Transcript Introduction to Power System Analysis

Introduction to Power System
Analysis
ET2105 Electrical Power System Essentials
Prof. Lou van der Sluis
02 April 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
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Test (2)
• An inductive current
A. leads
B. lags
the voltage
• A capacitive load
A. supplies
B. consumes
reactive power
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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
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The energy is stored in the
Electromagnetic Field
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Why…?
• Why AC and not DC ?
• Why a sinusoidal alternating voltage ?
• Why 50 Hz (or 60 HZ) ?
• Why three-phase systems ?
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Why AC and not DC ?
Break-even distance for HVDC
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Why a Sinusoidal Alternating Voltage ?
Triangular, sinusoidal and block
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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
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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
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Three Phase Systems (1)
Phase voltages in a balanced three-phase
system (50 Hz)
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Three Phase Systems (2)
The magnetic field generated by a three-phase
system is a rotating field
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Some basics
• 3 phase systems
• Power
• Voltage levels
• Phasors
• Per unit calculation
• Power system structure
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Three Single Phase Systems 
One Three Phase System
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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
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Balanced Three Phase System (2)
Vc
Ic
0
I n  I a  Ib  I c  0
Va
Ic
Ib
Vb
Ia
Ia
Ib
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Balanced system 
Single Phase calculation
Vc
Ic
120º
Va
Ib
Vb
Ia
120º
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Line-to-Line Voltage
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Three Phase Complex Power
• 3 x 1-phase complex power
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Power (1)
P: Active power (average value viR)
Q: Reactive power (average value viX)
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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
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Power (3)
S
Complex power
VA
|S|
Apparent power
VA
P
Active power
W
Average power
Q
Reactive power
var
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Series / Parallel
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Power Factor
Power factor  That part of the apparent power that is related to
the mean energy flow
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System Voltage Levels
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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
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Steady State Analysis (1)
50
V
100
30°
86.6
Example:
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Steady State Analysis (2)
Power
System
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Phasor/Vector Calculus
Real/imaginairy part:
Addition/substraction
Length/angle:
Multiplication/division
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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
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Time  Phasor
Current in phase
U = IR
Current lagging
U = jLI
Current leading
I = jCU
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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
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Power System Structure
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