Title of Invention

"A METHOD FOR OBTAINING A POWER WSING SIGNAL INDICATING A POWER SWING IN AN ELECTRIC POWER SUPPLY NETWORK"

Abstract

Current and voltage space vectors (i , i , u , u ) of the positive sequence system are formed from phase current and phase voltage sampling values (P', Q') of an electric power supply system, and power quantities of the positive sequence system are derived from them. System frequency components are eliminated from these power quantities by at least squares estimate, thus forming a measured active power quantity (c) of the positive sequence system and a measured reactive power quantity (Q) of the positive sequence system. By forming quotients with a measured current quantity of the positive sequence system, also obtained using the least squares estimate, impedance values (7) of the positive sequence system are also obtained. These are tested for monotony and abrupt changes and a suspected oscillation signal is formed, if app1icab1e. In addition, to an oscillation confirmation signal (M), the respective center point of the circle of the trajectory formed by the impedance values (7) of the positive sequence system is determined and compared with the reactance value (WX) of the positive sequence system with regard to its imaginary part. If a suspected oscillation signal and an oscillation confirmation signal occur simultaneously, the oscillation signal is formed.

Full Text

-1A- This invention relates to a method 'for obtaining a power swing signal indicating a power swing in an electric power supply network. Method for obtaining a signal which indicates oscillation in an electrical power supply network The invention relates to a method for obtaining a signal (oscillation signal) which iraicates oscillation in an electrical power supply network, in the case of which phase currents and phase voltages are sampled, forming phase current and phase voltage samples, and impedance values formed on the basis of the phase current and phase voltage samples are investigated in terms of their position with respect to an oscillation polygon, an oscillation suspicion signal being formed by comparison of impedances which follow one another in time. A method of this type is disclosed in German Laid-Open Specification DE 195 03 626 A. In the case of this method, impedance values are formed at predetermined time intervals on the basis of sampled current and voltage values. The first impedance value falling in an oscillation polygon and the preceding impedance value are used to determine the change in the impedance with respect to time, and an oscillation suspicion signal is produced if the change is less than a predetermined limit value. If further checking of the impedance values results in an impedance value which falls in a distance protection tripping polygon, the oscillation signal is produced provided the oscillation suspicion signal is still present. This method allows oscillations at a frequency of at most. 1 Hz to be identified. The invention is based on the object of specifying e method for obtaining an oscillation signal which makes it possible to identify higher-frequency oscillations. In order to achieve this object in the case of the method as specified initially, phase current and - 2 - phase voltage samples are used, according to the invention, to form current and voltage space vectors for the positive-sequence system of the power supply network, and the current and voltage space vectors for the positive-sequence system are used to form a positive-sequence system real-power parameter which is proportional to the instantaneous value of the positive-sequence system real power, and a positive-sequence system reactive-power parameter which is proportional to the positive-sequence system reactive power; a least-squares estimation is in each case used to eliminate network-frequency components from the positive-sequence system real-power parameter forming a real-power measurement variable, and from the positive-sequence system reactive-power parameter to form a reactive-power measurement variable; furthermore, the current space vectors of the positive-sequence system are used to form a positive-sequence system current parameter, and the positive-sequence system current parameter is used to form a positive-sequence system current measurement variable by means of a least-squares estimate and the quotient of the real-power measurement variable and the square of the positive-sequence system current measurement variable is used to produce positive-sequence system resistance values, and the quotient of the reactive-power measurement variable and the square of the positive-sequence system current measurement variable is used to produce positive-sequence system reactance values; positive-sequence system impedance values which follow one another in time and are in each case formed by positive-sequence system resistance and positive-sequence system reactance value associated with one another in time are Subjected to a monotonicity test and to a test for sudden changes and an oscillation suspicion signal is formed if monotonicity is present and there are no sudden changes and, apart from this, the positive-sequence system impedance values are used to determine, by estimation, the centre of a circle of a path curve, - 3 - which is formed from positive-sequence system impedance values, in relation to the respective positive-sequence system impedance value, and an oscillation confirmation signal is produced if the imaginary part cf the circle centre exceeds the absolute value of the positive-sequence