Voltage measurement method and power protection method under CVT transient response

Abstract

The present invention belongs to the field of voltage transformers and power system protection applications. To address the technical problem of difficulty in providing a voltage parameter suitable for power device decision-making during a transient response, the present invention provides a voltage measurement method and power protection method for CVT transient response. The method uses the primary voltage of the CVT as the measured quantity; establishes a discretized state-space model of the CVT equivalent circuit; uses the equivalent input voltage as the unknown input quantity, and establishes the relationship between the model output quantity, model state quantity, and the unknown input quantity; uses an unknown input observer (UIO) to estimate the unknown input quantity based on the collected model output quantity, thereby obtaining an estimated value of the equivalent input voltage; calculates an estimated value of the primary voltage based on the voltage divider ratio of the equivalent input voltage to the primary voltage and the estimated value of the equivalent input voltage, and the power protection device makes decisions based on the estimated value of the primary voltage. The present invention ensures the sensitivity and operating speed of the power protection device.

Description

Technical Field

[0001] The present invention relates to the field of voltage transformer and power system protection applications, and in particular to a voltage measurement method and a power protection method under CVT transient response. Background Art

[0002] A capacitive voltage transformer (CVT) is a cost-effective voltage conversion device that converts the high voltage (primary voltage) of a high-voltage or low-voltage circuit into a low voltage (secondary voltage). This secondary voltage serves as a reference quantity for instruments and relay protection devices, enabling measurement, metering, and protection. However, CVTs can exhibit poor transient response—that is, in the first few cycles after a disturbance, their secondary voltage may not closely track their primary voltage.

[0003] This poor response due to energy storage elements (such as coupling capacitors and compensation inductors) is more severe when the system impedance ratio (SIR) is large or the secondary load is highly inductive. As a result, the transient behavior of the CVT can lead to inaccurate voltage measurements and jeopardize the correct operation of equipment or solutions that require accurate measurements. The impact of this inaccuracy is most evident in power system protection applications, because when the transient response of the CVT is still present and the voltage measurement is inaccurate, the protection relay must make decisions quickly after a fault. Of all the protection devices, distance relays are the most susceptible to inaccurate CVT measurement results because they are prone to false tripping outside the fault range and disconnecting the transmission line.

[0004] The problem of distance relay overruns caused by CVT transients has traditionally been addressed by:

[0005] 1) Reduce the range of the relay;

[0006] 2) Introduce a fixed delay for region 1;

[0007] 3) Detect high SIR conditions and apply additional filtering to the measured voltage or introduce a delay in the relay's output decision.

[0008] However, the first two solutions only compromise between distance relay sensitivity and speed; the third approach struggles to accurately detect high SIR conditions. To address these issues, commercial off-the-shelf relays are equipped with more advanced solutions. However, some solutions depend on system parameters, and their performance is affected by changes in system topology; others slow the relay down when approaching the fault point. Furthermore, to address distance relay overruns caused by CVT transients, digital filters and artificial neural networks are widely used, but these solutions often suffer from at least the following drawbacks:

[0009] 1) A large amount of data is required for training;

[0010] 2) Affect the voltage waveform while eliminating CVT transient response;

[0011] 3) Depends on the operating point and parameters of the system;

[0012] 4) introducing delays in the operation of relays;

[0013] 5) High cost.

[0014] Therefore, how to accurately, efficiently and cost-effectively solve the measurement error caused by CVT transient response is a problem worthy of study and needs to be solved urgently. Summary of the Invention

[0015] The purpose of the present invention is to solve the above-mentioned difficulties in the prior art and provide a voltage measurement method under CVT transient response to solve the technical problem that it is difficult to provide a voltage parameter suitable for power device decision-making when a transient response occurs.

[0016] The present invention is achieved through the following technical solution: a method for measuring voltage under CVT transient response, wherein the CVT includes a capacitive voltage divider and a voltage transformer, wherein the primary voltage is divided by the capacitor to obtain an equivalent input voltage, and the equivalent input voltage is transmitted to the voltage transformer through the turns ratio to generate a secondary voltage, comprising the following steps:

[0017] The primary voltage of the CVT is taken as the measurement;

[0018] Establishing a discretized state space model of the CVT equivalent circuit: using the equivalent input voltage as an unknown input quantity, establishing a relationship between the model output quantity, the model state quantity, and the unknown input quantity;

[0019] Using an unknown input observer UIO, and estimating an unknown input quantity based on the collected model output quantity, thereby obtaining an estimated value of the equivalent input voltage;

[0020] The estimated value of the primary voltage is calculated according to the voltage division ratio of the equivalent input voltage to the primary voltage and the estimated value of the equivalent input voltage, thereby obtaining the value to be measured.

