INTER-AREA OSCILLATIONS DAMPING USING POLE ASSIGNMENT CONTROLLER WITH SELECTED VARIABLES TECHNIQUE

K.A. Sattar and M.A. Al-Taee

References

  1. [1] D.N. Koterev, C.W. Taylor, & W.A. Mittelstadt, Modal validation for the August 10, 1996 WSCC system outage, IEEETrans. Power Systems, 14, 1999, 967–979. doi:10.1109/59.780909
  2. [2] Y. Mansour, Application of eigenanalysis to the Western NorthAmerica power system, IEEE Pub. No. 90TH0292-3-PWR,1990, 97–104.
  3. [3] IEEE Power System Engineering Committee, Proposed termsand definitions for power system stability, IEEE Trans on PAS,101 (7), 1982, 1891–1898.
  4. [4] E.V. Larsen & D.A. Swan, Applying power system stabilizers,Part 1/3, IEEE Trans. on PAS, 100, 1981, 3017–3046.
  5. [5] P. Kundur, M. Klein, G.J. Rogers, & M.S. Zywno, Applicationof power system stabilizers for enhancement of overall systemstability, IEEE Trans. on PERS, 4 (2), 1989, 614–629.
  6. [6] S. Hyrano, T. Michigami, A. Kurita, D.B. Klapper, N.W.Miller, J.J. Sanches-Gasca, & T.D. Younkins, Functional designs for a system wide multi-variable damping controller,IEEE Trans. on Power Systems, 5 (4), 1990, 1127–1136. doi:10.1109/59.99362
  7. [7] CIGRE technical brochure on control of power system oscillations, Study committee Pub. No. 38TF07-01, 1997.
  8. [8] R.T. Byerly, R.J. Bennon, & D.E. Sherman, Eigenvalue analysisof synchronizing power flow oscillations in large electric powersystems, IEEE Trans. on PAS, 1101 (1), 1982, 235–243. doi:10.1109/TPAS.1982.317343
  9. [9] N. Martins, Efficient eigenvalue and frequency response methods applied to power system small signal stability analysis,IEEE Trans. on Power Systems, 3 (1), 1986, 217–226.
  10. [10] D.Y. Wong, G.J. Rogers, B. Porreta, & D. Kundur, Eigenvalueanalysis of very large power systems, IEEE Trans. on PowerSystems, 3 (2), 1988, 472–480. doi:10.1109/59.192898
  11. [11] P. Kundur, G.J. Rogers, D.Y. Wong, L. Wang, & M.G. Lauby,A comprehensive computer program package for small signalstability analysis of power systems, IEEE Trans. on PowerSystems, 5(4), 1990, 1076–1083. doi:10.1109/59.99355
  12. [12] M.T. Gibbard, N. Martins, J. Sanchez, N. Uchida, V. Vittal, &L. Wang, Recent applications of linear analysis techniques,IEEE Trans. on Power Systems, 16 (1), 2001, 154–162. doi:10.1109/59.910792
  13. [13] L. Rouco & I. Perez-Arriaja, Multi-area analysis of small signalstability in large electric power systems by SMA, IEEE Trans.on Power Systems, 8 (3), 1993, 1257–1265. doi:10.1109/59.260869
  14. [14] K.A. Sattar, M.A. Al-Taee, & I.I. Hammad, Damping of powersystem oscillations using improved pole assignment controller,Journal Dirasat/Engineering Sciences (Jordan), 30(1), 2003,173–187.Appendix 1A1.1 List of Symbolsf: nominal frequency, HzKpi: gain associated with area-i transfer function,Hz/p.u. MWKr: reheat coefficientPm: turbine mechanical output power, p.u. MWPR: area rated power, WPd: area real power load, p.u. MWPtie-i: power flow limit of tie line-i, p.u. MWRi: governor speed regulation parameter,Hz (p.u. MW)−1Tm: mechanical torque, N · mTij: synchronizing torque coefficient of tie line (i-j),p.u. MW rad−1Tpi: area-i time constant, sT1T2: time constants of the hydro governor, sT3: time constant of valve positioning, sTCH: steam chest time constant, sTR: reheat time constants, sTw: water flow time constant, sXE: governor valve position, p.u. MWA1.2 Power System State EquationsThe state equations of the three areas and tie lines of thepower system are derived as follows.(i) The hydro generating unit is represented by the following set of state equations:∆˙f1 = −1Tp1∆f1 +Kp1Tp1∆Pm1−Kp1Tp1∆Pd1−Kp1Tp1∆Ptie-1 (35)∆ ˙PR1 = −1T1∆PR1−1T1R1∆f1 +1T1u1 (36)∆ ˙Pm1 =2TRT1T2R1∆f1 −2Tw∆Pm1+2Tw+2T2∆XE1 −2T2−2TRT1T2×∆PR1 −2TRT1T2u1 (37)(ii) The reheat thermal generating unit is represented bythe following set of state equations:∆˙f2 = −1Tp2∆f2 +Kp2Tp2∆Pm2−Kp2Tp2∆Pd2−Kp2Tp2∆Ptie-2 −Kp2Tp2a12∆Ptie-1 (38)∆ ˙PR2 = −1TCH1∆PR2−1TCH1∆XE2 (39)∆ ˙Pm2 = −2TR∆Pm2 +1TR−KrTCH1×∆PR2 +KrTCH2∆XE2 (40)283(iii) The non-reheat turbine differs from the reheat turbineonly in the existence of the time constant in the reheatturbine. The following set of state equations describesthis unit:∆˙f3 = −1Tp3∆f3 +Kp3Tp3∆Pm3 −Kp3Tp3a23× ∆Ptie-2 −Kp3Tp3∆Pd3(41)∆ ˙Pm3 = −1TCH2∆Pm3 +1TCH2∆XE (42)Appendix 2A =−1Tp1Kp1Tp10 0 0 0 0 0 0 0 0−Kp1Tp102TRR1T1T2−2Tw2Tw+2T2−2T2+2TRT1T20 0 0 0 0 0 0 0 0−TRR1T1T20−1T11T2+TRT1T20 0 0 0 0 0 0 0 0−1R1T10 0 −1T10 0 0 0 0 0 0 0 00 0 0 0−1Tp2Kp2Tp20 0 0 0 0a12Kp2Tp2Kp2Tp20 0 0 0 0−1TR1TR−KrTCH1KrTCH10 0 0 0 00 0 0 0 0 0−1TCH10 0 0 0 0 00 0 0 0−1R2T30 0−1T30 0 0 0 00 0 0 0 0 0 0 0−1Tp3Kp3Tp30 0−Kp3a23Tp30 0 0 0 0 0 0 0 0−1TCH21TCH20 00 0 0 0 0 0 0 0−1R3T30−1T30 0T12 0 0 0 −T12 0 0 0 0 0 0 0 00 0 0 0 T23 0 0 0 −T23 0 0 0 0BT=0 −2TRT1T2TRT1T21T10 0 0 0 0 0 0 0 00 0 0 0 0 0 01T30 0 0 0 00 0 0 0 0 0 0 0 0 01T30 0GT=−Kp1Tp10 0 0 0 0 0 0 0 0 0 0 00 0 0 0 −Kp2Tp20 0 0 0 0 0 0 00 0 0 0 0 0 0 0 −Kp3Tp30 0 0 0∆ ˙XE3 = −1R3T3∆f3−1T3∆XE3 +1T3u3 (43)(iv) The tie line power deviations between system areas aregiven by:∆ ˙Ptie-1 = T12∆f1 − T12∆f2 (44)∆ ˙Ptie-2 = T23∆f2 − T23∆f3 (45)284

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