Phase-shift control of transients in electrical power systems

Phase.shift control of transients in electrical power systems V M Cheban, A P Dolgov, A G Fishov and G S Ptushkin Electrical Engineering Institute, Novosibirsk, USSR

Phase-shift control is considered to be a useful means of improving the dynamic stability of electrical transmissions with automatic reclosing and of synchronous motors with two excitation windings. The technique ameliorates the restart conditions of large synchronous motors being energized with emergency supply, and enhances the control of the intersystem power flow due to 'weak' interconnections. The paper presents the results of theoretical and experimental investigations related to these problems.

I. I n t r o d u c t i o n Traditional ways of improving steady-state and dynamic stability, by altering only the moduli of operational parameters mostly in the area of power generation, are usually insufficiently effective. One method of solving the corresponding problems may be by using the phase-shift control technique implying a purposeful varying of arguments of operational parametersL In the 1960s, the use of discrete phase control for improving the dynamic stability of single-line power transmission was researched at the Novosibirsk Electrical Engineering Institute and the Moscow Power Engineering Institute 2, 3 Later, studies performed at Novosibirsk covered the possible application of phase control to: the artificial stability of power transmission, the optimization of flow distribution in heterogeneous networks, the improvement of transmission capability, and two-circuit transmission dynamic stability with various relationships x/r 4. Another way in which phase control can regulate the conditions within a power system is by the application of electric machines with two windings on the rotor. The special machine has two excitation winding voltages which can be regulated. By varying the value and direction of the flow in each of the windings, the vector of the resultant flow can be turned and set in the required position. This technique of constructing a controlled synchronous machine with tw,o windings on the rotor may be accomplished by various modifications s. One of them, known as EMF 'emergency' phase control, is being investigated at the Novosibirsk Electrical Engineering Institute. Investigations on the applications of phase control are being undertaken in other countries also 6, 7. The present paper discusses the use of phase control in the following areas: Received: 30 September 1980

38

• control of dynamic transients and improvement of the dynamic stability of electrical transmissions with automatic reclosing (AC) with a simultaneous decrease in the reclosing current • control of the restarting of large synchronous motors • control of intersystem power flow due to 'weak' interconnections

I I. N o t a t i o n rotor angle referred to infinite busbar, deg power at machine terminals rotor angle at fault initiation rotor angle at fault clearance maximum angle of swing angle of phase-shift insertion infinite busbar voltage direct, quadrature and summary components of EMF if exciting current I primary current Kd, Kq rates of field fixture along d and q axes Up = arctg(Ed/Eq) angle displacement of the resultant EMF relative to the axis Y 2 2Y21, , conductivity matrices of separate multipole systems Zr, Yr resistance and conductivity of equivalent circuit of the transformer /~T,KT direct or conjugating transformer ratio KT modulus of complex transformer ratio excitation voltage along d axes Ut-d excitation voltage along q axes time-constant excitation winding Tj rotor mechanical constant @z resultant flow coupling of excitation winding

8 P 8o 51 82 u VB Ea, Eq, Es

I II. Physical concepts of phase control In analysing electromechanical transients under conditions of phase control, one should distinguish between phase shifts of current and voltage vectors associated with the voltage drop in power circuits (Sz) and phase angles governed either by the scheme of transformer winding connections or by the operation of phase-shift devices 8N. The angle 5N has no functional connection with the steady-state conditions of the radial network. In the case of interconnected circuits, pairs of transformers,

0142-0615/81/010038-07 $02.00 © 1981 IPC BusinessPress

Electrical Power & Energy Systems

connection groups of which ensure mutual compensation of phase shift, are widely used. This permits their phase shifts to be neglected in the estimation of steady-state stability and transients. However, such an approach does not allow a similar approximation to be made in interconnectedcircuit calculations, these circuits having various phase shifts because of the transformer winding connections at transient phase control. Under phase control in power systems, phase shifts are commonly represented by complex transformer ratios. In some special cases, however, phase shifts may be taken into account by the replacement of angular characteristics or the corresponding change of the angle 6z.

~=S,+zx8 d

E

In the case of a synchronous machine with two excitation windings, phase control is implemented due to the change in the value and phase of the synchronous generator resultant EMF at the change of the flow components and, respectively, the EMF along the d and q axes (see Figure 2).

