University of Erlangen-Nuremberg Faculty of Engineering Sciences

Transcription

1 University of Erlangen-Nuremberg Faculty of Engineering Sciences Institute of Electrical Power Systems Prof. Dr.-Ing. G. Herold

2 Analytical Method for Investigation of three-phase Converter Systems in steady state operation based on Space Phasors 6 th International Conference Electric Power Quality and Supply Reliability Pärnu, Estonia, August 2729, 28 Prof. Dr.-Ing. Gerhard Herold University of Erlangen-Nürnberg Institute of Electrical Power Systems Prof. Dr.-Ing. G. Herold 2

3 Characteristics of state variables in symmetrical converter systems (scs) All space phasors of symmetrical 3-phase ac systems with converter loads in steady state are of the 6-pulse type: h h 2h v6th6 a v6t with 6 3 Harmonic coefficients 6 j 2 ˆ n t V c v t e dt n Ordinal numbers c 6 6 for n6 6k otherwise k,, 2,3, Prof. Dr.-Ing. G. Herold 3

4 Im i Typical 6-pulse space phasor i 6 Iˆ e jt Rei Prof. Dr.-Ing. G. Herold 4

5 Periodicity of the state variables in steady state & boundary conditions All of the 3-phase state variables of the scs are in steady state operation 6-pulse space phasors. 2 a v v 3 z z All of the dc state variables of the scs are periodically with the same period v v 3 dz dz Prof. Dr.-Ing. G. Herold 5

6 Steadiness of the state variables The converter changes its operation mode one times in the space phasor period. The steadiness conditions at the transition angle are: v v z dz v v z dz Solving the state space equation of the scs with respect to the boundary & steadiness conditions we get all of its voltages and currents in steady state. Prof. Dr.-Ing. G. Herold 6

7 Symmetrical converter system symm. 3-phase ac network T S R dc network Usually a converter changes its operation mode in each space phasor period from three active valves (commutation) to two 3 5 Here: valves, 2, 3 valves 2,3 Prof. Dr.-Ing. G. Herold 7

8 Symmetrical converter system symm. 3-phase ac network R T S dc network Usually a converter changes its operation mode in each space phasor period from three active valves (commutation) to two 3 5 Here: valves, 2, 3 valves 2,3 Prof. Dr.-Ing. G. Herold 8

9 Symmetrical converter system during commutation The scs consists of two orthogonal components during commutation: i k Im 23 au p space phasor network commutation circuit k Re au p space phasor network i d 2 3 u d 23 dc network dc circuit during commutation dk 2 2 vzc a vzk a v 3 zdk Prof. Dr.-Ing. G. Herold 9

10 Symmetrical converter system outside of commutation The scs consists of two orthogonal components outside of commutation as well: Im 23 u p space phasor network i d 2 u d 2 dc network dc circuit outside of commutation de Re u p space phasor network ul no load circuit outside of commutation l 2 2 v ze vzl aa v 3 zde Prof. Dr.-Ing. G. Herold

11 Symmetrical converter systems described by four single-phase circuits If the dc network only consists of one branch there are 4 very simple and similar single-phase circuits circuit u Z u pn n pdn u pn space phasor network Z n u pdn 3 comm. c. Imaup dc c. during c. Reaup Zd u dc c. outs. of c. Im up Zd u no load c. Re u p pd pd Prof. Dr.-Ing. G. Herold

12 u,i, Symmetrical converter system with resistiveinductive impedances i d i da i udka u i R i R u dk,5 t 2 dc current and voltage u vr u vr t 2 ac phase current and voltage Prof. Dr.-Ing. G. Herold 2

13 Symmetrical converter system with resistiveinductive impedances, Im v i v u p u v u v space phasors in a synchronuos rotating coordinate system i v Rev,8 Prof. Dr.-Ing. G. Herold 3

