Classifications

• • H—ELECTRICITY
  • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
  • H02H—EMERGENCY PROTECTIVE CIRCUIT ARRANGEMENTS
  • H02H1/00—Details of emergency protective circuit arrangements
  • H02H1/04—Arrangements for preventing response to transient abnormal conditions, e.g. to lightning or to short duration over voltage or oscillations; Damping the influence of dc component by short circuits in ac networks
  • H02H1/046—Arrangements for preventing response to transient abnormal conditions, e.g. to lightning or to short duration over voltage or oscillations; Damping the influence of dc component by short circuits in ac networks upon detecting saturation of current transformers
• • H—ELECTRICITY
  • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
  • H02H—EMERGENCY PROTECTIVE CIRCUIT ARRANGEMENTS
  • H02H6/00—Emergency protective circuit arrangements responsive to undesired changes from normal non-electric working conditions using simulators of the apparatus being protected, e.g. using thermal images
  • H02H6/005—Emergency protective circuit arrangements responsive to undesired changes from normal non-electric working conditions using simulators of the apparatus being protected, e.g. using thermal images using digital thermal images

Definitions

• the invention relates to a method for detecting saturation in a current transformer, based on the association of several saturation criteria making it possible to detect a saturation phase when these criteria are satisfied simultaneously.
• the method implements digital processing of samples obtained by a measurement with low-pass filtering of the secondary current of the transformer to eliminate the harmonics.
• a conventional current transformer is generally permanently affected by a residual flux, this flux therefore being present at the time of the first acquisition of a current measurement.
• This means that the secondary circuit of the transformer has retained a magnetic flux corresponding to the last value (possibly attenuated) of the flow of current flowing through this secondary circuit at the time when a previous measurement was interrupted.
• the phenomenon of remanence of the magnetic flux is well known and is linked to the ferromagnetic properties of the transformer core. Recall that a magnetic flux is an algebraic quantity, which can therefore take positive or negative values.
• the absolute value of these two extreme values of the remanent flux can be defined as a certain percentage of a maximum value S max of current flow beyond which the linearity of the response of the transformer is no longer ensured. .
• This value S max can be considered as a maximum flux threshold, and the same value of opposite sign designated by S m j_ n can be considered as a minimum flux threshold. Any current transformer can thus be classified according to this threshold percentage. For example, a class called TPY corresponds to a percentage of 20%, and therefore the maximum value ⁇ _rem_haut that the residual flux of a TPY transformer can take is equal to 20% of the threshold S max of maximum flux.
• the possible saturation phenomena pose serious problems.
• the measurement error of a current transformer during a saturation phase can cause an inadvertent triggering of the system. This can in particular occur in the event of a fault (such as a short circuit) external to the busbar zone to which the system is assigned, which leads to untimely opening of the circuit breakers protecting the zone and therefore a constraint for the operator. It is therefore important to be able to detect as quickly as possible the appearance of a saturation regime of a transformer associated with the protection system, in order to inhibit the triggering of this system during the periods during which the secondary current of the transformer has a significant distortion compared to the primary current.
• relatively durable saturation regime is understood to mean a succession of close saturation phases, also called saturation slots in the following, and spanning a duration greater than the signal period. primary current. Reference may be made to FIGS. 10 and 11 of the present for the representation of such saturation slots.
• the triggering of the protection system must be inhibited over the duration of a saturation window. It is therefore particularly desirable that the duration of a slot be as short as possible and that two consecutive slots be separated by a time interval corresponding to a phase of unsaturation. During such an unsaturation phase, the secondary current is approximately proportional to the primary current and the protection system is thus informed by sufficiently reliable current measurements to be able to locate the location of the fault.
• An objective targeted by most of the existing methods for processing the secondary current signal for detecting transformer saturation phases is to be able to detect the start and end of such a phase as quickly as possible, and therefore to be able to determine with sufficient reliability the saturation slots during a saturated operating mode of the transformer.
