CN108959768A - Complex scene power frequency electric field calculation method based on subregion Analogue charge method - Google Patents
Complex scene power frequency electric field calculation method based on subregion Analogue charge method Download PDFInfo
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Abstract
The present invention provides a kind of method that can efficiently, accurately calculate the power frequency electric field of power transmission and transformation system in complex scene.Complex scene power frequency electric field calculation method based on subregion Analogue charge method, including the following contents: a, modeling establish threedimensional model according to the real space region of power-frequency electric field strength to be calculated；B, threedimensional model is divided into several submodel regions by region division；C, virtual boundary is respectively set for submodel region, wherein the virtual boundary in adjacent submodel region intersects two-by-two in the setting of virtual boundary；D, the current potential approach of each submodel region virtual boundary is determined；E, according to the current potential approach of each submodel region virtual boundary, the charge simulation value in each submodel region is determined；F, according to determining charge simulation value, the power-frequency electric field strength in each submodel region is calculated.The present invention demonstrates the high efficiency and reliability of this calculation method by emulation experiment, can provide Technical Reference for the calculating and research of the power frequency electric field under power transmission and transformation system complex scene.
Description
Technical field
The present invention relates to analysis of electric field technical fields, more particularly to the complex scene power frequency based on subregion Analogue charge method
Electric Field Calculation method.
Background technique
Low-voltage is increased and carries out long distance power transmission to grid power transmission by power plant, and it is smaller that same power voltage gets over high current,
The small loss on the line of electric current is small.Therefore multiple power transformation is needed during current transmission, we are electric current during this
Conveying be known as power transmission and transformation.Power transmission and transformation system mainly includes two parts, ultra-high-tension power transmission line and substation.As high pressure is defeated
The continuous improvement of electric line voltage class, (power frequency electric field refers to by 50Hz or 60Hz at any time the power frequency electric field that power transmission and transformation system generates
Between sinusoidal variations charge generate electric field) have become the very important problem of field of environment protection, therefore, for power transmission and transformation system
The calculating of power frequency electric field is extremely important in system.
Currently, the calculating application of power frequency electric field is more widely Analogue charge method, Analogue charge method in power transmission and transformation system
Have the characteristics that principle is simple, unknown quantity is few, solving speed is fast, accuracy is high.But in many cases, around power transmission and transformation system
Environment is more complicated, such as there are trees, building or vehicles around ultra-high-tension power transmission line, in such cases with simulation electricity
It is huge that lotus method can have a calculation amount when calculating complex three-dimensional model, or even because that calculation amount is more than calculator memory is imponderable
Problem.It, will not be by the insufficient limitation of calculator memory, computer even if therefore, it is necessary to study one kind under complex environment
Also the method for the power frequency electric field of power transmission and transformation system can efficiently, be accurately calculated.
Summary of the invention
The present invention provides a kind of side that can efficiently, accurately calculate the power frequency electric field of power transmission and transformation system in complex scene
Method.
The solution of the present invention is as follows:
Complex scene power frequency electric field calculation method based on subregion Analogue charge method, including the following contents:
A, it models, threedimensional model is established according to the real space region of power-frequency electric field strength to be calculated；
B, threedimensional model is divided into several submodel regions by region division；
C, virtual boundary is respectively set for submodel region, wherein adjacent submodel area two-by-two in the setting of virtual boundary
The virtual boundary in domain intersects；
D, the current potential approach of each submodel region virtual boundary is determined；
E, according to the current potential approach of each submodel region virtual boundary, the mould in each submodel region is determined
Quasi- charge value；
F, according to determining charge simulation value, the power-frequency electric field strength in each submodel region, each submodule are calculated
The power-frequency electric field strength in type region is the electric field strength for characterizing entire area of space.
Preferably, in step a, when modeling, power transmission line is equivalent at cylinder, and building is equivalent at cuboid, trees
Trunk it is equivalent at cylindrical body, tree crown is equivalent at cone or hemisphere, vehicle are equivalent at cuboid.
Preferably, in step a, power transmission line charge simulation use line charge, building, trees, vehicle charge simulation
Using a charge.
Preferably, in step d and step e, each submodel region void is determined using Analogue charge method and alternative method
The current potential approach on quasi- boundary and the charge simulation value in each submodel region.
Preferably, in step d, the method for determining the current potential approach of each submodel region virtual boundary is:
D1, one of submodel region Ω is givennVirtual boundary Γn' initial potential valueIn the submodel area
Domain ΩnOn, according to Analogue charge method formula, calculate submodel region ΩnCharge simulation CmΩn；
D2, according to Analogue charge method formula, with the charge simulation Cm acquiredΩnFind out adjacent submodel region Ωn+1Void
Quasi- boundary Γn+1' potential value
D3, according to Analogue charge method formula, in adjacent submodel region Ωn+1On, pass through adjacent submodel region Ωn+1's
Virtual boundary Γn+1' potential valueFind out charge simulation CmΩn+1；
D4, with the charge simulation Cm acquiredΩn+1, according to Analogue charge method formula, find out submodel region ΩnFictitious line
Boundary Γn' potential value
D5, with the submodel region Ω acquirednVirtual boundary Γn' potential valueAccording to Analogue charge method public affairs
Formula solves submodel region ΩnOn charge simulation C (m+1)Ωn；
D6, with the charge simulation C (m+1) acquiredΩnFind out adjacent submodel region Ωn+1Virtual boundary Γn+1' electricity
Place value
D7, whenWithDifference meet potential errors require when, that is, determine submodel region ΩnVirtual boundary
Γn' current potential approach, whenWithDifference meet potential errors require when, that is, determine submodel region
Ωn+1Virtual boundary Γn+1' current potential approach, wherein m, n are the natural number greater than 0.