system reactance value of tne respective positive-sequence system impedance, and; if the oscil-lation suspicion signal and the oscillation confirmation signal are present at the same time, the oscillation signal is formed if the last positive-sequence system impedance value to be formed is within the oscillation polygon, German Patent Specification DE 41 00 646 C2 admittedly discloses a method and an arrangement to protect distance-protection devices against undesirable tripping during transient power oscillations, in the case of which method at least one blocking signal for the distance-protection device is produced by the time derivative of an electrical parameter related to the power, ana undesirable tripping of the distance device is prevented using an impedance-locus curve, but in this case the respectively resulting cnanges in the real power and in the reactive power are related, after difference formation, to the complex power, and this quotient is used to form an oscillation signal. One advantage of the method according to the invention is that it allows oscillations to be identified quickly, in which case it is clearly possible to distinguish oscillations from three-pole faults. In addition, the method according to the invention makes it possible to identify relatively high-frequency oscillations, to be precise even when the rotor angle varies non-uniformly over time. A further major advantage of the method according to the invention is that, owing to the least-squares estimate, the path curve which is in each case formed from the positive-sequence system impedance values that follow one another in time is well smoothed and can thus be evaluated well . Advantageously, in the case of the method according to the invention, in the case of positive-sequence system impedance values which are located within the oscillation polygon and are in each case formed by positive-sequence system resistance and positive-sequence system reactance associated witn one another in time, positive-sequence system resistance values which follow one another in time are monitored for compliance with a minimum rate of change, and if the rate is less than this rate, the oscillation signal is cancelled. In order to explain the invention further, in the accompanying drawings, Figure 1 shows an exemplary embodiment of an arrangement for carrying out the method according to the invention, Figure 2 shows a diagram with an illustration of the sequence of the method according to the invention. Figure 3 shows an impedance locus curve for oscillation processes. Figure 4 shows a diagram to explain the estimation of the respective centre of the circle of the path curve of the positive-sequence system impedance values. Figure 5 shows time profiles for the positive-sequence system real power parameter and the positive-sequence system reactive7power parameter, Figure 6 shows time profiles of the positive-sequence system real-power measurement variable and the positive-sequence system reactive-power measurement variable, and Figure 7 shows a path curve of the positive-sequence system impedance values for oscillations after a three- pole fault. Figure 1 shows a device 3 for forming current and voltage space vectors, which is connected on the input side in a manner that is not illustrated and via current transformers and voltage transformers to three phases of a three-phase electrical power supply line. Tne device 3 for forming space vectors is connected on the output side, inter alia, to a device 4 for forming - 5 - a positive-sequence system real-power parameter P' which is followed on the output side by a least-squares estimator 5. The least-squares estimator 5 as connected on the output side to one input of a quotient former 6. In addition, the device 3 has connected to it a device 7 for forming a positive-sequence system reactive-power parameter Q' which is followed by a further least-squares estimator 8; the output of this further estimator 8 produces a positive-sequence system reactive-power measurement variable Q, which is supplied, via one input, to a further quotient former 9. The current space vector ip of the device 3 is squared in a squarer 10, which is followed by an adder 11. The adder 11 has connected on its input side a further squarer 12 to whose input side the further current space vector ip of the device 3 is applied. The output side of the adder 11 is connected to a square-root forming stage 13, which is followed by a least-squares estimator 14 . The square-root forming stage 13 produces a positive-sequence system parameter i', from which a positive-sequence system current measurement variable i is formed by means of the least-squares estimator 14. The least-squares estimator 14 is connected via a square-forming stage 15 to further inputs of the quotient formers 6 and 9. The quotient former 6 forms positive-sequence system resistance values Wr, and the further quotient former 9 forms positive-sequence system reactance values Wx, which values are supplied to an evaluation device 16 which, if appropriate, emits an oscillation signal Sp at its output. The signal Sp can be produced, using the arrangement according to Figure 1, as follows: First of all, phase currents Ir, Is, It and phase voltages Ur, Us, Ut of the power supply network which is not illustrated but is formed, for example, by a three-phase power transmission line, are sampled in the device a for current and voltage space vector formation, forming phase current and phase voltage samples ur, us, ut, ir, is and it. These samples are subjected to a h transformation (Clarke transformation) , by which means transformed current samples and current space vectors 1 , 1 as well as transformed voltage samples and voltage space vectors u and u can be determined for the positive-sequence system {see "Koordmatentransformationen zur Behandlung von Mehrphasensystemen" [Coordinate transformations for handling multi-phase systems], H.