[go: up one dir, main page]
More Web Proxy on the site http://driver.im/

WO1993013581A1 - Reconstruction of saturated current transformer signals - Google Patents

Reconstruction of saturated current transformer signals Download PDF

Info

Publication number
WO1993013581A1
WO1993013581A1 PCT/SE1992/000863 SE9200863W WO9313581A1 WO 1993013581 A1 WO1993013581 A1 WO 1993013581A1 SE 9200863 W SE9200863 W SE 9200863W WO 9313581 A1 WO9313581 A1 WO 9313581A1
Authority
WO
WIPO (PCT)
Prior art keywords
current
current transformer
block
reconstruction
saturated
Prior art date
Application number
PCT/SE1992/000863
Other languages
French (fr)
Inventor
Magnus BJÖRKLUND
Bengt Carlsson
Murari Mohan Saha
Original Assignee
Asea Brown Boveri Ab
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Asea Brown Boveri Ab filed Critical Asea Brown Boveri Ab
Priority to EP93901453A priority Critical patent/EP0619922A1/en
Publication of WO1993013581A1 publication Critical patent/WO1993013581A1/en

Links

Classifications

    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01FMAGNETS; INDUCTANCES; TRANSFORMERS; SELECTION OF MATERIALS FOR THEIR MAGNETIC PROPERTIES
    • H01F27/00Details of transformers or inductances, in general
    • H01F27/42Circuits specially adapted for the purpose of modifying, or compensating for, electric characteristics of transformers, reactors, or choke coils
    • H01F27/422Circuits specially adapted for the purpose of modifying, or compensating for, electric characteristics of transformers, reactors, or choke coils for instrument transformers
    • H01F27/427Circuits specially adapted for the purpose of modifying, or compensating for, electric characteristics of transformers, reactors, or choke coils for instrument transformers for current transformers
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02HEMERGENCY PROTECTIVE CIRCUIT ARRANGEMENTS
    • H02H1/00Details of emergency protective circuit arrangements
    • H02H1/0007Details of emergency protective circuit arrangements concerning the detecting means
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02HEMERGENCY PROTECTIVE CIRCUIT ARRANGEMENTS
    • H02H1/00Details of emergency protective circuit arrangements
    • H02H1/04Arrangements 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
    • H02H1/046Arrangements 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

Definitions

  • TECHNICAL FIELD Within largely all distribution of electric power, monitoring systems for detecting short circuits and other abnormal states are needed. Instrument transformers for measuring current and voltage therefore constitute an important and integrated part of control, monitoring and protective devices in most power distribution systems. It is, of course, very important that these measuring devices correctly reproduce the quantities they are designed to measure, both with regard to static and dynamic values. Since both control and monitoring devices and particularly protective devices are nowadays based on instantaneous value measurement, very high demands are placed on good dynamic conformity during the measurements.
  • a typical example is a differential protection device which, when a current transformer saturation occurs, may lead to an external fault being incorrectly detected as an intersystem fault. It is therefore of great importance to be able to detect whether a current transformer has become subjected to such a current that it has become magnetically saturated.
  • the present invention describes a method for reconstructing, during saturation, with the aid of the distorted secondary current, the primary current which causes the saturation. A reconstruction is also performed of the secondary current which would have been obtained unless the current transformer had become saturated.
  • the invention also comprises a method for detecting saturation and detecting when the saturation ceases.
  • the invention also comprises a device for carrying out the method.
  • Figure 1 shows an equivalent diagram for a current transformer seen from the secondary side.
  • FIG. 2 shows a flow diagram according to the invention.
  • Equations (3), (4) and (5) describe the model in continuous time.
  • x(k + 1) Ad(L ⁇ ) x(k) + B d (L ⁇ ) i p (k) (6)
  • i s (k) C s x(k) (7)
  • i ⁇ (k) C ⁇ x(k) (8)
  • a d (L ⁇ ) e A c (L ⁇ )h (9)
  • B d (L ⁇ ) e A c (L ⁇ )s ds B c (L ⁇ ) (10)
  • i(k) i(t)
  • t kh (12) where k is a running index.
  • T means transposition
  • is a parameter vector
  • a regression vector
  • K is a gain vector.
  • One way of calculating "K” is shown in B Carlsson, "Digital Differentiating Filters and Model Based Fault Detection” , PhD thesis , Department of Technology, Uppsala University, Uppsala, Sweden, 1989 , pp . 72-76.
  • LiTh-ISY-I 120 from the Department of Electrical Engineering, Linköping University, Linköping entitled “Estimation of the primary current in a saturated transformer” , 1991, presented by K W Chen and S T Glad, a method is described based on a Kalman filter applied to a signal model which is based on Taylor series expansion and connected to a current transformer model . Otherwise , continuous time is used here with a time-varying Kalmangain, which per se requires a high numerical capacity. To detect saturation, a simple detector is used, based on the variance of the estimated fault .