Preferably, in step d7, whenWithDifference meet potential errors require when, at this time determine in son
Model area ΩnOn charge simulation be CmΩn, CmΩnIt indicates in submodel region ΩnIn, in each point that the m times alternately calculates
The set of charge and line charge, whenWithDifference meet potential errors require when, at this time determine in submodule
Type region Ωn+1On charge simulation be CmΩn+1, CmΩn+1It indicates in the Ω n+1 of submodel region, is alternately calculated at the m times
The set of each point charge and line charge, wherein m, n are the natural number greater than 0.
Preferably, in submodel region ΩnThe Analogue charge method interleaved computation virtual boundary Γ of middle usen' potential value with
And the formula of charge simulation is:
In submodel region Ωn+1The Analogue charge method interleaved computation virtual boundary Γ of middle usen+1' potential value and mould
The formula of quasi- charge is:
In two formulas:
Pτn、Pτ(n+1)Respectively indicate submodel region ΩnWith submodel region Ωn+1Interior lines charge coefficients matrix；
Pqn、Pq(n+1)Respectively indicate submodel region ΩnWith submodel region Ωn+1Interior Point Charge System matrix number；
PΓn′、PΓ(n+1)′Respectively indicate submodel region ΩnVirtual boundary Γn' and submodel region Ω n+1's is virtual
Boundary Γn+1' neighbouring Point Charge System matrix number；
τn、τ(n+1)Respectively indicate submodel region ΩnWith submodel region Ωn+1Interior linear charge density；
qn、q(n+1)Respectively indicate submodel region ΩnWith submodel region Ωn+1Interior charge；
q′n、q′(n+1)Respectively indicate submodel region ΩnVirtual boundary Γn' and submodel region Ωn+1Virtual boundary
Γn+1' neighbouring point charge；
Respectively indicate submodel region ΩnWith submodel region Ωn+1The corresponding current potential of interior line charge
Value；
Respectively indicate submodel region ΩnWith submodel region Ωn+1The electricity that interior dot-charge pair is answered
Place value；
Respectively indicate submodel region ΩnVirtual boundary Γn' and submodel region Ωn+1It is virtual
Boundary Γn+1' potential value answered of neighbouring dot-charge pair.
Preferably, threedimensional model is divided into two sub- model areas, the virtual boundary in two submodel regions intersects.
Preferably, in step d, the method for determining the current potential approach of each submodel region virtual boundary is:
D1, one of submodel region Ω is given1Virtual boundary Γ1' initial potential valueIn the submodel area
Domain Ω1On, according to Analogue charge method formula, calculate submodel region Ω1Charge simulation CmΩ1；
D2, according to Analogue charge method formula, with the charge simulation Cm acquiredΩ1Find out adjacent submodel region Ω2It is virtual
Boundary Γ2' potential value
D3, according to Analogue charge method formula, in adjacent submodel region Ω2On, pass through adjacent submodel region Ω2Void
Quasi- boundary Γ2' potential valueFind out charge simulation CmΩ2；
D4, with the charge simulation Cm acquiredΩ2, according to Analogue charge method formula, find out submodel region Ω1Virtual boundary
Γn' potential value
D5, with the submodel region Ω acquired1Virtual boundary Γ1' potential valueAccording to Analogue charge method public affairs
Formula solves submodel region Ω1On charge simulation C (m+1)Ω1；
D6, with the charge simulation C (m+1) acquiredΩ1Find out adjacent submodel region Ω2Virtual boundary Γ2' potential value
D7, whenWithDifference meet potential errors require when, that is, determine submodel region Ω1Virtual boundary
Γ1' current potential approach, whenWithDifference meet potential errors require when, that is, determine submodel region Ω2Virtually
Boundary Γ2' current potential approach, wherein m is the natural number greater than 0.
In step d7, whenWithDifference meet potential errors require when, at this time determine in submodel region
Ω1On charge simulation be CmΩ1, CmΩ1It indicates in submodel region Ω1In, in each point charge and line that the m times alternately calculates
The set of charge, whenWithDifference meet potential errors require when, at this time determine in submodel region Ω2On mould
Quasi- charge is CmΩ2, CmΩ2It indicates in submodel region Ω 2, the collection of each point charge and line charge that are alternately calculated at the m times
It closes, wherein m is the natural number greater than 0.
Preferably: further including step g, by the power-frequency electric field strength in each calculated submodel region and using not
The step of electric field strength in the calculated whole threedimensional model of subregional algorithm carries out simulating, verifying.
The present invention is based on the complex scene power frequency electric field calculation methods of subregion Analogue charge method, by the sky under complex scene
Between region divided, Analogue charge method is used for the domain divided, power frequency electric field is calculated, accordingly even when multiple
Under heterocycle border, will not by the insufficient limitation of calculator memory, computer also can efficiently, accurately calculate power transmission and transformation system
Power frequency electric field；In addition, the present invention is by emulation experiment, using this method, under power transmission line, there are when building and a large amount of trees
Power frequency electric field distribution calculated, draw under power transmission line there are building, trees and there are have around building and building
Power frequency electric field distribution map around when a large amount of trees is compared with current existing total algorithm, and the curve of emulation experiment is basic
It reaches unanimity, demonstrates the validity and accuracy of this subregion calculation method.
Detailed description of the invention
Fig. 1 is the unit line charge electric Field Calculation analysis chart that arbitrary point generates in space.
Fig. 2 is the schematic diagram in Overlapping region.
