Power System Stability GENERATOR CONTROL AND PROTECTION

Transcription

1 Power System Stability

2 Outline Basis for Steady-State Stability Transient Stability Effect of Excitation System on Stability Small Signal Stability Power System Stabilizers Speed Based Integral of Accelerating Power Case Studies

3 Mechanical and Electrical Torque Applied to the Shaft T e T G T M ω

4 Stator, Rotor, and Resultant MMFs and Torque Angle R A F 2 B' C' ω F 1 C B A'

5 Synchronous Machine Tied to Infinite Bus Xg ET EHV EO Infinite Bus XL Eg XT XE =X T +X L

6 Steady State Electrical Power Output P e EgET = sinδ Xg

7 Phasor Diagram - Generator Tied to Infinite Bus Eg I δ ET E jixe jixg

8 Transient Stability

9 Rubber Band Analogy Rubber Bands Weights

10 Change in Electrical Torque Te = Ts δ + TD ω

11 Transient Stability Illustration P MAX 3 P DECEL 4 Insufficient Retarding Torque Power P M 1 2 P ACCEL Stable Retarding Torque Turbine Power Unstable, machine loses Synchronism δ 9 Power Angle- δ 18

12 Effect of Fault Clearing Time - Equal Area Not Possible P E Power P M Unit pulls out of sync Fault Breaker clears δ

13 Effect of Fault Clearing Time - Equal Area Substantial Margin Rotor decelerates due to P E max exceeding mechanical power Power P E System returns to steady state, system stable P M Fault δ Breaker clears faults Equal Area substantial margin

14 Effect of the Excitation System on Stability

15 Steady State Electrical Power Output P e EgET = sin Xg δ

16 Effect of High Initial Response Power Excitation System B P E-A A P E P E-B Fast excitation system Maximum field forcing First swing, system recovers P M Machine will lose synchronism δ

17 Small Signal Stability

18 Change in Electrical Torque Te = Ts δ + TD ω

19 Inter-Unit Oscillations Xg1 E g1 Eo Hertz Xg2 E g2

20 Local Mode Oscillations X g X L Eo E g.7-2 Hertz

21 Inter-Area Oscillations <.5 Hertz Xg1 XL Xg2 E g1 Eg2

22 Block Diagram of Generator Under Voltage Regulator Control V REF K4 T M Exciter E fd - + Ψ Σ K G ex (s) Σ fd + 3 K 2 Σ + 1+sT v 1 Field circuit T e - + ω Σ r 1 2Hs +K D K 1 ω s δ K6 1 1+sT R E Voltage transducer t Σ + + K 5

23 Power System Stabilizers

24 The "Swing Equation" 2H d ω 2 dt δ 2 = T T K ω m e D r

25 Small Signal Version of "Swing Equation" T = T δ + T e s D ω

26 Response of Speed and Angle to Small Disturbances δ Stable Positive Ts Positive T D ω T D T Te s δ δ Oscillatory Instability Positive Ts Negative T D ω T D T s T e δ

27 PSS with AVR, Exciter and Generator G P S (s) ωr K4 δ v s T M V REF E fd Ψ K fd + T e G ex (s) 3 K Σ Σ sT 3 Σ - + v 1 Exciter Field circuit - Σ + 1 ω 2Hs +K D ωr s K 1 δ K6 1 1+sT R E Voltage transducer t Σ + + K 5

28

29 PSS Theory of Operation Speed Based Stabilizers

30 Speed-Based Stabilizer High-Pass Filter Torsional Filter Stabilizer Gain & Phase Lead Limits Vstmax Speed s T6 s T5 1 + s T A1 s + A2 s Ks1 1 + s T1 1 + s T2 1 + s T3 1 + s T4 Output Vstmin

31 PSS Theory of Operation Dual Input Stabilizers

32 Small Signal Version of "Swing Equation" T = T δ + T e s D ω

33 Speed Deviation from Net Accelerating Power d 1 ω = ( r dt H T m T e K ω ) D r 2

34 Accelerating Power Based on Integral of Mechanical and Electrical Power 1 ω = [ T T ] 2H m e

35 Block Diagram of Dual-Input Power System Stabilizer High-Pass Filters Ramp-Tracking Filter Stabilizer Gain & Phase Lead Limits Vstmax Freq stw1 1 + stw1 stw2 1 + st w2 + + Σ N 1+sT 8 M (1+sT 9 ) + - Σ K s1 1+sT 2 1+ st 4 1+sT 1 1+ st 3 Output Vstmin High-Pass Filters & Integrator Power st w3 1+sT w3 K s2 1+sT 7

36 Speed Derived from VT and CT Signals I t E I E t jx q I t Generator q-axis d-axis ω

37 Accelerating-Power Design (Speed Input) High-Pass Filters Compensated Frequency Equivalent to Rotor Speed s Tw1 1 + s Tw1 s Tw s Tw2 Generator Speed Deviation Signal (i.e. no steady state component)

38 Integral of Electrical Power Block Diagram High-Pass Filters & Integrator Active Power s Tw3 1 + s Tw3 K s T7 Integral-of-Power Deviation

39 Output Stage of PSS to AVR Stabilizer Gain & Phase Lead Limits Vstmax Filtered Speed Ks1 1 + s T1 1 + s T2 1 + s T3 1 + s T4 Output to AVR Vstmin

40 Case Studies

41 Case 1 - Hydro Generator without PSS Time (seconds)

42 Case 1 - Hydro Generator with PSS Time (seconds) Dual Input Stabilizer, Phase Lead=(1+.5s)/(1+.1s), Gain=4

43 Case 2 - On-line Step Response Frequency Type PSS Ks=6, 92MW Hydro Turbine Generator A single input PSS measures only frequency, power or speed

44 Case 2 - On-line Step Response Dual input PSS Ks=7.5, 92MW Hydro Turbine Generator The PSS monitors frequency and power for superior performance

45 Case 3 Step Response All generators in service, Stabilizer OFF

46 Case 3 Step Response All generators in service, Stabilizer Gain = 1

47 Case MW Nuclear Unit - Baseline.875 WATTS 1 POSTLIM OUT GEN TERM V.1 PSS OUT x GEN TERM F.1 TEST OUT Time (Sec) Time (Sec)

48 Case MW Nuclear Unit - Final Setting.87 WATTS x1-3 2 POSTLIM OUT GEN TERM V 15 x1-3 PSS OUT x1-4 6 GEN TERM F.1 TEST OUT Time (Sec) Time (Sec)

49 Case 5 SCT/PPT Phase Compensation Requirements Phase (degrees) MW 41 MW 28 MW 14 MW 7 MW stabilizer phase compensation Frequency (Hz)

50 Case 5: On-Line Step Test with PSS Off Terminal V (kv) Active Power (MW) Reactive Power (MVAr) Gen Freq (Hz) Field (Vdc) 16 8 Field (Adc) Time (seconds)

51 Case 5: On-Line Step Test with PSS On Terminal V (kv) Active Power (MW) Reactive Power (MVAr) Gen Freq (Hz) Field (Vdc) PSS+Test (%) Time (seconds)

52 Case 6: Off-Line Step of Reference Test

53 Case 6: On-Line Step of Reference Test - PSS Off

54 Case 6: Off-Line Step of Reference Test PSS On

55 Power System Stability A function of fast protective relaying PSS is used to provide damping to prevent power system oscillations Provide damping via excitation control PSS has little effect on first swing stability, but restores damping lost by adding high initial response excitation systems Many different stabilizing schemes exist - focus on integral of accelerating power

56 QUESTIONS?