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CN105139091B - A kind of capacitor capacitance value and its trend method based on time series method - Google Patents

A kind of capacitor capacitance value and its trend method based on time series method Download PDF

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CN105139091B
CN105139091B CN201510532475.XA CN201510532475A CN105139091B CN 105139091 B CN105139091 B CN 105139091B CN 201510532475 A CN201510532475 A CN 201510532475A CN 105139091 B CN105139091 B CN 105139091B
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capacitance value
time
capacitance
formula
change trend
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CN105139091A (en
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周文
段晓波
胡文平
饶群
王生彬
毛志芳
郭捷
王磊
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State Grid Corp of China SGCC
Electric Power Research Institute of State Grid Hebei Electric Power Co Ltd
Hebei Electric Power Construction Adjustment Test Institute
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State Grid Corp of China SGCC
Electric Power Research Institute of State Grid Hebei Electric Power Co Ltd
Hebei Electric Power Construction Adjustment Test Institute
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Abstract

The present invention relates to power quality analysis technical field, in particular to a kind of capacitor capacitance value and its trend method based on time series method.Capacitor capacitance value and its variation tendency are effectively predicted for prior art shortage, the present invention provides a kind of capacitor capacitance value and its trend method based on time series method.The present invention passes through collecting sample data, establishes capacitance variation trend prediction model, establishes capacitor value prediction model and predict that capacitance realizes effective, the Accurate Prediction to capacitor capacitance value and its variation tendency.It is more thorough that algorithm design of the invention considers, implementation cost is lower, and prediction effect is reliable, all has good suitability with the existing all kinds of capacitors of power industry, has a extensive future.

Description

A kind of capacitor capacitance value and its trend method based on time series method
Technical field
The present invention relates to power quality analysis technical field, in particular to a kind of capacitor capacitance based on time series method Value and its trend method.
Background technique
With the development of modern industry, the non-linear electrical equipments such as converter, electric arc furnaces and out-of-balance load are straight The fields such as stream transmission of electricity, metallurgy, chemical industry and electric railway are used widely, these non-linear electrical equipments can produce at runtime Raw a large amount of reactive power demand, and a large amount of harmonic injection power grids are generated, cause voltage waveform distortion, power quality decline.? Installation shunt capacitor is compensating power and filters out that harmonic wave is mostly important and application in electric system and vast power consumer Extensive technological means.
In electric system, if the shunt capacitor installed at substation and load often operate in it is more severe humorous In wave environment, built-in electrical insulation shortens dramatically accelerated ageing, service life, and may cause accident.The capacitor of aging can Amplification can be generated to harmonic current, aggravate Harmfulness Caused by Harmonics, there may be harmonic resonances when serious, make several times of amplified harmonic current Even tens times, the danger of overcurrent and overvoltage is caused, capacitor and reactor is made to damage or burn.With large capacity aggregation type For capacitor, if its internal existing small capacitances element fault, although having substantially no effect on its power frequency stable state reactive compensation performance, But harmonic wave be easy to cause its internal fault protection misoperation, influences the normal work of capacitor.
If the capacitance and its variation tendency of capacitor can be predicted, it can tell whether capacitor will damage.Therefore, It is necessary to predict capacitor capacitance value and its variation tendency, to prevent capacitor catastrophic failure, expand accident range.
Summary of the invention
Capacitor capacitance value and its variation tendency are effectively predicted for prior art shortage, the present invention provides one kind Capacitor capacitance value and its trend method based on time series method.
