Advances in Power and Energy Systems

Transient Stability of Synchronous Generator for Selected Events BORIS CINTULA, ŽANETA ELESCHOVÁ, ANTON BELÁŇ, MARTIN LIŠKA Department of Electrical Power Engineering Slovak University of Technology in Bratislava Ilkovičova 3, 812 19 Bratislava SLOVAKIA [email protected], http://www.kee.fei.stuba.sk Abstract: - The paper deals with the issue of dynamic stability of synchronous generator, in the first part are described the indicators of dynamic stability and basic principles of the solution. The second part contains the results of dynamic simulations analysis of selected events which are compared in terms of the significance of their impact on the synchronous generator dynamic stability. Key-Words: - Synchronous Generator, Dynamic Stability, Method of Area Equality, Critical Clearing Time, Short Circuit, Breaker Failure Relay d 2δ ω 0 ∆P , = Tm S n dt 2

1 Introduction During the power system operation arise a lot of fast changes, which can cause a disproportion between production and consumption of electricity what also means big changes of rotor angles. Fast changes in power system consist for example of switching operations, source or load outages, but the most frequently the short circuits, what is associated with step change of impedance of power system. Synchronous generators respond to fast changes in electromechanical swings and during these swings can generators get into a situation when the rotor angle stabilises at a new value or the rotor angle will grow to a loss of synchronism. [1] In real operation, each generator complies with condition of static stability. But it is necessary to add that a generator which complies with a condition of static stability does not have to comply with dynamic stability. The main difference between the assessment of static and dynamic stability is that in static stability is determined the ability of generator to operate in a steady state and in dynamic stability is determined and investigated the impact and course of transient state to synchronous generator.

(1)

ω0 – nominal angular velocity of generator; Tm – mechanical time constant of generator; Sn – nominal power of generator. For theoretical analysis of dynamic stability using the method of area equality can be used the simplified model of power system in Fig.1 and its equivalent scheme in Fig.2. The method of area equality application for transient state (short circuit on one of the power lines) is shown in Fig.3, curve I - state before short circuit, II – short circuit on the line, III – outage the line after short circuit. The border of dynamic stability (δcrit) is determined by method of area equality – accelerating and breaking area, what means to comply with a following condition: (2) S+ < S−

Fig.1 Simplified model of power system for transient stability for examination of generator

2 Assessment of Dynamic Stability For qualitative assessment of the synchronous generator dynamic stability is used method of area equality, the solution which is defined the border of the dynamic stability – critical angle δcrit. Further solution of kinetic equation (1) can be provided the critical clearing time (CCT).

ISBN: 978-1-61804-128-9

Fig.2 Equivalent scheme of simplified model of power system

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takes longer than CCT duration, then it is possible to come to a loss of generator synchronism. It is possible to determine the CCT duration by simulation experiment or calculation come out from the kinetic equation (1) t crit (CCT ) =

2M

ω 0 P0

(δ crit − δ 0 ),

(3) ω0 – nominal angular velocity of generator; M – mechanical rotor torque of generator; P0 – generator power before short circuit; δ0 – rotor angle of generator (by P0); δcrit – critical rotor angle of generator.

Fig.3 Graphic application of method of area equality for transient state – short circuit on power line [1]

But this equation is valid only if the power from generator is during the 3-phase short circuit equal zero, i.e. it is 3-phase short circuit on the bus bar where the generator power is connected to. [1] The time courses of generator rotor angle are in Fig.5, where the tripping is shown at: • 1 – critical time (CCT), • 2 – shorter time than CCT • 3 – longer time than CCT.

The most serious failure in terms of dynamic stability is 3-phase short circuit. In Fig.4 are shown the power characteristics of 3-phase bus bar short circuit.

