CN104573219B - The method that a kind of DC power transmission line electric-field intensity and radio interference are calculated - Google Patents

Abstract

The invention discloses a kind of method that DC power transmission line electric-field intensity and radio interference are calculated, solve prior art and conventional method has the problem of fluctuating physical features can not directly set wire image charge for transmission line wire section；In addition, the ill posed problem of full scale equation can be left using lienarized equations such as gauss-newton methods by solving DC power transmission line.Contrasted with traditional partial discharge method, the present invention improves test efficiency, by verification experimental verification, with practicality and feasibility.

Description

The method that a kind of DC power transmission line electric-field intensity and radio interference are calculated

Technical field

The invention belongs to technical field of electric power, more particularly in high pressure, extra-high voltage field, DC power transmission line electric-field intensity And the method that radio interference is calculated.

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, however as voltage The raising of grade, the emphasis of concern and circuit design of its electromagnetic environmental impact increasingly by the public considers.Under DC line Side total electric field, gas current, D.C. magnetic field, and corona produce radio interference and audible noise can be occupied to along it is bright Production and life produce certain influence.Research shows that radio interference level is the important electricity of DC power transmission line environmental impact assessment One of magnetic environment index, its main harm is to cause the radio signal interferences such as radio broadcasting, TV around transmission line of electricity.

Document《Twisted wire corona inception voltage is analyzed under negative direct current》、《The positive direct-current electricity of steel-cored aluminium strand under high altitude condition Dizzy starting voltage analysis》Positive and negative direct current twisted wire corona inception voltage, document based on gas discharge theory analysis《High aititude ± 800kV DC power transmission lines electromagnetic environment is measured》UHVDC Transmission Lines radio interference characteristic research, above-mentioned theory are carried out It is plane that transmission line wire vertical cross section is selected in analysis and the actual measurement of operation test, with reference to field domain boundary condition, profit With mark spy-Carl Menger method, progressively image method carries out radio interference analysis and calculating.But actual transmission line wire hangs down Straight section is often in uneven terrain.Complex wires vertical cross section is cannot be directly used to based on the computational methods in above-mentioned document DC line electric-field intensity and radio interference are calculated under physical features.

Document《HVAC power transmission line electromagnetic environment characteristic analysis in the case of complicated landform》、《Superelevation under complex terrain The power frequency electric field of pressure transmission line》Analogue charge method based on optimization has carried out HVAC power transmission line in the case of complicated landform Electromagnetic environment characteristic analysis, but this method is to set the position of charge simulation by rule of thumb.Document《Consider that the transmission of electricity of meteorological condition is led Line power frequency electric field New calculating method》、《Scissors crossing transmission pressure three-dimensional power frequency electromagnet field computation》Entered respectively using genetic algorithm Transmission pressure sag and extra-high voltage insulator the grading ring optimization of row electric field inverse operation, but conventional method is led just for flat Line section, using the charge inducing for setting the equivalent Earth Surface of image charge, has rough ground for transmission line wire section The situation of gesture, it is impossible to which wire image charge is directly set.

The content of the invention

In order to solve the above problems, a kind of DC power transmission line electric-field intensity and radio interference that the present invention is provided are calculated Method, comprise the following steps that：

S1：Determine charge simulation locus

The position of charge simulation meets the constraints of formula (1)；To improve, resolution ratio will divide sub-conductor and lightning conducter is led Line is using 10 binary codings, and image charge is using 10 binary codings；

(x in formula (1)_i,y_i) and (x_j,y_j) it is to divide the charge simulation coordinate in sub-conductor and lightning conducter wire, (x_k,y_k) For the image charge coordinate below Earth Surface, R₁And R₂For division sub-conductor and the radius of lightning conducter wire, A and N are respectively to keep away The quantity of charge simulation and total charge simulation quantity in thunder line wire；f(x_k,y_k) it is the letter for describing Earth Surface full curve Number；

S2：Charge simulation position initial population P (t) generation

The charge simulation of division sub-conductor and lightning conducter wire is distributed in the annulus of diameter 1/4, each image charge respectively It is located at the vertical equidistant mirror position in relative ground respectively；

