CN104573219A - Method for calculating direct-current transmission line electric field intensity and radio interference - Google Patents

Abstract

The invention discloses a method for calculating direct-current transmission line electric field intensity and radio interference. The method solves the problems that in the prior art and a traditional method, a transmission line lead section has waved relief, so that lead mirror image charge cannot be directly set, and ill-posed problems of an original equation can be solved when a direct-current transmission line adopts linear equations such as a Gauss-Newton method. Compared with a traditional partial discharge method, experimental efficiency is improved, and the method has practicability and feasibility through experimental verification.

Description

A kind of method that DC power transmission line electric field intensity and radio interference calculate

Technical field

The invention belongs to technical field of electric power, particularly relate in high pressure, extra-high voltage field, the method that DC power transmission line electric field intensity and radio interference calculate.

Background technology

High pressure or extra-high voltage direct-current transmission technology are widely used in the power transmission engineering of transferring electricity from the west to the east main channel, but along with the raising of electric pressure, the emphasis of concern and line design that its electromagnetic environmental impact is more and more subject to the public is considered.Total electric field below DC line, gas current, D.C. magnetic field, and the radio interference that produces of corona and audible noise can on occupying bright production along the line and life produces certain impact.Research shows, radio interference level is one of important electromagnetic environment index of DC power transmission line environmental impact assessment, and its main harm is the radio signal interference such as radio broadcasting, TV caused around transmission line of electricity.

Document " under negative direct current, twisted wire corona inception voltage is analyzed ", the positive dc corona starting potential of steel-cored aluminium strand " under the high altitude condition analyze " be positive and negative direct current twisted wire corona inception voltage based on gas discharge theoretical analysis, document " High aititude ± 800kV DC power transmission line electromagnetic environment is measured " has carried out UHVDC Transmission Lines radio interference characteristic research, the all selected transmission line wire vertical profile of actual measurement of above-mentioned theory analysis and running test is plane, in conjunction with field domain boundary condition, utilize mark spy-Carl Menger method, progressively image method carries out radio interference analysis and calculation.But the transmission line wire vertical profile of reality is often in uneven terrain.DC line electric field intensity and radio interference under complex wires vertical profile physical features can not be directly used in based on the computing method in above-mentioned document to calculate.

Document " under complicated topographic features HVAC power transmission line electromagnetic environment characteristic analysis ", the power frequency electric field of extra high voltage network " under the complex terrain " have carried out HVAC power transmission line electromagnetic environment characteristic analysis under complicated topographic features based on the Analogue charge method optimized, but the method is the position arranging charge simulation by rule of thumb.Document " considering the transmission pressure power frequency electric field New calculating method of meteorological condition ", " the three-dimensional power frequency electromagnetic field of scissors crossing transmission pressure calculates " utilize genetic algorithm to carry out transmission pressure sag and the optimization of extra-high voltage insulator grading ring of electric field inverse operation respectively, but classic method is only for smooth wire section, utilize the induced charge that image charge equivalence Earth Surface is set, there is for transmission line wire section the situation of fluctuating physical features, cannot wire image charge be directly set.

Summary of the invention

In order to solve the problem, the method that a kind of DC power transmission line electric field intensity provided by the invention and radio interference calculate, concrete steps are as follows:

S1: determine charge simulation locus

According to charge simulation ratio juris, in the charge simulation locus span of formula (1), wire and the charge simulation coordinate of lightning conducter and the center of its place sub-conductor are done difference, obtains wire and lightning conducter charge simulation span is corresponding diameter; Charge simulation in formula (1) in the wire of non-computational field domain, lightning conducter, or must be positioned at below Earth Surface, and therefore the position of charge simulation meets the constraint condition of formula (1); For improving resolution, wire and lightning conducter are adopted 10 binary codings, image charge adopts 10 binary codings;

$\left\{\begin{array}{cc}{(x_i-x_{0i})}^2+{(y_i-y_{0i})}^2<R_1^2& (i=1...M)\\ {(x_j-x_{0j})}^2+{(y_j-y_{0j})}^2<R_2^2& (j=1...A)\\ f(x_k,y_k)<0& (k=1...N-A)\end{array}\right.---\left(1\right)$

(x in formula (1) _i, y _i) and (x _j, y _j) be the charge simulation coordinate in oidiospore wire and lightning conducter, (x _k, y _k) be the mirror image charge simulation coordinate below Earth Surface, R ₁and R ₂for the radius of oidiospore wire and lightning conducter, A and N is respectively the quantity of charge simulation in lightning conducter and total charge simulation quantity.F (x _k, y _k) for describing the function of Earth Surface continuous curve;

S2: the generation of charge simulation position initial population P (t)

The charge simulation of wire and lightning conducter wire is all distributed in the annulus of diameter 1/4 respectively, and each image charge lays respectively at the equidistant mirror position on Relative vertical ground;

