CN104569749A - Method for judging high altitude long air gap lightning flashover - Google Patents

Abstract

The invention discloses a method for judging high altitude long air gap lightning flashover. The method comprises the following steps: s1, obtaining a continuous pilot initial voltage value by referring to an air density correction method of Rizk; s2, judging whether the pilot starts or not according to the magnitude of the pilot starting voltage and the applied voltage, the ratio of the applied voltage to the gap length and the magnitude of the pilot development minimum average field strength correction value; s3, after the pilot starts, calculating the length of the pilot development by utilizing the integral of a pilot development speed formula on time; s4, the size of the gap length and the size of the end length are compared to judge whether flashover occurs. The method can fully take the influence of the altitude height on the long air gap lightning flashover characteristic into consideration, so that the calculation of the lightning withstand level of the insulator and the air gap lightning stroke in the high altitude area and the evaluation of the lightning trip-out rate are more accurate and reliable.

Description

A kind of method of discrimination of High aititude long air gap lightning stroke flashover

Technical field

The present invention relates to transmission line of electricity lightning protection field, particularly a kind of method of discrimination of High aititude long air gap lightning stroke flashover.

Background technology

Lightning stroke trip is the main cause causing transmission line malfunction, and the accurate Calculation of lightning surge and the correct assessment of lightning stroke trip, for the Lightning performance improving transmission line of electricity, ensure that the safe and stable operation of electric system is significant.The lightning impulse flashover property of electric transmission line isolator and tower head clearance is the basis of computational scheme lightning surge and lightning outage rate, therefore, choose accurate flashover criterion for accurate computing electric power line superpotential, correctly assess tripping rate with lightning strike, ensure that the safe and stable operation of electric system is significant.

At present, the insulator adopted when computational scheme lightning withstand level both at home and abroad or the flashover criterion of clearance comprise U _50%method, volt-second characteristic method, integral method and guide's law of development etc.The wherein process that develops based on guide of first inducing defecation by enema and suppository, flashover is judged whether by leader length, comparatively additive method applicability is wider, can be judged to insulate whether flashover more accurately, but the first inducing defecation by enema and suppository model overwhelming majority used at present is low altitude area acquisition, and sea level elevation directly affects the flashover property of insulator and clearance, the pilot model being applicable to high altitude localities needs to carry out more deep research.

Summary of the invention

In order to overcome the shortcoming of prior art existence with not enough, the invention provides a kind of method of discrimination of High aititude long air gap lightning stroke flashover.

The present invention adopts following technical scheme:

A method of discrimination for High aititude long air gap lightning stroke flashover, comprises the steps:

S1, according to the air density correction method of Rizk, obtains continuous leader starting potential formula, and calculates continuous leader starting voltage value according to actual condition;

S2 compares the size of the magnitude of voltage be applied on long air gap and the continuous leader starting voltage value of trying to achieve, and be applied to the size that average field-strength that the voltage on long air gap produces in gap and guide develop minimum average field-strength modified value, judge that whether guide is initial;

After S3 guide is initial, utilizes the integration of guide's speed of development formula to the time to try to achieve the length of guide's development, and try to achieve the length in surplus air gap, the length in described surplus air gap is the difference of the length that the length of long air gap and guide are developed;

S4 compares surplus air gap length and end and to jump the size of length, judges whether flashover, when surplus air gap length be less than end jump length time, then think gap breakdown, i.e. insulator arc-over.

Described guide's speed of development and length formula are specially:

$\frac{\mathrm{dl}}{\mathrm{dt}}=k(u\left(t\right)-E_{l}l)(\frac{u\left(\text{t}\right)-E_{l}l}{d_g-l}-\mathrm{\δ}{E}_0)$

$l=\underset{0}{\overset{t}{\∫}}k(u\left(t\right)-E_{l}l)(\frac{u\left(t\right)-E_{l}l}{d_g-l}-\mathrm{\δ}{E}_0)\mathrm{dt}$

In formula, E _lrepresent leader channel average field-strength, the lightning impulse voltage that dummy is added in long air gap two ends, high altitude localities is that u (t), δ represent air relative density, E ₀for the minimum average field-strength of guide's development, l represents the length that guide is developed, and t represents the time, k and E ₀it is coefficient;

Described k and E ₀obtain in accordance with the following steps:

S3.1 does the lightning impulse test of positive polarity in altitude test base, obtain the raw data of insulator volt-second characteristic, and carry out matching by the volt-second characteristic described function form that IEC recommends, judge to obtain optimum matching trial curve by goodness of fit computing formula;

S3.2 estimates k and E according to the lightning stroke flashover photo of shooting and guide in the temporal development speed in certain moment and length formula ₀interval;

The formula that S3.3 is calculated from guide's speed of development, k and E that each group is fixing ₀calculate a voltage-time curve, based on k and E ₀on the impact of voltage-time curve, in conjunction with enumerative technique, in the scope described in S3.2, adjust k and E ₀numerical value, make calculated curve close to trial curve;

S3.4 utilizes the goodness of fit to evaluate the degree of closeness of calculated curve and trial curve, k and E when fit value is maximum ₀be the coefficient of required guide's speed of development formula.

