An Investigation of Controlled System Separation Following Transient Instability

Transcription

1 NATIONAL POER SYSTEMS CONFERENCE, NPSC An Investigation of Controlled System Separation Following Transient Instability K. N. Shubhanga, A. M. Kulkarni, Abstract In this paper, a study has been carried out to understand the separation patterns of generator rotor angles following a transient instability condition on power system in the context of controlled system separation. In this regard, the two important issues - identification of the MOI, which tells us about the possible location of separation, and timing of separation with the objective of splitting the system into stable islands following instability - are addressed. Trajectory Sensitivity of phase angle across lines with respect to clearing time are used to identify critical cut-sets. This information is utilised in a transient stability program to effect changes in the network connectivity following fault clearing at the desired time instants. Study has been carried out on machine bus New England system and machine bus China system. Keywords Power system transient stability, Loss of synchronism, Controlled system separation,trajectory Sensitivity. I. INTRODUCTION T is well known that transient instability following a large disturbance can render integrated operation of a power system unviable. If appropriate action is not taken, it can induce a blackout over a wide area of the network. In order to minimize this, it is necessary to detect loss of synchronism and separate system at optimal locations or shed generators if required. Of these, detecting loss of synchronism is a complex task as it involves the discrimination of unstable from stable operating condition of a system. The process of system separation, if necessary, is initiated following a successful detection of instability. There has been a continuous effort in the system protection field to develop a robust scheme to detect of loss of synchronism. In [], [], a scheme is presented to detect loss of synchronism when the relative phase angle of generators increases and exceeds a preset threshold. It also describes a methodology to decide minimum number of generators to be shed. In [], Tamotsu, et.al., have proposed a scheme to detect loss of synchronism using measured power and current through a distinct line connecting two groups of generators. Using real time measurement systems, processing subsystems and well connected communication network a coordinated defense strategy has been developed in [] to protect system against loss-of-synchronism. Ohura, et.al., [] have presented a curve fitting technique to predict future behaviour of swings. In [], an adaptive model of a system is employed to identify out-of-step condition of generators. These methods basically used synchronized sampling technique to get angle information of important generators. In [], Padiyar, et. al., have developed a technique based on the concept of potential energy of a line, to accurately determine the loss-of-synchronism using local measurements such as voltage and current in a line. For a successful system separation and formation of stable The work was supported by the Department of Science and Technology (DST), Gov. of India, under the scheme no. III-()/-ET. The authors are with Department of Electrical Engineering, Indian Institute of Technology Bombay Mumbai,, INDIA, anil@ee.iitb.ac.in islands, the knowledge of the following aspects are important []:. Separation pattern related to rotor angle stability.. Optimal location(s) for system separation.. The generation - load balance within each island.. Stability level of each island. This paper investigates these issues through detailed time domain simulations. Simulation studies are carried-out to understand the separation patterns of rotor angles for different contingencies. This involves identification of Mode of Instability (MOI) i.e., group of generators that tend to separate from the rest when the fault is cleared so that the system is critically unstable. to identify the generators that are sensitive to change in system configuration. to determine the stability of islands which can contain noncoherent generators, where the stability is determined by the sensitivity of the MOI and time taken for separation. to determine the feasibility of system separation along various critical cut-sets. Thus, the simulation study involves two important aspects: first to predict the MOI and then to use this knowledge to effect changes in the post fault system using the developed