DC power transmission line conductive line surfaces greatest gradient and electric field intensity under Analogue charge method calculation of complex wire vertical profile physical features is utilized to need the problem solved to have: the 1) position of charge simulation and the quantity of electric charge in bipolar conductor and ground wire; 2) position of bipolar conductor and ground wire image charge and the quantity of electric charge; For this reason, the target of charge simulation locus is that the charge simulation of optimum results meets error in advance in the potential errors that match point produces, meet the optimization aim of formula (2) based on all charge simulations of principle of least square method at the current potential that match point produces, evaluate individual quality by formula (2) as fitness function:

M is the match point quantity of conductive line surfaces in formula (2), Q and the potential vectors of the match point that the electricity vector sum of unknown charge simulation is known respectively, for the current potential of wire, lightning conducter or Earth Surface i-th match point;

S3: judge convergence

If | f _max-f _min| < ε, then export optimizing result, stops iteration, go to step S4; Otherwise proceed to S5; Wherein f _max, f _minbe respectively functional value that is optimum in current population and the poorest individuality, ε is given accuracy, preferred ε≤0.5%;

S4: regularization

In formula (2), for realizing being similar to nonlinear operator F (Q), utilize Taylor's formula by F (the Q+ δ Q) Taylor expansion at Q place, when || enough hour of δ Q||, adopt first-order approximation and ignore remaining high-order in a small amount, obtaining formula (3);

$F(Q+\mathrm{\&delta;Q})=F\left(Q\right)+\frac{\&PartialD;F}{\&PartialD;Q}\mathrm{\&delta;Q}+\frac{1}{2}\frac{{\&PartialD;}^{2}F}{\&PartialD;Q^2}{\left(\mathrm{\&delta;Q}\right)}^2+R(Q,\mathrm{\&delta;Q})\&ap;F\left(Q\right)+\frac{\&PartialD;F}{\&PartialD;Q}\mathrm{\&delta;Q}---\left(3\right)$

Q*=Q+ δ Q is made to be equation exact Solutions, then can obtain following linear operator equation formula (4) by formula (3) at the Q place close to Q*:

Adopt linearization (4) the formula equations such as gauss-newton method can leave over full scale equation ill-posed problem and Ill-posed characteristic, therefore need to introduce Regularization Technique, namely refer in linear algebraic process, ill-posed problem is normally defined by one group of linear algebraic equation, and this group system of equations derives from the ill-posed inverse problem of very large conditional number usually, large conditional number means that round-off error or other error seriously can affect the result of problem;

But adopting traditional Levenberg-Marquardt method (arranging civilian Burger-Ma Kuaertefa) to be the method for creeping regularization be applied on δ Q, the method Problems existing has: 1) because regularization is applied to δ Q but not Q causes to control for the feature solved; 2) Exact Solutions Q* relies on initial solution Q ⁰with minimize path δ Q ^k; 3) distinct methods is adopted to solve δ Q ^kthe Exact Solutions Q* obtained is different; 4) increase of target function value may be caused when δ Q is larger.

For this reason, for overcoming prior art defect, employing regularization is applied to the overall regularization method on Q, simultaneously according to the not only restricted step and obtain new descent direction of the Trust Region strategy with global convergence, if the equation after nonlinear problem (2) formula and linearization is equivalence in the region that size is η, simultaneously in conjunction with the formula (4) of linearization process, in this region, show that a best δ Q is such as formula (5) based on overall regularization by optimization problem:

In formula (5), W is linear operator, and η is trusted zones size, and μ (η) is penalty function;

For the optimization problem shown in (5) formula, the necessary condition utilizing f to be minimum solution to be the gradient of f be zero point, obtain the linear equation of formula (6):

Q ^k+1＝Q ^k+δQ

In formula (6), for the transposition of Jacobi matrix;

What the solving of the non-linear least square problem of formula (2) and formula (5) was summed up as its normal equation solves such as formula (6);

S5: selection, crossover and mutation

In S3, if do not meet | f _max-f _min| < ε, need carry out selection, the crossover and mutation of population:

Wherein, selective rule sorts to individuality according to fitness size, and therefrom choose i the maximum individuality of fitness, (7) carry out select probability P according to the following formula _s(x _i):

$P_s\left(x_i\right)=f\left(x_i\right)/\underset{i}{\mathrm{\&Sigma;}}f\left(x_i\right)---\left(7\right)$

Crossover rule adopts two interleaved modes, adaptive crossover mutation P _cfor formula (8):

$P_C=\left\{\begin{array}{cc}0.9-\frac{0.3\&times;(f_{\max }-f^{\&prime;})}{f_{\max }-f_{\mathrm{avg}}}& f^{\&prime;}\&GreaterEqual;f_{\mathrm{avg}}\\ 0.9& f^{\&prime;}\&GreaterEqual;f_{\mathrm{avg}}\end{array}\right.---\left(8\right)$

