CN105139091A - Capacitor capacitance value and change trend forecasting method based on time series method - Google Patents

Abstract

The invention relates to the technical field of power quality analysis, and particularly relates to a capacitor capacitance value and change trend forecasting method based on a time series method. For the lack of effective capacitor capacitance value and change trend forecasting in the prior art, the invention provides the capacitor capacitance value and change trend forecasting method based on the time series method. According to the invention, sample data are collected; a capacitance value change trend forecasting model is established; a capacitance value forecasting model is established; a capacitance value is forecasted; and effective and accurate capacitor capacitance value and change trend forecasting is realized. The algorithm provided by the invention has the advantages of comprehensive design consideration, low implementation cost, reliable forecasting effect and broad application prospect, and is compatible with various types of capacitors of the existing power industry.

Description

A kind of capacitor electrode capacitance based on time series method and trend method thereof

Technical field

The present invention relates to power quality analysis technical field, particularly a kind of capacitor electrode capacitance based on time series method and trend method thereof.

Background technology

Along with the development of modern industry, the non-linear electrical equipments such as converter, electric arc furnaces and out-of-balance load are used widely in fields such as direct current transportation, metallurgy, chemical industry and electric railways, these non-linear electrical equipments operationally can produce a large amount of reactive power demands, and produce a large amount of harmonic injection electrical network, cause voltage waveform distortion, the quality of power supply declines.In electric system and vast power consumer, install shnt capacitor is the most important and widely used technological means of compensating power and filtering harmonic wave.

In electric system, if the shnt capacitor of transformer station and load place installing often operates in comparatively severe harmonic environment, its built-in electrical insulation will speed up aging, and serviceable life shortens dramatically, and may be accidents caused.Aging capacitor may produce harmonic current and amplify, and aggravation Harmfulness Caused by Harmonics, may produce harmonic resonance time serious, make amplified harmonic current several times even tens times, cause excess current and superpotential danger, makes capacitor and reactor damage or burns.For Large Copacity integrated capacitor, if its inner existing small capacitances element fault, although substantially do not affect its power frequency stable state reactive-load compensation performance, harmonic wave easily causes its internal fault protection misoperation, affects the normal work of capacitor.

If capacitance and the variation tendency thereof of capacitor can be predicted, just distinguishable go out capacitor whether will damage.Therefore, be necessary to predict capacitor electrode capacitance and variation tendency thereof, to prevent capacitor catastrophic failure, expansion accident scope.

Summary of the invention

Lack the effective prediction to capacitor electrode capacitance and variation tendency thereof for prior art, the invention provides a kind of capacitor electrode capacitance based on time series method and trend method thereof.

Technical scheme of the present invention is:

Based on capacitor electrode capacitance and the trend method thereof of time series method, comprise the following steps:

(a) collecting sample data

Moment of putting into operation from capacitor starts, to the moment of carrying out predicting, to be divided by the Cumulative Elapsed Time of capacitor successively, using the average electrical capacitance of each time interval H inner capacitor as a sample C according to constant duration H _i, wherein i=1,2 ..., N, for N is sample size; By each sample C _igive sample moment T (i), T (i)=i, i=1,2 ..., N.

B () sets up capacitance variation trend prediction model

(b-1) capacitance variation trend Δ C is calculated _n

The capacitance variation trend Δ C in T (i) moment is calculated according to formula 1 _i:

ΔC _i＝C _i+1-C _i(1)

In formula 1, Δ C _ifor the capacitance variation trend in T (i) moment, C _ifor the capacitance in T (i) moment, C _i+1for the capacitance in T (i+1) moment, i=1,2 ..., N.

The sample data utilizing formula 1 and step (a) to collect calculates T (1) successively, T (2) ..., the capacitance variation trend Δ C in T (N-1) moment ₁, Δ C ₂..., Δ C _n-1.

The capacitance variation trend Δ C in T (N) moment _nrelevant with the capacitance variation trend in a front k moment, see formula 2:

${\mathrm{\ΔC}}_N=\underset{p=1}{\overset{k}{\Σ}}{\mathrm{\ω}}_p{\mathrm{\ΔC}}_{N-p}---\left(2\right)$

In formula 2, Δ C _nfor the capacitance variation trend in T (N) moment, Δ C _n-pfor the capacitance variation trend in T (N-p) moment, ω _pfor the capacitance variation trend Δ C in T (N-p) moment _n-pto the capacitance variation trend Δ C in T (N) moment _naffect weights.