  • the invention relates to a numerical method which, via discrete-time measurements of the secondary current i s (k) from a current transformer, reconstructs the primary current and the secondary current in case of saturation of current transformers and a method for detecting saturation as well as for detecting when saturation ceases.
  • the reconstruction takes place with the aid of current transformer models of an unsaturated and a saturated current transformer as well as a signal model of the primary current, wherein the the current transformer models are fed from the signal model and saturation is decided by a decision logic unit when the output signal from the saturated current transformer model gives a better description of the secondary current than what the output signal from the unsaturated current transformer model gives.
  • the output signals i pr (k) and i sr (k) in case of a decision about saturated current transformer consist of a reconstructed primary current i pn (k) and a reconstructed secondary current i sn (k) and, in case of a decision about unsaturated current transformer, of a reconstructed primary current i pn (k) and an actually measured secondary current i s (k).
  • the invention also relates to a device for carrying out the above-mentioned methods.
  • the invention is based on the current transformer model which is described by equations (1) and (2) and the general state-space model described by equations (3), (4) and (5).
  • the invention is based on discretization according to equations (9) and (10), a sampled signal model according to equations (13) ... (16), and on the above-described combined signal and current transformer model which is described by equations (17) ... (25).
  • two values of the inductance L ⁇ are used, which is denoted
  • a d (L ⁇ s ) e A c (L ⁇ s ) h
  • the numerical method according to the invention completes a number of steps for each sampled measurement of the secondary current.
  • the different steps comprise reconstruction from an unsaturated model of a current transformer, reconstruction from a saturated model, detection of saturation, as well as decision about returning from a saturated to an unsaturated state.
  • i pn (k) is a reconstruction of the primary current
  • i sn (k) is a reconstruction of the secondary current
  • the invention is further based on the fact that the effect of i s (k) on the state reconstruction (k) is shut off as soon as a saturation has occurred. This is done with the aid of the gain parameter "g" which, the first time a saturated state is detected, is changed from 1 to 0. This means that during saturation, the currents will be reconstructed based on measurements of the secondary current prior to saturation.
  • the invention calculates and uses a state reconstruction (k) for the saturated model which is determined by the state reconstruction (k-d-1), that is, a state reconstruction obtained d+1 samples earlier.
  • the counter for the variable d shows that equation (40) is true for a number of consecutive samples d > f according to block B5, a decision about saturation is made, which takes place in the block B6 where also the variable M is set equal to 0.
  • block B8 will deliver a value of the primary current i pr (k) which is equal to the reconstructed primary current i pn (k) and a value of the reconstructed secondary current i sr (k) which is equal to the measured secondary current i s (k).
  • the output signal i pr (k) from block B8 will then be represented by the reconstructed primary current i pn (k) and the output signal i sr (k) by the reconstructed secondary current i sn (k).
  • a preferred embodiment with two current transformer models is used, one representing an unsaturated model and the other a saturated model.
  • several current transformer models based on fixed magnetizing inductances with a value which lies between those corresponding to a nominal and a saturated value, may be used.
  • the signal model may also consist of harmonics according to equation (11).
  • a variant of an embodiment with regard to detection of saturation may be replaced by another detection principle, for example a method described in SE 9100917-5.
  • the reconstructed magnetizing current i ⁇ when saturation has been determined, may be stored. During saturation, the magnetizing current will be practically equal to the reconstructed primary current i p (k). This means that the magnetizing current increases drastically during saturation. Information to the effect that saturation has ceased may be obtained when the magnetizing current decreases below the stored value. It is, of course, also possible to use i s (k) directly to make a decision about restoration to an unsaturated state.
  • a device for carrying out the method according to the invention preferably forms an integral part of a protective relay where current measurement takes place with the aid of current transformers. From the design point of view, the device may be arranged in the form of a number of blocks according to Figure 2 or constitute an integrated device.

