CN103399190B - Based on the computing method of the distribution line induced overvoltage of PSCAD/EMTDC - Google Patents

Abstract

The present invention relates to a kind of computing method of the distribution line induced overvoltage based on PSCAD/EMTDC, the key step of the method comprises the PSCAD/EMTDC circuit model setting up lightning induction line, design induced overvoltage calculates self-defined element, and the PSCAD/EMTDC circuit model of lightning induction line is become the model of lightning induction line in PSCAD/EMTDC with the self-defined component encapsulation of induced overvoltage.Adopt these computing method to calculate the induced overvoltage of distribution line more easily by building model, and it is analyzed.Overcome the shortcoming that experimental formula is inaccurate and numerical computation method is complicated, improve the efficiency that induced overvoltage is analyzed.

Description

Based on the computing method of the distribution line induced overvoltage of PSCAD/EMTDC

Technical field

The invention belongs to technical field of electricity, specifically, relate to a kind of computing method of distribution line induced overvoltage.

Background technology

Power distribution network is directly connected with user in electric system and distributes the important step of electric energy to user, and its safe and reliable operation is most important.Overhead distribution has a very wide distribution, and is very easily struck by lightning, and because its shaft tower height is lower, the shielding action of Adjacent Buildings is comparatively large, and the probability that thunder attacks circuit directly is little, in addition because its dielectric level is lower, makes induced lightening become the major reason of insulation flashover.Therefore should analyze induced overvoltage characteristic.

At present, the computing method of lightning induced voltage mainly contain regular method and numerical computation method two kinds.The amplitude of regular method use experience formulae discovery induced overvoltage, there is certain deviation in its result of calculation on the one hand, can not analyze on the other hand to induced overvoltage waveform; Numerical computation method is by program calculation Lightning Electromagnetic Fields and solve field wire coupling model calculating induced overvoltage, comparison of computational results is accurate, but because boundary condition treatment is complicated, the induced overvoltage calculating zinc oxide surge arresters, erection coupling ground wire and multipoint line is more difficult, and need update routine during circuit changes in spatial distribution, therefore not easily the thunderbolt performance under different lightning protection measures is carried out analysis and compared, thus determine rational lightning protection measures.

Summary of the invention

The object of the present invention is to provide a kind of induced overvoltage computing method based on PSCAD/EMTDC, as calculating direct lightning strike superpotential, the induced overvoltage of distribution line can be calculated by building model more easily, and it is analyzed.Overcome the shortcoming that experimental formula is inaccurate and numerical computation method is complicated, improve the efficiency that induced overvoltage is analyzed.

Technical scheme of the present invention is: a kind of computing method of the distribution line induced overvoltage based on PSCAD/EMTDC, comprise the following steps:

(1) calculate the electromagnetic field that thunderbolt produces, detailed process is: adopt dipole technique, calculates the level of electric field under lightning induction, vertical component and transverse field strength component; Introduce soil resistivity parameter, on dipole technique method basis, according to the horizontal component of electric field under Cooray-Rubinstein formula correction calculating lightning induction;

(2) set up the PSCAD/EMTDC circuit model of lightning induction line: the isotimic computing electric circuit deriving lightning induction line according to electromagnetic field-circuit coupling model, in PSCAD/EMTDC, set up the Type Equivalent Circuit Model of lightning induction line according to isotimic computing electric circuit;

(3) design induced overvoltage and calculate self-defined element, the design of the self-defined element of induced overvoltage comprises parameters input frame and mathematics computing model, line construction, return-stroke model and the earth etc. are calculated desired parameters and are transferred to mathematics computing model by parameters input frame, mathematics computing model comprises circuit electrical parameter calculation, Electromagnetic Calculation, phase-model transformation and Equivalent Circuit Parameter calculating etc., wherein Electromagnetic Calculation calculates, by parameters such as parameter box adjusting circuit structure, return-stroke model and the earth according to mathematical model in step (1);

(4) model of lightning induction line in PSCAD/EMTDC is set up, every section of circuit uses induced overvoltage module simulation, and induced overvoltage module calculates self-defined component encapsulation by the PSCAD/EMTDC circuit model of lightning induction line and induced overvoltage and forms;

(5) set up the overall realistic model of induced overvoltage, call the induced overvoltage module of lightning induction line, the relevant device models such as induced overvoltage module and shaft tower, insulator, lightning arrester are connected by actual conditions, moving calculation line influence superpotential;

(6) change line construction, set up the overall realistic model of new induced overvoltage, the annexation of the relevant device models such as the induced overvoltage module of change lightning induction line and shaft tower, insulator, lightning arrester, reruns computational scheme induced overvoltage.