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

In formula (2) M be oidiospore conductive line surfaces match point quantity, Q andThe electricity of unknown charge simulation is vectorial respectively With the potential vectors of known match point,For division sub-conductor, the electricity of i-th of match point of lightning conducter wire or Earth Surface Position；

S3：Judge convergence

If | f_max-f_min|<ε, then export optimizing result, stops iteration, goes to step S4；Otherwise it is transferred to S5；Wherein f_max,f_min Optimal and worst individual functional value in respectively current population, ε is the given degree of accuracy；

S4：Regularization

In formula (2), to realize to the approximate of nonlinear operator F (Q), the Thailand using Taylor's formula by F (Q+ δ Q) at Q Expansion is strangled, when | | δ Q | | when sufficiently small, using first approximation and to ignore remaining high-order a small amount of, obtain formula (3)；

It is equation to make Q*=Q+ δ QExact Solutions, then can obtain as follows by formula (3) at the Q close to Q* Linear operator equation formula (4)：

With reference to the formula (4) of linearization process, an optimal δ Q is drawn such as based on global regularization and by optimization problem Formula (5)：

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 point for being zero using the gradient that the necessary condition that f is minimal solution is f is obtained The linear equation of formula (6)：

Q^k+1=Q^k+δQ

In formula (6),For the transposition of Jacobian matrix；

The solution of the non-linear least square problem of formula (2) and formula (5) is attributed to the solution such as formula (6) of its normal equation；

S5：Selection, intersection and variation

In S3, if being unsatisfactory for | f_max-f_min|<ε, need to carry out the selection of population, intersect and make a variation：

Wherein, selection rule is that individual is ranked up according to fitness size, therefrom chooses maximum of i fitness Body, according to the following formula (7) carry out select probability P_s(x_i)：

Crossover rule is using two interleaved modes, adaptive crossover mutation P_cFor formula (8)：

In formula (8), f_avgFor the average fitness of colony, f' is the larger adaptive value of two intersection individuals, f_maxFor current kind The functional value of optimum individual in group；

The rule that makes a variation is that each individual every two binary codings are randomly generated into a number between (0,1), if More than the aberration rate of individual, then the coding becomes 0 by 1, or becomes 1 by 0, and otherwise the coding does not make a variation, P_mMutation probability is Formula (9)：

In formula (9), f_avgFor the average fitness of colony, f randomly generates one for every two binary codings of each individual The individual number between (0,1), f_maxFor the functional value of optimum individual in current population；

Then, more excellent individual is retained, it is smaller to substitute parent Population adaptation value with the larger individual of the adaptive value of progeny population Same number individual, i.e. P (t)=P (t+1), improve obtain optimum individual probability, regard the new population currently retained as step Rapid S2 initial population is recalculated；

S6：Judgement formula (6)It is to turn S12；Otherwise S7 is turned；

S7：Calculate δ Q, f^k,f^k+1,f₁ ^k+1

Suitable δ Q are determined by the trust region method of formula (6)：

Δ f is the change of Nonlinear Parameter value, Δ f in formula₁It is the change for linearizing desired value, while f^k+1,f^kIt is k respectively + 1 and k iterative nonlinear desired value, f₁ ^k+1It is k+1 iterative linearized desired value, circular such as formula (11)：

In formula (11), f^k+1,f^kIt is k+1 and k iterative nonlinear desired value, f respectively₁ ^k+1It is k+1 iterative linearized Desired value, W is linear operator, Q andThe potential vectors of match point known to the electricity vector sum of respectively unknown charge simulation；

S8：Judge f^k>f^k+1, it is to turn S9；Otherwise trusted zones size η is changed into original 0.9 times, i.e. 0.9 η, is transferred to S7 Iterative calculation；

S9：JudgeIn formula, Δ f is the change of Nonlinear Parameter value, Δ f₁It is linearisation desired value Change, τ be trusted zones control parameter；IfTurn S10；Otherwise, trusted zones size η is changed into original 1.1 times, i.e. 1.1 η, are transferred to S7 and iterate to calculate again；

