CN111444592B - Transformer broadband admittance model and building method - Google Patents
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Abstract
The invention discloses a transformer broadband admittance model and a method for establishing the same, wherein the model comprises broadband admittance Y A 、Y B And Y C And their equivalent circuits. The method comprises the following steps: 1) Acquisition of Y A 、Y B And Y C Discrete frequency data points; 2) Approximating the frequency response characteristics of the broadband admittance by using the expression of the rational function partial sum; 3) Transforming the continuous frequency response state equation set into a discrete state equation set representing a transformer broadband admittance model by using a central difference method; 4) Establishing broadband admittance Y based on Type-94 element simulation in ATP-EMTP A And Y B Is equivalent to the broadband admittance Y C The Cauer equivalent circuit simulation established in the ATP-EMTP is used for further establishing an equivalent circuit of a broadband admittance model of the transformer and representing the high-frequency transient characteristic of the transformer. The invention can obtain all parameters only by port test, does not need detailed parameters in the transformer, and can stably run without passive correction.
Description
Technical Field
The invention relates to the field of transformer model establishment, in particular to a transformer broadband admittance model and an establishment method.
Background
As one of the most important devices in the power system, the electromagnetic transient characteristics of the transformer are important for the simulation research of the whole power system. The high-frequency transient characteristic of the transformer is influenced by the appearance and the installation topological structure, and the transmission characteristic of the transformer can change along with the frequency due to the influence of inductance effect and capacitance effect of components such as a winding, an oil tank, an iron core and the like. In the rapid electromagnetic transient analysis of power systems, it is very important to build accurate high frequency models of transformers. The solid-state transformer is a key device for actively regulating voltage and current in the intelligent power grid, and has important significance in transient research and design strategies, wherein the configuration of parameters such as capacitance, leakage inductance and the like of the high-frequency transformer determines the dynamic and steady-state performances of the solid-state transformer to a great extent. The operation state of the solid-state transformer is comprehensively mastered, and the method has important significance for the design and control strategy of the renewable energy system.
The transformer broadband electromagnetic transient model can be divided into three models, namely a white box model, a black box model and a gray box model from the modeling method. The white box model is mostly based on finite element calculation, and a lumped parameter network capable of accurately describing the broadband characteristic of the transformer is obtained by solving complex electromagnetic field problems, but parameters are difficult to obtain. The black box model regards the transformer as a black box, and its parameters can be obtained by measuring the port characteristics of the transformer by frequency sweep. The gray box model is an improved white box model, the circuit structure of which is the same lumped parameter network as the white box model, but the model parameters of which are obtained by measuring the port characteristics of the transformer through frequency sweeping.
In the prior art, a plurality of high-frequency models of the transformer exist, but the high-frequency models of the transformer still have some defects and limitations, such as difficult determination of parameters of the models, difficult realization of the models in electromagnetic transient simulation software and the like. This makes it difficult to apply these high frequency transformer models to accurate fast electromagnetic transient analysis, including simulation studies of transformer interactions with the system, transfer of overvoltage between transformer windings, etc.
Disclosure of Invention
The object of the present invention is to solve the problems of the prior art.
The technical scheme adopted for realizing the purpose of the invention is that the method for establishing the broadband admittance model of the transformer mainly comprises the following steps:
1) Construction from broadband admittance Y A Broadband admittance Y B Broadband admittance Y C A pi-type wide-frequency admittance circuit model is formed;
2) Determining broadband admittance Y in pi-type broadband admittance equivalent model A Broadband admittance Y B Broadband admittance Y C The main steps are as follows:
2.1 Measuring an S parameter matrix of a transformer port, wherein the S parameter matrix has the expression:
wherein, the S parameter matrix is used for describing the relation between the input signal and the output signal of the transformer. a. b represents the incident and reflected scatter variations, respectively. V (V) j Representing the voltage. I j Is a current. j=1 represents the primary side of the transformer. j=2 represents the secondary side of the transformer. Z is Z j Representing the reference impedance.
2.2 The S parameter matrix is transformed to obtain a Y parameter matrix, namely:
2.3 Constructing a broadband admittance Y based on the relation between the Y parameter matrix and the port variable A Broadband admittance Y B Broadband admittance Y C The transformer pi-type wide frequency admittance circuit is formed.