transient stability program. The prediction of MOI is carried out observing the sensitivity of phase angle across various branches with respect to fault clearing time. This paper deals with coherence of generators in an island. Issues related to generation-load balance and emergency control actions are not considered this paper. The paper is structured as follows: In section II a brief introduction to trajectory sensitivity analysis is given. This analysis is used to predict the MOI, and hence to get useful information about cut-sets. Also, features of the developed transient stability program are described. In section III, case studies are presented for machine, bus New England system [] and machine, bus China system []. II. METHOD OF ANALYSIS A. Determination of Critical Cut-sets The prediction of MOI is a major step in detecting transient instability. This prediction is a complex task as it depends on fault location, fault duration, generator/load model employed and inertia of the machines. MOI is also sensitive to change in system parameters, i.e., whether a high or low impedance line is tripped, or compensated. This complicates the prediction of loss of synchronism of generators, optimal location of system separation and time of separation. In this regard, the observability of the MOI in the transmission system is an important issue. Various observables that can be used for predicting the MOI are

2 NATIONAL POER SYSTEMS CONFERENCE, NPSC current through branches and phase angle across various lines when the system is critically unstable. It is observed that the deviation of trajectory form the nominal for a small change in parameter gives a better insight into the behaviour of a system. Therefore, in the present study Trajectory Sensitivity (TS) approach is followed to predict the MOI. Trajectory sensitivity analysis [], [] basically amounts to linearizing a system around a nominal trajectory rather than around an equilibrium point. This is motivated by the fact that the trajectory sensitivity of system variables with respect to system parameters change very rapidly than the underlying system trajectory. Hence, properties which are not obvious from the actual system trajectories are often evident from the trajectory sensitivities. However, the computation of trajectory sensitivities is a complex task as it requires the integration of additional set of differential equations along with system differential equations. If Simultaneous Implicit method is used to simulate the original system, then TS computation is relatively easy []. However, if TS with respect to many parameters are required, then the computational burden can be significant. Also, discontinuities necessitate the calculation of jump conditions []. Numerical evaluation of TS is relatively convenient and easy to implement. In this paper, trajectory sensitivity of phase angle across various branches ( ) with respect to clearing time are used to decide critical cut-sets. The steps followed are:. TS of with respect to clearing time are obtained numerically [].. The critical cut-sets are identified looking at branches having relatively high value of sensitivity. This step does not require the knowledge the critical value of clearing time as the TS are obtained at nominal value much smaller than the critical value. B. Transient Stability Program To study the behaviour of a system due to controlled system separation following transient instability, a transient stability program has been developed, in which line(s) and/or transformer(s) can be tripped at a predetermined time after the fault is cleared. To create instability, fault clearing time is set slightly higher than the critical value. The tripping of elements is decided using the knowledge about critical cut-sets obtained from TS of. Thus, one can separate the system into groups either along the MOI or to form any desired generator group. This can be done either simultaneously or sequentially. Here, the trip time can be set to any desired value in order to study the effect of timing of separation on the stability of islands which contain non-coherent generators. The method of analysis developed above is applied to machine and machine systems and the results are given in the following section. A. machine bus system III. RESULTS The proposed analysis is applied to a machine, bus power system. The single line diagram of the system is shown in Fig.. Generators are modelled using the two-axis model with AVR and PSS. The transmission line/transformer resistances are also considered. Loads are modelled