Current Measurement Under Current Transformer Saturation, Distribution Transformer Status Detection, and Protection Method

Abstract

The present invention belongs to the field of electrical equipment detection, and solves the technical problem of being difficult to provide reliable electrical parameters when a current transformer is saturated. The present invention provides a current measurement method, a distribution transformer state detection method, and a protection method under the saturation of a current transformer. A state space model of the current transformer is established: a functional relationship between a state vector, an input vector, and an output vector is constructed, the state space model is rewritten in the form of a polyhedron, and a corresponding linear parameter varying observer LPV is designed to observe the state space model in the form of a polyhedron according to the input vector and the output vector, so as to obtain an estimated value of the state vector; the estimated value of the state vector is substituted into the magnetic flux equation of the primary current, and the estimated value of the primary current is calculated. By using the estimated value of the primary current measured by the present invention for state detection and fault protection of a distribution transformer, the reliability of the operation of the distribution transformer is improved.

Description

Technical Field

[0001] The present invention belongs to the field of electrical equipment detection, and specifically relates to a current measurement method under current transformer saturation, as well as a state detection method and a protection method for a distribution transformer. Background Art

[0002] With the rapid development of the country, the continuous development of the social and economic level and the continuous enrichment of people's material life, the demand for electricity is increasing day by day. The distribution transformer is one of the core components of the entire power system and is a key link to ensure the power supply effect of the society. With the continuous improvement of people's living standards, the state detection and fault diagnosis of the distribution transformer are crucial.

[0003] In order to detect and protect the distribution transformer, multiple current transformers are connected to the high side of the distribution transformer to meet different needs. For example, for the overcurrent, short-circuit, overload, differential protection, etc. of the transformer, current signals (secondary current) are taken from the current transformer; for the measurement components such as the load, current, and watt-hour meter of the transformer, current signals (secondary current) are also taken from the current transformer.

[0004] However, the saturation of the current transformer will cause the phase angle of the measured current (secondary current) to lead and the amplitude to decrease, which is one of the main reasons for the stray operation of the transformer differential scheme under through faults. Inevitably, it will feed unreliable signals to the corresponding relays. Currently, in engineering practice, harmonic blocking elements or multi-slope characteristics and other technologies are usually used to avoid relay failures during the saturation of the current transformer as much as possible, but these solutions may damage the sensitivity and timeliness of the differential scheme and reduce its efficiency during through faults. Therefore, it is crucial to solve the problems brought by the saturation of the current transformer. Summary of the Invention

[0005] The purpose of the present invention is to solve the problems existing in the above-mentioned prior art, and provide a current measurement method under current transformer saturation to solve the technical problem of being difficult to provide reliable electrical parameters when the current transformer is saturated.

[0006] The present invention is realized through the following technical solutions: A current measurement method under current transformer saturation includes the following steps:

[0007] Establish a state space model of the current transformer: construct the functional relationship between the state vector, the input vector, and the output vector, where the state vector is composed of the leakage flux of the primary winding, the leakage flux of the secondary winding, and the core flux, the input vector is the primary voltage, and the output vector is the secondary current;

[0008] Rewrite the state - space model into a polyhedron form and design a corresponding Linear Parameter - Varying (LPV) observer to observe the state - space model in polyhedron form based on the input vector and output vector, so as to obtain the estimated value of the state vector;

[0009] Substitute the estimated value of the state vector into the flux equation of the primary current to calculate the estimated value of the primary current.

[0010] Furthermore, the state - space model of the current transformer is as follows:

[0011]

[0012] In the formula, \(X(t)\) represents the state vector, \(X(t)=[\lambda CT,1 \lambda CT,2 \lambda CT,m \) T , \(\lambda CT,1 \) represents the magnetic flux linkage of the primary winding, \(\lambda CT,2 \) represents the magnetic flux linkage of the secondary winding, \(\lambda CT,m \) represents the core magnetic flux; represents the first - order derivative of \(X(t)\); \(A(\lambda CT,m )\) represents the state matrix, and \(A(\lambda CT,m )\) is a function of the core magnetic flux \(\lambda CT,m \); \(B\) represents the input matrix, \(B = [1\ 0\ 0] T \); \(U(t)\) represents the input vector, \(U(t)=[V CT,p \), \(V CT,p \) represents the primary voltage; \(Y(t)\) represents the output vector, \(Y(t)=[I CT,s \), \(I CT,s \) represents the secondary current; \(C\) represents the output matrix.

