CN113190949B - Time domain construction method of CVT (continuously variable transmission) broadband simulation model - Google Patents

Abstract

The invention discloses a time-domain construction method of a CVT broadband simulation model. The steps include: 1) using a network analyzer to obtain the scattering parameter matrix S of the CVT, and calculating the voltage transmission characteristic H of the CVT; 2) converting the voltage transmission characteristic H into A continuous state-space equation in the time domain; 3) converting the continuous state-space equation into a circuit model, thereby obtaining a CVT broadband simulation model. The time domain construction method of the capacitive voltage transformer broadband simulation model proposed by the present invention is simple, and only needs a network analyzer to realize the measurement of scattering parameters, which solves the difficulty of passive correction of the current CVT broadband simulation model and easily leads to accuracy After the network is synthesized, there are many circuit components and complex model structure, etc. CVT modeling problems.

Description

A Time Domain Construction Method of CVT Wideband Simulation Model

technical field

The invention relates to the field of electric power technology, in particular to a method for constructing a CVT broadband simulation model in the time domain.

Background technique

As an important primary device in the power system, the CVT adopts the method of capacitor voltage division and multi-stage step-down of the electromagnetic unit to obtain the standard secondary side voltage. It not only has all the functions of the conventional electromagnetic transformer, but also effectively suppresses the capacitance parameters in the power grid. The ferromagnetic resonance caused by matching is an important basis for the measurement, protection and control of power systems. However, due to the complex structure of the CVT and the changeable application scenarios, although in the steady state operation stage, the secondary side voltage of the CVT only follows the primary side signal change, once a high frequency transient occurs, the output of the CVT will not be able to follow the change of the primary side. It is easy to cause the malfunction of the relay, and cause great trouble to the control protection and fault location based on the CVT transient signal. Therefore, it is necessary to establish an accurate CVT broadband simulation model to provide a basic model for power system analysis and protection research.

At present, the research on CVT broadband simulation model mainly adopts the black box model, but the structure of the traditional black box model is complex, and there are micro passive problems, the passive circuit will cause the model to be unstable and easy to diverge, and the passive correction will cause the model Accuracy is reduced. Therefore, it is necessary to further explore the construction method of the CVT broadband simulation model.

Contents of the invention

The object of the present invention is to provide a kind of time domain construction method of CVT broadband simulation model, comprises the following steps:

1) Obtain the scattering parameter matrix S of the CVT by using a network analyzer, and calculate the voltage transmission characteristic H of the CVT.

The scattering parameter matrix S of the CVT is as follows:

In the formula, S ₁₁ , S ₁₂ , S ₂₁ , and S ₂₂ represent the scattering parameters of the CVT port. Subscript 1 and subscript 2 indicate the serial number of the CVT port.

The voltage transfer characteristic H of the CVT is as follows:

2) Converting the voltage transfer characteristic H into a continuous state-space equation in the time domain, the steps include:

2.1) Use the vector matching method to fit the voltage transfer characteristic H to the state space equation H(s), namely:

H(s)＝C(sI-A) ^-1 B+D+sE (3)

In the formula, A is an N-order diagonal matrix with poles as diagonal elements. B is a unit matrix of order N×1. C is a residue matrix of order 1×N. D and E are constants, and the linear term E is usually set to 0 during the fitting process. I is a unit vector. s=jω represents a Laplacian operator.

2.2) Utilizing the reverse pull transformation to transform the state-space equation (3) into the continuous state-space equation of the time domain shown in formula (5), the steps include:

2.2.1) Set the state variable x and the output variable as follows:

In the formula, u is the voltage.

2.2.2) According to the formula (4), the state-space equation (3) is reversed to Laplace transform, and the continuous state-space equation in the time domain is obtained:

In the formula, k is the kth moment. x _k is the state variable at the kth moment. y _k is the output current variable at the kth moment. u _k is the voltage variable at the kth moment. x' _k is a continuous state variable.

3) converting the continuous state space equation into a circuit model, thereby obtaining a CVT broadband simulation model, the steps include:

3.1) Using the central difference method to discretize the continuous state space equation, we get:

In the formula, h is the sampling time. x _k+1 is the state variable at the k+1th moment. u _k+1 is the voltage variable at the k+1th moment. y _k+1 is the output current variable at the k+1th moment.

