CC BY
14
УДК 621.316.925
ABOUT SATURATION OF TRANSFORMERS OF THE CURRENT DIFFERENTIAL PROTECTION OF THE ELECTRIC MOTOR AT START-UP
N.N. Kurguzov, L.I. Kurguzova, M.N. Kurguzova
PSU named after S. Toraighyrov
Бастагщы кезецде элгктрк,озгалпщышты icxe к,оск,анда жлбер'тепйн токтыц апериодтык, к;урастыратыныны мен айнымалы жишютц epKin к;урастыратыныц куатты асинхронды козгалпщышыныц дифференциалды к,оргауыныц ток трансформаторлары н терец т олъиупырудыц салыстырмилы талдауы жасалгак Айнымалы жишкпйц еркш курастыратындарыныц дифференциалды к,оргаудыц ток трансформаторлары взектерт узак^а тым созылган терец пюльщтыру мен баланс емеспиц (небаланстыц) узак/пы етпет тогыныц пайда болуына себеп бола тыны корсетигген Айнымалы житктщ ерюн курастыратындарыныц ток трансформаторлары взектерш алгаищы тольндпырудыц уацыт кезецтщ аналитикальщ формуласы алынган
Проведен сравнительный анализ глубокого насыщения трансформаторов тока дифференциальной защиты мощного асинхронного электродвигателя апериодической составляющей пускового тока и свободной составляющей переменной частоты в начальный период пуска электродвигателя. Показано, что свободные составляющие переменной частоты могут вызвать более продолжительное глубокое насыщение сердечников трансформаторов тока дифференциальных защит и появление длительного переходного тока небаланса. Получено аналитическое выражение для момента времени первого насыщения сердечников трансформаторов тока свободной составляющей переменной частоты.
The comparative analysis of deep saturation of current transformers of differential protection of the powerful asynchronous electric motor with an unidirectional component a starting current and a free component of variable frequency at the initial stage of start-up of the electric motor is carried out. It is shown, that free components of variable frequency can cause much prolonged deep saturation of cores of current transformers of differential protection and occurrence of prolonged transitive current of imbalance. Analytical expression for the moment of time of the first saturation of current transformers cores of a free current of variable frequency is gained.
In the practice of exploitation of electric power stations and substations with powerful electric motors of alternative current [ 1 ], cases of false work of longitudinal differential protection of electric motors executed on the relay with sated current transformers were repeatedly registered.
In [2,3] it is established that the principal cause of occurrence of the significant periodic current of imbalance-it the current of variable frequency at the initial moment of start-up of the electric motor is. At the same time, in a number of sources, for example [4,5], it is affirmed that the reason of false operations of differential protection of powerful electric motors are currents of imbalance caused by saturation of current transformers (CT) of differential protection with unidirectional components of the current of the stator at the initial stages of start-up, instead of currents of variable frequency.
The present work describes the analysis of saturation of CT of longitudinal differential protection with free components of the starting current in the modes of start-up of electric motors of the capacity of4000 and 8000 kW with the help of mathematical model of object «the asynchronous electric motor -longitudinal differential protection». The known equations describing processes in the asynchronous electric motor [6] and longitudinal differential protection [7] are
taken as a basis of mathematical model of the object« the asynchronous electric motor - longitudinal differential protection.
The current equivalent mesh connection of the rotor and the standard assumptions were used for high-power electric motors with strong dependence of parameters of the wiring of the rotor on the effect of current displacement:
• the voltage applied to the stator winding is sinusoidal;
• all three poles of switching device (the switch in the circuit of the stator winding of the electric motor) become isolated simultaneously;
• the stator and the deep bar rotor have three-phase symmetric windings;
• distribution of the magnetic field of each winding along the circle of the air backlash is sinusoidal;
• losses of steel are not taken into account;
• availability of rotor slot and non-uniformity of the pole gap do not influence on the magnetic conductance.
The voltage on connection terminals of the electric motor is designed calculated with the prediction of power failures on active and jet resistance of the mains (step-down transformers, conductor lines and power cables).