In formula (8), f _avgfor the average fitness of colony, f' is the individual larger adaptive values of two intersections, f _maxfor the functional value of optimum individual in current population;

Variation rule is that every two binary codings of each individuality are produced a number between (0,1) at random, if be greater than individual aberration rate, then this coding 1 becomes 0, or becomes 1 by 0, otherwise this coding does not make a variation, P _mmutation probability is formula (9):

$P_m=\left\{\begin{array}{cc}0.2-\frac{0.5\&times;(f_{\max }-f)}{f_{\max }-f_{\mathrm{avg}}}& f\&GreaterEqual;f_{\mathrm{avg}}\\ 0.2& f\&GreaterEqual;f_{\mathrm{avg}}\end{array}\right.---\left(9\right)$

In formula (9), f _avgfor the average fitness of colony, f is that every two binary codings of each individuality produce a number between (0,1), f at random _maxfor the functional value of optimum individual in current population;

Then, retain more excellent individuality, the identical number substituting parent Population adaptation value less with the individuality that the adaptive value of progeny population is larger is individual, i.e. P (t)=P (t+1), improve the probability obtaining optimum individual, the initial population of the new population of current reservation as step S2 is recalculated;

S6: judge formula (6) then turn S12; Otherwise turn S7;

In engineering reality, formula (6) need iterative computation repeatedly, by substantial operation time; For Practical Project, formula (6) calculating needs can be met;

S7: calculate δ Q, f ^k, f ^k+1, f ₁ ^k+1

The trust region method of through type (6) determines the δ Q be applicable to:

Δf＝f ^k+1-f ^k(10)

Δf ₁＝f ₁ ^k+1-f ^k

In formula, Δ f is the change of Nonlinear Parameter value, Δ f ₁the change of linearization desired value, f simultaneously ^k+1, f ^kk+1 and k iterative nonlinear desired value respectively, f ₁ ^k+1be k+1 iterative linearized desired value, circular is such as formula (11):

In formula (11), f ^k+1, f ^kk+1 and k iterative nonlinear desired value respectively, f ₁ ^k+1be k+1 iterative linearized desired value, W is linear operator, Q and the potential vectors of the match point that the electricity vector sum of unknown charge simulation is known respectively;

S8: judge f ^k> f ^k+1, then S9 is turned; Otherwise trusted zones size η is become original 0.9 times, i.e. 0.9 η, proceed to S7 iterative computation;

S9: judge in formula, Δ f is the change of Nonlinear Parameter value, Δ f ₁be the change of linearization desired value, τ is trusted zones controling parameters; If turn S10; Otherwise, trusted zones size η is become original 1.1 times, i.e. 1.1 η, proceeds to S7 iterative computation again;

S10: judge whether to be greater than maximum iteration time

In practical engineering calculation, for avoiding a large amount of computing, need to set maximum iteration time, maximum iteration time of the present invention is less than or equal to 1000 times, preferably 200 times; If be greater than maximum iteration time, turn S5; Otherwise, turn S11;

S11: carry out f by formula (12) ^k+1k+1 iterative nonlinear desired value calculate, Q ^k+1k+1 iteration, then turn S4;

Q ^k+1＝Q ^k+δQ (12)

f ^k＝f ^k+1

Wherein, f ^k+1, f ^kk+1 and k iterative nonlinear desired value respectively, Q ^k+1, Q ^kthe electricity vector of k+1 and k the unknown charge simulation of iteration respectively;

S12: computing electric power line shows electric field intensity

$\left\{\begin{array}{c}{E}_x=\frac{1}{2\mathrm{\&pi;}{\mathrm{\&epsiv;}}_0}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\left(\frac{x-x_i}{L_i^2}\right)Q_i\\ E_y=\frac{1}{2\mathrm{\&pi;}{\mathrm{\&epsiv;}}_0}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\left(\frac{y-y_i}{L_i^2}\right)Q_i\\ E=\sqrt{E_x^2+E_y^2}\end{array}\right.---\left(13\right)$

In formula (13), E is the size of electric field intensity, and its component is respectively E _xand E _y, L _ifor charge simulation is to the distance of calculation level.Therefore, calculate DC bipolar conductive line surfaces each point field intensity based on formula (13), solve wire maximized surface field intensity E _max;

S13: the radio interference level calculating any landform

In conjunction with the parameter such as distance of wire radius and calculation level distance positive pole, the CISPR recommend method that DC line radio interference level calculates is such as formula (14):

$G=38+1.6(E_{\max }-24)+46\mathrm{lg\; r}+5\mathrm{lg\; n}+33\lg \frac{20}{R}+\mathrm{\&Delta;}{E}_f+\mathrm{\&Delta;}{E}_w---\left(14\right)$