• patent document DE 3 938 154 is a method of detecting saturation using vectorial calculations on current rotary vectors. This method, as well as examples of implementation applied to a digital differential protection system, are disclosed in more detail in the following publication: HOSEMANN G ET AL, "Modal saturation detector for digital differential protection", IEEE Transactions on Power Delivery , New York, vol. 8 no. 3, July 1, 1993.
• a patent saturation detection method based on the continuous determination of the absolute values of the secondary current and its derivative is also known from patent document EP 0 506 035. values being compared with appropriate threshold criteria allowing the recognition of significant distortions of the secondary current signal when these criteria are satisfied simultaneously.
• An objective of the invention is to provide a reliable, efficient and economical method for determining saturation slots during a saturated oncturing regime of a current transformer.
• the method described below is particularly economical in particular in terms of computing power compared to other recent methods, since it does not require reconstruction of the primary current signal. It also makes it possible to save on the cost of current transformers which are used in a protection system, by making it possible to specify transformers less efficient than usual and to operate them at the limits of their real performances.
• the method according to the invention also aims to guarantee good stability of the differential protection in the event of a fault occurring outside the monitoring zone of this protection system.
• the subject of the invention is a method of detecting saturation in a current transformer, based on the association of at least two saturation criteria making it possible to detect a saturation phase when said criteria are satisfied simultaneously, putting implementing digital processing of samples obtained by a measurement with low-pass filtering of the secondary current of the transformer in order to eliminate the harmonics therefrom, this transformer being affected by a residual flux of indefinite positive or negative value, characterized in that a first saturation criterion takes into account the calculation of an instantaneous prediction error which is a function of the difference between the measured secondary current and the predicted secondary current using a mathematical model, in that a second criterion of saturation takes into account the instantaneous algebraic flux calculated by integration of the secondary current sampled by comparing this algebraic flow with a positive threshold as well as with a negative threshold, and in that this comparison is initialized by exaggerating the probabilities of satisfying this second criterion of saturation at the beginning of the measurement in particular by an overestimation of the absolute value of the residual flux from the transformer
• a relative prediction error is calculated by performing the ratio between the standard deviation of the absolute value of the instantaneous prediction error and the deviation type of the absolute value of the measured current, the first saturation criterion being satisfied as soon as this relative error is greater than a given percentage.
• the relative position of the instantaneous algebraic flow with respect to at least one of the positive or negative thresholds is corrected if the threshold in question is crossed by this flux algebraic in the absence of saturation, the correction consisting notably in decreasing in absolute value at least one extreme value of the residual flux.
• a saturation phase is established if at least one of the thresholds is crossed by the algebraic flow while the first saturation criterion is simultaneously satisfied.
• FIG. 1 represents a conventional electrical modeling of a current transformer.
• FIG. 2 represents a saturated secondary current signal, showing the distortion with respect to the predicted unsaturated secondary current signal.
• FIG. 3 illustrates the sampling of a saturated secondary current signal, and shows the calculation at using a mathematical model of the unsaturated predicted signal and calculating the instantaneous prediction error.
• FIG. 4 represents the sampled measurements of a secondary current signal superimposed on the corresponding primary current signal, passing from an unsaturated regime to a saturated regime.
• FIG. 5 represents the variations of the instantaneous algebraic flow of secondary current measured, this flow being calculated from sampled measurements of the secondary current signal represented in FIG. 4, and represents the saturation threshold S max beyond which the linearity of the transformer response is no longer guaranteed.
• FIG. 6 represents the curves of the two extreme flows which surround the real instantaneous current flow, these extreme flows being calculated from the algebraic flow of FIG. 5 taking into account the extreme values which surround the residual flux.
• FIG. 7 represents the two extreme fluxes of FIG. 6, the continuous components of which have been corrected in the event of a saturation threshold being exceeded outside of a transformer saturation regime.
• Figures 8, 8a and 8b illustrate a method of comparison and flux correction, outside the saturation regime, equivalent to that illustrated in Figures 6 and 7.
• FIG. 9 simultaneously represents the sampled measurements of a saturated secondary current signal, a prediction error curve obtained from these measurements using the mathematical model illustrated in FIG. 3, the corresponding relative prediction error curve , and logic signals translating the verification of a saturation criterion.
