CN112485509B - Transient overvoltage measuring device and method based on nonlinear broadband model - Google Patents
Transient overvoltage measuring device and method based on nonlinear broadband model Download PDFInfo
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Abstract
The application discloses a transient overvoltage measurement device and method based on a nonlinear broadband model, relates to the technical field of transient voltage measurement, and solves the problem that CVT cannot meet the measurement requirement of transient overvoltage. The application comprises a connecting point between a resistor R1 and a capacitor C2 of a capacitor unit of a CVT, and an electromagnetic unit model, wherein the electromagnetic unit model comprises a steady-state module and a high-frequency module, the steady-state module is connected with the high-frequency module, the steady-state module comprises a compensation reactor, a transformer and a resonance damper, the left two ports of the high-frequency module are respectively connected with a medium-voltage point of the CVT or a high-frequency voltage input end and ground of the capacitor unit, the right two ports are respectively connected with an electromagnetic unit model output and ground, and the electromagnetic unit model output is also an output end of the integral CVT model. Through the application, the CVT can obtain the capability of measuring the high-frequency voltage, and the measurement requirement on the transient overvoltage is met.
Description
Technical Field
The application relates to the technical field of transient voltage measurement, in particular to a transient overvoltage measurement device and method based on a nonlinear broadband model.
Background
Transient voltages with high frequency content in power systems have become a leading cause of power system failure. The transient overvoltage can be directly caused by the factors such as lightning impulse, switching action and the like, so that faults such as flashover, short circuit, insulation breakdown and the like are caused, even the power equipment is directly damaged, and serious personnel and economic losses are caused.
With the complexity of the power grid structure and the rise of voltage class, the reliability of the power system and the equipment is more subject to the damage caused by transient overvoltage. The accurate monitoring of the transient overvoltage has important values for reliable operation, insulation design, fault early warning, fault analysis, system protection and the like of the power equipment.
The accident of transient voltage is complex and various, and the generated transient voltage waveform will also contain abundant frequency components. Currently, a large number of Capacitive Voltage Transformers (CVT) are used for voltage monitoring in power grids of 110kV and above. However, CVT can only be used for measuring power frequency voltage, so that it is difficult to meet the requirement of transient overvoltage monitoring, and most of CVT spread spectrum methods proposed at present are based on linear models, only can spread spectrum to harmonic frequency bands, and cannot meet the requirement of transient overvoltage measurement.
Disclosure of Invention
The technical problems to be solved by the application are as follows: the CVT cannot meet the measurement requirement of transient overvoltage, and the application provides a device and a method for measuring transient overvoltage based on a nonlinear broadband model, which solve the problems.
The application is realized by the following technical scheme:
the transient overvoltage measuring device based on the nonlinear broadband model comprises an electromagnetic unit model connected to a connection point between a resistor R1 and a capacitor C2 of a capacitor unit of the CVT;
the electromagnetic unit model comprises a steady-state module and a high-frequency module, the steady-state module is connected with the high-frequency module, the steady-state module is a physical model formed by elements with physical significance, the steady-state module comprises a compensation reactor, an intermediate transformer and a resonance damper, the left two ports of the high-frequency module are respectively connected with the high-frequency voltage input end and the ground of a medium-voltage point or a capacitor unit of the CVT, the right two ports of the high-frequency module are respectively connected with the electromagnetic unit model output and the ground, and the electromagnetic unit model output is also the output end of the integral CVT model.
Further, the high-frequency module is an equivalent circuit which is synthesized by a foster II-type RLCG circuit after pi-type equivalent of the admittance parameters of the two-port network.
Further, the model of the steady-state module related to the compensating reactor is composed of a compensating inductance L s And equivalent resistance R s The right side of the compensating reactor is connected with an intermediate transformer which is constructed based on a classical T-shaped circuit and comprises a leakage reactance L of a primary side winding T1 And copper loss R T1 Leakage reactance L of secondary side winding T2 And copper loss R T2 The right port of the secondary winding is used for outputting an electromagnetic unit model, and an excitation branch between the primary winding and the secondary winding is used for routing a nonlinear resistor R m And nonlinear inductance L m The resistor Rm and the secondary side of the inductor Lm are connected in parallel, and then the damper is connected in parallel.
