CN105975751A - Truncated versatile distribution model representing renewable energy power probability distribution - Google Patents

Abstract

The invention discloses a truncated versatile distribution model representing renewable energy power probability distribution. Compared with common normal, beta and versatile distribution in current renewable energy power representation, truncated versatile distribution has a bounded truncation characteristic that other distribution does not have. In the aspect of representing the renewable energy power distribution, the model has higher fitting precision on one hand and ensures the boundedness of a distribution function on the other hand, and a CDF (Cumulative Distribution Function) and an inverse function of the distribution function both have closed analytical expressions, so that the model is more suitable for economic dispatching of a power system using renewable energy including wind, power and the like. By comparison with fitting effects of other common distribution on actual wind power distribution of a wind power plant and actual photovoltaic power distribution of a photovoltaic power station, the advantages of a mentioned probability distribution model are verified. A method has high promotion values and good application prospects.

Description

A kind of characterize regenerative resource power probability distribution block general distributed model

Technical field

The invention belongs to operation and control of electric power system field, relate to a kind of characterize regenerative resource power probability distribution Block general distributed model.

Background technology

In recent years, the regenerative resource of China was fast-developing.In regenerative resource, wind-powered electricity generation and photovoltaic generation account for mainly Position.By in by the end of June, 2015, whole nation wind-powered electricity generation adds up grid connection capacity 105,530,000 kilowatts, occupies first place in the world.Whole world wind-power electricity generation ability Reaching 432,420,000 kilowatts in the end of the year 2015, the relatively end of the year 2014 increase by 17%, exceed nuclear energy power generation first.National Energy Board 2015 Annual data shows, by the end of the year 2015, China's photovoltaic generation adds up installed capacity 43,180,000 kilowatts, becomes whole world photovoltaic generation dress The country that machine capacity is maximum.Wherein, photovoltaic plant 37,120,000 kilowatts, distributed 6,060,000 kilowatts, annual electricity generating capacity 39200000000 kilowatt hour. Along with the large-scale development of regenerative resource, regenerative resource exerts oneself the natural quality of randomness to electric power netting safe running and scheduling Control etc. brings huge challenge.

In recent years, the probability distribution of wind power is studied by the most a large amount of scholars, and photovoltaic power probability Distribution research at present is less.Therefore this patent is mainly with wind power probability distribution as object of study, then photovoltaic power is discussed general Rate is distributed.For the stochastic problems of wind power, most efficient method is exactly as a kind of probability distribution table using wind power Show.Classical mode both domestic and external is mostly the historical data containing wind power prediction and measured value (or measurement error) to be carried out point Case, is first according to predictive value branch mailbox, measured value (or measurement error) rectangular histogram added up after branch mailbox at this in pre-measuring tank, then makes It is fitted by mathematical distribution, obtains wind power measured value (or measurement error) probability distribution of this pre-measuring tank, note herein The wind-powered electricity generation measured value (or measurement error) being distributed as under certain pre-measuring tank distribution, be essentially conditional probability distribution.General at wind-powered electricity generation Rate density sign aspect, Chinese scholars has carried out a large amount of basic research, is broadly divided into four classes.

(1) based on histogrammic wind power characterizing method.Will after predictive value branch mailbox the measured data of this case according to one Fixed group, away from making rectangular histogram, uses the actual wind power distribution that this rectangular histogram characterizes in this pre-measuring tank.This type of theoretical method On the most accurate because the rectangular histogram i.e. actual distribution of wind-powered electricity generation actual power, but there is an obvious defect in the method, i.e. counts Calculate speed issue.Rectangular histogram essentially corresponds to the probability distribution of discontinuous variable, and discrete calculation adds scheduling model The quantity of middle variable, and then reduce calculating speed, need the very fast fields such as speed that calculate to have the biggest answering in Real-Time Scheduling etc. Use limitation.The most only cannot be fitted with a certain distribution in wind-powered electricity generation probability density and not be strict with calculating speed Time, rectangular histogram just can be used to process.

(2) wind power characterizing method based on normal distribution (also referred to as Gauss distribution).Normal distribution is as a kind of classical Distribution, is widely used wind-powered electricity generation probability distribution research early stage, but the method exists a lot of open defect.Normal distribution curve is Symmetrical centered by average, in the case of actual wind power probability distribution curve is distorted, normal distribution without Method characterizes this distortion；Wind power for some time scale is distributed, the such as wind power prediction of minute level, actual wind Electrical power probability distribution curve presents spike near predictive value, and normal distribution cannot characterize this spike；Normal distribution is not Bounded is distributed, often interval beyond actual wind power when characterizing wind power, causes bigger error；Normal distribution Cumulative Distribution Function (Cumulative Distribution Function, CDF) and its inverse function do not possess Guan Bi resolution table Reach form, therefore calculate speed and be nothing like some probability distribution possessing Guan Bi parsing expression-form.