S10：Judge whether to be more than maximum iteration

In practical engineering calculation, to avoid a large amount of computings, it is necessary to set maximum iteration, maximum iteration is less than etc. In 1000 times；If more than maximum iteration, turning S5；Otherwise, S11 is turned；

S11：F is carried out by formula (12)^k+1K+1 iterative nonlinears desired value calculate, Q^k+1K+1 iteration, then turn S4；

Wherein, f^k+1,f^kIt is k+1 and k iterative nonlinear desired value, Q respectively^k+1, Q^kIt is that k+1 and k iteration are unknown respectively The electricity vector of charge simulation；

S12：Computing electric power line surface field intensity

In formula (13), E is the size of electric-field intensity, and its component is respectively E_xAnd E_y, L_iFor charge simulation to calculate point away from From；Therefore, DC bipolar oidiospore conductive line surfaces each point field strength is calculated based on formula (13), solves the maximum surface field of division sub-conductor Strong E_max；

S13：Calculate the radio interference level of any landform；

With reference to oidiospore wire radius and calculating point apart from the parameters such as the distance of positive pole, DC line radio interference level The CISPR of calculating recommends method such as formula (14)：

G is extra-high voltage direct-current radio interference level, E in formula_maxFor the maximum surface electric field intensity of division sub-conductor, r is quantum splitting Sub-conductor radius, n is division oidiospore number of lead wires, and R is space length of the reference point to nearest division sub-conductor；ΔE_fFor interference Frequency correction term, Δ E_f=5 [1~2 (log10f)²], f is interfering frequency, the negligible Δ E in scene_f；ΔE_wFor meteorological correction, Fair weather takes 0dB V/m, and bad weather takes 3dB V/m；

S14：Calculate audible noise；

Audible noise P_dBThe calculation formula (15) recommended using American Electric Power research institute (EPRI)：

In formula (15), E_maxFor the maximum surface electric field intensity of division sub-conductor, d is quantum splitting sub-conductor diameter, and n divides for division Sub-conductor number, D is that positive pole divides sub-conductor with calculating the distance of point, k_nFor correction term, during n >=3, k_nWhen=0, n=2, k_n= When 2.6dB, n=1, k_n=7.5dB.

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

1. the present invention solves prior art and conventional method just for flat wire section, using setting image charge The charge inducing of equivalent Earth Surface, has a case that fluctuating physical features for transmission line wire section, it is impossible to directly sets and leads The problem of line image charge；

2. the present invention solves DC power transmission line can leave full scale equation discomfort using lienarized equations such as gauss-newton methods Determine problem；

3. being contrasted with traditional partial discharge method, the present invention improves test efficiency and improves calculation process, is tested through overtesting Card, with practicality and feasibility.

Brief description of the drawings

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

Fig. 2 is using 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 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 are calculated, specific steps are such as Under：

S1：Determine charge simulation locus

According to the principle of Analogue charge method, in the charge simulation locus span of formula (1), by wire and lightning conducter Charge simulation coordinate do difference with the center of sub-conductor where it, obtain wire and lightning conducter charge simulation span for pair The diameter answered；Charge simulation in formula (1) must in the wire, lightning conducter of non-computational field domain, or positioned at Earth Surface with Under, therefore the position of charge simulation meets the constraints of formula (1)；Wire and lightning conducter are used 10 two to improve resolution ratio Scale coding, image charge is using 10 binary codings；

(x in formula (1)_i,y_i) and (x_j,y_j) it is to divide the charge simulation coordinate in sub-conductor and lightning conducter, (x_k,y_k) it is big Mirror image charge simulation coordinate below ground surface, R₁And R₂For division sub-conductor and the radius of lightning conducter, A and N are respectively lightning conducter The quantity of interior charge simulation and total charge simulation quantity.f(x_k,y_k) it is the function for describing Earth Surface full curve.