[0021] Furthermore, the following parameters in the CVT equivalent circuit are used as model outputs: CVT compensation reactor current i1, load current i s and the secondary voltage V s ;

[0022] The following current and voltage parameters in the CVT equivalent circuit are used as model state variables:

[0023] Current parameters include: compensation reactor current i1, voltage transformer primary current i2, voltage transformer secondary current i3, protection relay current is , the magnetizing inductance current i on the secondary side of the voltage transformer m And the inductor current i in the ferromagnetic resonance suppression circuit f ;

[0024] Voltage parameters include: represents the voltage divided by the equivalent capacitor in the Thevenin equivalent circuit of the capacitive voltage divider, represents the voltage division of the stray capacitance C3 on the primary side of the voltage transformer, Indicates the voltage division of the filter capacitor of the ferromagnetic resonant filter in the voltage transformer.

[0025] Furthermore, the discretized state space model of the CVT equivalent circuit is expressed as follows:

[0026] X[k+1]=AX[k]+BV T [k]

[0027] Y[k]=CX[k]

[0028] Where X[k] represents the model state at time k; Y[k] represents the model output at time k; V T [k] represents the unknown input at time k; A represents the discretized state matrix, B represents the discretized input matrix, and C represents the discretized output matrix.

[0029] Furthermore, the discretized state matrix A is: T s represents the discrete time step, A C Represents a continuous state matrix:

[0030]

[0031] Where n represents the turns ratio, C e represents the equivalent capacitance in the Thevenin equivalent circuit of the capacitor voltage divider, C3 represents the stray capacitance on the primary side of the voltage transformer, and C f Represents the filter capacitor of the ferromagnetic resonance filter, R C Indicates the resistance of the iron core on the primary side of the voltage transformer, R f Represents the filter resistance of the ferromagnetic resonance filter, R represents the compensation reactor resistance, R1 represents the resistance of the primary side of the voltage transformer, R2 represents the resistance of the secondary side of the voltage transformer, L0 represents the load inductance, L1 represents the inductance of the primary side of the voltage transformer, L2 represents the inductance of the secondary side of the voltage transformer, L m It represents the magnetizing inductance of the iron core on the primary side of the voltage transformer, and L represents the inductance of the compensation reactor.

[0032] Furthermore, the discretized input matrix B is: Ts represents the discrete time step, A C represents the continuous state matrix, B c represents a continuous input matrix;

[0033]

[0034] Where n represents the turns ratio, and L represents the inductance of the compensation reactor.

[0035] Furthermore, the discretized output matrix C is:

[0036] Where, T s represents the discrete time step, C c represents a continuous state matrix;

[0037]

[0038] Where R f Indicates the filter resistance of the ferromagnetic resonance filter.

[0039] Furthermore, the model output on a window of size l+1, i.e., Y[k] to Y[k+l], is collected and given to the unknown input observer UIO to estimate the model state X[k] at time k, according to the following formula:

[0040]

[0041] Where, Represents the estimated value of the model state, and E and F are both UIO matrices; the E and F matrices are designed as follows:

[0042] E=A-FO L

[0043] Where, O L =[C T (CA) T … (CA L ) T ] T

[0044] F=[F1 F2]N

[0045] Where, F2=B,

[0046] N∈R 8×9 , and is determined by the following formula:

[0047]

[0048]

[0049] Where O is the zero matrix;

[0050] Matrix F1 is designed to stabilize UIO, S1 and S2 are represented by NO L The two sub-matrices decomposed.

[0051] Furthermore, the estimated value of the model state quantity is substituted into the following formula to calculate the estimated value of the equivalent input voltage:

[0052]

[0053] Where, is the estimated value of the equivalent input voltage at time k, and G is a matrix satisfying GB=1.

[0054] Furthermore, the estimated value of the primary voltage is calculated as follows:

[0055]

[0056] Where C1 and C2 represent the capacitance of the two series capacitors in the capacitive voltage divider; Represents an estimate of the primary voltage.

[0057] The present invention also provides a power protection method under CVT transient response, which adopts the voltage measurement method under CVT transient response of the present invention to obtain an estimated value of the primary voltage, and the power protection device makes a decision based on the estimated value of the primary voltage.