(3) wind power characterizing method based on beta distribution.In terms of up-to-date wind power probability distribution research, shellfish Tower distribution gradually replaces normal distribution.Compared to normal distribution, beta distribution possess can the considerable advantage of off-axis, i.e. its probability is close Curve can be asymmetric for degree function (Probability Density Function, PDF).Further, survey due to wind power Value interval is zero to installed capacity, therefore the independent variable bounded characteristic of beta distribution becomes the big advantage of one.But same, just it is similar to State is distributed, and the wind power for some time scale is distributed, and the such as wind power prediction of minute level, actual wind power is general Rate distribution curve presents spike near predictive value, and beta distribution cannot characterize this spike；Beta distribution CDF and its against letter Count and the most do not possess Guan Bi parsing expression-form, therefore calculating speed is nothing like some probability possessing Guan Bi parsing expression-form and divides Cloth.

(4) wind power characterizing method based on general distribution.Along with the further research of wind-powered electricity generation probability distribution problem, remove Outside above-mentioned normal state and the classical distribution of beta two kinds, doctor Zhang Zhaosui proposes a kind of brand-new distribution form, entitled general Distribution, in order to characterize wind power distribution.Being distributed compared to normal distribution and beta, general distribution curve is more flexible, and logical Fitting effect more accurately can be possessed with off-axis with distribution curve, can the distribution of the accurate various time scale of matching；More important , the CDF of general distribution and its inverse function possess Guan Bi and resolve expression-form, can be greatly improved calculating in a lot of applications Speed.But, general distribution also has certain shortcoming, the most non-bounded.When characterizing the actual distribution of some pre-measuring tank, often The same with normal distribution, probability density curve can exceed actual wind power distributed area.

Generally speaking, the conventional probability distribution of wind-powered electricity generation distribution, the fitting effect of general distribution are characterized the most both at home and abroad Being better than beta distribution, both are better than normal distribution, but are distributed compared to the beta of bounded, and general distribution exists lacking of non-bounded Fall into, constrain its further genralrlization.And in terms of actual wind-powered electricity generation prediction, wind power output predictive value is near power interval end points Data are the most more, such as, cover 46709 groups of predictions and measured value data, the wherein measured value of east certain wind energy turbine set about time a year and a half The data falling into 0-0.02p.u. installed capacity account for the 28.67% of total data.This rule directly result in pre-measuring tank near 0 reality In measured value distribution, can be higher in measured value rectangular histogram at 0, non-bounded such as now normal distribution and general distribution etc. is often distributed 0p.u. can be exceeded, cause error of fitting even scheduling error.Although therefore general distribution is better than normal state and shellfish in terms of fitting effect Tower is distributed, but the characteristic of its non-bounded constrains its application, and this patent, as background, proposes a kind of new distribution form, Fitting effect, boundedness and mathematics properties all have more outstanding effect.

Based on general distributed model, this patent proposes a kind of new distribution form, entitled blocks general distribution (Truncated Versatile distribution), this distribution inherits matching accuracy and the mathematics of general distributed model Analyticity, prior, possess the characteristic bounded that current normal state, beta and general distributed model do not possess and blocked Property, characterizing in terms of renewable energy source power distribution, especially when more measured value press close to distributed area border (0p.u. and Time 1p.u.), on the one hand ensure that the bounded of distribution, prior, the more rule of laminating renewable energy source power distribution, greatly Improve greatly fitting precision.

Summary of the invention

The present invention is directed to the defect of prior art, it is provided that a kind of for characterizing blocking of regenerative resource power probability distribution General distributed model.

The technical scheme that the present invention provides is a kind of in order to characterize renewable energy source power measured value (or measurement error) point The mathematical distribution model of cloth, it is mainly characterized by the plan that it is outstanding to regenerative resource measured power (or measurement error) rectangular histogram Close the mathematical characteristic that characteristic, boundedness and CDF and inverse function thereof are reversible.