In formula, G is extra-high voltage direct-current radio interference level, E _maxfor wire maximized surface field intensity, r is sub-conductor radius, and n is split conductor number, and R is the space length of reference point to nearest wire; Δ E _ffor interfering frequency correction term, Δ E _f=5 [1 ~ 2 (log10f) ²], f is interfering frequency, and Δ E can be ignored in scene _f; Δ E _wfor meteorological correction item, fair weather gets 0dBV/m, and bad weather gets 3dB V/m;

S14: calculate audible noise

Audible noise P _dBadopt the computing formula (15) that American Electric Power research institute (EPRI) is recommended:

$P_{\mathrm{dB}}=56.9+1.24\lg \frac{E_{\max }}{25}+25\lg \frac{d}{4.45}+18\lg \frac{n}{2}-10\mathrm{lgD}+0.02D+k_n---\left(15\right)$

In formula (15), E _maxfor wire maximized surface field intensity, d is sub-conductor diameter, and n is split conductor number, and D is the distance of positive wire and calculation level, k _nfor correction term, during n>=3, k _nduring=0, n=2, k _nwhen=2.6dB, n=1, k _n=7.5dB.

The present invention compared with the existing technology, has the following advantages and beneficial effect:

1. the invention solves prior art and classic method only for smooth wire section, utilize the induced charge that image charge equivalence Earth Surface is set, there is for transmission line wire section the situation of fluctuating physical features, the problem of wire image charge cannot be directly set;

2. the invention solves DC power transmission line adopts the lienarized equations such as gauss-newton method can leave over full scale equation ill-posed problem;

3. contrast with traditional office method of putting, invention increases test efficiency and improve calculation process, through verification experimental verification, there is practicality and feasibility.

Accompanying drawing explanation

Fig. 1 is calculation flow chart of the present invention;

Fig. 2 adopts the present invention and prior art measured result comparison diagram described in the embodiment of the present invention.

Embodiment

Below in conjunction with drawings and Examples, technical scheme of the present invention is clearly and completely described.

As shown in Figure 1, a kind of method that DC power transmission line electric field intensity and radio interference calculate, concrete steps are as follows:

S1: determine charge simulation locus

According to charge simulation ratio juris, in the charge simulation locus span of formula (1), wire and the charge simulation coordinate of lightning conducter and the center of its place sub-conductor are done difference, obtains wire and lightning conducter charge simulation span is corresponding diameter; Charge simulation in formula (1) in the wire of non-computational field domain, lightning conducter, or must be positioned at below Earth Surface, and therefore the position of charge simulation meets the constraint condition of formula (1); For improving resolution, wire and lightning conducter are adopted 10 binary codings, image charge adopts 10 binary codings;

$\left\{\begin{array}{cc}{(x_i-x_{0i})}^2+{(y_i-y_{0i})}^2<R_1^2& (i=1...M)\\ {(x_j-x_{0j})}^2+{(y_j-y_{0j})}^2<R_2^2& (j=1...A)\\ f(x_k,y_k)<0& (k=1...N-A)\end{array}\right.---\left(1\right)$

(x in formula (1) _i, y _i) and (x _j, y _j) be the charge simulation coordinate in oidiospore wire and lightning conducter, (x _k, y _k) be the mirror image charge simulation coordinate below Earth Surface, R ₁and R ₂for the radius of oidiospore wire and lightning conducter, A and N is respectively the quantity of charge simulation in lightning conducter and total charge simulation quantity.F (x _k, y _k) for describing the function of Earth Surface continuous curve.

S2: the generation of charge simulation position initial population P (t)

The charge simulation of wire and lightning conducter wire is all distributed in the annulus of diameter 1/4 respectively, and each image charge lays respectively at the equidistant mirror position on Relative vertical ground;

DC power transmission line conductive line surfaces greatest gradient and electric field intensity under Analogue charge method calculation of complex wire vertical profile physical features is utilized to need the problem solved to have: the 1) position of charge simulation and the quantity of electric charge in bipolar conductor and ground wire; 2) position of bipolar conductor and ground wire image charge and the quantity of electric charge; For this reason, the target of charge simulation locus is that the charge simulation of optimum results meets error in advance in the potential errors that match point produces, meet the optimization aim of formula (2) based on all charge simulations of principle of least square method at the current potential that match point produces, evaluate individual quality by formula (2) as fitness function:

M is the match point quantity of conductive line surfaces in formula (2), Q and the potential vectors of the match point that the electricity vector sum of unknown charge simulation is known respectively, for the current potential of wire, lightning conducter or Earth Surface i-th match point;

S3: judge convergence

If | f _max-f _min| < ε, then export optimizing result, stops iteration, go to step S4; Otherwise proceed to S5; Wherein f _max, f _minbe respectively functional value that is optimum in current population and the poorest individuality, ε is given accuracy, preferred ε≤0.5%;