• FIG. 10 represents a diagram illustrating the method used in the invention for determining saturation phases of a current transformer.
• FIG. 11 graphically represents the implementation of the method used in the invention for determining the saturation slots of a transformer passing from a normal regime at saturated regime, applied to a concrete example of sampled measurements of the transformer secondary current.
• FIG. 12 graphically represents the implementation of the method used in the invention, applied to another example of sampled measurements of the secondary current of a transformer.
• Figure 1 the classic electrical modeling shown for any current transformer uses only common components such as resistors and inductors.
• the transformer primary is characterized by its resistance Rp and by its inductance Lp.
• a magnetizing inductance L ⁇ is present at the intermediate part of the transformer.
• the transformer secondary is characterized by its resistance R s .
• the input current present at the transformer primary is called i p and the output current available at the secondary is called i s .
• the instantaneous magnetic flux of the secondary current is by definition equal to the flux )mes ⁇ t) that we measure in calculating the area of the secondary current as a function of time multiplied by the resistance R s of the secondary.
• This calculation is detailed further in Figure 5.
• a saturated secondary current signal i s is represented on its fundamental period T Q , showing the distortion with respect to the unsaturated signal î s which can be predicted by sinusoidal extrapolation. It can be seen that even in the presence of a saturated regime, there are brief phases of unsaturation of durations typically less than a quarter of a period, during which the secondary current has an almost sinusoidal shape and is therefore approximately proportional to the primary current. These unsaturation phases are all the shorter the higher the saturation of the transformer. As mentioned above, it is particularly desirable that consecutive saturation slots detected during a saturated transformer speed be determined with sufficient precision to appear separated by time intervals which correspond to these brief phases of unsaturation.
• a saturated secondary current signal is sampled with a sampling frequency l / T e to obtain a series of digital values Y ⁇ for example coded on 16 bits. It is clearly seen that a very pronounced saturation phase begins between the instants corresponding respectively to the samples k-1 and k, these instants being separated by a duration equal to the sampling period T e of the signal.
• a value ⁇ k of the unsaturated signal î s for a sample k is predicted using a mathematical model of sinusoidal extrapolation. This model is preferably based on a second order self-regressive method with fixed coefficients, but nothing prohibits using another method or using this method with an order greater than two if the available computing power allows it. .
• the fixed coefficients A ⁇ _ and A 2 are preferably chosen respectively equal to
• the prediction error is zero or almost zero if the current transformer is not saturated and if the primary current is not disturbed at the time of the measurement.
• the secondary current i s measured and the secondary current î s predicted are then identical.
• the prediction error will deviate from zero if a phase of saturation or disturbance of the primary current appears.
• the prediction error deviates from zero, this does not necessarily mean that the transformer is saturated. Indeed, in the event of a fault appearing in the network surrounding the transformer, a discontinuity may appear on the primary current signal of the transformer and be reflected on the secondary current signal, thus causing the appearance of a prediction error peak. In general, a rapid change of phase and amplitude at the high voltage level does not necessarily imply saturation of the transformer. It follows from the above that the prediction error does not constitute a sufficient criterion in itself to conclude with certainty that the current transformer is saturated.
• a second saturation criterion must be applied in parallel with the calculation of the prediction error in order to detect saturation with certainty, and this second criterion must take into account the magnetic flux present in the secondary circuit of the current transformer .
• a saturation of a transformer appears when the real magnetic flux in the secondary circuit exceeds in absolute value a maximum flux threshold S max .
• the second saturation criterion alone would be sufficient to conclude that the actual flux as well as the maximum flux threshold could be determined with precision.
• it is practically impossible to have a sufficiently reliable determination of these quantities as explained in the following.
• the maximum flux threshold for a given transformer its real value is not known precisely in the absence of prior measurement. Indeed, the characteristics announced by the manufacturers of transformers are systematically as a precaution lower than the actual performance of these devices, and may even sometimes be far below these actual performances. To this uncertainty is also added the fact that the maximum flux threshold is proportional to the resistance R s of the secondary circuit of the transformer, this resistance not being known with precision since it depends in particular on the secondary current measurement devices which are connected to the secondary circuit.