The technical solution of the present invention is as follows:
A kind of capacitor capacitance value and its trend method based on time series method, comprising the following steps:
(a) collecting sample data
Putting into operation constantly since capacitor until at the time of prediction, successively the accumulation of capacitor is transported The row time is divided according to constant duration H, using the average capacitance value of each time interval H inner capacitor as a sample Ci, it is sample size that wherein i=1,2 ..., N, which are N,；By each sample CiAssign a sample moment T (i), T (i)=i, i= 1,2,…,N。
(b) capacitance variation trend prediction model is established
(b-1) capacitance variation trend Δ C is calculatedN
The capacitance variation trend Δ C at T (i) moment is calculated according to formula 1i:
ΔCi=Ci+1-Ci (1)
In formula 1, Δ CiFor the capacitance variation trend at T (i) moment, CiFor the capacitance at T (i) moment, Ci+1For T (i+ 1) capacitance at moment, i=1,2 ..., N；
It is successively calculated T (1) using formula 1 and the collected sample data of step (a), T (2), the electricity at Λ, T (N-1) moment Capacitance variation tendency Δ C1,ΔC2,…,ΔCN-1；
The capacitance variation trend Δ C at T (N) momentNIt is related with the capacitance variation trend at preceding k moment, see formula 2:
In formula 2, Δ CNFor the capacitance variation trend at T (N) moment, Δ CN-pFor the capacitance variation at T (N-p) moment Trend, ωpFor the capacitance variation trend Δ C at T (N-p) momentN-pTo the capacitance variation trend Δ C at T (N) momentNInfluence Weight；P expression T (N) the 1st moment to any one moment between k-th of moment before the moment；
(b-2) weight ω is calculatedp
Weight ω is calculated according to formula 3p:
ωp=rp·sN-p(ΔCN-p) (3)
In formula 3, rpIt is chronological order to weight ωpInfluence factor and
sN-p(ΔCN-p) it is T (N-p) moment capacitance variation speed to weight ωpInfluence factor, sN-p(ΔCN-p) It calculates according to formula 4.
In formula 4, sj(ΔCj) it is influence factor of T (j) the moment capacitance variation speed to weight,
(b-3) capacitance variation trend prediction model is established
The substitution formula 2 of formula 3~4 is obtained into capacitance variation trend prediction model, sees formula 5:
(c) it establishes capacitor value prediction model and predicts capacitance CN+1
Capacitor value prediction model is established according to formula 1, sees formula 6:
CN+1=CN+ΔCN (6)
In formula 6, CN+1For the capacitance at T (N+1) moment, CNFor the capacitance at T (N) moment, Δ CNFor T (N) moment Capacitance variation trend；Capacitance CNIt is collected by step (a)；Capacitance variation trend Δ CNIt is calculated by step (b)； By capacitance CNWith capacitance variation trend Δ CNIt substitutes into formula 6 and prediction capacitance C is calculatedN+1。
Specifically, r in step (b-2)pCalculating according to formula (7):
In formula 7, rpIt is chronological order to weight ωpInfluence factor, p=1,2 ..., k；
Number at the time of k indicates choose when capacitance variation trend prediction.
Specifically, r in step (b-2)pIt is calculated using analytic hierarchy process (AHP).
Specifically, k=4 in step (b).
Beneficial effects of the present invention: the present invention is different from conventionally used prediction technique to the prediction of capacitance, common Prediction is the direct capacitance using capacitance prediction subsequent time for the previous period.The change of present invention combination capacitance at any time Law has initially set up capacitance variation trend prediction model, is realized by means of the prediction to capacitance variation trend to electricity The prediction of capacitance, do so capacitance predict than directly it is more acurrate.Prediction technique in the present invention is not only simply Time series method, two factors involved in invention, first is that capacitance variation speed, second is that the sequencing of time.Factor one Influence of the capacitance variation speed to prediction result is calculated using s type distribution function, is not belonging to time series method.Factor two belongs to Time series method, the calculation method of factor two includes two methods, first is that mean value method, two are combined with adding for analytic hierarchy process (AHP) Weigh the method for moving average.Present invention combination capacitance variation speed and the sequencing of time the two factors, establish capacitance Trend model and capacitor value prediction model simultaneously predict capacitance.It is more thorough that algorithm design of the invention considers, real Apply that cost is relatively low, prediction effect is reliable, all has good suitability, application prospect with the existing all kinds of capacitors of power industry It is wide.
Specific embodiment
Embodiment uses capacitor capacitance value and its trend method of the invention, and specific implementation step is such as Under:
(a) collecting sample data
Putting into operation constantly since capacitor until at the time of prediction, successively the accumulation of capacitor is transported The row time is divided according to constant duration H, using the average capacitance value of each time interval H inner capacitor as a sample Ci, it is sample size that wherein i=1,2 ..., N, which are N,；By each sample CiAssign a sample moment T (i), T (i)=i, i= 1,2,…,N。
When the Cumulative Elapsed Time to capacitor carries out constant duration division, for the last remaining period, when Its runing time ignores this section when being less than H/2；When being no less than H/2 between when it is operated, by being averaged for the period inner capacitor Capacitance is also used as a sample.
