CN107870290B - A kind of direction finding precision analysis method suitable for Arbitrary Planar Array - Google Patents
A kind of direction finding precision analysis method suitable for Arbitrary Planar Array Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/12—Testing dielectric strength or breakdown voltage ; Testing or monitoring effectiveness or level of insulation, e.g. of a cable or of an apparatus, for example using partial discharge measurements; Electrostatic testing
- G01R31/1227—Testing dielectric strength or breakdown voltage ; Testing or monitoring effectiveness or level of insulation, e.g. of a cable or of an apparatus, for example using partial discharge measurements; Electrostatic testing of components, parts or materials
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
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Abstract
The invention discloses a kind of direction finding precision analysis methods suitable for Arbitrary Planar Array, comprising: establishes coordinate system to Arbitrary Planar Array, the geometric center of array is enabled to be located at coordinate origin；With the direction finding precision of carat Metro lower bound assessment array, need to calculate three important parameters: amplitude, direct current offset and first phase according to the coordinate of each antenna first；Carat Metro lower bound is listed about true bearing angle, the function expression of true pitch angle, relation curve of the carat Metro lower bound about true bearing angle and true pitch angle is drawn accordingly, if carat Metro lower bound is relatively small in the range of some true bearing angle, true pitch angle, direction finding precision is relatively high at this.The invention proposes a kind of direction finding precision analysis methods suitable for Arbitrary Planar Array, are applicable in application conditions any in substation, have directive function to preferred arrangement aerial array.The aerial array optimized by this method, Measure direction performance with higher and lesser array sizes.
Description
Technical field
The invention belongs to Partial Discharge Detecting Technology field more particularly to a kind of direction finding essences suitable for Arbitrary Planar Array
Spend analysis method.
Background technique
Power equipment is numerous in open type substation, it is ensured that system safe and stable operation is significant.Shelf depreciation is to set
The sign of standby insulation degradation, if will not gradually develop the disruptive discharge for equipment, bringing to substation can not estimate by early detection
The economic loss of amount.Nowadays common Partial Discharge Detecting Technology is sensor to be fixedly mounted on transformer, gas-insulated
On the single equipments such as combined electric appliance equipment, but the equipment such as breaker, disconnecting switch are lacked and are paid close attention to.For this purpose, British scholar proposes
The inspection platform for establishing a packaged type carries out comprehensive part to whole station power equipment using UHF antenna array and puts
Electro-detection.However, the array element spacing of aerial array has been more than 1.1m, is not easy to inspection to guarantee system accuracy.
To reduce array sizes, routing inspection efficiency is improved, it is special that super-resolution direction-finding algorithm is applied to substation's shelf depreciation
In VHF direction finder system.With invariable rotary Subspace algorithm (Estimation of Signal Parameters via
Rotational Invariance Techniques, ESPRIT) super-resolution direction-finding algorithm of the algorithm for representative, angle point
The ability of distinguishing breaches the restriction of traditional " Rayleigh limit ", makes system that can also possess higher resolving power under lesser array sizes
With direction finding precision.However, result of study shows that the method for arranging of aerial array has the direction finding precision of ESPRIT algorithm both at home and abroad
Significant impact.At present to the research of aerial array method for arranging, several arrays of different shapes are often selected, then pass through emulation
The direction finding precision for comparing them with experiment, thus the matrix arrangement for selecting performance best.In fact, this method has limitation
Property, the array with optimum performance is not often in the column of selection.
Therefore, a kind of direction finding precision analysis method suitable for Arbitrary Planar Array is needed, in the hope of being suitable for any application
Scene instructs array optimization to arrange.
Summary of the invention
The purpose of the present invention is to provide a kind of direction finding precision analysis methods suitable for Arbitrary Planar Array.
The present invention adopts the following technical scheme that realize:
A kind of direction finding precision analysis method suitable for Arbitrary Planar Array, includes the following steps:
1) coordinate system is established to Arbitrary Planar Array, the geometric center of the planar array is enabled to be located at coordinate origin；
2) direction finding precision of the planar array is assessed with carat Metro lower bound, needs to calculate three according to the coordinate of each antenna first
A important parameter: amplitude, direct current offset and first phase；
3) carat Metro lower bound is listed about true bearing angle, the function expression of true pitch angle, draws carat accordingly
Relation curve of the Metro lower bound about true bearing angle and true pitch angle, if at some true bearing angles, true pitch angle
Carat Metro lower bound is relatively small in range, then direction finding precision is relatively high at this.