A kind of characterize regenerative resource power probability distribution block general distributed model, it is characterised in that based on following Definition:

If random variable of continuous type X obey form parameter be α, β and γ block general distribution, then be designated as:

X～V (α, β, γ) (1)

Wherein, form parameter α, β and γ meet:

α ＞ 0, β ＞ 0 ,-∞ ＜ γ ＜+∞ (2)

The probability density function (Probability Density Function, PDF) blocking general distribution is defined as:

Wherein m, n represent standardization interval, i.e. block the interval of the general distribution strict non-zero of PDF, are characterizing wind-powered electricity generation actual measurement During value, m=0, n=1；

Block cumulative distribution function (Cumulative Distribution Function, the CDF) definition of general distribution For:

$F\left(x\right)=\left\{\begin{array}{cc}0& x<m\\ \frac{{(1+e^{-\mathrm{\&alpha;}(x-\mathrm{\&gamma;})})}^{-\mathrm{\&beta;}}-{(1+e^{-\mathrm{\&alpha;}(m-\mathrm{\&gamma;})})}^{-\mathrm{\&beta;}}}{{(1+e^{-\mathrm{\&alpha;}(n-\mathrm{\&gamma;})})}^{-\mathrm{\&beta;}}-{(1+e^{-\mathrm{\&alpha;}(m-\mathrm{\&gamma;})})}^{-\mathrm{\&beta;}}}& m\&le;x\&le;n\\ 1& x>n\end{array}\right.---\left(4\right)$

Definition generalized constant k is shown below；

K=(1+e^-α(n-γ))^-β-(1+e^-α(m-γ))^-β (5)

Wherein, 0 < k < 1；

After introducing generalized constant, formula (3) (4) can be abbreviated as respectively:

$F\left(x\right)=\left\{\begin{array}{cc}0& x<m\\ \frac{1}{k}\&CenterDot;\&lsqb;{(1+e^{-\mathrm{\&alpha;}(x-\mathrm{\&gamma;})})}^{-\mathrm{\&beta;}}-{(1+e^{-\mathrm{\&alpha;}(m-\mathrm{\&gamma;})})}^{-\mathrm{\&beta;}}\&rsqb;& m\&le;x\&le;n\\ 1& x>n\end{array}\right.---\left(7\right)$

For giving a certain confidence level c, its inverse function:

$F^{-1}\left(c\right)=\mathrm{\&gamma;}-\frac{1}{\mathrm{\&alpha;}}ln({\left(k\&CenterDot;c+{\left(1+e^{-\mathrm{\&alpha;}(m-\mathrm{\&gamma;})}\right)}^{-\mathrm{\&beta;}}\right)}^{-1/\mathrm{\&beta;}}-1)---\left(8\right)$

Parameter calculates and comprises the following steps:

Step 1: input wind energy turbine set or photovoltaic plant historical statistical data, historical statistical data includes sufficient amount of prediction Value and measured value combine；

Step 2: to every pair of data, carrying out branch mailbox according to predictive value, case number is set to M1；

Step 3: for the data of i case, carry out branch mailbox according to measured value, case number is set to M2, draws rectangular histogram；

Step 4: use and block the rectangular histogram that each the pre-measuring tank described in general fitting of distribution step 3 is corresponding, cut Three parameters of open close distribution: α, β, γ.

The present invention is distributed by the measured value of the various different distributions of analysis and summary measuring tank pre-to renewable energy source power, than The advantage relatively absorbing various distribution, proposes a kind of new probability Distribution Model characterizing the distribution of renewable energy source power, claims to block General distribution.The present invention compares and blocks general distribution and other the most conventional signs regenerative resource (as a example by wind-powered electricity generation) The distribution function of power distribution, analyzes the mathematics advantage blocking general distribution.Empirical tests, it is known that having of technical solution of the present invention Effect property, has good promotional value and application prospect.

Accompanying drawing explanation

Fig. 1 is the impact on blocking general distribution PDF curve of the alpha parameter blocking general distribution of the embodiment of the present invention.

Fig. 2 is the impact on blocking general distribution PDF curve of the β parameter blocking general distribution of the embodiment of the present invention.

Fig. 3 is the impact on blocking general distribution PDF curve of the γ parameter blocking general distribution of the embodiment of the present invention.

Fig. 4 be the Irish wind energy turbine set 0.00-0.02p.u. pre-measuring tank normal distribution of the embodiment of the present invention, beta distribution, General distribution, block general distribution for histogrammic fitting result chart.

Fig. 5 is the illiteracy east wind electric field 0.02-0.04p.u. pre-measuring tank normal distribution of the embodiment of the present invention, beta distribution, leads to With distribution, block general distribution for histogrammic fitting result chart.

