CN104281885B - A kind of non-lightning stroke flashover risk index Forecasting Methodology of power distribution network arrester - Google Patents

A kind of non-lightning stroke flashover risk index Forecasting Methodology of power distribution network arrester Download PDF

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CN104281885B
CN104281885B CN201410472758.5A CN201410472758A CN104281885B CN 104281885 B CN104281885 B CN 104281885B CN 201410472758 A CN201410472758 A CN 201410472758A CN 104281885 B CN104281885 B CN 104281885B
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msub
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mtd
tau
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CN104281885A (en
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胡玉涛
李勇
韩利鹏
熊超
安芷瑶
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State Grid Corp of China SGCC
State Grid Liaoning Electric Power Co Ltd
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State Grid Corp of China SGCC
State Grid Liaoning Electric Power Co Ltd
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q50/00—Systems or methods specially adapted for specific business sectors, e.g. utilities or tourism
    • G06Q50/06—Electricity, gas or water supply

Abstract

The invention belongs to power transmission and distribution monitoring technical field, more particularly to a kind of non-lightning stroke flashover risk index Forecasting Methodology of power distribution network arrester.Including：Step 1：Establish the time series of the non-lightning stroke flashover risk index Evolution System of arrester；Step 2：Reconstitution time sequence（1）The phase space of representative filthy sedimentation index evolution Kind of Nonlinear Dynamical System；Step 3：Calculate the phase point of subsequent time in phase space；Step 4：Calculate non-lightning stroke flashover risk index predicted value.Present invention prediction is accurate, and the non-lightning stroke flashover risk index prediction model of power distribution network arrester of practical implementation is adapted to by establishing, and have effectively achieved the accurate prediction to the non-lightning stroke flashover risk index of arrester.To the severe changeable area of the power distribution network nature meteorological condition such as coastal, riverine, it is possible to achieve complete reliable forecast system, is not influenced by the adverse circumstances.

Description

A kind of non-lightning stroke flashover risk index Forecasting Methodology of power distribution network arrester
Technical field
The invention belongs to power transmission and distribution monitoring technical field, more particularly to a kind of non-lightning stroke flashover risk of power distribution network arrester refers to Number Forecasting Methodology.
Background technology
In the process of running, due to lightning arrester insulation surface contamination, internal valve block failure etc. can cause power distribution network arrester Arrester flashover breakdown in the case of non-lightning stroke discharges, since arrester should be open-circuit condition in power grid normal operation, once Generation flashover discharges, and may result in electric network fault, and at present, the appraisal procedure that non-lightning stroke flashover occurs for arrester is mainly logical Cross and statistical analysis is carried out to non-lightning stroke flashover, summarize the research of its rule etc..
Increasingly complicated for power system operating mode, the challenge of coastal and more haze environment, the non-lightning stroke flashover of arrester is tight Ghost image rings the safe operation of power grid, it is necessary to carry out the Basic Problems research of its occurrence risk prediction in a deep going way.
The content of the invention
In view of the deficiencies of the prior art, the present invention provides a kind of non-lightning stroke flashover risk index prediction side of power distribution network arrester Method, the non-lightning stroke flashover risk index prediction model of power distribution network arrester of practical implementation is adapted to by establishing, with effectively Solve the accurate prediction to the non-lightning stroke flashover risk index of arrester.