S4: regularization

In formula (2), for realizing being similar to nonlinear operator F (Q), utilize Taylor's formula by F (the Q+ δ Q) Taylor expansion at Q place, when || enough hour of δ Q||, adopt first-order approximation and ignore remaining high-order in a small amount, obtaining formula (3);

$F(Q+\mathrm{\&delta;Q})=F\left(Q\right)+\frac{\&PartialD;F}{\&PartialD;Q}\mathrm{\&delta;Q}+\frac{1}{2}\frac{{\&PartialD;}^{2}F}{\&PartialD;Q^2}{\left(\mathrm{\&delta;Q}\right)}^2+R(Q,\mathrm{\&delta;Q})\&ap;F\left(Q\right)+\frac{\&PartialD;F}{\&PartialD;Q}\mathrm{\&delta;Q}---\left(3\right)$

Q*=Q+ δ Q is made to be equation exact Solutions, then can obtain following linear operator equation formula (4) by formula (3) at the Q place close to Q*:

Adopt linearization (4) the formula equations such as gauss-newton method can leave over full scale equation ill-posed problem and Ill-posed characteristic, therefore need to introduce Regularization Technique, namely refer in linear algebraic process, ill-posed problem is normally defined by one group of linear algebraic equation, and this group system of equations derives from the ill-posed inverse problem of very large conditional number usually, large conditional number means that round-off error or other error seriously can affect the result of problem;

But adopting traditional Levenberg-Marquardt method (arranging civilian Burger-Ma Kuaertefa) to be the method for creeping regularization be applied on δ Q, the method Problems existing has: 1) because regularization is applied to δ Q but not Q causes to control for the feature solved; 2) Exact Solutions Q* relies on initial solution Q ⁰with minimize path δ Q ^k; 3) distinct methods is adopted to solve δ Q ^kthe Exact Solutions Q* obtained is different; 4) increase of target function value may be caused when δ Q is larger.

For this reason, for overcoming prior art defect, employing regularization is applied to the overall regularization method on Q, simultaneously according to the not only restricted step and obtain new descent direction of the Trust Region strategy with global convergence, if the equation after nonlinear problem (2) formula and linearization is equivalence in the region that size is η, simultaneously in conjunction with the formula (4) of linearization process, in this region, show that a best δ Q is such as formula (5) based on overall regularization by optimization problem:

In formula (5), W is linear operator, and η is trusted zones size, and μ (η) is penalty function;

For the optimization problem shown in (5) formula, the necessary condition utilizing f to be minimum solution to be the gradient of f be zero point, obtain the linear equation of formula (6):

Q ^k+1＝Q ^k+δQ

In formula (6), for the transposition of Jacobi matrix;

The solving of the non-linear least square problem of formula (2) and formula (5) is summed up as solving such as formula (6) of its normal equation.

S5: selection, crossover and mutation

In S3, if do not meet | f _max-f _min| < ε, need carry out selection, the crossover and mutation of population:

Wherein, selective rule sorts to individuality according to fitness size, and therefrom choose i the maximum individuality of fitness, (7) carry out select probability P according to the following formula _s(x _i):

$P_s\left(x_i\right)=f\left(x_i\right)/\underset{i}{\mathrm{\&Sigma;}}f\left(x_i\right)---\left(7\right)$

Crossover rule adopts two interleaved modes, adaptive crossover mutation P _cfor formula (8):

$P_C=\left\{\begin{array}{cc}0.9-\frac{0.3\&times;(f_{\max }-f^{\&prime;})}{f_{\max }-f_{\mathrm{avg}}}& f^{\&prime;}\&GreaterEqual;f_{\mathrm{avg}}\\ 0.9& f^{\&prime;}\&GreaterEqual;f_{\mathrm{avg}}\end{array}\right.---\left(8\right)$

In formula (8), f _avgfor the average fitness of colony, f' is the individual larger adaptive values of two intersections, f _maxfor the functional value of optimum individual in current population;

Variation rule is that every two binary codings of each individuality are produced a number between (0,1) at random, if be greater than individual aberration rate, then this coding 1 becomes 0, or becomes 1 by 0, otherwise this coding does not make a variation, P _mmutation probability is formula (9):

$P_m=\left\{\begin{array}{cc}0.2-\frac{0.5\&times;(f_{\max }-f)}{f_{\max }-f_{\mathrm{avg}}}& f\&GreaterEqual;f_{\mathrm{avg}}\\ 0.2& f\&GreaterEqual;f_{\mathrm{avg}}\end{array}\right.---\left(9\right)$

In formula (9), f _avgfor the average fitness of colony, f is that every two binary codings of each individuality produce a number between (0,1), f at random _maxfor the functional value of optimum individual in current population;