Fig. 3 is the process signal of the complex scene power frequency electric field calculation method the present invention is based on subregion Analogue charge method
Figure.
Fig. 4 be below the complex scene power frequency electric field calculation method power transmission line the present invention is based on subregion Analogue charge method from
The top view of the threedimensional model of real space region electric field strength at the 1.5m of ground.
Fig. 5 is to calculate power transmission line lower section 1.5m power frequency electric field from the ground using subregion Analogue charge method based on Fig. 4 model
With the calculated result contrast schematic diagram for calculating 1.5m power frequency electric field from the ground below power transmission line using total algorithm.
Fig. 6 is the top view that the threedimensional model in real space region of building and trees is respectively present below power transmission line.
Fig. 7 is based on Fig. 6 model, using there are the power frequency electric fields of building under subregion Analogue charge method calculating power transmission line
There are the power frequency electric field of building, the calculated result contrast schematic diagrams of the two with using total algorithm to calculate under power transmission line.
Fig. 8 be based on Fig. 6 model, using subregion Analogue charge method calculate under power transmission line there are the power frequency electric field of trees with
Using there are the power frequency electric field of trees, the calculated result contrast schematic diagrams of the two under total algorithm calculating power transmission line.
Fig. 9 is the top view that the threedimensional model in real space region of building and trees is existed simultaneously below power transmission line.
Figure 10 is to be calculated using subregion Analogue charge method based on Fig. 9 model and existed simultaneously building and tree under power transmission line
The simulation result diagram of the power frequency electric field of wood.
Specific embodiment
Below by specific embodiment, further the present invention will be described in detail:
Complex scene power frequency electric field calculation method of the present embodiment based on subregion Analogue charge method, including the following contents:
A, it models, threedimensional model is established according to the real space region of power-frequency electric field strength to be calculated；
B, threedimensional model is divided into several submodel regions by region division；
C, virtual boundary is respectively set for submodel region, wherein adjacent submodel area two-by-two in the setting of virtual boundary
The virtual boundary in domain intersects；
D, the current potential approach of each submodel region virtual boundary is determined；
E, according to the current potential approach of each submodel region virtual boundary, the mould in each submodel region is determined
Quasi- charge value；
F, according to determining charge simulation value, the power-frequency electric field strength in each submodel region, each submodule are calculated
The power-frequency electric field strength in type region is the electric field strength for characterizing entire area of space.
Specifically, in the present embodiment, complex scene locating for power transmission and transformation system, with there are buildings, tree under power transmission line
It is illustrated for wood and vehicle.Wherein, when modeling, power transmission line is equivalent at cylinder in step a, building it is equivalent at
Cuboid, the trunk of trees is equivalent at cylindrical body, and tree crown is equivalent at cone or hemisphere, vehicle are equivalent at cuboid.Due to
The length of power transmission line is far longer than the radius of power transmission line, therefore power transmission line charge simulation is calculated using line charge, does not consider shaft tower
With the influence of insulator, line electricity pressure drop, the charge simulation use point charge calculating of building, trees, vehicle are not considered.
Power transmission line charge simulation uses line charge, i.e., has limit for length's line segment, each line for what power transmission line was divided into several a length of L
Section is equivalent with line charge, can calculate and acquire the current potential that each line segment line charge is generated in space arbitrary point, as shown in Figure 1 be three
In dimension space coordinate, line segment P is solved1P2In the schematic diagram of a scenario of the current potential of P point.
The calculation formula (1) for the current potential that the line charge of a length of L is generated in space arbitrary point are as follows:
Formula linear charge density τ are as follows: τ (u)=au+b, a, b are undetermined constant, and D is distance of the source point to unknown point.For
Simplify and calculate, time-limited line charge is considered as normal linear charge, it may be assumed that τ (u)=b, a=0.
In the present embodiment, the charge simulation of building, trees, vehicle is calculated using point charge, any point Q exists in space
The calculation formula (2) for the current potential that any point P (x, y, z) is generated are as follows:
In formula, R is the distance of source point P to unknown point Q.
In the present embodiment, line charge gets up with point charge bonded, is based on Analogue charge method, establishes equation (3):
In formula, P τ and PqThe respectively coefficient of potential matrix answered of line charge and dot-charge pair, τ and q be line charge to be asked and
Point charge column vector,WithFor match point current potential column vector.The coefficient of potential, with the type of charge, the position of selection and
Dielectric constant with field domain is related, can be calculated in advance according to above-mentioned parameter, match point current potential, in the line on given boundary
The selected known current potential of section surface.
By above-mentioned formula (1), formula (2) and equation (3), calculated line charge and point charge are needed by verification,
The method for the verification that Analogue charge method and the present embodiment refer to belongs to the prior art, and details are not described herein.
As shown in Fig. 2, being eclipsed area schematic.It is assumed that region Ω, is broken down into two sons of lap
Region Ω1And Ω2, i.e. Ω1∪Ω2=Ω, Ω1∩Ω2≠ 0, subregion Ω1And Ω2The virtual boundary of lap is denoted as respectively
Γ1' and Γ2’。
This programme utilizes Schwarz alternative method.
Three-dimensional Laplace equation is as follows:
Schwarz alternative method can be described as follows formula (4):
Wherein, i=0,1,2 ...
Formula (5):
Wherein, i=0,1,2 ...