¢ Motor 82

\;

i

,\

q

a

q~v

E,

v~

E S - ~

V-.-.¢'7 :3Vo 8-v

c

J

d

Figure 2 System bar voltage vector position and synchronous machine EMF; (a) in initial condition, (b) at end of emergency condition, (c) at beginning of post emergency condition with phase shift in stator circuit, (d) as (c) but while changing excitation current in rotor windings

The emergency voltage supply -+Ufa q is determined by the moment of sharp disturbance at stating the character and intensity of the disturbance. The excitation voltage along the longitudinal axis may be increased (decreased) by Ka times voltage. KaUfa o is supplied to the transverse winding providing the vector displacement of the resultant EMF. While changing the position of the excitation flow vector E and the resultant moment-angular characteristics, the parameters are changing; these parameters determine the rotor motion in postemergency conditions (see Figure 1). p

Ger~ml0~

2 2 . = (Eqi +Eai)Yii slnct/i +EqucYij(~i]

--EducYij cos (tS/j

-

-

P = E2yii sinai/+ F_2tcYijsin(5 - up) o %

, j

~o.,2o0

\i

oti/)

Otij);

P~

-~o-,2oo

/

b

The above is illustrated by considering a discrete phase shift during a dynamic transient at the switching off and reclosing of a synchronous machine (generator or motor) associated with an infinite system (see Figure 1). Phase effects in an electric network result in a change of the vector position U, and a decrease in the geometric difference between the vector of the inner EMF of the synchronous machine and the power voltage vector of the infinite system; they step currents down at the onset of a postemergency condition (see Figure 2).

q

(1)

Phase effects alter the balance between the acceleration power and the braking of synchronous machines and, as a result, improve dynamic stability.

I \

IV.

b

Modelling of phase control

While calculating the operational parameters of a power system, phase effects may be described by equations analogous to those of a transformer with a complex transformer ratio.

!

Phase effects on the operational parameters can be estimated by the analytical dependences of the power network equivalent circuit generalized parameters as a function of the phase effect insertion. 8o

Bi

V

8

C

Figure 1 Dynamic transient in simplest system with and without phase shift

Vol 3 No 1 January 1981

To determine these dependences, the equivalent circuit may be divided into two multipole subsystems, one of which comprises the phase-shift nodes and the other all the remaining elements of the power network.

39

By the complex solution of the basic equations for these multipole subsystems, the relationship between the EMF of the sources and the active node currents can be established.

I= [Y22- Y21(y~ll)+ y~]))-i y121/~-

(2)

Thus, the conductivities of the operating nodes, taking account of the phase effect, are determined by the matrix expression: V :

(3)

Y~]))-' Yl2

Y22 - - V,21ttll[V(l) +

Matrix -11vO)determines the conductivities of the adjoining nodes of the phase-shift devices. Matrix -Hv(2)determines the conductivities of the phase-shift devices only if the power systems constrains one phase-shift device, then

In the latter case, the complex transformer ratio reflects the change in the value and phase of the generator EMF, these changes occurring with the retardation which is determined by the time constants of the rotor windings. In this particular case, the transformer equivalent circuit conductivities and resistances Z T and l I T are equal to zero. The phase effect of the voltage in the power network can be estimated by using the voltage distribution ratio matrix. For determining these ratios in the equivalent circuit, three kinds of nodes are used: those which adjoin phase-shift devices, active nodes and nodes in which it is necessary to control voltage. Then the matrix of the voltage distribution ratios is determined in the following way: D = (I/33

y(2) 11

(4)

=

Analytical relationships between the conductivities and the complex ratios are described by the equations: Yii =Yii' -- (B 1{i)+B2(i ) K ~ +B3(i t

)/(T COSt))/,&

2

¢

2

*"

"

"

Yii = Yi] + (CRi) + C2(ii)Kr + C3(ii)KT + C4(ij)KT)[ A t

(5)

Y3, Y I ~ Y l a ) - ' ( Y 3 x Y ~ Y I : - Y32)

(6)

The elements of the matrix may be expressed as in relationship (1).

V. Theoretical estimation of dynamic transient phase-control efficiency The efficiency of phase control may be vividly illustrated by the single-circuit power transmission. The active power of the single-circuit transmission, taking account of the phase shift, may be expressed in the following simple way:

Yii = Yii + (Cl(i) + C2(ii)KT + C4(ii)KT + C3(i])I~T)/ A P = EsuY sin (8 - v) =Pm sin (8 - v)

(7)

A = A 1+ A2K~ + 2A 3KT cos u t

where ij are the numbers of the active nodes;y~j,y~i and Yji are the conductivities of the second multipole subsystem; and A, B and C are the constants to be determined by the equivalent circuit parameters. The above equations are true for phase effects in the power network or for an electric machine with two rotor windings.