A further improvement of the present invention lies in that Arbitrary Planar Array described in step 1) is the packet arbitrarily arranged in the plane
Planar array containing N number of array element, array element are UHF antenna.
A further improvement of the present invention lies in that in step 1), the array element coordinate (x of the geometric center of the planar array0, y0)
Calculation formula it is as follows
In formula, xiAnd yiIt is the abscissa and ordinate of i-th of array element respectively, i=1 ... N, N are array element number.
A further improvement of the present invention lies in that in step 2), the carat Metro lower bound, that is, attainable minimum of direction-finding system institute
Angle measurement error can quantify direction finding precision, and carat Metro lower bound numerical value is smaller, and direction finding precision is higher.
A further improvement of the present invention lies in that amplitude A, direct current offset B and first phase γ are defined as follows formula in step 2):
A further improvement of the present invention lies in that carat Metro lower bound is about true bearing angle and true pitching in step 3)
The function expression at angle includes azimuthal carat of Metro lower bound χ1The carat Metro lower bound χ of (θ, φ) and pitch angle2(θ, φ)
About the function expression of true bearing angle θ and true pitch angle φ, such as following formula:
A further improvement of the present invention lies in that drafting carat Metro lower bound is about true bearing angle and really in step 3)
The relation curve of pitch angle includes four relation curves, i.e. pass of the azimuthal carat of Metro lower bound about true bearing angle altogether
Be curve, azimuthal carat of Metro lower bound about the relation curve of true pitch angle, pitch angle carat Metro lower bound about
The relation curve of the relation curve at true bearing angle and the carat Metro lower bound of pitch angle about true pitch angle.
The present invention have it is following the utility model has the advantages that
The present invention provides a kind of direction finding precision analysis methods suitable for Arbitrary Planar Array.At present both at home and abroad to array
The research of method for arranging often selects the array of several regular geometric shapes, by the survey for emulating and testing more different arrays
To precision, to select optimum array.In fact, this method has limitation, often the array with optimum performance does not exist
The column of selection.Blank is studied both at home and abroad in order to make up, and inventors herein proposes the analysis method for General Cell direction finding precision, it is right
There is directive significance in the array arrangement studied under different application scene.
Further, the present invention has summarized the direction finding precision of Arbitrary Planar Array with true bearing angle, true pitch angle
Changing rule.It is found by mathematical derivation, azimuth, the direction finding precision of pitch angle are equal relative to true bearing angle (0~360 °)
Change in sinusoidal rule, the period is 180 °.For this purpose, having summed up the parameter of reflection direction finding precision changing rule: amplitude, direct current are inclined
It moves, first phase.Wherein, amplitude represents the severe degree of direction finding precision variation, the smaller the better；Direct current offset is the benchmark direction finding of system
Precision is the bigger the better；First phase affects array, and wherein direction finding precision is low, and where direction finding precision is high, should close in conjunction with site environment
Reason setting.Experiments verify that being integrally improved 30% by the array df precision that this method optimizes, array sizes are reduced
40%, it is applicable in partial discharge detection on site and positioning.
Further, present embodiments can apply in the development process of substation's partial-discharge ultrahigh-frequency cruising inspection system, the system
It can be greatly decreased and the cost of on-line measuring device is installed on a large scale in substation, have to guarantee power equipment safety operation great
Meaning.
Detailed description of the invention
Fig. 1 is a kind of flow chart of the direction finding precision analysis method suitable for Arbitrary Planar Array of the present invention.
Fig. 2 is the aerial array arrangement for the first array that the present invention is set.
Fig. 3 is the aerial array arrangement for the second array that the present invention is set.
Fig. 4 is situation of change of the azimuthal carat of Metro lower bound of the invention obtained in simulations with true bearing angle.
Fig. 5 is the carat Metro lower bound for the pitch angle that the present invention obtains in simulations with the situation of change at true bearing angle.
Fig. 6 is situation of change of the azimuthal carat of Metro lower bound of the invention obtained in simulations with true pitch angle.
Fig. 7 is the carat Metro lower bound for the pitch angle that the present invention obtains in simulations with the situation of change of true pitch angle.
Fig. 8 is the waveform for the local discharge signal that the present invention obtains in an experiment.
Fig. 9 is the frequency spectrum for the local discharge signal that the present invention obtains in an experiment.
Figure 10 is variation relation of the azimuth angle measurement error in an experiment of the invention with true bearing angle.
Specific embodiment
Description of specific embodiments of the present invention with reference to the accompanying drawings and examples.