as constant impedance type. The system data is taken from []. Fig.. machine, bus New England power system Fault at bus, Line cleared: -: A three phase fault at bus is considered followed by tripping of line (-) to clear the fault. For this fault, the critical clearing time obtained is. s. Machines and separate together from the rest when the system is critically unstable. (see Fig. ) Fault bus: Line cleared:... & Fig.. Plots of rotor angles To determine the critical cut-sets the trajectory sensitivities of are obtained at a nominal clearing time of. s and are shown in Fig.. φ br sensitivity.... ( )T Fault bus: Line cleared: ( ) ( ) ( ) ( ) ( )T.. Fig.. Trajectory sensitivity of The figure shows that lines (- and -), (-)T, (- )T and (- and -) form major cut-sets as they have

3 INDIAN INSTITUTE OF TECHNOLOGY, KHARAGPUR, DECEMBER -, relatively higher sensitivity peaks compared to others branches. Using this information the feasibility of successful system separation and timing of separation is studied using the transient stability program.. hen lines are tripped along cut-set (- and -), it separated machine from the rest of the machines. If the timing of separation is less than. s, the rest of the generators formed a stable group as shown in Fig.. For a timing more than. s it splits the system into three groups, i.e., machine, machines and, and the rest (see Fig. ). Note that this trip time approximately lies in the time range during which the TS of for the cut-set reaches its peak value. Line tripped: ( )T Trip time:. s Fault bus:, Line cleared: m/c. Fig.. Rotor angle plots for tripping of transformer (-) Fault Bus:, Line cleared: Lines tripped: ( ) & ( ) Trip time:. s m/c Line tripped: ( )T Trip time:. s Fault bus:, Line cleared: m/c. m/c. Fig.. Rotor angle plots for tripping of lines (- and -) Fig.. Rotor angle plots for tripping of transformer (-) Fault bus:, Line cleared: Lines tripped: ( ) & ( ) Trip time:. s m/cs. & m/c. Fig.. Rotor angle plots for tripping of lines (- and -). A transformer is tripped along cut-set (-) to separate machine from the rest of the machines. The rest of the group formed a stable island (see Fig. ) when the timing of separation is less than. s. For a trip timing more than. s machine also separated forming three groups as shown in Fig... In this case machine is separated by tripping transformer (-). It can be seen from Fig. that even for a very small tripping time of. s, the remaining generators did not form a stable group. Machine also separated irrespective of timing of separation.. The feasibility of separating machines and together, is verified by tripping lines along ( - and -). In this case, the tripping is done along the MOI. It is noted that upto a trip time of s the separation resulted in two stable groups, i.e., machines and, and the rest of generators. Figs. and show the the rotor angles for a trip time of. s and s respectively. Fault at bus, Line cleared: -: A three phase fault at bus is considered followed by tripping of line (-) to clear the fault. For this fault, the critical clearing time obtained is. s. In this case, there are several groups of separating machines constituted by (,), (,,,), (,,) and as shown in Fig.. Critical cut-sets are determined by obtaining the trajectory sensitivity of with respect to clearing time at a nominal clearing time of. s. From Fig., it is evident that lines (- and -), ( -)T and (- and -) form critical cut-sets as they exhibit relatively high sensitivity compared to the remaining branches. It is to be noted that the peak value of sensitivity for various branches occur at different instants of time, indicating that the prediction of MOI is difficult and is Line tripped: ( )T Trip time=. s Fault bus:, Line cleared: m/c. m/c. Fig.. Rotor angle plots for tripping of transformer (-)

4 NATIONAL POER SYSTEMS CONFERENCE, NPSC Fault bus: Line cleared: Fault bus:, Line cleared: Lines tripped : ( ) & ( ) Trip time =. s m/c & φ br sensitivity..... ( )T ( ) ( ) ( ) ( ).. Fig.. Rotor angle plots for tripping of lines (- and -) Fig.. Trajectory sensitivity of Trip time = s Fault bus:, Line cleared: ( ) Lines tripped : ( ) & ( ) m/c & Fig.. Rotor angle plots for tripping of lines (- and -) Fault bus:, Line cleared: Lines tripped: ( ) & ( ) Trip time =. s m/c. Fig.. Rotor angle plots for tripping of lines (- and -) susceptible to change due to change in system parameters. The knowledge of critical cut-sets is used to study the effect of system separation on the formation of stable islands.. Tripping of lines (- and -) separated machine from the