Further, the steady state module portion related to the damper is selected and constructed based on a schematic diagram of the type of damper in the CVT.
Further, the capacitor unit of the CVT includes capacitors C connected in sequence 1 Resistance R 1 Capacitance C 2 And resistance R 2 Wherein the capacitance C 1 Front-connected high-voltage input terminal, resistor R 2 And the rear is grounded.
The transient overvoltage measurement method based on the nonlinear broadband model comprises the following steps:
step 1, an electromagnetic unit model is built, the electromagnetic unit model steady-state module and a high-frequency module are connected, the steady-state module is a physical model comprising independent elements, the steady-state module comprises a compensation reactor, a transformer and a resonance damper, the left two ports of the high-frequency module are respectively connected with a high-frequency voltage input end and ground of a CVT middle voltage port or a capacitor unit of the CVT, the right two ports of the high-frequency module are respectively connected with an electromagnetic unit model output and ground, the electromagnetic unit model output is also an output end of the integral CVT model, a characteristic curve about current is acquired for a nonlinear element in the electromagnetic unit model through a voltammetry, a voltammetry experimental result is simulated into a form of I=f (U), a nonlinear inductance is simulated into a form of I=f (ψ), I is current, U is voltage, and ψ is a magnetic chain;
measuring component data of leakage reactance and resistance of windings in the transformer through short circuit and open circuit experiments of the transformer, and calculating capacitance data by adopting loss angle measurement results according to resistance components related to capacitance;
step 2, constructing an equivalent circuit of the high-frequency module: acquiring admittance parameters of an electromagnetic unit, calculating admittance parameters of a steady-state module and an electromagnetic unit model, calculating admittance parameters of a high-frequency module, calculating admittance parameters of each sub-module of a pi-type equivalent circuit after pi-type equivalence, obtaining an expression of each sub-module of the pi-type equivalent circuit after vector matching, and comprehensively constructing an equivalent circuit of a final high-frequency module by using a Forst II-type RLCG circuit according to the expression;
and step 3, inverting and calculating the waveform of the input port of the model, collecting the output waveform of the CVT output end, and calculating the waveform of the CVT input port by adopting a numerical calculation method and a recursive convolution method according to the kirchhoff voltage/current law. The application has the following advantages and beneficial effects:
through the application, the CVT can obtain the capability of measuring the high-frequency voltage, and the measurement requirement on the transient overvoltage is met.
Drawings
The accompanying drawings, which are included to provide a further understanding of embodiments of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the principles of the application. In the drawings:
FIG. 1 is a circuit diagram of a nonlinear wideband model according to the present application.
Fig. 2 is a pi-type equivalent circuit diagram of the high frequency module of the present application.
FIG. 3 is an embodiment of the present applicationR is equivalent to 0 And a resistor branch circuit diagram.
FIG. 4 is R in an embodiment of the application i 、L i And (3) a branch circuit diagram.
FIG. 5 is a graph of R in an embodiment of the application i L i C i G i And a series-parallel branch circuit diagram.
Fig. 6 is a circuit diagram of a nonlinear broadband model of a middleless port in an embodiment of the application.
Fig. 7 is a pi-type equivalent circuit diagram of a nonlinear broadband model without a medium voltage port in an embodiment of the application.
Fig. 8 is a CVT model of a cascade of two-port networks of the second processing mode in an embodiment of the application.
Detailed Description
Hereinafter, the terms "comprises" or "comprising" as may be used in various embodiments of the present application indicate the presence of inventive functions, operations or elements, and are not limiting of the addition of one or more functions, operations or elements. Furthermore, as used in various embodiments of the application, the terms "comprises," "comprising," and their cognate terms are intended to refer to a particular feature, number, step, operation, element, component, or combination of the foregoing, and should not be interpreted as first excluding the existence of or increasing likelihood of one or more other features, numbers, steps, operations, elements, components, or combinations of the foregoing.
In various embodiments of the application, the expression "or" at least one of a or/and B "includes any or all combinations of the words listed simultaneously. For example, the expression "a or B" or "at least one of a or/and B" may include a, may include B or may include both a and B.
