A Algorithm for the Three-Pole Controlled Auto-Reclosing of ShuntCompensated Transmission Lines with a Optimization for the second and
third Pole
G. Pilz*, P. Schegner
Technical University of
Dresden (Germany)
C. Wallner
Siemens AG Berlin,
(Germany)
H. M. Muhr, S. Pack
University of Graz
(Austria)
Abstract
This paper presents an algorithm for auto-reclosing of shunt compensated transmission lines. Thealgorithm uses signal analysis methods to estimate the future voltage shape over the circuit-breaker.Based on this voltage shape switching instants are estimated in the zero crossings. The minimizationof the probability of a prearcing is reduced be adding time shift parameters. These parameters take thelimited rise of strength recovery of the circuit breaker and the mutual influence of the coupling of the
poles by a three-pole auto-reclosing into consideration. The advantage of the descript method is
significant reduction of the switching overvoltage.Keywords
During the dead time of an auto-reclosing of a shunt compensated transmission line transient phenomena on the line side are excited. The transient phenomena depend on the parameter of thetransmission line and the level of compensation. The reclosing after the dead time may generateovervoltages, which are up to four times higher than the nominal amplitude of the line-to-earthvoltage. Normally a lightning arrester or a closing resistor had to be installed to limit the overvoltage.A powerful reduction of the switching overvoltage is also possible by reclosing the transmission linein a optimal switching instant. To do this it is necessary to analyze the voltage over the main switchingcontacts, to predict the voltage shape and to identify a optimal switching instant. The voltage on the
bus-bar side of the circuit-breaker is the nominal voltage, which is sinusoidal with constant amplitudeand frequency. The parameters of the voltage on the line side of the circuit-breaker differ in frequency,damping ratio and amplitude. The waveform of this voltage depends on the design of the transmissionline and the connected compensation equipment. The resonant circuit (shunt reactor and transmissionline capacitance) and the induced voltage from the other phases define the resulting line-to-earthvoltage of each phase. The frequency of voltages of the different phases can differ. During the deadtime of a single-pole auto-reclosing two phases are still feeded the nominal voltage, that means
operated with the nominal frequency. During a three-pole auto-reclosing the frequency of each phaseis mainly defined by the resonant circuit of the individual phases. The real time processing ability is a
further criterion for the development of an algorithm for controlled closing. The maximum calculationtime is limited by the dead time of the auto-reclosing cycle, which depends on the voltage level.
Two algorithms for prediction of the future voltage are presented in chapter two. The first algorithmis based on the pattern recognition. This method analyzes the envelope curve of the voltage signal.Therefore it is not possible to reclose in the zero crossing of the voltage, which is the optimal instantfor this switching task. The reclosing operation can take place only in a nodal point of the voltage. Thestate of the art applied methods are using pattern recognition algorithms [1], [2]. The second algorithmis based on the Prony Method. The method composes the voltage signal by a sum of sinusoidal,exponential damped functions. The parameters of these functions are the amplitude, the dampingfactor, the frequency and the phase shift. The lowest recognizable frequency is independent of theevaluation window of the Prony Method. Another advantage of the Prony Method is a high resolutionin the frequency domain. Signals with small frequency differences will be exactly determined. Via theestimation of the signal components it is not only possible to calculate accurately the voltage zerocrossing across the switching contacts of the circuit-breaker as possible switching instant, but also therate of voltage rise in this point. So it is now possible to shift the switching instant, if the rise ofvoltage in the zero crossing is greater than the rise of the characteristic curve of strength recovery ofthe circuit-breaker. The switching overvoltage will be minimized. The connection between the rise of
voltage at the zero crossing and the strength recovery of the circuit-breaker is explained in chapterthree. In addition the selection of the optimal sequence of the switching instants of a three-pole auto-reclosing will be in this chapter discussed. The selection of the switching instant of the second andthird pole is in this case complicated, because after closing the first pole the estimated zero crossingsfor the second and third poles are no longer valid. A recalculation of the future voltage shape of thesetwo poles is not possible, because postpone between the closing of the three phases should be minimal.The first algorithm is optimized for a standard processor. The second algorithm is more complex andcalculates optimized switching instants for the second and third pole. This leads to an additionalreduction of the switching overvoltage.