-H. Jahn and R. Kasper, Archive fur Elektrotechnik [Archive for Electrical Engineering], 56 (1974) pages 105-111) : (1) These transformed samples and space vectors are used in the device 4 to form a positive-sequence system real-power parameter p' which is proportional to the instantaneous value of the positive-sequence system real power, in accordance with the following equation: In the following text, it is assumed that the positive-sequence system real-power parameter P' in the event of a short circuit or a mains system oscillation has a time profile which can be described by the following signal model: where y2 denotes samples of the current and voltage space vectors, T denotes a time constant which will be explained later, 0 denotes the network frequency and TA denotes the sampling period. - 7 - If a positive-sequence system real-power parameter is considered, the first term in the equation describes a sinusoidal signal component of the positive-sequence system real-power parameter P' which decays exponentially with time and oscillates at the network frequency, the second term describes a further signal component of the positive-sequence system reai-power parameter P' which decays exponentially with time and oscillates at the network frequency, the first and the other signal component being mutually orthogonal, since the other signal component is in the form of cosine. C denotes a component measurement value of the positiversequence system real-power parameter P' which oscillates at an oscillation frequency, the component measurement value C being time-dependent and thus denoting an instantaneous value. The signal model according to equation (3) assumes that, in the event of a three-pole short circuit, virtually no real power and thus no positive-sequence system real power eithex are any longer consumed, so that the positive-sequence system real-power parameter P' in the event of such a short circuit must fall to a very low value - close to zero; this fall in the positive-sequence system real-power parameter P' is taken into account by the first two terms in the equation (3). The signal model according to equation (3) also covers power oscillations, to be precise by -the third term and by the oscillation component measurement value C; specifically, the oscillation component measurement value C takes account of those frequency components in the positive-sequence system real-power parameter P' which are below the network frequency and are thus characteristic of network oscillations. The positive-sequence system real-power parameter P' is transferred to the least-squares estimator 5, in which the network-frequency components in the positive-sequence system real-power parameter P' are removed, and a positive-sequence system real-power - 8 - measurement variable P is formed. This positive-sequence system real-power measurement variable p corresponds to the oscillation component measurement value C, which oscillates at an oscillation frequency in time, of the positive-sequence system real-power parameter P' . In a corresponding manner, the device 7 and the further least-squares estimator 8 are used to form, from the positive-sequence system reactive-power paramter Q' which is formed according to the following equation (4), the positive-sequence system reactive-power measurement variable Q, which likewise corresponds to the oscillation component measurement value C of the positive-sequence system reactive-power parameter Q' . The building blocks 10 to 13 in Figure 1 are used, in accordance with the relationship (5) (5) "o form a positive-sequence system current parameter i from which, using the signal model specified above and by means of the least-squares estimate in the building block 14, the positive-sequence system current measurement variable i is formed, which corresponds to the oscillation component value C in the positive sequence system current parameter i'. The quotients which are formed by means of the quotient formers 6 and 9 are used to produce positive sequence system resistance values Wr and positive-sequence system reactance values Wx, - 9 - which are processed in the evaluation device 16. Before describing this in more detail, it is intended to explain in more detail the procedure for the least-squares estimate. The estimating method uses a limited part of the signal of the sampled space vector to calculate the coefficients A, B and C in the signal model specified above in equation {3} : This model rule provides, via the parameter C, the amplitude of the respectively estimated space-vector component. The terms with the parameters A and B model the 50 Hz components produced by aperiodic components. The amplitude of the 50 Hz oscillation decays with the time constant T of the total impedance if, for this analysis, one assumes a single-pole equivalent circuit of a power supply line which is supplied from two equivalent machines and has two equivalent impedances. The coefficient set A to C is determined using the least-squares method as is described, for example, in the dissertation "Digitale Impedanzme verfahren auf der Basis von Identifikationsinethoden" [Digital impedance measurement method based on identification methods] by A. Jurisch, TH