Solution procedure is as follows:
Set virtual boundary Γ1' first solution be u0, it may be assumed that in boundary Γ1The upper value for keeping former boundary condition, in fictitious line
Boundary Γ1' on limit initial solution as u0；Given initial solution u0The solving virtual boundary Γ first on formula (4) afterwards2' first solution,
Obtain virtual boundary Γ2' first solution；Then in Γ2The upper value for keeping former boundary condition, according to virtual boundary Γ2' first
Solution, calculates virtual boundary Γ using formula (5) again1' on value, as virtual boundary Γ1' second solution, virtual boundary Γ1’
On this second solution as second using formula (4) boundary condition value, i.e., according to virtual boundary Γ1' second solution, benefit
With calculation formula (4), virtual boundary Γ is acquired2' second solution；Then further according to virtual boundary Γ '2Second solution, in formula
(5) virtual boundary Γ is acquired in1' third solution ..., such alternating iteration is until the front and back two acquired before and after respective subregion
The error of secondary solution is less than the desired limits of error, if relative error is less than 1%, and then can get the formula in whole region
Approximate solution.
In the present embodiment, specifically, determining each height using Analogue charge method and alternative method in step d and step e
Charge simulation value in the current potential approach of model area virtual boundary and each submodel region.In the present embodiment, by
In the submodel region for having lap adjacent two-by-two, there is certain influence between each other, therefore in the meter of the present embodiment
This influence between the submodel region adjacent two-by-two of lap is contemplated in calculation method, rather than it is adjacent two-by-two
Submodel region, since usually farther out, mutual influence is smaller, therefore, in the present embodiment ignores non-adjacent two for distance
Influence between submodel region.
As shown in figure 3, the method for determining the current potential approach of each submodel region virtual boundary is in step d:
D1, one of submodel region Ω is givennVirtual boundary Γn' initial potential valueIn the submodel area
Domain ΩnOn, according to Analogue charge method formula, solve submodel region ΩnCharge simulation CmΩn；
D2, according to Analogue charge method formula, with the charge simulation Cm acquiredΩnFind out adjacent submodel region Ωn+1Void
Quasi- boundary Γn+1' potential value
D3, according to Analogue charge method formula, in adjacent submodel region Ωn+1On, pass through adjacent submodel region Ωn+1's
Virtual boundary Γn+1' potential valueFind out charge simulation CmΩn+1；
D4, with the charge simulation Cm acquiredΩn+1, according to Analogue charge method formula, find out submodel region ΩnFictitious line
Boundary Γn' potential value
D5, with the submodel region Ω acquirednVirtual boundary Γn' potential valueAccording to Analogue charge method public affairs
Formula solves submodel region ΩnOn charge simulation C (m+1)Ωn；
D6, with the charge simulation C (m+1) acquiredΩnFind out adjacent submodel region Ωn+1Virtual boundary Γn+1' electricity
Place value
D7, whenWithDifference meet potential errors require when, that is, determine submodel region ΩnVirtual boundary
ΓnCurrent potential approach, whenWithDifference meet potential errors require when, that is, determine submodel region
Ωn+1Virtual boundary Γn+1' current potential approach, wherein m, n are the natural number greater than 0.
In step d7, whenWithDifference meet potential errors require when, at this time determine in submodel region
ΩnOn charge simulation be CmΩn, CmΩnIt indicates in submodel region ΩnIn, in each point charge and line that the m times alternately calculates
The set of charge, whenWithDifference meet potential errors require when, at this time determine in submodel region
Ωn+1On charge simulation be CmΩn+1, CmΩn+1It indicates in the Ω n+1 of submodel region, each point electricity alternately calculated at the m times
The set of lotus and line charge, wherein m, n are the natural number greater than 0.
In the present embodiment, in step d7 and step e, the potential errors include absolute error or absolute error
And relative error.Absolute error refers to that the difference of exact value and calculated value, relative error are the ratio of absolute error and exact value
Multiplied by 100%, in the present embodiment, absolute error can be 1V, and relative error can be 1% or 0.1%.
In the present embodiment, in submodel region ΩnThe Analogue charge method interleaved computation virtual boundary Γ of middle usen' current potential
The formula (6) of approach and charge simulation is:
In submodel region Ωn+1The Analogue charge method interleaved computation virtual boundary Γ of middle usen+1' current potential approach with
And the formula (7) of charge simulation is:
In formula (6) and formula (7):
Pτn、Pτ(n+1)Respectively indicate submodel region ΩnWith submodel region Ωn+1Interior lines charge coefficients matrix；
Pqn、Pq(n+1)Respectively indicate submodel region ΩnWith submodel region Ωn+1Interior Point Charge System matrix number；
Pn′、PP(n+1)’Respectively indicate submodel region ΩnVirtual boundary Γn' and submodel region Ω n+1 fictitious line
Boundary Γn+1' neighbouring Point Charge System matrix number；
τn、τ(n+1)Respectively indicate submodel region ΩnWith submodel region Ωn+1Interior linear charge density；
qn、q(n+1)Respectively indicate submodel region ΩnWith submodel region Ωn+1Interior charge；
q′n、q′(n+1)Respectively indicate submodel region ΩnVirtual boundary Γn' and submodel region Ωn+1Virtual boundary
Γn+1' neighbouring point charge；
Respectively indicate submodel region ΩnWith submodel region Ωn+1The corresponding current potential of interior line charge
Value；
Respectively indicate submodel region ΩnWith submodel region Ωn+1The electricity that interior dot-charge pair is answered
Place value；
Respectively indicate submodel region ΩnVirtual boundary Γn' and submodel region Ωn+1It is virtual
Boundary Γn+1' potential value answered of neighbouring dot-charge pair.
