EE 333 POWER SYSTEMS ENGNEERNG Lecture 2 ntroduction Dr. Lei Wu Departent of Electrical and Coputer Engineering Clarkson University
Resilient Underground Microgrid in Potsda, NY Funded by NYSERDAR + National Grid Project Tea: Project is anaged by Clarkson Project partner are National Grid GE Energy Consulting Nova Energy Specialists 2
Resilient Underground Microgrid in Potsda, NY Project objective Design of a resilient, counity icrogrid in the NY North Country to iprove disaster response. Construct a National Grid underground syste for power and counications nterconnect ~ 12 entities: National Grid service facility, Clarkson University, SUNY Potsda, Canton-Potsda Hospital, illage of Potsda buildings, plus coercial providers of fuel, food, and other essential eergency services. 3
Resilient Underground Microgrid in Potsda, NY
Resilient Underground Microgrid in Potsda, NY
Useful Links EEE EEE Power and Energy Society (PES) North Aerican Electric Reliability Corporation (NERC) Federal Energy Regulatory Coission (FERC) U. S. Energy nforation Adinistration EEE Sart Grid Newsletter 6
Course schedule (Subject to changes) ntroduction to Power Systes Power systes developent and trend Chapter 1 2 hours Fundaentals Phasors, real and reactive power, network equations, three-phase Chapter 2 6 hours Transforers deal & practical transforer, equivalent circuit, per unit syste connections Chapter 3 6 hours Transission Line Paraeters Resistance, inductance and capacitance, conductor bundling, electric field Chapter 4 3 hours Transission Lines: Steady- State Operation Short, ediu, and long line odels, reactive copensation Chapter 5 3 hours Midter Exa Hour Exa Power Flows arious ethods for power flow study, coputer siulation ethod Chapter 6 7 hours Syetrical Coponent Derivation and use of syetrical coponents for syste odeling Chapter 8 3 hours Unsyetrical Faults Unsyetrical fault current calculations Chapter 9 5 hours Final Exa 7
EE 333 POWER SYSTEMS ENGNEERNG Fundaentals Reading: Chapter 2.1; 2.3 ; 2.4 ; 2.5 Hoework 1 will be posted on the course website Dr. Lei Wu Departent of Electrical and Coputer Engineering
Outline Phasors Coplex power Network equations Balanced three-phase circuits 9
Phasors The goal of phasor analysis is to facilitate the analysis of constant frequency ac power systes v(t) = ax cos(ωt + θ v ) = cos(ωt + θ v ) i(t) = ax cos(ωt + θ i ) = cos(ωt + θ i ) ω = 2π f f, where is 50Hz or 60Hz Root Mean Square (RMS) voltage of sinusoid values T 0 2 2 1 = v( t) dt = T 2 ax 2 10
Phasors Starting fro a DC syste algebraic equations ( ) = R + R 1 2 For an AC syste with inductive load differential equations ( ) di t v( t) = Rii( t) + Li dt 11
Phasors n steady-state, ( t) ( ) icos ωt+ θ = v ( ) di t v = Li dt d Li [ icos( ωt+ θ )] dt ( ω θ ) = ωili i ( ω θ ) icos t+ sin t+ v icos( ωt+ θv ) ω c ω + θ = + ilii os t + ( ω θ ) + ji isin( ωt+ θ ) icos t+ v v π 2 = Liiω π θv = θ + 2 π π = ωiliicos ωt+ θ + + jiωili isin ωt+ θ + 2 2 12
Phasors j j ωt+ θ t+ + v 2 = ωi i i ( ω θ ) ie L e π jθ j v jωt jθ 2 jωt ie ie = ωiliie ie ie θ ( ω θ ) + ji isin( ωt+ θ ) icos t+ j v j ie = jiωili ie = iz L v θ v π π = ωiliicos ωt+ θ + + jiωili isin ωt+ θ + 2 2 Siilarly, we can get Z C and j i ω i C π 1 jθv ie 2 jθ e i 2 Z L jiωil Z R R 13
Phasor Representation Root ean square (RMS) cosine-referenced voltage phasor is: jθ = e = θ = cosθ + jsinθ jθ = e = θ = cosθ + jsinθ Euler s dentity jθ e = cosθ + jsinθ Conjugate * ( cosθ jsinθ ) ( cosθ jsinθ ) = + = j θ = e = θ * 14
Coplex Power Coplex power is the instantaneous consuption of energy S * W var ( * ) ( ) ( θ θ ) jsin( θ θ ) = = θ θ = θ θ = cos + = P + jq =S cos θ θ θ ( θ ) -- apparent power (volt-aperes, A) -- power factor (leading or lagging) -- power angle 15
Power Triangle S ( θ θ ) jsin( θ θ ) = cos + = P + jq 1 Q θ θ = tan P P P power factor = = S P + Q 1 2 2 Exa ple: A load draw s 100 kw w ith a leading pf of 0.85. W hat are φ (pow er factor angle), Q and S? φ = - cos 0.85 = 31.8 100kW S = = 117.6 k A 0.85 Q = 117.6 sin( 31.8 ) = 62.0 k ar 16
θ Unity power factor,, Current is in phase with voltage Pure resistive load Z = R Absorb positive real power = θ = = θ Z R θ = 0 cos( θ θ ) = 1 * 2 * S = = θ θ = 0 R R 17
Lagging power factor,, Pure inductive load θ Absorb positive reactive power Z = jω L = jx L S = θ θ > 0 sin( θ θ ) > 0 = = θ = θ Z jxl XL 2 * 2 π * π π = = θ θ = XL 2 XL 2 18