CN102393493B - Method and system for acquiring electromagnetic transient time domain current response of cylindrical conductor - Google Patents
Method and system for acquiring electromagnetic transient time domain current response of cylindrical conductor Download PDFInfo
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- CN102393493B CN102393493B CN2011102264138A CN201110226413A CN102393493B CN 102393493 B CN102393493 B CN 102393493B CN 2011102264138 A CN2011102264138 A CN 2011102264138A CN 201110226413 A CN201110226413 A CN 201110226413A CN 102393493 B CN102393493 B CN 102393493B
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Abstract
The invention discloses a method and system for acquiring the electromagnetic transient time domain current response of a cylindrical conductor, which are used for solving the problem of difficulty in realizing the practicability of the conventional computing method in the electromagnetic transient process of a cylindrical conductor. The method comprises the following steps of: decomposing voltage signals applied to the two ends of the conductor on the aspect of time domain by using a step function series approximating method for voltage signals according to the step function series, and representing into the overlapping form of a series of step voltages; combining a time domain current response which corresponds to each decomposed step voltage according to the time domain current response of the conductor to a unit step voltage signal; and acquiring the time domain current responses of the cylindrical conductor to the applied voltage signals. By adopting the system, voltage signals in any form applied to the two end of the cylindrical conductor or an equivalent cylindrical conductor can be processed, the voltage signals are discretized, numerical value operation can be performed with a computer, and the computing accuracy and speed are increased.
Description
Technical field
The electromagnetic field transient state that the present invention relates to conductor is calculated field, relates more specifically to a kind of method and system that obtains time domain current-responsive in the cylindrical conductor electromagnetic transient.
Background technology
In the calculating of cylindrical conductor electromagnetic field transient state process, the general method that adopts mainly can be divided at present: two kinds of time domain calculating and frequency-domain calculations.The core of above method is all to solve Bessel's equation.Be non-circular cylindrical conductor for cross section, calculate again after also noncircular cross section can being equivalent to the circle of homalographic.
The time domain computing method of cylindrical conductor are to solve the conductor heat conduction problem to propose at first by H.S.Carslaw and J.C.Jaeger, and by people such as Edward J.Tuohy, introduce electricity field, but the method only is defined as the diffusion process of conductive surface electromotive force current density when constant, does not set up the relation between conductor both end voltage and electric current.
The frequency-domain calculations method of cylindrical conductor is proposed by R.J.Hill, constant this characteristic of the resistance of conductor and inductance value when the method is utilized cylindrical conductor current signal frequency stabilization, Bessel's equation is converted to frequency domain, circuit integral body is carried out frequency-domain calculations, finally result is adopted the inverse fourier transform method to go to time domain, obtain its time solution.It is comparatively accurate that the method is calculated, but due to when Practical Project utilizes, a large amount of elements can't be converted to frequency domain representation, as rectifier, motor etc., so the method is difficult to realize in practical engineering calculation.
In sum, the diffusion process of current density when present time domain computing method are can only calculating conductor surface electrical kinetic potential constant, but in actual applications because the electromotive force of conductive surface is normally uncertain, so limited the range of application of the method; And the frequency-domain calculations method is in the engineering calculation of reality, because a large amount of components and parts can't be converted to frequency domain representation and can not calculate, so also limited of the problem that can solve.
And along with the fast development of D.C. high voltage transmission and field of track traffic; calculating to conductor electromagnetic field transient state process is had higher requirement on practicality, particularly at the aspects such as electromagnetic transient simulation, relay protection algorithm research and fixed value adjusting of electric system, have great significance.
In a word, needing the urgent technical matters that solves of those skilled in the art is how can realize cylindrical conductor electromagnetic transient computing method practical.
Summary of the invention
Technical matters to be solved by this invention is how to realize practical in practical engineering application of cylindrical conductor electromagnetic transient computing method.
In order to address the above problem, the invention discloses a kind of method of obtaining cylindrical conductor time domain current-responsive in electromagnetic transient, comprising:
At first the voltage signal that is applied to cylindrical conductor or equivalent circular cylindricality conductor two ends is carried out filtering processing and conversion process before sampled measurements;
Voltage signal is carried out sampled measurements, and deduct the magnitude of voltage of a upper sampling instant with the magnitude of voltage that each sampling instant obtains, obtain the voltage change of current time, described voltage change is also the some component voltage values after voltage signal is decomposed according to step function progression approach method;
According to corresponding time domain current-responsive of each component voltage value that preceding method obtains, this time domain current-responsive is the current-responsive that produces of Unit-step function signal and the product of this component voltage value; The time domain current-responsive that all component voltage values are corresponding carries out the combination in time domain, just can obtain in electromagnetic transient the time domain current-responsive in cylindrical conductor under the free voltage signal or equivalent circular cylindricality conductor.