More specifically, the present embodiment is illustrated for threedimensional model to be divided into two sub- model areas:
A, it models, threedimensional model is established according to the real space region of power-frequency electric field strength to be calculated, when modeling, will transmit electricity
Line is equivalent at cylinder, and building is equivalent at cuboid, and the trunk of trees is equivalent at cylindrical body, and tree crown is equivalent at cone or half
Sphere, vehicle are equivalent at cuboid.Since the length of power transmission line is far longer than the radius of power transmission line, power transmission line charge simulation
Calculated using line charge, do not consider the influence of shaft tower and insulator, do not consider line electricity pressure drop, building, trees, vehicle mould
Quasi- charge is calculated using point charge；
Power transmission line charge simulation uses line charge, i.e., has limit for length's line segment, each line for what power transmission line was divided into several a length of L
Section is equivalent with line charge, can calculate and acquire the current potential that each line segment line charge is generated in space arbitrary point, as shown in Figure 1 be three
In dimension space coordinate, line segment P is solved1P2In the schematic diagram of a scenario of the current potential of P point.
The calculation formula (1) for the current potential that the line charge of a length of L is generated in space arbitrary point are as follows:
Formula linear charge density τ are as follows: τ (u)=au+b, a, b are undetermined constant, and D is distance of the source point to unknown point.For
Simplify and calculate, time-limited line charge is considered as normal linear charge, it may be assumed that τ (u)=b, a=0.
In the present embodiment, the charge simulation of building, trees, vehicle is calculated using point charge, any point Q exists in space
The calculation formula (2) for the current potential that any point P (x, y, z) is generated are as follows:
In formula, R is the distance of source point P to unknown point Q.
In the present embodiment, line charge gets up with point charge bonded, is based on Analogue charge method, establishes equation (3):
In formula, P τ and PqThe respectively coefficient of potential matrix answered of line charge and dot-charge pair, τ and q be line charge to be asked and
Point charge column vector,WithFor match point current potential column vector.The coefficient of potential, with the type of charge, the position of selection and
Dielectric constant with field domain is related, can be calculated in advance according to above-mentioned parameter, match point current potential, in the line on given boundary
The selected known current potential of section surface.
By above-mentioned formula (1), formula (2) and equation (3), calculated line charge and point charge are needed by verification,
The method for the verification that Analogue charge method and the present embodiment refer to belongs to the prior art, and details are not described herein.
B, threedimensional model is divided two sub- model areas by region division, and two sub- model areas are overlapped.
C, virtual boundary is respectively set for submodel region in the setting of virtual boundary, wherein two model areas it is virtual
Boundary intersects.
D, the current potential approach of each submodel region virtual boundary is determined, comprising the following steps:
In step d, the method for determining the current potential approach of each submodel region virtual boundary is:
D1, one of submodel region Ω is given1Virtual boundary Γ1' initial potential valueIn the submodel area
Domain Ω1On, according to Analogue charge method formula, calculate submodel region Ω1Charge simulation CmΩ1；
D2, according to Analogue charge method formula, with the charge simulation Cm acquiredΩ1Find out adjacent submodel region Ω2It is virtual
Boundary Γ2' potential value
D3, according to Analogue charge method formula, in adjacent submodel region Ω2On, pass through adjacent submodel region Ω2Void
Quasi- boundary Γ2' potential valueFind out charge simulation CmΩ2；
D4, with the charge simulation Cm acquiredΩ2, according to Analogue charge method formula, find out submodel region Ω1Virtual boundary
Γn' potential value
D5, with the submodel region Ω acquired1Virtual boundary Γ1' potential valueAccording to Analogue charge method public affairs
Formula solves submodel region Ω1On charge simulation C (m+1)Ω1；
D6, with the charge simulation C (m+1) acquiredΩ1Find out adjacent submodel region Ω2Virtual boundary Γ2' potential value
D7, whenWithDifference meet potential errors require when, that is, determine submodel region Ω1Virtual boundary
Γ1' current potential approach, whenWithDifference meet potential errors require when, that is, determine submodel region Ω2Virtually
Boundary Γ2' current potential approach, wherein m is the natural number greater than 0.
In submodel region Ω1The Analogue charge method interleaved computation virtual boundary Γ of middle use1' current potential approach and
The formula (8) of charge simulation is:
In submodel region Ω2Middle useCurrent potential approach and mould
The formula (9) of quasi- charge is:
In formula (8) and formula (9):
Pτ1、Pτ2Respectively indicate submodel region Ω1With submodel region Ω2Interior lines charge coefficients matrix；
Pq1、Pq2Respectively indicate submodel region Ω1With submodel region Ω2Interior Point Charge System matrix number；
PΓ1’、PΓ2’Respectively indicate submodel region Ω1Virtual boundary Γ1' and submodel region Ω 2 virtual boundary
Γ2' neighbouring Point Charge System matrix number；
τ1、τ2Respectively indicate submodel region Ω1With submodel region Ω2Interior linear charge density；
q1、q2Respectively indicate submodel region Ω1With submodel region Ω2Interior charge；
q′1、q′2Respectively indicate submodel region Ω1Virtual boundary Γ1' and submodel region Ω2Virtual boundary Γ2’
Neighbouring point charge；
Respectively indicate submodel region Ω1With submodel region Ω2The corresponding potential value of interior line charge；
Respectively indicate submodel region Ω1With submodel region Ω2The potential value that interior dot-charge pair is answered；
Respectively indicate submodel region Ω1Virtual boundary Γ1' and submodel region Ω2Virtual boundary
Γ2' potential value answered of neighbouring dot-charge pair.