• the real flux is estimated with an uncertainty which is a function of the magnetic remanence characteristics of the current transformer, due to the uncertainty on the real value of the remanent flux.
• FIG 4 the sampled measurements of a secondary current signal i s are shown in superposition with the corresponding primary current signal Ip during an unsaturated regime of a current transformer.
• this secondary current signal undergoes a low-pass filtering to eliminate harmonics.
• the first sample is acquired at a time close to 80 signal sampling periods, on a time scale whose origin is arbitrary.
• a strong symmetrical fault current is established at the level of the primary circuit, causing a significant increase in the amplitude of the primary current Ip.
• the transformer goes into saturated mode, regime during which saturation phases are established for which the secondary current i s has a strong distortion compared to the primary current Ip.
• the curve of the measured flux ⁇ me s varies sinusoidally with the same fundamental period as the secondary current i s , and has a phase shift of ⁇ / 2 with respect to the curve of i s .
• the flow measured presents an extremum when the current i s goes through zero.
• the measured flux presents brief phases during which it remains substantially constant, hence a shape in trays of the extremes of this flux. These phases correspond approximately to the real saturation slots of the transformer, slots which one wishes to determine with precision.
• the reading of the plates of the extremes of the flux makes it possible to define saturation thresholds S max and S m; [ n with the same absolute value and opposite signs, so that any extremum of the flux is greater in absolute value than the threshold value S max .
• the saturation thresholds s max and s min represented correspond substantially to the real limits of response linearity of the transformer.
• the low excursion margin of the low flux ie the absolute value of the difference between the negative saturation threshold S m _ n and the minimum value of the low flux, is much smaller than the low excursion margin of the measured flux ⁇ m es •
• the hypothesis of a negative remanent flux equal to the extreme value ⁇ _rem_bas amounts to considerably increasing the risks of saturation, since a slight increase in the amplitude of the secondary current i s could be enough to increase the amplitude of the real flux so as to make it cross the negative saturation threshold.
• this hypothesis remains valid in this example since the low flux does not cross the negative saturation threshold in the absence of saturation.
• the remanent flux must at most be equal to a positive value r_rem_max such that the high excursion margin of the estimated real flux is almost zero, and similarly be at least equal to a negative value ⁇ _rem_ min such that the excursion margin low of the estimated real flux is almost zero.
• FIG. 7 illustrates a method according to the invention for refining the estimate of the residual flux outside the saturation regime, which is equivalent to refining the estimate of the real flux.
• the recognition of an unsaturated operating mode of the transformer is carried out by constantly checking that the first saturation criterion based on the calculation of the prediction error is not satisfied. As explained above, one can be certain of an absence of saturation if the prediction error on the secondary current signal is less in absolute value than a threshold close to zero.
• This method can of course be applied analogously to correct the low flux if the latter has a minimum below the negative saturation threshold S m -j_ n .
• ⁇ _Min a corrected low flux designated by ⁇ _Min in what follows and equal to the sum ⁇ _bas + ⁇ -.
• the correction of the relative position of the high flow or the low flow compared to a respectively positive or negative saturation threshold results by the calculation of a corrected high or low flux ⁇ _Max or ⁇ _Min of which at least one extremum is tangent to the saturation threshold considered, so as not to cross this threshold in the absence of saturation.
• the correction of the position of an extreme flux relative to a saturation threshold therefore amounts to supposing that the saturation limit of the estimated actual flux is reached without being exceeded, that is to say that the margin of excursion is high or low. of this estimated flow is reduced to zero.
• the algorithms for recognizing extremes of the measured flux for the correction of the high flux or of the low flux consist in verifying out of saturation the following relationships for three successive samples k-2, k-1, and k of the measured flux: estunminimum flux flux as (k-1) - S m i n and or
• ⁇ _haut (k-1) is a maximum of high flux
• the absolute value of a saturation threshold is to reduce the excursion margin of the estimated real flux, in a similar way to what happens when the absolute value of the remanent flux of the transformer is overestimated, which is equivalent to exaggerating the probabilities of crossing of the saturation threshold by the flux at the beginning of the measurement. It is thus possible to satisfy the second saturation criterion which takes into account the magnetic flux, while the first saturation criterion based on the instantaneous prediction error is not satisfied. However, as explained above, it is not realistic to observe the crossing of a saturation threshold if the first saturation criterion is not satisfied, since this condition implies an absence of saturation phase.