3.2) Formula (6) is simplified to obtain:

Among them, vector α and vector μ are as follows:

α＝(2I-Ah) ^-1 (2I+Ah) (8)

μ＝(2I-Ah) ^-1 h (9)

3.3) The modified state variable is:

为k+1时刻状态变量修正值。In the formula,

is the corrected value of the state variable at time k+1.

3.4) Substitute formula (10) into formula (7) to get:

为k时刻状态变量修正值。In the formula,

is the corrected value of the state variable at time k.

矩阵G如下所示：Among them, the identity matrix

The matrix G looks like this:

G＝D+CμB (13)

更新公式(11)，得到CVT宽频仿真模型：3.4) Let the output vector

Update formula (11) to get the CVT broadband simulation model:

In the formula, i _s,k is the time-domain current vector at time k. y _s,k+1 is the time domain output vector at time k+1.

The technical effect of the present invention is unquestionable. The time domain construction method of the capacitive voltage transformer broadband simulation model proposed by the present invention is simple, and only a network analyzer is needed to realize the measurement of scattering parameters, which solves the problem of the current CVT broadband simulation model. Passive correction of the simulation model is difficult and easily leads to a decrease in accuracy. After network synthesis, there are many circuit components and complex model structures. CVT modeling problems.

Description of drawings

Figure 1 is a schematic diagram of scattering parameter measurement;

Fig. 2 is the fitting result of voltage transfer function;

Figure 3 is the Norton equivalent structure;

Figure 4 is the experimental waveform of lightning impulse voltage

Figure 5 shows the comparison between the measured lightning voltage waveform of the CVT and the simulation results;

Figure 6 is a flowchart of the method.

Detailed ways

The present invention will be further described below in conjunction with the examples, but it should not be understood that the scope of the subject of the present invention is limited to the following examples. Without departing from the above-mentioned technical ideas of the present invention, various replacements and changes made according to common technical knowledge and conventional means in this field shall be included in the protection scope of the present invention.

Example 1:

Referring to Fig. 1 to Fig. 6, a kind of time-domain construction method of CVT (capacitive voltage transformer) broadband simulation model comprises the following steps:

1) Obtain the scattering parameter matrix S of the CVT by using a network analyzer, and calculate the voltage transmission characteristic H of the CVT. The time-domain construction method of CVT broadband simulation model is used to establish the broadband time-domain circuit model of capacitive voltage transformer.

The scattering parameter matrix S of the CVT is as follows:

In the formula, S ₁₁ , S ₁₂ , S ₂₁ , and S ₂₂ represent the scattering parameters of the CVT port. Subscript 1 and subscript 2 indicate the serial number of the CVT port.

The voltage transfer characteristic H of the CVT is as follows:

2) Converting the voltage transfer characteristic H into a continuous state-space equation in the time domain, the steps include:

2.1) Use the vector matching method to fit the voltage transfer characteristic H to the state space equation, namely H(s):

H(s)＝C(sI-A) ^-1 B+D+sE (3)

In the formula, A is an N-order diagonal matrix with poles as diagonal elements. B is a unit matrix of order N×1. C is a residue matrix of order 1×N. D and E are constants, and the linear term E is usually set to 0 during the fitting process. I is a unit vector. s represents the Laplacian operator, s=jω

2.2) Utilize the inverse pull transformation to transform the state-space equation (3) into the continuous state-space equation in the time domain shown in formula (5), the steps are as follows:

make:

In the formula, u is the voltage.

By inverse Laplace transform, the continuous state-space equation in the time domain is obtained:

In the formula, k is the kth moment. x _k is the state variable at the kth moment. y _k is the output current variable at the kth moment. u _k is the voltage variable at the kth moment. x' _k is a continuous state variable.

3) converting the continuous state space equation into a circuit model, thereby obtaining a CVT broadband simulation model, the steps include:

3.1) Using the central difference method to discretize the continuous state space equation, we get:

In the formula, h is the sampling time. x _k+1 is the state variable at the k+1th moment. u _k+1 is the voltage variable at the k+1th moment. y _k+1 is the output current variable at the k+1th moment.