Expressions (such as "first", "second", etc.) used in the various embodiments of the application may modify various constituent elements in the various embodiments, but the respective constituent elements may not be limited. For example, the above description does not limit the order and/or importance of the elements. The above description is only intended to distinguish one element from another element. For example, the first user device and the second user device indicate different user devices, although both are user devices. For example, a first element could be termed a second element, and, similarly, a second element could be termed a first element, without departing from the scope of various embodiments of the present application.
It should be noted that: if it is described to "connect" one component element to another component element, a first component element may be directly connected to a second component element, and a third component element may be "connected" between the first and second component elements. Conversely, when one constituent element is "directly connected" to another constituent element, it is understood that there is no third constituent element between the first constituent element and the second constituent element.
The terminology used in the various embodiments of the application is for the purpose of describing particular embodiments only and is not intended to be limiting of the various embodiments of the application. As used herein, the singular is intended to include the plural as well, unless the context clearly indicates otherwise. Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which various embodiments of the application belong. The terms (such as those defined in commonly used dictionaries) will be interpreted as having a meaning that is the same as the context of the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein in connection with the various embodiments of the application.
For the purpose of making apparent the objects, technical solutions and advantages of the present application, the present application will be further described in detail with reference to the following examples and the accompanying drawings, wherein the exemplary embodiments of the present application and the descriptions thereof are for illustrating the present application only and are not to be construed as limiting the present application.
As shown in FIG. 1, the model is serially connected with C after the left input end 1 、R 1 、C 2 And R is 2 The connection point between R1 and C2, which forms the capacitive element of the CVT, is followed by the electromagnetic element model.The electromagnetic unit is divided into a steady-state module and a high-frequency module. The steady-state module is a physical model formed by all specific independent elements below the high-frequency module, specifically, the compensating reactor model consists of a compensating inductance L s And equivalent resistance R s And the two are connected in series. The right side of the compensating reactor is connected with a steady-state model of the intermediate transformer. The steady-state model of the intermediate transformer is constructed based on a classical T-shaped circuit and comprises leakage reactance L of primary side and secondary side windings T1 、L T2 And copper loss R T1 、R T2 The right end opening of the secondary winding is the output of the whole model. Excitation branch route nonlinear resistor R between primary and secondary side windings m And nonlinear inductance L m And are connected in parallel. R is R m And L is equal to m The secondary side is connected with a damper in parallel, and the damper module is used for constructing a model according to a schematic diagram of the CVT damper type. The high-frequency module is a two-port model, the left two ports are respectively connected with the inlet of the electromagnetic unit and the ground, and the right two ports are respectively connected with the output of the model and the ground.
For selection of relevant elements in the model, the elements in the capacitive unit and electromagnetic unit steady state modules shown in fig. 1 can be divided into linear elements and nonlinear elements.
The nonlinear element may obtain a characteristic curve of the nonlinear element by voltammetry, specifically, the result of the voltammetry experiment is fitted to a form of i=f (U) by using a polynomial of odd degree, and the nonlinear inductance is fitted to a form of i=f (ψ).
In the linear element, the value of the main element can be obtained by the CVT nameplate or manufacturer. The leakage reactance and resistance of the windings can be measured by short circuit and open circuit experiments of the transformer. R of capacitor unit 1 And R is 2 The resistive component may be calculated from the loss angle measurements.
Thus, the capacitor unit and the electromagnetic unit steady-state module are constructed.
The final form of construction of the high frequency module is to build a pi-type equivalent circuit model consisting of inductance, capacitance, resistance or conductance. The first step is to obtain the admittance parameter (Y parameter) of the high frequency module. And measuring scattering parameters (S parameters) of the electromagnetic unit by using a vector network analyzer, namely measuring the scattering parameters of the electromagnetic unit by using a two-port network formed by a port on the left side of Ls (a pressure port in the CVT) and a model output port. The measurement frequency of the scattering parameter is set according to the target high-frequency voltage band to be measured after CVT spread.
The scattering parameter can be converted into a Y parameter by equation (1).
Wherein Z is 01 And Z 02 For port matching impedance, 50Ω is typically taken. The parameter calculated by the formula (1) is an admittance parameter of the whole electromagnetic unit of the CVT model.