• the relative position of the high flux ⁇ _haut compared to the saturation threshold S max is equivalent to that of the measured flux ⁇ m es P ar compared to the reduced saturation threshold S +, and that in particular the excess of high flux ⁇ + is also calculated as an excess of the measured flux ⁇ mes P ar compared to the reduced threshold S +.
• the relative position of the measured flux with respect to the reduced positive saturation threshold S + is corrected for the fact that this threshold is crossed by the flux in the absence of saturation.
• the two correction methods presented are therefore equivalent. In particular, they amount to decreasing in absolute value at least one extreme value of the residual flux.
• the correction is equivalent to decreasing the positive value ⁇ _rem_haut since this value is excessive by a quantity of flux ⁇ + which can be determined using one or the other of these methods.
• this method for correcting the relative position of the measured flux with respect to a positive or negative saturation threshold results in the calculation of a corrected flux respectively F max or F m; ⁇ _ n of which at least one extremum is tangent to the considered saturation threshold.
• the algorithms for recognizing extremes of the measured flux are similar to those described for the first correction method.
• This corrected positive threshold can be used to be compared to the measured flux in order to establish whether the second saturation criterion is satisfied.
• a corrected negative threshold S'- S m -j_ n - ⁇ __rem_bas + ⁇ -, which can be different from the threshold S '+ in absolute value. It is understood that it is not necessary in this case to define two flows F max and F m -j_ n , since only the measured flow must be compared with the corrected thresholds S '+ and S'- for the application of the second saturation criterion.
• the first two curves simultaneously represent the sampled measurements Y k of a saturated secondary current signal i s and a prediction error curve DDYj () obtained from these measurements using the mathematical model illustrated in Figure 3.
• the prediction error curve has very narrow positive and negative peaks.
• such smoothing consists in performing the calculation of a relative prediction error, of positive sign, defined as the ratio between the standard deviation ⁇
• a standard deviation is by definition equal to the square root of the variance, the latter being defined as the arithmetic mean of the squares of the deviations from the mean.
• the calculation of a standard deviation for an instantaneous prediction error D (Y k ) takes into account the calculation of the standard deviation performed for the instantaneous prediction error D (Y k _ ⁇ ) of the sample of previous current.
• the prediction error signal can be smoothed by any other appropriate calculation method, without departing from the scope of the invention.
• the distortion phases of the secondary current signal i s are characterized by bumps of the relative prediction error signal, bumps which are much wider than the corresponding peaks of the prediction error signal.
• this first saturation criterion which takes into account the calculation of an instantaneous prediction error must be associated with the second saturation criterion which takes into account the calculation of the algebraic flux, in order to allow the detection of a phase saturation of transformer when these criteria are met simultaneously.
• the method of associating these two criteria is summarized by the logic diagram in Figure 10.
• FIGS. 11 and 12 Concrete examples of application of the saturation detection method according to the invention are shown in FIGS. 11 and 12.
• a first window represents the curve of the sampled secondary current signal i s of a transformer passing from a normal regime to a saturated regime.
• the first sample is acquired at a time noted tg.
• the fundamental period of the primary current is equal to 50 Hz, and the transition to saturated mode is here caused by an eightfold increase in the amplitude of this current.
• an aperiodic component appears on the primary current with a time constant equal to 60 ms.
• a second window represents the relative prediction error curve ⁇ r calculated as shown in the example in FIG. 9.
• a threshold S Q corresponding to a percentage of relative error close to zero is defined empirically.
• a third window represents the curve of the measured flux ⁇ mes calculated by integration of the secondary current, as explained in figure 5. Because this current i s has just started a negative half-cycle shortly before time to, it is logical that the calculation by integration produces a curve ⁇ me s whose most values are negative.
• S + S max - ⁇ _rem_haut
• the S + and S- saturation thresholds are set at the beginning of the measurement, provided to be able to inform the processing system with an estimate of s saturation max threshold beyond which the linearity of the transformer response is no longer ensured.