T

)

//"

--

I~

Motor conditions [ I I I

[

"

I

8 i (P)

/

I

,=~2Ooo

I'N

["~

where u is the input voltage of the power transmission and y is the mutual conductivity between the EMF of the synchronous machine and the constant voltage bars. The angle range within which reclosing with phase shift does not result in distortion of the dynamic stability is determined by the conditions of acceleration and braking power balance. Figure 3 illustrates the boundaries of the stability areas to be set in the coordinates of the initial operating power P0 and the reclosing angle for various values of the phase shift that allow estimation of the stability limits. An advantage of discrete phase control is a considerable increase in the reclosing angle or the power limit at the fixed value. The reclosing current will be minimal if the value of the angle of misalignment between the voltage at the end of the power transmission and the EMF vector of the synchronous machine is equal to zero. The periodic component of the reclosing current is determined in the following way:

I

8,.

I = {[u 2 + E 2 - 2Eu cos(8 - v)] .y}X/2

(8)

Generator conditions

,=,zo*l ~ . k : ¢ ,:6o*J~ Iv = 0 ° ~

/

/

/

Investigations have shown that the conduction 6 = v is optimal as far as the minimal reclosing current and the dynamic stability resource are concerned.

/

VI. Phase control of intersystem power flow over 'weak" interconnections Figure 3 Dynamic stability regions in phase shift control

40

Intersystem power transmissions where the resolving power is no more than 15% of the smallest power subsystem are

Electrical Power & Energy Systems

associated with 'weak' interconnections. Irregular oscillations of the power flow over these lines are divided into low and high (secondary) frequencies. The use of effective power-supply control systems to limit intersystem power flow oscillation sharply decreases the value of the lowfrequency component. To limit the high-frequency component, it is necessary to improve considerably the dynamic characteristics of the power factors to be used. Besides, the operating economy decreases. A means of effectively influencing the high-frequency component may be by phase control in intersystem power transmission, to be performed on the basis of phase controllers with continuous or smallstep discrete angle control. Such control may be implemented at small cost with the transformers having longitudinal-transverse voltage control and a respective limited range of angle variation. The future application of these devices to the control of intersystem power flow depends, to a great extent, on the quality of reclosing under load systems. Figure 4 represents transients in a two-machine system with 'weak' interconnections and small-step discrete phase control of the power flow.

0.2

I 0.1

-0.1

I

-0.2

I

I

I

I

150

120 --

2

90

60

To evaluate the application of phase control to intersystem power transmission, the requirements of phase controller characteristics and the selection of control laws, it is wise to use amplitude-frequency characteristics (AFC), determined with the operation of regulating devices being taken into account. AFC will present the characteristic of the system as a certain nonlinear filter

w(co) =

tu2(co) I

50

I

I

I

0

I

2

Time,

3

[

I

4

5

6

s

Figure 4 Interconnection power transmission transients; (I) and (2) with phase control, (3) and (4) without phase control

lu,(co) l u 1(co) = A s i n c o t

(9)

where lul(co)l and lu2(co)l are the amplitudes of the input and output coordinate systems, respectively. The nonbalance of power in one of the subsystems affecting the oscillations of exchange power between the subsystems is taken as the input value. The input value may be any of the system coordinates under analysis (power flow, angles, etc.). Allowing for the fact that active disturbances (power nonbalance in subsystems) may be presented as the sum of various frequency harmonic components, the AFC reflects the system properties with regard to the processes to be analysed. To obtain the AFC, a series of system conditions differing in the active harmonic disturbance frequency co (Figure 5) is calculated. As can be seen from Figure 5, phase control has influenced only dynamics (T < 10 s). Phase control efficiency is characterized by such parameters as angle control range A~max,control pitch A6 and permissible interval between reclosing (At reclosing). Preliminary estimation of these limit values has shown that it is necessary to have ASmax/> 80 °, AS ~. 5-8% and A t n ~ 0 . 5 s. From the AFC and analysis result obtained from the harmonic composition of the power-flow oscillations over intersystem communication, one can determine a real increase of power transmission capability. However, such

Vol 3 No 1 January 1981

f j j f f ~ ~ ~

//I ~

i//// 5

I0

Figure 5 Power flow amplitude-frequency characteristics for interconnection power transmission 500 kV; (1) without phase control, (2) with phase control increasing the power transmission synchronics, (3) with phase control ensuring suppression of high-frequency oscillations

control does not exclude the violation of parallel subsystem operation due to large disturbances associated with faults. The use of automatic reclosing with the phase-shift multiple of 2/3n for improving stability in such intersystem transmission is especially expedient as both during and after the period of stability violation the velocity of subsystem mutual motion is negligible.

