Transcript Document 7788679

Introduction to Power System
Analysis
ET2105 Electrical Power System Essentials
Prof. Lou van der Sluis
26 May 2016
Delft
University of
Technology
Electrical Power System Essentials
Test (1)
• The average power of the instantaneous power dissipated in an
AC circuit is called
A. Complex power S
B. Apparent power |S|
C. Active power P
D. Reactive power Q
1. Introduction to Power System Analysis
Electrical Power System Essentials
2 | 33
ET2105
Test (2)
• An inductive current
A. leads
B. lags
the voltage
• A capacitive load
A. supplies
B. consumes
reactive power
1. Introduction to Power System Analysis
Electrical Power System Essentials
3 | 33
ET2105
Electrical Power System Essentials
Outline
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
1. Introduction to Power System Analysis
Electrical Power System Essentials
4 | 33
ET2105
The energy is stored in the
Electromagnetic Field
1. Introduction to Power System Analysis
Electrical Power System Essentials
5 | 33
ET2105
Why…?
• Why AC and not DC ?
• Why a sinusoidal alternating voltage ?
• Why 50 Hz (or 60 HZ) ?
• Why three-phase systems ?
1. Introduction to Power System Analysis
Electrical Power System Essentials
6 | 33
ET2105
Why AC and not DC ?
Break-even distance for HVDC
1. Introduction to Power System Analysis
Electrical Power System Essentials
7 | 33
ET2105
Why a Sinusoidal Alternating Voltage ?
Triangular, sinusoidal and block
1. Introduction to Power System Analysis
Electrical Power System Essentials
8 | 33
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
1. Introduction to Power System Analysis
Electrical Power System Essentials
9 | 33
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:
Phys :: f  1.52.5
• Increases the eddy current losses:
Peddy :: f 2 2
• Increases the cable and line impedance
1. Introduction to Power System Analysis
Electrical Power System Essentials
10 | 33
ET2105
Three Phase Systems (1)
Phase voltages in a balanced three-phase
system (50 Hz)
1. Introduction to Power System Analysis
Electrical Power System Essentials
11 | 33
ET2105
Three Phase Systems (2)
The magnetic field generated by a three-phase
system is a rotating field
1. Introduction to Power System Analysis
Electrical Power System Essentials
12 | 33
ET2105
Some basics
• 3 phase systems
• Power
• Voltage levels
• Phasors
• Per unit calculation
• Power system structure
1. Introduction to Power System Analysis
Electrical Power System Essentials
13 | 33
ET2105
Three Single Phase Systems 
One Three Phase System
1. Introduction to Power System Analysis
Electrical Power System Essentials
14 | 33
ET2105
Balanced Three Phase System (1)
Vc
Ic
• Voltages in the 3 phases have
the same amplitude, but differ
120 electrical degrees in phase
• Equal impedances in the 3
phases
Va
Ib
Ia
Vb
1. Introduction to Power System Analysis
Electrical Power System Essentials
15 | 33
ET2105
Balanced Three Phase System (2)
Vc
Ic
0
I n  I a  Ib  I c  0
Va
Ic
Ib
Vb
Ia
Ia
Ib
1. Introduction to Power System Analysis
Electrical Power System Essentials
16 | 33
ET2105
Balanced system 
Single Phase calculation
Vc
Ic
120º
Va
Ib
Vb
Ia
120º
1. Introduction to Power System Analysis
Electrical Power System Essentials
17 | 33
ET2105
Line-to-Line Voltage
1. Introduction to Power System Analysis
Electrical Power System Essentials
18 | 33
ET2105
Three Phase Complex Power
• 3 x 1-phase complex power
1. Introduction to Power System Analysis
Electrical Power System Essentials
19 | 33
ET2105
Power (1)
P: Active power (average value viR)
Q: Reactive power (average value viX)
1. Introduction to Power System Analysis
Electrical Power System Essentials
20 | 33
ET2105
Power (2)
How to calculate P and Q from the voltage and
current phasor ?
I*
V

I
• Inductive load consumes reactive power (Q>0)
• Current lags the supply voltage
Positive
• Capacitive load generates reactive power (Q<0)
• Current leads the supply voltage
Negative
1. Introduction to Power System Analysis
Electrical Power System Essentials
21 | 33
ET2105
Power (3)
S
Complex power
VA
|S|
Apparent power
VA
P
Active power
W
Average power
Q
Reactive power
var
1. Introduction to Power System Analysis
Electrical Power System Essentials
22 | 33
ET2105
Series / Parallel
1. Introduction to Power System Analysis
Electrical Power System Essentials
23 | 33
ET2105
Power Factor
Power factor  That part of the apparent power that is related to
the mean energy flow
1. Introduction to Power System Analysis
Electrical Power System Essentials
24 | 33
ET2105
System Voltage Levels
1. Introduction to Power System Analysis
Electrical Power System Essentials
25 | 33
ET2105
Steady State Analysis: f = 50 Hz
• f = 50Hz   = v/f = 3e8/50 = 6000km
6000 km
• Modelling with R, G, L and C
L
C/2 C/2
1. Introduction to Power System Analysis
Electrical Power System Essentials
26 | 33
ET2105
Steady State Analysis (1)
50
V
100
30°
86.6
Example:
1. Introduction to Power System Analysis
Electrical Power System Essentials
27 | 33
ET2105
Steady State Analysis (2)
Power
System
1. Introduction to Power System Analysis
Electrical Power System Essentials
28 | 33
ET2105
Phasor/Vector Calculus
Real/imaginairy part:
Addition/substraction
Length/angle:
Multiplication/division
1. Introduction to Power System Analysis
Electrical Power System Essentials
29 | 33
ET2105
Network Elements
Element
Time domain
Phasor domain
Resistance
v = iR
V = IR
Reactor
v = L (di/dt)
V = jLI = jXI
Capacitor
i = C (dv/dt)
I = jCV = jBV
1. Introduction to Power System Analysis
Electrical Power System Essentials
30 | 33
ET2105
Time  Phasor
Current in phase
U = IR
Current lagging
U = jLI
Current leading
I = jCU
1. Introduction to Power System Analysis
Electrical Power System Essentials
31 | 33
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
1. Introduction to Power System Analysis
Electrical Power System Essentials
32 | 33
ET2105
Power System Structure
1. Introduction to Power System Analysis
Electrical Power System Essentials
33 | 33
ET2105