Zittau, 1990. The intention is to use the existing samples to determine, for the model according to equation (3), the coefficients A, B and C, such that the sum of the least squares between the samples y1 and sample y, calculated in accordance with equation (3) becomes a minimum, quality criterion; function according to equation (3); - 10 (vector with Che coefficients A, B and C to be determined (10) . To achieve the minimizing object, the quality criterion must be derived in accordance with the parameters. For the signal model according to equation ( 3), this then gives: resulting in the vector y1 if the equation (3) is represented as a point product of and k. T denotes the period of the network-frequency oscillations of the power supply network. If one solves equation {11} for the parameter vector k, then this results in equation (13) for determining the parameter vector, whose substitution in the signal model according to equation (3) leads to the best model of the measured signal in the sense of the least squares. - 11 - If, in accordance with the above statements, the positive-sequence system resistance values Wr and the positive-sequence system reactance values Wx are calculated on the basis of an associated distance protection device, then a path curve in the R-X plane is available and, if the values of Wr and/or Wx change, the preconditions for the presence of an oscillation can be tested. The path-curve test is broken down into a monotonicity test and a test for a sudden signal change. The monotonicity test tests the profile of positive-sequence system resistance values Wr which follow one another in time for monotonicity. This test is carried out only if no oscillation has yet been identified - the path curve of the positive-sequence system impedance values Z (formed from Wr and Wx) has not yet reached the oscillation polygon PPOL. (see Fig. 3), since, in the case of synchronous oscillation, the monotonicity condition would be infringed at the inversion point on the path curve of the oscillation. During an oscillation, all that is tested is whether the positive-sequence system resistance values Wr which follow one another in time in the positive-sequence system impedance vector have a minimum rate of change. If the positive-sequence system impedance vector remains stationary during an identified oscillation, this can no longer be an oscillation. Fig. 2 shows the changeover of the criteria for the monotonicity test. The monotonicity test is carried out over a number N {which must be chosen suitably) of curve points. The following criterion is used: The test for the minimum rate of change uses a threshold value, which must be defined, for the positive-sequence system resistance change within a sampling interval. - 12 - A test for sudden signal changes is carried out in parallel with the monotonicity test. Sudden changes in the positive-sequence system impedance vector preclude any oscillation. The decision as to whether oscillation is present is made on the basis of the change with time in the positive-sequence system resistance Wr and the positive-sequence system reactance WX. These changes are calculated by differentiation of Wr and Wx. Since this differentiation is particularly sensitive numerically, good smoothing of the measurement variables P, Q and i by means of the least-squares estimator is of critical importance . The differentiation of the positive-sequence system resistance and the positive-sequence system reactance of the measurement variable Wr and Wx for the path-curve test is carried out using a 1st order method: where "k" denotes the latest sample. The following tests are carried out in this block: Test of the two Wr values in eacn case resulting from adjacent positive-sequence system resistance values Wr, for deviations which are less than a threshold value over a number of intervals. A non-steady-state process is taking place if the criterion is not satisfied more than once. Test of the two Wx values in each case resulting from adjacent positive-sequence system reactance values Wx for deviations that are less than a threshold value over a number of intervals. If a test of the derivatives in the X-direction reveals a sudden signal change, the total derivative of the (R, X) path curve is also tested for a sudden change. A sudden change is identified if the change d2 has amounted to a proportion, governed - 13 - by the positive-sequence system impedance, of Z and, at the same time, the instantaneous value for dZ differs by a threshold value from the dZ formed in the preceding measurement cycle. These tests test the characteristic patterns of an oscillation process. If all these criteria are satisfied, then there is a major suspicion of oscillation, and an oscillation suspicion signal is produced in the evaluation device 16. The maximum detectable oscillation frequency is governed by defining a suitable time interval in which these monotonicity tests are carried out. The described test makes it possible to differentiate between rapid compensation processes and oscillations. In order to avoid overoperation of the oscillation identification, a test is also carried out, when there is a suspicion of oscillation, to determine whether the path curve, which is identified as being continuous, of the (R, X) path curve also has features which indicate an unstable steady-state network condition. The characteristic of the impedance measured at the installation location of a protection device operating using the method according to the invention is used for identification of the difference