In the present embodiment, time interval H value is 15 days.It, can be in sample when time interval H takes 15 days through repetition test This acquisition not only guarantees sampling precision when calculating, but also can rationally control the calculation amount of sampling, and it is time-consuming to shorten sampling.
(b) capacitance variation trend prediction model is established
(b-1) capacitance variation trend Δ C is calculatedN
The capacitance variation trend Δ C at T (i) moment is calculated according to formula 1i:
ΔCi=Ci+1-Ci (1)
In formula 1, Δ CiFor the capacitance variation trend at T (i) moment, CiFor the capacitance at T (i) moment, Ci+1For T (i+ 1) capacitance at moment, i=1,2 ..., N.
It is successively calculated T (1) using formula 1 and the collected sample data of step (a), T (2), the electricity at Λ, T (N-1) moment Capacitance variation tendency Δ C1,ΔC2,…,ΔCN-1。
The capacitance variation trend Δ C at T (N) momentNIt is related with the capacitance variation trend at preceding k moment, see formula 2:
In formula 2, Δ CNFor the capacitance variation trend at T (N) moment, Δ CN-pFor the capacitance variation at T (N-p) moment Trend, ωpFor the capacitance variation trend Δ C at T (N-p) momentN-pTo the capacitance variation trend Δ C at T (N) momentNInfluence Weight, p expression T (N) the 1st moment to any one moment between k-th of moment before the moment.In the present embodiment, the value of k is 4., can be under the premise of guaranteeing capacitance and its trend accuracy when k=4 through repetition test, reasonable control meter Calculation amount avoids calculating from taking long time.
(b-2) weight ω is calculatedp
The present embodiment is calculating weight ωpWhen do not use only simple time series method, also fully considered influence power Value ωpTwo factors, first is that capacitance variation speed, second is that the sequencing of time, is shown in formula 3.
ωp=rp·sN-p(ΔCN-p) (3)
In formula 3, rpIt is chronological order to weight ωpInfluence factor, andsN-p(ΔCN-p) it is T (N-p) moment capacitance variation speed is to weight ωpInfluence factor.
(i.e. capacitance variation speed is to weight ω for factor onepInfluence) using S type distribution function calculate capacitance variation Influence of the speed to prediction result, is not belonging to time series method.Consider capacitance variation speed to weight ωpInfluence when, it is first First analyze the operation characteristic of capacitor.In many cases, with the growth of capacitor runing time, the capacitor of most capacitors Value can show the rule successively decreased, and also have partial capacitor its capacitance within the shorter a period of time for starting to put into operation certainly It can first increase, but finally can also show downward trend.The variation tendency of capacitance is to reflect the size of capacitance variation. By the definition of capacitance variation trend it is found that capacitor capacitance value is the increase with its variation tendency and is increased, reduces and subtract It is small, meet the variation characteristic of S type distribution function.Capacitance variation trend increases or reduces the variation speed that reaction is capacitance Degree.In conclusion influence s of the capacitance variation speed to capacitanceN-p(ΔCN-p) calculating of S type distribution function can be used, see public affairs Formula 4.
In formula 4, sj(ΔCj) it is influence factor of T (j) the moment capacitance variation speed to weight,
(sequencing of time is to weight ω for factor twopInfluence) belong to time series method, the calculation method of factor two Including two methods, first is that mean value method, two are combined with the method for weighted moving average of analytic hierarchy process (AHP).
R is calculated using mean value methodpWhen, rpCalculating according to formula (7):
In formula 7, rpIt is chronological order to weight ωpInfluence factor, p=1,2 ..., k；K indicates to carry out capacitor Number at the time of selection when value trend.
K=4 in the present embodiment, then r1=r2=r3=r4=1/4.