For the admittance parameter calculation of the high frequency module in fig. 1, the form of subtraction of equation (2) is adopted.
Y High Frequency ＝Y CVT electromagnetic unit -Y Steady state (2)
For the steady state module shown in FIG. 1, it is considered as an admittance matrix behind a two-port networkThe admittance parameter values under each frequency point can be calculated according to the theoretical formula of admittance parameters of the constructed steady-state module, or the impedance matrix value under each frequency point can be calculated according to the theoretical formula, and then the impedance matrix value is calculated, so that the admittance parameters of the steady-state module can be obtained. The damper branch may be optionally omitted during theoretical calculations.
The high-frequency module is further implemented in an equivalent circuit, and the pi-type circuit in circuit synthesis is adopted for the equivalent, as shown in fig. 2.
The admittance parameters of the three high-frequency sub-modules at each frequency point can be calculated by an admittance parameter matrix of the high-frequency module, as shown in a formula (3).
Y Black box-A ＝Y 11 +Y 12
Y Black box-B ＝-(Y 12 +Y 21 )/2
Y Black box-C ＝Y 12 +Y 22 (3)
The second step of implementing the equivalent circuit is to fit a rational function continuous in the frequency domain as shown in equation (4) to the three sub-modules using an improved vector matching method.
Wherein a is j Is pole, c j For the remainder, d is a constant term and N is an order.
And (3) vector matching is carried out on the admittance parameters of each sub-module calculated by the formula (3), so that an expression of the form of the formula (4) of each sub-module can be obtained.
The last step of implementing the equivalent circuit is to construct the equivalent circuit according to the Forst II type circuit comprehensive theory after acquiring the data expressions of the three high-frequency submodules. Specifically, the expression of the type (4) of each sub-module may be expressed as a foster partial expression and expression as shown in the formula (5).
Wherein, represents complex conjugation. P (P) ri And r i Respectively representing the i-th real pole and the remainder. P (P) ci 、P ci *、r ci And r ci * Respectively representing the i-th pair of complex conjugate poles and residuals. h is a constant term. The admittance parameters shown in formula (5) can be used for RLCG circuit synthesis. Wherein the constant isItem h, which can be equivalently represented as R in FIG. 3 0 And the resistance of the resistor branch is 1/h.
For the real pole term, we can synthesize R as shown in FIG. 4 i 、L i The value of the branch is shown as a formula (6).
For the complex conjugate pole terms, one can synthesize one R as shown in FIG. 5 i L i C i G i A series-parallel branch, wherein R i 、L i Sequentially connected with C i 、G i The value of which is shown in formula (7) in series.
And connecting the branches in parallel to form an equivalent circuit of the sub-module. Thus, the construction of the whole CVT nonlinear broadband model is completed.
After the CVT nonlinear broadband model is built, the CVT input waveform can be calculated according to the CVT output signal and the model inversion.
Specifically, according to kirchhoff voltage theorem and kirchhoff current theorem, the output port and the output port of the CVT nonlinear broadband equivalent circuit model shown in fig. 2 are associated. The specific mathematical calculation method after the association adopts different modes aiming at the capacitance unit, the electromagnetic unit steady-state module and the electromagnetic unit high-frequency module.
The same method is adopted for calculating the branch current and the element voltage of the steady-state modules of the capacitor unit and the electromagnetic unit, namely, the current and the voltage of each element are calculated step by step in the time domain towards the input end according to the volt-ampere relation of each element. Since the CVT nonlinear broadband model contains capacitive inductive elements, differential forms are involved in the calculation process. In the inversion calculation process, a multi-step method in numerical analysis is used to solve the differential expression. In particular, if f (x n ,t n ) Is a differential equation requiring solution calculation in the inversion calculation process, and is expressed as a solution x in a formula (8) n Recursion can be performed according to the previous k-step, h being the step size.
x n+1 ＝a o x n +h[b o f(x n ,t n )+b 1 f(x n-1 ,t n-1 )+…+b k-1 f(x n-k+1 ,t n-k+1 )](8)
The coefficients are as follows:
when the method is used for carrying out inversion calculation on the CVT nonlinear broadband model, k is more than or equal to 3.
