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Oscillation Analysis Example

Oscillation Analysis Example. Starrett Interactive Session #3. Transdemo.m. Pbus = large vs Yshunt = large. Small System Example. R + j X. J xd’. I. E / d. I = E /d /[R + j(xd’ + X)] S = E /d I* = E /d {E /d /[R + j(xd’ + X)]}* = E 2 /[R - j(xd’ + X)] = mostly reactive.

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Oscillation Analysis Example

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  1. Oscillation Analysis Example Starrett Interactive Session #3

  2. Transdemo.m • Pbus = large vs Yshunt = large

  3. Small System Example R + j X J xd’ I E/ d I = E/d /[R + j(xd’ + X)] S = E/d I* = E/d {E/d /[R + j(xd’ + X)]}* = E2/[R - j(xd’ + X)] = mostly reactive

  4. 4-Generator System

  5. Eigenvalues TIME FREQUENCY DAMPING MODE REAL IMAGINARY CONSTANT HERTZ RATIO ---- ----------- ---------- -------- --------- --------- 2 -0.2138E-01 0.8951E+01 0.4678E+02 1.4245 0.0024 4 -0.4273E-01 0.2087E+01 0.2340E+02 0.3322 0.0205 6 -0.6410E-01 0.8951E+01 0.1560E+02 1.4245 0.0072

  6. Participation Factors EIGENVALUE: -0.021 8.951J -0.043 2.087J -0.064 8.951J ST TYPE REAL IMAG REAL IMAG REAL IMAG ---------------------------------------------------------------------------------------------------- 1 CGEN 1 0.774 -0.403 -0.221 -0.005 0.770 0.410 2 CGEN 2 0.770 -0.410 -0.221 0.005 0.773 0.403 3 CGEN 1 0.823 -0.502 -0.195 -0.004 0.818 0.510 4 CGEN 2 0.819 -0.510 -0.195 0.004 0.823 0.502 5 CGEN 1 0.717 0.431 1.000 0.020 0.721 -0.428 6 CGEN 2 0.721 0.424 1.000 -0.020 0.717 -0.431 7 CGEN 1 0.872 0.489 0.855 0.018 0.877 -0.481 8 CGEN 2 0.877 0.481 0.855 -0.018 0.872 -0.489

  7. Right Eigenvectors EIGENVALUE: -0.021 8.951J -0.043 2.087J -0.064 8.951J ST TYPE REAL IMAG REAL IMAG REAL IMAG --------------------------------------------------------------------------------------------- 1 CGEN 1 -0.314 -0.600 0.311 0.000 -0.313 0.600 2 CGEN 2 -0.067 0.035 -0.003 -0.149 0.067 0.035 3 CGEN 1 0.373 0.639 0.312 0.000 0.373 -0.639 4 CGEN 2 0.071 -0.042 -0.003 -0.149 -0.072 -0.041 5 CGEN 1 -1.236 -0.038 1.414 0.000 -1.236 0.038 6 CGEN 2 -0.004 0.138 -0.014 -0.677 0.005 0.138 7 CGEN 1 1.414 0.000 1.367 0.000 1.414 0.000 8 CGEN 2 0.000 -0.158 -0.013 -0.655 -0.001 -0.158

  8. Left Eigenvectors EIGENVALUE: -0.021 8.951J -0.043 2.087J -0.064 8.951J ST TYPE REAL IMAG REAL IMAG REAL IMAG -------------------------------------------------------------------------------------------- 1 CGEN 1 -0.001 -0.404 -0.492 0.010 0.003 0.404 2 CGEN 2 -3.618 -0.020 0.000 1.027 3.618 -0.021 3 CGEN 1 -0.008 0.409 -0.433 0.009 -0.012 -0.409 4 CGEN 2 3.661 0.095 0.000 0.905 -3.661 0.096 5 CGEN 1 -0.185 0.104 0.491 -0.010 -0.186 -0.102 6 CGEN 2 0.917 1.665 0.000 -1.026 -0.917 1.665 7 CGEN 1 0.194 -0.109 0.434 -0.009 0.195 0.107 8 CGEN 2 -0.959 -1.739 0.000 -0.907 0.959 -1.740

  9. Project Goal: • We have a device to change line reactance • We want to damp system oscillations • We want to improve transient stability

  10. Use 6-Generator System • Increase all loads 20% • Increase all generators 20%

  11. Requirements • Determine which modes are the interarea modes • Use MPOF’s to select 4 candidate transmission lines • Use transient simulations to determine sensitivity of CCT to line reactance

  12. You design the procedure!

  13. Demos & Data • transdemo.m • eigdemo.m • mpof6.m • pst_var_mpof.m • mac_em_mpof.m • data6m.m

  14. Brainstorming 1 • Finding interarea modes . . .

  15. Brainstorming 2 • Selecting candidate lines . . .

  16. Brainstorming 3 • Finding transient sensitivities . . .

  17. Questions?

  18. Next: Dr. Sudhoff’s Turn . . .

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