R is calculated using analytic hierarchy process (AHP)pWhen, Judgement Matricies in the case where k=4 are as follows:
It is computed, r=[0.4658 0.2771 0.1611 0.0960], i.e. r1=0.4658, r2=0.2771, r3= 0.1611, r4=0.0960, that is, as prediction n-hour capacitance variation trend Δ CNWhen, by preceding k (this reality of n-hour Apply k=4 in example) to be respectively as follows: the N-1 moment be 0.4658 to influence factor caused by the chronological order at a moment, N-2 Moment is 0.2771, and the N-3 moment is 0.1611, and the N-4 moment is 0.0960.
(b-3) capacitance variation trend prediction model is established
The substitution formula 2 of formula 3~4 is obtained into capacitance variation trend prediction model, sees formula 5:
(c) it establishes capacitor value prediction model and predicts capacitance CN+1
Capacitor value prediction model is established according to formula 1, sees formula 6:
CN+1=CN+ΔCN (6)
In formula 6, CN+1For the capacitance at T (N+1) moment, CNFor the capacitance at T (N) moment, Δ CNFor T (N) moment Capacitance variation trend；Capacitance CNIt is collected by step (a)；Capacitance variation trend Δ CNIt is calculated by step (b)； By capacitance CNWith capacitance variation trend Δ CNIt substitutes into formula 6 and prediction capacitance C is calculatedN+1。
When using mean value method calculating rpWhen, the average value prediction model of capacitance is obtained, sees formula 8:
In formula 8, CN+1For the capacitance at T (N+1) moment, CNFor the capacitance at T (N) moment, Δ CN-pWhen for T (N-p) The capacitance variation trend at quarter, sN-p(ΔCN-p) it is influence factor of T (N-p) the moment capacitance variation speed to capacitance.Electricity Capacitance CNIt is collected by step (a), capacitance variation trend Δ CN-pSample data is collected by step (a) and formula 1 is counted It obtains, sN-p(ΔCN-p) sample data is collected by step (a) and formula 4 is calculated, k=4.
When using analytic hierarchy process (AHP) calculating rpWhen, the weighted prediction model of capacitance is obtained, sees formula 9:
In formula 9, CN+1For the capacitance at T (N+1) moment, CNFor the capacitance at T (N) moment, Δ CN-pWhen for T (N-p) The capacitance variation trend at quarter, sN-p(ΔCN-p) it is influence factor of T (N-p) the moment capacitance variation speed to capacitance, rp It is chronological order to weight ωpInfluence factor.Capacitance CNIt is collected by step (a), capacitance variation trend Δ CN-pSample data is collected by step (a) and formula 1 is calculated, sN-p(ΔCN-p) sample number collected by step (a) It is calculated according to formula 4, rpIt is calculated using analytic hierarchy process (AHP), k=4.
The present invention establishes two kinds of capacitor value prediction models of average value and weight estimation.By comparison, average value predicts mould Type is more simple compared with weighted prediction model, conveniently, is suitable for estimating roughly to capacitance, and the prediction knot of weighted prediction model Fruit is relatively more accurate, is suitable for the higher occasion of prediction result accuracy requirement.Time series method institute is based in the present invention The two kinds of capacitor value prediction models established not are directly to predict the capacitance of subsequent time, but when first prediction obtains this Then the capacitance variation trend at quarter is predicted to obtain the capacitance of subsequent time by capacitance variation trend model.Using this The reason of kind of modeling pattern, is that the capacitance of most of capacitors can all be showed with the increase of its runing time and successively decreases Rule also has partial capacitor its capacitance within the shorter a period of time for starting to put into operation that can first increase certainly, but most Downward trend can be also showed eventually.It can be seen that the variation tendency of certain moment capacitance and the variation at the front several moment become Gesture has very strong correlation.In view of this changing rule of capacitance is first predicted using prediction model built in the present invention Then the capacitance variation trend at certain moment predicts subsequent time capacitance, so first it is ensured that capacitance variation direction The correctness of (increase or reduce), then by considering chronological order and the two factors of capacitance variation speed to electricity Dynamic weighting function is combined with analytic hierarchy process (AHP), obtains reasonable weight, can be further improved pre- by the influence characteristic of capacitance Survey the accuracy of capacitance.But if directly capacitance is predicted, then not necessarily can guarantee the correct of its variation tendency Property.