Filtering processing and the conversion process of described voltage signal before sampling refers to higher hamonic wave filtering and analog-to-digital conversion process.
Described method also comprises, obtains the detail parameters of target circle cylindrical conductor, and described parameter comprises: conductivity, relative permeability, radius and conductor length; If target conductor is non-cylindrical, must be for being equivalent to the conductor of cylindrical conductor;
Equivalent circular cylindricality conductor refers to that xsect is non-circular even cylindrical conductor, described xsect is that the even cylindrical conductor that non-circular even cylindrical conductor can be equivalent to the circular cross section of homalographic calculates, and according to the cylindrical conductor after equivalence, obtains its detail parameters.
Described method also comprises, utilizes kelvin effect and the current density diffusion formula of cylindrical conductor under step voltage, and acquisition Unit-step function signal is applied to the time domain current-responsive on the unit length cylindrical conductor.
The invention also discloses a kind of system of obtaining cylindrical conductor time domain current-responsive in electromagnetic transient, described system comprises:
The voltage signal processing module, be used for that the voltage signal that is applied to cylindrical conductor or equivalent circular cylindricality conductor two ends is carried out filtering before sampled measurements and process and change; Described voltage signal processing module comprises higher hamonic wave filtering device and modulus switching device.
The voltage signal acquisition module, be used for gathering and recording the magnitude of voltage of different sampling instants; Described voltage signal acquisition module comprises the collecting device of voltage signal and the memory device of record sampling numerical value.
Step voltage progression module, be used for calculating and recording the voltage change of each sampling instant with respect to a upper sampling instant, and described voltage change refers to the some component voltage values after voltage signal decomposes according to step function progression approach method; Described step voltage progression module comprises the computing equipment that can calculate neighbouring sample voltage change constantly and the memory device that records the component voltage value.
Time domain currents combination module, be used for calculating time domain current-responsive corresponding to each component voltage value, and the time domain current-responsive that will obtain makes up; Described time domain currents combination module comprises the treatment facility that can calculate and make up time domain current-responsive corresponding to each component voltage value.
Compared with prior art, the present invention has the following advantages:
At first, the present invention adopts step function progression to approach the method for voltage signal, problem is changed into the time domain current-responsive in conductor when solving the Unit-step function signal and being applied to the cylindrical conductor two ends, and after voltage signal being expressed as the form of step function progression, the corresponding time domain current-responsive of each in progression step voltage can solve, then all these time domain current-responsives are carried out the combination in time domain, just can obtain the time domain current-responsive of cylindrical conductor electromagnetic transient.The method has been divided into several steps that are easy to realize with the electro-magnetic transient computation process of complexity, has improved the dirigibility of using.
Secondly, because the voltage signal of arbitrary form can utilize step function progression approach method to be similar to, approximate precision depends on the interval of sampling instant, samples more intensive, and precision is higher.Therefore, the voltage signal that is applied to the arbitrary form on cylindrical conductor can utilize this method to calculate, and this electromagnetic field transient state at DC feedback circuit, subway line etc. has stronger practicality in calculating.
Again, be equivalent to voltage signal has been carried out the discretize processing after voltage signal utilizes step function progression to approach, follow-up calculating can utilize computing machine to carry out numerical operation, has greatly improved speed and the accuracy of calculating.
Description of drawings
Fig. 1 is the described method flow diagram that obtains the time domain current-responsive of cylindrical conductor electromagnetic transient of the embodiment of the present invention;
Fig. 2 is the schematic diagram of the current-responsive of the Unit-step function signal that in the embodiment of the present invention, cylindrical conductor applied and generation thereof;
Fig. 3 is the schematic diagram that adopts step function progression approach method to represent to voltage signal in the embodiment of the present invention;
Fig. 4 adopts the schematic diagram of corresponding cylindrical conductor current-responsive after the step function series expression to voltage in the embodiment of the present invention;
Fig. 5 is the unit module structural representation that the described system of the embodiment of the present invention comprises.
Embodiment
For above-mentioned purpose of the present invention, feature and advantage can be become apparent more, the present invention is further detailed explanation below in conjunction with the drawings and specific embodiments.
The present invention can use accomplished in many ways, can be the specialized equipment with single-minded function, also can share the simulation calculation platform with other function (as MATLAB, RTDS).
With reference to Fig. 1, the method flow diagram of the time domain current-responsive that obtains the cylindrical conductor electromagnetic transient described in the embodiment of the present invention.