S2：Charge simulation position initial population P (t) generation

The charge simulation of wire and lightning conducter wire is distributed in the annulus of diameter 1/4 respectively, and each image charge distinguishes position Equidistant mirror position in Relative vertical ground；

DC power transmission line conductive line surfaces greatest gradient under complex wires vertical cross section physical features is calculated using Analogue charge method And electric-field intensity needs to have the problem of solution：1) position of charge simulation and the quantity of electric charge in bipolar conductor and ground wire；2) it is bipolar to lead The position and the quantity of electric charge of line and ground wire image charge；Therefore, the target of charge simulation locus is the simulation electricity of optimum results Lotus meets advance error in the potential errors that match point is produced, based on all charge simulations of principle of least square method in match point The current potential of generation meets the optimization aim of formula (2), i.e., formula (2) is evaluated to the quality of individual as fitness function：

In formula (2) M be conductive line surfaces match point quantity, Q andRespectively known to the electricity vector sum of unknown charge simulation Match point potential vectors,For wire, the current potential of i-th of match point of lightning conducter or Earth Surface；

S3：Judge convergence

If | f_max-f_min|<ε, then export optimizing result, stops iteration, goes to step S4；Otherwise it is transferred to S5；Wherein f_max,f_min Optimal and worst individual functional value in respectively current population, ε is the given degree of accuracy, preferably ε≤0.5%；

S4：Regularization

In formula (2), to realize to the approximate of nonlinear operator F (Q), the Thailand using Taylor's formula by F (Q+ δ Q) at Q Expansion is strangled, when | | δ Q | | when sufficiently small, using first approximation and to ignore remaining high-order a small amount of, obtain formula (3)；

It is equation to make Q*=Q+ δ QExact Solutions, then can obtain as follows by formula (3) at the Q close to Q* Linear operator equation formula (4)：

Full scale equation ill-posed problem and Ill-posed characteristic can be left by linearizing (4) formula equation using gauss-newton method etc., therefore be needed Regularization Technique is introduced, that is, is referred in linear algebraic process, ill-posed problem is typically to be defined by one group of linear algebraic equation , and this group of equation group is typically derived from the ill-posed inverse problem of very big conditional number, and big conditional number means rounding-off Error or other errors can severely impact the result of problem；

But use traditional Levenberg-Marquardt methods (the literary Burger-Ma Kuaertefa of row) to be to apply regularization The method of creeping on δ Q is added in, the problem of this method is present has：1) lead to not because regularization is applied to δ Q rather than Q for solution Feature is controlled；2) Exact Solutions Q* relies on initial solution Q⁰With minimum path δ Q^k；3) δ Q are solved using distinct methods^kObtain Exact Solutions Q* is different；4) increase of target function value may be caused when δ Q are larger.

Therefore, to overcome prior art defect, the global regularization method on Q is applied to using regularization, while basis Trust Region strategy with global convergence not only restricted step and obtains new descent direction, if nonlinear problem (2) formula With the equation after linearisation size for η region in it is equivalent, in combination with the formula (4) of linearization process, based on global canonical Change and an optimal δ Q such as formula (5) is drawn in the region 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 point for being zero using the gradient that the necessary condition that f is minimal solution is f is obtained The linear equation of formula (6)：

Q^k+1=Q^k+δQ

In formula (6),For the transposition of Jacobian matrix；

The solution of the non-linear least square problem of formula (2) and formula (5) is attributed to the solution such as formula (6) of its normal equation.

S5：Selection, intersection and variation

In S3, if being unsatisfactory for | f_max-f_min|<ε, need to carry out the selection of population, intersect and make a variation：

Wherein, selection rule is that individual is ranked up according to fitness size, therefrom chooses maximum of i fitness Body, according to the following formula (7) carry out select probability P_s(x_i)：

Crossover rule is using two interleaved modes, adaptive crossover mutation P_cFor formula (8)：

In formula (8), f_avgFor the average fitness of colony, f' is the larger adaptive value of two intersection individuals, f_maxFor current kind The functional value of optimum individual in group；

The rule that makes a variation is that each individual every two binary codings are randomly generated into a number between (0,1), if More than the aberration rate of individual, then the coding becomes 0 by 1, or becomes 1 by 0, and otherwise the coding does not make a variation, P_mMutation probability is Formula (9)：

In formula (9), f_avgFor the average fitness of colony, f randomly generates one for every two binary codings of each individual The individual number between (0,1), f_maxFor the functional value of optimum individual in current population；

