A FUZZY VARIABLE STRUCTURE CONTROLLER FOR TRANSIENT STABILITY ENHANCEMENT OF FLEXIBLE AC TRANSMISSION SYSTEM

P.K. Dash and M.H. Naeem

References

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  15. [15] P. Kundur, Power system stability and control (McGraw Hill,1994).Appendix 1Generator Dynamic EquationsThe dynamics of each synchronous machine is modelled bythree differential equations given by:δ·= ω − ω0; δ·=dδdtω·=πH(Pm − Pe)e ·q(Efd0 + ∆Efd − eq− (xd − xd)id)τ d0and−6.0 ≤ Efd ≤ 6.0Pe = eqiq + (xd − xd)id iqThe PSS control output is given byupss = KδsTQ1 + sTQ1+ sT11 + sT2whereKδ = 0.24, TQ = 0.4, T2 = 0.3Appendix 2Modelling of UPFCLet us assume that an ideal series connected voltage sourceof magnitude Vc and reactance Xse is present between twobuses (s, r) in a power system as shown in Fig. A2.Figure A.1. Voltage source representation of series con-verter.The Norton’s equivalent of the circuit shown in Fig.A.1 is represented in Fig. A.2.Figure A.2. Current source representation of series con-verter.Ise = −jBse Vc in parallel with the line where Bse = 1/Xse.213The current source Ise corresponds to the injectionpowers Ss and Sr where:Ss = Vs(Ise)∗(A.1)Sr = Vr(Ise)∗(A.2)The injection power Ss and Sr are simplified to:Ss = Vs(jBseρV jαse )∗= −Bseρ|Vse|2sin(α) − jBseρ|Vse|2cos(α) (A.3)Sr = Vr(−jBseρV jαse )∗= Bseρ|Vs| · |Vs| sin(θ + α)+ jBseρ|Vs| · |Vr| cos(θsr + α) (A.4)whereVc = ρVse ejαand θsr = θs − θr.Based on the explanation above, the injection modelof a series connected voltage source can be represented bytwo dependent loads as shown in Fig. A.3.Figure A.3. UPFC injection model.The apparent power supplied by the series voltagesource converter is:Sconv2 = VcI∗sr = ρejαVsVs + Vc − Vrj Xse∗(A.5)SoPconv2 = Bseρ|Vs| · |Vr| sin(θsr + α) − Bseρ|Vs|2sin(α)(A.6)Qconv2 = −Bseρ|Vs| · |Vr| cos(θsr + α) + Bseρ|Vs|2cos(α)+ Bseρ2|Vs|2(A.7)Appendix 3Generator Data (Pbase = 1000 MVA)Equivalent gen. Generator 1 Generator 2 Generator 3Type Thermal Hydro HydroCapacity 5500 MVA 1800 MVA 1800 MVAInertia 4 s 4 s 4 sconstant (H)d-axis 2.00 p.u. 1.00 p.u. 1.00 p.u.reactance (Xd)q-axis 1.90 p.u. 0.60 p.u. 0.60 p.u.reactance (Xq)d-axis transient 0.25 p.u. 0.30 p.u. 0.30 p.u.reactance (Xq)Field time 6.00 s 6.00 s 6.00 sconstant (τdo)AVR gains (Ke) 30 10 10AVR time 0.05 s 0.05 s 0.05 sconstant (τe)Transmisssion lines (double circuit)L1 = 350 km, x = 0.20 Ω/km (compensated line)L2 = 50 km, x = 0.34 Ω/km, L3 = 50 km, x = 0.34 Ω/kmLoads (p.u.) in admittance formYL1 = 6.0 − j 1.2, YL2 = 0.1 − j 0.010, YL3 = 0.1 − j 0.010,YL4 = 1.0 − j 0.2UPFC dataxse = 0.0006, Vcr max = 0.1, Vcr min = −0.1, Vcp max = 0.1,Vcp min = −0.1, Vdc base = 31.113 kV, C = 5500 µFsController DataFuzzy-PL1p1 = 2.0, L1r1 = 2.0, L1p2 = 2.0, L1r2 = 2.0, L2p1 = 2.0,L2r1 = 2.0, L2p2 = 2.0, L2r2 = 2.0, Cp1 = 0.5, Cr1 = 1.5,Cp2 = 0.5, Cr2 = 1.5 and λ = 0.5.PI controllerKpp1 = 0.01,Kip1 = 0.4, Kpr1 = 0.01,Kir1 = 0.01, Kir1 = 0.4,Kpp2 = 0.01, Kip2 = 0.4, Kpr2 = 0.01, Kir2 = 0.4The second subscript of all parameters in the controllerdata corresponds to either phase (p) or reactive (r) voltagecomponent and the third to the UPFC number.214

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