(b-2) weights ω is calculated _p

Weights ω is calculated according to formula 3 _p:

ω _p＝r _p·s _N-p(ΔC _N-p)(3)

In formula 3, r _pfor time order and function order is to weights ω _pinfluence factor and s _n-p(Δ C _n-p) for T (N-p) moment capacitance variation speed is to weights ω _pinfluence factor, s _n-p(Δ C _n-p) calculating according to formula 4.

$s_j\left({\mathrm{\ΔC}}_j\right)=\left\{\begin{array}{c}2{\left(\frac{{\mathrm{\ΔC}}_j-a}{b-a}\right)}^2,{\mathrm{\ΔC}}_j\≤0\\ 1-2{\left(\frac{{\mathrm{\ΔC}}_j-b}{b-a}\right)}^2,{\mathrm{\ΔC}}_j\≥0\end{array}\right.---\left(4\right)$

In formula 4, s _j(Δ C _j) for T (j) moment capacitance variation speed is to the influence factor of weights, $a=\underset{j}{min}\left\{{\mathrm{\ΔC}}_j\right\},b=\underset{j}{\max }\left\{{\mathrm{\ΔC}}_j\right\},j=1,2,...,N-1.$

(b-3) capacitance variation trend prediction model is set up

Formula 3 ~ 4 is substituted into formula 2 and obtains capacitance variation trend prediction model, see formula 5:

${\mathrm{\ΔC}}_N=\underset{p=1}{\overset{k}{\Σ}}{r}_p\·s_{N-p}\left({\mathrm{\ΔC}}_{N-p}\right)\·{\mathrm{\ΔC}}_{N-p}---\left(5\right)$

C () is set up capacitance forecast model and is predicted capacitance C _n+1

Set up capacitance forecast model according to formula 1, see formula 6:

C _N+1＝C _N+ΔC _N(6)

In formula 6, C _n+1for the capacitance in T (N+1) moment, C _nfor the capacitance in T (N) moment, Δ C _nfor the capacitance variation trend in T (N) moment; Capacitance C _ncollected by step (a); Capacitance variation trend Δ C _ncalculated by step (b); By capacitance C _nwith capacitance variation trend Δ C _nsubstitute into formula 6 and calculate prediction capacitance C _n+1.

Concrete, r in step (b-2) _pcalculating according to formula (7):

$r_p=\frac{1}{k}---\left(7\right)$

In formula 7, r _pfor time order and function order is to weights ω _pinfluence factor, p=1,2 ..., k.

Concrete, r in step (b-2) _panalytical hierarchy process is utilized to calculate.

Concrete, k=4 in step (b).

Beneficial effect of the present invention: the prediction of the present invention to capacitance is different from usually Forecasting Methodology used, common prediction is the capacitance of the capacitance prediction subsequent time directly used for the previous period.The present invention, in conjunction with capacitance rule over time, first establishes capacitance variation trend prediction model, and by means of the prediction realized the prediction of capacitance variation trend capacitance, it is more accurate than directly predicting capacitance to do like this.Forecasting Methodology in the present invention is not only simple time series method, relate to two factors in invention, and one is capacitance variation speed, and two is sequencings of time.Factor one adopts s type distribution function to calculate capacitance variation speed to the impact predicted the outcome, and does not belong to time series method.Factor two belongs to time series method, and the computing method of factor two comprise two kinds of methods, and one is mean value method, and two is the methods of weighted moving average combining analytical hierarchy process.The present invention, in conjunction with capacitance variation speed and these two factors of the sequencing of time, establishes capacitance variation trend prediction model and capacitance forecast model and predicts capacitance.It is comparatively thorough that algorithm design of the present invention is considered, implementation cost is lower, and prediction effect is reliable, all has good suitability, have a extensive future with the existing all kinds of capacitor of power industry.