The step of technical scheme is realized is as follows：
A kind of non-lightning stroke flashover risk index Forecasting Methodology of power distribution network arrester, comprises the following steps：
Step 1：Establish the time series of the non-lightning stroke flashover risk index Evolution System of arrester：
Non- lightning stroke flashover number, rainfall, humidity, wind speed are measured in Fixed Time Interval, by non-lightning stroke flashover The ratio of number and arrester whole discharge time is as non-lightning stroke flashover risk index, i.e.,：
Then, in a series of moment t1,t2,...,tn(n is natural number, n=1,2 ...) obtains non-lightning stroke flashover risk and refers to Number, temperature, humidity, wind speed time series：
Step 2：The phase of filthy sedimentation index evolution Kind of Nonlinear Dynamical System representated by reconstitution time sequence (1) is empty Between FY：
PFiFor the phase point in the time series Phase Space of reconstruct, i=1,2 ..., N, τjtAnd mjtTime delay and Embedded dimensions for t time series of jth, the Embedded dimensions m=m of phase space reconstruction1+m2+...+ m5；
Delay time TjtSelection use mutual information method, on delay time TjtMutual information function be：
Take mutual information function INTER(τjt) τ when first appearing minimumjtAs the time delay of phase space reconfiguration, wherein PROB(fvjt,i) it is in the i-th moment fvjt,iThe probability of appearance,For in the i-th moment fvjt,iWithTogether When the probability that occurs, i=1,2 ..., N；
Embedded dimensions mjtBy differential correlation function：
MjtM during secondary zero crossingjtValue is definite, MjtFor given Accuracy Controlling Parameter, ε is phase point set in advance Between Euclidean distanceUpper limit value, H () is Heaviside sign functions：
Step 3：Calculate the phase point of subsequent time in phase space：
In phase space FYMiddle calculating establishes weight function according to known N number of phase point：
Wherein：I=1,2 ..., N, i-th of phase point to phase space central point and arrive PFcentrDistance be di=‖ PFi- PFcentr‖, dminIt is diIn minimum value.The linear fit function for establishing the unknown phase point of subsequent time is：
PFN+1=ae+bPFN (6)
Wherein, i=1,2 ..., N, e=(1,1 ..., 1)T, a, b are fitting parameter, application weighting least square method：
By FunLocal derviation is asked to have parameter a, b：
Fitting parameter a, b can be obtained by solving equation group, then can calculate next unknown phase point prediction value is：
PFN+1=a+bPFN (9)
Step 4：Calculate non-lightning stroke flashover risk index predicted value：
The PF that will be calculated in step 3N+1As the N+1 phase point in phase space (2), then phase space newly can be obtained For：
Make τjt=1 (jt=1,2 ..., 5), can obtain fv therein1,N+1As non-lightning stroke flashover risk index predicted value.
Advantages of the present invention and have the beneficial effect that：
(1), prediction is accurate, and the non-lightning stroke flashover risk index of power distribution network arrester of practical implementation is adapted to by establishing Prediction model, have effectively achieved the accurate prediction to the non-lightning stroke flashover risk index of arrester.
(2), to the severe changeable area of the power distribution network nature meteorological condition such as coastal, riverine, it is possible to achieve complete reliable Forecast system, is not influenced by the adverse circumstances.
Brief description of the drawings：
The non-lightning stroke flashover risk index prediction flow charts of Fig. 1
Embodiment：
Embodiment 1：
The present invention is described in detail with reference to embodiment and attached drawing.
As shown in Figure 1, a kind of filthy sedimentation index forecasting method of power distribution network overhead transmission line, comprises the following steps：
Step 1：Establish the time series of filthy sedimentation index Evolution System：
In the present embodiment, non-lightning stroke flashover number, rainfall, humidity, wind speed are measured within 40 equally spaced periods, It is non-lightning stroke flashover risk index by the non-lightning stroke flashover number conversion that each moment measures：
When then obtaining one 5 dimension being made of non-lightning stroke flashover risk index, rainfall, humidity, the measurement data of wind speed Between sequence：
Step 2：The phase of filthy sedimentation index evolution Kind of Nonlinear Dynamical System representated by reconstitution time sequence (11) is empty Between：
By：
And：
Try to achieve delay time Tjt=3 and Embedded dimensions mjt=6 pairs of time serieses progress phase space reconfigurations, jt=1,2 ..., 5, then it can obtain phase space：
Step 3：Calculate the phase point of subsequent time in phase space：
Choose PF7For phase space central point, each phase point and PF are calculated6Between di=‖ PFi-PF6‖, by：
Fitting parameter a=12.98, b=6.47 can be solved, then can calculate the next unknown phase point prediction value of phase space is：
PFN+1=1.298+6.471 × PFN (13)
Step 4：Calculate filthy sedimentation exponential forecasting value：
The PZ that formula (13) is tried to achieveN+1Bring phase space into, can obtain：
Take τjt=2 (jt=1,2 ..., 5), the then fv isolated1,N+1, it is non-lightning stroke flashover risk index predicted value.