For the calculation of the high-frequency module of the electromagnetic unit, a mode of recursive convolution in the time domain is mainly adopted. In the inversion calculation process, the voltages across the three high frequency sub-modules of the electromagnetic unit shown in fig. 2 are known, and the current of the sub-modules needs to be calculated. Because each sub-module is formed by connecting a plurality of RLCG circuits in parallel, the current of each branch circuit is calculated respectively, and finally the currents are added. The pure resistance branch circuit can directly calculate the current of the branch circuit by using ohm law according to the existing branch circuit voltage. For the branches shown in fig. 4 and 5, a recursive convolution in the time domain is used to calculate the branch current from the known branch voltage. Specifically, the branch shown in fig. 4 and 5 is considered as a linear system, which takes the branch voltage as an input and the main resistance voltage of the branch as an output, to construct a transfer function.
The transfer function of the branch shown in FIG. 4 is
Wherein R/L is the remainder of the equation, and R/L is the pole of the equation. The transfer function of the branch shown in FIG. 5 is
Wherein R is 1 R is the resistance on the main circuit of the branch circuit 2 Is the inverse of the conductance value on the parallel branch. Wherein the expression (11) is further converted into an expression of the form of a leave-pole like the expression (10) as shown in the expression (12). K is the remainder and P is the pole.
According to the transfer function and the known branch voltage, a recursive convolution method is adopted to calculate the resistance voltage, and then ohm law is adopted to calculate the current of the resistance. Specifically, the above transfer function is subjected to inverse laplace transform to become an impulse response expression in the time domain, as shown in expression (13).
Where n is the number of poles, there are two poles for the branch shown in fig. 4, i.e. one pole, and for the branch shown in fig. 5. K (K) i To be reserved, P i Is a pole. For each pair of residue-poles, the formula shown in FIG. 14 is used to calculate the voltage U according to the branch branch (t) performing recursive calculation of the voltage U of the resistor in the time domain R (t)。
U R (n)＝m·U R (n-1)+p·U branch (n)+p·U branch (n-1) (14)
Wherein, the liquid crystal display device comprises a liquid crystal display device,
for transfer functions of a plurality of residue-pole pairs, the output waveforms of each residue-pole pair are obtained according to the equation (14), and then added.
After the value of the resistance voltage is calculated, the current of the branch circuit can be calculated by applying ohm's law, and the acquisition of the voltage and current parameters of the high-frequency module can be completed.
In the CVT nonlinear broadband model, the output voltage is the branch voltage of the submodule C. However, since the sub-module B has a bridge structure, the branch voltage of the sub-module B is unknown during the calculation to the model high voltage output port. Therefore, the voltage of the end point (medium voltage point) on the left side of the sub-module B can be traversed within a certain range under the time point, the total current of the end point of the sub-module B at the time point can be calculated by knowing the branch voltage of the sub-module B at each traversing point, and the current of the steady-state module can be calculated after knowing the currents of the sub-module C and the sub-module B, so that the calculation can be carried out leftwards from the steady-state module, and when the voltage of the traversing node (medium voltage point) is reversely calculated, whether the traversing value is reasonable or not is judged by comparing with the traversing value. And further calculating to the high-voltage input end, so as to calculate the voltage waveform of the output port and complete waveform recovery.
Based on the above embodiment, the above model and calculation method are suitable for the spread spectrum development of a laboratory or CVT at the factory stage of the manufacturer, or the application of the above method to a CVT with a medium pressure point, because the measurement from the medium pressure point is required. Whereas for a large number of CVT's already commissioned at the substation site they are generally not equipped with medium voltage ports for measurement work of the electromagnetic units. Thus, the model shown in fig. 6 can be used, in which the high frequency module is connected in parallel with the two-port model of the whole CVT, so that the relevant measurement work can be carried out directly from the high-voltage input and output ports of the CVT.
The whole CVT model is a steady-state module, and the admittance matrix of the high-frequency module can be calculated by the formula (2).