Embodiment

Embodiment adopts capacitor electrode capacitance of the present invention and trend method thereof, and its concrete implementation step is as follows:

(a) collecting sample data

Moment of putting into operation from capacitor starts, to the moment of carrying out predicting, to be divided by the Cumulative Elapsed Time of capacitor successively, using the average electrical capacitance of each time interval H inner capacitor as a sample C according to constant duration H _i, wherein i=1,2 ..., N, for N is sample size; By each sample C _igive sample moment T (i), T (i)=i, i=1,2 ..., N.

When carrying out constant duration to the Cumulative Elapsed Time of capacitor and dividing, for the last remaining time period, when being less than H/2 when it is operated, ignore this section; When being no less than H/2 when it is operated, using the average electrical capacitance of this time period inner capacitor also as a sample.

In the present embodiment, time interval H value is 15 days.Through repetition test, when time interval H gets 15 days, both can ensure sampling precision when sample collection calculates, again can conservative control sampling calculated amount, shorten sampling consuming time.

B () sets up capacitance variation trend prediction model

(b-1) capacitance variation trend Δ C is calculated _n

The capacitance variation trend Δ C in T (i) moment is calculated according to formula 1 _i:

ΔC _i＝C _i+1-C _i(1)

In formula 1, Δ C _ifor the capacitance variation trend in T (i) moment, C _ifor the capacitance in T (i) moment, C _i+1for the capacitance in T (i+1) moment, i=1,2 ..., N.

The sample data utilizing formula 1 and step (a) to collect calculates T (1) successively, T (2) ..., the capacitance variation trend Δ C in T (N-1) moment ₁, Δ C ₂..., Δ C _n-1.

The capacitance variation trend Δ C in T (N) moment _nrelevant with the capacitance variation trend in a front k moment, see formula 2:

${\mathrm{\ΔC}}_N=\underset{p=1}{\overset{k}{\Σ}}{\mathrm{\ω}}_p{\mathrm{\ΔC}}_{N-p}---\left(2\right)$

In formula 2, Δ C _nfor the capacitance variation trend in T (N) moment, Δ C _n-pfor the capacitance variation trend in T (N-p) moment, ω _pfor the capacitance variation trend Δ C in T (N-p) moment _n-pto the capacitance variation trend Δ C in T (N) moment _naffect weights.In the present embodiment, the value of k is 4.Through repetition test, during k=4, can under the prerequisite ensureing capacitance and trend accuracy thereof, conservative control calculated amount, avoids calculating consuming time long.

(b-2) weights ω is calculated _p

The present embodiment is at calculating weights ω _ptime not use only simple time series method, also taken into full account and affected weights ω _ptwo factors, one is capacitance variation speed, and two is sequencings of time, sees formula 3.

ω _p＝r _p·s _N-p(ΔC _N-p)(3)

In formula 3, r _pfor time order and function order is to weights ω _pinfluence factor, and s _n-p(Δ C _n-p) for T (N-p) moment capacitance variation speed is to weights ω _pinfluence factor.

(namely capacitance variation speed is to weights ω for factor one _pimpact) adopt S type distribution function to calculate capacitance variation speed to the impact predicted the outcome, do not belong to time series method.Consider that capacitance variation speed is to weights ω _paffect time, first analyze the operation characteristic of capacitor.In many cases, along with the growth of capacitor working time, the capacitance of most capacitor can present the rule of successively decreasing, and certainly also has partial capacitor its capacitance within the shorter a period of time starting to put into operation first to increase, but finally also can present downtrending.Namely the variation tendency of capacitance reflects the size of capacitance variation.From the definition of capacitance variation trend, capacitor electrode capacitance increases along with the increase of its variation tendency, reduces and reduce, meeting the variation characteristic of S type distribution function.The pace of change that the increase of capacitance variation trend or reduction reaction are capacitance.In sum, capacitance variation speed affects s to capacitance _n-p(Δ C _n-p) S type distribution function can be adopted to calculate, see formula 4.

