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

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

References

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  14. [14] K.A. Sattar, M.A. Al-Taee, & I.I. Hammad, Damping of power system oscillations using improved pole assignment controller, Journal Dirasat/Engineering Sciences (Jordan), 30(1), 2003, 173–187. Appendix 1 A1.1 List of Symbols f: nominal frequency, Hz Kpi: gain associated with area-i transfer function, Hz/p.u. MW Kr: reheat coefficient Pm: turbine mechanical output power, p.u. MW PR: area rated power, W Pd: area real power load, p.u. MW Ptie-i: power flow limit of tie line-i, p.u. MW Ri: governor speed regulation parameter, Hz (p.u. MW)−1 Tm: mechanical torque, N · m Tij: synchronizing torque coefficient of tie line (i-j), p.u. MW rad−1 Tpi: area-i time constant, s T1T2: time constants of the hydro governor, s T3: time constant of valve positioning, s TCH: steam chest time constant, s TR: reheat time constants, s Tw: water flow time constant, s XE: governor valve position, p.u. MW A1.2 Power System State Equations The state equations of the three areas and tie lines of the power system are derived as follows. (i) The hydro generating unit is represented by the following set of state equations: ∆˙f1 = − 1 Tp1 ∆f1 + Kp1 Tp1 ∆Pm1− Kp1 Tp1 ∆Pd1 − Kp1 Tp1 ∆Ptie-1 (35) ∆ ˙PR1 = − 1 T1 ∆PR1− 1 T1R1 ∆f1 + 1 T1 u1 (36) ∆ ˙Pm1 = 2TR T1T2R1 ∆f1 − 2 Tw ∆Pm1 + 2 Tw + 2 T2 ∆ XE1 − 2 T2 − 2TR T1T2 × ∆PR1 − 2TR T1T2 u1 (37) (ii) The reheat thermal generating unit is represented by the following set of state equations: ∆˙f2 = − 1 Tp2 ∆f2 + Kp2 Tp2 ∆Pm2− Kp2 Tp2 ∆Pd2 − Kp2 Tp2 ∆Ptie-2 − Kp2 Tp2 a12∆Ptie-1 (38) ∆ ˙PR2 = − 1 TCH1 ∆PR2− 1 TCH1 ∆XE2 (39) ∆ ˙Pm2 = − 2 TR ∆Pm2 + 1 TR − Kr TCH1 × ∆PR2 + Kr TCH2 ∆XE2 (40) 283 (iii) The non-reheat turbine differs from the reheat turbine only in the existence of the time constant in the reheat turbine. The following set of state equations describes this unit: ∆˙f3 = − 1 Tp3 ∆f3 + Kp3 Tp3 ∆Pm3 − Kp3 Tp3 a23 × ∆Ptie-2 − Kp3 Tp3 ∆Pd3 (41) ∆ ˙Pm3 = − 1 TCH2 ∆Pm3 + 1 TCH2 ∆XE (42) Appendix 2 A = −1 Tp1 Kp1 Tp1 0 0 0 0 0 0 0 0 0 −Kp1 Tp1 0 2TR R1T1T2 −2 Tw 2 Tw + 2 T2 −2 T2 + 2TR T1T2 0 0 0 0 0 0 0 0 0 −TR R1T1T2 0 −1 T1 1 T2 + TR T1T2 0 0 0 0 0 0 0 0 0 −1 R1T1 0 0 − 1 T1 0 0 0 0 0 0 0 0 0 0 0 0 0 −1 Tp2 Kp2 Tp2 0 0 0 0 0 a12Kp2 Tp2 Kp2 Tp2 0 0 0 0 0 −1 TR 1 TR − Kr TCH1 Kr TCH1 0 0 0 0 0 0 0 0 0 0 0 −1 TCH1 0 0 0 0 0 0 0 0 0 0 −1 R2T3 0 0 −1 T3 0 0 0 0 0 0 0 0 0 0 0 0 0 −1 Tp3 Kp3 Tp3 0 0 −Kp3a23 Tp3 0 0 0 0 0 0 0 0 0 −1 TCH2 1 TCH2 0 0 0 0 0 0 0 0 0 0 −1 R3T3 0 −1 T3 0 0 T12 0 0 0 −T12 0 0 0 0 0 0 0 0 0 0 0 0 T23 0 0 0 −T23 0 0 0 0 BT =         0 − 2TR T1T2 TR T1T2 1 T1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 T3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 T3 0 0         GT =          − Kp1 Tp1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 − Kp2 Tp2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 − Kp3 Tp3 0 0 0 0          ∆ ˙XE3 = − 1 R3T3 ∆f3− 1 T3 ∆XE3 + 1 T3 u3 (43) (iv) The tie line power deviations between system areas are given by: ∆ ˙Ptie-1 = T12∆f1 − T12∆f2 (44) ∆ ˙Ptie-2 = T23∆f2 − T23∆f3 (45) 284

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