By Haifeng Wang, Wenjuan Du
This ebook offers the study and improvement effects on energy structures oscillations in 3 different types of analytical equipment. First is damping torque research which used to be proposed in 1960’s, additional constructed among 1980-1990, and customary in undefined. moment is modal research which constructed among the 1980’s and 1990’s because the strongest process. ultimately the linearized equal-area criterion research that's proposed and built lately. The publication covers 3 major varieties of controllers: strength approach Stabilizer (PSS), proof (Flexible AC Transmission structures) stabilizer, and ESS (Energy garage platforms) stabilizer. The ebook presents a scientific and distinctive advent at the topic because the reference for functions and educational learn.
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Extra info for Analysis and Damping Control of Power System Low-frequency Oscillations
1 Linearized Model of a Single-Machine … 29 0 Eq À Vb cos d Vb sin d þ Vb sin d xqR x0dR À Á 0 Eq Vb V2 xq À x0d ¼ 0 sin d À b 0 sin 2d xdR 2 xdR xqR Pt = Vb cos d ð2:34Þ From Eqs. 33), it can be obtained that À Á À Á E0q À Vb cos d Eq ¼ E0q þ xd À x0d id ¼ E0q þ xd À x0d x0dR À Á 0 0 Eq xdR xd À xd Vb cos d ¼ 0 À x0dR xdR ð2:35Þ where xdR ¼ xd þ xt . From Eqs. 33), it can have Vb sin d xq Vb sin d ¼ ; xqR xqR ð2:36Þ E0q À Vb cos d xt E0q Vb x0d cos d ¼ þ vtq = Vb cos d þ xt id ¼ Vb cos d þ xt x0dR x0dR x0dR vtd = Vb sin d À xt iq ¼ Vb sin d À xt Hence, the simpliﬁed model of single-machine inﬁnite-bus power system is as follows: : d ¼ x0 ðx À 1Þ 1 : x ¼ ½Pm À Pt À Dðx À 1Þ M Á 1 À 0 E_ q ¼ 0 ÀEq þ Efd Tdo Á 1 KA À 0 E_ fd ¼ À E0fd þ Vtref À Vt þ upss TA TA ð2:37Þ where À Á E0q Vb V2b xq À x0d sin 2d Pt ¼ 0 sin d À xdR 2 x0dR xqR À Á E0q xdR xd À x0d Vb cos d Eq ¼ 0 À x0dR xdR Efd ¼ vtd ¼ Efd0 þ E0fd qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ xt E0q Vb x0d cos d xq Vb sin d ; vtq ¼ 0 þ ; Vt ¼ v2td þ v2tq 0 xdR xqR xdR ð2:38Þ 2 A Single-Machine Inﬁnite-Bus Power System … 30 The model is a group of 4 ﬁrst-order differential equations plus 6 algebraic equations.
VM 6 40 0 0 k2 0 0 .. 0 0 0 3 0 0 7 7 7 0 5 kM ð2:51Þ That is VÀ1 AV ¼ K ð2:52Þ where 2 V ¼ ½ v1 v2 ... k1 60 6 vM ; K ¼ 6 40 0 0 k2 0 0 0 0 .. 0 3 0 0 7 7 7 0 5 kM 2 A Single-Machine Inﬁnite-Bus Power System … 34 Denote 2 V À1 wT1 6 wT 6 2 ¼6 6 .. 4 . 3 7 7 7 ¼ ½ w1 7 5 . . w M T ¼ WT w2 ð2:53Þ wTM From Eqs. 53), obviously it can have wTi A ¼ wTi ki ; i ¼ 1; 2; . ; M ð2:54Þ Hence, wTi is called the left eigenvector corresponding to eigenvalue ki . If a new state variable vector z is introduced and deﬁned to be X ¼ VZ ð2:55Þ From Eqs.
Hence, from Fig. 14, it can have K1 Electromechanical oscillation loop _ 1 Ms + D Δω ω0 s ΔTe Fig. 3 Damping Torque Analysis s2 Dd þ 43 D x0 K1 x0 sDd þ Dd þ DTe ¼ 0 M M M ð2:89Þ If ﬁrstly the contribution from the lower part of Heffron–Phillips model, DTe , is not considered, the electromechanical oscillation loop of generator shown in Fig. 90) in fact is the linearized model of the single-machine inﬁnite-bus power system when the dynamic of exciter and the AVR are not considered. This is the case when the generator is modelled only by the rotor motion equation in Eq.
Analysis and Damping Control of Power System Low-frequency Oscillations by Haifeng Wang, Wenjuan Du