In the next calculation and circuit synthesis, this can be done in two ways. The first way is to directly analyze the method according to the present application based on the model of fig. 6, and the pi-type equivalent circuit of the nonlinear broadband model without medium voltage port is shown in fig. 7, and the admittance expressions of the three sub-modules of the model shown in fig. 7 can be calculated by the formulas (2) and (3). And further performing rational function fitting on the three sub-modules by using a vector matching method. And then comprehensively constructing the equivalent circuits of the three sub-modules by using the Forst type II circuit theory. In waveform inversion calculation of the model shown in fig. 7, the voltage of the high-voltage input port can be directly traversed due to the presence of the bridging structure (sub-module B). And under each traversed voltage value, the branch current of the submodule B and the branch current of the submodule C can be calculated, and further, in a steady-state model, the calculation is performed rightward. A second approach based on the model shown in fig. 6 is to use the cascading of transmission parameters (T-parameters) to transform into the model shown in fig. 2. That is, the CVT model can be considered as a cascade of two-port networks as shown in fig. 8, assuming negligible capacitive element spur parameters. The T-parameter of the overall model can be multiplied by the point of the transmission parameters of two cascade modules, namely:
T cvt ＝T 1 ·T 2 (16)
the S-parameters of the overall CVT model are converted into T-parameters according to equation (17).
The T parameter of the capacitor cell module can be directly derived from the theoretical formula. Thus, in case the capacitive element T parameter is reversible, the electromagnetic element T parameter can be calculated by equation (18).
T 2 ＝T cvt ·T 1 -1 (18)
After the T parameter of the electromagnetic unit is acquired, the T parameter can be converted into a Y parameter matrix according to a formula (19). To this end, the model and related methods shown in fig. 2 may be constructed in the manner described in this section, and the inversion calculation of the input waveform may be performed.
In CVT without medium-voltage point, if leakage reactance L of winding parameters T And winding resistance R T Are not readily available, and both elements can be omitted in the steady state module.
The foregoing description of the embodiments has been provided for the purpose of illustrating the general principles of the application, and is not meant to limit the scope of the application, but to limit the application to the particular embodiments, and any modifications, equivalents, improvements, etc. that fall within the spirit and principles of the application are intended to be included within the scope of the application.
Claims (1)
1. The transient overvoltage measurement method based on the nonlinear broadband model is characterized by comprising the following steps of:
step 1, an electromagnetic unit model is built, the electromagnetic unit model is connected to a connection point between a resistor R1 and a capacitor C2 of a capacitor unit of a CVT, the electromagnetic unit model comprises a steady-state module and a high-frequency module, the steady-state module is connected with the high-frequency module, the steady-state module is a physical model comprising independent elements, the steady-state module comprises a compensation reactor, a transformer and a resonance damper, the left two ports of the steady-state module are respectively connected to a medium-voltage point and the ground of the CVT, the right two ports of the steady-state module are respectively connected to the output of the electromagnetic unit model and the ground of the capacitor unit of the CVT, the left two ports of the high-frequency module are respectively connected to the high-frequency voltage input end and the ground of the capacitor unit of the CVT, the right two ports of the electromagnetic unit model are respectively connected to the output end of the overall CVT model, a characteristic curve about current is acquired for a nonlinear element in the electromagnetic unit model through a volt-ampere method, a volt-ampere experimental result is simulated into a nonlinear resistor I=f (U) in an odd polynomial mode, the nonlinear inductance is simulated into a form I=f (U), and the voltage I=f is a magnetic chain;
measuring component data of leakage reactance and resistance of windings in the transformer through short circuit and open circuit experiments of the transformer, and calculating related resistance components of the capacitor unit by adopting loss angle measurement results;
step 2, constructing an equivalent circuit of the high-frequency module: acquiring admittance parameters of an electromagnetic unit model, calculating admittance parameters of a steady-state module, calculating admittance parameters of a high-frequency module, calculating admittance parameters of each sub-module of a pi-type equivalent circuit after pi-type equivalence, obtaining an expression of each sub-module of the pi-type equivalent circuit after vector matching, and comprehensively constructing an equivalent circuit of a final high-frequency module by using a Forst II-type RLCG circuit according to the expression; thus, the construction of the whole CVT nonlinear broadband model is completed;
and step 3, inverting and calculating the waveform of the nonlinear broadband model input port, and collecting the output waveform of the CVT output end.
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