CN115112934A - Harmonic and transient voltage measurement method based on broadband model of capacitive voltage transformer - Google Patents
Harmonic and transient voltage measurement method based on broadband model of capacitive voltage transformer Download PDFInfo
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- G—PHYSICS
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- G01R15/04—Voltage dividers
- G01R15/06—Voltage dividers having reactive components, e.g. capacitive transformer
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- G—PHYSICS
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- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
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Abstract
The invention discloses a harmonic and transient voltage measurement method based on a broadband model of a capacitor voltage transformer, which comprises the following steps: 1) establishing a wideband admittance pi model of the capacitive voltage transformer; 2) acquiring broadband admittance parameters of the capacitor voltage transformer; converting the S parameter of the two ports into a Y parameter; 3) obtaining a continuous state space equation representing the broadband response characteristic; 4) converting a continuous state space equation representing the broadband response characteristic into a discrete state space equation; 5) deriving to obtain a reverse discrete state space equation of the capacitor voltage transformer based on the discrete state space equation; 6) designing a harmonic and transient voltage measurement algorithm of the capacitor voltage transformer based on a reverse discrete state space equation; 7) and completing the measurement of the primary side voltage harmonic and the transient voltage. The invention discloses a method for measuring the secondary side voltage u of a known capacitor voltage transformer 2 Under the condition, the primary side voltage u is obtained through iterative calculation 1 Therefore, signals such as harmonic waves, transient voltage and the like can be monitored.
Description
Technical Field
The invention relates to the field of capacitance voltage transformer transient voltage and harmonic measurement, in particular to a method for measuring harmonic and transient voltage based on a capacitance voltage transformer broadband model.
Background
The new energy grid-connected scale of intermittent power generation such as wind power, solar energy and the like is increased year by year, and in addition, the wide application of various power electronic equipment on the power utilization side causes the proportion of nonlinear load in a power grid to be continuously increased, so that the problems of harmonic waves, transient states and the like in a power system are increasingly serious, the normal operation of various equipment and various precise instruments based on power frequency design in the power grid is greatly threatened, and meanwhile, the operation cost of the equipment and the power grid is greatly increased. The Capacitor Voltage Transformer (CVT) is a voltage measuring device widely used in power systems, and is also a main device for providing voltage signals for harmonic and transient voltage monitoring of national grid companies. Since power quality is a problem to be considered again on the basis of ensuring the safety and reliability of the power system, solving the power quality monitoring problem mainly starts from the CVT for harmonic and transient voltage measurement.
However, when the existing CVT measures signals such as harmonic wave and transient voltage, the working point of a power frequency series resonance circuit consisting of equivalent capacitance of a capacitive voltage divider and inductance of a compensation reactor in the CVT will deviate, the amplitude-frequency and phase-frequency characteristics of the transformation ratio show serious nonlinearity, the bandwidth is extremely narrow, and the harmonic wave monitoring task is difficult to complete.
Disclosure of Invention
The invention aims to provide a harmonic and transient voltage measuring method based on a broadband model of a capacitor voltage transformer, which comprises the following steps of:
1) establishing a wideband admittance pi model of the capacitive voltage transformer based on a two-port network.
The two admittance port sides of the wideband admittance pi model of the capacitive voltage transformer are as follows:
in the formula I 1 、I 2 、V 1 、V 2 Is the two port current voltage. Y is A 、Y B 、Y C Is a wide frequency pi admittance model parameter.
2) And measuring S parameters of two ports of the capacitor voltage transformer so as to obtain broadband admittance parameters of the capacitor voltage transformer. And converting the S parameter of the two ports into the Y parameter.
The device for measuring S parameters of the capacitive voltage transformer comprises a vector network analyzer.
3) And fitting the broadband admittance parameters by using a vector matching method to obtain a continuous state space equation representing the broadband response characteristic.
The continuous state space equation characterizing the broadband response is as follows:
in the formula, a is an N × N diagonal matrix, whose diagonal elements are poles, C is a 1 × N row vector, whose elements are residuals, B is an N × 1 column vector, whose elements are equal to 1, and D and E correspond to constant term and linear term coefficients, respectively.
Representing the derivative of the state variable vector. i is an output variable.
4) Converting a continuous state space equation representing the broadband response characteristic into a discrete state space equation:
in the formula, v k The capacitor voltage transformer voltage is iterated for the kth time; v. of k-1 The voltage of the capacitor voltage transformer is iterated for the (k-1) th time; i all right angle k The capacitor voltage transformer current is iterated for the kth time; x' k Is the k iteration intermediate parameter; x' k-1 Is the k-1 th iteration intermediate parameter; c is a 1 XN row vector, vector
G. α is as follows:
in the formula, parameter
Δ t is the time difference; a is an N multiplied by N diagonal matrix, and diagonal elements of the matrix are poles; b is an Nx 1 column vector with elements equal to 1;c is a 1 XN row vector with elements as residue; i is an identity matrix; d is a constant term.
