AC transmission was first demonstrated at an exhibition in Frankfurt am Main 1891

Transcription

1 History of the power systems A transmission was first demonstrated at an exhibition in Frankfurt am Main 89 DA300 HE EERA POWER SYSEM 70 kw transferred 75 km from auffen hydropower station to the exhibition area at V Stefan undberg stefan.lundberg@chalmers.se Department of Energy and Environment Division of Electric Power Engineering halmers University of technology History of the power systems in Sweden First 3-phase transmission system installed in Sweden between Hellsjön and Grängesberg 893 voltage 9650 V, 70 Hz, 70 kw Fundamentals of Electric Power Energy - Ability to perform work, [J], [Ws], [kwh] ( kwh 3.6 MJ Voltage - Measured between two points [V], [kv] - Equivalent to pressure in a water pipe urrent - 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 First 400 kv system Harsprånget Hallsberg 95 Series compensation introduced 954 Direct urrent (D / Alternating urrent (A Why is A used? he two main factors that formed the power system ransformer (only works on A Robust and cheep motor (rotating flux u (t U i (t Root-Mean-Square i (t peak 0 Only for sinusoidal waveforms u (t U peak cos(ωt α i (t peak cos(ωt β ω πf

2 Alternating urrent (A mpedance jω j ω U peak peak ω πf cos( ωt α cos( ωt β Express the sinusoidal voltage and current as complex rotating phasors and use values for the amplitude Re ωt α { U e } α j Re U e e 443 U Re ωt β { e } β j Re e e 443 ω ω t t Since all phasors are rotating with the same speed, we select one as the reference and observe all others relative to this one. his gives that the rotation disappears and the voltage and currents can be expressed as complex number (constan U U α β u Ri ( R ( R U R R R di ( U jω j ω du( i ( U j j ω ω Why three phase system? hree phase voltage and current re enfassystem Ett trefassystem U U U 3 U R U S U re enfaseratorer Elnät Belastning En trefaserator Σ 0 Phasors for the voltages ine to ine U - 3U f Phase (to ground U cos( ω cos( ωt ϕ Single phase p ( nstantaneous power P average 0 Apparent power S U * P jq Active power P U cosϕ Reactive power Q U sinϕ Power Rate of energy flow [W] [ VA] [ W] [ VAr] P 3U Q 3U Angle between voltage and current ϕ α β p( u ( i ( u ( i ( u ( i ( P R R S S { u ( i ( u ( i ( u ( i ( } 0 S 3U * hree phase R R S S 3U * P jq cosϕ 3 U sin ϕ 3 U,, cosϕ sin ϕ

3 Power Rate of energy flow [W] Power Rate of energy flow [W] 3-phase Power [W] Reactive power flow What is reactive power? onsider an alternating current line flowing in a line Reactive power flow What is reactive power? onsider a line segment of, for example, 00 km in a long transmission line he current causes a magnetic field around the conductor he field strength is highest close to the conductor surface he field energy density is proportional to the square of the field strenght he field is built up and eleminated with the double of the network frequency in each phase W Q W Q he distance between the phases is about 0 m. t is not possible to transfer the energy directly between the neighboring phases. he energy must be transported to some place where the conductors are connected (a erator or a transformer. Reactive power flow What is reactive power? How much energy is involved? onsider a line segment of 00 km and a current of ka (rms value; the energy at the current peak is Reactive power flow What is reactive power? Due to the presence of the reactive power, the system cannot be used up to its thermal limit WQ iˆ line 0.(000 kj 00 t is the same energy needed to lift a 500 kg car up to 7 meters. his is done each 0 ms, in each phase. 7 m Need for reactive power compensation for better utilization of the system

4 Power flow P,Q Voltages at the ends of a transmission line (same phase ( δ E s E s,0 E r E r,δ Active/reactive power at sending end E s s P real s Q imag * ( Es ( Es EsEr sinδ Es p * Es( Es Er cosδ Esq Active/reactive power at receiving ende r r P r Q imag real( Er ( Er * Er Es sinδ * Er ( Er Es cosδ s (sending end r (receiving end δ s (sending end r (receiving end Power flow Structure of the Electric Power System E E E sinδ E E cosδ j j p q j omplex power toe : * S E E( p j q P jq m E E cos δ q E sin δ p E E cos δ je sin δ E sin δ δ E E E E cos δ Re Active/reactive power to E : EE sinδ P E p E ( E E cosδ Q Eq Active power from E to E : EE P P P sin δ Reactive power consumption of the transmission line: ( E E EE δ Q Q Q cos E ransmission 400, 0 kv Regionalnät 30 kv Distributionsnät 70, 40, 30, 0,0 kv Kunder 400 V (ndustri 0-30 kv ω r turbine J s R load What happens if the turbine power does not match the load power? Power balancing Power balancing Source: Svenska Kraftnät Svenska Kraftnät: dωr J turbine P ω turbine r turbine P ω r Pload P πf ωr n grid p 4π dfgrid P J n f p turbine P grid Source: Svenska Kraftnät

5 Reservoir (energy storage Hydro Power Station he erator transforms the rotational energy into electric energy Profile over the electric energy consumption in Sweden for a typical summer day, winter day and the highest consumption day th of December 00 ontrol gate Screen Step-up transformer On the 3rd of February 0 Sweden used MW between he kinetic energy of the water is transformed into rotation of the erator shaft (rotational kinetic energy Elåret 00 Källa: Svenska Kraftnät och Svensk Energi P max P min Production planing astkurva Baskraft: Kärnkraft, fossil förbränning, (vattenkraf opplast - Gasturbin, vatten, m.m. 4 Göteborg atitude 57.7 º 00 m of solar cells Statistical cloudiness Sun tracking Efficiency: MPP 0.95 Power electronics 0.95 Solar cells 0.5 Solar Plant Power [kw] ntegrated power during year kwh Effekt (kw Solerator vs idpunkt idpunkt (timme ime [Hour] otal input energy to Sweden Sweden electric energy production Källa: SB Elåret 00

6 Electric energy production and ussage in Sweden for 00800, Wh/week Electric energy flow to and from Sweden 008, GWh Elåret 00 Källa: Svensk Energi Källa: Svenska Kraftnät och Svensk Energi Normalized electric production mix for the Nordic countries Electric energy production in Sweden: 45,0 Wh år 007 (v 65,5; k 64,3 46,0 Wh år 008 (v 68,6; k 6,3; v,0 33,7 Wh år 009 (v 65,3; k 50,0; v,5 44,9 Wh år 00 (v 66,8; k 55,6; v 3,5 46,9 Wh år 0 (v 66,0; k 58,0; v 6, Elåret 00 Källa: Svensk Energi vhydro power knuclear power vwind power nstalled peak power in Sweden 0..3, MWel Electric energy consumption in Sweden divided on different consumers Hydro power 6 97 Wind power 899 Nuclear power Other thermal power Källa: SB Elåret 00

7 Electric energy consumption for households in Sweden (investigated 007 ypical household he End he consumption is higher in winter time in the Nordic countries, but in warm countries it is opposite Do you have any questions? Elåret 00 Källa: Energimyndigheten