rest of generators. It is observed that for a timing of separation upto. s the rest of the generators formed a single stable group (Fig. ). However, when the trip time is more than. s the separation resulted in several machines separating from each other (see Fig. ). To show the effect of timing of separation on the coherence of generators in a group, the lines are tripped at a time of. s. Fig. clearly shows that there is a better coherence among the generators in the group compared to a trip time of. s (Fig. ).. hen transformer (-) is tripped, it separated machine from the rest. However, this separation is ineffective in making the rest of generators a stable group. Fig. shows several machines separating from each other for a trip time of. s.. In this case, lines are tripped along the cut-set (- and - ). For a trip time upto. s the separation resulted in the formation of two stable groups consisting of machines,,,,, and, and, and (see Fig. ). hen the timing of separation is more than. s the system split into three groups as shown in Fig.. Comparison of Figs. and indicates the effect of timing of separation on the degree of coherence between generators in each group. Fault bus: Line cleared: Fault bus:, Line cleared: Rotor angle w.r.to COI in rad. m/c &,, &, & Fig.. Plots of rotor angles Lines tripped: ( ) & ( ) Trip time =. s & Fig.. Rotor angle plots for tripping of lines (- and -)

5 INDIAN INSTITUTE OF TECHNOLOGY, KHARAGPUR, DECEMBER -, Fault bus:, Line cleared: Fault bus:, Line cleared: Lines tripped: ( ) & ( ) Trip time =. s m/c. Lines tripped: ( ) & ( ) Trip time =. s Fig.. Rotor angle plots for tripping of lines (- and -) Fig.. Rotor angle plots for tripping of lines (- and -) Lines tripped: ( )T Trip time =. s Fault bus:, Line cleared: &,,,,, & Fig.. Rotor angle plots for tripping of transformer (-) B. machine, bus system The single line diagram of this system is shown in Fig.. Generators are modelled in detail using the two-axis model with AVR and PSS. The data is taken from []. For a fault at bus, line - is tripped to clear the fault. The critical clearing time obtained is. s. Machine separated from the rest when the system is critically unstable (Fig.). Similar to machine case, trajectory sensitivity of, obtained at a nominal clearing time of. s, is used to obtain the critical cut-sets. Fig. shows that lines (-, - and - ), (-, - and -), (-, - and -) and (- and -) are prominent cut-sets. The effect of system separation along these cut-sets are studied using the developed tran- Rotor angles (w.r. to COI) in rad. Fault bus:, Line cleared: Lines tripped: ( ) & ( ) Trip time =. s Fig.. Rotor angle plots for tripping of lines (- and -) Fig.. machine bus China system sient stability program.. Lines -, - and - are tripped to separate machine from the rest. Note that the tripping is done along the MOI. It can be seen from Figs. and that for a trip time of. s and s respectively, the separation did not help in improving the coherence among the generators in the other group, but it splits the system into three or four groups. It is found that in order to achieve the desired separation the trip time should be quite large. This behaviour can be due to the fact that the peak sensitivity for these lines occur at a time around. s (see Fig. ).. In this case, lines are tripped along the cut-set (-, - and -) to spit the system in two major groups. For a time of separation of. s and greater, the system divided into three groups as shown in Fig., constituted by machines to, to and. hen the trip time is less than. s the system separated into two groups as desired. Fig. shows the machines grouping for a trip time of s.. Machines, and are separated by tripping lines -, - and -. For a trip time upto s, the tripping of lines resulted in the formation of three groups as shown in Fig.. It is found that to get two stable groups of machines as desired, the trip time should lie between to. s (see Fig. ) beyond which the separation led to several machines separating from each other. This time range is close to the time instant at which