For example, downward trend is showed as k=4 and in T (N-3), T (N-2), T (N-1) and T (N) moment capacitance, That is CN≤CN-1≤CN-2≤CN-3When, directly the capacitance at T (N+1) moment is measured in advance using conventional methodThere is CN+1≥CN, the capacitance at gained T (N+1) moment is greater than the capacitance at T (N) moment, That is capacitance variation trend is changed, and becomes ascendant trend from decline, it is clear that the capacitance prediction accuracy of conventional method It is extremely low.C is obtained using capacitor value prediction model of the inventionN+1=CN+ΔCN,Due to Δ CN-p≤ 0, Obtain Δ CN≤ 0, there is CN+1≤CN, capacitance variation trend do not change.It can be seen that capacitance and its variation of the invention Law forecasting is highly improved compared with the accuracy that conventional method is predicted.
It should be noted that calculating r using analytic hierarchy process (AHP)pTechnology be this field common knowledge, even if of the invention It is not described in detail, those skilled in the art are it is also evident that above step.
Embodiment described above is merely a preferred embodiment of the present invention, and the simultaneously exhaustion of the feasible implementation of non-present invention.It is right For persons skilled in the art, any aobvious to made by it under the premise of without departing substantially from the principle of the invention and spirit and The change being clear to should be all contemplated as falling within claims of the invention.

Claims (4)

1.一种基于时间序列法的电容器电容值及其变化趋势预测方法，其特征在于其包括以下步骤：1. a capacitor capacitance value and its variation trend prediction method based on time series method, it is characterized in that it comprises the following steps: (a)采集样本数据(a) Collect sample data 从电容器开始投入运行时刻开始到进行预测的时刻为止，依次将电容器的累积运行时间按照等时间间隔H进行划分，将每一时间间隔H内电容器的平均电容值作为一个样本Ci，其中i＝1,2,…,N，N为样本容量；将每一样本Ci赋予一个样本时刻T(i)，T(i)＝i，i＝1,2,…,N；From the time when the capacitors are put into operation to the time when the prediction is made, the cumulative operation time of the capacitors is divided into equal time intervals H in turn, and the average capacitance value of the capacitors in each time interval H is taken as a sample C i , where i= 1,2,...,N,N is the sample size; assign each sample C i to a sample time T(i), T(i)=i, i=1,2,...,N; (b)建立电容值变化趋势预测模型(b) Establish a prediction model for the change trend of capacitance value (b-1)计算电容值变化趋势ΔCN (b-1) Calculate the change trend of capacitance value ΔC N 按照公式1计算T(i)时刻的电容值变化趋势ΔCi：Calculate the capacitance value change trend ΔC i at time T(i) according to formula 1: ΔCi＝Ci+1-Ci (1)ΔC i =C i+1 −C i (1) 公式1中，ΔCi为T(i)时刻的电容值变化趋势，Ci为T(i)时刻的电容值，Ci+1为T(i+1)时刻的电容值，i＝1,2,…,N；In formula 1, ΔC i is the change trend of the capacitance value at time T(i), C i is the capacitance value at time T(i), C i+1 is the capacitance value at time T(i+1), i=1, 2,…,N; 利用公式1和步骤(a)采集到的样本数据依次计算T(1),T(2),…,T(N-1)时刻的电容值变化趋势ΔC1,ΔC2,…,ΔCN-1；Use formula 1 and the sample data collected in step (a) to sequentially calculate the change trend of capacitance value at T(1), T(2),..., T(N-1) time ΔC 1 ,ΔC 2 ,...,ΔC N- 1 ; T(N)时刻的电容值变化趋势ΔCN与前k个时刻的电容值变化趋势有关，见公式2：The change trend of capacitance value at T(N) time ΔC N is related to the change trend of capacitance value at the first k time, see formula 2: 