$s_j\left({\mathrm{\ΔC}}_j\right)=\left\{\begin{array}{c}2{\left(\frac{{\mathrm{\ΔC}}_j-a}{b-a}\right)}^2,{\mathrm{\ΔC}}_j\≤0\\ 1-2{\left(\frac{{\mathrm{\ΔC}}_j-b}{b-a}\right)}^2,{\mathrm{\ΔC}}_j\≥0\end{array}\right.---\left(4\right)$

In formula 4, s _j(Δ C _j) for T (j) moment capacitance variation speed is to the influence factor of weights, $a=\underset{j}{min}\left\{{\mathrm{\ΔC}}_j\right\},b=\underset{j}{\max }\left\{{\mathrm{\ΔC}}_j\right\},j=1,2,...,N-1.$

(sequencing of time is to weights ω for factor two _pimpact) belong to time series method, the computing method of factor two comprise two kinds of methods, and one is mean value method, and two is the methods of weighted moving average combining analytical hierarchy process.

Mean value method is adopted to calculate r _ptime, r _pcalculating according to formula (7):

$r_p=\frac{1}{k}---\left(7\right)$

In formula 7, r _pfor time order and function order is to weights ω _pinfluence factor, p=1,2 ..., k.K=4 in the present embodiment, then r ₁=r ₂=r ₃=r ₄=1/4.

Analytical hierarchy process is adopted to calculate r _ptime, when k=4, Judgement Matricies is:

$A=\left[\begin{array}{cccc}1& 2& 3& 4\\ 1/2& 1& 2& 3\\ 1/3& 1/2& 1& 2\\ 1/4& 1/3& 1/2& 1\end{array}\right]$

As calculated, r=[0.46580.27710.16110.0960], i.e. r ₁=0.4658, r ₂=0.2771, r ₃=0.1611, r ₄=0.0960, namely as prediction n-hour capacitance variation trend Δ C _ntime, be respectively by the influence factor that produces of time order and function order in k (in the present embodiment k=4) individual moment before n-hour: the N-1 moment was the 0.4658, the N-2 moment be the 0.2771, the N-3 moment is 0.1611, and the N-4 moment is 0.0960.

(b-3) capacitance variation trend prediction model is set up

Formula 3 ~ 4 is substituted into formula 2 and obtains capacitance variation trend prediction model, see formula 5:

${\mathrm{\ΔC}}_N=\underset{p=1}{\overset{k}{\Σ}}{r}_p\·s_{N-p}\left({\mathrm{\ΔC}}_{N-p}\right)\·{\mathrm{\ΔC}}_{N-p}---\left(5\right)$

C () is set up capacitance forecast model and is predicted capacitance C _n+1

Set up capacitance forecast model according to formula 1, see formula 6:

C _N+1＝C _N+ΔC _N(6)

In formula 6, C _n+1for the capacitance in T (N+1) moment, C _nfor the capacitance in T (N) moment, Δ C _nfor the capacitance variation trend in T (N) moment; Capacitance C _ncollected by step (a); Capacitance variation trend Δ C _ncalculated by step (b); By capacitance C _nwith capacitance variation trend Δ C _nsubstitute into formula 6 and calculate prediction capacitance C _n+1.

When employing mean value method calculates r _ptime, obtain the mean value forecast model of capacitance, see formula 8:

$C_{N+1}=C_N+\underset{p=1}{\overset{k}{\Σ}}\frac{{\mathrm{\ΔC}}_{N-p}}{k}\·s_{N-p}\left({\mathrm{\ΔC}}_{N-p}\right)---\left(8\right)$

In formula 8, C _n+1for the capacitance in T (N+1) moment, C _nfor the capacitance in T (N) moment, Δ C _n-pfor the capacitance variation trend in T (N-p) moment, s _n-p(Δ C _n-p) for T (N-p) moment capacitance variation speed is to the influence factor of capacitance.Capacitance C _ncollected by step (a), capacitance variation trend Δ C _n-psample data is collected and formula 1 calculates, s by step (a) _n-p(Δ C _n-p) collect sample data by step (a) and formula 4 calculates, k=4.