• saturation slots corresponding to a so-called positive saturation of the transformer can be determined as soon as the measured flux exceeds the positive threshold.
• the first two slots of positive saturation are shown hatched in a fourth window in the figure, and correspond to the simultaneous satisfaction of the following two saturation criteria:
• the first slot appears at an instant t s which marks the start of the saturation regime, and ends at an instant t pe which marks the start of a short phase of unsaturation during which the protection system is authorized to use the current measurements supplied by the transformer despite the saturated transformer speed.
• a fifth window firstly represents the curve of the measured flux ⁇ me s as well as the negative saturation threshold S- fixed at the start of the measurement, the latter
• the sample corresponding to the first minimum of the measured flux is detected at fifteen sampling periods after the instant tg marking the
• the first two slots of negative saturation are shown hatched in a sixth window in the figure, and correspond to the simultaneous satisfaction of the following two saturation criteria:
• the first negative saturation window appears at an instant tp e + ⁇ and marks the end of the first phase of no saturation following the first slot of positive saturation, the value ⁇ corresponding to the short duration of this phase of unsaturation.
• the saturation slots each have a duration which is less than the fundamental period of the primary current, with the exception here of the first slot.
• the duration of a time slot is as short as possible, and in particular remains less than the fundamental period of the current. This condition reflects the need to be able to activate the protection system with which the transformer is associated as quickly as possible in the event of an internal fault in the zone monitored by this system, including in the event that transformer saturation occurs during this internal fault.
• the saturation detection method according to the invention generates an erroneous saturation slot just before the measured flux is adapted relative to the negative threshold.
• the logical condition "( ⁇ mes ⁇ S-) AND ( ⁇ r >SQ)" is verified here for a very short time at the beginning of the measurement, when there is no real saturation of the transformer at the moment. Because of its very short duration compared to the fundamental period of the current, this erroneous slot has no annoying effect on the operation of the protection system.
• the fact that the duration of the first saturation slot exceeds that of the fundamental period of the current is caused by the relatively long duration of the time constant of the aperiodic which appears on the primary current.
• a time constant here equal to 60 ms is indeed much greater than the 20 ms of the fundamental period of a current in 50 Hz. This represents an unfavorable case tending to decrease the performance of the system protection in the event of an internal fault in its surveillance zone during the first saturation window.
• the average duration of the first saturation slots tends to decrease, in particular the duration of the first slot.
• FIG. 12 is shown graphically an example more favorable than the previous one for implementing the method according to the invention, in order to determine the saturation slots of a saturated regime of the transformer. It is assumed that the same current transformer is used, and that the primary current without saturation is the same as in the example in FIG. 11. It is also assumed that the transition to saturated mode is caused by an eightfold multiplication of the amplitude of this current. However, we consider here that there is no aperiodic component which appears on the primary current, which amounts to saying that the time constant is zero.
• the opposite saturation thresholds S + and S- correspond to those of the previous example. Because the secondary current has just begun a positive half just before the acquisition of the first sample, it is logical that the calculation by integration produces a curve ⁇ me that most values are positive. As in the example shown in FIG. 8a, the measured flux must here be adapted with respect to the positive saturation threshold S + and remains unchanged to be compared with the negative saturation threshold S-.
• the saturation slots are determined in the same way as explained in the previous example, and are represented in a fourth window in FIG. 12. It can be seen that the first slot, which appears at an instant t s marking the start of the saturation regime, is of duration much less than that observed in the previous example and less than the fundamental period of the current. The other saturation slots each have a duration shorter than that of the first.
• the time interval ⁇ that a phase of unsaturation lasts is comparable to that found in the previous example.
• a few sampled measurements of the secondary current can be used by the protection system to locate a possible internal fault in the surveillance zone.

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• Engineering & Computer Science (AREA)
• Power Engineering (AREA)
• Measuring Instrument Details And Bridges, And Automatic Balancing Devices (AREA)
• Measurement Of Current Or Voltage (AREA)
• Protection Of Transformers (AREA)

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