Lightning impulse voltage value u (t) at long air gap two ends, high altitude localities and long air gap length d that average field-strength that the voltage on long air gap produces in gap equals to apply is applied in described S2 _gratio; The minimum average field-strength modified value of described guide's development is that air relative density δ and guide develop minimum average field-strength E ₀product.

Described goodness of fit computing formula is:

$R^2=1-[\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(y_i-{\hat{y}}_i)}^2/\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(y_i-\stackrel{\‾}{y})}^2]$

Wherein, R ²for the goodness of fit, y _ifor raw data, for fitting data; represent the mean value of raw data, n represents test number (TN).

Described guide in the temporal development speed in certain moment and length formula is:

$\left\{\begin{array}{c}\stackrel{\‾}{v_1}=k(u\left(\stackrel{\‾}{t_1}\right)-d_{l1}{E}_l)(\frac{u\left(\stackrel{\‾}{t_1}\right)-l_1{E}_l}{d_g-d_{l2}}-\mathrm{\δ}{E}_0)\\ \stackrel{\‾}{v_2}=k(u\left(\stackrel{\‾}{u_2}\right)-d_{l2}{E}_l)(\frac{u\left(\stackrel{\‾}{t_2}\right)-l_2{E}_l}{d_g-d_{l2}}-\mathrm{\δ}{E}_0)\end{array}\right.$

In formula: calculating formula be:

$\left\{\begin{array}{c}\stackrel{\‾}{v_i}=\frac{l_{i+1}-l_i}{t_{i+1}-t_i}\\ \stackrel{\‾}{t_i}=\frac{t_{i+1}+t_i}{2}\\ \stackrel{\‾}{l_i}=\frac{l_{i+1}+l_i}{2}\end{array}\right.$

Wherein, represent guide's speed of development and the leader length in this moment in i-th moment and this moment respectively, l represents the length of guide.

In described S4, the last length that jumps is 1/3rd of long air gap length.

In described S2, guide is initial must meet following two conditions simultaneously:

(1) magnitude of voltage be applied on long air gap is greater than the continuous leader starting voltage value of trying to achieve;

(2) be applied to the average field-strength that the voltage on long air gap produces in gap and be greater than the modified value that guide develops minimum average field-strength.

Described continuous leader starting potential

U _lccomputing formula is:

$U_{\mathrm{lc}}=\frac{\frac{V_0}{E_{\mathrm{cr}}}\×E_a}{1+\frac{V_0}{E_{\mathrm{cr}}}\×\frac{1}{\mathrm{\δ}{d}_g}}$

In formula: E _afor average streamer field intensity, E _crrepresent critical field strength, d _grepresent gap length, δ represents air relative density, q _lrepresent the line density that first guide space ionizes, ε ₀represent the specific inductive capacity in vacuum.

Required k and E ₀value is applicable to the positive polarity lightning impulse flashover of High aititude I string and V insulator string.

Beneficial effect of the present invention:

The High aititude long gap lightning stroke flashover method of discrimination provided in the present invention considers the difference of the average voltage breakdown that the atmospheric density difference under different air pressure causes, accurately can calculate the superpotential of power transmission line in high altitude region and correctly assess tripping rate with lightning strike, and be applicable to the positive polarity lightning current impulse flashover differentiating random waveform, directive function can be played to the lightning protection of high altitude localities and design.

Accompanying drawing explanation

Fig. 1 is workflow diagram of the present invention.

Embodiment

Below in conjunction with embodiment and accompanying drawing, the present invention is described in further detail, but embodiments of the present invention are not limited thereto.