Fig. 6 is the illiteracy east wind electric field 0.04-0.06p.u. pre-measuring tank normal distribution of the embodiment of the present invention, beta distribution, leads to With distribution, block general distribution for histogrammic fitting result chart.

Fig. 7 is the illiteracy east wind electric field 0.00-0.02p.u. pre-measuring tank normal distribution of the embodiment of the present invention, beta distribution, leads to With distribution, block general distribution for histogrammic fitting result chart.

Fig. 8 be the Irish wind energy turbine set 0.18-0.20p.u. pre-measuring tank normal distribution of the embodiment of the present invention, beta distribution, General distribution, block general distribution for histogrammic fitting result chart.

Fig. 9 be the Irish wind energy turbine set 0.42-0.44p.u. pre-measuring tank normal distribution of the embodiment of the present invention, beta distribution, General distribution, block general distribution for histogrammic fitting result chart.

Figure 10 is Ireland of the embodiment of the present invention and covers east wind electric field normal distribution, beta distribution, general distribution, blocks General distribution is compared for histogrammic error of fitting.

Figure 11 is Ireland of the embodiment of the present invention and covers east wind electric field normal distribution, beta distribution, general distribution, blocks General distribution Area comparison out-of-limit for histogrammic matched curve.

Figure 12 is that the Shandong photovoltaic plant 0.00-0.05p.u. pre-measuring tank normal distribution of the embodiment of the present invention, beta divide Cloth, general distribution, block general distribution for histogrammic fitting result chart.

Figure 13 is that the Shandong photovoltaic plant 0.05-0.10p.u. pre-measuring tank normal distribution of the embodiment of the present invention, beta divide Cloth, general distribution, block general distribution for histogrammic fitting result chart.

Figure 14 is that the Shandong photovoltaic plant 0.30-0.35p.u. pre-measuring tank normal distribution of the embodiment of the present invention, beta divide Cloth, general distribution, block general distribution for histogrammic fitting result chart.

Figure 15 is that the Shandong photovoltaic plant 0.70-0.75p.u. pre-measuring tank normal distribution of the embodiment of the present invention, beta divide Cloth, general distribution, block general distribution for histogrammic fitting result chart.

Figure 16 is the Shandong photovoltaic plant normal distribution of the embodiment of the present invention, beta distribution, general distribution, it is general to block Distribution is compared for histogrammic error of fitting.

Figure 17 is the Shandong photovoltaic plant normal distribution of the embodiment of the present invention, beta distribution, general distribution, it is general to block It is distributed Area comparison out-of-limit for histogrammic matched curve.

Figure 18 is the method flow schematic diagram of the present invention.

Detailed description of the invention

In order to make the purpose of the embodiment of the present invention, technical scheme, advantage become apparent from, below in conjunction with the embodiment of the present invention Technical scheme is introduced with accompanying drawing.

The technical scheme that the present invention provides is a kind of new probability distribution for matching renewable energy source power, and principle is such as Under:

By wind energy turbine set or the prediction of photovoltaic plant historical power and measured data standardization, pre-according to renewable energy source power Historical power data are carried out branch mailbox by the difference of measured value, under different capacity prediction level, utilize and block general distribution function plan Closing the distribution of measured power under different pre-measuring tank, obtain correspondence blocks general distributed constant.

1, proposition and the Parameter analysis of general distributed model are blocked.

1.1 block general distributed model.

If random variable of continuous type X obey form parameter be α, β and γ block general distribution, then be designated as:

X～V (α, β, γ) (1)

Wherein, form parameter α, β and γ meet:

α ＞ 0, β ＞ 0 ,-∞ ＜ γ ＜+∞ (2)

The probability density function (Probability Density Function, PDF) blocking general distribution is defined as:

Wherein m, n represent standardization interval, i.e. block the interval of the general distribution strict non-zero of PDF, are characterizing wind-powered electricity generation actual measurement During value, m=0, n=1.

The cumulative distribution function (CDF) blocking general distribution is defined as:

$F\left(x\right)=\left\{\begin{array}{cc}0& x<m\\ \frac{{(1+e^{-\mathrm{\&alpha;}(x-\mathrm{\&gamma;})})}^{-\mathrm{\&beta;}}-{(1+e^{-\mathrm{\&alpha;}(m-\mathrm{\&gamma;})})}^{-\mathrm{\&beta;}}}{{(1+e^{-\mathrm{\&alpha;}(n-\mathrm{\&gamma;})})}^{-\mathrm{\&beta;}}-{(1+e^{-\mathrm{\&alpha;}(m-\mathrm{\&gamma;})})}^{-\mathrm{\&beta;}}}& m\&le;x\&le;n\\ 1& x>n\end{array}\right.---\left(4\right)$

For convenience of period, definition generalized constant k is shown below, and will be described below its meaning.