Fig.4 Transient stability assessment for 3-phase short circuit on the bus bar [2] Based on above the dynamic stability of synchronous generator can be classified into three basic states: 1) if S+ = S− - border of dynamic stability (critical angle value) 2) if S+ < S− - preservation of dynamic stability 3) if S+ > S− - loss of dynamic stability

Fig.5 Time behaviour of generator rotor angle [1]

2.1 Factors Affecting the Length of CCT The factors affecting the CCT duration are: • short circuit power in substation, where the power from the generator is exported, • value of voltage in substation, where the power from the generator is exported, • operational condition of generator, i.e. underexcited or overexcited generator. [3]

3 Critical Clearing Time (CCT) Critical clearing time (CCT) is important indicator of dynamic stability and to know its duration is considered a practical assessment of dynamical stability of synchronous generator. CCT indicates how long the generator is able to work in 3-phase short circuit at the nearest bus bar where the generator is connected to and after the short circuit preserve in synchronous operation. If the short circuit tripping takes shorter than CCT duration, then the generator is dynamically stable. In case the short circuit tripping

ISBN: 978-1-61804-128-9

In Fig.6 is shown the CCT course of the voltage in the substation, where the generator power is connected to. In the course it is possible to see that the CCT duration strongly depends on operational generator conditions, i.e. if the generator works in underexcited or overexcited state. In Fig.7 is shown the CCT course of the short circuit power in the substation, where the generator power is connected to. Point of this course is to

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show that CCT duration depends on short circuit power as well, but from figure it is clear is not very significant. Based on the facts above it is necessary to consider in determining CCT duration with calculations for overexcited state (Qgen=max), underexcited state (Qgen=min) and zero reactive power supply (Qgen=0).

5 Dynamic Simulations of Selected Events Simulations of the dynamic stability of synchronous generator were realised in according to simplified model of power system in Fig.8.

Fig.8 Model of power system for assessment of transient stability (G1-Synchronous Generator; T1-Generator Transformer; BFR-Breaker Failure Relay; QM-Circuit Breaker; V1-Power Line)

Fig.6 Influence of voltage on CCT duration in transmission power substation [3]

The aim of this part was to simulate and compare the selected events (events N-1 and N-k), which can arise in the power system and therefore it is necessary to consider these events in the analysis of dynamic stability. Dynamic simulations were realised in the following generator operational parameters G1: Sn = 259MVA, Un=15,8kV, PG = 221,7MW, QG= 29,9MVAr (overexcited state). Dynamic simulations were realised for the following selected events: 1) bus bar short circuit in substation with three circuit breakers per two branches where the generator power is exported, 2) 3-phase short circuit on power line V1, 3) 3-phase short circuit on power line V1 with failure of circuit breaker QM1, 4) 3-phase short circuit on power line V1 with failure of circuit breaker QM2, 5) 3-phase short circuit on power line V1 with failure of circuit breakers QM1, QM2.

Fig.7 Influence of short circuit power on CCT duration in transmission power substation [3]

4 Assessment of Dynamic Stability of Power System Dynamic stability can be investigated for one generator but also for the whole power system. The procedure for the power system assessment of dynamic stability consists of the CCT determination for all generators connected to power system. The most often used method for dynamic stability assessment is dynamic simulations of power system mathematical model. This way can be also evaluated the dynamic simulations for events N-1, N-k or break-up points verification. CCT calculations are realised the most in developing of defense plans, connecting new sources, operation preparations and maintenance states.

ISBN: 978-1-61804-128-9

5.1 3-phase Busbar Short Circuit in Substation with Three Circuit Breakers per Two Branches The simulation of dynamic stability was focused on monitoring of generator behavior during the 3-phase bus bar short circuit in the substation with three circuit breakers per two branches (Fig.9). This substation is characterised by the operational safety (highly strong side), what also confirm the simulation. The most often, this type of

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breakers per two branches caused a generator swinging but this failure did not cause a generator emergency shutdown. The generator stabilised approximately 10s after the failure at a new balance value and it is dynamically stable.

substation is used for power export from power plants.

5.2 3-phase Short Circuit on Power Line V1 The generator G1 behaviour is shown in Fig.11. From this figure it is clear that the failure caused a swinging but still remained in operation and it is dynamically stable. Generator stabilised at a new balance value approximately 9s after the failure.