When employing analytical hierarchy process calculates r _ptime, obtain the weighted prediction model of capacitance, see formula 9:

$C_{N+1}=C_N+\underset{p=1}{\overset{k}{\Σ}}{r}_p\·s_{N-p}\left({\mathrm{\ΔC}}_{N-p}\right)\·{\mathrm{\ΔC}}_{N-p}---\left(9\right)$

In formula 9, C _n+1for the capacitance in T (N+1) moment, C _nfor the capacitance in T (N) moment, Δ C _n-pfor the capacitance variation trend in T (N-p) moment, s _n-p(Δ C _n-p) for T (N-p) moment capacitance variation speed is to the influence factor of capacitance, r _pfor time order and function order is to weights ω _pinfluence factor.Capacitance C _ncollected by step (a), capacitance variation trend Δ C _n-psample data is collected and formula 1 calculates, s by step (a) _n-p(Δ C _n-p) collect sample data by step (a) and formula 4 calculates, r _pemploying analytical hierarchy process calculates, k=4.

The present invention establishes mean value and weight estimation two kinds of capacitance forecast models.By contrast, mean value forecast model comparatively weighted prediction model is more simple, convenient, be suitable for estimating roughly capacitance, and predicting the outcome of weighted prediction model is relatively more accurate, is suitable for the occasion higher to the accuracy requirement that predicts the outcome.Based on two kinds of capacitance forecast models that time series method is set up in the present invention, be not directly the capacitance of subsequent time is predicted, but first prediction draws the capacitance variation trend in this moment, then obtained the capacitance of subsequent time by the prediction of capacitance variation trend model.The capacitance of most of capacitor all can present the rule of successively decreasing along with the increase of its working time to adopt the reason of this modeling pattern to be, certainly also there is partial capacitor its capacitance within the shorter a period of time starting to put into operation first to increase, but finally also can present downtrending.As can be seen here, certain moment capacitance variation tendency and before it variation tendency in several moment there is very strong correlativity.Consider this Changing Pattern of capacitance, adopt forecast model of building in the present invention, first predict the capacitance variation trend in certain moment, then subsequent time capacitance is predicted, so first can ensure the correctness of capacitance variation direction (increase or reduce), then by considering time order and function order with these two factors of capacitance variation speed to the influence characteristic of capacitance, dynamic weighting function is combined with analytical hierarchy process, obtain rational weight, the accuracy of prediction capacitance can be improved further.If but directly capacitance is predicted, then differ and ensure the correctness of its variation tendency surely.

Such as, all downtrending is presented, i.e. C as k=4 at T (N-3), T (N-2), T (N-1) and T (N) moment capacitance _n≤ C _n-1≤ C _n-2≤ C _n-3time, adopt classic method directly to record in advance the capacitance in T (N+1) moment there is C _n+1>=C _n, the capacitance in gained T (N+1) moment is greater than the capacitance in T (N) moment, and namely capacitance variation trend there occurs change, becomes ascendant trend from decline, and the capacitance prediction accuracy of obvious classic method is extremely low.Capacitance forecast model of the present invention is adopted to obtain due to Δ C _n-p≤ 0, obtain Δ C _n≤ 0, there is C _n+1≤ C _n, capacitance variation trend does not change.As can be seen here, capacitance of the present invention and Changing Pattern prediction thereof are highly improved compared with the accuracy of classic method prediction.

It should be noted that, adopt analytical hierarchy process to calculate r _ptechnology be the common practise of this area, even if the present invention is not described in detail, those skilled in the art also should know above step.

The above embodiment is only the preferred embodiments of the present invention, and and the feasible enforcement of non-invention exhaustive.For persons skilled in the art, to any apparent change done by it under the prerequisite not deviating from the principle of the invention and spirit, all should be contemplated as falling with within claims of the present invention.