K=(1+e^-α(n-γ))^-β-(1+e^-α(m-γ))^-β (5)

After introducing generalized constant, formula (3) (4) can be abbreviated as respectively:

$F\left(x\right)=\left\{\begin{array}{cc}0& x<m\\ \frac{1}{k}\&CenterDot;\&lsqb;{(1+e^{-\mathrm{\&alpha;}(x-\mathrm{\&gamma;})})}^{-\mathrm{\&beta;}}-{(1+e^{-\mathrm{\&alpha;}(m-\mathrm{\&gamma;})})}^{-\mathrm{\&beta;}}\&rsqb;& m\&le;x\&le;n\\ 1& x>n\end{array}\right.---\left(8\right)$

Can prove that 0 < k < 1 below.

For given a certain confidence level c, due to c ∈ [0,1], therefore its inverse function:

$F^{-1}\left(c\right)=\mathrm{\&gamma;}-\frac{1}{\mathrm{\&alpha;}}ln({\left(k\&CenterDot;c+{\left(1+e^{-\mathrm{\&alpha;}(m-\mathrm{\&gamma;})}\right)}^{-\mathrm{\&beta;}}\right)}^{-1/\mathrm{\&beta;}}-1)---\left(6\right)$

1.2 block general distributed constant analysis.

Taking m=0, n=1, block in general distribution three parameter, parameter γ can move horizontally distribution curve (horizontal parameters), Notice that owing to ensure that at [0,1] interior PDF integration be 1, therefore curve will occur large change, such as Fig. 1 institute when near border Show；Parameter beta can change the deflection (deflection parameter) of distribution curve, as shown in Figure 2；The height that parameter alpha can change distribution curve is (perpendicular Straight parameter), as shown in Figure 3.

Such as Fig. 3, when α takes very close to the positive number of 0, block general distribution form and level off to and be uniformly distributed.

Be uniformly distributed, the distribution of exponential, normal distribution, beta and the PDF of the common mathematical distribution such as general distribution and CDF has following mathematical property, and what this patent was proposed block general distribution is likewise supplied with these character.Wherein, the mathematics of PDF Matter includes:

(1)f(x)≥0；

(2)

(3) F (x) is continuous function；

(4) to any some x, perseverance has Pr{X=x}=0；

(5) at the continuity point of f (x), F (x) can lead, and has F ' (x)=f (x).

The mathematical property of CDF includes:

(1)0≤F(x)≤1；

(2) F (-∞)=0, F (+∞)=1；

(3) F (x) is the nondecreasing function of x；

(4) F (x) has continuity on the right, i.e.

2, general distributed model character is blocked.

2.1 block general distributed model engineering properties.

In terms of engineer applied, block general distribution and there is following engineering properties:

(1) character 1: block general distribution and can relatively accurately characterize any predicted time yardstick and any predictive value condition Under pre-measuring tank in regenerative resource power probability distribution.

Blocking general distribution to be distributed compared to normal distribution and beta, curve shape is more flexible, and fitting effect is more preferable, especially It is the spike behavior for short-term time scale, and the fitting effect blocking general distribution is better than normal distribution and beta distribution.Cut Why open close distribution has the strongest versatility, be owing to its three form parameter α, β and γ.By regulation three Form parameter, PDF and the CDF curve blocking general distribution can deform flexibly so that it is farthest approaching to reality can be again Raw energy power probability distribution, therefore block general distribution and can preferably simulate actual wind-powered electricity generation than conventional normal state and beta distribution The probability density characteristics of power.

Block general distribution compared to general distribution, in the actual measurement of the pre-measuring tank near regenerative resource power interval end points In Distribution value matching, effect is more preferable, non-in the measured value fitting of distribution of the pre-measuring tank of regenerative resource power interval end points Basically identical with general distributed effect.

(2) character 2: the independent variable span blocking general distribution is a finite interval that can adjust, and is more suitable for Characterize the renewable energy source power distribution being similarly finite interval.