Claims (1)

1. a kind of non-lightning stroke flashover risk index Forecasting Methodology of power distribution network arrester, it is characterised in that comprise the following steps：
Step 1：Establish the time series of the non-lightning stroke flashover risk index Evolution System of arrester：
Non- lightning stroke flashover number, rainfall, humidity, wind speed are measured in Fixed Time Interval, by non-lightning stroke flashover number With the ratio of arrester whole discharge time as non-lightning stroke flashover risk index, i.e.,：
Then, in a series of moment t1,t2,...,tn, n is natural number, n=1,2 ..., obtain non-lightning stroke flashover risk index, temperature Degree, humidity, wind speed time series：
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Step 2：The phase space F of filthy sedimentation index evolution Kind of Nonlinear Dynamical System representated by reconstitution time sequence (1)Y：
<mrow> <msub> <mi>F</mi> <mi>Y</mi> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>PF</mi> <mn>1</mn> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>fv</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>fv</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msub> <mi>fv</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>m</mi> <mn>1</mn> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <msub> <mi>&amp;tau;</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msub> <mi>fv</mi> <mrow> <mi>j</mi> <mi>t</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>fv</mi> <mrow> <mi>j</mi> <mi>t</mi> <mo>,</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> </mrow> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msub> <mi>fv</mi> <mrow> <mi>j</mi> <mi>t</mi> <mo>,</mo> <mn>1</mn> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>m</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <msub> <mi>&amp;tau;</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>...</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>PF</mi> <mi>i</mi> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>fv</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>fv</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>i</mi> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msub> <mi>fv</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>i</mi> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>m</mi> <mn>1</mn> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <msub> <mi>&amp;tau;</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msub> <mi>fv</mi> <mrow> <mi>j</mi> <mi>t</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>fv</mi> <mrow> <mi>j</mi> <mi>t</mi> <mo>,</mo> <mi>i</mi> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> </mrow> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msub> <mi>fv</mi> <mrow> <mi>j</mi> <mi>t</mi> <mo>,</mo> <mi>i</mi> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>m</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <msub> <mi>&amp;tau;</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>...</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>PF</mi> <mi>N</mi> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>fv</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>fv</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msub> <mi>fv</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>m</mi> <mn>1</mn> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <msub> <mi>&amp;tau;</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msub> <mi>fv</mi> <mrow> <mi>j</mi> <mi>t</mi> <mo>,</mo> <mi>N</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>fv</mi> <mrow> <mi>j</mi> <mi>t</mi> <mo>,</mo> <mi>N</mi> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> </mrow> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msub> <mi>fv</mi> <mrow> <mi>j</mi> <mi>t</mi> <mo>,</mo> <mi>N</mi> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>m</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <msub> <mi>&amp;tau;</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
PFiFor the phase point in the time series Phase Space of reconstruct, i=1,2 ..., N,τjtWith mjtTime delay and Embedded dimensions for t time series of jth, the Embedded dimensions m=m of phase space reconstruction1+m2+...+m5；
Delay time TjtSelection use mutual information method, on delay time TjtMutual information function be：
<mrow> <msub> <mi>I</mi> <mrow> <mi>N</mi> <mi>T</mi> <mi>E</mi> <mi>R</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;tau;</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>&amp;RightArrow;</mo> <mi>N</mi> </mrow> </munder> <msub> <mi>P</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>B</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>fv</mi> <mrow> <mi>j</mi> <mi>t</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>fv</mi> <mrow> <mi>j</mi> <mi>t</mi> <mo>,</mo> <mi>i</mi> <mo>+</mo> <msub> <mi>&amp;tau;</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mi>l</mi> <mi>n</mi> <mfrac> <mrow> <msub> <mi>P</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>B</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>fv</mi> <mrow> <mi>j</mi> <mi>t</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>fv</mi> <mrow> <mi>j</mi> <mi>t</mi> <mo>,</mo> <mi>i</mi> <mo>+</mo> <msub> <mi>&amp;tau;</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>P</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>B</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>fv</mi> <mrow> <mi>j</mi> <mi>t</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>)</mo> </mrow> <msub> <mi>P</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>B</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>fv</mi> <mrow> <mi>j</mi> <mi>t</mi> <mo>,</mo> <mi>i</mi> <mo>+</mo> <msub> <mi>&amp;tau;</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
