacitor i = C (dv/dt) I = jCV = jBV
311. Introduction to Power System Analysis | 33
Electrical Power System Essentials ET2105
Time PhasorCurrent in phase
Current lagging
Current leading
U = IR
U = jLI
I = jCU
321. Introduction to Power System Analysis | 33
Electrical Power System Essentials ET2105
Per-Unit Normalization
• 156150 V 1.041 pu (150000 V = 1 pu)• Advantageous to calculating with percentages
• 100% * 100% = 10000/100 = 100%• 1 pu * 1 pu = 1 pu
• Define 2 base quantities Example:
Base quantity Value
Voltage
(apparent) Power
Current
Impedance