Preferably: in the mathematical model of lightning induction line, the design of the self-defined element of induced overvoltage is by FORTRAN programming realization.

The invention has the beneficial effects as follows:

After establishing the model of lightning induction line in PSCAD/EMTDC, only the correlation models such as this model and shaft tower, insulator, lightning arrester need be connected by actual conditions, operation can calculate induced overvoltage, its computation process and direct lightning strike superpotential similar, apply easy, more suitable engineering staff uses; And when line construction changes, do not need to revise application program, only need the corresponding model of change lightning induction line in PSCAD/EMTDC and the connection of other models, application is simple.By the simulation of different circuit models, emulate the induced overvoltage of different line construction, be more convenient for determining rational lightning protection measures, to power circuit installation guideline.

Accompanying drawing explanation

Accompanying drawing 1 is induced overvoltage modular model structural representation of the present invention.

Accompanying drawing 2 is the isotimic computing electric circuit schematic diagram deriving lightning induction line according to electromagnetic field-circuit coupling model of the present invention.

Accompanying drawing 3 is self-defined induced overvoltage component models mathematics computing model program flow diagram of the present invention.

Embodiment

Below in conjunction with accompanying drawing, the present invention will be further described in detail.

Based on the computing method of the distribution line induced overvoltage of PSCAD/EMTDC, mainly comprise the following steps:

(1) calculate the electric field level of thunderbolt generation, vertical component and transverse magnetic field components computing method and comprise following steps:

1) lightning channel is equivalent to vertical channel between connection cloud ground, be continuous print dipole by lightning channel subdivision, calculate the electromagnetic field that each dipole produces respectively, each dipole electromagnetic field is carried out total electromagnetic field that vector summing just can obtain the generation of lightning channel electric current.Adopt Master and Uman to derive the electric Field Calculation model obtained, calculate the electric field level component of thunder and lightning main discharge generation, vertical component and transverse magnetic field components;

${+\∫}_{-H}^H[\frac{3r(z-z^{\′})}{{\mathrm{cR}}^4}i(z^{\′},t-R/c)+\frac{r(z-z^{\′})}{c^2{R}^3}\frac{\∂i(z^{\′},t-R/c)}{\∂t}]{\mathrm{dz}}^{\′}\}$

${+\∫}_{-H}^H[\frac{2{(z-z^{\′})}^2-r^2}{{\mathrm{cR}}^4}i(z^{\′},t-R/c)-\frac{r^2}{c^2{R}^3}\frac{\∂i(z^{\′},t-R/c)}{\∂t}]{\mathrm{dz}}^{\′}\}$

Wherein, with be respectively electric field level component, vertical component and transverse field strength component; ε ₀and μ ₀be respectively permittivity of vacuum and magnetic permeability; C is the light velocity; R, the radial coordinate of spatial point, position angle and axial coordinate is respectively with z; R is the distance that current dipole arrives unknown point; H is lightning channel height.

2) consider that soil resistivity is when affecting, electric field level component on dipole technique basis, by Cooray-Rubinstein formulae discovery:

This formula is frequency-domain calculations formula, wherein, for considering the electric field level component of soil resistivity impact; ε _rgfor soil relative dielectric constant; σ is ground conductivity, is reciprocal relation with soil resistivity.Use vector matching technology that the complex frequency domain expression formula of above formula is decomposed into multiple rational fraction sum, being derived by pull-type inverse transformation is similar to time-domain expression:

$\left\{\begin{array}{c}{x}_{k,n}=x_{k,n-1}{e}^{(a_k/{\mathrm{\τ}}_G)\mathrm{\Δt}}+(e^{(a_k/{\mathrm{\τ}}_G)\mathrm{\Δt}}-1)\×[{\mathrm{\τ}}_G(H_n-H_{n-1})/\left(a_k^2\mathrm{\Δt}\right)+H_{n-1}/a_k]\\ -(H_n-H_{n-1})/a_k,k=1...N_{\mathrm{RA}}\\ E_{r,n}^{\mathrm{\σ}}=E_{r,n}-\mathrm{\η}{H}_n-\mathrm{\η}\underset{k=1}{\overset{N_{\mathrm{RA}}}{\mathrm{\Σ}}}{r}_k{x}_{k,n}\end{array}\right.$

Wherein, N _rAfor decomposing the number of rear rational fraction; τ _g=ε ₀ε _rg/ σ; a _k, r _kbe respectively limit and the residual of rational fraction.