3.2) Formula (6) is simplified to obtain:

Among them, vector α and vector μ are as follows:

α＝(2I-Ah) ^-1 (2I+Ah) (8)

μ＝(2I-Ah) ^-1 h (9)

3.3) The modified state variable is:

为k+1时刻状态变量修正值。In the formula,

is the corrected value of the state variable at time k+1.

3.4) Substitute formula (10) into formula (7) to get:

为k时刻状态变量修正值。In the formula,

is the corrected value of the state variable at time k.

矩阵G如下所示：Among them, the identity matrix

The matrix G looks like this:

G＝D+CμB (13)

更新公式(11)，得到CVT宽频仿真模型：3.4) Let the output vector

Update formula (11) to get the CVT broadband simulation model:

In the formula, i _s,k is the time-domain current vector at time k. y _s,k+1 is the time domain output vector at time k+1.

The CVT broadband simulation model (14) is used to reflect the CVT running state.

Example 2:

A time-domain construction method of a CVT (capacitive voltage transformer) broadband simulation model, comprising the following steps:

1) Obtain the scattering parameter matrix S of the CVT by using a network analyzer, and calculate the voltage transmission characteristic H of the CVT.

The specific method to calculate the broadband voltage transfer function from the scattering parameters is as follows:

Consider the CVT as a two-port network, use the network analyzer E5061B to obtain the scattering parameter matrix S of the CVT, and calculate the voltage transfer function of the CVT, the formula is:

2) The voltage transfer characteristic H is fitted and transformed into a state-space equation in the time domain by vector matching method and reverse pull transformation.

The voltage transfer function is fitted to the form of state space equation by vector matching method, the formula is:

H(s)＝C(sI-A) ^-1 B+D+sE

make:

Through the reverse pull transformation, the above equation is transformed into a continuous state space equation in the time domain:

In the formula, k is the kth moment. x _k is the state variable at the kth moment. y _k is the output current variable at the kth moment. u _k is the voltage variable at the kth moment.

Among them, A is an N-order diagonal matrix with poles as diagonal elements. B is a unit matrix of order N×1. C is a residue matrix of order 1×N. D and E are constants. In the process of vector matching, the linear item is generally 0, so E=0 can be set.

3) Convert the mathematical model into a circuit model through the discrete state equation and Norton equivalent, and establish an accurate CVT broadband simulation model.

The concrete method of described broadband admittance model construction is:

Using the central difference method to discretize the continuous state space equation, the discrete state equation is equivalent to a current source structure with Norton equivalent

Among them, h is the sampling time.

Simplify further to get:

in:

α＝(2I-Ah) ^-1 (2I+Ah)

μ＝(2I-Ah) ^-1 h

make:

but:

in:

G=D+CμB

make:

but:

Example 3:

The experiment of applying the method of constructing the broadband simulation model of capacitive voltage transformer based on the discrete state equation, the steps include:

准确级为：0.2/0.5/3P，额定容量为10/10/10VA，额定变比为350:1的电容式电压互感器，利用上述方法测量和获取CVT的宽频仿真模型参数和结构。1) Select a rated voltage

Accuracy class: 0.2/0.5/3P, rated capacity 10/10/10VA, rated transformation ratio 350:1 capacitive voltage transformer, use the above method to measure and obtain the CVT broadband simulation model parameters and structure.

2) According to the experimental platform shown in Figure 1, the CVT is regarded as a two-port network, and the network analyzer E5061B is used to obtain 4801 frequency points that obey the logarithmic distribution within 5 Hz to 1 MHz and the corresponding scattering parameters S, and calculate CVT broadband voltage transfer function H.

3) The voltage transfer characteristic H is fitted and converted by vector matching method and reverse pull transformation. The results are shown in Figure 2. The solid line in the figure is the measured voltage waveform on the low-voltage side of the CVT, and the dashed line is the voltage waveform on the simulated CVT low-voltage side. . All voltage amplitudes in Figures 2, 4, and 5 are normalized based on the input voltage.