Then, more excellent individual is retained, it is smaller to substitute parent Population adaptation value with the larger individual of the adaptive value of progeny population Same number individual, i.e. P (t)=P (t+1), improve obtain optimum individual probability, regard the new population currently retained as step Rapid S2 initial population is recalculated；

S6：Judgement formula (6)Then turn S12；Otherwise S7 is turned；

Engineering in practice, formula (6)Need iterative calculation multiple, a large amount of operation times will be expended；For Practical Project, formula (6)Calculating needs can be met；

S7：Calculate δ Q, f^k,f^k+1,f₁ ^k+1

Suitable δ Q are determined by the trust region method of formula (6)：

Δ f is the change of Nonlinear Parameter value, Δ f in formula₁It is the change for linearizing desired value, while f^k+1,f^kIt is k respectively + 1 and k iterative nonlinear desired value, f₁ ^k+1It is k+1 iterative linearized desired value, circular such as formula (11)：

In formula (11), f^k+1,f^kIt is k+1 and k iterative nonlinear desired value, f respectively₁ ^k+1It is k+1 iterative linearized Desired value, W is linear operator, Q andThe potential vectors of match point known to the electricity vector sum of the unknown charge simulation of difference；

S8：Judge f^k>f^k+1, then S9 is turned；Otherwise trusted zones size η is changed into original 0.9 times, i.e. 0.9 η, is transferred to S7 and changes In generation, calculates；

S9：JudgeIn formula, Δ f is the change of Nonlinear Parameter value, Δ f₁It is linearisation desired value Change, τ be trusted zones control parameter；IfTurn S10；Otherwise, trusted zones size η is changed into original 1.1 times, i.e. 1.1 η, are transferred to S7 and iterate to calculate again；

S10：Judge whether to be more than maximum iteration

In practical engineering calculation, to avoid a large amount of computings, it is necessary to set maximum iteration, maximum iteration of the present invention Less than or equal to 1000 times, preferably 200 times；If more than maximum iteration, turning S5；Otherwise, S11 is turned；

S11：F is carried out by formula (12)^k+1K+1 iterative nonlinears desired value calculate, Q^k+1K+1 iteration, then turn S4；

Wherein, f^k+1,f^kIt is k+1 and k iterative nonlinear desired value, Q respectively^k+1, Q^kIt is that k+1 and k iteration are unknown respectively The electricity vector of charge simulation；

S12：Computing electric power line shows electric-field intensity

In formula (13), E is the size of electric-field intensity, and its component is respectively E_xAnd E_y, L_iFor charge simulation to calculate point away from From.Therefore, DC bipolar conductive line surfaces each point field strength is calculated based on formula (13), solves the maximum surface electric field intensity E of wire_max。

S13：Calculate the radio interference level of any landform

Combination wire radius and calculating are put apart from parameters such as the distances of positive pole, what DC line radio interference level was calculated CISPR recommends method such as formula (14)：

G is extra-high voltage direct-current radio interference level, E in formula_maxFor the maximum surface electric field intensity of wire, r is sub-conductor radius, n For split conductor number, R is space length of the reference point to nearest wire；ΔE_fFor interfering frequency correction term, Δ E_f=5 [1~2 (log10f)²], f is interfering frequency, the negligible Δ E in scene_f；ΔE_wFor meteorological correction, fair weather takes 0dB V/m, bad weather Take 3dB V/m；

S14：Calculate audible noise

Audible noise P_dBThe calculation formula (15) recommended using American Electric Power research institute (EPRI)：

In formula (15), E_maxFor the maximum surface electric field intensity of wire, d is sub-conductor diameter, and n is split conductor number, and D leads for positive pole Line and the distance for calculating point, k_nFor correction term, during n >=3, k_nWhen=0, n=2, k_nWhen=2.6dB, n=1, k_n=7.5dB.