Embodiment

As shown in Figure 1, a kind of method of discrimination of High aititude long air gap lightning stroke flashover, comprises the steps:

S1, according to the air density correction method of Rizk, obtains continuous leader starting potential formula, and calculates continuous leader starting voltage value according to actual condition;

Described continuous leader starting voltage value U _lcformula be:

$U_{\mathrm{lc}}=\frac{\frac{V_0}{E_{\mathrm{cr}}}\×E_a}{1+\frac{V_0}{E_{\mathrm{cr}}}\×\frac{1}{\mathrm{\δ}{d}_g}}$

Wherein, E _afor average streamer field intensity, E _crrepresent critical field strength, d _grepresent gap length, l represents the length that guide is developed, d _frepresent surplus air gap length, δ represents air relative density (relevant to sea level elevation), q _lrepresent the line density that first guide space ionizes, ε ₀represent the specific inductive capacity in vacuum.

Positive polarity thunder and lightning streamer average field-strength is 500kV/m, obtains E _cr/ V ₀=0.0516, bring U into _lcthe computing formula relational expression that obtains continuous leader starting potential and relative air density and gap length be:

$U_{\mathrm{lc}}=\frac{9690}{1+\frac{19.38}{\mathrm{\δ}{d}_g}}$

Can obtain gap length by computing formula is above 7.1m, 2100m height above sea level place, and when air relative density is 0.7848, continuous leader starting potential is 2164kV.

S2 compares the size of the magnitude of voltage be applied on long air gap and the continuous leader starting voltage value of trying to achieve, and be applied to the size that average field-strength that the voltage on long air gap produces in gap and guide develop minimum average field-strength modified value, judge that whether guide is initial;

Be applied in described S2 that average field-strength that the voltage on long air gap produces in gap equals to apply at lightning impulse voltage value u (t) at long air gap two ends, high altitude localities and the gap length d of air _gratio; It is that air relative density δ and guide develop minimum average field-strength E that described guide develops minimum average field-strength modified value ₀product.

Guide is initial must meet following two conditions simultaneously:

(1) magnitude of voltage be applied on long air gap is greater than the continuous leader starting voltage value of trying to achieve;

(2) be applied to average field-strength that the voltage on long air gap produces in gap to be greater than guide and to develop minimum average field-strength modified value.

2164kV is greater than when being applied to the instantaneous voltage on insulator or long air gap in the present embodiment, and time, guide is initial;

After S3 guide is initial, utilizes the integration of guide's speed of development formula to the time to try to achieve the length of guide's development, and try to achieve the length in surplus air gap, the length in described surplus air gap is the difference of the length that the length of long air gap and guide are developed;

Described guide's speed of development and guide are developed length formula and are specially:

$\frac{\mathrm{dl}}{\mathrm{dt}}=k(u\left(t\right)-E_{l}l)(\frac{u\left(\text{t}\right)-E_{l}l}{d_g-l}-\mathrm{\δ}{E}_0)$

$l=\underset{0}{\overset{t}{\∫}}k(u\left(t\right)-E_{l}l)(\frac{u\left(t\right)-E_{l}l}{d_g-l}-\mathrm{\δ}{E}_0)\mathrm{dt}$

Wherein, E _lrepresent leader channel average field-strength, the present embodiment is that 50kV/m, l represent the length that guide is developed, t represents the time, and δ represents air relative density, is 0.7848 at 2100m sea level elevation place, u (t) is the lightning impulse voltage that dummy is added in long air gap two ends, high altitude localities, E ₀for the minimum average field-strength of guide's development, k is coefficient.

Described k and E ₀obtain in accordance with the following steps:

S3.1 does the lightning impulse test of positive polarity in altitude test base, obtain the raw data of insulator volt-second characteristic, and carry out matching by the volt-second characteristic described function form that IEC recommends, judge to obtain optimum matching trial curve by goodness of fit computing formula, described raw data comprises the flashover moment of flashover voltage and correspondence.

Goodness of fit computing formula is:

$R^2=1-[\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(y_i-{\hat{y}}_i)}^2/\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(y_i-\stackrel{\‾}{y})}^2]$

Wherein, R ²for the goodness of fit, y _ifor raw data, for fitting data; represent the mean value of raw data;

S3.2 estimates k and E according to the lightning stroke flashover photo of shooting and guide in the temporal development speed in certain moment and length formula ₀interval;

Described guide in the temporal development speed in certain moment and length formula is:

$\left\{\begin{array}{c}\stackrel{\‾}{v_1}=k(u\left(\stackrel{\‾}{t_1}\right)-l_1{E}_l)(\frac{u\left(\stackrel{\‾}{t_1}\right)-l_1{E}_l}{d_g-l_1}-\mathrm{\δ}{E}_0)\\ \stackrel{\‾}{v_2}=k(u\left(\stackrel{\‾}{t_2}\right)-l_2{E}_l)(\frac{u\left(\stackrel{\‾}{t_2}\right)-l_2{E}_l}{d_g-l_2}-\mathrm{\δ}{E}_0)\end{array}\right.$

