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Improvement of transient stability by sequentially switched autoreclosing circuit breaker
Electric Power Systems Research, 2 (1979) 215 - 219
215
© Elsevier Sequoia S.A., Lausanne - - P r i n t e d in the Netherlands
Improvement of Transient Stability by Sequentially Switched Autoreclosing Circuit Breaker
K. P. B A S U and M U K H T A R
AHMAD
Department of Electrical Engineering, ZH College of Engineering and Technology, Aligarh Muslim University, Aligarh (India) (Received July 12, 1979)
SUMMARY
Autoreclosing circuit breakers are frequently used to improve the transient stability limit of a power system. But the system may fail to maintain stability even after a successful reclosure for high values of prefault power transfer. A sequential switching scheme employing three fast-acting isolators in addition to the autoreclosing circuit breaker is suggested. It improves the transient stability limit of the transmission system considerably. A simple mathematical analysis reveals the extent of stability improvement. Complete constraint clauses have been formulated for the switching scheme and a block diagram of the logic circuit is presented. The proposed scheme finds its immediate application in a single circuit tie-line between two systems.
INTRODUCTION
Autoreclosing circuit breakers, with both 3-pole and 1-pole tripping arrangements, are commonly employed in an interconnecting line for increasing the transient stability limit. But the deionization time of a single-phase fault arc path in an uncompensated transmission line may be extremely high [1]. Therefore circuit breakers with only 3-pole tripping and reclosing arrangements are frequently employed for all types of transmission line faults. After a successful autoreclosure the stability of the system depends on the amount of prefault power transfer through the line, the inertia constant of the machine, and the time elapsed Q between fault initiation and line re. energisation. This time t~ includes the relay operating time tr, the breaker tripping time
tb, and the autoreclosure dead time ta. The
maximum time tc which can be allowed after fault initiation to reclosure of the breaker may be much less than te for the system to be just stable, particularly for higher values of power transfer and low inertia constant. The basic theory of a sequential switching scheme to improve the transient stability limit has been presented by the authors in a previous paper [2]. However, that scheme finds its application limited to radial transmission lines having unidirectional power flow. This disadvantage has now been removed and the present scheme can be employed in any transmission line connecting two systems and having the possibility of power flow in both directions.
THE EXISTING SCHEME
The simplified schematic diagram shown in Fig. 1 (excluding isolators IS2 and IS3) indicates the connection of the two systems with equivalent power so.urces GI and G2 at the two ends. To obtain a simplified dynamic model of the system, it is assumed that all the losses in the system, damping and saliency in the machines, and governor and regulator action during transient periods can be neglected. The two-machine system can always be reduced to an equivalent single machine having an equivalent angular momentum M connected to an infinite bus-bar. The machine induced voltage E and the infinite bus voltage V are shown in Fig. 2. For motoring action (reverse power flow), the machine voltage E' is indicated by broken lines. At initiation of the fault, which is assumed to be a 3-phase dead short circuit (severest condition), the power transfer through the
216 BUS2
8us I
tI '~--A _ F --"1
--x¢-_N Fig. 1. Schematic diagram showing the connection of the two systems with equivalent power sources G 1 and G 2 at the two ends.
line becomes zero. Therefore the swing equation can be written as d25
(i)
M --~--~-= p o
small values of the inertia constants. Since with the increase in rating of machines inertia constants have decreased, values of the equivalent inertia constant from 2 to 4 only have been considered.
where P0 is the prefault power transfer and M = H / ~ f o , in which H is the p.u. equivalent
inertia constant and fo is the steady-state frequency of the system. The critical clearing angle 6~ up to which the machine may be allowed to swing without losing stability may be obtained by applying equal-area criteria [3] and is given by 8c = cos-I [r(~ -- 2sin-lr) -- cos(sin-lr)]
(2)
where r = Po/Pm;Pm is the steady-state stability limit of the system, assumed to be 1 p.u., and r is a measure of transmission capability. A system equipped with fast-acting relays and circuit breakers requires a total time te of about 0,35 s [3] for autoreclosing. If the angular displacement 8e in this time exceeds the critical clearing angle 5c, the system will be unstable. As seen from Table 1, the transient stability limit of the system is low for
/ /
V~
\
Fig. 2. Phasor diagram.