As shown in Figure 1, a kind of direction finding precision analysis method suitable for Arbitrary Planar Array of the present invention, including walk as follows
It is rapid:
1) coordinate system is established to Arbitrary Planar Array, the geometric center of the planar array is enabled to be located at coordinate origin；
Coordinate system is established to Arbitrary Planar Array described in this step, the geometric center of array is O, the coordinate (x of O0,y0)
For (0,0), each array element coordinate meets following relationship in array:
In formula, xiAnd yiIt is the abscissa and ordinate of i-th of array element respectively, i=1 ... N, N are array element number.
As one embodiment, the first array and second array are made of four superfrequency array elements #1, #2, #3 and #4,
The geometric center of array at coordinate origin O, as shown in Fig. 2, in the first array #1~#4 array element coordinate be respectively (0,
0.2), (- 0.2,0), (0, -0.2) and (0.2,0), as shown in figure 3, in second array #1~#4 array element coordinate be respectively (-
0.17,0.1), (- 0.17, -0.1), (0.17, -0.1) and (0.17,0.1), unit are rice.θ is discharge source in XOY plane
Project the angle of opposite X-axis positive direction, i.e. true bearing angle；φ is discharge source XOY plane institute opposite with the line of coordinate origin O
At angle, i.e., true pitch angle.
2) direction finding precision of the planar array is assessed with carat Metro lower bound, needs to calculate three according to the coordinate of each antenna first
A important parameter: amplitude, direct current offset and first phase；
Amplitude A described in this step, direct current offset B and first phase γ, are defined as follows formula:
As one embodiment, the array element coordinate of the first array in Fig. 2 and Fig. 3 and second array is updated to formula respectively
(2) it is calculated, amplitude A, direct current offset B and the first phase γ for obtaining the first array are 0 °, 0.08 ° and 0 ° respectively；Second array
Amplitude A, direct current offset B and first phase γ be 0.0378 °, 0.0778 ° and 90 ° respectively.
3) a carat function expression of the Metro lower bound about true bearing angle and true pitch angle is listed, draws carat accordingly
Relation curve of the Metro lower bound about true bearing angle and true pitch angle, if at some true bearing angles, true pitch angle
Carat Metro lower bound is relatively small in range, then direction finding precision is relatively high at this.
Carat Metro lower bound is listed described in this step about true bearing angle, the function expression of true pitch angle,
Include azimuthal carat of Metro lower bound χ1The carat Metro lower bound χ of (θ, φ) and pitch angle2(θ, φ) is about true bearing angle θ
With the function expression of true pitch angle φ, such as following formula
As one embodiment, by the amplitude A of the first array being calculated above and second array, direct current offset B and
First phase γ is updated in formula (3), obtains the carat Metro lower bound χ at the first array orientation angle1The carat of (θ, φ) and pitch angle beauty
Sieve lower bound χ2The function expression of (θ, φ) about true bearing angle θ and true pitch angle φ, as follows:
Similarly, azimuthal carat of Metro lower bound χ of second array also can be obtained1Under the carat Metro of (θ, φ) and pitch angle
Boundary χ2The function expression of (θ, φ) about true bearing angle θ and true pitch angle φ, as follows:
Drafting carat Metro lower bound is about true bearing angle, the relation curve of true pitch angle described in this step, altogether
Include four relation curves, i.e. relation curve, azimuthal carat of the azimuthal carat of Metro lower bound about true bearing angle
Metro lower bound is bent about the relationship at true bearing angle about relation curve, the carat Metro lower bound of pitch angle of true pitch angle
Relation curve of the carat Metro lower bound about true pitch angle of line, pitch angle.
As one embodiment, in order to study the carat Metro lower bound at azimuth and pitch angle with the change at true bearing angle
Change, enabling true pitch angle is 30 °, as a result as shown in Figure 4 and Figure 5；Similarly, in order to study the carat Metro at azimuth and pitch angle
Lower bound is with the variation of true pitch angle, and enabling true bearing angle is 30 °, as a result as shown in Figure 6 and Figure 7.
It can be seen from Fig. 4 and Fig. 5 the azimuth of the first array, pitch angle Measure direction performance not with true bearing angle
Change and change, carat Metro floor value is 0.17 °；The azimuth of second array, pitch angle carat Metro lower bound with true
Azimuth is in sinusoidal variations rule, and the period is 180 °, when true azimuth is in the range of [- 135 °, -45 °] and [45 °, 135 °]
When interior, the azimuth direction finding precision of second array is higher than the first array, and the pitch angle direction finding precision of second array is lower than first
Array.