Then, retain more excellent individuality, the identical number substituting parent Population adaptation value less with the individuality that the adaptive value of progeny population is larger is individual, i.e. P (t)=P (t+1), improve the probability obtaining optimum individual, the initial population of the new population of current reservation as step S2 is recalculated;

S6: judge formula (6) then turn S12; Otherwise turn S7;

In engineering reality, formula (6) need iterative computation repeatedly, by substantial operation time; For Practical Project, formula (6) calculating needs can be met;

S7: calculate δ Q, f ^k, f ^k+1, f ₁ ^k+1

The trust region method of through type (6) determines the δ Q be applicable to:

Δf＝f ^k+1-f ^k(10)

Δf ₁＝f ₁ ^k+1-f ^k

In formula, Δ f is the change of Nonlinear Parameter value, Δ f ₁the change of linearization desired value, f simultaneously ^k+1, f ^kk+1 and k iterative nonlinear desired value respectively, f ₁ ^k+1be k+1 iterative linearized desired value, circular is such as formula (11):

In formula (11), f ^k+1, f ^kk+1 and k iterative nonlinear desired value respectively, f ₁ ^k+1be k+1 iterative linearized desired value, W is linear operator, Q and the potential vectors of the match point that the electricity vector sum of unknown charge simulation is known respectively;

S8: judge f ^k> f ^k+1, then S9 is turned; Otherwise trusted zones size η is become original 0.9 times, i.e. 0.9 η, proceed to S7 iterative computation;

S9: judge in formula, Δ f is the change of Nonlinear Parameter value, Δ f ₁be the change of linearization desired value, τ is trusted zones controling parameters; If turn S10; Otherwise, trusted zones size η is become original 1.1 times, i.e. 1.1 η, proceeds to S7 iterative computation again;

S10: judge whether to be greater than maximum iteration time

In practical engineering calculation, for avoiding a large amount of computing, need to set maximum iteration time, maximum iteration time of the present invention is less than or equal to 1000 times, preferably 200 times; If be greater than maximum iteration time, turn S5; Otherwise, turn S11;

S11: carry out f by formula (12) ^k+1k+1 iterative nonlinear desired value calculate, Q ^k+1k+1 iteration, then turn S4;

Q ^k+1＝Q ^k+δQ (12)

f ^k＝f ^k+1

Wherein, f ^k+1, f ^kk+1 and k iterative nonlinear desired value respectively, Q ^k+1, Q ^kthe electricity vector of k+1 and k the unknown charge simulation of iteration respectively;

S12: computing electric power line shows electric field intensity

$\left\{\begin{array}{c}{E}_x=\frac{1}{2\mathrm{\&pi;}{\mathrm{\&epsiv;}}_0}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\left(\frac{x-x_i}{L_i^2}\right)Q_i\\ E_y=\frac{1}{2\mathrm{\&pi;}{\mathrm{\&epsiv;}}_0}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\left(\frac{y-y_i}{L_i^2}\right)Q_i\\ E=\sqrt{E_x^2+E_y^2}\end{array}\right.---\left(13\right)$

In formula (13), E is the size of electric field intensity, and its component is respectively E _xand E _y, L _ifor charge simulation is to the distance of calculation level.Therefore, calculate DC bipolar conductive line surfaces each point field intensity based on formula (13), solve wire maximized surface field intensity E _max.

S13: the radio interference level calculating any landform

In conjunction with the parameter such as distance of wire radius and calculation level distance positive pole, the CISPR recommend method that DC line radio interference level calculates is such as formula (14):

$G=38+1.6(E_{\max }-24)+46\mathrm{lg\; r}+5\mathrm{lg\; n}+33\lg \frac{20}{R}+\mathrm{\&Delta;}{E}_f+\mathrm{\&Delta;}{E}_w---\left(14\right)$

In formula, G is extra-high voltage direct-current radio interference level, E _maxfor wire maximized surface field intensity, r is sub-conductor radius, and n is split conductor number, and R is the space length of reference point to nearest wire; Δ E _ffor interfering frequency correction term, Δ E _f=5 [1 ~ 2 (log10f) ²], f is interfering frequency, and Δ E can be ignored in scene _f; Δ E _wfor meteorological correction item, fair weather gets 0dBV/m, and bad weather gets 3dB V/m;

S14: calculate audible noise

Audible noise P _dBadopt the computing formula (15) that American Electric Power research institute (EPRI) is recommended:

$P_{\mathrm{dB}}=56.9+1.24\lg \frac{E_{\max }}{25}+25\lg \frac{d}{4.45}+18\lg \frac{n}{2}-10\mathrm{lgD}+0.02D+k_n---\left(15\right)$

In formula (15), E _maxfor wire maximized surface field intensity, d is sub-conductor diameter, and n is split conductor number, and D is the distance of positive wire and calculation level, k _nfor correction term, during n>=3, k _nduring=0, n=2, k _nwhen=2.6dB, n=1, k _n=7.5dB.