Landscapes

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

Abstract

The invention relates to a numerical method which via discrete-time measurements of the secondary current (is(k)) from a current transformer reconstructs the primary current (ipr(k)) and the secondary current (isr(k)) of a saturated current transformer, which takes place in a block B1 and a method for detecting saturation as well as for detecting when saturation ceases, which takes place in blocks B2, B3, B4, B5, B6 and B7. The output signals of the method are obtained via a block B8 and upon a decision about saturated current transformer, the output signals consist of the reconstructed primary current (ipn(k)) and the reconstructed secondary current (isn(K)) and upon a decision about unsaturated current transformer, the output signals consist of the reconstructed primary current (ipn(k)) and the measured secondary current (is(k)). The invention also relates to a device for carrying out said methods.

Description

Reconstruction of saturated current transformer signals
TECHNICAL FIELD Within largely all distribution of electric power, monitoring systems for detecting short circuits and other abnormal states are needed. Instrument transformers for measuring current and voltage therefore constitute an important and integrated part of control, monitoring and protective devices in most power distribution systems. It is, of course, very important that these measuring devices correctly reproduce the quantities they are designed to measure, both with regard to static and dynamic values. Since both control and monitoring devices and particularly protective devices are nowadays based on instantaneous value measurement, very high demands are placed on good dynamic conformity during the measurements.
Due to practical and economic reasons it is not possible to dimension current transformers so as to avoid saturation at all fault current levels. Therefore, during a fault condition a current of such a high value may arise that the current transformer becomes magnetically saturated, whereby the waveform of the delivered current becomes distorted. This leads to considerable problems, especially for current measuring numeral protective relays, since these will then receive false information on which to base the decisions to take action. A typical example is a differential protection device which, when a current transformer saturation occurs, may lead to an external fault being incorrectly detected as an intersystem fault. It is therefore of great importance to be able to detect whether a current transformer has become subjected to such a current that it has become magnetically saturated. The present invention describes a method for reconstructing, during saturation, with the aid of the distorted secondary current, the primary current which causes the saturation. A reconstruction is also performed of the secondary current which would have been obtained unless the current transformer had become saturated. The invention also comprises a method for detecting saturation and detecting when the saturation ceases. The invention also comprises a device for carrying out the method.
BRIEF DESCRIPTION OF THE DRAWINGS
Figure 1 shows an equivalent diagram for a current transformer seen from the secondary side.
Figure 2 shows a flow diagram according to the invention.
BACKGROUND ART, THE PROBLEMS One way of reducing the effect of a current transformer saturation is to use some method for detecting saturation. Several such methods exist, which is clear, inter alia, from SE 90100917-5. When a saturation has been determined, the conditions for breaking the current are made more conservative in existing protective relays. This assumption, however, has some apparent shortcomings; for example, it means that a short-circuit current may be allowed to act for an unacceptably long period of time, which in turn may lead to negative effects on the network. A further problem in this connection is to detect when the saturation ceases.
A general description of current transformers, both in steady and transient states, is given by A Wright in "Current Transformers, Their Transient and Steady State Performance", Chapman and Hall Ltd., 1968. A model which is suitable for further study of the behaviour of current transformers at different magnetizing states is described, inter alia, by T Conrad, J Schlabbach and R Speh in "Verfahren zur Korrektur der verzerrten Sekundarstrόme von Stromwandlern", etzArchiv Bd., Vol. 6, 1984, in which it is referred to an equivalent diagram according to Figure 1 where ip = stepped down primary current is = secondary current Lμ = magnetizing inductance
Rfe = loss resistance in the iron core R2 = resistance of burden, winding, and conductors L2 = inductance of burden and leakage inductance N2/N1 = current transformer ratio The differential equations for the circuit according to Figure 1 will then be
(1) h
(2)
Figure imgf000005_0001
It should be pointed out here that the values of both Lμ and Rfe vary in dependence on the primary current via the magnetizing current. In the following description, however, Rfe will be assumed to be constant. When the magnetizing current exceeds a certain value, Lμ will decrease drastically. The greater part of the stepped down current will then be conducted via the magnetizing inductance, which results in the severely distorted secondary current. In the following description, the term "primary current" will be used only for "the stepped down primary current".
It should be pointed out here that the magnetizing current iμ is needed in explicit form to be able to calculate Lμ. The differential equations (1) and (2) can be solved with numerical methods, which, inter alia, is clear from an article by T Conrad, J. Schlabbach and R Speh: "Verfahren zur Korrektur der verzerrten Sekundarstrόme von Stromwandlern" published in etzArchiv Bd., Vol 6, pp 77-79, 1984. In these calculations a special algorithm has been used for Lμ which provides a saturated value which is only 60 times lower than the unsaturated value. The result of the calculations and the simulations which have been made show a fairly good reconstruction of the primary current. The value of the method described must, however, be considered to be relatively limited. This is due, among other thing, to the saturated value of Lμ in reality being rather 1000 times lower than the unsaturated value. Considering, in addition, the transfer functions corresponding to the differential equations, it will be seen that a high gain is required to reconstruct the primary current. This means that the method used is probably sensitive to measurement disturbances and since no disturbances are used during the simulations, the usefulness of this method in practice must be considered doubtful.
Differential equations of the types according to (1) and (2) can be described in state-space form according to known technique, see, for example, T Kailath, Linear Systems, Prentice-Hall. Inc., Englewood Cliffs, N. J. 1980, pp. 50- 60. A general state-space model for the current transformer is given by dx/dt = Ac(Lμ)x + Bc(Lμ)ip (3) is = Cs x (4) iμ = Cμ x ( 5 ) where it has been indicated that the state matrix Ac and the vector Bc depend on Lμ, which in turn is dependent on the magnetizing current iμ. The selections of state-space representations which are utilized in the invention will be described under the summary of the invention.
