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A Study of De-Excitation after Abrupt 3-phase Short Circuit of a Hydraulic Generator CHEN, Xianming ZHU, Xiaodong WANG,,Wei Nanjing Automation Research Institute P.O.Box 323, Nanjing ,210003, PRC Email: [email protected] ASTRACT The paper describes simulation results of de-excitation of a hydraulic generator after abrupt 3-phase short circuit. The mathematical model of the generator is built on “Park equations of synchronous machine”. In order to avoid undue complexity the effect of damping winding on rotor is ignored. In addition, the non-linear no-load characteristics of the generator is expressed approximately by an analysis expression, that facilitates the simulation and raises confidence level of it. Finally, an example of de-excitation simulation with non-linear resistors ZnO for a 700 Mw hydraulic generator of Three-gorge power plant with help of MATLAB/Simulink is given . Keywords: de-excitation, hydraulic generator, 3-phase short circuit, simulation 1 INTRODUCTION De-excitation of a large hydraulic generator is an important matter, which influences safety of generators. Specially, there are 26 hydraulic generators of 700Mw have been or will be installed in Three-gorge hydro-power plant in China. According latest estimating, there will be about one hundred such hydraulic generators which will be installed in southwest area of China in next decade. De-excitation of no-load hydraulic generator while mal-forced excitation happened has been studied [1]. However, another very important de-excitation situation, namely de-excitation after abrupt 3-phase short-circuit of hydraulic generators is still unsolved. That is why the paper will deal with it. The paper describes the comparison results of amount of magnetic energy absorbed for de-excitation of the generator after abrupt 3-phase short circuit sustaining different time. There are two cases considered here, t.e. de-excitation after abrupt 3-phase short circuit of no-load and loading generator. 2. PARK EQUATIONS GENERATOR OF SYNCHRONOUS In order to simplify discussion, the effect of damping winding on rotor of generator is neglected. Park differential equations of voltage in d ,q axis are as follows: U d pd q p ri d (1) U q pq d p ri q (2) U f i f r f p f (3) The equations of magnetic flux linkage in real physical values: (4) d Ld id L'ad i f /K q Lq iq (5) f Lad id K L f i f (6) It should be noted that parameters of synchronous machine usually represent in per unit. Besides, there are some different ways for conversion between quantities of stator and rotor. In order to have real image for simulation both quantities of stator and rotor should be represented in real physical values. In that case, it is necessary to introduce conversion coefficient concerned to above Park equations. Relationship between quantities of stator and rotor of generator may only be represented via magnetic flux linkage. So when all quantities of stator and rotor adopted are represented by their real physical values, the conversion can be simply implemented by conversion factor K for magnetic flux linkage from rotor to stator. Substitute equations (4),(5),(6) to (1),(2),(3) and use the accustom of Simulink, it can obtain following equations: (S=d/dt –--differential operator) U d S (Ld id L'ad i f / K ) X q iq rid (7) U q S (Lq iq ) X d id 2fL'ad i f / K riq U f r f i f S ( Lad Kid L f i f ) (8) (9) In equations (7),.(8),(9) all parameters and quantities of stator are in real physical values, and the same as for all parameters and quantities of rotor. Only a conversion factor K is introduced between magnetic flux linkage of stator and rotor. It should be noted that in order to distinguish d axis mutual inductance for stator from that for rotor. Lad is used for d axis mutual inductance of stator, and Lad’ for that of rotor. 