Lecture 2 Introduction

Transcription

1 EE 333 POWER SYSTEMS ENGNEERNG Lecture 2 ntroduction Dr. Lei Wu Departent of Electrical and Coputer Engineering Clarkson University

2 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

3 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

4 Resilient Underground Microgrid in Potsda, NY

5 Resilient Underground Microgrid in Potsda, NY

6 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

7 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

8 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

9 Outline Phasors Coplex power Network equations Balanced three-phase circuits 9

10 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 = v( t) dt = T 2 ax 2 10

11 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

12 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

13 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 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

14 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

15 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

16 Power Triangle S ( θ θ ) jsin( θ θ ) = cos + = P + jq 1 Q θ θ = tan P P P power factor = = S P + Q Exa ple: A load draw s 100 kw w ith a leading pf of W hat are φ (pow er factor angle), Q and S? φ = - cos 0.85 = kW S = = k A 0.85 Q = sin( 31.8 ) = 62.0 k ar 16

17 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

18 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