3) Improved vector matching method for broadband admittance Y A Broadband admittance Y B Broadband admittance Y C Fitting the discrete frequency data points of the broadband admittance, approximating the frequency response characteristic of the broadband admittance by using the expression of the rational function partial sum, and mainly comprising the following steps:
3.1 A continuous frequency response characteristic expression of broadband admittance is established, namely:
wherein f(s) is the frequency response; n is the fitting order; d is a constant term, e is a linear term coefficient, which are all real numbers, r k And p k The remainder and the pole of the frequency domain response f(s), respectively, are typically real or conjugate complex pairs. k represents a kth order fit.
3.2 Converting equation (3) into a state space equation form, namely:
f(s)＝C(sI-A) -1 B+D+Es (4)
where A is an N diagonal matrix, its diagonal elements are poles in equation (3), B is an N1 column vector, its elements are equal to 1, C is a 1N row vector, its elements are remainders in equation (3), and D and E correspond to the constant term D and the linear term coefficient E in equation (3), respectively.
3.3 Defining a state variable x, namely:
where v(s) is a voltage variable.
3.4 Bringing the state variable x into the state equation (4), and carrying out reverse pull transformation on the formula (4) to obtain a state equation set, namely:
i＝Cx+Dv+Ev (6)
in the method, in the process of the invention,is the differentiation of the state variable; i represents current data, which is an output variable.
4) The method for transforming the continuous frequency response state equation set into the discrete state equation set representing the broadband admittance by using the center difference method mainly comprises the following steps:
4.1 Using a central difference method to transform the continuous state equation set into a discrete state equation set representing broadband admittance, namely:
i k ＝Cx k +Dv k (7)
4.2 Simplification of equation (7):
x k ＝αx k-1 +λBv k +μBv k-1
i k ＝Cx k +Dv k
wherein, the calculation coefficients alpha, lambda and mu are respectively as follows:
4.3 Overwriting the state variable with x' k ：
x′ k ＝x k -λBv k (9)
4.4 State variable x' k And (3) carrying out the formula (8) to obtain a discrete state equation set:
i k ＝Cx′ k +Gv k (10)
wherein,and G satisfies the following formula:
G＝D+CλB (11)
5) And inputting the voltage data of the previous moment, the state variable and the voltage data of the transformer at the current moment into a discrete state equation set to obtain current data at the current moment, thereby further representing the high-frequency transient characteristic of the transformer.
6) And establishing an equivalent circuit model of the pi-type wide-frequency admittance model in the ATP-EMTP.
The broadband admittance Y A And Y B Is established by ATP-EMTP using Type-94 element simulation based on discrete state equation; the Type-94 element is a Norton current source element composed of a controlled current source and parallel conductance, and the Type-94 element is parallel resistor R inf And a single-phase ideal transformer to maintain the stability of data output by the pi-type wide-frequency admittance equivalent model. The broadband admittance Y C The simulation of the Cauer equivalent circuit built in ATP-EMTP.
A model built by the method for building the broadband admittance model of transformer includes the broadband admittance Y with pi-type connection A 、Y B And Y C The method comprises the steps of carrying out a first treatment on the surface of the The broadband admittance Y A 、Y B And Y C Respectively represented by the equivalent circuits thereof, and further represents a broadband admittance model for representing the high-frequency transient characteristics of the transformer.
The invention has the advantages that the invention adopts a black box model, the parameter acquisition is simple, all parameters can be acquired only by port test, the detailed parameters in the transformer are not needed, the model can stably run without passive correction, and a Cauer equivalent circuit is adopted to represent Y in a broadband admittance model C The model becomes more stable.
Drawings
FIG. 1 is a diagram of a broadband admittance model of a transformer according to the present invention;
FIG. 2 is a WBA module diagram;
FIG. 3 is a flow chart of a subroutine of the calculation by array in the WBA module;
FIG. 4 is a circuit diagram of a transformer broadband admittance model implemented in ATPDraw according to the present invention;
FIG. 5 is a graph showing the comparison of actual measurement and simulation of lightning impulse tests performed on an air-borne transformer;
fig. 6 is a graph showing actual measurement and simulation comparison of lightning impulse test performed on a load transformer.
Detailed Description
The present invention is further described below with reference to examples, but it should not be construed that the scope of the above subject matter of the present invention is limited to the following examples. Various substitutions and alterations are made according to the ordinary skill and familiar means of the art without departing from the technical spirit of the invention, and all such substitutions and alterations are intended to be included in the scope of the invention.