PROPOSED SCHEME
In the proposed sequential switching scheme, after the fault initiation the machine accelerates (for forward power flow). The angle 5 increases and so the phasor ER moves towards Vy and crosses it after some time. If the RYB phases of bus 1 are synchronized with the YBR phases of bus 2 at this time, then the stability of the system may be maintained. For reverse power flow, phasor E R will be moving towards VB and therefore the RYB phases of bus 1 should be synchronized with the BRY phases of bus 2. To achieve this, the following sequence of operations is necessary. (i) Trip circuit breakers CB1 and CB2 to isolate the fault. (ii) Open isolator IS1 and close IS2 (for forward power flow), or IS3 (for reverse power flow). All three isolators should be designed for very high-speed operation. (iii) Reclose CB2 and CB1. If the change in speed is negligible the equal-area criterion of stability can be applied for this case also. Therefore the accelerating power when the systems are disconnected, as given by the power angle curve (Fig. 3), must he less than the retarding power after reclosing for the systems to remain in step. The power-angle curve after reclosing must be
217 TABLE 1 Prefault power P0 (p.u.) Prefault angle 50 (deg) Critical clearing angle 5 c (deg) H=2 Angular displacement after 0.35 s 5e (deg) Stability with autoreclosing Stability with sequential switching H=3 Angular displacement after 0.35 s 5 e (deg) Stability with autoreclosing Stability with sequential switching H=4 Angular displacement after 0.35 s 5 e (deg) Stability with autoreclosing Stability with sequential switching
0.1
0.2
0.3
5.7
11.5
17.4
20.5
22
23
26.8
30
134.5
115.6
101.2
95.4
92.2
89.4
84.2
79.6
32.7
65.5
98.4
113.8
<
0.35
0.375
123
0.40
131.6
)
<
Not required
>
Stable
Stable
Stable
83.2
89.5
95.6
47.5
71.4 Stable
<
19.2
38.5
57.9
67
<
Stable
<
Not required
shifted by 120 ° from the prefault curve. For different values of the inertia constants, the equal-area criterion is applied for different prefault power transfers and the stability of the systems determined. The results with simple autoreclosing and with sequential switching are compared in Table 1. It is found that for inertia constants in the range 2 - 3 the improvement in the power transfer capability of the system is considerable. For higher values of the inertia constants, reclosing is not allowed before the angle 5e reaches the value of 120 °, otherwise an unwanted reversal of power flow will take place. In this case, the systems drift apart consider-
165
72.2
Unstable
,(
107.2
116.6
Unstable
(
Not requiredL
<
149
0.5
Unstable
Stable.
23.7
0.45
Stable
Stable
77.6
86 <
~>
f
Unstable
97.0 Unstable
Stable
Unstable
ably and the sequential switching scheme is not useful. Therefore the scheme is useful either for two small systems connected together, or for a small system connected to a large system through a single transmission line. For the system when 5e is less than 2~/3, the reclosure must be carried out after the angular separation reaches 2~/3; for this a minimum time delay of tmin should be provided: tmin =
--50
5e <
3 27f
=
te
5e ~
3
SEQUENTIAL SWITCHING ARRANGEMENT
! °"I p. /
~ ' ~ \ \ \ ~\ \ \ \ \
:V 2\ $o
;o
--
~'o ,ae ~Anyle
2;,o
~oo"
Fig. 3. Equal-area criterion for stability: A 1 < A 2.
Since the isolator operations depend on the amount and the direction of the prefault power flow at the bus 1 end, a six-step power relay (PR) with two sets of low-, medium- and high-power terminals (for forward and reverse power flow) is counected at bus 1. The prefault powers for which the system is stable with simple autoreclosing give the values of
218
the low-power setting, for which no isolator operation is needed. The values of P0 for w h i c h train is greater than te indicate medium power, and values of P0 corresponding to tm~ ~< te indicate high values of power. For the last t w o cases, isolator operation is necessary. Selection of isolators to be closed and opened depends not only on the direction of the prefault power flow b u t also on the particular isolator in the closed condition at that time. Supposing IS2 is in the ON position, then for medium and high prefault power the autoreclosing operation should be carried o u t as follows: open IS2 and close IS3 for forward power flow, or close IS1 for reverse power flow. Again, for medium power, the closing of CB1 should be carried out only when V1/~ leads V2/_0 slightly {referring to Fig. 1) for forward power and Vll_a lags slightly behind V2/-0 for reverse power. Such a check may be performed easily by connecting the potential transformer secondaries to the phase comparator to ensure that 0~< ~ ~< e o r - - e ~<~<~0, as the case may be. e represents a preset reference angle and its value is very small. For high values of power this check is n o t necessary, and CB1 can be closed immediately after the isolator operation is over. Since any transient change in power should n o t be considered, the power relay should be designed on the principle of the m a x i m u m demand indicator meter. The o u t p u t of power relay should indicate the average power flow for a very short period, say a b o u t two seconds, and is held for the next two seconds. Therefore, the o u t p u t from the power relay is available even during the tripped condition of CB1. CONSTRAINT CLAUSES