(2) set up the PSCAD/EMTDC circuit model of lightning induction line: the isotimic computing electric circuit deriving lightning induction line according to electromagnetic field-circuit coupling model, in PSCAD/EMTDC, set up the Type Equivalent Circuit Model of lightning induction line according to isotimic computing electric circuit;

Circuit coupling model describes the induced voltage of circuit, the relation between electric current and Lightning Electromagnetic Fields, can the induced overvoltage of computational scheme by solving field wire coupling model.Adopt Agrawal field-line coupling model, carry out the derivation of equivalent circuit, the Agrawal model on many wires road is:

$\frac{\∂}{\∂x}\left[v_i^s(x,t)\right]+\left[L_{\mathrm{ij}}^{\′}\right]\frac{\∂}{\∂t}\left[i_i(x,t)\right]=\left[E_x^e(x,h_i,t)\right]$

$\frac{\∂}{\∂x}\left[i_i(x,t)\right]+\left[C_{\mathrm{ij}}^{\′}\right]\frac{\∂}{\∂t}\left[v_i^s(x,t)\right]=0$

Wherein be respectively conductor inductance and capacitance matrix; for scattering voltage vector, unit is kV; [i _i(x, t)] be line current vector, unit is kA; for incident electric fields horizontal component vector, unit is kV/m.In above formula, voltage is scattering voltage, and the total voltage (kV) on wire is calculated as follows:

$\left[v_i(x,t)\right]=\left[v_i^s(x,t)\right]-\underset{0}{\overset{h_i}{\∫}}\left[E_z^i(x,z,t)\right]\mathrm{dz}$

Wherein, for incident electric fields vertical component, unit is kV/m.Right [i _i(x, t)] carry out phase-model transformation, obtain Agrawal wave equation in modulus,

$\frac{\∂}{\∂x}\left[v_i^m(x,t)\right]+\left[L_m\right]\frac{\∂}{\∂t}\left[i_i^m(x,t)\right]=T_V^{-1}\left[E_x^e(x,h_i,t)\right]$

$\frac{\∂}{\∂x}\left[i_i^m(x,t)\right]+\left[C_m\right]\frac{\∂}{\∂t}\left[v_i^m(x,t)\right]=0$

In formula, [L _m], [C _m] be the inductance in modulus, capacitance matrix, t _v, T _ifor scattering voltage, current transformation matrix, known desirable T _v=T _i=T, matrix T calculates according to Jacobi method, now, [C _m]=μ ₀ε ₀[L _m] ^-1, modulus wave velocity is modulus characteristic impedance matrix adopt method of characteristic to analyze Agrawal model, the isotimic computing electric circuit of derivation induced overvoltage as shown in Figure 2.In figure, power values is calculated as follows:

$\left[i_L^p\left(t\right)\right]=\left[i_i(x_2,t-T_D)\right]-Y\left[v_i^s(x_2,t-T_D)\right]$

$\left[i_R^p\left(t\right)\right]=\left[i_i(x_1,t-T_D)\right]+Y\left[v_i^s(x_1,t-T_D)\right]$

$\left[i_L^i\left(t\right)\right]=Y\underset{x_1}{\overset{x_2}{\∫}}\left[E_x^e(x,t-\frac{x-x_1}{v})\right]\mathrm{dx}$

$\left[i_R^i\left(t\right)\right]=Y\underset{x_1}{\overset{x_2}{\∫}}\left[E_x^e(x,t-\frac{x_2-x}{v})\right]\mathrm{dx}$

$\left[v_L^e\left(t\right)\right]=\left[h_i{E}_z^i(x_1,z,t)\right]$

$\left[v_R^e\left(t\right)\right]==\left[h_i{E}_z^i(x_2,z,t)\right]$

Wherein, x ₁, x ₂(x ₁< x ₂) be the horizontal ordinate at circuit two ends, Y=T [Z _ci] ^-1t ^-1, T _d=l/c, l are line length, and in figure, resistance value calculates according to matrix Y.Voltage in above formula is scattering voltage, L and R be indication circuit left end and circuit right-hand member respectively, characterize the impact of circuit wave process, characterize electric field level component to the impact of circuit, characterize E-field normal component to the impact of circuit, obtain complete induced overvoltage isotimic computing electric circuit figure.