[0058] Compared with the prior art, the present invention has the following beneficial effects:

[0059] 1. The present invention uses the primary voltage as the measured value to alleviate the secondary voltage distortion caused by the deviation transient response of the CVT, thereby providing a voltage parameter suitable for power device decision-making when a transient response occurs.

[0060] 2. The present invention enables power system protection equipment, such as relays, to effectively solve the problem of CVT deviation transient response and the resulting over-limit problem of distance relays under the condition of CVT secondary voltage distortion while ensuring the sensitivity and operating speed of the power protection device.

[0061] 3. The present invention models a CVT in state space representation and uses unknown input observations to estimate the state and primary voltage of the CVT, and models it as an unknown input with significant independence from system parameters and fault parameters, which can be implemented as a built-in function of the power system relay. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 is the equivalent circuit diagram of the capacitive voltage transformer CVT;

[0063] Figure 2 The Thevenin equivalent conversion circuit diagram of the capacitive voltage transformer CVT;

[0064] Figure 3 Flowchart for calculating the estimated value of the CVT primary voltage according to this embodiment. DETAILED DESCRIPTION

[0065] The present invention is further described in detail below with reference to the accompanying drawings:

[0066] 1) Establish a discretized state space model of the CVT equivalent circuit

[0067] refer to Figure 1 As shown, the equivalent circuit of the capacitor voltage transformer CVT is established, V p It represents the voltage before passing through the capacitor voltage divider (including coupling capacitors C1 and C2), compensation reactor L and its resistor R, transformer core, etc., i.e. primary voltage; V T Indicates the equivalent input voltage obtained by dividing the primary voltage by the capacitors (coupling capacitors C1 and C2); the equivalent input voltage V T The voltage is transferred to the voltage transformer through the turns ratio n to generate the secondary voltage.

[0068] refer to Figure 2 As shown in the figure, the Thevenin equivalent conversion circuit of the capacitive voltage transformer CVT (the capacitive voltage divider of the CVT is replaced by its equivalent Thevenin voltage divider, and the primary of the CVT is converted to the secondary, that is, all primary side parameters are transferred to the secondary side), is composed of V T =V p ×C1 / (C1+C2)Thevenin voltage and C e =C1+C2 equivalent capacitance composition, and all parameters are transferred to V using its turns ratio (i.e. n) T The secondary side. V T / n represents the equivalent primary voltage after conversion, V s is the secondary voltage of the CVT for power system applications. The state space model of the CVT is obtained by combining Figure 1 The differential equation associated with the equivalent circuit is written as follows:

[0069]

[0070]

[0071]

[0072]

[0073]

[0074]

[0075]

[0076]

[0077]

[0078] Where i1, i2, i3 and i s They represent the currents of the compensation reactor, the primary of the voltage transformer, the secondary of the voltage transformer, and the protection relay, respectively. All currents are transferred to the secondary of the voltage transformer. In addition, i m and i f It is the magnetizing inductance current transmitted to the secondary side and the inductance current in the ferroresonance suppression circuit.

[0079] Rearranging these equations in matrix form gives:

[0080]

[0081] Where V T (t) is the unknown input, A C ∈R 9×9 is the state matrix, expressed as formula (3). In addition, X(t)∈R 9×1 、B C ∈R 9×1 are the state vector and input matrix respectively, as shown in the following equations.

[0082]

[0083]

[0084]

[0085] Determine the output equation. Select the CVT input, output current, and output voltage as the output of the model. The output equation of the state-space model is expressed as:

[0086] Y(t)=C c X(t) (5)

[0087] Where C C ∈R 3×9 is the output matrix, defined as follows.

[0088]

[0089] The obtained state space equations (2) and (5) are suitable for numerical implementation in digital relays. The continuous matrix in (2) and A C and BC Discretized into .

[0090]

[0091]

[0092] Where, T s represents the discrete time step, the discretization model of CVT can be expressed as

[0093] X[k+1]=AX[k]+BV T [k] (8a)

[0094] Y[k]=CX[k] (8b)

[0095] Where X[k] and Y[k] are the state and output vectors at time k respectively. T [k] represents the equivalent input voltage of the CVT at time k.