41

In particular, an asynchronous run on 'weak' interconnections is characterized by an oscillation period of 6-8 s. Under these conditions, the fast action of modern switching apparatus is quite sufficient for ANB (automatic reclosing) with phase shift.

I

'I 1 ]o-I

1 1 1

i

_j_

I

T

v~

L~_

Vl I. Phase control of dynamic conditions on the basis of synchronous machines with two excitation windings

]

Depending on the tasks and conditions of synchronous machines with lengthwise-longitudinal-transverse transients, the phase control EMF (PCE) may be either continuous, and be carried out under steady-state or quasi steady-state conditions of operation, or short-time, for the duration of the dynamic transient only. In the first case, the AC machine works in so-called asynchronized synchronous conditions. Now in establishing a field on the rotor side and ensuring steady-state conditions, both windings with an AC slip frequency current flow should participate equally s. Another principle of operation of the synchronous machine with double excitation is when an additional transverse winding has mainly regulating functions and acts in emergency conditions to be restricted in time. In dynamic conditions, DC voltage is supplied to the excitation windings with a certain combination of signs Ufd = KdUfd o = Ufd o +- A u f d

(10)

ul,q = K q ( g l u f d o ) = + Aul, q

This allows the class of the machines used to be extended with the properties of turnable axes of magnetizing. A considerable phase shift (6~0 ~ 50 °) and the maximum effect from a transverse regulator is obtained with corn240

~

Ploce of phose- shift insertion

] /=270kin

-220kV

Figure 7

G 200MW

220 kV power transmission diagram for field time

paratively equal EMFs and respective powers developed along the axes for the period of PCE. The most favourable result in PCE is obtained in the case of longitudinal-transverse focusing, that is, PCE with a gained amplitude E. Such a law of control is the most effective one for modern turboand hydrogenerators with the increased values Tao(5/8c) uTj(5/lOc), when by the moment of emergency or cut-off there is the possibility both for amplitude damping d/is and its slipping at the expense of the transverse component of the flow. As an illustration, Figure 6 presents limit dependences 6 ( 0 for various levels of emergency longitudinal-transverse excitation. The figures in parentheses represent the duration of the 3-phase short circuit in seconds, the dynamic stability being maintained. The change of the resultant EMF components and, hence, the efficiency of the PCE effect depend first of all on the time constants of the excitation windings along the axes and the magnitude of the voltages applied to the rotor rings.

. . . . . . . . . . . . . . .

The use of a transverse winding with increased active resistance and a small time constant is permissible because it is for only a short time. The required ampere-turns may be obtained at the expense of an increase in current intensity in this winding. The transverse winding with a small time Constant increases the efficiency of a two-winding machine in emergency conditions and also allows simplification of the design of the synchronous machine with asymmetrical excitation windings.

120

VIII. Field experiments of dynamic stability phase control

o

to

I

1.28

256 Time, s

Figure 6 Calculated curves fi(t) at various levels of longitudinal-transverse excitation: (1) Ufd = U f d o , U f q = O, (2) Utd = 1.41UfdO, Ufq = O; (3) Ufd = 0.5 Ufdo,

Ufq

= 0.9

= 1.41

42

Ufdo;

(4)

Ufdo, Ufq =

Ufd = Ufdo, Ufq = Ufdo; Ufd 0

(5)

Ufd

VIII.1 Power transmission o f 220 M W Tests were carried out in April 1977 along the power transmission line of 220 kV, 220 km in the interconnection system of Siberia. A schematic diagram of the power transmission and its main characteristics is given in Figure 7. The experiment program was designed to" •

estimate the efficiency of the phase control as a means of enhancing the possibility of automatic reclosing to

Electrical Power & Energy Systems

i

improve the dynamic stability and considerably decrease the switching current show in principle the feasibility of transient phase control with the use of standard circuits of basic communication on the basis of commercial electrical equipment; the control over a dynamic transient was achieved using aerial switches with the aid of line B-1 and bypassing switch B-2

t

-

: I8.SkA

-

Under phase control at the discharges from the bars to the switch B-2 the circular reclosing of phases with a shift of 120 ° was carried out. The fault disturbance was simulated by 3-phase switchingoff by the switchgear B-I which was accompanied by essentially the total drop of the generator active power.

"%

--

~

~mol=320

ml

Then at the calculated time, the switchgear B-2 was on, thus performing a discrete phase control with v = + 120 °. The transient then over and the generator being unloaded to a certain extent, the pertinent inverse transient was carried out by cutting out switch B-2 and cutting in B-1 which corresponded to a phase shift of v = - 120 ° or v = + 240 °. Such test cycles were carried out with a stepwise rise of the initial conditions Po active power until the generator fell out of step. The data of the last two experiments (limit steady-state and unstable transient) are reflected in the table where they are compared with the identical results of analogous dynamic transients without phase control and also with the results of preliminary calculations and experiments on the electrodynamic model. The oscillograms illustrating characteristic dynamic transients with and without phase control are shown in Figures 8 and 9.