angle 6 between the rotors of the two equivalent machines mentioned above. On the assumption that the impedance between the two equivalent machines is purely inductive, the point of the measured impedance vector at the relay installation location describes an ellipse with a centre on the imaginary axis as the path curve. The upper part of the ellipse occurs for angle differences up to a maximum of +90°. The lower part of between-90o - 14 - imaginary part of the centre of the circle is greater than the X-values of the measured path curve, then the network is at an unstable steady-state operating point and the impedance path curve can reach the tripping polygon. Fig. 3 illustrates this situation; The derivatives for the path-curve test are formed using a 2nd order method: The centre of the impedance ellipse on the imaginary axis is estimated, using the following rule, for each computation step using the derivatives of the positive-sequence system resistance values Wr and positive-sequence system reactance values Wx obtained by means of the least-squares estimators: This rule results from a parametric representation of the path-curve equation with the ellipse angle as a parameter, and its derivation with subsequent coefficient comparison. In order to achieve the minimizing object, it is necessary to derive the quality criterion on the basis of the parameter Wx0. For the signal model according to equation (3), this then gives, at the time k under consideration for N previous samples: The derivatives of the positive-sequence system resistance and positive-sequence system reactance values are in this case formed using a 2nd order method corresponding to equation (19): - 15 - In order to distinguish whether the instantaneously measured value pair (Wr, Wx] is located in the steady-state stable or unstable region of the impedance locus curve, the estimated value for Wxo is compared with the instantaneous measurement value for Wx: The signal M is thus active as an oscillation confirmation signal once an unstable steady-state curve point has been found. The number N of curve points used for the estimation must be defined in a suitable manner. However, the estimation of the centre uses only those curve points for which the ratio Wr/Wx is less than a threshold value which must be defined. This minimizes measurement errors in the determination of centre of the circle. If the abovementioned requirement is satisfied, the curve points describe curve sections with an extremely flat curve profile. If less than two curve points in an estimation are suitable for estimating the centre of the circle, it can be assumed that the entire curve has an extremely flat curve profile. Such a curve profile occurs in the case of network oscillations if the rotor voltages of both equivalent machines are of roughly the same magnitude. Thus, in this case, it is also possible to assume an unstable steady-state network condition. The oscillation confirmation signal M is likewise active in this case. The test for an unstable curve point can work successfully only if the path-curve section to be investigated contains no discontinuities or inversion processes. Figure 4 shows the de-ermined centres for a synchronous oscillation. Figure 4 clearly shows that a path-curve centre is estimated at the inversion point, which would indicate a stable operating point in the R-X plane. In order to avoid such misinterpretation of the estimated centre of the curve in the case of a synchronous oscillation, the test is carried out at an unstable curve point only until an oscillation has been identified, that is to say the path curve has entered the oscillatior polygon PPOL. Since only a successfully completed test at an unstable curve point can lead to oscillation identification, this test can be dispensed with while oscillation is identified. Since the test for an unstable curve point is carried out only once the monotonicity test and the test for sudden changes in the impedance vector have been successfully completed, discontinuities in the path-curve section to be investigated can be precluded. In order to illustrate further the method according to the invention. Figure 5 shows the profile of the calculated positive-sequence system real-power parameter P' and that of the calculated positive-sequence system reactive-power parameter Q' over the time t for a three-pole fault. The influence of the 50 Hz component when a fault occurs at the time T can clearly be seen. In comparison with this, the profiles of the positive-sequence system real power P and of the positive-sequence system reactive-power measurement variable Q according to Figure 6 are considerably improved, for the same fault case, owing to the elimination of the 50 Hz components by means of the least-squares estimators 5 and 8 according to Figure 1. Figure 6 shows a power supply network after a three-pole fault, as a consequence of which oscillations occur after fault clearing. The calculations carried out using the parameters P and Q and with the positive-sequence system current 1 lead to a path curve from the values Wr and Wx of the positive-sequence system impedance, as is illustrated in Figure 7. In this case, Zl denotes the tripping polygon of an inner zone, and Z2 the tripping polygon of an outer zone of an associated distance-protection device. 