In order to verify correctness of the present invention, usability, this programme adopts embodiment to be illustrated.

As shown in Figure 2, section positive wire is 37m to ground level, sea level elevation 1264m, temperature 22.1 DEG C ~ 23.5 DEG C, humidity 47% ~ 52%, wind speed 0.3m/s, the landform peak-valley difference along circuit parallel direction in line span residing for section is 1.2m to the maximum, the radio interference background of section be according to master gauge fix on circuit charged time distance line 400m beyond measured value be 23.6dB, meet radio interference background at least than the requirement of circuit radio interference value 10dB.The radio interference value that mark spy-Carl Menger method that existing the most frequently used technique computes relief affects and progressively image method result of calculation have immediately below the two poles of the earth is maximum, region outside the two poles of the earth is attenuation trend, it is the regular distribution increased afterwards that first decays between the two poles of the earth, its result of calculation is less than in-site measurement value simultaneously, and the radio interference overall distribution rule of this section of calculating of the present invention and the size of in-site measurement value are consistent.

Claims (1)

1. a method for DC power transmission line electric field intensity and radio interference calculating, is characterized in that,

S1: determine charge simulation locus

The position of charge simulation meets the constraint condition of formula (1); For improving resolution, wire and lightning conducter are adopted 10 binary codings, image charge adopts 10 binary codings;

$\left\{\begin{array}{c}{(x_i-x_{0i})}^2+{(y_i-y_{0i})}^2<R_1^2(i=1...M)\\ {(x_j-x_{0j})}^2+{(y_j-y_{0j})}^2<R_2^2(j=1...A)\\ f(x_k,y_k)<0,(k=1...N-A)\end{array}\right.---\left(1\right)$

(x in formula (1) _i, y _i) and (x _j, y _j) be the charge simulation coordinate in oidiospore wire and lightning conducter, (x _k, y _k) be the mirror image charge simulation coordinate below Earth Surface, R ₁and R ₂for the radius of oidiospore wire and lightning conducter, A and N is respectively the quantity of charge simulation in lightning conducter and total charge simulation quantity; F (x _k, y _k) for describing the function of Earth Surface continuous curve;

S2: the generation of charge simulation position initial population P (t)

The charge simulation of wire and lightning conducter wire is all distributed in the annulus of diameter 1/4 respectively, and each image charge lays respectively at the equidistant mirror position on Relative vertical ground;

Formula (2) is evaluated individual quality as fitness function:

M is the match point quantity of conductive line surfaces in formula (2), Q and the potential vectors of the match point that the electricity vector sum of unknown charge simulation is known respectively, for the current potential of wire, lightning conducter or Earth Surface i-th match point;

S3: judge convergence

If | f _max-f _min| < ε, then export optimizing result, stops iteration, go to step S4; Otherwise proceed to S5; Wherein f _max, f _minbe respectively functional value that is optimum in current population and the poorest individuality, ε is given accuracy;

S4: regularization

In formula (2), for realizing being similar to nonlinear operator F (Q), utilize Taylor's formula by F (the Q+ δ Q) Taylor expansion at Q place, when || enough hour of δ Q||, adopt first-order approximation and ignore remaining high-order in a small amount, obtaining formula (3);

$F(Q+\mathrm{\&delta;Q})=F\left(Q\right)+\frac{\&PartialD;F}{\&PartialD;Q}\mathrm{\&delta;Q}+\frac{1}{2}\frac{{\&PartialD;}^{2}F}{\&PartialD;Q^2}{\left(\mathrm{\&delta;Q}\right)}^2+R(Q,\mathrm{\&delta;Q})\&ap;F\left(Q\right)+\frac{\&PartialD;F}{\&PartialD;Q}\mathrm{\&delta;Q}---\left(3\right)$

Q*=Q+ δ Q is made to be equation exact Solutions, then can obtain following linear operator equation formula (4) by formula (3) at the Q place close to Q*:

In conjunction with the formula (4) of linearization process, in this region, show that a best δ Q is such as formula (5) based on overall regularization by optimization problem:

In formula (5), W is linear operator, and η is trusted zones size, and μ (η) is penalty function;

For the optimization problem shown in (5) formula, the necessary condition utilizing f to be minimum solution to be the gradient of f be zero point, obtain the linear equation of formula (6):

Q ^k+1＝Q ^k+δQ

In formula (6), for the transposition of Jacobi matrix;

What the solving of the non-linear least square problem of formula (2) and formula (5) was summed up as its normal equation solves such as formula (6);

S5: selection, crossover and mutation

In S3, if do not meet | f _max-f _min| < ε, need carry out selection, the crossover and mutation of population:

Wherein, selective rule sorts to individuality according to fitness size, and therefrom choose i the maximum individuality of fitness, (7) carry out select probability P according to the following formula _s(x _i):

