A NOVEL FEEDBACK LINEARIZING STATCOM CONTROLLER FOR POWER SYSTEM DAMPING

N.C. Sahoo, R. Ranjan, P.K. Dash, and G. Panda

References

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  17. [17] A.R. Bergen, Power system analysis (Englewood Cliffs, NJ:Prentice-Hall, 1986).AppendixNomenclature:δ rotor angle with respect to the infinitebus system voltageM effective inertia constantEqtransient q-axis voltagexd d-axis reactancexq q-axis reactancexdd-axis transient reactanceEfd direct excitation voltageTdo equivalent transient rotor time constantPm mechanical powerPe, Qe active and reactive powerThe subscript “0” indicates the initial value.Linear Impedance Load:Y = G − jB,Load bus voltage = Vrd + jVrq,Load current = (GVrd + BVrq) + j(GVrq − BVrd)Nonlinear Impedance Load:PL = PL0VrVr0n1,QL = QL0VrVr0n2where n1 and n2 are the indices (>0)Rectifier Load:Figure A1. Structure of rectifier load.Vdc,r =3√2πVr,LL cos β −3xridc,rπ,irL =√6πidc,r,and cos γ = cos β −idc,rxr√2Vr,LL,β = firing angle, γ = phase difference between ac-side voltage and current. Pdc,r = 0.8, Rdc,r = 7, β = 100, xr = 0.1Induction Motor Load [15]:A third-order induction motor model is taken as givenbelow.Stator Vds = Ed− X Iqs and Vqs = Eq− X IdsRotor T0dEqdt= −Eq+X2mXrIds − sXrRrEdand T0 dEddt= −Ed+X2mXrIqs − sXrRrEqTorqueEquation 2Hdsdt= TL − (EqIqs + EdIds).TL = k0ωr = k0ωs(1 − s) = kL(1 − s),X = XsXr − X2mXr, T0=XrωsRr,s =ωs − ωrωs,Xs = 1.2287, Xr = 1.2233, Xm = 1.18, Rr = 0.0053, ωs =2πf0, H = 0.41, Rs = 0.0079, Vds and Vqs correspond tovoltages of the load-bus.Synchronous Generator Mathematical Model:The synchronous generator is described by a third-ordernonlinear mathematical model [16, 17]:289dδdt= ∆ω,d∆ωdt=1M[Pm − Pe],dEqdt=1Tdo[Efd − Eq− (xd − xd)id]where ∆ω = ω − ω0.AVR and PSS:The excitation system of the generator consists of anautomatic voltage regulator (AVR) with a power systemstabilizer (PSS). The complete system is shown in Fig. A2.Figure A2. AVR + PSS control system of the generatingsystem.System Data:ω0 = 2πf0, f0 = 50 Hz, Re = 0.05 p.u., Res = Re, ω0Le(=Xe) = 0.15 p.u., Xes = Xe, Rp = 0.04 p.u., ω0Lp(=Xp) =0.1 p.u., Rdc = 150, C = 5000 µF, xd = 1.9 p.u., xq = 1.6 p.u,xd= 0.17 p.u., Tdo = 4.314 sec., M = 0.03 p.u., Ke = 50,Te = 0.1 sec, Kpw = 5, Kiw = 12, Emaxfd = 6 p.u., Eminfd =−6 p.u., umaxpss = 0.01 p.u., uminpss = −0.01 p.u., PL0 = 0.1 p.u.,QL0 = 0.1 p.u., n1 = n2 = 2.0Cascade PI Controller for Distribution System:Kpv = 0.5, Kiv = 100, Kpm = 0.5, Kim = 1,Kpc = 1, Kic = 10, Kpα = 0.5, Kiα = 0.5Cascade PI Controller for Generation System:Kpv = 1, Kiv = 10 , Kpm = −0.01 , Kim = −0.1,Kpc = 1, Kic = 2, Kpα = −0.1, Kiα = −0.1Feedback Linearizing Controller (For Both Distributionand Generation System):Desired pole locations for computation of K11 and K12 are:s1 = −100 and s2 = −10. Desired pole locations for compu-tation of K21, K22 and K23 are: s1 = −200, s2 = −100, ands3 = −50.

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