公式2中，ΔCN为T(N)时刻的电容值变化趋势，ΔCN-p为T(N-p)时刻的电容值变化趋势，ωp为T(N-p)时刻的电容值变化趋势ΔCN-p对T(N)时刻的电容值变化趋势ΔCN的影响权值；p表示T(N)时刻前第1个时刻到第k个时刻之间的任一个时刻；In formula 2, ΔC N is the change trend of capacitance value at time T(N), ΔC Np is the change trend of capacitance value at time T(Np), and ω p is the change trend of capacitance value at time T(Np) ΔC Np versus T( N) the influence weight of the capacitance value change trend ΔC N at time; p represents any time between the 1st time before the T(N) time to the kth time; (b-2)计算权值ωp (b-2) Calculate the weight ω p 按照公式3计算权值ωp：Calculate the weight ω p according to formula 3: ωp＝rp·sN-p(ΔCN-p) (3)ω p =r p ·s Np (ΔC Np ) (3) 公式3中，rp为时间先后顺序对权值ωp的影响因素并且sN-p(ΔCN-p)为T(N-p)时刻电容值变化速度对权值ωp的影响因素，sN-p(ΔCN-p)的计算按照公式4：In Equation 3, r p is the influence factor of time sequence on the weight ω p and s Np (ΔC Np ) is the influence factor of the change rate of the capacitance value on the weight ω p at the time of T(Np), and the calculation of s Np (ΔC Np ) is based on formula 4: 公式4中，sj(ΔCj)为T(j)时刻电容值变化速度对权值的影响因素， In formula 4, s j (ΔC j ) is the influence factor of the capacitance value change speed on the weight value at the time of T(j), (b-3)建立电容值变化趋势预测模型(b-3) Establish a prediction model for the change trend of capacitance value 将公式3～4代入公式2得到电容值变化趋势预测模型，见公式5：Substitute Equations 3 to 4 into Equation 2 to obtain the capacitance value change trend prediction model, see Equation 5: (c)建立电容值预测模型并预测电容值CN+1 (c) Establish a capacitance value prediction model and predict the capacitance value C N+1 根据公式1建立电容值预测模型，见公式6：Establish a capacitance value prediction model according to Equation 1, see Equation 6: CN+1＝CN+ΔCN (6)C N+1 = C N +ΔC N (6) 公式6中，CN+1为T(N+1)时刻的电容值，CN为T(N)时刻的电容值，ΔCN为T(N)时刻的电容值变化趋势；电容值CN由步骤(a)采集得到；电容值变化趋势ΔCN由步骤(b)计算得到；将电容值CN和电容值变化趋势ΔCN代入公式6计算得到预测电容值CN+1。In formula 6, C N+1 is the capacitance value at the time of T(N+1), C N is the capacitance value at the time of T(N), ΔC N is the change trend of the capacitance value at the time of T(N); the capacitance value C N It is collected in step (a); the capacitance value change trend ΔC N is calculated in step (b); the capacitance value C N and capacitance value change trend ΔC N are substituted into formula 6 to calculate the predicted capacitance value C N+1 . 2.根据权利要求1所述的一种基于时间序列法的电容器电容值及其变化趋势预测方法，其特征在于步骤(b-2)中rp的计算按照公式(7)：2. a kind of capacitor capacitance value and its variation trend prediction method based on time series method according to claim 1 is characterized in that the calculation of r p in step (b-2) is according to formula (7): 公式7中，rp为时间先后顺序对权值ωp的影响因素，p＝1,2,…,k；In formula 7, r p is the influence factor of time sequence on the weight ω p , p=1,2,...,k; k表示进行电容值变化趋势预测时选取的时刻数目。k represents the number of moments selected when predicting the change trend of the capacitance value. 3.根据权利要求1所述的一种基于时间序列法的电容器电容值及其变化趋势预测方法，其特征在于步骤(b-2)中rp利用层次分析法计算。3 . The method for predicting the capacitance value of a capacitor based on a time series method and its change trend according to claim 1 , wherein in step ( b -2), rp is calculated by using AHP. 4 . 4.根据权利要求1或2或3所述的一种基于时间序列法的电容器电容值及其变化趋势预测方法，其特征在于步骤(b)中k＝4。4 . The method for predicting capacitor capacitance value and its change trend based on a time series method according to claim 1 , 2 or 3 , wherein k=4 in step (b). 5 .
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