14 Symmetrical converter system with resistiveinductive impedances characteristic lines ud id pd 2 p 3 4 p 5 max max Operation diagramm broken lines: inductive impedances only 6 7 border for inverter operation Prof. Dr.-Ing. G. Herold 4

15 Symmetrical converter system with series resonant circuit power system i i 2 Z i i 2 Z2n u u u SK L C i 3 u L u C u v u pn Z 3 X c u c udn single line diagramm 4 equivalent circuits Prof. Dr.-Ing. G. Herold 5

16 Symmetrical converter system with a series resonant circuit n n n k n de ndk n l Q K S kn Q K S kn, 5, 2 Eigenfrequencies of the 4 circuits depending on the resonant frequency of the series resonant circuit and its reactive power n SK Prof. Dr.-Ing. G. Herold 6

17 u SKR Symmetrical converter system with a series u pr u cr resonant circuit Operation far from the resonant point u vr i 3R u pr ac phase voltages and currents i 2R i 3R i R t 2 circuit n n n 3 2k with k,, 2, 3, m n 2 SK nsk,7 3,27 n k de dk l n 3 3,37 3, 2,997 2,97 m Prof. Dr.-Ing. G. Herold 7

18 Symmetrical converter system with a series resonant circuit Operation in the resonant point circuit n n n k de dk l n 5,89 5, 3 4,979 4,853 m 5 4 u SKR u cr n 2 SK nsk 47,58 6,898 4 u pr u vr t 2 ac phase voltages Prof. Dr.-Ing. G. Herold 8

19 Symmetrical converter system with a series resonant circuit u pr u SKR Operation in optimum working point u vr i 3R u cr i 2R ac phase voltages and currents i 3R n SK 5 circuit n n n k de dk l 4,233 4,32 4,9 4,48 i R t 2 nm 4,3 Prof. Dr.-Ing. G. Herold 9

20 Symmetrical converter system with a series resonant circuit Operation in the optimum working point v T N p st harmonic,95,78,92,873 total,83,767,9,872 Power factor correction id2 i2 id i udsk usk,85, 47, 35 Reduction of distortion idsk isk i5sk isk,685,664 Distortion of the filter current Prof. Dr.-Ing. G. Herold 2

21 Periodicity of the state variables in steady state & boundary conditions in a 2-pulse scs jav v 6 z z v v 6 dz dz Im u u N u si u si u N 2-pulse space phasor of the Voltages in an inductive scs operating at the maximum power line u p Re u Prof. Dr.-Ing. G. Herold 2

22 2-pulse scs with resistive-inductive impedances u,i u hr u,i u hr i R i R t 2 t 2 Voltage at the PCC and current in a 2-pulse scs for = Voltage at the PCC and current in a 2-pulse scs at the short circuit line Prof. Dr.-Ing. G. Herold 22

23 Thyristor controlled reactor (TCR) the basic element of thyristor based FACTS i u p u p 2 Thyristor Controlled Reactor TCR i i L u c X c Thyristor Controlled Series Capacitor TCSC X X L X u L 2 2 p u p 2 X i i 2 X X X 3 2 i u L p u X p 2 L X L2 X c u c Static Var Compensator SVC All of symmetrical systems with TCR are of 6-pulse type Prof. Dr.-Ing. G. Herold 23

24 TCR with 3 & 2 active valves u pr i is i T t 2 i R i R t 2 Phase voltage and current Symmetrical phase currents Prof. Dr.-Ing. G. Herold 24

25 TCR with 3 & 2 active valves Im i Space phasor of phase currents Rei Prof. Dr.-Ing. G. Herold 25

26 TCR with 2 & active valves u,i u pr is i T i R t 2 t 2 i R Phase voltage and current Symmetrical phase currents Prof. Dr.-Ing. G. Herold 26

27 i Thyristor controlled reactor (TCR) the basic element of thyristor based FACTS 3&2V 2&V i e i Rms current, first harmonic and harmonic distortion depending on the firing angle i D 6 3 Prof. Dr.-Ing. G. Herold 27