In chapter four the results of the simulations are presented. First the simulations of switchingcompensated transmission lines with ATP are illustrated. A sensitivity analysis could be accomplished
by varying the parameters of the transmission lines (e.g. degree of compensation, length of the
transmission line, one or three pole auto-reclosing). The calculated waveforms are the input data forthe programmed real-time algorithms. The programming takes place in MATLAB. The results of thereal time calculation are the switching instants. With this result a complete simulation of the auto-reclosing is carried out. The breaker operating time and the limited rise of characteristic curve of thecircuit-breaker are considered. The quality of a controlled reclosing is determined by the size ofcalculated switching voltage.
2 Estimation of the Future Voltage
2.1 Pattern Recognition
The algorithm for the estimation of the futurevoltage must be work in a loop. This loop isdivided into individual time windows. Thevoltage over the circuit-breaker is scanned inthe first window. The envelope of the scannedvoltage is calculated and likewise the voltageover the circuit-breaker is scanned in thesecond window. The calculation of theenvelopes for the second scanning, the shiftof the first envelopes at the window lengthand the comparison of the two envelopes take
place in the third window. The voltage overthe circuit-breaker is just as again scanned. If a correspondence between the envelopes of the first and
second window is detected, a controlled switching instant could be calculated. The envelope of thesecond data window is shifted at two window lengths for this purpose and a node of the voltage isdefined as switching instant. If no correspondence between the both envelopes is detected, theenvelope of the first window will be deleted and the envelope of the second window is used as
reference sample. This reference sample mustthen be compared with the envelope of thethird window. A valid result, the controlledclosing operation or the expiration of a definedtime slot interrupts this loop. The time slotdefines, how long the control device may delaythe closing signal to the circuit-breaker.
The absolute value of the voltage shape ofan 80% compensation transmission line duringthe dead time an auto-reclosing is representedin Fig.1 (thin black line). The strong verticallines mark the borders of the individualwindows (length 100ms). In this example thecomparison between the envelope of the first(green squares) and the second window is
positive. Therefore the envelope of the secondwindow (blue circle) is shifted to the time of
the fourth window. In this future window theswitching instant at the time index 0,39s isselected. To give the possibility to compare theresult, the absolute value of the voltage for thisfourth window is also shown in the figure.
In Figure 2a the same task is illustrated for a compensation degree of 30%. The results of theestimation are insufficient. But if the individual window length were made smaller (length 90ms, seeFigure 2b), the result for a controlled closing would be sufficient. The strong dependence of the resultson the selected window length is a big disadvantage of this method, because the estimation must take
place with a fix window length for all possible compensations. Further disadvantages of this methodare the neglect of the damping of the voltage and the ability only to estimate switching instants in thenodal point of the voltage. Especially the switching instants are too inaccurate for a three-pole auto-
reclosing, because the influence of the individual poles among themselves can not be taken intoconsideration. A better estimation of the future voltage is necessary for this task. The advantages ofthis method are the lower demand of power of microprocessors and the allowed high noise to signalratio.
2.2 Prony Method
The estimation of the future voltage via the Prony Method works also in a loop with data windows.These windows have likewise a constant length. The voltage over the circuit-breaker is scanned ineach individual window. The N data samples x[1],…, x[n],…, x[ N ] with the constant sample interval T of the first window are the starting points of the calculation. This vector can be described with thefollowing summation with a p-term complex exponential model.
( )( )[ ]∑=+−+=
p
k
k k k k jT n f j An x
1
12exp][ θ π α (1)
In this equation Ak is the amplitude, α k the damping factor in s-1, f k the sinusoidal frequency in Hzand θ k the sinusoidal initial phase in radians. If the data samples are real, the complex exponentialmust occur in complex conjugate pairs of equal amplitude. The eq. (1) may expressed in the form
∑=
−= p
k
nk k z hn x
1
1][ , (2)
where the complex constants hk and z k are defined as( )θ j Ah k k exp= , (3)
( )[ ]T f j z k k k π α 2exp += . (4)
The goal for the Prony Method is to minimize the squared error over all sampled data with respectto the complex parameters and the number of exponents. A detailed representation of the algorithm isin Appendix A and in [3].