Example 1:
referring to fig. 1, a method for establishing a broadband admittance model of a transformer mainly includes the following steps:
1) Construction from broadband admittance Y A Broadband admittance Y B Broadband admittance Y C The formed pi-type wide-frequency admittance circuit model determines Y in the pi-type wide-frequency admittance equivalent model A 、Y B And Y C The main steps are as follows:
1.1 Measuring an S parameter matrix of a transformer port, wherein the S parameter matrix has the expression:
wherein, the S parameter matrix is used for describing the relation between the input signal and the output signal of the transformer. a. b represents the incident and reflected scatter variations, respectively. V (V) j Representing the voltage. I j Is a current. j=1 represents the primary side of the transformer. j=2 represents the secondary side of the transformer. Z is Z j Representing the reference impedance.
1.2 The S parameter matrix is transformed to obtain a Y parameter matrix, namely:
1.3 Constructing a broadband admittance Y based on the relation between the Y parameter matrix and the port variable A Broadband admittance Y B Broadband admittance Y C The transformer pi-type wide frequency admittance circuit is formed.
2) Improved vector matching method for broadband admittance Y A Width of the steel sheetAdmittance of frequency Y B Broadband admittance Y C Fitting and approximating the frequency response characteristics of the broadband admittance by using the expression of the rational function partial sum, the main steps are as follows:
2.1 A continuous frequency response characteristic expression of broadband admittance is established, namely:
wherein f(s) is the frequency response; n is the fitting order; d is a constant term, e is a linear term coefficient, which are all real numbers, r k And p k The remainder and the pole of the frequency domain response f(s), respectively, are typically real or conjugate complex pairs. k represents a kth order fit.
2.2 Converting equation (3) into a state space equation form, namely:
f(s)＝C(sI-A) -1 B+D+Es (4)
where A is an N diagonal matrix, its diagonal elements are poles in equation (3), B is an N1 column vector, its elements are equal to 1, C is a 1N row vector, its elements are remainders in equation (3), and D and E correspond to the constant term D and the linear term coefficient E in equation (3), respectively. s represents the s-th set of input data.
2.3 Defining a state variable x, namely:
where v(s) is a voltage variable. I corresponds to the current vector.
2.4 Bringing the state variable x into the state equation (4), and carrying out reverse pull transformation on the formula (4) to obtain a state equation set, namely:
i＝Cx+Dv+Ev (6)
in the method, in the process of the invention,is the differentiation of the state variable; i represents current data, which is an output variable.
3) The method for transforming the continuous frequency response state equation set into the discrete state equation set representing the broadband admittance by using the center difference method mainly comprises the following steps:
3.1 Using a central difference method to transform the continuous state equation set into a discrete state equation set representing broadband admittance, namely:
i k ＝Cx k +Dv k (7)
3.2 Simplification of equation (7):
x k ＝αx k-1 +λBv k +μBv k-1
i k ＝Cx k +Dv k
wherein, the calculation coefficients alpha, lambda and mu are respectively as follows:
3.3 Overwriting the state variable with x' k ：
x′ k ＝x k -λBv k (9)
3.4 State variable x' k And (3) carrying out the formula (8) to obtain a discrete state equation set:
i k ＝Cx′ k +Gv k (10)
wherein the updated vectorAnd the parameter matrix G satisfies the following equation:
G＝D+CλB (11)
4) And inputting the voltage data of the previous moment, the state variable and the voltage data of the transformer at the current moment into a discrete state equation set to obtain current data at the current moment, thereby further representing the high-frequency transient characteristic of the transformer.
5) And establishing an equivalent circuit model of the broadband admittance model of the transformer.
The broadband admittance Y A And Y B The equivalent model of (2) is established by the simulation of the discrete state equation set based on the Type-94 element in ATP-EMTP; the Type-94 element is a Norton current source element formed by a controlled current source and parallel conductance; the broadband admittance Y A And Y B The equivalent circuit model of (a) is formed by connecting Type-94 elements in parallel with resistor R inf And a single-phase ideal transformer to ensure the data stability of the broadband admittance equivalent circuit model output. After ATP-EMTP is compressed using a express command, the broadband admittance Y A And Y B The equivalent model input/output interfaces (P1, P2) of the WBA equivalent module is obtained by editing. The broadband admittance Y C Represented by a Cauer equivalent circuit simulation established in ATP-EMTP.