Equations (3), (4) and (5) describe the model in continuous time. In "Computer Controlled Systems", p. 37, Prentice Hall, Inc., 1984, by K J Åstrόm and B Wittenmark, there is described a method which discretizes the equations, whereby the following sampled state model is obtained. x(k + 1) = Ad(Lμ) x(k) + Bd(Lμ) ip(k) (6) is(k) = Cs x(k) (7) iμ(k)= Cμ x(k) (8)
Here
Ad(Lμ) = eAc(Lμ)h (9) Bd(Lμ) = eAc(Lμ)sds Bc(Lμ) (10)
Figure imgf000007_0001
where h is the sampling interval. To calculate (9) and (10), it is assumed that Lμ, which is a function of the magnetizing current iμ, is constant during the sampling interval.
A model of a primary circuit upon a short circuit, which is often described in the literature (see, e.g. "Digital protective relaying through recursive least-squares identification" by A Isaksson, published in IEE Proc. Pt. C, Vol. 135, No. 5, 1988, p. 441) describes the primary current as ip(t) = d0e-t/τ + (
Figure imgf000008_0001
cnsin(ωcnt + Φn)) (11) n=1 where τ is the time constant of the circuit, m is the number of harmonic components, ωc is the fundamental frequency, and Φn the phase shift.
To describe the primary current during a short circuit, in, inter alia, "Estimation of the primary current in a saturated transformer", by K W Chen and S T Glad: Report LiTh-ISY-I 120, 1991, Department of Electrical Engineering, Linköping University, Linkόping, Sweden, the assumption is made that the exponential term is replaced by a Taylor series expansion. However, it is obvious to use a fixed, predetermined value of τ. This reduces the number of parameters to be estimated while at the same time the model becomes less sensitive to unmodelled harmonics and noise.
For a general continuous time signal i(t), the corresponding sampled value is denoted i(k), that is, i(k) =i(t) |t=kh (12) where k is a running index.
It is part of the prior art that a sampled version of (11) via linear regression can be written in state-space form as ip(k) = φTθ(k) (13) θ(k + 1) = F θ(k) (14)
According to conventional recursive technique, T means transposition, θ is a parameter vector, and φ a regression vector. According to M S Sachdev, H C Wood and N C Johnson: "Kalman filtering applied to power system measurements for relaying", IEEE Trans, on PAS, Vol. PAS-104, No. 12, 1985 pp. 3565-3571, φ and F for the case m = 1 can be written as φ T = (1 1 0) (15) -h/τ 0 0
F = cos(ωch) sin(Gch) (16)
-sin(ωch) cos (ωch
Figure imgf000009_0003
Figure imgf000009_0002
Now, if the output signal ip(k) from the signal model according to (13) and (14) is taken as input signal to the current transformer model according to (6), (7) and (8), the resultant system according to known technique (see, e.g., "Control System Toolbox", The Math Works, Inc, p. 2.149) can be written as z(k + 1) = At z(k) (17) ip(k) = Cpt z(k) (18) is(k) = Cst z(k) (19) iμ(k) = Cμt z (k) (20) where
(21)
Figure imgf000009_0001
Cpt = (φT 0 0) (22)
Cst = (0 0 0 Cs) (23) Cμt = (0 0 0 Cμ) (24 ) and where the used state vector is given by z(k) = (θ(k)T x(k)T)T (25)
In similar model contexts it is common to use a Kalman filter to reconstruct the state vector z(k). The general method for such filtering is described, inter alia, in "Optimal Filtering", by B D O Anderson and J B Moore, Prentice Hall, 1979, p. 44.
If a fixed value of Lμ is used, At in equation (17) will become a constant matrix. It is then possible to utilize a stationary Kalman filter, which provides the reconstruction (k) = At
Figure imgf000010_0001
(k-1) + K( is(k) - Cst At
Figure imgf000010_0002
(k-1)) (26)
Here, "K" is a gain vector. One way of calculating "K" is shown in B Carlsson, "Digital Differentiating Filters and Model Based Fault Detection" , PhD thesis , Department of Technology, Uppsala University, Uppsala, Sweden, 1989 , pp . 72-76. In a report LiTh-ISY-I 120 from the Department of Electrical Engineering, Linköping University, Linköping entitled "Estimation of the primary current in a saturated transformer" , 1991, presented by K W Chen and S T Glad, a method is described based on a Kalman filter applied to a signal model which is based on Taylor series expansion and connected to a current transformer model . Otherwise , continuous time is used here with a time-varying Kalmangain, which per se requires a high numerical capacity. To detect saturation, a simple detector is used, based on the variance of the estimated fault . SUMMARY OF THE INVENTION
The invention relates to a numerical method which, via discrete-time measurements of the secondary current is(k) from a current transformer, reconstructs the primary current and the secondary current in case of saturation of current transformers and a method for detecting saturation as well as for detecting when saturation ceases. The reconstruction takes place with the aid of current transformer models of an unsaturated and a saturated current transformer as well as a signal model of the primary current, wherein the the current transformer models are fed from the signal model and saturation is decided by a decision logic unit when the output signal from the saturated current transformer model gives a better description of the secondary current than what the output signal from the unsaturated current transformer model gives. The output signals ipr(k) and isr(k) in case of a decision about saturated current transformer consist of a reconstructed primary current ipn(k) and a reconstructed secondary current isn(k) and, in case of a decision about unsaturated current transformer, of a reconstructed primary current ipn(k) and an actually measured secondary current is(k).
The invention also relates to a device for carrying out the above-mentioned methods.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
The invention is based on the current transformer model which is described by equations (1) and (2) and the general state-space model described by equations (3), (4) and (5).
The following state-space description is used in equations (3), (4) and (5) Ac(Lμ) = (27)
Bc(Lμ) = (28)
Figure imgf000012_0001
Cs = (0 1) (29)
Cμ = (1 0) (30)
Further, the invention is based on discretization according to equations (9) and (10), a sampled signal model according to equations (13) ... (16), and on the above-described combined signal and current transformer model which is described by equations (17) ... (25). According to the invention, two values of the inductance Lμ are used, which is denoted
Lμn = the nominal value of the magnetizing inductance Lμs = the saturated value of the magnetizing inductance This means that according to the invention two state-space descriptions or models are obtained, whereby also the matrix At according to equation (21) is given two values according to
0
Ant = Bd(LμnT Ad(Lμn) (31)
Figure imgf000012_0002
Figure imgf000012_0003
(32)Ast = Bd(LμsT Ad(Lμs)
Figure imgf000013_0005
Figure imgf000013_0004
Now, operating with two different values of the inductance Lμ means at the same time that two different values of Ad and Bd are obtained according to the following
(9n)
Ad(Lμn) = eAc(Lμn)h
(9s)
Ad(Lμs) = eAc (Lμs) h
(10n)
Bd(Lμn) = eAc(Lμn) sds Bc(Lμn)
Figure imgf000013_0002
(10s) eAc(Lμs)sds Bc(Lμs)
Bd(Lμs) ) =
Figure imgf000013_0003
(27n)
Ac(Lμn) =
(27s)
Ac(Lμs) =
(28n)
Bc(Lμn)=
(28s)
Bc ((Lμs) =
Figure imgf000013_0001