Circuit diagram according to Fig. 2, sets up this equivalent circuit in PSCAD/EMTDC, and every section of circuit under Lightning Electromagnetic Fields excitation can with this equivalent circuit equivalent.

(3) design induced overvoltage and calculate self-defined element, the design of the self-defined element of induced overvoltage comprises parameters input frame and mathematics computing model, line construction, return-stroke model and the earth etc. are calculated desired parameters and are transferred to mathematics computing model by parameters input frame, mathematics computing model comprises circuit electrical parameter calculation, Electromagnetic Calculation, phase-model transformation and Equivalent Circuit Parameter calculating etc., wherein Electromagnetic Calculation calculates, by parameters such as parameter box adjusting circuit structure, return-stroke model and the earth according to mathematical model in step (1);

The design of the self-defined element of induced overvoltage adopts formula translation coding to realize, comprise two parts content, one is the design of mathematics computing model Script, two is designs of parameters input frame inputfield, can input lightning return stroke model parameter, lightning current parameter, line construction parameter and the earth parameter etc. by parameters input frame, mathematics computing model carries out Electromagnetic Calculation, circuit electrical parameter calculation, phase-model transformation calculating and the calculating of equivalent circuit component parameters etc. according to the parameter that parameters input frame inputs.

As shown in Figure 3, the program circuit of mathematics computing model Script is: after self-defined induced overvoltage component models brings into operation, and by input frame input parameter information, the simulation time in procedure judges PSCAD/EMTDC, if simulation time is 0, then calculates t, y and R also preserves, and calculates lightning induction the line not horizontal component of electric field, vertical component preserving in the same time everywhere.If simulation time is not 0, then read a upper emulation moment circuit scattering voltage and current in PSCAD/EMTDC, circuit in the read data files not horizontal component of electric field and vertical component in the same time everywhere, and power values, the voltage source value of induced overvoltage isotimic computing electric circuit under calculating corresponding moment lightning induction, and output in the equivalent circuit that PSCAD/EMTDC builds.

(4) set up the model of lightning induction line in PSCAD/EMTDC, every section of circuit uses induced overvoltage module simulation, and induced overvoltage module is made up of the PSCAD/EMTDC circuit model of lightning induction line and the self-defined component encapsulation of induced overvoltage.

(5) the overall realistic model of induced overvoltage is set up, call the induced overvoltage module of lightning induction line, in PSCAD, call the existing model of the parts such as shaft tower, insulator, lightning arrester simultaneously, induced overvoltage module is connected by actual conditions with relevant device models such as shaft tower, insulator, lightning arresters, namely an induced overvoltage module is called between adjacent Tower Model, block mold is emulated, moving calculation thunder and lightning induction voltage.

(6) line construction is changed, set up the overall realistic model of new induced overvoltage, the annexation of the relevant device models such as the induced overvoltage module of change lightning induction line and shaft tower, insulator, lightning arrester, reruns and calculates new thunder and lightning induction voltage.

Claims (2)

1., based on computing method for the distribution line induced overvoltage of PSCAD/EMTDC, it is characterized in that, comprise the following steps:

(1) calculate the electromagnetic field that thunderbolt produces, detailed process is: adopt dipole technique, calculates the level of electric field under lightning induction, vertical component and transverse field strength component; Introduce soil resistivity parameter, on dipole technique method basis, according to the horizontal component of electric field under Cooray-Rubinstein formula correction calculating lightning induction; Concrete computation process comprises the following steps:

A, lightning channel is equivalent to connects vertical channel between cloud ground, be continuous print dipole by lightning channel subdivision, calculate the electromagnetic field that each dipole produces respectively, each dipole electromagnetic field is carried out total electromagnetic field that vector summing just can obtain the generation of lightning channel electric current, adopt Master and Uman to derive the electric Field Calculation model obtained, calculate the electric field level component of thunder and lightning main discharge generation, vertical component and transverse magnetic field components;