[0013] Furthermore, the state matrix \(A(\lambda CT,m )\) is as follows:

[0014]

[0015] In the formula, \(R CT,1 \) represents the resistance of the primary winding, \(L CT,1 \) represents the inductance of the primary winding, \(R CT,2 \) represents the resistance of the secondary winding, \(L CT,2 \) represents the inductance of the secondary winding, \(R b \) represents the resistance of the current - transformer load, \(L b \) represents the inductance of the current - transformer load, \(\lambda CT,m \) represents the core magnetic flux, \(n CT \) represents the turns ratio;

[0016] f(\lambda CT,m ) = 1 / LCT,m (λ CT,m ), L CT,m (λ CT,m ) is a function of λ CT,m , and L CT,m represents a variable inductor, and the magnitude of L CT,m depends on the core magnetic flux λ of the current transformer CT,m , and is obtained from the excitation curve or excitation test of the current transformer.

[0017] Further, the output matrix C CT is as follows:

[0018]

[0019] where n CT represents the turns ratio, L b represents the inductance of the current transformer load, and L CT,2 represents the inductance of the secondary winding.

[0020] Further, the state - space model in the form of a polyhedron:

[0021]

[0022] where the matrices and A( f CT ) are constant matrices; μ1 and μ2 are variable parameters, and μ1 and μ2 are defined as follows:

[0023]

[0024] Assume that L CT,m is bounded between and , and f(λ CT,m ) is also bounded between and , as follows:

[0025] Further, the state matrix A(λ CT,m ) is decomposed into

[0026] Further, the linear parameter - varying observer LPV is as follows:

[0027]

[0028] where represents the estimated value of the state vector X(t), Z(t) represents the state variable of the linear parameter - varying observer LPV, Denotes the first derivative of Z(t); the matrices N1, N2, L1, L2, G, and H are all design matrices that satisfy the accuracy and stability conditions of the linear parameter varying observer LPV;

[0029] To make the error of the linear parameter varying observer LPV asymptotically zero, the following accuracy conditions must be satisfied:

[0030]

[0031] PA( f CT ) - L2C - N2P = 0

[0032] PB - G = 0

[0033] where P = I + HC, and I is the 3×3 identity matrix;

[0034] For the linear parameter varying observer LPV to be asymptotically stable, the following stability conditions must be satisfied:

[0035] and

[0036] where φ represents the common matrix, φ = φ T ≥ 0.

[0037] Furthermore, the flux equation of the primary current:

[0038]

[0039] In the formula, I CT,p represents the primary current, λ CT,m represents the core flux, λ CT,1 represents the magnetic flux linkage of the primary winding, and L CT,1 represents the inductance of the primary winding.

[0040] The present invention also provides a method for detecting the state of a distribution transformer under current transformer saturation. The estimated value of the primary current of the current transformer on the high-voltage side of the distribution transformer is obtained by using the current measurement method under current transformer saturation described in the present invention and the estimated value of the primary current is used as the electrical parameter of the state detection device.

[0041] The present invention also provides a method for protecting a distribution transformer under current transformer saturation. The estimated value of the primary current of the current transformer on the high-voltage side of the distribution transformer is obtained by using the current measurement method under current transformer saturation described in the present invention and the estimated value of the primary current is used as the electrical parameter of the protection device.

[0042] Compared with the prior art, the beneficial effects of the present invention are:

[0043] 1. Since the phase angle of the secondary current leads and the amplitude decreases when the current transformer saturates, the secondary current is no longer a reliable electrical parameter. The present invention uses the primary current to replace the secondary current to improve the reliability of the electrical parameter.