3. SIMULATION FOR SOLVING DIFFERENTIAL EQUATIONS A method utilized here for simulation is solving differential equation directly so as to avoid complex calculation burden. As an example, Fig.1 shows the Simulink structure scheme for solving differential equation (7) with integral operator 1/S, proposed by authors. In order to facilitate calculation of magnetic field energy of the generator. An approximate expression of N-LC of generator is adopted here [2]. That is: Uo=L i f , if i f <= Ib (10) Uo=(M* i f )/(N+ i f ) , Fig.1 Scheme for solving differential equation Practice proved that the method for solving differential equations is very convenient. Fig.2 shows the full structure scheme for resolving the topic of the paper ,which includes differential equations (7), (8),(9) ,etc .In Fig.2 modules “Eq.1”,”Eq.2”,”Eq.3” represent expressions (7),(8),(9) respectively. if i f >Ib (11) Where Ib is excitation current of intersect point of both above functions. If a real N-LC is known, then suitable coefficients L, M, N can be determined by try and error method. For the conventional N-LC they can be adopted as follows: L=1.1, M=1.95, N=0.95. After substituting them to above expressions, Then can be found Ib=0.823. The last two rows of Table 1 shows U0’ the substituted N-LC. The error between the substituted N-LC U0’ and conventional N-LC U0 is so small that the former used for engineering calculation is fully permitted. The direct-axis inductance corresponding to main magnetic flux Lad’ equals: If if, <=Ib=0.823 then: Lad’=λL (12) If if >Ib=0.823 then Lad’=λUo / i f ,namely, Lad’=λM/(N+ i f )=1.95λ/(0.95+ i f ) (13) Coefficient λ is used for getting real value of Lad’ in henry. Expressions (12),(13) is implemented by module “inductance” in Fig.2 N-LC of a no-load generator is represented as follows: Uo=f(if) For a loading generator it becomes: U=f(if±id) Where U represents E.M.C behind leakage reactance Xp. id represents armature reaction of d axis stator current. When load of generator is inductive, negative sign should be used. Positive sign is for capacitive. Fig.2 Simulation structure for voltage build up, short circuit & de-excitation of generator It is well known that no-load characteristic(N-LC) of hydraulic generator is non-linear. It should be noted that for a reasonably designed hydraulic generators in economic and technical aspects, N-LC may not differ from the following conventional characteristic Uo=f(if) (in per unit) too much. Table 1 Conventional N-LC ( in first 2 rows) Uo 0 0.55 1.0 1.21 1.33 1.4 0 0.5 1.0 1.5 2.0 2.5 i Fig.3 De-excitation circuit of generator Module “d,q->a,b,c” in Fig.2 is used for stator current conversion from d, q axis component to a, b, c phase current. Module “de-ex” is used for implementation of de-excitation with non-linear resistor ZnO and for magnetic energy (W,Wr) calculation. Fig.3 shows de-excitation circuit of the generator. Here the field equation for de-excitation becomes: (14) 0 r f i f kiaf S (Lad Kid L f i f ) Uo' where ki f =Ux is voltage drop on non-linear resistor f 0 0.55 1.0 1.194 1.322 1.412 Here 1 per unit excitation current corresponds no-load rated terminal voltage (1 per unit) of the generator. a R. Assuming α=1, R becomes linear resistor. For non-linear resistor ZnO a=0.046,SiC a=0.28-0.36, Selection of k depends on allow reverse voltage adopted. When 3-phase short circuit happens to a no-load generator, that means electric circuit structure is changed. In order to deal with this change in simulation, it may be considered that an external 3-phase voltage with same amplitude but opposite direction of E.M.F of no-load generator , applies to its stator terminals so, that no current output from stator. Abrupt 3-phase short circuit happens when the external voltage becomes zero. Fig.4 shows equivalence scheme of no-load generator. In order Fig.4 Equivalence scheme of no-load generator to produce external 3-phase voltage above mentioned module “no-load” in Fig.2 is used. For no-load generator id=iq=0, then Eq..(7),(8),(9) become: (15) U d S ( L'ad i f / K ) U q 2fL'ad i f / K (16) U f r f i f SL f i f (17) And module ”no-load” is formed on them. Its output voltages Ud, Uq are just the same as E.M.F produced by modules “Eq.1”,”Eq.2”,”Eq.3” for no-load generator. The voltage building up process of generator may also be observed. Clock1 in Fig.2 is for control instant of 3-phase short circuit. Clock is for control instant of de-excitation. Usually before start simulation values of some parameters concerned must be given in “ command window ” of Simulink. 