E, it is determined using Analogue charge method and alternative method according to the current potential approach of each submodel region virtual boundary
Charge simulation value in each submodel region, charge simulation value described here include the value of line charge with point charge, including
The following contents:
In step d7, whenWithDifference meet potential errors require when, at this time determine in submodel region
Ω1On charge simulation be CmΩ1, CmΩ1It indicates in submodel region Ω1In, in each point charge and line that the m times alternately calculates
The set of charge, whenWithDifference meet potential errors require when, at this time determine in submodel region Ω2On mould
Quasi- charge is CmΩ2, CmΩ2It indicates in submodel region Ω 2, the collection of each point charge and line charge that are alternately calculated at the m times
It closes, wherein m is the natural number greater than 0.
F, according to determining charge simulation value, the power-frequency electric field strength in each submodel region is calculated.
Further include step g in the present embodiment, by each calculated submodel region power-frequency electric field strength with adopt
The step of carrying out simulating, verifying with the electric field strength in the calculated whole threedimensional model of not subregional algorithm, it is specific to emulate
It verifies as follows:
Specifically, modeling to power transmission line, ignore the influence of fitting and insulator of steel tower etc., power transmission line has certain
Arc sag does not consider line electricity pressure drop, and level ground is considered as smooth ground, for split conductor, transmission pressure is equivalent
Processing is Round wires, and equivalent cylindrical wire radius at this time can be replaced using equivalent redius Ri, and calculation formula is as follows:
In formula: R is split conductor radius, and n is time conducting wire radical, and r is sub-conductor radius.
Power transmission line has its catenary equation of certain arc sag are as follows:
In formula: γ is conducting wire than carrying the load on i.e. unit conductor length section, h0Minimum distance, σ are led overhead line over the ground
The stress of line minimum point.
Specifically, consider to apply three-phase symmetrical sinusoidal voltage on conducting wire, with virtual value phasor representation voltage, then power transmission line
The phase voltage of each phase conductor can be expressed as:
Each phase current potential real and imaginary parts calculation formula is as follows:
θ in formula is initial phase angle.In view of the practical operation situation of transmission line of electricity, using 1.05 times of voltage rating in terms of
Voltage is calculated, phase voltage is calculated as follows:
The calculation of the above-mentioned phase voltage provided gives the calculation of selected match point potential value.
According to handling above simplifying for transmission line of electricity system, power frequency electric field simulation result and measured value can be made to have certain
Deviation, but the building of computation model ensure that power frequency electric field distribution maximum value within the scope of calculated result is controlled, with
This, which carrys out problem analysis, can fully ensure the reasonability of complex scene power frequency electric field environment under power transmission line.
One: time 500kV quadripartion power transmission line of emulation experiment is parallel with y-axis, power transmission line center phase at x=-20m,
Height is 20m, if Fig. 4 is the model top view.Using subregion algorithm, whole region is divided near y-axis comprising transmission of electricity
The subregion Ω of line and the earth1It only include the subregion Ω of the earth2.Y=is calculated with total algorithm and subregion algorithm respectively
Electric field strength at 0m and y=40m cross-sectional distance ground 1.5m, total algorithm described in the present embodiment, i.e., subregion is not counted
It calculates, directly carries out the method for the calculating of power frequency electric field using Analogue charge method to entire area of space.Calculated result such as Fig. 5 institute
Show.In the case where subregion separately includes power transmission line and do not include power transmission line, subregion is calculated and overall calculation result is accidentally
In poor allowed band, the algorithm is more accurate for the calculating of such situation.
Emulation experiment two: verifying is under complex environment, based on the complex scene power frequency electric field of subregion Analogue charge method
The accuracy of calculation method.
Specifically, ignoring the influence of fitting and insulator of steel tower etc., power transmission line is simplified to Parabolic arc, no
Consider line electricity pressure drop, is Round wires by transmission pressure equivalent process, equivalent cylindrical wire radius at this time can use etc.
Effect radius Ri is replaced, its calculation formula is:In formula, R is split conductor radius, and n is time conducting wire radical, and r is
Sub-conductor radius.Power transmission line has its catenary equation of certain arc sag are as follows:In formula, γ is conducting wire than carrying i.e. unit
Load on conductor length section, h0Overhead line minimum distance over the ground, the stress of σ conducting wire minimum point；
Consider to apply three-phase symmetrical sinusoidal voltage on conducting wire, with virtual value phasor representation voltage, then power transmission line is respectively mutually led
The phase voltage of line can be expressed as:
Each phase current potential real and imaginary parts calculation formula is as follows:
θ in formula is initial phase angle.In view of the practical operation situation of transmission line of electricity, using 1.05 times of voltage rating in terms of
Voltage is calculated, phase voltage is calculated as follows:
According to handling above simplifying for transmission line of electricity system, can make power frequency electric field simulation result near complex scene with
Measured value has certain deviation, but the building of computation model ensure that the maximum value of power frequency electric field distribution is controlled in calculated result
Within the scope of, the reasonability of complex scene power frequency electric field environment under power transmission line can fully be ensured by carrying out problem analysis with this.
Each complex scene under power transmission line is simplified, and level ground is considered as smooth ground, and building is considered as rectangular
Body, the trunk of trees are considered as cylindrical body, and tree crown is considered as taper, and whole region is divided into two sub-regions, model top view
As shown in Figure 6.
Complex scene under power transmission line is equipped with twice 500kV power transmission lines, wherein a feedback wire center is mutually located at x=-
At 18m, there is a building in a height of 28m, power transmission line lower section.Another feedback wire center is mutually located at x=18m, is highly 20m,
There are trees below power transmission line.There are building subregion calculating building is attached about Fig. 6 scene for subregion algorithm and total algorithm
The calculating analysis of electric field strength is as shown in fig. 7, subregion algorithm and total algorithm are deposited about Fig. 6 scene at the 1.5m of short distance ground
It analyzes in the calculating that trees subregion calculates the electric field strength at the 1.5m of ground near building as shown in figure 8, can from figure
To find out, the power-frequency electric field strength and the calculated power frequency of total algorithm that are calculated using the subregion Analogue charge method of the present embodiment
Electric field strength is almost the same, illustrates reliability when the present embodiment subregion Analogue charge method calculates power-frequency electric field strength and accurate
Property.