Fig.9 Substation with three circuit breakers per two branches [4] The simulation of the dynamic stability was modelled for the 3-phase short circuit arising on bus bar W2 when both bus bars are in operation at time of short circuit. Differential bus bar protection on W2 responds on this failure and sends trip commands to the circuit breakers QM13 and QM23, which are disconnected at time 100ms after the failure and the substation remains in continuous operation. Ability to remain in continuous operation after 3-phase bus bar short circuit is the highly strong side of this type of substation in comparison with other classical substation with single bus bar. In case of 3-phase bus bar short circuit in substation with single bus bar for power export from power plant has to be the generator emergency shutdown. It is necessary to add that despite generator maintaining continuous operation, this failure has a significant impact on the dynamic stability. The generator behavior under the given operational parameters and modeled event (at the time until 10s after the failure) is shown in Fig.10.

Fig.11 Behavior of the synchronous generator after the short circuit on the line V1 (vt-voltage at the generator terminals; ang-rotor angle, efdelectromotive voltage; it-current; pg-active power; spd-frequency)

5.3 3-phase Short Circuit on Power Line V1 with Failure of Circuit Breaker QM1 The next modelled situation was the 3-phase short circuit on the line V1 with the failure of circuit breaker QM1. The line is protected by distance protection in protection zone where the short circuit arose. Distance protection responded on this failure and sent the trip commands to the circuit breakers at the beginning and the end of the line (QM1, QM2). The circuit breaker QM2 tripped the line until 100ms, but the circuit breaker QM1 failed. In case of circuit breaker failure on the line the nearest BFR (Breaker Failure Relay) responds to this failure. BFR is installed in every substation and its tripping time is longer than the circuit breaker tripping time, i.e. more than 100ms. In this modelled situation was the BFR tripping time set for 350ms (where is included circuit breaker tripping time – 100ms and BFR setting time – 250ms). BFR1 responded to the circuit breaker failure at time 350ms after the short circuit and sent the trip commands to circuit breakers on all bus bar branches.

Fig.10 Behavior of the synchronous generator after the bus bar short circuit in the substation with 1,5 circuit breaker for a branch (vt-voltage at the generator terminals; ang-rotor angle, efdelectromotive voltage; it-current; pg-active power; spd-frequency) In Fig.10 it can be seen that the 3-phase bus bar short circuit in substation with three circuit

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circuit breaker QM2 (vt-voltage at the generator terminals; ang-rotor angle, efd-electromotive voltage; it-current; pg-active power; spd-frequency)

Synchronous generator response to this event is shown in Fig.12, where it can be seen the generator stabilisation at new balance value after the swinging approximately until 11s after the short circuit. Generator is dynamically stable.

5.5 3-phase Short Circuit on Power Line V1 with Failure of Circuit Breakers QM1, QM2 The simulation of dynamic stability was focused on monitoring of generator behavior during the 3-phase bus bar short circuit in the substation with three circuit breakers per two branches (Fig.9). The circuit breaker failure on both sides of the line belongs among very low probability events but the dynamic simulations have to be verified anyway. Short circuit arose on the line V1; the distance protection responded and sent the trip commands to the circuit breakers on both sides of the line (QM1, QM2) which failed. Therefore, the BFR responded on both sides of the line at time 350ms and all branches of both bus bars were tripped. The generator swung after both BFR responding the most and stabilised at a new balance value until 11s, i.e. generator is dynamically stable and even this event did not cause a loss of synchronism (Fig.14).

Fig.12 Behavior of the synchronous generator after the short circuit on the line V1 with the failure of circuit breaker QM1 (vt-voltage at the generator terminals; ang-rotor angle, efd-electromotive voltage; it-current; pg-active power; spd-frequency)

5.4 3-phase Short Circuit on Power Line V1 with Failure of Circuit Breaker QM2 The next modelled situation was the 3-phase short circuit on the line V1 with the failure of circuit breaker QM2. At first sight, it is a similar situation as the one above, but in fact it is significantly different situation because the power system model (Fig.8) is interconnected system what means that the tripping times change will also strongly change an impact on the dynamic stability of the generator. Finally, the simulation confirms this fact. Equally as the situation above, the line is protected by distance protections. The short circuit arose in the protected zone of distance protection on the line V1. The distance protection sent the trip commands to the circuit breakers at the beginning and the end of the line (QM1 and QM2). The circuit breaker QM1 tripped the line until 100ms, but the circuit breaker QM2 failed. Subsequently, the BFR2 responds to the circuit breaker QM2 failure and trips all bus bar branches at time 350ms. The generator (Fig.13) is after the BFR responding swung again but until 9s is stabilised at a new balance value, i.e. it is dynamically stable.

