dat300 the electrical power system · elåret 2015 industry households commercial transmission...

Chalmers University of Technology

DAT300

THE ELECTRICAL POWER SYSTEM

Jimmy [email protected]

Department of Electrical Engineering

Division of Electric Power Engineering

Chalmers University of technology


History 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


History 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


Fundamentals 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


t (ms)

U I

325V

14.1A Upeak

Ipeakα

β

-5 0 5 10 15 20

IRMS

URMS

T=1/f

f

tIti

tUtu

peak

peak

πω

βω

αω

2

)cos()(

)cos()(

=

−=

−=

Direct Current (DC) / Alternating Current (AC)

Iti

Utu

=

=

)(

)(

2)(

1

0

2

RMS

peakT I

dttiT

I == ∫

RMS = Root-Mean-Square

Only for sinusoidal waveforms


The two main factors that formed the power system

• Transformer (only works on AC)

• Robust and cheep motor (rotating flux)

Why is AC used?


f

tIti

tUtu

peak

peak

πω

βω

αω

2

)cos()(

)cos()(

=

−=

−=

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)


ωC

1j−Ljω

Impedance

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

=

−=−=

=


Reactive power (Q) flow – What is reactive power?

A mathematical description of the phase shift between voltage and current


Reactive power (Q) flow – Why care?

Due to the presence of the reactive power, the system cannot be used up

to its thermal limit and its voltage variation limits

Need for reactive power compensation for better utilization of the system


+

U1

–

+U3

–

+U2

–

Tre enfassystem

BelastningTre enfas-

generatorer Elnät

Ett trefassystem

UR UTUS

I Σ= 0En trefas-generator

+

–

+

–

+

–

Why three phase system?

LoadThree one phase generator

Grid

Three one phase systemOne three phase system

One three phase generator

The lowest number of phases that could create a rotating electric field


Three phase voltage and current


Line-to-line phasors for the voltages

fL-L 3UU =

Line to Line Phase (to ground)


dttitutp )()()( =

∫=T

dttituT

P0

)()(1

{ }∫ ++=T

TTSSRR dttitutitutituT

P0

)()()()()()(1

)()()()()()()( titutitutitutp TTSSRR ++=

)cos(2)(

)cos(2)(

ϕω

ω

−=

=

tIti

tUtu

RMS

RMS

Single phase Three phase

[ ]VA* jQPIUS RMSRMS +==

ϕϕ

ϕϕ

sin3sin3

cos3cos3

*3*3

,

,

,

RMSRMSLLRMSRMS

RMSRMSLLRMSRMS

RMSRMSLLRMSRMS

IUIUQ

IUIUP

jQPIUIUS

−

−

−

==

==

+===

Power – Rate of energy flow [W]

αβϕ −=Angle between voltage and current

Apparent power

[ ]VArsinϕRMSRMS IUQ =

Active power[ ]WcosϕRMSRMS IUP =

Reactive power

Instantaneous

power

average



3-phase Power [W]


( )L

rspsss

X

EEIEIEP

δsin real

*

===

( )L

rssqsss

X

EEEIEIEQ

)cos( imag

* δ−===

Active/reactive power at sending endEs

LXδ,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 flow


Voltages at the ends of a transmission line (same phase)

s = 1 (sending end)r = 2 (receiving end)

δ

( )δ


2212121 jcos

jsin

qp IIX

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 flows = 1 (sending end)r = 2 (receiving end)


Structure of the Electric Power System


Sven

ska K

raftnät: w

ww

.svk.se

• Transmission 400, 220 kV

• Regional 130 kV

• Distribution 70, 40, 30, 20,10 kV

• Local 400 V (Industry 10-130 kV)

Source: Svenska Kraftnät

Power balancing


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 the load power?


Electric energy consumption in Sweden

divided on different consumers 1970–2015

Källa: SCB

Elåret 2015

Industry

Households

Commercial

Transmission losses

Boilers


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

The consumption is higher in winter time in the Nordic countries, but in warm countries it is opposite

Time


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

Not measured

Refrigerators,

Freezers

Lighting

Cooking

Dishwasher

Laundry

Computers

etc

Other


240 6 12 18

Base load: Nuclear, Renewables

Peak load -Gas turbines, hydro, m.m.

Pmax

Pmin

Load curve

Production planing

Hydro, CHP


Total input energy to Sweden 1973–2015

Källa: SCB

Elåret 2015

Nuclear (Losses)

Nuclear (Netto)

Hydro + Wind

Bio and waste

Natural gas

Oil

Coal


Installed peak power in Sweden, MWel

Elåret 2015

Hydro Oil and gas turbines

CHP Nuclear Wind Solar

Source:


Electricity production in Sweden, TWhel

Elåret 2015

Hydro

Oil and gas turbines

CHP

Nuclear

Wind

Source:


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

[k

W]

Efficiency:

MPP 0.95

Power electronics 0.95

Solar cells 0.15


Normalized electric production mix for

the Nordic countries

Elåret 2013

Hydro

Oil and gas turbines

CHP

Nuclear

Wind

Geothermal

Source:


Spot market price for 2015-03-27


The End

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