Emulation experiment three, verifying is to there are when a large amount of trees, being based on subregion charge simulation around building under power transmission line
The accuracy of the complex scene power frequency electric field calculation method of method.
Specifically, ignoring the influence of fitting and insulator of steel tower etc., power transmission line is simplified to Parabolic arc, no
Consider line electricity pressure drop, is Round wires by transmission pressure equivalent process, equivalent cylindrical wire radius at this time can use etc.
Effect radius Ri is replaced, its calculation formula is:In formula, R is split conductor radius, and n is time conducting wire radical, and r is
Sub-conductor radius.Power transmission line has certain arc sag, catenary equation are as follows:In formula, γ is that conducting wire is i.e. more single than carrying
Load on the conductor length section of position, h0 overhead line minimum distance over the ground, the stress of σ conducting wire minimum point；
Consider to apply three-phase symmetrical sinusoidal voltage on conducting wire, with virtual value phasor representation voltage, then power transmission line is respectively mutually led
The phase voltage of line can be expressed as:
Each phase current potential real and imaginary parts calculation formula is as follows:
θ in formula is initial phase angle.In view of the practical operation situation of transmission line of electricity, using 1.05 times of voltage rating in terms of
Voltage is calculated, phase voltage is calculated as follows:
According to handling above simplifying for transmission line of electricity system, can make power frequency electric field simulation result near complex scene with
Measured value has certain deviation, but the building of computation model ensure that the maximum value of power frequency electric field distribution is controlled in calculated result
Within the scope of, the reasonability of complex scene power frequency electric field environment under power transmission line can fully be ensured by carrying out problem analysis with this.It is defeated
Each complex scene under electric wire is simplified, and level ground is considered as smooth ground, and building is considered as cuboid, the tree of trees
Dry to be considered as cylindrical body, tree crown is considered as taper.
A time 500kV quadripartion power transmission line, center phase is at x=15m, a height of 25m, has a building below power transmission line
At x=-13m, y=0, long 20m, wide 6m, high 12m.Taper tree parameter is same as above, and is located at x=-5m, every 5m kind
One is planted, totally 6, model top view is as shown in Figure 9.
Its calculated result is as shown in Figure 10.Since entire model calculation amount is excessive, if being calculated with common 8G microcomputer,
There is the case where Out of Memory, and can make to calculate using subregion rule and go on smoothly.
The present embodiment, the complex scene power frequency electric field calculation method based on subregion Analogue charge method are imitated by above
True experiment demonstrates the high efficiency and reliability of this calculation method, can be the power frequency electric field under power transmission and transformation system complex scene
Calculating and research provide Technical Reference.
Claims (10)
1. the complex scene power frequency electric field calculation method based on subregion Analogue charge method, which is characterized in that including the following contents:
A, it models, threedimensional model is established according to the real space region of power-frequency electric field strength to be calculated；
B, threedimensional model is divided into several submodel regions by region division；
C, virtual boundary is respectively set for submodel region in the setting of virtual boundary, wherein adjacent submodel region two-by-two
Virtual boundary intersects；
D, the current potential approach of each submodel region virtual boundary is determined；
E, according to the current potential approach of each submodel region virtual boundary, the simulation electricity in each submodel region is determined
Charge values；
F, according to determining charge simulation value, the power-frequency electric field strength in each submodel region, each submodel area are calculated
The power-frequency electric field strength in domain is the electric field strength for characterizing entire area of space.
2. the complex scene power frequency electric field calculation method according to claim 1 based on subregion Analogue charge method, special
Sign is, in step a, when modeling, power transmission line is equivalent at cylinder, and building is equivalent at cuboid, the trunk etc. of trees
Imitate into cylindrical body, tree crown is equivalent at cone or hemisphere, vehicle are equivalent at cuboid.
3. the complex scene power frequency electric field calculation method according to claim 1 or 2 based on subregion Analogue charge method,
Be characterized in that, in step a, power transmission line charge simulation use line charge, building, trees, vehicle charge simulation use point
Charge.
4. the complex scene power frequency electric field calculation method according to claim 1 based on subregion Analogue charge method, special
Sign is: in step d and step e, determining each submodel region virtual boundary using Analogue charge method and alternative method
Charge simulation value in current potential approach and each submodel region.
5. the complex scene power frequency electric field calculation method according to claim 4 based on subregion Analogue charge method, special
Sign is, in step d, the method for determining the current potential approach of each submodel region virtual boundary is:
D1, one of submodel region Ω is givennVirtual boundary Γn' initial potential valueIn submodel region Ωn
On, according to Analogue charge method formula, calculate submodel region ΩnCharge simulation CmΩn；
D2, according to Analogue charge method formula, with the charge simulation Cm acquiredΩnFind out adjacent submodel region Ωn+1Virtual boundary
Γn+1' potential value
D3, according to Analogue charge method formula, in adjacent submodel region Ωn+1On, pass through adjacent submodel region Ωn+1It is virtual
Boundary Γn+1' potential valueFind out charge simulation CmΩn+1；
D4, with the charge simulation Cm acquiredΩn+1, according to Analogue charge method formula, find out submodel region ΩnVirtual boundary
Γn' potential value
D5, with the submodel region Ω acquirednVirtual boundary Γn' potential valueAccording to Analogue charge method formula, ask
Solve submodel region ΩnOn charge simulation C (m+1)Ωn；
D6, with the charge simulation C (m+1) acquiredΩnFind out adjacent submodel region Ωn+1Virtual boundary Γn+1' potential value
D7, whenWithDifference meet potential errors require when, that is, determine submodel region ΩnVirtual boundary Γn'
Current potential approach, whenWithDifference meet potential errors require when, that is, determine submodel region Ωn+1It is empty
Quasi- boundary Γn+1' current potential approach, wherein m, n are the natural number greater than 0.