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Figure 5: Time shift parameters for circuit breakers
with prearcing voltage characteristiccurve of 75kV/ms, 100kV/ms and125kV/ms
Other point is the fact that the system status for the second and third closing pole of a three-poleauto-reclosing during the reclosing operation is changing. Therefore the estimated zero crossings areno more valid. A new estimation is not possible. The algorithm for selection of the optimal switchinginstants must consider this problem also.
3.1 Single-Pole Auto-Reclosing
The estimated future voltage shape will be divided into possible switching windows. The zero crossingwith the smallest rise of the voltage will be selected within each window. These zero crossings arethen the possible switching instants. The length of the windows must meet two criteria. The length ofthe window should be not too short, because otherwise no zero crossings with small rises are existingin the window. On the other hand the window length should not too large, because otherwise no fastreaction to a closing command is possible.
Two algorithms are illustrated to minimize the switching voltage under consideration of the limitedrise of the prearcing voltage characteristic curve. By an addition of a fixed time parameter to theestimated zero crossing the switching instant will be shifted in positive direction. The probability of a
prearcing decreases with the magnitude of the time shift parameter. But the smallest possibleswitching voltage will also increase. Anyway a small probability of prearcing will be left, if the time
shift parameter is not great enough. The addition of a variable time shift parameter is a better solution.The rise of voltage in the zero crossing is the parameter for the size of the variable time shift parameter. The calculation of this parameter is easy with the knowledge of the exact future voltageshape. The connection between the rise of voltage and the variable time shift parameter will beestimated by a sensitivity analysis. A large number of opening operations of compensated transmissionlines were simulated with ATP. Thereby the input parameters for the simulation (e.g. compensationdegree, length of transmission line) were changed in a wide range. Then a virtual curve of strengthrecovery was lined up at all zero crossings. If the intersection point between the virtual curve of
prearcing voltage characteristic and the voltage is before the zero crossing, this curve will be timeshifted as long as the intersection point is after the zero crossing. The rise of voltage at the zerocrossing and the shift parameter are stored.
The results of the simulations are illustrated in Fig.5. The time shift parameter for a circuit-breaker
with a rise of the prearcing voltage characteristic curve of 100kV/ms (system level 380kV) in relationto the rise of the voltage at the zero crossing is represented with red crosses. No time shift is necessaryup to a rise of prearcing voltage characteristic curve of 60kV/ms. The picture shows, that themagnitude of the time shift parameter depends not only on the rise of voltage in the zero crossing,
because the voltage on the line side consist of several harmonics. The accuracy of the descript methodis sufficient for a real time application. The approximated straight line at the left side of the scatterplotgives the minimum time shift parameter for a circuit-breaker with a prearcing voltage characteristiccurve of 100kV/ms. No time shift parameter will added if the rise of voltage at the zero crossing issmaller then 60kV/ms. The value of the time shift parameter for rises which are greater then 60kV/mswill be calculated with the parameter of the approximated straight line.
The approximated lines for circuit-breakers with prearcing voltage characteristic curve of 75kV/msand 125kV/ms are also shown in the figure.With a steeper characteristic the size of thenecessary time shift will be smaller.
3.2 Three-Pole Auto-Reclosing
The first algorithm named method A is anextension of the algorithm for the single-poleauto-reclosing. The estimation of the windowwith the smallest rise at the zero crossing andthe adding of a first time shift parameter take
place for all three poles. In addition theswitching sequence of the poles during the
reclosing operation had to be estimated andthen a second time shift had to be added to
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Figure 6: Method A for selection of the swit-
ching instants
Figure 7: Method B for selection of the
switching instantsthe switching instants off the second and third switching pole.
An example is shown in Fig.6. The phase L3 is switch at first. The time shift parameters in the polesL1 and L2 are consisting of two parts. The calculation of the first time shift parameter is based on thelimited rise of the prearcing voltage characteristic curve of the circuit-breaker and the calculation ofthe second time shift parameter is based on the sequence of the pole switching.