Example 2:
a model built by the method for building the broadband admittance model of transformer includes pi-type connected broadband admittance Y A 、Y B And Y C The method comprises the steps of carrying out a first treatment on the surface of the The broadband admittance Y A 、Y B And Y C Represented by their equivalent circuits, respectively, and further representing a broadband admittance model for characterizing the high-frequency transient characteristics of the transformer.
Example 3:
referring to fig. 2 to 6, a simulation experiment for establishing a broadband admittance model of a transformer mainly comprises the following steps:
1) Referring to FIG. 2, an equivalent electrical of broadband admittance is established in ATPDraw through Type-94 elementThe circuit block, type-94 element is a norton current source element represented by a controlled current source and parallel conductance. Equivalent conductance G of Norton current source Norton =g, the total current flowing into the Type-94 element port is equivalent to the current of the broadband admittance. Fig. 2 (a) is a Type-94 element equivalent circuit model, fig. 2 (b) is a broadband admittance equivalent model, and fig. 2 (c) is a WBA equivalent module.
And a single-phase ideal transformer with a transformation ratio of 1:1 is connected in series before the Type-94 element, and the Type-94 element which is grounded by default is converted into ungrounded, so that broadband admittance is convenient for electromagnetic transient modeling of the transformer.
The front end of the equivalent module is connected with a resistor R in parallel inf ＝10 7 Omega for maintaining numerical stability during simulation. After the ATP-EMTP is compressed by adopting a compression command, the input/output interface and the icon of the ATP-EMTP are edited to obtain the WBA equivalent module.
2) Referring to fig. 3, the subroutine is implemented by an array to calculate, n (n=n 1 +2n 2 ) Is the fitting order, n 1 Is the number of real poles, n 2 Is the number of conjugate poles, and the calculation of the real number and the conjugate complex number pairs is independent, wherein the calculation result of the conjugate pairs is placed in two adjacent elements of the array. Notably, x 1 And v 1 The state variable and the port voltage for the last time step, respectively. Finally, the output current i is equal to the source current i s And admittance current.
3) Referring to fig. 4, the WBA module provided by the present invention can directly implement the equivalent circuit of the broadband admittance model in ATP-EMTP, but if all the broadband admittances are replaced by the norton current source module, the model may cause unstable calculation, i.e. the model can normally perform under certain working conditions, but under some working conditions, non-convergence calculation occurs. The reason for this is that the stability of the model can be improved by further improving the vector matching method due to improper selection of parameters in the vector matching fitting. However, the invention adopts another more convenient correction method, and the Y in the broadband admittance model is represented by the Cauer equivalent circuit C Meter of broadband admittance equivalent model under most working conditionsThe convergence result can be obtained, so that the transformer hybrid model becomes more stable, and the method can be applied to electromagnetic transient simulation of a power system.
4) The actual measurement and simulation comparison of lightning impulse tests performed on transformers under different load conditions uses the broadband admittance model of the transformer of example 1 and the implementation method thereof in EMTP. The lightning excitation is a standard lightning wave of 1.2/50 mu s generated by a signal generator in combination with a power amplifier, and the peak value is 100V. In the lightning impulse test, the transformer is excited at t=5μs, and as shown in fig. 5, the comparison between the actual measurement of the secondary lightning overvoltage of the transformer and the simulation waveform shows that the peak error of the simulation waveform and the actual measurement waveform is 0.2%. As shown in fig. 6, the peak error between the actual measurement waveform and the simulation waveform of the primary side lightning current of the transformer is 1.3% when the transformer is loaded (10Ω). The comparison result shows that the simulation result of the transformer broadband model is very similar to the actual measurement waveform, and the effectiveness of the model in high-frequency electromagnetic transient simulation is verified.