$P_s\left(x_i\right)=f\left(x_i\right)/\underset{i}{\mathrm{\&Sigma;}}f\left(x_i\right)---\left(7\right)$

Crossover rule adopts two interleaved modes, adaptive crossover mutation P _cfor formula (8):

$P_C=\left\{\begin{array}{cc}0.9-\frac{0.3\&times;(f_{\max }-f^{\&prime;})}{f_{\max }-f_{\mathrm{avg}}}& f^{\&prime;\&GreaterEqual;f_{\mathrm{avg}}}\\ 0.9& f^{\&prime;}\&GreaterEqual;f_{\mathrm{avg}}\end{array}\right.---\left(8\right)$

In formula (8), f _avgfor the average fitness of colony, f' is the individual larger adaptive values of two intersections, f _maxfor the functional value of optimum individual in current population;

Variation rule is that every two binary codings of each individuality are produced a number between (0,1) at random, if be greater than individual aberration rate, then this coding 1 becomes 0, or becomes 1 by 0, otherwise this coding does not make a variation, P _mmutation probability is formula (9):

$P_m=\left\{\begin{array}{cc}0.2-\frac{0.5\&times;(f_{\max }-f)}{f_{\max }-f_{\mathrm{avg}}}& f^{\&GreaterEqual;f_{\mathrm{avg}}}\\ 0.2& f\&GreaterEqual;f_{\mathrm{avg}}\end{array}\right.---\left(9\right)$

In formula (9), f _avgfor the average fitness of colony, f is that every two binary codings of each individuality produce a number between (0,1), f at random _maxfor the functional value of optimum individual in current population;

Then, retain more excellent individuality, the identical number substituting parent Population adaptation value less with the individuality that the adaptive value of progeny population is larger is individual, i.e. P (t)=P (t+1), improve the probability obtaining optimum individual, the initial population of the new population of current reservation as step S2 is recalculated;

S6: judge formula (6) then turn S12; Otherwise turn S7;

S7: calculate δ Q, f ^k, f ^k+1, f ₁ ^k+1

The trust region method of through type (6) determines the δ Q be applicable to:

Δf＝f ^k+1-f ^k(10)

Δf ₁＝f ₁ ^k+1-f ^k

In formula, Δ f is the change of Nonlinear Parameter value, Δ f ₁the change of linearization desired value, f simultaneously ^k+1, f ^kk+1 and k iterative nonlinear desired value respectively, f ₁ ^k+1be k+1 iterative linearized desired value, circular is such as formula (11):

In formula (11), f ^k+1, f ^kk+1 and k iterative nonlinear desired value respectively, f ₁ ^k+1be k+1 iterative linearized desired value, W is linear operator, Q and be respectively the potential vectors of the known match point of the electricity vector sum of unknown charge simulation;

S8: judge f ^k> f ^k+1, then S9 is turned; Otherwise trusted zones size η is become original 0.9 times, i.e. 0.9 η, proceed to S7 iterative computation;

S9: judge in formula, Δ f is the change of Nonlinear Parameter value, Δ f ₁be the change of linearization desired value, τ is trusted zones controling parameters; If turn S10; Otherwise, trusted zones size η is become original 1.1 times, i.e. 1.1 η, proceeds to S7 iterative computation again;

S10: judge whether to be greater than maximum iteration time

In practical engineering calculation, for avoiding a large amount of computing, need to set maximum iteration time, maximum iteration time is less than or equal to 1000 times; If be greater than maximum iteration time, turn S5; Otherwise, turn S11;

S11: carry out f by formula (12) ^k+1k+1 iterative nonlinear desired value calculate, Q ^k+1k+1 iteration, then turn S4;

Q ^k+1＝Q ^k+δQ (12)

f ^k＝f ^k+1

Wherein, f ^k+1, f ^kk+1 and k iterative nonlinear desired value respectively, Q ^k+1, Q ^kthe electricity vector of k+1 and k the unknown charge simulation of iteration respectively;

S12: computing electric power line shows electric field intensity

$\left\{\begin{array}{c}{E}_x=\frac{1}{2\mathrm{\&pi;}{\mathrm{\&epsiv;}}_0}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\left(\frac{x-x_i}{L_i^2}\right)Q_i\\ E_y=\frac{1}{2\mathrm{\&pi;}{\mathrm{\&epsiv;}}_0}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\left(\frac{y-y_i}{L_i^2}\right)Q_i\\ E=\sqrt{E_x^2+E_y^2}\end{array}\right.---\left(13\right)$

In formula (13), E is the size of electric field intensity, and its component is respectively E _xand E _y, L _ifor charge simulation is to the distance of calculation level; Therefore, calculate DC bipolar conductive line surfaces each point field intensity based on formula (13), solve wire maximized surface field intensity E _max;

S13: the radio interference level calculating any landform;

S14: calculate audible noise.