This algorithm calculates not an optimum for the second and third switching pole. Especially if thedifferences between the individual switching instants are great, then high switching voltages couldoccur. A second algorithm named method B is optimized. Again the estimation of the windows withthe future voltage shape is carried out. Then the zero crossing with the smallest rise of voltage for allthree poles will be estimated. The pole with the smallest rise at the zero crossing is selected as the
third switching pole, if there are zero crossings in the two other poles before this estimated zerocrossing. The zero crossings in the two other poles are then the first and second switching instants. Ifthere are not preliminary zero crossings in the two other poles, the pole with the second smallest riseof voltage in the zero crossing will be selected as the third switching pole. This loop will be executedup to a valid result.
Fig.7 shows an example for that method. The zero crossing with the smallest rise is in pole L3. The preliminary zero crossings in pole L1 (second switching pole) and L2 (first switching pole) determinethe other two switching instants. Again a time shift parameters are added to the found switchinginstants. This is done identically to method A, dependent on the sequence of the poles and limited riseof the prearcing voltage characteristic curve of the circuit-breaker.
The small time differences between the switching instants are the advantage of the method. But thesecond method has higher demands on the power of the processor than the first method.
4 Results of the Simulation
Simulations of auto-reclosing were carried out in ATP for the examination of the algorithms. The parameters of the transmission line (e.g. length, transposition, damping), short-circuit power of thesupply system, compensation degree and the position of the failure was varied. Disconnections weresimulated in a first step. The voltage shapes over the circuit-breaker are the input data for the real-timealgorithm. The toolbox xPC from MATLAB was used as real-time environment. A Pentium PC with350MHz was the target hardware. This processor meets the demands for a single pole auto-reclosing.A higher performance is needed for a three-pole auto-reclosing. This switching task was simulated inan offline modus. The only difference between the target hardware and a real control device is theconnection to the input and output signals. In the used real-time environment the input datas are stored
in a data file. The implementation of a I/O-interface will be released in later version. The estimatedswitching instants are the outputs of the algorithms. A complete simulation of an auto-reclosingincluding the controlled closing is now possible in ATP. The circuit-breaker will modelled inconsideration of his operating time and his prearcing voltage characteristic curve. The operating time
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Figure 8: Example for the simulation of acontrolled closing during a three-poleauto-reclosing
Figure 9: Results of single-pole auto-reclosingswith different time shift parameters
Figure 10: Results of three-pole auto-reclosingswith method A and B
was defined with 50ms and the rise of the prearcing voltage characteristic curve with100kV/ms for a voltage level of 380kV. Thecalculated switching voltage is the
performance index of the algorithms.Fig.8 shows a simulation for a controlled
reclosing of a three-pole auto-reclosing withthe algorithm of method A. The switchingvoltage of the first switching pole isapproximately 60kV. The voltage over thecircuit-breaker breaks down after theintersection of the voltage line with the
prearcing voltage characteristic curve of thecircuit-breaker. Also the induction of transients from L1 in L2 and L3 is shown. The time shift
parameter of the second switching pole was sufficient, but for the third switching pole the time shift parameter was too small.
4.1
Single-Pole Auto-ReclosingFig.9 shows the results of the single-pole auto-reclosing with different time shift parameters.The switching voltage is presented on the x-axis and the relative number of the estimatedswitching variations on the y-axis. There areround about 10000 auto-reclosings of differenttransmission line systems had been simulated.The switching voltage of a controlled reclosingwithout a time shift parameter is marked with ared line. Very low switching voltages are onlyachieved for 30% for all reclosings. The rise of
voltage in the estimated zero crossings aregreater then the rise of the prearcing voltage characteristic curve of the circuit-breaker for theremaining reclosings. The maximum switching voltage is 630kV.
If the estimated switching instant is shifted with a fix time shift parameter a very low switchingvoltage could not be achieved for all simulations. High switching voltages were estimated only for12% (time shift of 1ms – blue line) respectively for 9% (time shift of 1.5ms – green line) of allreclosings. The best results will be achieved with a variable time shift. No prearcing in all reclosingswas detected. The maximum switching voltage was 70kV, which is nearly a tenth of the maximumswitching voltage for the other simulations.