Wherein, with be respectively electric field level component, vertical component and transverse field strength component; ε ₀and μ ₀be respectively permittivity of vacuum and magnetic permeability; C is the light velocity; R, the radial coordinate of spatial point, position angle and axial coordinate is respectively with z; R is the distance that current dipole arrives unknown point; H is lightning channel height;

B, consider that soil resistivity is when affecting, electric field level component on dipole technique basis, by Cooray-Rubinstein formulae discovery:

This formula is frequency-domain calculations formula, wherein, for considering the electric field level component of soil resistivity impact; ε _rgfor soil relative dielectric constant; σ is ground conductivity, is reciprocal relation with soil resistivity, uses vector matching technology that the complex frequency domain expression formula of above formula is decomposed into multiple rational fraction sum, and being derived by pull-type inverse transformation is similar to time-domain expression:

$\left\{\begin{array}{c}{x}_{k,n}=x_{k,n-1}{e}^{\left(a_k/{\mathrm{\&tau;}}_G\right)\mathrm{\&Delta;}t}+\left(e^{\left(a_k/{\mathrm{\&tau;}}_G\right)\mathrm{\&Delta;}t}-1\right)\&times;\&lsqb;{\mathrm{\&tau;}}_G\left(H_n-H_{n-1}\right)/\left(a_k^2\mathrm{\&Delta;}t\right)+H_{n-1}/a_k\&rsqb;\\ -\left(H_n-H_{n-1}\right)/a_k,k=\mathrm{1...}{N}_{RA}\\ E_{r,n}^{\mathrm{\&sigma;}}=E_{r,n}-{\mathrm{\&eta;H}}_n-\mathrm{\&eta;}\underset{k=1}{\overset{N_{RA}}{\&Sigma;}}{r}_k{x}_{k,n}\end{array}\right.$

Wherein, N _rAfor decomposing the number of rear rational fraction; τ _g=ε ₀ε _rg/ σ; a _k, r _kbe respectively limit and the residual of rational fraction;

(2) set up the PSCAD/EMTDC circuit model of lightning induction line: the isotimic computing electric circuit deriving lightning induction line according to electromagnetic field-circuit coupling model, in PSCAD/EMTDC, set up the Type Equivalent Circuit Model of lightning induction line according to isotimic computing electric circuit; Its computation process is:

Adopt Agrawal field-line coupling model, carry out the derivation of equivalent circuit, the Agrawal model on many wires road is:

$\frac{\&part;}{\&part;x}\&lsqb;v_i^s(x,t)\&rsqb;+\&lsqb;L_{ij}^{\&prime;}\&rsqb;\frac{\&part;}{\&part;t}\&lsqb;i_i(x,t)\&rsqb;=\&lsqb;E_x^e(x,h_i,t)\&rsqb;$

$\frac{\&part;}{\&part;x}\&lsqb;i_i(x,t)\&rsqb;+\&lsqb;C_{ij}^{\&prime;}\&rsqb;\frac{\&part;}{\&part;t}\&lsqb;v_i^s(x,t)\&rsqb;=0$

Wherein [L' _ij], [C ' _ij] be respectively conductor inductance and capacitance matrix; for scattering voltage vector, unit is kV; [i _i(x, t)] be line current vector, unit is kA; for incident electric fields horizontal component vector, unit is kV/m; In above formula, voltage is scattering voltage, and the total voltage (kV) on wire is calculated as follows:

$\&lsqb;v_i(x,t)\&rsqb;=\&lsqb;v_i^s(x,t)\&rsqb;-\underset{0}{\overset{h_i}{\&Integral;}}\&lsqb;E_z^i(x,z,t)\&rsqb;dz$

Wherein, for incident electric fields vertical component, unit is kV/m, right [i _i(x, t)] carry out phase-model transformation, obtain Agrawal wave equation in modulus,

$\frac{\&part;}{\&part;x}\&lsqb;v_i^m(x,t)\&rsqb;+\&lsqb;L_m\&rsqb;\frac{\&part;}{\&part;t}\&lsqb;i_i^m(x,t)\&rsqb;=T_V^{-1}\&lsqb;E_x^e(x,h_i,t)\&rsqb;$