Methods for converting a continuous state space equation characterizing a broadband response characteristic into a discrete state space equation include center difference methods.
5) Deriving to obtain a reverse discrete state space equation of the capacitor voltage transformer based on the discrete state space equation;
6) establishing a harmonic and transient voltage measuring module of the capacitor voltage transformer based on a reverse discrete state space equation;
7) and monitoring the secondary side voltage of the capacitor voltage transformer, inputting the secondary side voltage into the harmonic and transient voltage measuring module to obtain the primary side voltage of the capacitor voltage transformer, and thus completing the measurement of the harmonic and transient voltage of the primary side voltage.
Primary side voltage of kth iteration capacitor voltage transformer
As follows:
in the formula (I), the compound is shown in the specification,
the secondary side voltage of the capacitor voltage transformer is iterated for the kth time; vector quantity
G′、
Respectively as follows:
it is worth explaining that the method for measuring the harmonic wave and the transient voltage utilizes a vector network analyzer to measure S parameters, fits the broadband admittance parameters through a vector matching method, constructs a capacitive voltage transformer broadband admittance pi model based on a two-port network, and finally deduces a discrete state space equation of the pi model to obtain an inversion equation which can calculate the primary side voltage only by taking the secondary side voltage of the capacitive voltage transformer as input, thereby realizing the method for measuring the harmonic wave and the transient voltage.
The technical effect of the invention is undoubted, and the invention only knows the secondary side voltage u of the capacitor voltage transformer 2 Under the condition, the primary side voltage u is obtained by iterative calculation 1 Therefore, signals such as harmonic waves, transient voltage and the like can be monitored.
The harmonic and transient voltage measuring method based on the broadband model of the capacitor voltage transformer is rigorous in theory, is strictly derived from a formula, and is good in harmonic and transient voltage measuring effect.
According to the harmonic and transient voltage measuring method based on the broadband model of the capacitor voltage transformer, the harmonic and transient voltage can be measured only by performing frequency scanning on equipment to obtain parameters, and the method is convenient for practical engineering application.
The method for measuring the harmonic and transient voltages based on the broadband model of the capacitor voltage transformer, provided by the invention, only needs one parameter for the capacitor voltage transformer with the same type and small parameter difference, and has certain universality.
Drawings
Fig. 1 is a flow chart of harmonic and transient voltage measurement.
Fig. 2 shows a pi-type wide-frequency admittance circuit of the CVT.
Fig. 3 is the Y parameter of the CVT. Fig. 3(a), 3(b), 3(c), and 3(d) show the Y11 parameter, Y12 parameter, Y21 parameter, and Y22 parameter of the CVT, respectively.
Fig. 4 is an exemplary diagram of the method for calculating the primary-side voltage of the CVT.
Detailed Description
The present invention will be further described with reference to the following examples, but it should be understood that the scope of the subject matter described above is not limited to the following examples. Various substitutions and alterations can be made without departing from the technical idea of the invention and the scope of the invention is covered by the present invention according to the common technical knowledge and the conventional means in the field.
Example 1:
referring to fig. 1, 2, 3 and 4, a method for measuring harmonic and transient voltages based on a wideband model of a capacitor voltage transformer includes the following steps:
1) establishing a wideband admittance pi model of the capacitive voltage transformer based on a two-port network.
The square of the admittance two ports of the wideband admittance pi model of the capacitive voltage transformer is as follows:
in the formula I 1 、I 2 、V 1 、V 2 Is the two port current voltage. Y is A 、Y B 、Y C Is a wide frequency pi admittance model parameter.
2) And measuring the S parameter of the two ports of the capacitor voltage transformer so as to obtain the broadband admittance parameter of the capacitor voltage transformer. And converting the S parameter of the two ports into the Y parameter.
The device for measuring the S parameter of the capacitor voltage transformer comprises a vector network analyzer.
3) And fitting the broadband admittance parameters by using a vector matching method to obtain a continuous state space equation representing the broadband response characteristic.
The continuous state space equation characterizing the broadband response is as follows:
wherein A is an N × N diagonal matrix with poles as diagonal elements, C is a 1 × N row vector with residue as elements, and B is an N × 1 column vector with elementsEqual to 1, D and E correspond to constant term and linear term coefficients, respectively.