For the first array, second array it can be seen from Fig. 6 and Fig. 7, azimuthal direction finding precision is with true pitching
The increase at angle and reduce, and the direction finding precision of pitch angle is improved with the increase of true pitch angle.When true azimuth is 30 °
When, the direction finding precision at the first array orientation angle is higher than second array, and the direction finding precision of the first array pitch angle is lower than second gust
Column.
It can be seen that influence of the array arrangement to partial discharge detecting system is very big, substation's practical application need to be combined
In demand, analyze array df precision, thus reasonable selection array method for arranging.
A kind of direction finding precision analysis method suitable for Arbitrary Planar Array proposed in order to further illustrate the present invention
Practicability has carried out the direction finding precision test of shelf depreciation in laboratory, has used previously described second array as extra-high
The method for arranging of frequency aerial array.Setting simulation discharge source, the waveform and frequency spectrum such as Fig. 8 of the ultrahigh frequency electromagnetic wave signal issued
With shown in Fig. 9.The direction-finding system is realized by Denoising Algorithm and the narrowband ESPRIT Direction Finding Algorithm reaches estimation to the wave of discharge source.Figure
10 for discharge source under different location azimuth, pitch angle angle measurement error, it is seen that azimuth, pitch angle direction finding precision exist
6 ° hereinafter, azimuth direction finding precision is higher wherein when true azimuth is less than -30 ° or is greater than 30 °.The high direction finding of the system
The characteristic of precision and small array sizes meets the demand of live Partial Discharge Detection, demonstrates this method and applies to shelf depreciation inspection
Survey the feasibility with direction-finding system.
As it will be easily appreciated by one skilled in the art that it is described above only as case study on implementation of the invention, not to limit
The present invention, any modification, replacement or the change made all within the spirits and principles of the present invention, should be included in of the invention
Within protection scope.
Claims (7)
1. a kind of direction finding precision analysis method suitable for Arbitrary Planar Array, which comprises the steps of:
1) coordinate system is established to Arbitrary Planar Array, the geometric center of the planar array is enabled to be located at coordinate origin；
2) direction finding precision of the planar array is assessed with carat Metro lower bound, needs to calculate three weights according to the coordinate of each antenna first
Want parameter: amplitude, direct current offset and first phase；
3) carat Metro lower bound is listed about true bearing angle, the function expression of true pitch angle, draws carat Metro accordingly
Relation curve of the lower bound about true bearing angle and true pitch angle, if at some true bearing angle, the range of true pitch angle
Interior carat Metro lower bound is relatively small, then direction finding precision is relatively high at this.
2. a kind of direction finding precision analysis method suitable for Arbitrary Planar Array according to claim 1, which is characterized in that
Arbitrary Planar Array described in step 1) is the planar array comprising N number of array element arbitrarily arranged in the plane, and array element is extra-high
Frequency antenna.
3. a kind of direction finding precision analysis method suitable for Arbitrary Planar Array according to claim 2, which is characterized in that
In step 1), the array element coordinate (x of the geometric center of the planar array0, y0) calculation formula it is as follows
In formula, xiAnd yiIt is the abscissa and ordinate of i-th of array element respectively, i=1 ... N, N are array element number.
4. a kind of direction finding precision analysis method suitable for Arbitrary Planar Array according to claim 1, which is characterized in that
In step 2), the attainable minimum angle measurement error of carat Metro lower bound, that is, direction-finding system institute can quantify direction finding precision, and
Carat Metro lower bound numerical value is smaller, and direction finding precision is higher.
5. a kind of direction finding precision analysis method suitable for Arbitrary Planar Array according to claim 3, which is characterized in that
In step 2), amplitude A, direct current offset B and first phase γ are defined as follows formula:
6. a kind of direction finding precision analysis method suitable for Arbitrary Planar Array according to claim 5, which is characterized in that
In step 3), function expression of the carat Metro lower bound about true bearing angle and true pitch angle includes azimuthal carat
Metro lower bound χ1The carat Metro lower bound χ of (θ, φ) and pitch angle2(θ, φ) is about true bearing angle θ's and true pitch angle φ
Function expression, such as following formula:
7. a kind of direction finding precision analysis method suitable for Arbitrary Planar Array according to claim 6, which is characterized in that
In step 3), relation curve of the carat Metro lower bound about true bearing angle and true pitch angle is drawn, altogether includes four relationships
Curve, i.e. azimuthal carat of Metro lower bound about the relation curve at true bearing angle, azimuthal carat of Metro lower bound about
Relation curve and pitch angle of the carat Metro lower bound about true bearing angle of the relation curve of true pitch angle, pitch angle
Relation curve of the carat Metro lower bound about true pitch angle.
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