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

As shown in Fig. 2 section positive wire is 37m to ground level, and height above sea level 1264m, 22.1 DEG C~23.5 DEG C of temperature, It is to the maximum in humidity 47%~52%, wind speed 0.3m/s, line span residing for section along the landform peak-valley difference of circuit parallel direction 1.2m, the radio interference background of section be according to standard gauge be scheduled on circuit it is powered when distance line 400m beyond measured value be 23.6dB, meets requirement of the radio interference background at least than circuit radio interference value 10dB.Existing the most frequently used technology meter Calculate mark spy-Carl Menger method of relief influence and progressively image method result of calculation has the radio interference immediately below the two poles of the earth Value is maximum, and it is increased regular distribution after first decay between attenuation trend, the two poles of the earth that the region outside the two poles of the earth, which is in, while it calculates knot Fruit is less than in-site measurement value, and radio interference overall distribution rule and the in-site measurement value of the calculating of the present invention section is big It is small to be consistent.

Claims (1)

1. a kind of method that DC power transmission line electric-field intensity and radio interference are calculated, it is characterised in that

S1：Determine charge simulation locus

The position of charge simulation meets the constraints of formula (1)；To improve, resolution ratio will divide sub-conductor and lightning conducter wire is adopted With 10 binary codings, image charge is using 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) it is to divide the charge simulation coordinate in sub-conductor and lightning conducter wire, (x_k,y_k) it is big Image charge coordinate below ground surface, R₁And R₂For division sub-conductor and the radius of lightning conducter wire, A and N are respectively lightning conducter The quantity of charge simulation and total charge simulation quantity in wire；f(x_k,y_k) it is the function for describing Earth Surface full curve；

S2：Charge simulation position initial population P (t) generation

The charge simulation of division sub-conductor and lightning conducter wire is distributed in the annulus of diameter 1/4, each image charge difference respectively Positioned at the vertical equidistant mirror position in relative ground；

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

In formula (2) M be oidiospore conductive line surfaces match point quantity, Q andRespectively known to the electricity vector sum of unknown charge simulation Match point potential vectors,For division sub-conductor, the current potential of i-th of match point of lightning conducter wire or Earth Surface；

S3：Judge convergence

If | f_max-f_min|<ε, then export optimizing result, stops iteration, goes to step S4；Otherwise it is transferred to S5；Wherein f_max,f_minRespectively For optimal and worst individual functional value in current population, ε is the given degree of accuracy；

S4：Regularization

In formula (2), to realize to the approximate of nonlinear operator F (Q), Taylor's exhibition using Taylor's formula by F (Q+ δ Q) at Q Open, when | | δ Q | | when sufficiently small, using first approximation and to ignore remaining high-order a small amount of, obtain formula (3)；

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

It is equation to make Q*=Q+ δ QExact Solutions, then can be obtained at the Q close to Q* by formula (3) such as lower linear Operator equation (4)：

With reference to the formula (4) of linearization process, an optimal δ Q such as formula is drawn based on global regularization and by optimization problem (5)：

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 point for being zero using the gradient that the necessary condition that f is minimal solution is f obtains formula (6) linear equation：

In formula (6),For the transposition of Jacobian matrix；

The solution of the non-linear least square problem of formula (2) and formula (5) is attributed to the solution such as formula (6) of its normal equation；

S5：Selection, intersection and variation

In S3, if being unsatisfactory for | f_max-f_min|<ε, need to carry out the selection of population, intersect and make a variation：

Wherein, selection rule is that individual is ranked up according to fitness size, therefrom chooses the maximum individual of i fitness, presses Select probability P is carried out according to following formula (7)_s(x_i)：

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

Crossover rule is using two interleaved modes, adaptive crossover mutation P_cFor formula (8)：

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

In formula (8), f_avgFor the average fitness of colony, f' is the larger adaptive value of two intersection individuals, f_maxFor in current population The functional value of optimum individual；

The rule that makes a variation is that each individual every two binary codings are randomly generated into a number between (0,1), if being more than The aberration rate of individual, then the coding becomes 0 by 1, or becomes 1 by 0, and otherwise the coding does not make a variation, P_mMutation probability is formula (9)：

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

In formula (9), f_avgFor the average fitness of colony, f for every two binary codings of each individual randomly generate one Number between (0,1), f_maxFor the functional value of optimum individual in current population；