Claims (4)

1., based on capacitor electrode capacitance and the trend method thereof of time series method, it is characterized in that it comprises the following steps:

(a) collecting sample data

Moment of putting into operation from capacitor starts, to the moment of carrying out predicting, to be divided by the Cumulative Elapsed Time of capacitor successively, using the average electrical capacitance of each time interval H inner capacitor as a sample C according to constant duration H _i, wherein i=1,2 ..., N, for N is sample size; By each sample C _igive sample moment T (i), T (i)=i, i=1,2 ..., N;

B () sets up capacitance variation trend prediction model

(b-1) capacitance variation trend Δ C is calculated _n

The capacitance variation trend Δ C in T (i) moment is calculated according to formula 1 _i:

ΔC _i＝C _i+1-C _i(1)

In formula 1, Δ C _ifor the capacitance variation trend in T (i) moment, C _ifor the capacitance in T (i) moment, C _i+1for the capacitance in T (i+1) moment, i=1,2 ..., N;

The sample data utilizing formula 1 and step (a) to collect calculates T (1) successively, T (2) ..., the capacitance variation trend Δ C in T (N-1) moment ₁, Δ C ₂..., Δ C _n-1;

The capacitance variation trend Δ C in T (N) moment _nrelevant with the capacitance variation trend in a front k moment, see formula 2:

${\mathrm{\ΔC}}_N=\underset{p=1}{\overset{k}{\Σ}}{\mathrm{\ω}}_p{\mathrm{\ΔC}}_{N-p}---\left(2\right)$

In formula 2, Δ C _nfor the capacitance variation trend in T (N) moment, Δ C _n-pfor the capacitance variation trend in T (N-p) moment, ω _pfor the capacitance variation trend Δ C in T (N-p) moment _n-pto the capacitance variation trend Δ C in T (N) moment _naffect weights;

(b-2) weights ω is calculated _p

Weights ω is calculated according to formula 3 _p:

ω _p＝r _p·s _N-p(ΔC _N-p)(3)

In formula 3, r _pfor time order and function order is to weights ω _pinfluence factor and s _n-p(Δ C _n-p) for T (N-p) moment capacitance variation speed is to weights ω _pinfluence factor, s _n-p(Δ C _n-p) calculating according to formula 4:

$s_j\left({\mathrm{\ΔC}}_j\right)=\left\{\begin{array}{c}2{\left(\frac{{\mathrm{\ΔC}}_j-a}{b-a}\right)}^2,{\mathrm{\ΔC}}_j\≤0\\ 1-2{\left(\frac{{\mathrm{\ΔC}}_j-b}{b-a}\right)}^2,{\mathrm{\ΔC}}_j\≥0\end{array}\right.---\left(4\right)$

In formula 4, s _j(Δ C _j) for T (j) moment capacitance variation speed is to the influence factor of weights, $a=\underset{j}{min}\left\{{\mathrm{\ΔC}}_j\right\},b=\underset{j}{\max }\left\{{\mathrm{\ΔC}}_j\right\},j=1,2,...,N-1;$

(b-3) capacitance variation trend prediction model is set up

Formula 3 ~ 4 is substituted into formula 2 and obtains capacitance variation trend prediction model, see formula 5:

${\mathrm{\ΔC}}_N=\underset{p=1}{\overset{k}{\Σ}}{r}_p\·s_{N-p}\left({\mathrm{\ΔC}}_{N-p}\right)\·{\mathrm{\ΔC}}_{N-p}---\left(5\right)$

C () is set up capacitance forecast model and is predicted capacitance C _n+1

Set up capacitance forecast model according to formula 1, see formula 6:

C _N+1＝C _N+ΔC _N(6)

In formula 6, C _n+1for the capacitance in T (N+1) moment, C _nfor the capacitance in T (N) moment, Δ C _nfor the capacitance variation trend in T (N) moment; Capacitance C _ncollected by step (a); Capacitance variation trend Δ C _ncalculated by step (b); By capacitance C _nwith capacitance variation trend Δ C _nsubstitute into formula 6 and calculate prediction capacitance C _n+1.

2. a kind of capacitor electrode capacitance based on time series method according to claim 1 and trend method thereof, is characterized in that r in step (b-2) _pcalculating according to formula (7):

$r_p=\frac{1}{k}---\left(7\right)$

In formula 7, r _pfor time order and function order is to weights ω _pinfluence factor, p=1,2 ..., k.

3. a kind of capacitor electrode capacitance based on time series method according to claim 1 and trend method thereof, is characterized in that r in step (b-2) _panalytical hierarchy process is utilized to calculate.

4. a kind of capacitor electrode capacitance based on time series method according to claim 1 or 2 or 3 and trend method thereof, is characterized in that k=4 in step (b).