For the sequential operation of the isolators and circuit breakers certain constraint clauses [4] may be formulated: (i) CB1 and CB2 should be tripped to isolate any transmission line fault. (ii) CB1 and CB2 should be reclosed after the autoreclosure dead time ta. Timers may be used to count this time. (iii) For medium and high power, CB1 should n o t be closed until the isolator operation is over. (iv) In the case of medium power a check for V1 leading V2 for forward p o w e r flow and
V1 lagging V2 for reverse power flow is necessary before the reclosure of CB1. In this case CB1 is always closed after CB2, as potential V2 is only available after the reclosure of CB2. (v) Isolator operation is n o t needed for low power flow. (vi) Closing or opening of any isolator should only be carried out when CB1 is in the O F F position. (vii) For medium and high p o w e r in any direction, the isolator which is ON should be opened. (viii) For medium and high power in the forward direction, IS1 should be closed, provided IS3 is in the ON position. (ix) For medium or high power in the reverse direction, IS1 should be closed, provided IS2 is in the ON position. Similar constraint clauses may be formulated for closing of other isolators. Signals corresponding to the ON and O F F positions of isolators are obtained from their auxiliary contacts. When isolator operation is in progress, the command signal may be disturbed. Therefore, the CB1 trip signal should be transformed into pulse form, so that the command signals for the isolators are also obtained in pulse forms which are maintained by the holding circuits (bistables) until the respective operation is over. The holding circuits are then reset. Signals corresponding to the completion of closing and opening of the respective isolators are also held till CB1 is reclosed and then those holding circuits are reset. On the basis of these constraint clauses, a block diagram of the switching operation has been developed and is shown in Fig. 4. Here P indicates the pulse former or differentiator, holding circuits are bistables and A N D / O R represent the AND/OR logic gates.
CONCLUSION
Calculations on a simplified dynamic model of a transmission system point o u t clearly the limitations of autoreclosing circuit breakers in improving the transient stability limit. A sequential switching scheme employing three fast-acting isolators in conjunction with autoreclosing circuit breakers improves the stability of the system to a large extent. The scheme is simple and economical and can be employed
215
© Elsevier Sequoia S.A., Lausanne - - P r i n t e d in the Netherlands
Improvement of Transient Stability by Sequentially Switched Autoreclosing Circuit Breaker
K. P. B A S U and M U K H T A R
AHMAD
Department of Electrical Engineering, ZH College of Engineering and Technology, Aligarh Muslim University, Aligarh (India) (Received July 12, 1979)
SUMMARY
Autoreclosing circuit breakers are frequently used to improve the transient stability limit of a power system. But the system may fail to maintain stability even after a successful reclosure for high values of prefault power transfer. A sequential switching scheme employing three fast-acting isolators in addition to the autoreclosing circuit breaker is suggested. It improves the transient stability limit of the transmission system considerably. A simple mathematical analysis reveals the extent of stability improvement. Complete constraint clauses have been formulated for the switching scheme and a block diagram of the logic circuit is presented. The proposed scheme finds its immediate application in a single circuit tie-line between two systems.
INTRODUCTION
Autoreclosing circuit breakers, with both 3-pole and 1-pole tripping arrangements, are commonly employed in an interconnecting line for increasing the transient stability limit. But the deionization time of a single-phase fault arc path in an uncompensated transmission line may be extremely high [1]. Therefore circuit breakers with only 3-pole tripping and reclosing arrangements are frequently employed for all types of transmission line faults. After a successful autoreclosure the stability of the system depends on the amount of prefault power transfer through the line, the inertia constant of the machine, and the time elapsed Q between fault initiation and line re. energisation. This time t~ includes the relay operating time tr, the breaker tripping time
tb, and the autoreclosure dead time ta. The
maximum time tc which can be allowed after fault initiation to reclosure of the breaker may be much less than te for the system to be just stable, particularly for higher values of power transfer and low inertia constant. The basic theory of a sequential switching scheme to improve the transient stability limit has been presented by the authors in a previous paper [2]. However, that scheme finds its application limited to radial transmission lines having unidirectional power flow. This disadvantage has now been removed and the present scheme can be employed in any transmission line connecting two systems and having the possibility of power flow in both directions.