4. A SIMULATION EXAMPLE An example of de-excitation of a hydraulic generator of 700 Mw for Three-gorge power plant on left-shore after abrupt 3-phase short circuit is given here. (data provided from ABB Corp.) Its main data as follows: Rated power: 700Mw Rated voltage: 20Kv Rated speed: 75 r.p.m Rated power factor: 0.9 Rated field voltage, current: 475.9 V , 4158 A Field voltage, current at rated terminal voltage of no-load generator: 191.8V, 2352 A. Self-shunt static 10.1s Td 3.2s excitation system adopted. Tdo Ta 0.28s (unsaturated/saturated) xd 0.3 1 5/ 0.2 9 5 xd 0.939 / 0.835 x 0.24 / 0.2 and r fd 0.1144(130o C) '' d Obviously, the parameters provided above is not enough for simulation. Appendix shows calculation or selection of all parameters concerned in detail. Fig.6A,6B show whole processes of field current if and d,q axis stator current id ,iq during rated voltage building up, 3-phase short circuit at t1=46” and de-excitation at t2=48” of 700Mw generator. Fig.3C shows variation of d axis mutual inductance Lad’ during that period. It is a constant 0.803H in first section, then decreases in saturation section of N-LC, and returns to 0.803H after 3-phase short circuit. The time for voltage building up is long owing to Tdo’=10.1” of 700Mw generator. In order to be more clearly, other pictures in Fig.6 only show in part interval from t=45” to 50”. Fig.6D,6F show if, id and iq, Fig6E : if—id(f) in interval of short circuit and de-excitation. Where if—id(f) is effective field current, equals real field current if minus equivalent d axis armature reaction id(f). That causes Lad’ located in non-saturation section. It can be seen that there are large ac component superimposing on dc current of if ,id ,iq. Fig.6G,6H,6I show short circuit phase current ia, ib ,ic , Fig.6J,6K: q axis stator voltage Uq, magnetic energy in same interval. De-excitation time here is 0.69” Table 1 shows the magnetic energy W, Wr absorbed by varistor ZnO and field winding of 700 Mw generator at different short circuit sustaining interval. In Fig.6 the latter is t2-t1=48”--46”=2”. Tabel 1 Interval sec. 2” 1” 0.5” 0.1” W MJ 2.81 3.845 4.554 5.32 Wr MJ 0.375 0.588 0.765 1.0258 In order to obtained abrupt 3-phase short circuit and de-excitation of loading generator, field current if and voltage Uf, stator voltage in d, q axis Ud, Uq must be determined in accordance to load of generator with simplified vector diagram (Fig.5) of synchronous generator in steady state . Fig.5 Simplified steady state vector diagram of synchronous generator Assuming that terminal voltage U, load current I, and power factor cosΦ are given, then power angleδ can be calculated as follows(18): (A) (B) (C) (D) (E) (G) (H) (J) (F) (I) (K) Fig.6 Simulation results of no-load ,3-phase short circuit & de-excitation of 700Mw generator U IXq . sin( 90 ) sin (18) o Where Xq is q axis synchronous reactance. And Ud=Usinδ Uq=Ucosδ In addition, field current and voltage for such load must be given so as to obtain steady state operation condition of the generator. Fig.7 shows the simulation results of an abrupt 3-phase short circuit and de-excitation of the loading 700Mw generator . The steady state of the generator is assumed : Ud=0, Uq=(20/√3)Kv=11547v (rated phase voltage) and field current if =4158A (rated field current). Uf=if×rf. For implementing simulation here module “no-load ” is replaced by a transfer switch controlled by Clock1 in Fig.2, which changes Ud ,Uq from value mentioned just above to both zero. Besides, values of Uf ,if are put into proper places of module “ Eq.3” in Fig.2. Fig.7A,7B,7C show if, if -id(f) ,and id,iq of 700Mw generator in interval of abrupt 3-phase short circuit at t1=46”and de-excitation at t2=48”. Fig.7D,7E,7F show stator phase current ia ,ib ,ic of 700 Mw generator in same interval. Fig.7G shows the magnetic energy concerned ,and Table 2 