In formula: calculating formula be:

$\left\{\begin{array}{c}\stackrel{\‾}{v_i}=\frac{l_{i+1}-l_i}{t_{i+1}-t_i}\\ \stackrel{\‾}{t_i}=\frac{t_{i+1}+t_i}{2}\\ \stackrel{\‾}{l_i}=\frac{l_{i+1}+l_i}{2}\end{array}\right.$

Wherein, represent guide's speed of development and the leader length in this moment in i-th moment and this moment respectively, according to the photo taken in the positive polarity lightning impulse flashover test of the Kunming extra-high voltage Experimental Base of 2100m height above sea level in this method, estimate k and E ₀interval be respectively [0.3 × 10 ^-6, 0.6 × 10 ^-6] and [300,700];

The formula that S3.3 is calculated from guide's speed of development, k and E that each group is fixing ₀calculate a voltage-time curve, based on k and E ₀on the impact of voltage-time curve, in conjunction with enumerative technique, in the scope described in S3.2, adjust k and E ₀numerical value, make calculated curve close to trial curve;

The step-length of enumerating of the coefficient k in the present embodiment gets 0.01 × 10 ^-6, E ₀step-length of enumerating get 5.

S3.4 calculates the goodness of fit between curve and trial curve drawn by model according to goodness of fit computing formula, k and E when fit value is maximum ₀be required leader development model coefficient.The coefficient k of trying to achieve and E ₀optimum solution and corresponding fit value as following table:

Under obtaining the positive polarity lightning impulse of 2100m Altitude Regions thus, I type and V-type insulator guide speed of development formula are respectively:

$\frac{\mathrm{dl}}{\mathrm{dt}}=0.73(u\left(t\right)-50l)(\frac{u\left(t\right)-50l}{d_g-l}-0.7848\×495)$ I goes here and there

$\frac{\mathrm{dl}}{\mathrm{dt}}=0.53(u\left(t\right)-50l)(\frac{u\left(t\right)-50l}{d_g-l}-0.7848\×440)$ V goes here and there

By guide's speed of development formula above, the length l of guide's development in any time I insulator string and V insulator string lightning impulse can be obtained.

S4 compares surplus air gap length and end and to jump the size of length, judges whether flashover, when surplus air gap length be less than end jump length time, then think that gap breakdown, i.e. insulator arc-over, the described end length that jumps is 1/3rd of long air gap length.

The first inducing defecation by enema and suppository flashover criterion that the method is recommended based on CIGRE, has taken into full account the impact of sea level elevation on flashover property, is applicable to differentiate the insulator of high altitude localities and the positive polarity lightning impulse flashover of clearance.

Above-described embodiment is the present invention's preferably embodiment; but embodiments of the present invention are not limited by the examples; change, the modification done under other any does not deviate from Spirit Essence of the present invention and principle, substitute, combine, simplify; all should be the substitute mode of equivalence, be included within protection scope of the present invention.

Claims (9)

1. a method of discrimination for High aititude long air gap lightning stroke flashover, is characterized in that, comprises the steps:

S1, according to the air density correction method of Rizk, obtains continuous leader starting potential formula, and calculates continuous leader starting voltage value according to actual condition;

S2 compares the size of the magnitude of voltage be applied on long air gap and the continuous leader starting voltage value of trying to achieve, and be applied to the size that average field-strength that the voltage on long air gap produces in gap and guide develop minimum average field-strength modified value, judge that whether guide is initial;

After S3 guide is initial, utilizes the integration of guide's speed of development formula to the time to try to achieve the length of guide's development, and try to achieve the length in surplus air gap, the length in described surplus air gap is the difference of the length that the length of long air gap and guide are developed;

S4 compares surplus air gap length and end and to jump the size of length, judges whether flashover, when surplus air gap length be less than end jump length time, then think gap breakdown, i.e. insulator arc-over.