THE EXISTING SCHEME
The simplified schematic diagram shown in Fig. 1 (excluding isolators IS2 and IS3) indicates the connection of the two systems with equivalent power so.urces GI and G2 at the two ends. To obtain a simplified dynamic model of the system, it is assumed that all the losses in the system, damping and saliency in the machines, and governor and regulator action during transient periods can be neglected. The two-machine system can always be reduced to an equivalent single machine having an equivalent angular momentum M connected to an infinite bus-bar. The machine induced voltage E and the infinite bus voltage V are shown in Fig. 2. For motoring action (reverse power flow), the machine voltage E' is indicated by broken lines. At initiation of the fault, which is assumed to be a 3-phase dead short circuit (severest condition), the power transfer through the
216 BUS2
8us I
tI '~--A _ F --"1
--x¢-_N Fig. 1. Schematic diagram showing the connection of the two systems with equivalent power sources G 1 and G 2 at the two ends.
line becomes zero. Therefore the swing equation can be written as d25
(i)
M --~--~-= p o
small values of the inertia constants. Since with the increase in rating of machines inertia constants have decreased, values of the equivalent inertia constant from 2 to 4 only have been considered.
where P0 is the prefault power transfer and M = H / ~ f o , in which H is the p.u. equivalent
inertia constant and fo is the steady-state frequency of the system. The critical clearing angle 6~ up to which the machine may be allowed to swing without losing stability may be obtained by applying equal-area criteria [3] and is given by 8c = cos-I [r(~ -- 2sin-lr) -- cos(sin-lr)]
(2)
where r = Po/Pm;Pm is the steady-state stability limit of the system, assumed to be 1 p.u., and r is a measure of transmission capability. A system equipped with fast-acting relays and circuit breakers requires a total time te of about 0,35 s [3] for autoreclosing. If the angular displacement 8e in this time exceeds the critical clearing angle 5c, the system will be unstable. As seen from Table 1, the transient stability limit of the system is low for
/ /
V~
\
Fig. 2. Phasor diagram.
PROPOSED SCHEME
In the proposed sequential switching scheme, after the fault initiation the machine accelerates (for forward power flow). The angle 5 increases and so the phasor ER moves towards Vy and crosses it after some time. If the RYB phases of bus 1 are synchronized with the YBR phases of bus 2 at this time, then the stability of the system may be maintained. For reverse power flow, phasor E R will be moving towards VB and therefore the RYB phases of bus 1 should be synchronized with the BRY phases of bus 2. To achieve this, the following sequence of operations is necessary. (i) Trip circuit breakers CB1 and CB2 to isolate the fault. (ii) Open isolator IS1 and close IS2 (for forward power flow), or IS3 (for reverse power flow). All three isolators should be designed for very high-speed operation. (iii) Reclose CB2 and CB1. If the change in speed is negligible the equal-area criterion of stability can be applied for this case also. Therefore the accelerating power when the systems are disconnected, as given by the power angle curve (Fig. 3), must he less than the retarding power after reclosing for the systems to remain in step. The power-angle curve after reclosing must be
217 TABLE 1 Prefault power P0 (p.u.) Prefault angle 50 (deg) Critical clearing angle 5 c (deg) H=2 Angular displacement after 0.35 s 5e (deg) Stability with autoreclosing Stability with sequential switching H=3 Angular displacement after 0.35 s 5 e (deg) Stability with autoreclosing Stability with sequential switching H=4 Angular displacement after 0.35 s 5 e (deg) Stability with autoreclosing Stability with sequential switching
0.1
0.2
0.3
5.7
11.5
17.4
20.5
22
23
26.8
30
134.5
115.6
101.2
95.4
92.2
89.4
84.2
79.6
32.7
65.5
98.4
113.8
<
0.35
0.375
123
0.40
131.6
)
<
Not required
>
Stable
Stable
Stable
83.2
89.5
95.6
47.5
71.4 Stable
<
19.2
38.5
57.9
67
<
Stable
<
Not required
shifted by 120 ° from the prefault curve. For different values of the inertia constants, the equal-area criterion is applied for different prefault power transfers and the stability of the systems determined. The results with simple autoreclosing and with sequential switching are compared in Table 1. It is found that for inertia constants in the range 2 - 3 the improvement in the power transfer capability of the system is considerable. For higher values of the inertia constants, reclosing is not allowed before the angle 5e reaches the value of 120 °, otherwise an unwanted reversal of power flow will take place. In this case, the systems drift apart consider-
165
72.2
Unstable
,(
107.2
116.6
Unstable
(
Not requiredL
<
149
0.5
Unstable
Stable.
