L1-Introduction_to_Power_System_Analysis.ppt

introduction to power system slides

1. Introduction to Power System
Planning and Analysis

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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
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

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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:
•Increases the eddy current losses:
•Increases the cable and line impedance
1.5 2.5
::

hys
P f
2 2
::
eddy
P f

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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)
•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

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Balanced Three Phase System (2)
Va
Vb
Vc
Ia
Ic
Ib
0   
n a b c
I I I I
Ia
Ic
Ib
0

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Balanced system 
Single Phase calculation
Va
Ia
Vb
Ib
120º
Vc Ic
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 vi
R
)
Q: Reactive power (average value vi
X
)

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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

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Power (3)
SComplex power VA
|
S|
Apparent power VA
PActive power
Average power
W
QReactive 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
Modelling with R, G, L and C
6000 km
L
C/2C/2

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Steady State Analysis (1)
Example:
86.686.6
100100
3030°°
5500 VV

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Steady State Analysis (2)
PowerPower
SystemSystem

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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
Current lagging
Current leading
U = IR
U = jLI
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