Fig.14 Behavior of the synchronous generator after the short circuit on the line V1 with the failure of circuit breakers QM1 and QM2 (vt-voltage at the generator terminals; ang-rotor angle, efdelectromotive voltage; it-current; pg-active power; spd-frequency)

6 Conclusion The simulated events in this paper can be sorted in terms of the significance of their impact on the dynamic stability of synchronous generator from the most affecting as follows: 1. 3-phase short circuit on power line V1 with failure of circuit breakers QM1, QM2 2. 3-phase short circuit on power line V1 with failure of circuit breaker QM1 3. 3-phase short circuit on power line V1 with failure of circuit breaker QM2 4. 3-phase short circuit on power line V1

Fig.13 Behavior of the synchronous generator after the short circuit on the line V1 with the failure of

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Advances in Power and Energy Systems

One of all simulated events is the bus bar short circuit. But this only one is quite relevant to compare with other events because in this situation there is a special type of substation and an electrically near short circuit will have always more significant impact on the dynamic stability of synchronous generator than other short circuits at different power system points. Resulting from the simulations can be stated that short circuit tripped at fast time (100ms) do not jeopardise the dynamic stability as significant as the short circuits tripped at slow time (BFR – in case of this paper 350ms).

References: [1] Reváková, D., Eleschová, Ž., Beláň, A., Prechodné javy v elektrizačných sústavách, Bratislava, Vydavateľstvo STU, 2008, 180 s, ISBN 978-80-227-2868-3. [2] Eleschová, Ž., Beláň, A., CCT – Basic Criteria of Power System Transient Stability, The 11th International Scientific Conference EPE 2010, Brno, 2010, pp. 157-161, ISBN 978-80-2144094-4. [3] Eleschová, Ž., Beláň, A., Factors affecting the length of critical clearing time, The 9th International Scientific Conference Control of Power System 2010, Tatranské Matliare, 2010, pp. 1-7, ISBN 978-8089402-20-5. [4] Janíček, F., Arnold, A., Gorta, Z., Elektrické stanice, Bratislava, Vydavateľstvo STU, 2001, 286 s, ISBN 80-227-1630-8. [5] Paar, M., Toman, P., Distribution Network Reconfiguration Based on Minimal Power Losses, The 9th International Scientific Conference Electric Power Engineering 2008, Brno, 2008, pp. 211-215, ISBN 978-80-2143650- 3. [6] Orságová, J., Toman, P., Evaluation of Negative Effects of Distributed Generation, The Power Quality and Supply Reliability, Tallin, 2008, pp. 131-135, ISBN 978-1-42442500-6.

Table 1 Values of monitored parameters in the simulation of dynamic stability of synchronous generator

Event

bus bar short circuit 3-p short circuit on power line V1

Voltage at the Generator Terminals [kV]

Rotor Angle [ °]

Current [kA]

Active Power [MW]

min

max

min

max

min max

min

max

5,46

16,46

2,90

44,07

4,5

27,9

6,5

371,7

11,42 16,12 12,01 29,70

6,8

12,9 120,2 286,7

Acknowledgement

3-p short circuit on power line V1 with failure of QM1

10,16 16,76

3,49

51,34

3,8

18,4 107,9 392,6

3-p short circuit on power line V1 with failure of QM2

11,42 16,48

7,90

28,81

6,2

12,9 120,2 296,3

3-p short circuit on power line V1 with failure of QM1,QM2

10,68 16,77

1,40

56,23

3,2

17,5

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89,8

These publications are the result of implementation of the project: “Increase of Power Safety of the Slovak Republic” (ITMS:26220220077) supported by the Research & Development Operational Programme funded by the ERDF.

This work was done during implementation of the project Effective control of production and consumption of energy from renewable resources, ITMS code 26240220028, supported by the Research and Development Operational Program funded by the ERDF.

401,8

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