For normal distribution and the distribution of general distribution this independent variable value unbounded, near renewable energy source power district Between end points pre-measuring tank measured value fitting of distribution in, PDF matched curve is often or beyond regenerative resource power interval end points. This kind of situation can bring two problems:

1) bigger error of fitting, owing to the rectangular histogram area of actual distribution is 1, therefore when PDF matched curve is beyond interval During end points, it may appear that the area PDF curve matching area less than the 1 histogrammic situation equal to 1, it is clear that now can reduce matching Effect；

2) scheduling error, when PDF matched curve beyond interval endpoint time, in Unit Combination and economic load dispatching may Obtain regenerative resource schedule power less than 0p.u. or the situation more than 1p.u., it is clear that this is unacceptable.

It should be noted that beta distribution is also a bounded distribution, but its fitting effect and mathematics analyticity are far from As blocked general distribution, after can carry out labor discussion.

(3) character 3: block general distribution CDF and inverse function has the Guan Bi expression formula (Closed Form) of parsing, With blocking the algorithm that can simplify Economic Dispatch Problem when general distribution characterizes the distribution of regenerative resource power probability.

As a example by wind-powered electricity generation, in the probabilistic model containing wind-powered electricity generation economic load dispatching, for considering the uncertainty of wind power, generally In object function, count the expectation cost underestimating and over-evaluating actual wind power output, count in constraints and go out with actual wind-powered electricity generation Power is the chance constraint of stochastic variable.In the solution procedure of some dispatching algorithms as classical in equal incremental and successive linearization etc. Typically requiring the partial derivative of calculating target function and by constraints linearisation, the partial derivative of object function and chance constraint are to close The contrafunctional expression formula of CDF or CDF in wind power probability distribution.If characterizing wind power probability with blocking general distribution Distribution, then corresponding CDF and inverse function thereof can be drawn by analytical Calculation, and then improve the efficiency of economic load dispatching algorithm.Phase Under Bi, the CDF of normal state and beta distribution does not has the quality that, the CDF of the two typically passes through artificial look-up table or passes through The numerical integration of PDF obtains, and it is quick not as good as analytic method that it calculates speed.

2.2 relations blocking general distributed model and general distributed model.

Blocking general distribution is the improvement in general distributed basis and extension, and as m and n, to take negative infinite sum respectively the most infinite Time, k=1, to block general distribution and be general distribution, the most general distribution is the special case blocking general distribution.Further, when general point The PDF curve of cloth is under meeting a certain error, as entirely fallen in the definition territory of the amount of being fitted, then k ≈ 1, blocks general distribution General distribution can be reduced to.Block the clipped form that general distribution is general distribution, be also a kind of application of truncated distribution.

As a example by PDF, formula (5) also can be write as formula form:

K=F (n)-F (m) (9)

Wherein F (m) and F (n) is the CDF being truncated the most general distribution of function, and generalized constant k is general being distributed in The area that PDF on [m, n] is surrounded.As n>m time, have 0<k<1.

Therefore formula (7) also can be write as formula form:

Formula (10) has the form of truncation funcation, is to be truncated the truncation funcation that function is general distribution.

3, block general distribution and characterize wind power probability distribution.

3.1 fitting effect compare.

(1) predictive value is near the situation 1 of regenerative resource power interval end points:

Data 1: Ireland wind energy turbine set prediction and measured value data, it was predicted that value case: 0.00-0.02p.u., survey in this case Value branch mailbox M2=100, compares normal distribution, beta distribution, general distribution, blocks general distribution and imitate for histogrammic matching Really, as Fig. 4 and Figure 10,11.

Data 2: cover east prediction and measured value data, it was predicted that value case: 0.02-0.04p.u., measured value branch mailbox M2 in this case =50, compare normal distribution, beta distribution, general distribution, block general distribution for histogrammic fitting effect, such as Fig. 5 and Figure 10,11.

Data 3: cover east prediction and measured value data, it was predicted that value case: 0.04-0.06p.u., measured value branch mailbox M2 in this case =50, compare normal distribution, beta distribution, general distribution, block general distribution for histogrammic fitting effect, such as Fig. 6 and Figure 10,11.

Predictive value is when regenerative resource power interval end points, and the actual measurement rectangular histogram near 0p.u. still has certain height Degree, when the histogram height near border is not significantly larger than other rectangular histograms, i.e. data 1-3, now beta distribution can be through Crossing (0,0) point, normal distribution and general distribution curve can be out-of-limit.From the point of view of fitting effect, compare the root-mean-square error value of Figure 10, Blocking general distributed effect best, general distribution is taken second place, and beta and normal distribution fitting effect are the most bad；From the point of view of boundedness, The out-of-limit area of relatively Figure 11, it is out-of-limit that normal distribution and general distribution all have in various degree, and blocks general distribution and beta Distribution ensure that the bounded of PDF curve.