Then, retain more excellent individual, the less phase of parent Population adaptation value is substituted with the larger individual of the adaptive value of progeny population With number individual, i.e. P (t)=P (t+1) improves the probability for obtaining optimum individual, regard the new population currently retained as step S2 Initial population recalculate；

S6：Judgement formula (6)It is to turn S12；Otherwise S7 is turned；

S7：Calculate δ Q, f^k,f^k+1,f₁ ^k+1

Suitable δ Q are determined by the trust region method of formula (6)：

$\begin{array}{c}\mathrm{\&Delta;}f=f^{k+1}-f^k\\ {\mathrm{\&Delta;f}}_1=f_1^{k+1}-f^k\end{array}---\left(10\right)$

Δ f is the change of Nonlinear Parameter value, Δ f in formula₁It is the change for linearizing desired value, while f^k+1,f^kBe respectively k+1 and K iterative nonlinear desired value, f₁ ^k+1It is k+1 iterative linearized desired value, circular such as formula (11)：

In formula (11), f^k+1,f^kIt is k+1 and k iterative nonlinear desired value, f respectively₁ ^k+1It is k+1 iterative linearized target Value, W is linear operator, Q andThe potential vectors of match point known to the electricity vector sum of respectively unknown charge simulation；

S8：Judge f^k>f^k+1, it is to turn S9；Otherwise trusted zones size η is changed into original 0.9 times, i.e. 0.9 η, is transferred to S7 iteration Calculate；

S9：JudgeIn formula, Δ f is the change of Nonlinear Parameter value, Δ f₁It is to linearize changing for desired value Become, τ is trusted zones control parameter；IfTurn S10；Otherwise, trusted zones size η is changed into original 1.1 Times, i.e. 1.1 η are transferred to S7 and iterated to calculate again；

S10：Judge whether to be more than maximum iteration

In practical engineering calculation, to avoid a large amount of computings, it is necessary to set maximum iteration, maximum iteration is less than or equal to 1000 times；If more than maximum iteration, turning S5；Otherwise, S11 is turned；

S11：F is carried out by formula (12)^k+1K+1 iterative nonlinears desired value calculate, Q^k+1K+1 iteration, then turn S4；

$\begin{array}{c}{Q}^{k+1}=Q^k+\mathrm{\&delta;}Q\\ f^k=f^{k+1}\end{array}---\left(12\right)$

Wherein, f^k+1,f^kIt is k+1 and k iterative nonlinear desired value, Q respectively^k+1, Q^kIt is k+1 and the unknown simulation of k iteration respectively The electricity vector of electric charge；

S12：Computing electric power line surface field intensity

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

In formula (13), E is the size of electric-field intensity, and its component is respectively E_xAnd E_y, L_iFor charge simulation to the distance for calculating point； Therefore, DC bipolar oidiospore conductive line surfaces each point field strength is calculated based on formula (13), solves the maximum surface electric field intensity of division sub-conductor E_max；

S13：Calculate the radio interference level of any landform；

With reference to oidiospore wire radius and calculating point apart from parameters such as the distances of positive pole, DC line radio interference level is calculated CISPR recommend method such as formula (14)：

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

G is extra-high voltage direct-current radio interference level, E in formula_maxFor the maximum surface electric field intensity of division sub-conductor, r is that quantum splitting is led Line radius, n is division oidiospore number of lead wires, and R is space length of the reference point to nearest division sub-conductor；ΔE_fFor interfering frequency Correction term, Δ E_f=5 [1~2 (log10f)²], f is interfering frequency, the negligible Δ E in scene_f；ΔE_wFor meteorological correction, good day Gas takes 0dB V/m, and bad weather takes 3dB V/m；

S14：Calculate audible noise；

Audible noise P_dBThe calculation formula (15) recommended using American Electric Power research institute (EPRI)：

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

In formula (15), E_maxFor the maximum surface electric field intensity of division sub-conductor, d is quantum splitting sub-conductor diameter, and n leads for division oidiospore Line number, D is that positive pole divides sub-conductor with calculating the distance of point, k_nFor correction term, during n >=3, k_nWhen=0, n=2, k_n=2.6dB, During n=1, k_n=7.5dB.