The numerical method according to the invention completes a number of steps for each sampled measurement of the secondary current.
The different steps comprise reconstruction from an unsaturated model of a current transformer, reconstruction from a saturated model, detection of saturation, as well as decision about returning from a saturated to an unsaturated state.
When saturation is not detected, a parallel prediction takes place with both the unsaturated and the saturated current transformer model. With the unsaturated model, the reconstruction is performed from a Kalman filter with a pre-calculated gain K, with Ant according to equation (31), and with the C-parameters according to equations (22) and (23) as follows: n(k) = Ant
Figure imgf000014_0001
(k-1) + K.g.(is(k) - Cst Ant (k-1)) (33)
Figure imgf000014_0003
ipn(k) = Cpt
Figure imgf000014_0004
n(k) (34) isn(k) = Cst
Figure imgf000014_0002
n(k) (35)
Here, ipn(k) is a reconstruction of the primary current and isn(k) is a reconstruction of the secondary current.
The invention is further based on the fact that the effect of is(k) on the state reconstruction
Figure imgf000014_0005
(k) is shut off as soon as a saturation has occurred. This is done with the aid of the gain parameter "g" which, the first time a saturated state is detected, is changed from 1 to 0. This means that during saturation, the currents will be reconstructed based on measurements of the secondary current prior to saturation. To detect that saturation has occurred, a saturated model according to the invention can be used and the following relationships be utilized: (k) = (Ast)d+1 (k - d -1) (36)
Figure imgf000015_0001
iss(k) = Cst
Figure imgf000015_0002
(k) (37) with Ast according to equation (32). The variable "d" will be defined below after equation (40).
As is clear, the invention calculates and uses a state reconstruction
Figure imgf000015_0003
(k) for the saturated model which is determined by the state reconstruction
Figure imgf000015_0004
(k-d-1), that is, a state reconstruction obtained d+1 samples earlier.
According to the invention, the reconstruction error for the respective model is then calculated according to en = is(k) - isn(k) (38) es = is(k) - iss(k) (39)
In the following the invention will now be described with reference to a flow diagram according to Figure 2. The reconstruction method as described above and in accordance with equations (27) ... (39) takes place in a block B1, which is supplied with the sampled discrete-time secondary current is (k).
Next, a comparison is made between the absolute value of the reconstruction errors for the two models. According to the flow diagram in Figure 2, this takes place in block B2. If the reconstruction error calculated on the basis of the saturated model is smaller than the reconstruction error for the unsaturated model, that is, if
| es | < | en | (40) this indicates that a saturation has occurred. To prevent short disturbances from denoting a saturated state, it is required according to the invention that the inequality remains for a predetermined number (f) of consecutive samples for saturation to be determined. The control whether the saturation indication has existed during the above- mentioned number of samples is made by storing, in a variable "d" in the block B3, the number of consecutive times that equation (40) is true. This variable is set to zero if equation (40) is false. The first time equation (40) is true, that is, when d=1, the gain parameter g will be changed from g = 1 to g = 0, which is made in the block B4, which then restores this information to the block B1, equation (33), to prevent the distorted current signal from being allowed to influence the reconstruction. Now, if the counter for the variable d shows that equation (40) is true for a number of consecutive samples d > f according to block B5, a decision about saturation is made, which takes place in the block B6 where also the variable M is set equal to 0.
If the saturation indication determines that no saturation has occurred, block B7 will generate M = 1, which is passed to a block B8. To this block are supplied the sampled secondary current is (k), the primary current ipn(k) reconstructed by block Bl as well as the reconstructed secondary current isn(k). By an M = 1 from block B7, block B8 will deliver a value of the primary current ipr(k) which is equal to the reconstructed primary current ipn(k) and a value of the reconstructed secondary current isr(k) which is equal to the measured secondary current is(k).
Now, if the saturation indication remains for the preset number of samples f, the method according to the invention will understand that a saturation, that is, M = 0 according to the flow diagram, has occurred. The output signal ipr(k) from block B8 will then be represented by the reconstructed primary current ipn(k) and the output signal isr(k) by the reconstructed secondary current isn(k). The iteration goes on continuously in the usual way by setting k = k + 1, shown in principle by block B9.
As will be clear from the above, according to the invention a preferred embodiment with two current transformer models is used, one representing an unsaturated model and the other a saturated model. Within the scope of the invention, several current transformer models, based on fixed magnetizing inductances with a value which lies between those corresponding to a nominal and a saturated value, may be used.
Within the scope of the invention, the signal model may also consist of harmonics according to equation (11).
Within the scope of the invention, a variant of an embodiment with regard to detection of saturation, as described by means of blocks B2, B3 and B4, may be replaced by another detection principle, for example a method described in SE 9100917-5.
It is, of course, also important to be able to detect when a saturation ceases. One embodiment is described by the inequality (40) and the block B2, respectively. Also in this case, similar detection principles, capable of replacing the contents of blocks B2, B3 and B5 , fall within the scope of the invention. As an example, the reconstructed magnetizing current iμ, when saturation has been determined, may be stored. During saturation, the magnetizing current will be practically equal to the reconstructed primary current ip(k). This means that the magnetizing current increases drastically during saturation. Information to the effect that saturation has ceased may be obtained when the magnetizing current decreases below the stored value. It is, of course, also possible to use is(k) directly to make a decision about restoration to an unsaturated state. A device for carrying out the method according to the invention preferably forms an integral part of a protective relay where current measurement takes place with the aid of current transformers. From the design point of view, the device may be arranged in the form of a number of blocks according to Figure 2 or constitute an integrated device.
In an integrated embodiment all equations and logical decisions are included in a computer-based program which has the discrete-time, sampled secondary current is (k) as input signal and whose output signals, upon a decision on an unsaturated state, consist of ipr(k) = ipn(k) and isr(k) = is (k) and whose output signals, upon a decision on a saturated state, consist of ipr(k) = ipn(k) and isr(k) = isn(k).