2. the method for discrimination of a kind of High aititude long air gap lightning stroke flashover according to claim 1, it is characterized in that, described guide's speed of development and length formula are specially:

$\frac{\mathrm{dl}}{\mathrm{dt}}=k(u\left(t\right)-E_{l}l)(\frac{u\left(t\right)-E_{l}l}{d_g-l}-{\mathrm{\δE}}_0)$

$l=\underset{0}{\overset{t}{\∫}}k(u\left(t\right)-E_{l}l)(\frac{u\left(t\right)-E_{l}l}{d_g-l}-{\mathrm{\δE}}_0)\mathrm{dt}$

In formula, E _lrepresent leader channel average field-strength, the lightning impulse voltage that dummy is added in long air gap two ends, high altitude localities is that u (t), δ represent air relative density, E ₀for the minimum average field-strength of guide's development, l represents the length that guide is developed, and t represents the time, k and E ₀it is coefficient;

Described k and E ₀obtain in accordance with the following steps:

S3.1 does the lightning impulse test of positive polarity in altitude test base, obtain the raw data of insulator volt-second characteristic, and carry out matching by the volt-second characteristic described function form that IEC recommends, judge to obtain optimum matching trial curve by goodness of fit computing formula;

S3.2 estimates k and E according to the lightning stroke flashover photo of shooting and guide in the temporal development speed in certain moment and length formula ₀interval;

The formula that S3.3 is calculated from guide's speed of development, k and E that each group is fixing ₀calculate a voltage-time curve, based on k and E ₀on the impact of voltage-time curve, in conjunction with enumerative technique, in the scope described in S3.2, adjust k and E ₀numerical value, make calculated curve close to trial curve;

S3.4 utilizes the goodness of fit to evaluate the degree of closeness of calculated curve and trial curve, k and E when fit value is maximum ₀be the coefficient of required guide's speed of development formula.

3. method of discrimination according to claim 1, it is characterized in that, in described S2, be applied to lightning impulse voltage value u (t) at long air gap two ends, high altitude localities and long air gap length d that average field-strength that the voltage on long air gap produces in gap equals to apply _gratio; The minimum average field-strength modified value of described guide's development is that air relative density δ and guide develop minimum average field-strength E ₀product.

4. method of discrimination according to claim 2, is characterized in that, described goodness of fit computing formula is:

$R^2=1-[\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(y_i-{\hat{y}}_i)}^2/\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(y_i-\stackrel{\‾}{y})}^2]$

Wherein, R ²for the goodness of fit, y _ifor raw data, for fitting data; represent the mean value of raw data, n represents overall test number of times.

5. method of discrimination according to claim 2, is characterized in that, described guide in the temporal development speed in certain moment and length formula is:

$\left\{\begin{array}{c}\stackrel{\‾}{v_1}=k(u\left(\stackrel{\‾}{t_1}\right)-d_{l1}{E}_l)(\frac{u\left(\stackrel{\‾}{t_1}\right)-l_1{E}_l}{d_g-d_{l2}}-{\mathrm{\δE}}_0)\\ \stackrel{\‾}{v_2}=k(u\left(\stackrel{\‾}{t_2}\right)-d_{l2}{E}_l)(\frac{u\left(\stackrel{\‾}{t_2}\right)-l_2{E}_l}{d_g-d_{l2}}-{\mathrm{\δE}}_0)\end{array}\right.$

In formula: calculating formula be:

$\left\{\begin{array}{c}\stackrel{\‾}{v_i}=\frac{l_{i+1}-l_i}{t_{i+1}-t_i}\\ \stackrel{\‾}{t_i}=\frac{t_{i+1}+t_i}{2}\\ \stackrel{\‾}{l_i}=\frac{l_{i+1}+l_i}{2}\end{array}\right.$

Wherein, represent guide's speed of development and the leader length in this moment in i-th moment and this moment respectively, l represents the length of guide.

6. method of discrimination according to claim 1, is characterized in that, in described S4, the last length that jumps is 1/3rd of long air gap length.

7. method of discrimination according to claim 1, is characterized in that, in described S2, guide is initial must meet following two conditions simultaneously:

(1) magnitude of voltage be applied on long air gap is greater than the continuous leader starting voltage value of trying to achieve;

(2) be applied to the average field-strength that the voltage on long air gap produces in gap and be greater than the modified value that guide develops minimum average field-strength.

8. method of discrimination according to claim 1, is characterized in that, described continuous leader starting potential U _lccomputing formula is:

$U_{\mathrm{lc}}=\frac{\frac{V_0}{E_{\mathrm{cr}}}\×E_a}{1+\frac{V_0}{E_{\mathrm{cr}}}\×\frac{1}{{\mathrm{\δd}}_g}}$

In formula: E _afor average streamer field intensity, E _crrepresent critical field strength, d _grepresent gap length, δ represents air relative density, q _lrepresent the line density that first guide space ionizes, ε ₀represent the specific inductive capacity in vacuum.

9. method according to claim 2, is characterized in that, required k and E ₀value is applicable to the positive polarity lightning impulse flashover of High aititude I string and V insulator string.