Take mutual information function INTER(τjt) τ when first appearing minimumjtAs the time delay of phase space reconfiguration, wherein PROB (fvjt,i) it is in the i-th moment fvjt,iThe probability of appearance,For in the i-th moment fvjt,iWithAt the same time The probability of appearance, i=1,2 ..., N；
Embedded dimensions mjtBy differential correlation function：
<mrow> <msub> <mi>D</mi> <mrow> <mi>F</mi> <mi>C</mi> <mi>L</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>m</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>d</mi> <mrow> <mo>(</mo> <mi>l</mi> <mi>n</mi> <mo>(</mo> <mrow> <mfrac> <mn>1</mn> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mo>(</mo> <mrow> <msub> <mi>m</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> <msub> <mi>&amp;tau;</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> <mo>)</mo> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mo>(</mo> <mrow> <msub> <mi>m</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> <msub> <mi>&amp;tau;</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mi>t</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mi>i</mi> <mo>&amp;NotEqual;</mo> <mi>j</mi> <mi>t</mi> </mrow> <mrow> <mi>n</mi> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>m</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <msub> <mi>&amp;tau;</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> </mrow> </munderover> <mi>H</mi> <mrow> <mo>(</mo> <mrow> <mi>&amp;epsiv;</mi> <mo>-</mo> <mo>|</mo> <mo>|</mo> <msub> <mi>fv</mi> <mrow> <mi>j</mi> <mi>t</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>fv</mi> <mrow> <mi>j</mi> <mi>t</mi> <mo>,</mo> <mi>i</mi> <mo>+</mo> <msub> <mi>&amp;tau;</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> </mrow> </msub> <mo>|</mo> <mo>|</mo> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> <mo>/</mo> <mi>l</mi> <mi>n</mi> <mi>&amp;epsiv;</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>dm</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
MjtM during secondary zero crossingjtValue is definite, MjtFor given Accuracy Controlling Parameter, ε Europe between phase point set in advance Formula distanceUpper limit value, H () is Heaviside sign functions：
<mrow> <mi>H</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mn>0</mn> <mo>,</mo> <mi>x</mi> <mo>&lt;</mo> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0.5</mn> <mo>,</mo> <mi>x</mi> <mo>=</mo> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> <mo>,</mo> <mi>x</mi> <mo>&gt;</mo> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> </mrow>
Step 3：Calculate the phase point of subsequent time in phase space：
In phase space FYMiddle calculating establishes weight function according to known N number of phase point：
<mrow> <msub> <mi>TH</mi> <mrow> <mi>D</mi> <mi>I</mi> <mi>S</mi> <mi>T</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>PF</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>d</mi> <mi>min</mi> </msub> <mo>)</mo> </mrow> </mrow> </msup> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>d</mi> <mi>min</mi> </msub> <mo>)</mo> </mrow> </mrow> </msup> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
Wherein：I=1,2 ..., N, i-th of phase point to phase space central point and arrive PFcentrDistance be di=‖ PFi- PFcentr‖, dminIt is diIn minimum value, the linear fit function for establishing the unknown phase point of subsequent time is：
PFN+1=ae+bPFN (6)
Wherein, i=1,2 ..., N, e=(1,1 ..., 1)T, a, b are fitting parameter, application weighting least square method：
<mrow> <msub> <mi>F</mi> <mrow> <mi>u</mi> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mi>m</mi> <mi>i</mi> <mi>n</mi> <mo>{</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>TH</mi> <mrow> <mi>D</mi> <mi>I</mi> <mi>S</mi> <mi>T</mi> </mrow> </msub> <msup> <mrow> <mo>(</mo> <msub> <mi>PF</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <mi>a</mi> <mo>-</mo> <mi>b</mi> <mo>&amp;CenterDot;</mo> <msub> <mi>PF</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
By FunLocal derviation is asked to have parameter a, b：
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>TH</mi> <mrow> <mi>D</mi> <mi>I</mi> <mi>S</mi> <mi>T</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>PF</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <mi>a</mi> <mo>-</mo> <mi>b</mi> <mo>&amp;CenterDot;</mo> <msub> <mi>PF</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>TH</mi> <mrow> <mi>D</mi> <mi>I</mi> <mi>S</mi> <mi>T</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>PF</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <mi>a</mi> <mo>-</mo> <mi>b</mi> <mo>&amp;CenterDot;</mo> <msub> <mi>PF</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>PF</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