The detail parameters of described target circle cylindrical conductor comprises: conductivityσ, relative permeability μ, radius R, conductor length L etc.;
If target conductor is non-cylindrical, must be for being equivalent to the conductor of cylindrical conductor,, as rail etc., the non-cylindrical cross-sectional area of conductor is equivalent to the circle of homalographic, the above-mentioned parameter of reentrying, to calculate.
With reference to Fig. 2, when the Unit-step function signal was applied on the unit circle cylindrical conductor, the concrete grammar that calculates corresponding time domain current-responsive was as follows:
In 0 moment, voltage signal is undergone mutation, and at this moment the frequency of voltage signal can be considered to infinitely great.According to the definition of kelvin effect, can think that electric current concentrates on the top layer of cylindrical conductor substantially, unlimited few in the inner distribution of cylindrical conductor.Can think in computation process: the cylindrical conductor internal current is approximately equal to 0; Round conductor surface current density J
sCan be by Ohm law J
s=E
s/ σ=U/ σ calculates acquisition.
Other moment, because conductor internal current density J (r, t) can be regarded as meeting Maxwell equation and the constant diffusion process of surface current density.This process, the people such as Edward J.Tuohy introduce the Bessel's equation series method that R.J.Hill proposes, and its current density, J (r, t) about time t with the solution of diffusion radius r is:
In following formula, μ is relative permeability,
σ is conductivity,
J is current density,
J
sThe conductive surface current density,
J
0The zeroth order Bessel function of the first kind,
J
1The single order Bessel function of the first kind,
α
nIt is the root of zeroth order Bessel function of the first kind.
Time domain solution for the current in cylindrical conductor is:
In following formula, R is the cylindrical conductor radius,
When step voltage is t
0(t
0The situation of ≠ 0) constantly undergoing mutation, only need to be adjusted into t-t with the t in above-mentioned time domain solution for the current formula
0Get final product.
Described filtering processing and conversion refer to higher hamonic wave filtering and analog to digital conversion, its objective is for analog signal conversion is become digital signal, facilitate computing machine to process.
Voltage signal is sampled and recorded, and establishing adjacent sampling time interval is T.Deduct the magnitude of voltage of a upper sampling instant with the magnitude of voltage that each (for the first time) sampling instant obtains, obtain the voltage change of current time, described voltage change is also the some component voltage values after voltage signal is decomposed according to step function progression approach method.Its principle is as follows:
, with reference to Fig. 3, will adopt the progression approach method of step function to represent to the voltage signal that cylindrical conductor applies.Be located under the form of discrete sampling, voltage signal f (t) can use the following formula discrete representation, and T is sampling time interval, and nT sampled voltage brief note constantly is f[n]:
f[n]＝f(n·T)
Voltage discrete signal f[n] can approach with unit step signal U (t) progression:
In following formula, when n=0: f[n-1) T]=0
By f[n] series statement as can be known, f[n] can be expressed as the stacking pattern of a series of step voltage components, and the coefficient of Unit-step function U (nT) be exactly exactly before and after double sampling magnitude of voltage poor, i.e. { f (nT)-f[(n-1) T] }.
According to step 102, the current-responsive that produces when cylindrical conductor is applied Unit-step function signal U (t) is: I (t), so the corresponding current-responsive of Unit-step function U (nT) is I (t-nT).Therefore, step voltage component { f (nT)-f[n-1) T] } the corresponding current-responsive of U (nT) can be expressed as { f (nT)-f[(n-1) T] } I (t-nT).
With reference to Fig. 4, the calculating voltage signal is with the corresponding current-responsive of each step voltage component in step function series expression approximant, and these current-responsives are carried out combination in time domain, just can obtain under the voltage of arbitrary form in electromagnetic transient the time solution of current-responsive in cylindrical conductor:
The present invention also provides a kind of specific embodiments that can obtain the system of time domain current-responsive in the cylindrical conductor electromagnetic transient.
, with reference to Fig. 5, be the structural representation of System Implementation.Described system comprises voltage signal processing module 51, voltage signal acquisition module 52, step voltage progression module 53, time domain currents combination module 54.
Wherein said voltage signal processing module 51, comprise higher hamonic wave filtering device and modulus switching device, is used for the voltage signal that is applied to cylindrical conductor or equivalent circular cylindricality conductor two ends is carried out filtering processing and analog to digital conversion before sampled measurements;
Wherein said voltage signal acquisition module 52, comprise the collecting device of voltage signal and the memory device of record sampling numerical value, is used for gathering and recording the magnitude of voltage of different sampling instants;
Wherein said step voltage progression module 53, comprise the computing equipment that can calculate neighbouring sample voltage change constantly and the memory device that records the component voltage value, be used for calculating and recording the voltage change of each sampling instant with respect to a upper sampling instant, described voltage change refers to the some component voltage values after voltage signal decomposes according to step function progression approach method;
Wherein said time domain currents combination module 54, comprise the treatment facility that can calculate and make up time domain current-responsive corresponding to each component voltage value, be used for calculating time domain current-responsive corresponding to each component voltage value, and the time domain current-responsive that will obtain makes up.
