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Chalmers University of Technology
DAT300DAT300
TTHEHE EELECTRICALLECTRICAL PPOWEROWER SSYSTEMYSTEM
Stefan [email protected]
Department of Energy and Environment
Division of Electric Power Engineering
Chalmers University of technology
Chalmers University of Technology
History of the power systemsHistory of the power systems
AC transmission was first demonstrated at an exhibition in Frankfurt am Main 1891
170 kW transferred 175 km from Lauffen hydropower station to the exhibition area at 13000-14700 V
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History of the power systems in SwedenHistory of the power systems in Sweden
First 3-phase transmission systeminstalled in Sweden between Hellsjönand Grängesberg 1893voltage 9650 V, 70 Hz, 70 kW
First 400 kV system HarsprångetHallsberg 1952
Series compensation introduced1954
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Fundamentals of Electric PowerFundamentals of Electric Power
� Energy- Ability to perform work, [J], [Ws], [kWh] (1 kWh = 3.6 MJ)
� Voltage- Measured between two points [V], [kV]- Equivalent to pressure in a water pipe
� Current- Measure of rate of flow of charge through a conductor [A], [kA]- Equivalent to the rate of flow of water through a pipe.- Must have a closed circuit to have a current
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f
tIti
tUtu
peak
peak
πω
βω
αω
2
)cos()(
)cos()(
=
−=
−=
Direct Current (DC) / Alternating Current (AC)Direct Current (DC) / Alternating Current (AC)
Iti
Utu
=
=
)(
)(
2)(
1
0
2
RMS
peak
T Idtti
TI == ∫
RMS = Root-Mean-Square
Only for sinusoidal waveforms
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The two main factors that formed the power system
• Transformer (only works on AC)
• Robust and cheep motor (rotating flux)
Why is AC used?Why is AC used?
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f
tIti
tUtu
peak
peak
πω
βω
αω
2
)cos()(
)cos()(
=
−=
−=
Alternating Current (AC)Alternating Current (AC)
β
α
∠=
∠=
RMS
RMS
II
UU
{ }
{ }
=
⇒=
=
⇒=
−
−
−
−
tj
I
j
RMS
tj
RMS
tj
U
j
RMS
tj
RMS
eeIti
eIti
eeUtu
eUtu
ωβ
βω
ωα
αω
43421
43421
)(
)(
)(
)(
Re2)(
Re2)(
Re2)(
Re2)(
Express the sinusoidal voltage and current as complex rotating phasors and use RMS values for the amplitude
Since all phasors are rotating with the same
speed, we select one as the
reference and observe all others relative to this one.
This gives that the rotation disappears and the voltage
and currents can be expressed as complex
number (constant)
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ωC
1j−Ljω
ImpedanceImpedance
RR IRU
tRitu
=
= )()( RR
LX
IjXILjU
dt
tdiLtu
L
LLLL
ω
ω
=
==
=)(
)( LL
CX
IjXIC
jU
dt
tduCti
C
LCCC
ω
ω
1
1
)()( C
C
=
−=−=
=
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+
U1
–
+U3
–
+U2
–
Tre enfassystem
BelastningTre enfas-generatorer Elnät
Ett trefassystem
UR UTUS
I Σ= 0En trefas-generator
+
–
+
–
+
–
Why three phase system?Why three phase system?
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Three phase voltage and currentThree phase voltage and current
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Phasors for the voltagesPhasors for the voltages
fL-L 3UU =
Line to Line Phase (to ground)
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dttitutp )()()( =
∫=T
dttituT
P0
)()(1
{ }∫ ++=T
TTSSRRdttitutitutitu
TP
0
)()()()()()(1
)()()()()()()( titutitutitutpTTSSRR
++=
)cos(2)(
)cos(2)(
ϕω
ω
−=
=
tIti
tUtu
RMS
RMS
Single phase Three phase
[ ]VA* jQPIUS +==
ϕϕ
ϕϕ
sin3sin3
cos3cos3
*3*3
,
,
RMSRMSLLRMSRMS
RMSRMSLLRMSRMS
LL
IUIUQ
IUIUP
jQPIUIUS
−
−
−
==
==
+===
Power Power –– Rate of energy flow [W]Rate of energy flow [W]
βαϕ −=Angle between voltage and current
Apparent power
[ ]VArsinϕRMSRMS IUQ =
Active power[ ]WcosϕRMSRMS IUP =
Reactive power
Instantaneous
power
average
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Power Power –– Rate of energy flow [W]Rate of energy flow [W]
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Power Power –– Rate of energy flow [W]Rate of energy flow [W]
33--phase Power [W]phase Power [W]
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Reactive power flow Reactive power flow –– What is reactive power?What is reactive power?
� The current causes a magnetic fieldaround the conductor
� The field strength is highest close tothe conductor surface
� The field energy density is proportional to the square of the field strenght
� The field is built up and eleminatedwith the double of the networkfrequency in each phase
Consider an alternating current Iline flowing in a line
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Reactive power flow Reactive power flow –– What is reactive power?What is reactive power?
� The distance between the phases is about 10 m.
� It is not possible to transfer the energy directly between the neighboring phases.
� The energy must be transported to some place where the conductors are connected (a generator or a transformer).
Consider a line segment of, for example, 100 km in a long transmission line
QW∆
QW∆
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Reactive power flow Reactive power flow –– What is reactive power?What is reactive power?
How much energy is involved?