[0096] 2) Use unknown input observer UIO to estimate the primary voltage of CVT

[0097] Real-time acquisition of CVT secondary voltage V s The sampling values ​​of the primary current (i.e., the compensation reactor current i1) and the secondary current (i.e., the load current i s ) and combines it with the CVT state-space model for estimation. At each moment, the UIO uses the system state at the previous moment, as well as the system's output and known inputs, to estimate the current state and unknown inputs. To estimate the system state at time k (i.e., X[k]), the UIO samples the output signal over a window of size l+1 (i.e., Y[k] to Y[k+l]). The value of l depends on the system parameters, as shown below.

[0098] From time k to time k+1, the matrix form is as follows.

[0099] Y[k:k+1]=O L X[k]+J L V T [k:k+l] (9)

[0100] Where, T s is a discrete moment, so the discrete model of CVT is.

[0101] Y[k:k+l]=[Y[k] T Y[k+1] T …Y[k+l] T ] T (10a)

[0102] O L=[C T (CA) T … (CA L ) T ] T (10b)

[0103] V T [k:k+l]=[V T [k]V T [k+1]…V T [k+l]] T (10c)

[0104]

[0105] Where O is a zero matrix. The UIO of the estimated system state and unknown input at time k to k+1 is expressed as:

[0106]

[0107] Where, is the vector of estimated state, and E and F are UIO matrices. The two matrices E and F are designed as follows:

[0108] 1) When the error (difference between the estimated state and the actual state) is close to zero, the error of the UIO is obtained using (8a) and (11) as follows:

[0109]

[0110] By substituting Y[k:k+L] from equation (9).

[0111] e[k+1]=Ee[k]-(E-A+FO L )X[k]+FJ L V T [k:k+l]-BV T [k] (13)

[0112] When the following equation holds true, the UIO error converges to zero.

[0113] FJ L =[BO 9×1 … O 9×1 ] (14a)

[0114] E=A-FO L (14b)

[0115] First, we get F, and then we use equation (14b) to get the matrix E. When the following equation holds, the matrix satisfies (14a).

[0116] rank(J L)-rank(J L-1 )=1 (15)

[0117] Where, J L-1 Calculated by the following formula.

[0118]

[0119] Equation (15) is a necessary condition for the F matrix to satisfy (14a). By entering A, B, and C into equations (10d) and (16), we can calculate J L and J L-1 It has been proved that when l = 2, equation (15) is satisfied. Equation (15) is established, and the following form of F matrix satisfies equation (14a):

[0120] F=[F1 F2]N (17)

[0121] Where F2 is equal to B, and N∈R 8×9 It can be determined by the following formula.

[0122]

[0123] 2) The matrix F1 is designed to stabilize the UIO, i.e. to place the poles at the desired locations. By substituting Eq. (18) into Eq. (14b) and replacing NO L Decompose it into two sub-matrices S1 and S2, which are multiplied by the sub-matrices of F1 and F2 respectively, and the following equation is obtained:

[0124] E=(A-BS2)-F1S1 (19)

[0125] Where S1 and S2 are respectively composed of NO L If the following conditions are met, F1 stabilizes UIO.

[0126]

[0127] Use (11) to estimate the state of the system at each moment. Unknown input, that is, V T , can also be estimated at each moment using the following equation.

[0128]

[0129] Where, is the estimated value at time k, and G is a matrix satisfying GB = 1. Therefore, the estimated primary voltage of the CVT can be obtained using the following equation.

[0130]

[0131] Where C1 and C2 represent the capacitance of the two series capacitors in the capacitive voltage divider; Represents an estimate of the primary voltage.

[0132] In order to make the technical solution of the present invention easier to understand, the attached Figure 3 The flowchart for calculating the estimated value of the CVT primary voltage in this specific embodiment is shown as follows: the offline stage is used to complete the parameter calculation of the state space model (preparatory work); in the online stage, the UIO and its secondary voltage sampling values ​​are used to estimate the CVT primary voltage.

[0133] The above technical solution is only one embodiment of the present invention. For those skilled in the art, it is easy to make various types of improvements or modifications based on the principles disclosed in the present invention, and it is not limited to the technical solution described in the above specific embodiments of the present invention. Therefore, the above description is only preferred and does not have a restrictive meaning.