Representing the derivative of the state variable vector. i is an output variable.
4) And converting the continuous state space equation which represents the broadband response characteristic into a discrete state space equation.
The method for converting the continuous state space equation which characterizes the broadband response characteristic into the discrete state space equation comprises a central difference method.
The discrete state space equation is as follows:
in the formula, v k The voltage of the capacitor voltage transformer is iterated for the kth time; v. of k-1 The voltage of the capacitor voltage transformer is iterated for the (k-1) th time; i all right angle k The current of the capacitor voltage transformer is iterated for the kth time; x' k Is the k iteration intermediate parameter; x' k-1 Is the intermediate parameter of the k-1 iteration; c is a 1 XN row vector, vector
G. α is as follows:
in the formula, parameter
Δ t is the time difference; a is an N multiplied by N diagonal matrix, and diagonal elements of the matrix are poles; b is an Nx 1 column vector with elements equal to 1; c is a 1 XN row vector with elements as residue; i is an identity matrix; d is a constant term.
5) Deriving to obtain a reverse discrete state space equation of the capacitor voltage transformer based on the discrete state space equation;
6) establishing a harmonic and transient voltage measuring module of the capacitor voltage transformer based on a reverse discrete state space equation;
7) and monitoring the secondary side voltage of the capacitor voltage transformer, inputting the secondary side voltage into the harmonic and transient voltage measuring module to obtain the primary side voltage of the capacitor voltage transformer, and thus completing the measurement of the harmonic and transient voltage of the primary side voltage.
Primary side voltage of kth iteration capacitor voltage transformer
As follows:
in the formula (I), the compound is shown in the specification,
the voltage of the secondary side of the capacitor voltage transformer is iterated for the kth time; vector quantity
G′、
Respectively as follows:
example 2:
a harmonic and transient voltage measurement method based on a broadband model of a capacitor voltage transformer comprises the following steps:
1) constructing a capacitive voltage transformer broadband admittance pi model based on a two-port network;
2) measuring S parameters of two ports of the capacitor voltage transformer by adopting a vector network analyzer, and converting the S parameters into Y parameters;
3) fitting the broadband admittance parameters into a partial sum form of a rational function by using a vector matching method to obtain a continuous state space equation representing the broadband response characteristic;
4) converting a continuous state space equation set of the capacitance voltage transformer broadband admittance sub-model into a discrete state space equation by adopting a central difference method;
5) deriving to obtain a reverse discrete state space equation of the capacitor voltage transformer based on the discrete state space equation;
6) designing a harmonic and transient voltage measurement algorithm of the capacitor voltage transformer based on a reverse discrete state space equation;
7) according to a harmonic and transient voltage measurement algorithm of the capacitor voltage transformer, the inversion equation of the primary side voltage can be calculated by taking the secondary side voltage as an input variable, and the measurement of the harmonic and transient voltage of the primary side voltage is completed.
Example 3:
a harmonic and transient voltage measurement method based on a broadband model of a capacitive voltage transformer comprises the following steps:
1) constructing a wideband admittance pi model of the capacitor voltage transformer based on a two-port network. The admittance two-port equation is:
I 1 、I 2 、V 1 、V 2 is a two-port current voltage, Y A 、Y B 、Y C Is a wide frequency pi admittance model parameter.
2) And measuring the S parameter of the capacitor voltage transformer by adopting a vector network analyzer.
3) And performing parameter conversion by using the relation between the S parameter and the Y parameter of the two ports.
4) The vector matching method fits the broadband admittance parameters into the form of partial sum of rational functions:
wherein s ═ j ω, c n And a n The number of the reserved number and the pole of the function respectively can be real numbers or conjugate complex number pairs, and usually, in order to more accurately fit a complex curve with a resonance point, the pole often needs to contain the conjugate complex number pair; the parameters d and e are real constants; and N is a fitting order.
5) Transforming a continuous state space equation set of the capacitance voltage transformer broadband admittance sub-model into a discrete state space equation by adopting a center difference method:
in the formula, v k The capacitor voltage transformer voltage is iterated for the kth time; v. of k-1 The voltage of the capacitor voltage transformer is iterated for the (k-1) th time; i all right angle k The capacitor voltage transformer current is iterated for the kth time; x' k Is the k iteration intermediate parameter; x' k-1 Is the k-1 th iteration intermediate parameter; c is a 1 XN row vector, vector
G. α is as follows:
in the formula, parameter
Δ t is the time difference; a is an N multiplied by N diagonal matrix, and diagonal elements of the matrix are poles; b is an Nx 1 column vector with elements equal to 1; c is a 1 XN row vector, the elements of which are the residue; i is an identity matrix; d is a constant term.