gives the detail for different short circuit sustaining intervals. Table 2 Interval sec. 2” 1” 0.5” 0.1” W MJ 4.835 5.822 6.471 7.135 Wr MJ 0.876 1.14 1.33 1.585 Fig.7H shows the variation of d axis mutual inductance Lad’. Lad’ for loading 700Mw generator is a saturation value about 0.6H, it becomes unsaturation value 0.803H after short circuit. De-excitation time here is about 0.93 Sec. 5. CONCLUSION A). The paper shows the successful simulation of de-excitation after abrupt 3-phase short circuit of generators. In the mean time the saturation of N-LC is considered fully by using approximate analysis expressions. B).From the simulation, it can be seen : ---the less time short circuit sustained, the larger magnetic energy absorbed. ---value of d-axis mutual inductance Lad’ of loading generator is in saturation area ,and can be determined by simulation. The saturation can be ignored when 3-phase short circuit happens. Obviously armature reaction in this case is quite big to cancel some effect of field current. C). There is lack to discuss the quantitative matter of electric quantities such as if ,id, iq and ia ,ib ,ic,etc. because not enough parameters for simulation are given.. Some parameters were assumed by authors. . However, we hope that simulation method proposed by authors may be useful for electrical engineers to refer. Appendix Determination of parameters for 700Mw generator. ON STATOR SIDE: Rated stator current In=700×103/(20×0.9×√3)=22453a Base impendence Zb=20/(√3×22.453)=0.5143 ohms Phase voltage Ufφ=20/(√3)=11547V Xd=0.939×0.5143=0.483 ohms Ld=0.483/(2*pi*50)=0.00154 H Suppose Xp=0.17 Then: Xad=Xd-Xp=0.939-0.17=0.769 Xad=0.769×0.5143=0.3955 ohms Lad=0.3955/(2*pi*50)=0.00126 H Xf=Xad2/(Xd-Xd’)=0.948 Xfs=Xf-Xad=0.948-0.769=0.179 Suppose Xq=0.7Xd Xq=0.7×0.939×0.5143=0.338 ohms Lq=0.338/(2*pi*50)=0.001076 H Ta=X2/(2*pi*50*r) Resistancer of stator r= X2/(2*pi*50*Ta) Usually X2=0.5(Xd”+Xq”) or =√(Xd”×Xq”) General speaking: For hydraulic generator Xd”= 0.14----0.26 Xq”=0.15-----0.35 Suppose Xq”=0.34 Then: X2=0.5(0.24+0.34)=0.29 Or X2=√(0.24×0.34)==0.2856 Suppose X2=0.285 X2=0.285×0.5143=0.1466 ohms Stator resistance r=0.1466/(2*pi*50*0.28)=0.00167 ohms ON ROTOR SIDE: rf=0.5[(191.8/2352 )+0.1144]=0.098 ohms Lf=rf×Tdo’=10.1×0.098=0.99 H Lfs=(0.179/0.948)×0.99=0.187 H Lad’=(0.769/0.948) × 0.99=0.803 H For N-LC of 700Mw generator Lets L=1.1 ifo’=1/L=1/1.1=0.91 × 2352=2138a Base value of field current in “Xad” system ifb=0.769×2138=1644a Ufo=2352×0.098=230V id(f)) d axis stator current convert to rotor (field Winding; id(f)=id×1644/22453=id/13.66 Ratio K of magnetic flux linkage from stator side to rotor (field winding) side: K L'ad i fb Lad I n 0.803 1644 46.7 0.00126 22453 (A) Fig.7 (B) (D) (E) (G) ( H) (C) (F) Simulation results of abrupt 3-phase short circuit, de-excitation of loading 700 Mw generator Reference 1). CHEN Xianming et al “A simulation study of de-excitation of no-load water-wheel generators “ Paper Abstracts IP1-01 ICEE--C0178 ICEE-2005 July 10-14,2005 Kunming, China Full paper on CD : Industrial Process and Automation IP1-01 2). B.A.Torvenski “Universal no-load characteristic of synchronous generator and their analysis expressions” Journal of former USSR “Electric Force” factory pp45-54 No.2-3 1945 Leningrad (in Russian) Biographs CHEN, Xianming was born in Nanjing, China. He graduated from Dept.of EE Harbin polytechnic Institute, Heilongjiang province in1958 and has worked in several research Institutes in China. Now he is with NARI as a senior engineer. His interest is in power electronics and excitation of alternators. ZHU, Xiaodong He graduated from Dept.of EE Hehai University, Nanjing in 1992 and received M.S degree in 1995, since then he work in NARI. Now he is a senior engineer and his interest in power electronics and power plant control. WANG, Wei He graduated from Dept.of EE Wuhan Sciense&Technical Institute ,Wuhan, in 2001 And received M.S degree of NARI in 2004, Since then he is with NARI as an engineer. His interest is in application of power electronics, excitation of ac generators and digital simulation.