6 NATIONAL POER SYSTEMS CONFERENCE, NPSC Fualt bus:, Line cleared: m/c Fault bus:, Line cleared: Lines tripped: ( ), ( ) & ( ) Trip time = s & Fig.. Plots of rotor angles of generators Fig.. Rotor angles for tripping of lines (-, - and -) φ br sensitivity ( ) Fault bus:, Line cleared: ( ) ( ) ( ) ( ) ( ) ( ) ( ) Fault bus:, Line cleared: Lines tripped: ( ), ( )& ( ) Trip time =. s to m/c. to.... Fig.. Trajectory sensitivity of Fig.. Rotor angles for tripping of lines (-, - and -) the TS of of the cut-set is relatively high.. hen lines are tripped along the cut-set (- and -) machines and are separated together. Independent of timing of separation this tripping resulted in three groups constituted by machine, machines and and the rest (see Fig. ). IV. CONCLUSIONS In this paper, the separation patterns of rotor angles for different contingencies for two typical power systems are studied in the context of controlled system separation following the detection of out-of-step condition on power system. Trajectory sensitivity of phase angle across various branches are used to identify critical cut-sets. Using a transient stability program the feasibility of system separation along different cutsets are verified and the effect of timing of separation on the stability of islands are studied. Based on the studies carried out on two power systems following are the observations made: Successful separation can not always be guaranteed if tripping is done along cut-sets associated with the MOI. This behaviour is system dependent. It is feasible to get stable islands when separation is done along other cut-sets provided the TS of is high for those cut-sets. The timing of separation has a strong influence on the degree of coherence of generators in a group, i.e., the trip time decides the stability of an island which contains non-coherent generators. Fault bus:, Line cleared: Lines tripped: ( ), ( ) & ( ) Trip time =. s & Lines tripped: ( ), ( )& ( ) Trip time =. s Fault bus:, Line cleared: to to Fig.. Rotor angles for tripping of lines (-, - and -) Fig.. Rotor angles for tripping of lines (-, - and -)

7 INDIAN INSTITUTE OF TECHNOLOGY, KHARAGPUR, DECEMBER -, Fault bus:, Line cleared: Lines tripped: ( ), ( ) & ( ) Trip time =. s, & Fig.. Rotor angles for tripping of lines (-, - and -) Fault bus:, Line cleared: Lines tripped: ( ), ( ) & ( ) Trip time =. s, & [] O. Faucon and Laurent Dousset, Coordinated Defense Plan Protects Against Transient Instabilities, IEEE CAP, pp.-,july,. [] Y. Ohura, M. Suzuki, K.Yanagishi, M. Yamaura, K. Omata, T. Nakamura, S. Mitamura and H. atanabe, Predictive Out-of -Step Protection system based on observation of the Phase difference between Substations, IEEE Trans. on Power Delivery, Vol., No., pp -, Nov.. [] V. Centeno, A. G. Phadke, A Edris, J. Benton, M. Gaudi and G. Michel, An adaptive Out-of-Step Relay, IEEE Trans. on Power Delivery, Vol., No., pp -, Jan.. [] K.R.Padiyar and S. Krishna, On-line Detection of Loss of Synchronism using Locally Measurable Quantities, IEEE/PES Transmission and Distribution Conference and Exposition, Oct/Nov.. [] J. Van Eyssen, Introduction to a New application Philosophy for Out-of- Step protection, Developments in Power System Protection Conference, Pub.No., pp.-, IEE. [] K.R. Padiyar, Power System Dynamics - Stability and Control, Interline Publishing Ltd., Bangalore, India. [] Graham Rogers,Power System Oscillations, Kluwer Academic Publishers, Boston,. [] M. J. Laufenberg and M.A. Pai, A New Approach to Dynamic Security Assessment Using Trajectory Sensitivities, IEEE Trans. on Power Systems, Vol., No., pp. -, Aug.,. [] I.A. Hiskens and M. Akke, Analysis of the Nordel Power Grid Disturbance of January, Using Trajectory Sensitivities, IEEE Trans. on Power Systems, Vol., No., pp. -, Aug.,. [] I.A. Hiskens and M.A. Pai, Trajectory Sensitivity Analysis of Hybrid Systems, IEEE Trans. on Circuits and Systems Part I: Fundamental Theory and Applications, Vol., No., pp. -.,Feb., Fig.. Rotor angles for tripping of lines (-, - and -) On the formation of stable islands, it is necessary to ensure generation - load balance in each island to arrest frequency rise or decline. Moreover, the effect of other emergency control actions like generator or load tripping needs to be studied. REFERENCES [] M. Takahashi, K. Matsuzawa, M. Sato, K. Omata, R. Tsukui, T. Nakamura and S.Mizuguchi, Fast Generation Shedding Equipment based on the observation of Swings of generators,ieee Trans. on Power Systems, Vol., No., pp.-, May. [] K. Matsuzawa, K. Yanagihashi, J. Tsukita, M. Sato, T. Nakamura and A. Takeuchi, Stabilizing Control System Preventing Loss of Synchronism from Extension and its actual operating experience, IEEE Trans. on Power Systems, Vol., No., pp., Aug.. [] Tamotsu Minakwa, M.Sato, Y. Ichikawa and Y. Ishihara, A New Method for Detecting Loss of Synchronism Using Power and Current Measured on a line, IEEE Trans. on Power Delivery, Vol., No., pp.-, Jan.. Fault bus:, Line cleared: Lines tripped: ( ) & ( ) Trip time =. s & Fig.. Rotor angles for tripping of lines (- and -)