Claims

1. A method for reconstruction of saturated current transformer signals, characterized in that the reconstructed current transformer signals which comprise reconstructed primary current (ipr(k)) and reconstructed secondary current (isr(k)) are obtained via sampled discrete-time measurement of the secondary current (is(k)) and with the aid of at least two current transformer models and a signal model of the primary current.
2. A method for reconstruction of saturated current transformer signals according to claim 1, characterized in that the reconstruction is obtained with the aid of current transformer models of a saturated and an unsaturated current transformer.
3. A method for reconstruction of saturated currrent transformer signals according to claim 1, characterized in that the current transformer models are fed from the signal model.
4. A method for reconstruction of saturated current transformer models according to claim 1, characterized in that saturation is decided by a decision logic unit when the output signal from the saturated current transformer model gives a better description of the secondary current than what the output signal from the unsaturated current transformer model gives.
5. A method for reconstruction of saturated current transformer signals according to claims 1 to 4 and wherein the reconstruction and the saturation decisions are based on a combination of the signal model and the unsaturated and the saturated current transformer model and wherein the method is characterized by the following relationships n(k) = Ant (k-1) + K.g.(is(k) - Cst Ant -zn(k-1)) (33)
Figure imgf000020_0006
ipn(k) = Cpt
Figure imgf000020_0007
n(k) (34) isn (k) = Cst
Figure imgf000020_0008
(k) (35) where (k) is the state reconstruction based on an unsaturated current transformer model
F 0
Ant = (31)
Bd(LμnT Ad(Lμn)
Figure imgf000020_0001
Figure imgf000020_0002
e-h/τ 0 F = 0 cos(ωch) sin(ωch) (16) 0 -sin(ωch) cos(ωch)
Figure imgf000020_0005
Figure imgf000020_0003
Bd(Lμn) = eAc(Lμn)sds Bc(Lμn) (10n)
Figure imgf000020_0004
ωc is the frequency of the fundamental tone Lμn is the nominal magnetizing inductance φT = (1 1 0) (15)
Ad(Lμn) = eAc(Lμn)h (9n) Ac(Lμn)=
(27n)
Bc(Lμn)= (28n)
Figure imgf000021_0001
Rfe = loss resistance in the iron core
R2 = resistance of burden, winding, and conductors
L2 = inductance of burden and leakage inductance
K is a predetermined gain to the reconstruction according to equation (33) g is a gain parameter which may assume the value 0 or 1 and which, upon a decision about unsaturated state, assumes the value 1 ipn(k) is a reconstructed primary current isn(k) is a reconstructed secondary current
Cpt = (φT 0 0) (22)
Cst = (0 0 0 Cs) (23)
Cs = (0 1) (29) h = sampling interval τ = time constant of primary circuit and for detecting saturation, the following reconstruction, based on a saturated current transformer model, is used
Figure imgf000022_0003
(k) = (Ast)d+1
Figure imgf000022_0004
(k - d -1) (36) iss (k) = Cst
Figure imgf000022_0005
(k) (37) where
Figure imgf000022_0002
(k) is the state reconstruction based on a saturated current transformer model
Ast = (32)
Bd(LμsT Ad(Lμs)
Figure imgf000022_0006
Figure imgf000022_0007
Lμs is the magnetizing inductance for a saturated current transformer
Ad (Lμs) = e Ac(Lμs)h (9s)
Bd (Lμs) = eAc (Lμs ) sds Bc (Lμs) (10s)
Figure imgf000022_0008
Ac(Lμs) = (27s)
Bc(Lμs)= (28s)
Figure imgf000022_0001
after which the reconstruction error for the two models is determined according to en = is(k) - isn(k) (38) es = is(k) - iSS(k) (39) and when | es | < | en | (40) is true, a variable "d" is adapted to store the number of consecutive true samples and when d = 1, g is changed from 1 to 0 and if d > f, where "f" is a predetermined consecutive number of samples, it is decided that saturation has occurred, whereby the measured secondary current is(k) is replaced by the reconstructed secondary current isn(k) and when equation (40) is no longer true, or if the predetermined number of consecutive samples "f" is not achieved, the current transformer is considered not to be saturated.
6. A device for carrying out the method for reconstruction of saturated current transformer signals according to claims 1-5, characterized in that the device comprises a block Bl which has the sampled discrete-time secondary current is (k) as input signal and which is programmed with the equations
Ad(Lμ) = eAc(Lμ)h (9)
Bd(Lμ) = eAc(Lμ)sds Bc(Lμ) (10)
Figure imgf000023_0001
Ac(Lμ) = (27)
Bc(Lμ) = (28)
Figure imgf000024_0001
Cs = (0 1) (29)
Cμ = (1 0) (30)
Figure imgf000024_0012
Ant = (31)
Bd (Lμn) φT Ad (Lμn)
Figure imgf000024_0004
Figure imgf000024_0005
Figure imgf000024_0013
Ast = (32)
Bd(LμsT Ad(Lμs)
Figure imgf000024_0006
Figure imgf000024_0007
n(k) = Ant
Figure imgf000024_0002
(k-1) + K.g. (is(k) - Cst Ant (k-1)) (33)
Figure imgf000024_0003
ipn(k) = Cpt (k)
Figure imgf000024_0008
(34) isn (k) = Cst (k) (35)
Figure imgf000024_0009
(k) = (Ast)d+1 (k - d -1)
(36) iss(k) = Cst (k)
Figure imgf000024_0011
(37) en = is(k) - iSn(k) (38) es = is(k) - iss(k) (39) and with corresponding equations (9n), (9s), (10n), (10s), (27n), (27s), (28n) and with variables included defined according to claim 5 and that the values of en and es obtained in block B1 are arranged as input values to a block B2 which is adapted to determine whether
| es | < | en | (40) is true, and if this is the case, information about this is adapted to be supplied to a block B3 which stores the number of consecutive samples that equation (40) is true in a variable "d" and the first time that d = 1, this information is adapted to be supplied to a block B4 which is adapted to change the variable "g" in equation (33) from g = 1 to g = 0, which change is adapted to be returned to block B1 and that the consecutive value stored in the variable "d" in block B3 is adapted to be supplied to a block B5 adapted to check whether d > f where " f" is a preset value, and if this is the case, information about this is adapted to be supplied to a block
B6 for decision that saturation has occurred, whereby a variable M is set equal to 0 and that if equation ( 40 ) is false, information about this together with information as to whether the inequality of block B5 is false are adapted to be supplied to a block B7 for information that no saturation has occurred, whereby the variable M is set equal to 1 and that the current value of the variable M is adapted to be supplied to a block B8 together with the sampled measured value is(k) of the secondary current, the primary current ipn(k) reconstructed by block B1 and the reconstructed secondary current isn(k) and that when M = 0, block B8 is adapted to deliver a value ipr (k) of the primary current which is equal to the reconstructed value ipn(k) of the primary current and a value isr(k) of the secondary current which is equal to the reconstructed value isn(k) of the secondary current and that when M = 1, block B8 is adapted to deliver a value ipr (k) of the primary current which is equal to the reconstructed value ipn(k) of the primary current and a value isr(k) of the secondary current which is equal to the sampled measured value is (k) and that the iteration is adapted to continue by setting, in a block B9, k = k + 1.
PCT/SE1992/000863 1992-01-03 1992-12-14 Reconstruction of saturated current transformer signals WO1993013581A1 (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
EP93901453A EP0619922A1 (en) 1992-01-03 1992-12-14 Reconstruction of saturated current transformer signals