Claims

1. A method for measuring voltage during CVT transient response. The CVT includes a capacitive voltage divider and a voltage transformer. A primary voltage is divided by the capacitor to obtain an equivalent input voltage. The equivalent input voltage is transferred to the voltage transformer through a turns ratio to generate a secondary voltage. The method is characterized by: The primary voltage of the CVT is taken as the measurement; Establish a discretized state space model of the CVT equivalent circuit: take the equivalent input voltage as the unknown input, and establish the relationship between the model output, model state, and the unknown input. The discretized state space model of the CVT equivalent circuit is expressed as follows: X[k+1]=AX[k]+BV T [k] Y[k]=CX[k] Where X[k] represents the model state at time k; Y[k] represents the model output at time k; V T [k] represents the unknown input at time k; A represents the discretized state matrix, B represents the discretized input matrix, and C represents the discretized output matrix; The discretized state matrix A: T s represents the discrete time step, A C Represents a continuous state matrix: Where n represents the turns ratio, C e represents the equivalent capacitance in the Thevenin equivalent circuit of the capacitor voltage divider, C3 represents the stray capacitance on the primary side of the voltage transformer, and C f Represents the filter capacitor of the ferromagnetic resonance filter, R C Indicates the resistance of the iron core on the primary side of the voltage transformer, R f Represents the filter resistance of the ferromagnetic resonance filter, R represents the compensation reactor resistance, R1 represents the resistance of the primary side of the voltage transformer, R2 represents the resistance of the secondary side of the voltage transformer, L0 represents the load inductance, L1 represents the inductance of the primary side of the voltage transformer, L2 represents the inductance of the secondary side of the voltage transformer, L m represents the magnetizing inductance of the iron core on the primary side of the voltage transformer, and L represents the inductance of the compensation reactor; The discretized input matrix B is: T s represents the discrete time step, A C represents the continuous state matrix, B c represents a continuous input matrix; Where n represents the turns ratio, and L represents the inductance of the compensation reactor; The discretized output matrix C is: Where, T s represents the discrete time step, C c represents a continuous state matrix; Where R f Indicates the filter resistance of the ferromagnetic resonance filter; Using an unknown input observer UIO, and estimating an unknown input quantity based on the collected model output quantity, thereby obtaining an estimated value of the equivalent input voltage; The estimated value of the primary voltage is calculated according to the voltage division ratio of the equivalent input voltage to the primary voltage and the estimated value of the equivalent input voltage, thereby obtaining the value to be measured.

2. The voltage measurement method under CVT transient response according to claim 1, characterized in that: The following parameters in the CVT equivalent circuit are used as model outputs: CVT compensation reactor current i1, load current i s and the secondary voltage V s ; The following current and voltage parameters in the CVT equivalent circuit are used as model state variables: Current parameters include: compensation reactor current i1, voltage transformer primary current i2, voltage transformer secondary current i3, protection relay current i s , the magnetizing inductance current i on the secondary side of the voltage transformer m And the inductor current i in the ferromagnetic resonance suppression circuit f ; Voltage parameters include: represents the voltage divided by the equivalent capacitor in the Thevenin equivalent circuit of the capacitive voltage divider, represents the voltage division of the stray capacitance C3 on the primary side of the voltage transformer, Indicates the voltage division of the filter capacitor of the ferromagnetic resonant filter in the voltage transformer.

3. The voltage measurement method under CVT transient response according to claim 1, characterized in that: The model output on the window of size l+1, that is, Y[k] to Y[k+l], is collected and given to the unknown input observer UIO to estimate the model state X[k] at time k, according to the following formula: Where, Represents the estimated value of the model state, and E and F are both UIO matrices; the E and F matrices are designed as follows: E=A-FO L Where, O L =[C T (CA) T …(CA L ) T ] T F=[F1 F2]N Where, F2=B, N∈R 8×9 , and is determined by the following formula: Where O is the zero matrix; Matrix F1 is designed to stabilize UIO, S1 and S2 are represented by NO L The two sub-matrices decomposed.

4. The voltage measurement method under CVT transient response according to claim 3, characterized in that: Substitute the estimated value of the model state quantity into the following formula to calculate the estimated value of the equivalent input voltage: Where, is the estimated value of the equivalent input voltage at time k, and G is a matrix satisfying GB=1.

5. The voltage measurement method under CVT transient response according to claim 4, characterized in that: The estimated value of the primary voltage is calculated as follows: Where C1 and C2 represent the capacitance of the two series capacitors in the capacitive voltage divider; Represents an estimate of the primary voltage.

6. A power protection method under CVT transient response, characterized in that: The voltage measurement method under CVT transient response as claimed in any one of claims 1 to 5 is used to obtain an estimated value of the primary voltage, and the power protection device makes a decision based on the estimated value of the primary voltage.

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