Claims (6)
1. The method for establishing the broadband admittance model of the transformer is characterized by comprising the following steps of:
1) Construction from broadband admittance Y A Broadband admittance Y B Broadband admittance Y C A pi-type wide-frequency admittance circuit model is formed;
2) Broadband admittance Y in equivalent model for measuring pi-type broadband admittance through sweep frequency A Broadband admittance Y B Broadband admittance Y C Is a discrete frequency data point of (1);
3) Improved vector matching method for broadband admittance Y A Broadband admittance Y B Broadband admittance Y C Fitting the discrete frequency data points of the broadband admittance, and approximating the frequency response characteristic of the broadband admittance by using the expression of the rational function partial sum;
4) Transforming the continuous frequency response state equation set into a discrete state equation set representing a transformer broadband admittance model by using a central difference method;
5) The voltage data of the last moment, the state variables and the voltage data of the transformer at the current moment are input into a discrete state equation set to obtain current data at the current moment, so that the high-frequency transient characteristic of the transformer is represented;
the method for establishing the continuous frequency response state equation set of the broadband admittance by using the expression of the rational function partial sum comprises the following steps:
3.1 A continuous frequency response characteristic expression of broadband admittance is established, namely:
wherein f(s) is the frequency response; n is the fitting order; d is a constant term; e is a linear term coefficient; r is (r) k And p k The remainder and the pole of the frequency domain response f(s) are respectively; k represents a kth order fit;
3.2 Converting equation (1) into a state space equation form, namely:
f(s)＝C(sI-A) -1 B+D+Es (2)
wherein A is a diagonal matrix of N×N, and the diagonal element thereof is a pole in formula (1); b is an N x 1 column vector with elements equal to 1; c is a 1 XN row vector, the element of which is the remainder in equation (1); d and E correspond to the constant term D and the linear term coefficient E in the formula (1), respectively;
3.3 Defining a state variable x, namely:
wherein v(s) is a voltage variable;
3.4 Bringing the state variable x into the state equation (2), and carrying out reverse pull transformation on the formula (2) to obtain a state equation set, namely:
i＝Cx+Dv+Ev (4)
in the method, in the process of the invention,is the differentiation of the state variable; i represents current data, which is an output variable;
the method for transforming the continuous state equation set into the discrete state equation set for representing the broadband admittance model of the transformer by using the central difference method comprises the following steps:
4.1 Using a central difference method to transform the continuous state equation set into a discrete state equation set for representing the broadband admittance model of the transformer, namely:
i k ＝Cx k +Dv k (5)
4.2 Simplification of equation (5):
x k ＝αx k-1 +λBv k +μBv k-1
i k ＝Cx k +Dv k
wherein, the calculation coefficients alpha, lambda and mu are respectively as follows:
4.3 Overwriting the state variable with x' k ：
x′ k ＝x k -λBv k (7)
4.4 State variable x' k And (3) carrying out the formula (6) to obtain a discrete state equation set:
i k ＝Cx′ k +Gv k (8)
wherein,and G satisfies the following formula:
G＝D+CλB (9)。
2. the method for building a broadband admittance model of a transformer according to claim 1, wherein the broadband admittance Y is determined A Broadband admittance Y B Broadband admittance Y C The discrete frequency data points of (a) are as follows:
1) Measuring an S parameter matrix of a transformer port, wherein the S parameter matrix has the expression:
wherein, the S parameter matrix is used for describing the relation between the input signal and the output signal of the transformer; a. b represents an incident scattering variable and a reflected scattering variable, respectively; v (V) j Representing the voltage; i j Is a current; j=1 represents the primary side of the transformer; j=2 represents the transformer secondary side; z is Z j Representing a reference impedance;
2) Transforming the S parameter matrix to obtain a Y parameter matrix, namely:
3) Constructing a broadband admittance Y based on the relation between the Y parameter matrix and the port variable A Broadband admittance Y B Broadband admittance Y C The transformer pi-type wide frequency admittance circuit is formed.
3. The method for establishing the transformer broadband admittance model according to claim 1, wherein the pi-Type broadband admittance equivalent model is established by the discrete state equation set based on Type-94 element simulation in ATP-EMTP; the Type-94 element is a Norton current source element composed of a controlled current source and parallel conductance.
4. The method for building a broadband admittance model of a transformer according to claim 1, wherein the broadband admittance Y is as follows A And Y B The equivalent circuit model of (a) is formed by connecting Type-94 elements in parallel with resistor R inf And a single-phase ideal transformer to ensure the stability of data output by the broadband admittance equivalent circuit model.
5. The method for building a broadband admittance model of a transformer according to claim 1, wherein the broadband admittance Y is as follows C Represented by a Cauer equivalent circuit simulation of ATP-EMTP.
6. A model created by the method for creating a broadband admittance model of a transformer according to any of the claims 1-5, characterized in that it comprises a pi-type connection of broadband admittance Y A Broadband admittance Y B Broadband admittance Y C The method comprises the steps of carrying out a first treatment on the surface of the The broadband admittance Y A Broadband admittance Y B And the broadband admittance Y is respectively represented by an equivalent circuit thereof, and further represents a broadband admittance model for representing the high-frequency transient characteristic of the transformer.
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