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
SE9200011A SE469676B (en) 1992-01-03 1992-01-03 PROCEDURES FOR RECONSTRUCTION OF Saturated Current Transformer Signals AND DEVICE FOR IMPLEMENTATION OF THE PROCEDURE
SE9200011-6 1992-01-03

Publications (1)

Publication Number Publication Date
WO1993013581A1 true WO1993013581A1 (en) 1993-07-08

Family

ID=20384952

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/SE1992/000863 WO1993013581A1 (en) 1992-01-03 1992-12-14 Reconstruction of saturated current transformer signals

Country Status (4)

Country Link
EP (1) EP0619922A1 (en)
CA (1) CA2126867A1 (en)
SE (1) SE469676B (en)
WO (1) WO1993013581A1 (en)

Cited By (10)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP0788122A3 (en) * 1996-01-31 1997-11-05 Eaton Corporation Method and apparatus for measuring an ac current which saturates the core of a current transformer
EP0882990A2 (en) * 1997-06-04 1998-12-09 Siemens Aktiengesellschaft Method and apparatus for detecting and correcting a saturated current waveform of a current transformer
DE19928192A1 (en) * 1999-06-19 2000-12-21 Abb Patent Gmbh Current reconstruction method involves deriving maximum and minimum orientation points from at least two measurement windows superimposed on current measurement signal
FR2818433A1 (en) * 2000-12-20 2002-06-21 Schneider Electric Ind Sa DEVICE FOR DETERMINING THE PRIMARY CURRENT OF A CURRENT TRANSFORMER HAVING SATURATION CORRECTION MEANS
US6754616B1 (en) * 2000-01-31 2004-06-22 Fujitsu Limited Method of emulating an ideal transformer valid from DC to infinite frequency
US8395373B2 (en) 2008-03-28 2013-03-12 Abb Technology Ag Phasor estimation during current transformer saturation
DE102013210800A1 (en) * 2013-06-10 2014-12-11 Bender Gmbh & Co. Kg Integrated circuit with digital method for AC-sensitive differential current measurement
WO2017001950A1 (en) 2015-06-29 2017-01-05 Abb Technology Ltd. A method for correcting effect of saturation in current transformer and an intelligent electronic device therefor
WO2018122632A1 (en) * 2016-12-26 2018-07-05 Abb Schweiz Ag A method for detecting inrush and ct saturation and an inteligent electronic device therfor
CN117607520A (en) * 2023-11-24 2024-02-27 浙江科能达电气有限公司 Current sampling method, device and medium of current transformer in nonlinear region

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP0090095A1 (en) * 1982-03-29 1983-10-05 BBC Brown Boveri AG Method and device for evaluating the secondary current of a current transformer primary connected to an electric power supply line

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP0090095A1 (en) * 1982-03-29 1983-10-05 BBC Brown Boveri AG Method and device for evaluating the secondary current of a current transformer primary connected to an electric power supply line