[0044] 2. The primary current belongs to a large current and is difficult to measure directly. The present invention realizes the estimation of the magnitude of the primary current by constructing a state space model and an observer of the current transformer.

[0045] 3. The present invention uses the estimated value of the primary current for the state detection and fault protection of the distribution transformer, improving the reliability of the operation of the distribution transformer. Description of the Drawings

[0046] Figure 1 is the equivalent circuit diagram of the current transformer;

[0047] Figure 2 is the equivalent circuit diagram of the primary side of the circuit transformer;

[0048] Figure 3 is the current measurement method under the saturation of the current transformer in this specific embodiment. Specific Embodiment

[0049] The present invention will be further described in detail below with reference to the drawings:

[0050] I). Establishing the state space model of the current transformer

[0051] Referring to Figure 1 as shown, Figure 1 shows the equivalent circuit of the current transformer: the resistances and inductances of the primary and secondary windings are respectively modeled by R CT,1 , R CT,2 , L CT,1 and L CT,2 , and n CT is the turns ratio. The power loss and magnetization of the iron core are respectively modeled by the resistance R CT,c and the variable inductor L CT,m . The magnitude of L CT,m depends on the iron core magnetic flux of the current mutual inductance (λ T,m ) and can be obtained from the excitation curve or excitation test of the transformer. In addition, I CT,p , I CT,s ,, V CT,p and V CT,s respectively represent the primary current, secondary current, primary voltage and secondary voltage of the current transformer.

[0052] In order to obtain the primary current, the equivalent circuit of the primary side of the circuit transformer should be obtained. Referring to Figure 2As shown, in this figure, R b and L b represent the resistance and inductance of the current transformer load. However, for a current transformer, R CT,1 and L CT,1 are often ignored because in most current transformers, the primary winding has only one turn. In addition, R CT,c is usually also ignored because the core loss of the current transformer is usually negligible.

[0053] To obtain the state - space expression of the equivalent circuit in Figure 2 ), the KVL equations for the left, middle, and right loops are as follows:

[0054]

[0055] where λ CT,1 , λ CT,2 are the magnetic fluxes of the primary and secondary windings respectively, and are defined as follows:

[0056]

[0057] In equation (2), λ CT,l1 and are the leakage magnetic fluxes of the primary and secondary windings respectively, and λ T,m is the magnetic flux of the transformer core. Using equation (2) and the general magnetic - flux equation, the primary, secondary, and exciting currents of the transformer can be obtained using the following equations:

[0058]

[0059] Substituting equation (3) into equation (1) to obtain the state - space model of the current transformer, there is the following differential equation:

[0060]

[0061] where f(λ CT,m ) = 1 / L CT,m (λ CT,m ) is a function of λ CT,m . Assuming that L CT,m is bounded between and , f(λ CT,m ) is also bounded between and , as follows:

[0062]

[0063] Rewriting (4) in matrix form gives the following state - space representation:

[0064]

[0065] where A CT (λ CT,m ) is the state matrix of the current transformer, which is a function of λ CT,m , X CT is its state vector, B CT is its input matrix, U CT is its input vector, which only includes V CT,p . For the current transformer, V CT,p can be directly measured. The matrix A CT (λ CT,m ) and the vectors X CT and B CT are defined as follows:

[0066]

[0067] By taking I CT,s as the output, the output equation of the current transformer is defined as follows:

[0068] Y(t) = CX(t) (8)

[0069] where Y is the output vector and C is the output matrix, as follows:

[0070]

[0071] Assume that there is only one variable parameter in the state space model of the current transformer, i.e., f(λ CT,m ). It can be seen from Equation (5) that these parameters are all bounded. At this time, the state space model of the current transformer can be rewritten in the form of a polyhedron as follows:

[0072]

[0073] In the formula, the matrices and A( f CT ) are constant matrices; μ1 and μ2 are variable parameters, where μ1 and μ2 are defined as follows:

[0074]

[0075] II. Design of the Linear Parameter-Varying Observer LPV

[0076] To estimate the state of the above polyhedron equation, an observer must be designed such that: 1) it is accurate, i.e., the estimation error approaches zero as t → ∞; 2) it is stable. Existing research has shown that an observer of the following form can be used to estimate the state of the system in (10):