17 We Claim A method for obtaining a power-swing signal indicating a power swing in an electric power supply network, comprising the steps of: sampling phase currents and phase voltages by forming phase current samples and phase voltage samples respectively; investigating impedance values formed on the basis of the phase current samples and the phase voltage samples in terms of their position with respect to a power-swing polygon and forming a power-swing suspicion signal by comparison of impedance values following one another in time, characterized by the steps of forming current and voltage space vectors (i , i , u , u ) of the positive sequence system of the power supply network using the phase current samples and the phase voltage samples; forming a positive sequence system real power parameter (P') using the current and voltage space vectors (i , i , u , u ) , the positive sequence system real power parameter (P') being proportional to the instantaneous value of the positive sequence system real power; forming a positive sequence system reactive power parameter (QM using the current and voltage space vectors (i , i , u , u ) , the positive sequence system reactive power parameter (QM being proportional to the positive sequence system reactive power; using a least-squares estimation to eliminate network-frequency components from the positive sequence system real power parameter (PM forming a real power measurement variable (P); using a least-squares estimation to eliminate network-frequency components from the positive sequence system reactive power parameter (Q') forming a reactive power measurement variable (Q); forming a positive sequence system current parameter (i') using the current space vectors (i , i , ) ; forming a positive sequence system current measurement variable (i) by means of a least-squares estimate using the positive sequence system current parameter (iM; forming positive sequence system resistance values (Wr) using the quotient of the real power measurement variable (P) and the 18 square of the positive sequence system current measurement variable (i); forming positive sequence system reactance values (Wx) using the quotient of the reactive power measurement variable (Q) and the square of the positive sequence system current measurement variable (i); subjecting positive sequence system impedance values (Z) following one another in time to a monotonicity test and to a test for sudden changes, the positive sequence system impedance values (Z) being formed by positive sequence system resistance values (Wr) and positive sequence system reactance values (Wx) being associated with one another respectively; forming a power-swing suspicion signal if monotonicity is present and there are no sudden changes; determining, by estimation, the centre of a circle of a path curve in relation to the respective positive sequence system impedance value using the positive sequence system impedance values (Z), the path curve being formed from the positive sequence system impedance values (Z); producing a power-swing confirmation signal (M) if the imaginary part of the circle centre exceeds the absolute value of the positive sequence system reactance value (Wx) of the respective positive sequence system impedance (Z) and if the power-swing suspicion signal and the power-swing confirmation signal are present at the same time, forming a power-swing signal (Sp) if the last positive sequence system impedance value (Z) is within the power-swing polygon (PPOL). 2. The method as claimed in claim 1, wherein said method comprises the additional steps of : monitoring the chronologically successive impedance values (Z) formed by the positive Sequence system resistance values {Wr) and positive sequence reactance values (WX) for compliance with a minimum rate of change when the positive sequance system impedance values (Z) lie within the power-swi ng polygon (PPOL) ; and 19 cancelling the power-swing signal (Sp) if the rate of change is less than the minimum. Current and voltage space vectors (i , i , u , u ) of the positive sequence system are formed from phase current and phase voltage sampling values (P', Q') of an electric power supply system, and power quantities of the positive sequence system are derived from them. System frequency components are eliminated from these power quantities by at least squares estimate, thus forming a measured active power quantity (c) of the positive sequence system and a measured reactive power quantity (Q) of the positive sequence system. By forming quotients with a measured current quantity of the positive sequence system, also obtained using the least squares estimate, impedance values (7) of the positive sequence system are also obtained. These are tested for monotony and abrupt changes and a suspected oscillation signal is formed, if app1icab1e. In addition, to an oscillation confirmation signal (M), the respective center point of the circle of the trajectory formed by the impedance values (7) of the positive sequence system is determined and compared with the reactance value (WX) of the positive sequence system with regard to its imaginary part. If a suspected oscillation signal and an oscillation confirmation signal occur simultaneously, the oscillation signal is formed.

Documents:

01818-cal-1998 abstract.pdf

01818-cal-1998 claims.pdf

01818-cal-1998 correspondence.pdf

01818-cal-1998 description(complete).pdf

01818-cal-1998 drawings.pdf

01818-cal-1998 form-1.pdf

01818-cal-1998 form-18.pdf

01818-cal-1998 form-2.pdf

01818-cal-1998 form-3.pdf

01818-cal-1998 form-5.pdf

01818-cal-1998 g.p.a.pdf

01818-cal-1998 letters patent.pdf

01818-cal-1998 priority document.pdf

01818-cal-1998 reply f.e.r.pdf

1818-CAL-1998-(15-10-2012)-FORM-27.pdf

1818-CAL-1998-CORRESPONDENCE 1.1.pdf

1818-CAL-1998-FORM-27.pdf

1818-CAL-1998-PA.pdf