(2) predictive value is near the situation 2 of regenerative resource power interval end points:

Data 4: cover east prediction and measured value data, it was predicted that value case: 0.00-0.02p.u., measured value branch mailbox M2 in this case =200, compare normal distribution, beta distribution, general distribution, block general distribution for histogrammic fitting effect, such as Fig. 7 and Figure 10,11.

Predictive value near regenerative resource power interval end points time, if near border histogram height be significantly larger than During other rectangular histograms, i.e. data 4, now beta is distributed and can pass through (+∞, 0) point, and normal distribution and general distribution curve can be got over Limit.From the point of view of fitting effect, comparing the root-mean-square error value of Figure 10, block general distributed effect best, general distribution is taken second place, shellfish Tower and normal distribution fitting effect are the most bad；From the point of view of boundedness, compare the out-of-limit area of Figure 11, normal distribution and general distribution All have in various degree is out-of-limit, and blocks general distribution and beta distribution ensure that the bounded of PDF curve.

(3) predictive value is not close to the situation of regenerative resource power interval end points:

Data 5: Ireland wind energy turbine set prediction and measured value data, it was predicted that value case: 0.18-0.20p.u., survey in this case Value branch mailbox M2=50, compares normal distribution, beta distribution, general distribution, blocks general distribution for histogrammic fitting effect, As Fig. 8 and Figure 10,11.

Data 6: Ireland wind energy turbine set prediction and measured value data, it was predicted that value case: 0.42-0.44p.u., survey in this case Value branch mailbox M2=100, compares normal distribution, beta distribution, general distribution, blocks general distribution and imitate for histogrammic matching Really, as Fig. 9 and Figure 10,11.

When pre-measuring tank is not close to regenerative resource power interval end points, i.e. data 5,6, from the point of view of fitting effect, comparison diagram The root-mean-square error value of 10, blocks general distributed effect best, and general distribution is taken second place, and beta and normal distribution fitting effect are Difference.

3.2 fitting effect analyses.

Predictive value is when regenerative resource power interval end points, and the actual measurement rectangular histogram near 0p.u. still has certain height Degree, compared to normal distribution and general distribution, beta is distributed some superiority of withdrawing deposit out, it is ensured that boundedness, but its fitting effect Substantially not as blocking general distribution, its reason is as follows:

Predictive value is when regenerative resource power interval end points, when beta is distributed in matching, its PDF near 0, or Converging to (0,0), such as situation 1, now the histogram height near 0 is not significantly larger than other rectangular histograms；Diffuse to (+ ∞, 0), such as situation 2, now the histogram height near 0 is significantly larger than other rectangular histograms.And it practice, near 0 straight Side's figure often its height can't be so extreme, possesses blocking general distribution and can being truncated to a conjunction at 0 of bounded truncating Suitable value, matching more accurately is fitted.On the other hand, such as Fig. 7, beta distribution is dumb from the dropping characteristic of+∞, in order to Left side the two or three case fitting effect can be made more preferable, and beta distribution occurs in that dramatic decrease, greatly reduces fitting effect.When So, it is in the nature beta distribution and blocks the mathematics difference being standardized function of general distribution, sees below discussion.

Standard beta distribution (definition territory [0,1]) PDF:

$f_{beta}\left(x\right)=\frac{x^{u-1}{(1-x)}^{v-1}}{{\&Integral;}_0^1{z}^{u-1}{(1-z)}^{v-1}dz}---\left(11\right)$

$F_{beta}\left(x\right)=\frac{{\&Integral;}_0^x{z}^{u-1}{(1-z)}^{v-1}dz}{{\&Integral;}_0^1{z}^{u-1}{(1-z)}^{v-1}dz}---\left(12\right)$

Wherein, u and v is the parameter of beta distribution, meets pass calculated as below between they and sample average μ and standard deviation sigma System:

$\left\{\begin{array}{c}u=\frac{(1-\mathrm{\&mu;})\&CenterDot;{\mathrm{\&mu;}}^2}{{\mathrm{\&sigma;}}^2}-\mathrm{\&mu;}\\ v=\frac{1-\mathrm{\&mu;}}{\mathrm{\&mu;}}\&CenterDot;u\end{array}\right.---\left(13\right)$

When using beta distribution to characterize wind power probability distribution, the way asking for beta distributed constant at present is: first Calculate meansigma methods and the standard deviation of wind-powered electricity generation measured power original data set corresponding to i-th prediction power grade, then by them Substitution formula (13).