$\frac{\&part;}{\&part;x}\&lsqb;i_i^m(x,t)\&rsqb;+\&lsqb;C_m\&rsqb;\frac{\&part;}{\&part;t}\&lsqb;v_i^m(x,t)\&rsqb;=0$

In formula, [L _m], [C _m] be the inductance in modulus, capacitance matrix, t _v, T _ifor scattering voltage, current transformation matrix, known [L _ij'] [C _ij']=μ ₀ε ₀1 _n, desirable T _v=T _i=T, matrix T calculates according to Jacobi method, now, [C _m]=μ ₀ε ₀[L _m] ^-1, modulus wave velocity is modulus characteristic impedance matrix adopt method of characteristic to analyze Agrawal model, the isotimic computing electric circuit model of derivation induced overvoltage, in model, power values is calculated as follows:

$\begin{array}{c}\&lsqb;i_L^p\left(t\right)\&rsqb;=\&lsqb;i_i\left(x_2,t-T_D\right)\&rsqb;-Y\&lsqb;v_i^s\left(x_2,t-T_D\right)\&rsqb;\\ \&lsqb;i_R^p\left(t\right)\&rsqb;=\&lsqb;i_i\left(x_1,t-T_D\right)\&rsqb;+Y\&lsqb;v_i^s\left(x_1,t-T_D\right)\&rsqb;\end{array}$

$\&lsqb;i_L^i\left(t\right)\&rsqb;=Y\underset{x_1}{\overset{x_2}{\&Integral;}}\&lsqb;E_x^e(x,t-\frac{x-x_1}{v})\&rsqb;dx$

$\&lsqb;i_R^i\left(t\right)\&rsqb;=Y\underset{x_1}{\overset{x_2}{\&Integral;}}\&lsqb;E_x^e(x,t-\frac{x_2-x}{v})\&rsqb;dx$

$\&lsqb;v_L^e\left(t\right)\&rsqb;=\&lsqb;h_i{E}_z^i(x_1,z,t)\&rsqb;$

$\&lsqb;v_R^e\left(t\right)\&rsqb;==\&lsqb;h_i{E}_z^i(x_2,z,t)\&rsqb;$

Wherein, x ₁, x ₂(x ₁< x ₂) be the horizontal ordinate at circuit two ends, Y=T [Z _ci] ^-1t ^-1, T _d=l/c, l are line length, and in figure, resistance value calculates according to matrix Y, and the voltage in above formula is scattering voltage, L and R be indication circuit left end and circuit right-hand member respectively, characterize the impact of circuit wave process, characterize electric field level component to the impact of circuit, characterize E-field normal component to the impact of circuit, obtain complete induced overvoltage isotimic computing electric circuit figure;

(3) design induced overvoltage and calculate self-defined element, the design of the self-defined element of induced overvoltage comprises parameters input frame and mathematics computing model, parameters input frame is by line construction parameter, return-stroke model parameter and the earth parameter, be transferred to mathematics computing model, mathematics computing model comprises circuit electrical parameter calculation, Electromagnetic Calculation, phase-model transformation and Equivalent Circuit Parameter and calculates, wherein Electromagnetic Calculation calculates according to mathematical model in step (1), by parameter box adjusting circuit structural parameters, return-stroke model parameter and the earth parameter;

(4) model of lightning induction line in PSCAD/EMTDC is set up, every section of circuit uses induced overvoltage module simulation, and induced overvoltage module calculates self-defined component encapsulation by the PSCAD/EMTDC circuit model of lightning induction line and induced overvoltage and forms;

(5) the overall realistic model of induced overvoltage is set up, call the induced overvoltage module of lightning induction line, by induced overvoltage module and Tower Model, insulator model, lightning arrester model, be connected by actual conditions, moving calculation line influence superpotential;

(6) line construction is changed, set up the overall realistic model of new induced overvoltage, change the annexation of the induced overvoltage module of lightning induction line and Tower Model, insulator model, lightning arrester model, rerun computational scheme induced overvoltage.

2. the computing method of a kind of distribution line induced overvoltage based on PSCAD/EMTDC as claimed in claim 1, is characterized in that, the foundation of the self-defined element of described induced overvoltage adopts FORTRAN programming realization.