[0077]

[0078] In the formula, represents the estimated value of the state vector X(t), and Z(t) represents the state variable of the linear parameter varying observer LPV, represents the first derivative of Z(t); the matrices N1, N2, L1, L2, G, and H are all design matrices that satisfy the accuracy and stability conditions of the linear parameter varying observer LPV;

[0079] 1) Accuracy:

[0080] When t → ∞ then the observer of formula (12) is accurate. To meet this condition, the error of the observer, that is, can be obtained using (2) and (12):

[0081]

[0082] where P = I + HC, and I is the 3×3 identity matrix. By formulas (10) and (12), and differentiating formula (13), the dynamic error of the state estimation is obtained as:

[0083]

[0084] For the error to asymptotically approach zero, the following conditions must be met:

[0085]

[0086] By satisfying the constraints of formula (15), the right side of formula (14) is simplified to its first component, that is, (μ1N1 + μ2N2)e(t). Therefore, if the matrix (μ1N1 + μ2N2) is stable, the error of the observer will asymptotically approach zero.

[0087] 2) Stability:

[0088] To obtain a stable LPV observer, all the eigenvalues of (μ1N1 + μ2N2) in formula (14) should be located to the left of the imaginary axis in the complex plane. The following gives the sufficient conditions for ensuring the stability of the observer.

[0089] Theorem: If the common matrix φ = φ T ≥ 0 exists, then the polytopic LPV observer of formula (12) is asymptotically stable, such that

[0090] and

[0091] In summary, for the LPV observer designed for the current transformer to be stable and its error to approach zero, it is required that: 1) it is observable; 2) the conditions of formula (15) hold; 3) the conditions of formula (16) are satisfied.

[0092] (III) Calculation of the estimated value of the primary current and its application

[0093] Substitute the estimated value of the state vector into the flux equation of the primary current to calculate the estimated value of the primary current. The flux equation of the primary current is:

[0094]

[0095] In the formula, I CT,p represents the primary current, λ CT,m represents the core flux, λ CT,1 represents the magnetic flux linkage of the primary winding, and L CT,1 represents the inductance of the primary winding.

[0096] To make the present invention easier to understand, refer to Figure 3 the flowchart shown Figure 3 which shows the calculation process of the estimated value of the primary current. Among them, represents the estimated value of λ CT,m (t). The variable parameters μ1 and μ2 in the linear parameter varying observer LPV are updated through f(λ CT,m ). f(λ CT,m ) is continuously updated through the core flux λ CT,m to ensure the real-time nature of the primary current measurement.

[0097] A distribution transformer status detection method under current transformer saturation. The method uses the current measurement method under current transformer saturation of the present invention to obtain the estimated value of the primary current of the current transformer on the high voltage side of the distribution transformer and uses the estimated value of the primary current as the electrical parameter of the status detection device.

[0098] A distribution transformer status detection method under current transformer saturation. The method uses the current measurement method under current transformer saturation of the present invention to obtain the estimated value of the primary current of the current transformer on the high voltage side of the distribution transformer and uses the estimated value of the primary current as the electrical parameter of the status detection device.

[0099] The above technical solution is only one implementation mode of the present invention. For those skilled in the art, based on the disclosed principle of the present invention, it is very easy to make various types of improvements or deformations, not limited to the technical solution described in the above specific embodiments of the present invention. Therefore, the foregoing description is only preferred and does not have a restrictive meaning.

