DAT300 THE ELECTRICAL POWER SYSTEM

Transcription

1 DAT300 THE ELECTRCAL POWER SYSTEM Jimmy Ehnberg Department of Electrical Engineering Division of Electric Power Engineering Chalmers University of technology

2 History of the power systems AC transmission was first demonstrated at an exhibition in Frankfurt am Main kw transferred 175 km from Lauffen hydropower station to the exhibition area at V

3 History of the power systems in Sweden First 3-phase transmission system installed in Sweden between Hellsjön and Grängesberg 1893 voltage 9650 V, 70 Hz, 70 kw First 400 kv system Harsprånget Hallsberg 1952 Series compensation introduced 1954

4 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

5 Direct Current (DC) / Alternating Current (AC) 325V U 14.1A U peak α peak U u( i( U β t (ms) Root-Mean-Square 1 2 i( dt T T 0 peak Only for sinusoidal waveforms 2 T1/f u( i( U ω peak 2πf peak cos( ωt α) cos( ωt β )

6 Why is AC used? The two main factors that formed the power system Transformer (only works on AC) Robust and cheep motor (rotating flux)

7 Alternating Current (AC) Chalmers University of Technology u( i( ω U peak 2πf peak cos( ωt α) cos( ωt β ) Express the sinusoidal voltage and current as complex rotating phasors and use values for the amplitude u( u( i( i( 2 Re j( ωt α ) { U e } j( α ) 2 Re U e e U 2 Re j( ωt β ) { e } j( β ) 2 Re e e jωt jωt 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 (constan U U α β

8 mpedance jωl j 1 ωc u U Ri ( R ( R R R R u U X L L di ( L dt jωl jx L L( ωl L L L i U X du ( C dt 1 j C ωc 1 ωc C C( C C jx C L

9 Reactive power (Q) flow What is reactive power? A mathematical description of the phase shift between voltage and current

10 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

11 Why three phase system? Chalmers University of Technology + U 1 Tre enfassystem Three one phase system + U 2 Three Tre enfasgeneratorer one phase generator + U 3 Grid Elnät Load Belastning + U R One three Ett trefassystem phase system + U S One En trefasgenerator three phase generator + U T Σ 0 The lowest number of phases that could create a rotating electric field

12 Three phase voltage and current Chalmers University of Technology

13 Line-to-line phasors for the voltages U L-L 3U f Line to Line Phase (to ground)

14 S u( i( 2U 2 Single phase p ( u( i( dt 1 P T u( i( dt T 0 Apparent power U * P + jq Power Rate of energy flow [W] cos( ω cos( ωt ϕ) nstantaneous power average [ VA] S P 1 T T Chalmers University of Technology Angle between voltage and current ϕ β α 3U p( u ( i ( + u ( i ( u ( i ( { u ( i ( + u ( i ( u ( i ( } R R S S + 0 Three phase R R S S + * 3U L L, T T T * P + T dt jq Active power P U cosϕ [ W] P 3U cosϕ 3 U L L, cosϕ Reactive power Q U sinϕ [ VAr] Q 3U sin ϕ 3 U L L, sin ϕ

15 Power Rate of energy flow [W] Chalmers University of Technology

16 Power Rate of energy flow [W] Chalmers University of Technology 3-phase Power [W]

17 Power flow P,Q E s E s,0 X L E r E r,δ Active/reactive power at sending end E s Active/reactive power at receiving ende r P s real ( ) * Es E s p EsEr sinδ X L P r real ( ) Er * ErEs sinδ X L Q s imag ( ) Es * Es ( Es Er cosδ ) Esq X L Q r imag ( ) E r * Er ( Er Es cosδ ) X L

18 Voltages at the ends of a transmission line (same phase) ( ) δ δ s 1 (sending end) r 2 (receiving end)

19 s 1 (sending end) r 2 (receiving end) Power flow E E jx S m q 2 E sinδ X E E cosδ X j j 2 Complex power toe 2 : * 2 E2 E2 p 2 + jq2) P2 + j E p 2 2 E1 cos δ X E 1 ( Q E1 E 1 cos δ + je1 sin δ E 1 2 sin δ δ E2 E2 sin δ X E2 E 1 cos δ p q Re 2 Active/reactive power to E 2 : P2 E2 p2 Q E 2 E sinδ 1 X Active power from E 1 to E 2 : P 2 E 2 q2 P1 P2 E E1 sinδ X Reactive power consumption of the transmission line: 2 2 ( E + E 2E E δ ) 1 Q Q1 Q cos X E 2 2 ( E2 E1 cos δ ) X E 2 L X

20 Structure of the Electric Power System

21 Transmission 400, 220 kv Regional 130 kv Distribution 70, 40, 30, 20,10 kv Local 400 V (ndustry kv) Power balancing Source: Svenska Kraftnät Svenska Kraftnät:

22 ω r Tturbine J Tgen s X L R load Chalmers University of Technology What happens if the turbine power does not match the load power? Power balancing J dωr dt P turbine P gen T turbine ω T r ω T r Pload P 2πf ωr n gen grid p T turbine gen gen J 2 4π n 2 p df grid dt P turbine f P grid gen Source: Svenska Kraftnät

23 Electric energy consumption in Sweden divided on different consumers ndustry Households Commercial Transmission losses Boilers Elåret 2015 Källa: SCB

24 Profile over the electric energy consumption in Sweden for a typical summer day, winter day and the highest consumption day 22th of December 2010 On the 23rd of February 2011 Sweden used MW between The consumption is higher in winter time in the Nordic countries, but in warm countries it is opposite Elåret 2010 Time Källa: Svenska Kraftnät och Svensk Energi

25 Electric energy consumption for households in Sweden (investigated 2007) Typical household Other Not measured Refrigerators, Freezers Computers etc The consumption is higher in winter time in the Nordic countries, but in warm countries it is opposite Lighting Laundry Dishwasher Elåret 2010 Cooking Källa: Energimyndigheten

26 Production planing Chalmers University of Technology P max Load curve Peak load - Gas turbines, hydro, m.m. P min Hydro, CHP Base load: Nuclear, Renewables

27 Total input energy to Sweden Nuclear (Losses) Nuclear (Netto) Hydro + Wind Bio and waste Natural gas Oil Coal Elåret 2015 Källa: SCB

28 nstalled peak power in Sweden, MWel Hydro Oil and gas turbines CHP Nuclear Wind Solar Elåret 2015 Source:

29 Electricity production in Sweden, TWhel Hydro Oil and gas turbines CHP Nuclear Wind Source: Elåret 2015

30 Solar Plant Chalmers University of Technology Göteborg Latitude 57.7 º 200 m 2 of solar cells Statistical cloudiness Sun tracking Power [kw] Effekt (kw) Solgenerator vs Tidpunkt Efficiency: MPP 0.95 Power electronics 0.95 Solar cells Tidpunkt (timme) Time [Hour] ntegrated power during 1 year kwh

31 Normalized electric production mix for the Nordic countries Hydro Nuclear CHP Oil and gas turbines Wind Geothermal Elåret 2013 Source:

32 Spot market price for

33 The End Do you have any questions?