Fitting parameter a, b can be obtained by solving equation group, then can calculate next unknown phase point prediction value is：
PFN+1=a+bPFN (9)
Step 4：Calculate non-lightning stroke flashover risk index predicted value：
The PF that will be calculated in step 3N+1As the N+1 phase point in phase space, then the phase space that can be obtained newly is：
<mrow> <msubsup> <mi>F</mi> <mi>Y</mi> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>PF</mi> <mn>1</mn> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>fv</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>fv</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msub> <mi>fv</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>m</mi> <mn>1</mn> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <msub> <mi>&amp;tau;</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msub> <mi>fv</mi> <mrow> <mi>j</mi> <mi>t</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>fv</mi> <mrow> <mi>j</mi> <mi>t</mi> <mo>,</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> </mrow> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msub> <mi>fv</mi> <mrow> <mi>j</mi> <mi>t</mi> <mo>,</mo> <mn>1</mn> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>m</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <msub> <mi>&amp;tau;</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>...</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>PF</mi> <mi>i</mi> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>fv</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>fv</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>i</mi> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msub> <mi>fv</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>i</mi> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>m</mi> <mn>1</mn> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <msub> <mi>&amp;tau;</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msub> <mi>fv</mi> <mrow> <mi>j</mi> <mi>t</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>fv</mi> <mrow> <mi>j</mi> <mi>t</mi> <mo>,</mo> <mi>i</mi> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> </mrow> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msub> <mi>fv</mi> <mrow> <mi>j</mi> <mi>t</mi> <mo>,</mo> <mi>i</mi> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>m</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <msub> <mi>&amp;tau;</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>...</mn> </mtd> </mtr> <mtr> <mtd> <mtable> <mtr> <mtd> <mi>P</mi> <msub> <mi>F</mi> <mi>N</mi> </msub> <mo>=</mo> <mo>(</mo> <mi>f</mi> <msub> <mi>v</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> </mrow> </msub> <mo>,</mo> <mi>f</mi> <msub> <mi>v</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>f</mi> <msub> <mi>v</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>m</mi> <mn>1</mn> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <msub> <mi>&amp;tau;</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>f</mi> <msub> <mi>v</mi> <mrow> <mi>j</mi> <mi>t</mi> <mo>,</mo> <mi>N</mi> </mrow> </msub> <mo>,</mo> <mi>f</mi> <msub> <mi>v</mi> <mrow> <mi>j</mi> <mi>t</mi> <mo>,</mo> <mi>N</mi> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> </mrow> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>f</mi> <msub> <mi>v</mi> <mrow> <mi>j</mi> <mi>t</mi> <mo>,</mo> <mi>N</mi> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>m</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <msub> <mi>&amp;tau;</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <mi>P</mi> <msub> <mi>F</mi> <mrow> <mi>N</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mo>(</mo> <mi>f</mi> <msub> <mi>v</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mi>f</mi> <msub> <mi>v</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>+</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>f</mi> <msub> <mi>v</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>+</mo> <mn>1</mn> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>m</mi> <mn>1</mn> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <msub> <mi>&amp;tau;</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>f</mi> <msub> <mi>v</mi> <mrow> <mi>j</mi> <mi>t</mi> <mo>,</mo> <mi>N</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mi>f</mi> <msub> <mi>v</mi> <mrow> <mi>j</mi> <mi>t</mi> <mo>,</mo> <mi>N</mi> <mo>+</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> </mrow> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>f</mi> <msub> <mi>v</mi> <mrow> <mi>j</mi> <mi>t</mi> <mo>,</mo> <mi>N</mi> <mo>+</mo> <mn>1</mn> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>m</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <msub> <mi>&amp;tau;</mi> <mrow> <mi>j</mi> <mi>t</mi> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mtd> </mtr> </mtable> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>
Make τjt=1, jt=1,2 ..., 5, fv therein can be obtained1,N+1As non-lightning stroke flashover risk index predicted value.
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