Taking into account the accepted assumptions, the system of the equations describing processes in the asynchronous electric motor, becomes [6]:
рЧ = и
г за
Я Я
__Б_1р | 5 р
дв,а I Ба та
аБ
ОБ
Я
Я
рЧ>5(3 - идв,р" ь 'тр'
<ЗБ СБ
н га (!) га (I) та гр аг аг
р (0 п(1)
рЧф (1) \(3 + (1) ЧтР+ШТ- • стг
га
аг
рУ
р У
(2) га
К (2) к (2)
гр
ь(2) га ь(2) та
аг "аг
к (2) п (2)
(2) _ VI/ (2) , 14 г и/ (2) , (2).
Ф
ь(2) гр + ^(2) тР га ' "аг аг
та
У
У
Ба
га та
+
^ ьО ^ I-
аг аг
т
тр I ,(1) ,(2) аБ ь, ь__
аг
аг )
У „ Ч> п
. Ф гр т(3
Ь ,(1) т (2) Ь
аБ ь ь
аг
аг
1П
М =-
3 р] '
2 Ь
аБ
Ц, уму ; та эр Ба тр)
рю =
М-М
М)
¥ -У _ Ба та |
Ба I ' Бр
аБ
Ш _ VI/
бР тр
I
ОБ
сИ
Ба .
;и
и — и — Я 1 — I- п — ^ п IV I п м^ ,
дв,а Ба с Ба с ^ дв,р б|3 с б[3 с ^
= и
Я 1 о -I
БР
Where oc,(3 - system of coordinate
axes;
p- the symbol of differentiation on time;
^"s'^as" act've resistance and induction of dispersion of the winding of the stator;
sa s(3" magnetic linkage
wirings of the stator on axes;
n (\) T n>
K ,Lar- active resistance and leakage induction of the first loop of a winding of a rotor;
n (2) r (2)
'Lar- active resistance and
leakage induction of the second loop of
the winding of the rotor;
u/<0 ii/d) . ,
ra* r|3" magnetic linkage ol the
first loop of the winding of the rotor on
axes;
X1J( 2) 11/(2)
ra' r[5" magnetic linkage of the second loop of the winding of the rotor
on axes;
' mp - magnetic linkage of mutual induction on axes-
Us,a,Us,p- voltage of the power supply on axes;
^ a ' ^ fl, P ~ voltage on connection terminal of the electric motor on axes;
c- active resistance and induction of the power line;
co; - angular speed of rotat ion of an electric motor rotor;
M - the electromagnetic torque of the engine;
Mc(cor)_ the drag torque of the mechanism in the function from speed of rotation;
P,- number of poles pairs; 'jcc'^B" currents in the stator wiring on axes.
On fig. 1 the rating oscillogram of change in time of currents in phases A iKA and C /( of the stator winding the electric motor with the capacity of 4000 kW and is given the angular speed ii{r during the start-up, gained by mathematical modelling of processes in an electric drive.
Figure 1 - the Oscillogram of start-up of the electric motor
mug tin a.M5 ui inuc lb UUVIUUSIV
i. In the phase A the stator ig of the electric motor, the ectional component of the g current is absent. Therefore, placement of the current curve sed by imposing the starting : of the free component having le frequency on the periodic 5. In the phase A this result is the unidirectional component starting current and the free t>
are oauiv transiormed to secondarv
J
windings of CT. causing [2-4J saturation of CT cores and occurrence of significant transitive currents of imbalance. In figure 2 the settlement oscillogram of change in time of currents of shoulders and currents of imbalance in phases A and C of the longitudinal differential protection of the electric motor with the capacity of 4000 kW is given.
V V V V
MVWVVVVVVVVWWWVWVl
IAa
\j \ \
A A
J V \
V
AA.aj,sJ
Figure 2 - the Oscillogram of currents of shoulders and currents of imbalance of protection
om the oscillogram it is visible Let's analyse the opportunity of
e current of variable frequency entry of cores of the most loaded CT in
starting current of the electric the mode of deep saturation as a result
causes deep saturation of CT of the action of only the free current of
nd occurrence of the prolonged variable frequency in time, equal to the
ve current of imbalance. first half-cycle of this current. The
CUlCb <K
of the magnet T[
current initial « motor i contact: the stat< motor [ the val simulta of the s frequen [9] of simultai D
the free as the c start-up electric 4000 ar reach 0. a const; the un practice second; du ratio unidirec within tl Hence, t variable more ii n id i re
characteristic of magnetization CT such as TPOL-IO is close to rectangular. Therefore, in the analysis of the modes of deep magnetic saturation of their cores according to [7], we use the method of the rectangular characteristics of magnetization.