Consider a line segment of 100 km and a current of 1 kA (rms value); the
energy at the current peak is
kJiLW lineQ 100)21000(1.02
1ˆ2
1 22 ===
7 m
It is the same energy needed to lift a 1500
kg car up to 7 meters.
This is done each 10 ms, in each phase.
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Reactive power flow Reactive power flow –– What is reactive power?What is reactive power?
Due to the presence of the reactive power, the system cannot be used up
to its thermal limit
Need for reactive power compensation for better utilization of the system
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( )L
rspsss
X
EEIEIEP
δsin real
*
===
( )L
rssqsss
X
EEEIEIEQ
)cos( imag
* δ−===
Active/reactive power at sending endEs
LX
δ,rr EE →
I
0,ss EE →
QP,
( )L
srrr
X
EEIEP
δsin real
*
==
( )L
srrrr
X
EEEIEQ
)cos( imag
* δ−−==
Active/reactive power at receiving end Er
Power flowPower flow
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Voltages at the ends of a transmission line (same phase)Voltages at the ends of a transmission line (same phase)
s = 1 (sending end)r = 2 (receiving end)
δ
( )δ
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2212121 jcos
jsin
qpII
X
EE
X
E
jX
EEI −=
−+=
−=
δδ
22222*
22 j)j( QPIIEIES qp +=+==
Complex power to E2: X
EEIEP p
δsin12222 ==
Re
Im
δδ sincos 111 jEE +=E
X
EEIq
δcos122
−−=
δsin1E
I
δ 22 E=E
δcos12 EE −X
EI p
δsin12 =
Active/reactive power toE2:
Reactive power consumption of the transmission line:
( )X
EEEEE
XQQQ L
2
2122
2121 cos2
1=−+=−=∆ δ
Active power from E1 to E2 :
X
EEPPP
δsin1221 ===
X
EEEIEQ q
)cos( 122222
δ−−==
Power flowPower flows = 1 (sending end)r = 2 (receiving end)
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Structure of the Electric Power SystemStructure of the Electric Power System
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Svensk
a Kraftnät: w
ww
.svk.se
• Transmission 400, 220 kV
• Regionalnät 130 kV
• Distributionsnät 70, 40, 30, 20,10 kV
• Kunder 400 V (Industri 10-130 kV)
Source: Svenska Kraftnät
Power balancing
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Source: Svenska Kraftnät
Power balancingsI
loadR
LXrω
turbineTgenT
J
grid
genturbinegrid
p
p
grid
r
genload
genrgen
turbinerturbine
genturbiner
f
PP
dt
df
nJ
n
f
PP
TP
TP
TTdt
dJ
−=⇒
=
≈
=
=
−=
2
24
2
π
πω
ω
ω
ω
What happens if the turbine power does not match What happens if the turbine power does not match the load power?the load power?
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The generator transforms the rotational energy into electric energy
Control gate
Reservoir(energy storage)
The kinetic energy of the water is transformed into rotation of the generator shaft (rotational kinetic energy)
Step-up
transformer
Hydro Power Station
Screen
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Profile over the electric energy consumption in
Sweden for a typical summer day, winter day and the
highest consumption day 22th of December 2010
Källa: Svenska Kraftnät och Svensk EnergiElåret 2010
On the 23rd of
February 2011
Sweden used
26 000 MW
between 08-09
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240 6 12 18
Baskraft: Kärnkraft, fossil förbränning, (vattenkraft)
Topplast -Gasturbin, vatten, m.m.
Pmax
Pmin
Lastkurva
Production planing
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Integrated power during 1 year
24 000 kWh
Göteborg
Latitude 57.7 º
200 m2 of solar cells
Statistical cloudiness
Sun tracking
0 1000 2000 3000 4000 5000 6000 7000 8000 90000
5
10
15
20
25Solgenerator vs Tidpunkt
Tidpunkt (timme)
Eff
ekt
(kW
)
Solar Plant
Time [Hour]
Po
wer
[kW
]
Efficiency:
MPP 0.95
Power electronics 0.95
Solar cells 0.15
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Total input energy to Sweden 1973–2010
Källa: SCB
Elåret 2010
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Sweden electric energy production
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Electric energy production and ussage
in Sweden for 2008–2010, TWh/week
Källa: Svensk Energi
Elåret 2010
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Electric energy flow to and from Sweden 2008, GWh
Källa: Svenska Kraftnät och Svensk Energi
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Normalized electric production mix for
the Nordic countries
Källa: Svensk Energi
Elåret 2010
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Electric energy production in Sweden:
145,0 TWh år 2007 (v 65,5; k 64,3)
146,0 TWh år 2008 (v 68,6; k 61,3; v 2,0)
133,7 TWh år 2009 (v 65,3; k 50,0; v 2,5)
144,9 TWh år 2010 (v 66,8; k 55,6; v 3,5)
146,9 TWh år 2011 (v 66,0; k 58,0; v 6,1)
v=Hydro power
k=nuclear power
v=Wind power
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Installed peak power in Sweden 2011.12.31, MWel
Hydro power 16 197
Wind power 2 899
Nuclear power 9 363
Other thermal power 7 988
∑ 36 447
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Electric energy consumption in Sweden
divided on different consumers 1970–2010
Källa: SCB
Elåret 2010
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Electric energy consumption for
households in Sweden (investigated 2007)
Källa: EnergimyndighetenElåret 2010
The consumption is higher in winter time in the Nordic countries, but in warm countries it is opposite
Typical household
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The EndThe End
Do you have any questions?Do you have any questions?