23.7
0.45
Stable
Stable
77.6
86 <
~>
f
Unstable
97.0 Unstable
Stable
Unstable
ably and the sequential switching scheme is not useful. Therefore the scheme is useful either for two small systems connected together, or for a small system connected to a large system through a single transmission line. For the system when 5e is less than 2~/3, the reclosure must be carried out after the angular separation reaches 2~/3; for this a minimum time delay of tmin should be provided: tmin =
--50
5e <
3 27f
=
te
5e ~
3
SEQUENTIAL SWITCHING ARRANGEMENT
! °"I p. /
~ ' ~ \ \ \ ~\ \ \ \ \
:V 2\ $o
;o
--
~'o ,ae ~Anyle
2;,o
~oo"
Fig. 3. Equal-area criterion for stability: A 1 < A 2.
Since the isolator operations depend on the amount and the direction of the prefault power flow at the bus 1 end, a six-step power relay (PR) with two sets of low-, medium- and high-power terminals (for forward and reverse power flow) is counected at bus 1. The prefault powers for which the system is stable with simple autoreclosing give the values of
218
the low-power setting, for which no isolator operation is needed. The values of P0 for w h i c h train is greater than te indicate medium power, and values of P0 corresponding to tm~ ~< te indicate high values of power. For the last t w o cases, isolator operation is necessary. Selection of isolators to be closed and opened depends not only on the direction of the prefault power flow b u t also on the particular isolator in the closed condition at that time. Supposing IS2 is in the ON position, then for medium and high prefault power the autoreclosing operation should be carried o u t as follows: open IS2 and close IS3 for forward power flow, or close IS1 for reverse power flow. Again, for medium power, the closing of CB1 should be carried out only when V1/~ leads V2/_0 slightly {referring to Fig. 1) for forward power and Vll_a lags slightly behind V2/-0 for reverse power. Such a check may be performed easily by connecting the potential transformer secondaries to the phase comparator to ensure that 0~< ~ ~< e o r - - e ~<~<~0, as the case may be. e represents a preset reference angle and its value is very small. For high values of power this check is n o t necessary, and CB1 can be closed immediately after the isolator operation is over. Since any transient change in power should n o t be considered, the power relay should be designed on the principle of the m a x i m u m demand indicator meter. The o u t p u t of power relay should indicate the average power flow for a very short period, say a b o u t two seconds, and is held for the next two seconds. Therefore, the o u t p u t from the power relay is available even during the tripped condition of CB1. CONSTRAINT CLAUSES
For the sequential operation of the isolators and circuit breakers certain constraint clauses [4] may be formulated: (i) CB1 and CB2 should be tripped to isolate any transmission line fault. (ii) CB1 and CB2 should be reclosed after the autoreclosure dead time ta. Timers may be used to count this time. (iii) For medium and high power, CB1 should n o t be closed until the isolator operation is over. (iv) In the case of medium power a check for V1 leading V2 for forward p o w e r flow and
V1 lagging V2 for reverse power flow is necessary before the reclosure of CB1. In this case CB1 is always closed after CB2, as potential V2 is only available after the reclosure of CB2. (v) Isolator operation is n o t needed for low power flow. (vi) Closing or opening of any isolator should only be carried out when CB1 is in the O F F position. (vii) For medium and high p o w e r in any direction, the isolator which is ON should be opened. (viii) For medium and high power in the forward direction, IS1 should be closed, provided IS3 is in the ON position. (ix) For medium or high power in the reverse direction, IS1 should be closed, provided IS2 is in the ON position. Similar constraint clauses may be formulated for closing of other isolators. Signals corresponding to the ON and O F F positions of isolators are obtained from their auxiliary contacts. When isolator operation is in progress, the command signal may be disturbed. Therefore, the CB1 trip signal should be transformed into pulse form, so that the command signals for the isolators are also obtained in pulse forms which are maintained by the holding circuits (bistables) until the respective operation is over. The holding circuits are then reset. Signals corresponding to the completion of closing and opening of the respective isolators are also held till CB1 is reclosed and then those holding circuits are reset. On the basis of these constraint clauses, a block diagram of the switching operation has been developed and is shown in Fig. 4. Here P indicates the pulse former or differentiator, holding circuits are bistables and A N D / O R represent the AND/OR logic gates.
CONCLUSION
Calculations on a simplified dynamic model of a transmission system point o u t clearly the limitations of autoreclosing circuit breakers in improving the transient stability limit. A sequential switching scheme employing three fast-acting isolators in conjunction with autoreclosing circuit breakers improves the stability of the system to a large extent. The scheme is simple and economical and can be employed