The amplitude Ad of the free current of variable frequency at the initial stage of start-up of the electric motor at simultaneous short circuit of contacts of the switch in the circuit of the stator winding can reach the electric motor [2]. or even to exceed a little [8] the value of rated current. At non-simultaneous short circuit of contacts of the switch free currents of variable frequency can exceed by 1,4-1.8 times [9] of the values of currents at simultaneous short circuit of contacts.
Duration of the first half-cycle of the free current of variable frequency, as the carried out research of modes of start-up of the non-loaded and loaded electric motors with the capacity of 4000 and 8000 kW have shown, can reach 0,3-0,8 seconds (in comparison, a constant of time T attenuations of
a
the unidirectional component in practice is within the limits of 0,01-0.04 seconds [5] and, consequently, the duration of existence of the unidirectional component is practically within the limits of 0,03-0,16 seconds). Hence, the influence of free currents of variable frequency on cores CT will be more prolonged, than the unidirectional component of the
starting current.
Let's present the free secondary current as a not fading sinusoid roughly approximately:
f2sd =i'isd =A9'sin(»rt).
Magnetic linkage before saturation of core CT, taking into account [11]
4< = r2i'2s3dt + V
where1"-) - active resistance of secondary circuit CT;
^q - initial magnetic linkage, appropriate to residual magnetization of the core.
After the transformations executed according to [7.11] under condition of =0, we shall receive the expression of time of entry of core CT in the saturation caused bv the action of the first
J
half wave of the free component of the current of variable frequency (during the time of the first turn of the rotor at the angle of 180°);
1 B t . =—arccos(l--—)
sl en B
r m
Where - the induction of saturation of core CT;
B - the amplitude of the induction at the absence of saturation of the core.
Under calculating conditions for the electric motor with the capacity of 8000 kW the time of the first saturation of the most loaded CT longitudinal differential
th the data gained as a result of the of 300 MW.
CONCLUSIONS
1- ls shown, that iree of free current of variable frequency is mponents of variable frequency may gained, which can be used in the research jse more prolonged deep saturation 0f transitive modes of operation of CT
the cores of transformers of the "rent of differential protection.
2. The analytical expression for the le of the first saturation of cores CT
of longitudinal differential protection of electric motors using the method of the ordered impression of the initial current components.
THE LITERATURE
1. Slodarzh M.I., Frydman A.J. fferential protection of generators and ;h-voltage electric motors of variable rent.-Power station, 1971, № 5.
2. Bogdan A.V., Kurguzov N.N., rguzova L.I. Current imbalance of Terential protection of powerful ctric motors // Power station, 1980, № 3. 46-50.
3. Bogdan A.V., Kurguzov N.N., rguzova L.I., Alfiitov V.I. Differential itection of the synchronous electric motor »ower station, 1989, № 5, p. 70-72.
4. Kuzhekov S.L., Chmyhalov G.N., ihkerymov I.A. Differential protection ilectric motors //Electrotechnics, 1985, 8, p. 40-44.
5. Relay protection of electric •tors by the voltage higher than 1 kW/ .Korogodsky, S.L.Kuzhekov, 8.Paperno.-of M.: ergoatomizdat, 1987.-248 p.
, ¡6. Sivokobylenko V.F., Kostenko
i !
!. Mathematical modelling of electric
motors of own needs of electric power stations.-Donetsk, DPI, 1979.-110 p.
7. Electric circuits with magnetic elements in relay protection / A.D.Drozdov, A.S.Zasypkin. S.L.Kuzhekov etc.; Under edition V.V.PIatonov.-of M.: Energoatomizdat, 1986.-256 p.
8. Kuzhekov S.L., Shihkerimov I.A., Chmihalov G.N.protection of the electric motor from failure start-up // News of high schools of the USSR. Electromechanics, 1980, № 10, p. 67-72.
9. Kovach K.P., Rats 1. Transient processes in machines of alternative currents.-M.-L.: Gosenergoizdat, 1963.-744 p.
10. Liberzon E.M., Korolev E.P. Calculation of the safe loads in current circuits of relay protection.-M.: Energy. 1978.-264 p.
11. Drozdov A.D. Asymmetrical transient modes in electric systems and circuits of relay protection.-Novocherkassk: NP1, I977.-76 p.