6) The discrete equation of the step 5 is that of the primary side voltage of the known capacitor voltage transformerA system of discrete state equations of broadband admittance under conditions, wherein v k As input variables, i k As an output variable, the time-domain variation relationship between the broadband admittance voltage and the current can be characterized. The harmonic and transient voltage measuring method only needs to measure the secondary side voltage u 2 As input variables, the primary side voltage u can be calculated 1 Thereby obtaining the harmonic component of the power supply and the transient voltage. By derivation:
wherein each parameter is respectively:
voltage u at secondary side of known capacitor voltage transformer 2 Under the condition, the primary side voltage u of the inversion calculation can be obtained by n times of iteration of the formula 1 。
Claims (7)
1. A harmonic and transient voltage measurement method based on a broadband model of a capacitor voltage transformer is characterized by comprising the following steps:
1) and establishing a wideband admittance pi model of the capacitor voltage transformer based on the two-port network.
2) Measuring the S parameter of the two ports of the capacitor voltage transformer so as to obtain the broadband admittance parameter of the capacitor voltage transformer; converting the S parameter of the two ports into a Y parameter;
3) fitting the broadband admittance parameters by using a vector matching method to obtain a continuous state space equation representing the broadband response characteristic;
4) converting a continuous state space equation representing the broadband response characteristic into a discrete state space equation;
5) deriving to obtain a reverse discrete state space equation of the capacitor voltage transformer based on the discrete state space equation;
6) establishing a harmonic and transient voltage measuring module of the capacitor voltage transformer based on a reverse discrete state space equation;
7) and monitoring the secondary side voltage of the capacitor voltage transformer, inputting the secondary side voltage into the harmonic and transient voltage measuring module to obtain the primary side voltage of the capacitor voltage transformer, and thus completing the measurement of the harmonic and transient voltage of the primary side voltage.
2. The method according to claim 1, wherein the method for measuring the harmonic and transient voltages based on the wideband model of the capacitive voltage transformer comprises: the admittance two-port equation of the broadband admittance pi model of the capacitive voltage transformer is as follows:
in the formula I 1 、I 2 、V 1 、V 2 Is a two port current voltage; y is A 、Y B 、Y C Is a wide frequency pi admittance model parameter.
3. The method according to claim 1, wherein the method for measuring the harmonic and transient voltages based on the wideband model of the capacitive voltage transformer comprises: the measuring device for the S parameter of the capacitor voltage transformer comprises a vector network analyzer.
4. The method according to claim 1, wherein the method for measuring the harmonic and transient voltages based on the wideband model of the capacitive voltage transformer comprises: the continuous state space equation characterizing the broadband response is as follows:
in the formula, a is an N × N diagonal matrix, whose diagonal elements are poles, C is a 1 × N row vector, whose elements are residuals, B is an N × 1 column vector, whose elements are equal to 1, and D and E correspond to constant term and linear term coefficients, respectively.
Representing the derivative of the state variable vector x. i is an output variable.
5. The method according to claim 1, wherein the method for measuring the harmonic and transient voltages based on the wideband model of the capacitive voltage transformer comprises: methods for converting a continuous state space equation characterizing a broadband response characteristic into a discrete state space equation include center difference methods.
6. The method according to claim 1, wherein the method for measuring the harmonic and transient voltages based on the wideband model of the capacitive voltage transformer comprises: the discrete state space equation is as follows:
in the formula, v k The voltage of the capacitor voltage transformer is iterated for the kth time; v. of k-1 The voltage of the capacitor voltage transformer is iterated for the (k-1) th time; i.e. i k The capacitor voltage transformer current is iterated for the kth time; x' k Is the k timeIterating the intermediate parameters; x' k-1 Is the k-1 th iteration intermediate parameter; c is a 1 XN line vector, vector
G. α is as follows:
in the formula, parameter
Δ t is the time difference; a is an N multiplied by N diagonal matrix, and diagonal elements of the matrix are poles; b is an Nx 1 column vector with elements equal to 1; c is a 1 XN row vector with elements as residue; i is an identity matrix; d is a constant term.
7. The method according to claim 1, wherein the method for measuring the harmonic and transient voltages based on the wideband model of the capacitive voltage transformer comprises: primary side voltage of kth iteration capacitor voltage transformer
As follows:
in the formula (I), the compound is shown in the specification,
the voltage of the secondary side of the capacitor voltage transformer is iterated for the kth time; vector quantity
G′、
Respectively as follows:
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