By discretizing the state equation and Norton equivalent, the CVT broadband admittance mathematical model is converted into a broadband admittance circuit model as shown in Figure 3, and an accurate CVT broadband simulation model is established.

4) According to the above data, build a CVT broadband simulation model circuit, and apply the lightning impulse voltage waveform shown in Figure 4 on the high voltage side of the CVT. At the same time, the waveform is used as the model input signal and applied to the CVT broadband simulation model established in this paper. The measured and simulated results of the low-voltage side voltage waveform are shown in Figure 5. The solid line in the figure is the measured CVT low-voltage side voltage waveform, and the dotted line is the simulated CVT Low voltage side voltage waveform. It is calculated that the first peak error of the CVT broadband simulation model is 3.31%, which indicates that the CVT broadband simulation model can accurately represent the high-frequency voltage transmission characteristics of the CVT.

Claims (2)

1. A time domain construction method of a CVT broadband simulation model is characterized by comprising the following steps:

1) Acquiring a scattering parameter matrix S of the CVT by using a network analyzer, and calculating to obtain a voltage transmission characteristic H of the CVT;

the voltage transfer characteristic H of the CVT is as follows:

in the formula, S ₁₁ 、S ₁₂ 、S ₂₁ 、S ₂₂ A scattering parameter indicative of a CVT port; subscript 1 and subscript 2 represent CVT port serial numbers;

2) Converting the voltage transmission characteristic H into a continuous state space equation of a time domain;

the step of converting the voltage transfer characteristic H into a continuous state space equation in the time domain comprises:

2.1 Using a vector matching method to fit the voltage transfer characteristic H to a state space equation H(s), i.e.:

H(s)＝C(sI-A) ^-1 B+D+sE (2)

in the formula, A is an N-order diagonal matrix taking poles as diagonal elements; b is a unit array of Nx 1 order; c is a residue matrix of 1 XN order; D. e is a constant; i is a unit vector; s = j ω represents the laplacian operator;

2.2 Transforming the state space equation (2) into a time domain continuous state space equation as shown in equation (3) using an inverse pull transform, comprising the steps of:

2.2.1 Set state variable x and output variable y as follows:

wherein u is a voltage;

2.2.2 Inverse Laplace transform is performed on the state space equation (2) according to the formula (3) to obtain a continuous state space equation of the time domain:

in the formula, k is the kth moment; x is the number of _k Is a state variable at the kth moment; y is _k Outputting a current variable for the kth moment; u. u _k Is the voltage variable at the kth moment; x' _k Is a continuity state variable;

3) Converting the continuous state space equation into a circuit model so as to obtain a CVT broadband simulation model;

the step of converting the continuous state space equations into a circuit model comprises:

3.1 Discretizing a continuous state space equation by using a central difference method to obtain:

wherein h is the sampling duration; x is a radical of a fluorine atom _k+1 The state variable at the k +1 th moment; u. of _k+1 Voltage variable at the k +1 th moment; y is _k+1 Outputting a current variable for the k +1 th moment;

3.2 Simplifying equation (5) to obtain:

wherein, the vector α and the vector μ are respectively as follows:

α＝(2I-Ah) ^-1 (2I+Ah) (7)

μ＝(2I-Ah) ^-1 h (8)

3.3 Modified state variables are:

in the formula (I), the compound is shown in the specification,

correcting state variables for time k +1A value;

3.4 Substituting equation (9) into equation (6) yields:

in the formula (I), the compound is shown in the specification,

a state variable correction value at the time k;

wherein the identity matrix

Matrix G is as follows:

G＝D+CμB (12)

3.5 Order output vector

And (5) updating the formula (10) to obtain a CVT broadband simulation model:

in the formula i _s,k Time domain current vector at the k moment; y is _s,k+1 The time domain output vector is at the moment k + 1.

2. The time domain construction method of the CVT wideband simulation model according to claim 1, characterized in that a scattering parameter matrix S of the CVT is as follows:

in the formula, S ₁₁ 、S ₁₂ 、S ₂₁ 、S ₂₂ A scattering parameter indicative of a CVT port; subscript 1 and subscript 2 denote CVT port number.

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