4.2 Three-Pole Auto-Reclosing
Fig.10 shows the results for the three-poleauto-reclosing. The switching voltages for thefirst switching pole (red) are similar for bothmethods, because there are no great differences
between the methods for this first pole. Theswitching voltages of the second (blue) andthird (green) switching pole are in generalgreater. The switching voltages of these polesfor method A (solid line) are higher then formethod B (dashed line). It is a greater timeshift parameter for the second and thirdswitching pole in method A necessary then for
method B to prevent a prearcing. That’s the reason for different switching voltages. On the other hand,a greater switching window for method B is necessary to get these results. If the switching windows
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for both methods are equal, the results for the second and third switching pole will be similar. Bothmethods will minimize the switching voltage and the influence of the coupling of the three-poles.
5 Conclusion
The advantages of the exact estimation of the future voltage for a controlled closing operation of a
shunt compensated transmission line during an auto-reclosing have been shown in this paper. Theclosing operations in the optimal switching instant ensure a very low switching voltage. Theestimation of the exact future voltage shape minimized the probability of a prearcing. The minimumswitching voltage by a single-pole auto-reclosing will be limited by the characteristics of the circuit-
breaker. The algorithms minimize the effects of coupling between the three poles during the three-poleauto-reclosing. The real-time capability of the algorithm could be verified.
The next goals are the implementation of the algorithms on a testing device and checks on realtransmission lines.
Appendix A
A complete derivation of the Prony Method is in [3]. That’s why only a short introduction of theestimation of the both parameter h and z is on this place. The N data samples x[1],…, x[n],…, x[ N ] with
the constant sample interval T are the starting point.[ ] [ ] [ ]
[ ] [ ] [ ]
[ ] [ ] [ ]
[ ][ ]
[ ]
[ ][ ]
[ ]
+
+
−=
−−
+
−
p x
p x
p x
pa
a
a
p x p x p x
x p x p x
x p x p x
2
2
1
2
1
2212
21
11
MM
L
MOMM
L
L
(5)
This vector will be split in a matrix and a vector. The rule of the splitting is in eq.6. The parameter p specifies thereby the number of individual signals in the input signal. The coefficients of a polynomialare in the vector a. This vector will be calculated in the first step. The nulls of the polynomial are the
parameter z , which are estimated in the second step.
[ ][ ]
[ ]
=
⋅
−−− N x
x
x
h
h
h
z z z
z z z
z z z
p N
p
N N
p
p
MM
L
MOMM
L
L
2
1
2
1
112
11
11
2
1
1
002
01
(6)
The matrix Z must be prepared for the estimation of the vector h. Then the estimation of the futurevoltage with the parameter z and h is possible.
References
[1] Froehlich, K.; Hoelzl, C.; Stanek, M.; Carvalho, A.C.; Hofbauer, W.; Hoegg, P.; Avent, B.L.;Peelo, D.F.; Sawada, J.H., “Controlled closing on shunt reactor compensated transmission lines. I.Closing control device development”, Power Delivery, IEEE Transactions on ,Volume: 12 , Issue:2 , April 1997, Pages:734 – 740
[2] Cho, K.B., Kim, J.B., Shim, J.B., Park, J.W.,”Development of an Intelligent Autoreclosing Conceptusing Neuro-Fuzzy Technique – An Optimal Controlled Switching for Power System Operations”,CIGRE 1998 Session 13
[3] Marple, S. Lawrence, “Digital Spectral Analysis”, London: Prentice – Hall International, 1987
[4] Pilz, G., Schegner, P., Wallner, C., “Analysis of Noisy Voltage Signal with a high Resolution ofFrequency for the Closing of Transmission Lines” PSCC 2002, Sevilla
[5] Živanovič, R., Schegner, P., Seifert, O., Pilz, G. ”Identification of the Resonant-Grounded SystemParameters by Evaluating Fault Measurement Records“, IEEE Transactions on Power Delivery,submitted, accepted (it will be published)