Cited By (18)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP0788122A3 (en) * 1996-01-31 1997-11-05 Eaton Corporation Method and apparatus for measuring an ac current which saturates the core of a current transformer
EP0882990A2 (en) * 1997-06-04 1998-12-09 Siemens Aktiengesellschaft Method and apparatus for detecting and correcting a saturated current waveform of a current transformer
DE19723422C1 (en) * 1997-06-04 1998-12-10 Siemens Ag Method and device for detecting and correcting a saturated current profile of a current transformer
US6072310A (en) * 1997-06-04 2000-06-06 Siemens Aktiengesellschaft Method and device for detecting and correcting a saturated current profile of a current transformer
EP0882990A3 (en) * 1997-06-04 2000-11-02 Siemens Aktiengesellschaft Method and apparatus for detecting and correcting a saturated current waveform of a current transformer
DE19928192A1 (en) * 1999-06-19 2000-12-21 Abb Patent Gmbh Current reconstruction method involves deriving maximum and minimum orientation points from at least two measurement windows superimposed on current measurement signal
DE19928192B4 (en) * 1999-06-19 2005-08-25 Abb Patent Gmbh Process for the reconstruction of a stream
US6754616B1 (en) * 2000-01-31 2004-06-22 Fujitsu Limited Method of emulating an ideal transformer valid from DC to infinite frequency
US6611136B2 (en) 2000-12-20 2003-08-26 Schneider Electric Industries Sa Device for determining the primary current of a current transformer comprising saturation correction means
EP1217707A1 (en) * 2000-12-20 2002-06-26 Schneider Electric Industries SA Device for termination of primary current in a current transformer having saturation compensation means
FR2818433A1 (en) * 2000-12-20 2002-06-21 Schneider Electric Ind Sa DEVICE FOR DETERMINING THE PRIMARY CURRENT OF A CURRENT TRANSFORMER HAVING SATURATION CORRECTION MEANS
US8395373B2 (en) 2008-03-28 2013-03-12 Abb Technology Ag Phasor estimation during current transformer saturation
DE102013210800A1 (en) * 2013-06-10 2014-12-11 Bender Gmbh & Co. Kg Integrated circuit with digital method for AC-sensitive differential current measurement
US10564189B2 (en) 2013-06-10 2020-02-18 Bender Gmbh & Co. Kg Integrated circuit using a digital method for AC/DC-sensitive residual current measurement
WO2017001950A1 (en) 2015-06-29 2017-01-05 Abb Technology Ltd. A method for correcting effect of saturation in current transformer and an intelligent electronic device therefor
US10263507B2 (en) 2015-06-29 2019-04-16 Abb Schweiz Ag Method for correcting effect of saturation in current transformer and an intelligent electronic device therefor
WO2018122632A1 (en) * 2016-12-26 2018-07-05 Abb Schweiz Ag A method for detecting inrush and ct saturation and an inteligent electronic device therfor
CN117607520A (en) * 2023-11-24 2024-02-27 浙江科能达电气有限公司 Current sampling method, device and medium of current transformer in nonlinear region

Also Published As

Publication number Publication date
CA2126867A1 (en) 1993-07-08
SE469676B (en) 1993-08-16
EP0619922A1 (en) 1994-10-19
SE9200011D0 (en) 1992-01-03
SE9200011L (en) 1993-07-04

Similar Documents

Publication Publication Date Title
Aggarwal et al. New concept in fault location for overhead distribution systems using superimposed components
Hänninen Single phase earth faults in high impedance grounded networks: characteristics, indication and location
Smon et al. Local voltage-stability index using Tellegen's theorem
US7180300B2 (en) System and method of locating ground fault in electrical power distribution system
US7902813B2 (en) Protective digital relay device
Oliveira et al. Extended Park's vector approach-based differential protection of three-phase power transformers
EP2686691A1 (en) A method for detecting earth faults
WO1993013581A1 (en) Reconstruction of saturated current transformer signals
Khan et al. A phase-shifting transformer protection technique based on directional comparison approach
Goeritno et al. Injection Current into the Power Transformer as an Internal Fault Phenomena for Measuring the Differential Relay Performance.
Saleh et al. Second harmonic-based approach to identify a GIC flow in power transformers
Soliman et al. A robust differential protection technique for single core delta-hexagonal phase-shifting transformers
Raichura et al. IMPROVED TRANSFORMER DIFFERENTIAL PROTECTION BY ADAPTIVE PICKUP SETTING DURING MOMENTARY OVER-FLUXING CONDITION.
Oliveira et al. Application of Park's power components to the differential protection of three-phase transformers
Hamidi Protective Relay for Power Transformers Based on Digital Twin Systems
Aucoin et al. Feeder protection and monitoring system, Part I: design, implementation and testing
Tziouvaras et al. The effect of conventional instrument transformer transients on numerical relay elements
JP3041968B2 (en) Monitoring method for insulation deterioration of low-voltage live wires
Panova et al. Development of mathematical models of microprocessor-based relay protection devices for 220/110 kV nodal distribution substation in Matlab/Simulink
Senger et al. Proposal of a new sensitive ground overcurrent protection for high-impedance faults
Zocholl Integrated metering and protective relay systems
EP4372937A1 (en) A fault discrimination and a current transformer saturation detection for a differential protection system
Abi et al. Detection and localization of internal turn-to-turn short circuits in transformer windings by means of negative sequence analysis
Chaudhari et al. Common differential relaying scheme for the protection of various transformer configurations
Beiza et al. Multiphase transmission line modeling for voltage sag estimation

Legal Events

Date Code Title Description
AK Designated states

Kind code of ref document: A1

Designated state(s): CA

AL Designated countries for regional patents

Kind code of ref document: A1

Designated state(s): AT BE CH DE DK ES FR GB GR IE IT LU MC NL PT SE

DFPE Request for preliminary examination filed prior to expiration of 19th month from priority date (pct application filed before 20040101)
WWE Wipo information: entry into national phase

Ref document number: 2126867

Country of ref document: CA

WWE Wipo information: entry into national phase

Ref document number: 1993901453

Country of ref document: EP

WWP Wipo information: published in national office

Ref document number: 1993901453

Country of ref document: EP

WWW Wipo information: withdrawn in national office

Ref document number: 1993901453

Country of ref document: EP