Each embodiment in this instructions all adopts the mode of going forward one by one to describe, and what each embodiment stressed is and the difference of other embodiment that between each embodiment, identical similar part is mutually referring to getting final product.For system embodiment, because it is substantially similar to embodiment of the method, so description is fairly simple, relevant part gets final product referring to the part explanation of embodiment of the method.
Above to a kind of method and system that obtains the time domain current-responsive of cylindrical conductor electromagnetic transient provided by the present invention, be described in detail, applied specific case herein principle of the present invention and embodiment are set forth, the explanation of above embodiment just is used for helping to understand method of the present invention and core concept thereof; Simultaneously,, for one of ordinary skill in the art,, according to thought of the present invention, all will change in specific embodiments and applications, in sum, this description should not be construed as limitation of the present invention.
Claims (9)
1. a method of obtaining cylindrical conductor time domain current-responsive in electromagnetic transient, is characterized in that, comprising:
At first the voltage signal that is applied to cylindrical conductor or equivalent circular cylindricality conductor two ends is carried out waveform processing and conversion before sampled measurements;
Voltage signal is carried out sampled measurements, and deduct the magnitude of voltage of a upper sampling instant with the magnitude of voltage that each sampling instant obtains, obtain the voltage change of current time, described voltage change is also the some component voltage values after voltage signal is decomposed according to step function progression approach method;
The corresponding time domain current-responsive of each the component voltage value that obtains, this time domain current-responsive are the current-responsive that produces of Unit-step function signal and the product of this component voltage value; The time domain current-responsive that all component voltage values are corresponding carries out the combination in time domain, obtains in electromagnetic transient the time domain current-responsive in cylindrical conductor under the free voltage signal or equivalent circular cylindricality conductor.
2. the method for claim 1, is characterized in that, waveform processing and the conversion of voltage signal before sampled measurements refers to higher hamonic wave filtering and analog-to-digital conversion process.
3. the method for claim 1, is characterized in that, also comprises the detail parameters of obtaining cylindrical conductor, and described parameter comprises: conductivity, relative permeability, radius and conductor length;
Equivalent circular cylindricality conductor refers to that xsect is non-circular even cylindrical conductor, described xsect is that the even cylindrical conductor that non-circular even cylindrical conductor is equivalent to the circular cross section of homalographic calculates, and according to the cylindrical conductor after equivalence, obtains its detail parameters.
4. the method for claim 1, is characterized in that, also comprises and utilize kelvin effect and the current density diffusion formula of cylindrical conductor under step voltage, and acquisition Unit-step function signal is applied to the time domain current-responsive on the unit length cylindrical conductor.
5. a system of obtaining cylindrical conductor time domain current-responsive in electromagnetic transient, is characterized in that, comprising:
The voltage signal processing module, be used for that the voltage signal that is applied to cylindrical conductor or equivalent circular cylindricality conductor two ends is carried out filtering before sampled measurements and process and change;
The voltage signal acquisition module, be used for gathering and recording the magnitude of voltage of different sampling instants;
Step voltage progression module, be used for calculating and recording the voltage change of each sampling instant with respect to a upper sampling instant, and described voltage change refers to the some component voltage values after voltage signal decomposes according to step function progression approach method;
Time domain currents combination module, be used for calculating time domain current-responsive corresponding to each component voltage value, and the time domain current-responsive that will obtain makes up.
6. system as claimed in claim 5, is characterized in that, described voltage signal processing module comprises higher hamonic wave filtering device and modulus switching device.
7. system as claimed in claim 5, is characterized in that, described voltage signal acquisition module comprises the collecting device of voltage signal and the memory device of record sampling numerical value.
8. system as claimed in claim 5, is characterized in that, described step voltage progression module comprises the computing equipment that can calculate neighbouring sample voltage change constantly and the memory device that records the component voltage value.
9. system as claimed in claim 5, is characterized in that, described time domain currents combination module comprises the treatment facility that can calculate and make up time domain current-responsive corresponding to each component voltage value.
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| CN1404215A (en) * | 2002-11-01 | 2003-03-19 | 清华大学 | Asynchronous motor optimizing excitation control method based on magnetic-field saturated non-linear motor model |
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| Calculation and measurement of rail impedances applicable to remote short circuit fault currents;J.C.Brown等;《Electric Power Applications,IEEE Proceedings B》;19920731;第139卷(第4期);全文 * |
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