Figure 9 Dynamic transient of synchronous generator without phase control

/ku=~ 11.8kV /~ =2.SkA "-.UiM~-P= 3.42MWT

r

-

,+,

-

.llt

/. :v~ 230A •

=

_

~ : p~=__ ~.38AI~M~T ,

al.

:.

.=.,.

......................... llll~ll'" ~II . . . . . . . . . . . . ""::::,~t

.

'llr

IO 2 s

i

Figure 10 Oscillogram of 6.3 MW restarting synchronous motor with phase shift of --360 ° Vg =16kV min

i

Sm~--190°

I

0.2s Figure 8

D y n a m i c transient of synchronous generator w i t h

phase shift of 120 °

Vol 3 No 1 January 1981

Vl II .2 Restarting synchronous motors The experiments on restarting synchronous motors of 700 kW-6.3 MW at the discrete phase control in stator circuits have been carried out at a number of industrial enterprises in Western Siberia. Depending on the in situ conditions the value of the phase shift was selected to vary as - 1 2 0 °, - 2 4 0 ° or - 3 6 0 °. The last value is preferable in service. The time of reserve power supply was varied as a function of the motor loading and was determined by the automatic device. The oscillogram of restarting the 6.3 MW motor with the angle of phase shift of - 3 6 0 ° is presented in Figure 10. The oscillogram shows that the phase control aUows stability to be maintained, decreases the switching currents and decreases the time of the dynamic transient.

43

IX. Conclusions The theoretical foundations and physical concepts of power system transient phase control have been outlined. The mathematical model of phase effects has been made on the basis of the transformer equations with complex transformer ratios and allows the change of overall parameters of the equivalent circuits to be taken into account. The paper contains the theoretical estimation of the efficiency of the dynamic transient phase control accomplished both in stator circuits and on the basis of the synchronous machine with two excitation windings. The peculiarities of the conditions of 'weak' intersystem power transmission of simple structure allow phase control of various types to be effectively used for improving their stability and real transmissive capability. The results of field experiments prove the basic concepts of dynamic transient discrete phase control. They prove the efficiency of phase control as a means of improving dynamic stability and reducing current at ABP (automatic reclosing) with synchronous motors, fast-acting automatic reclosing along the lines with two-end supply. The paper has shown the possibilities of dynamic transient phase control on the basis of serial equipment with the use of standard circuits of the substation first commutation. This allows consideration of some of the problems of implementing the method in modern power systems.

44

X. References 1 qe6aH, B M HeKoTOpble sonpocbl qba3oaoro yl]paBJ]eHI4~ pe>K~maMn 3neKTpnqecK,x CHc'reM

'~)YleKTpI4qeCl"BO'No

10 (1974)

2 qe6an, B M Cnoco6 noBblmeHria ~rmaMrtqecKofi ycxo~tqrtBOCrri. BlonnexeHb ri3o6pexeHrifi, 1965, No 23 ABTOpcKoe c~eTenbcxBo No 176624 c npnopHTeTOM OX 2.03.1964 r

PO3aHOB, M H Cnoco6 nOBblmeHI,bq ~lI4]iaMI,lqecKoiTl yCTOfiqHBocTHnp~i Tpexqbaanoi AIIB Ha nm~nnx c ~ByXCTOpOHHI,IM nl,ITaHrleM. Tpyabl B33H '3neKTpoaHepreTnKn' (Bbln. 25, 1964) qe6aH, B M, FeoprnencKnfi B J], FeoprneacKaa C K, ~lonroa A H, Y~anon C H, Ko6bixea M H, IIlernoB I0 II 3KcnepHMeHTanbHoe nccne~oBaHne qbaaoBoro ynpaBneH~m ~ItHaMHqeCKHMHnepexoaaM~t '3neKxpHqecTBo' No 12 (1978) BOTBI,IHHI,IK M M, llIaKapaH IO F YnpaanneMan MalllnHa nepeMenHoro roKa. M.' HayKa' (1969)

6 Soper, I A and Fagg, A R 'Divided-winding rotor synchronous generators' Proc. IEEE Vol 116 No 1 (1969) O'Kelly, M G 'Improvement of power system transient stability by phase shift insertion' Proc. IEEE Vol 120 No 2 (1973)

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