Claims

1. A current measurement method under current transformer saturation, characterized in that, Including the following steps: Establish a state - space model of the current transformer: construct the functional relationship between the state vector, input vector, and output vector. Among them, the state vector consists of the leakage flux of the primary winding, the leakage flux of the secondary winding, and the core flux, the input vector is the primary voltage, and the output vector is the secondary current; Rewrite the state - space model into a polyhedron form and design a corresponding linear parameter - varying (LPV) observer to observe the state - space model in polyhedron form based on the input vector and output vector, so as to obtain the estimated value of the state vector; Substitute the estimated value of the state vector into the flux equation of the primary current to calculate the estimated value of the primary current; The state - space model of the current transformer is as follows: wherein, X(t) represents a state vector, X(t) = [λ CT,1 λ CT,2 λ CT,m T , λ CT,1 represents the magnetic flux of the primary winding, λ CT,2 represents the magnetic flux of the secondary winding, λ CT,m represents the core magnetic flux; represents the first derivative of X(t); A(λ CT,m ) represents a state matrix, A(λ CT,m ) is a function of the core magnetic flux λ CT,m ; B represents an input matrix, B = [1 0 0] T ; U(t) represents an input vector, U(t) = [V CT,p , V CT,p represents the primary voltage; Y(t) represents an output vector, Y(t) = [I CT,s , I CT,s represents the secondary current; C represents an output matrix;​ State matrix A(λ CT,m ) is as follows: where R CT,1 represents the resistance of the primary winding, L CT,1 represents the inductance of the primary winding, R CT,2 represents the resistance of the secondary winding, L CT,2 represents the inductance of the secondary winding, R b represents the resistance of the current transformer load, L b represents the inductance of the current transformer load, λ CT,m represents the core magnetic flux, n CT represents the turns ratio, R CT,c represents the resistance of the core; f(λ CT,m ) = 1 / L CT,m (λ CT,m ), where L CT,m (λ CT,m ) is a function of λ CT,m , and L CT,m represents a variable inductor, the magnitude of L CT,m depends on the core flux λ CT,m of the current transformer and is obtained from the excitation curve or excitation test of the current transformer.

2. The method for measuring current under current transformer saturation according to claim 1, wherein The output matrix C is as follows: where n CT represents the turns ratio, L b represents the inductance of the current transformer load, and L CT,2 represents the inductance of the secondary winding.

3. The method for measuring current under the saturation of a current transformer according to claim 1, characterized in that The state - space model in polyhedron form: wherein, the matrix and are constant matrices; μ1 and μ2 are variable parameters, wherein, μ1 and μ2 are defined as follows: Assume L CT,m is bounded between and , where is the upper bound of L CT,m , and is the lower bound of L CT,m . f(λ CT,m ) is also bounded between and as follows:

4. The method for measuring current under current transformer saturation according to claim 3, characterized in that, From the state matrix A(λ CT,m ) split out 5. The method for measuring current under current transformer saturation according to claim 3, characterized in that, The linear parameter - varying (LPV) observer is as follows: In the formula, represents the estimated value of the state vector X(t), and Z(t) represents the state variable of the linear parameter varying observer LPV, represents the first derivative of Z(t); the matrices N1, N2, L1, L2, G, and H are all design matrices that satisfy the accuracy and stability conditions of the linear parameter varying observer LPV; To make the error of the linear parameter - varying (LPV) observer asymptotically zero, the following accuracy conditions must be met: PB - G = 0 where P = I+HC, I is a 3×3 identity matrix, and C represents the output matrix; For the linear parameter - varying (LPV) observer to be asymptotically stable, the following stability conditions must be met: and Among them, represents a common matrix, 6. The method for measuring current under current transformer saturation according to claim 1, characterized in that The flux equation of the primary current: Where, I CT,p represents the primary current, λ CT,m represents the core magnetic flux, λ CT,1 represents the magnetic linkage of the primary winding, L CT,1 represents the inductance of the primary winding.

7. A method for detecting the state of a distribution transformer under the saturation of a current transformer, characterized in that, Obtain the estimated value of the primary current of the current transformer on the high-voltage side of the distribution transformer by using the current measurement method under current transformer saturation as described in any one of claims 1 to 6 And use the estimated value of the primary current As the electrical parameter of the state detection device.

8. A distribution transformer protection method under the saturation of a current transformer, characterized in that, Obtain an estimated value of the primary current of the current transformer on the high-voltage side of the distribution transformer by using the current measurement method under current transformer saturation as described in any one of claims 1 to 6 And use the estimated value of the primary current As the electrical parameter of the protection device.

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