# Analysis of Subsynchronous Resonance in Power Systems by K.R. Padiyar

By K.R. Padiyar

4. 2 research of induction generator impression: frequency scanning process eighty three four. three research of torsional interaction(TI) 87 four. four nation equations and eigenvalue research ninety six four. five An set of rules for computing torsional modes 108 four. 6 Countermeasures for SSR III four. 7 Torsional oscillations in parallel hooked up turbine turbines one hundred twenty 121 five. INTERACTIONS WITH energy process STABILIZER five. 1 creation 121 five. 2 easy thought within the program of PSS 122 five. three layout of PSS 126 five. four Torsional interplay with PSS one hundred thirty five. five A case examine 132 6. INTERACTIONS WITH HVDC CONVERTER keep watch over 137 6. 1 advent 137 6. 2 HVDC converters and keep an eye on 138 6. three Modelling of HVDC procedure for examine of torsional interactions 147 6. four research of torsional interactions -A simplified procedure 153 6. five A case learn 156 6. 6 A simplified damping torque research 161 6. 7 keep an eye on of torsional interplay 167 7. INTERACTIONS WITH SHUNT COMPENSATORS 169 7. 1 advent 169 7. 2 Static Var Compensator 171 7 . three Torsional Interactions with SVC 186 7. four Static Condenser(STATCON) 189 7. five Torsional interactions with STATCON 196 7. 6 A simplified research of torsional interplay with voltage controller two hundred eight. INTERACTIONS WITH sequence COMPENSATORS 205 eight. 1 creation 205 eight. 2 Thyristor managed sequence Compensator 206 eight. three Modelling of TCSC for SSR stories 216 eight. four Mitigation of SSR with TCSC 223 eight. five Static Synchronous sequence Compensator (SSSC) 229 8.

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Pd ". 87). 91) 40 ANALYSIS OF SUBSYNCHRONOUS RESONANCE IN POWER SYSTEMS where x! k = [Vd Vq ] Y; = lid iq ] U: The nonzero elements of [Ae], [Bed, [Bd and [C e] are defined below. Remarks 1. The matrix [Ae] has constant elements (ignoring saturation) except for elements Ae{l, 2) -A e{2, 1) -w. If the generator rotor speed w is held = = MODELLING OF TURBINE GENERATOR 41 constant at wo, then [Ae] is a constant matrix independent of the operating point. 2. 92) 'ljJq = ,. Xql q + (x q - x~) Xq 'ljJg = ,.

The mechanical torque is reduced by a factor of The inertia ft. and damping are reduced by factor of (fo)2. However, since all the equations are expressed in per unit (to be introduced later) there is no loss of generality in assuming that the machine has two poles (as stated earlier). 16) numerically, it is almost impossible to obtain analytical solution even when iJ = ~ is constant. This is due to the fact that the inductance matrix [L] is time varying and the computation of inverse of [L] is required.

4 Lkj f:. 64) Remarks = Xdh = Xad with Xad arbitrarily selected as Xad = Xd - xau similarly, Xqg = Xqk = Xaq with Xaq arbitrarily selected as 1. Note that xdf Xaq = Xq - xau 2. The per unit inductances are identical to per unit reactances. 3. In general, Xfh xdf = Xdh = Xde "# Xad. = Xde = Xdh However, Canay (1983) showed that if = Xd - Xc, = xdf where Xc is the per unit characteristic reactance, then Xfh 4. The use of Bfd (instead of vf) is convenient as, in steady state, the open circuit voltage at the terminals of a synchronous machine is Bfd .