6. the complex scene power frequency electric field calculation method according to claim 5 based on subregion Analogue charge method, special
Sign is: in step d7, whenWithDifference meet potential errors require when, at this time determine in submodel region
ΩnOn charge simulation be CmΩn, CmΩnIt indicates in submodel region ΩnIn, in each point charge and line that the m times alternately calculates
The set of charge, whenWithDifference meet potential errors require when, at this time determine in submodel region
Ωn+1On charge simulation be CmΩn+1, CmΩn+1It indicates in the Ω n+1 of submodel region, each point electricity alternately calculated at the m times
The set of lotus and line charge, wherein m, n are the natural number greater than 0.
7. the complex scene power frequency electric field calculation method according to claim 6 based on subregion Analogue charge method, special
Sign is: in submodel region ΩnThe Analogue charge method interleaved computation virtual boundary Γ of middle usen' potential value and simulation electricity
The formula of lotus is:
In submodel region Ωn+1The Analogue charge method interleaved computation virtual boundary Γ of middle usen+1' potential value and simulation electricity
The formula of lotus is:
In two formulas:
Pτn、Pτ(n+1)Respectively indicate submodel region ΩnWith submodel region Ωn+1Interior lines charge coefficients matrix；
Pqn、Pq(n+1)Respectively indicate submodel region ΩnWith submodel region Ωn+1Interior Point Charge System matrix number；
PΓn’、PΓ(b+1)’Respectively indicate submodel region ΩnVirtual boundary Γn' and submodel region Ω n+1 virtual boundary
Γn+1' neighbouring Point Charge System matrix number；
τn、τ(n+1)Respectively indicate submodel region ΩnWith submodel region Ωn+1Interior linear charge density；
qn、q(n+1)Respectively indicate submodel region ΩnWith submodel region Ωn+1Interior charge；
q′n、q′(n+1)Respectively indicate submodel region ΩnVirtual boundary Γn' and submodel region Ωn+1Virtual boundary
Γn+1' neighbouring point charge；
Respectively indicate submodel region ΩnWith submodel region Ωn+1The corresponding potential value of interior line charge；
Respectively indicate submodel region ΩnWith submodel region Ωn+1The potential value that interior dot-charge pair is answered；
Respectively indicate submodel region ΩnVirtual boundary Γn' and submodel region Ωn+1Virtual boundary
Γn+1' potential value answered of neighbouring dot-charge pair.
8. the complex scene power frequency electric field calculation method according to claim 1 or 6 based on subregion Analogue charge method,
It is characterized in that: threedimensional model being divided into two sub- model areas, the virtual boundary in two submodel regions intersects.
9. the complex scene power frequency electric field calculation method according to claim 8 based on subregion Analogue charge method, special
Sign is, in step d, the method for determining the current potential approach of each submodel region virtual boundary is:
D1, one of submodel region Ω is given1Virtual boundary Γ1' initial potential valueIn submodel region Ω1
On, according to Analogue charge method formula, calculate submodel region Ω1Charge simulation CmΩ1；
D2, according to Analogue charge method formula, with the charge simulation Cm acquiredΩ1Find out adjacent submodel region Ω2Virtual boundary
Γ2' potential value
D3, according to Analogue charge method formula, in adjacent submodel region Ω2On, pass through adjacent submodel region Ω2Fictitious line
Boundary Γ2' potential valueFind out charge simulation CmΩ2；
D4, with the charge simulation Cm acquiredΩ2, according to Analogue charge method formula, find out submodel region Ω1Virtual boundary Γn’
Potential value
D5, with the submodel region Ω acquired1Virtual boundary Γ1' potential valueAccording to Analogue charge method formula, ask
Solve submodel region Ω1On charge simulation C (m+1)Ω1；
D6, with the charge simulation C (m+1) acquiredΩ1Find out adjacent submodel region Ω2Virtual boundary Γ2' potential value
D7, whenWithDifference meet potential errors require when, that is, determine submodel region Ω1Virtual boundary Γ1'
Current potential approach, whenWithDifference meet potential errors require when, that is, determine submodel region Ω2Virtual boundary
Γ2' current potential approach, wherein m is the natural number greater than 0.
In step d7, whenWithDifference meet potential errors require when, at this time determine in submodel region Ω1On
Charge simulation be CmΩ1, CmΩ1It indicates in submodel region Ω1In, replace each point charge and line charge calculated at the m times
Set, whenWithDifference meet potential errors require when, at this time determine in submodel region Ω2On charge simulation
For CmΩ2, CmΩ2It indicates in submodel region Ω 2, the set of each point charge and line charge that are alternately calculated at the m times, wherein m
For the natural number greater than 0.
10. the complex scene power frequency electric field calculation method according to claim 1 or 6 based on subregion Analogue charge method,
It is characterized by also including step g, by the power-frequency electric field strength in each calculated submodel region and using not subregion
The step of electric field strength in the calculated whole threedimensional model of the algorithm in domain carries out simulating, verifying.
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