Noticing that beta distribution form is truncation funcation form, being truncated function is x^u-1(1-x)^v-1, denominator is for being truncated letter Number is at the PDF area in definition territory, namely the CDF of right margin deducts the CDF of left margin.

Blocking general distribution and beta distribution has all carried out standardization (blocking), its expression formula is all the shape of truncated distribution Formula, difference is that its truncation funcation is different.As it was previously stated, the truncation funcation blocking general distribution is general distribution, its spirit What activity significantly larger than beta was distributed is truncated function x^u-1(1-x)^v-1.Further, general being distributed in is blocked interval endpoint and can be connected Continuous value, the truncation funcation of beta distribution can only take 0 and the most infinite two kinds of values (not considering that it is uniformly distributed form), although bounded But do not possess truncating, therefore beta fitting of distribution effect is substantially not as blocking general distribution.

When predictive value is not close to regenerative resource power interval end points, blocks general distributed effect and general distribution is basic Unanimously, block general distribution the best, as it was previously stated, fitting effect is superior to beta distribution.

Conclusion:

Owing to blocking the bounded truncating of general distribution, block general distribution compared to general distribution, close at predictive value During regenerative resource power interval end points, fitting effect is substantially dominant, it was predicted that when value is not close to regenerative resource power interval end points Basically identical, and inherit general distribution CDF and the advantage of its inverse function existence Guan Bi expression formula.Block general distribution compared to Beta is distributed, and all possesses obvious advantage under any predictive value.

Therefore compared to the most conventional normal distribution, beta distribution and general distribution, block general distribution and possess more excellent Fitting effect and mathematics advantage, be more suitable for describe regenerative resource power probability distribution.

4, block general distribution and characterize photovoltaic power probability distribution.

By national energy office data, being similar to wind-power electricity generation, China's photovoltaic generation major part at present uses centralized access Form, i.e. photovoltaic plant, research photovoltaic power probability distribution is significant.Photovoltaic power probability distribution research at present is relatively Few, it is similar to wind power, this patent use is blocked general distribution and is fitted photovoltaic power probability distribution, and compares normal state Distribution, beta distribution and the fitting effect of general distribution.

The data acquisition predictive value in Shandong photovoltaic plant in March, 2016 and measured value rolling forecast information, resolution is 15min, notes being different from wind-powered electricity generation data, and photovoltaic data only record the time information of photovoltaic predictive value non-zero a few days ago, it was predicted that value case Number M1 takes 20.

Such as Figure 12-17, compared to normal distribution, beta distribution and general distribution, block general being distributed in and characterize photovoltaic merit Rate probability distribution aspect effect is more excellent.It is noted that due to the early morning and at dusk in every day, photovoltaic power predictive value and reality Measured value is relatively low, predictive value near interval endpoint time, be easier to possess certain height near the actual measurement rectangular histogram of 0p.u., right The requirement of distributed model boundedness is higher compared to wind-powered electricity generation, and the bounded truncating advantage blocking general distribution is bigger.

Claims (1)

1. one kind characterize regenerative resource power probability distribution block general distributed model, it is characterised in that based on following fixed Justice:

If random variable of continuous type X obey form parameter be α, β and γ block general distribution, then be designated as:

X～V (α, β, γ) (1)

Wherein, form parameter α, β and γ meet:

α ＞ 0, β ＞ 0 ,-∞ ＜ γ ＜+∞ (2)

The probability density function (Probability Density Function, PDF) blocking general distribution is defined as:

Wherein m, n represent standardization interval, i.e. block the interval of the general distribution strict non-zero of PDF, when characterizing wind-powered electricity generation measured value, M=0, n=1；

The cumulative distribution function (Cumulative Distribution Function, CDF) blocking general distribution is defined as:

$F\left(x\right)=\left\{\begin{array}{cc}0& x<m\\ \frac{{(1+e^{-\mathrm{\&alpha;}(x-\mathrm{\&gamma;})})}^{-\mathrm{\&beta;}}-{(1+e^{-\mathrm{\&alpha;}(m-\mathrm{\&gamma;})})}^{-\mathrm{\&beta;}}}{{(1+e^{-\mathrm{\&alpha;}(n-\mathrm{\&gamma;})})}^{-\mathrm{\&beta;}}-{(1+e^{-\mathrm{\&alpha;}(m-\mathrm{\&gamma;})})}^{-\mathrm{\&beta;}}}& m\&le;x\&le;n\\ 1& x>n\end{array}\right.---\left(4\right)$

Definition generalized constant k is shown below；

K=(1+e^-α(n-γ))^-β-(1+e^-α(m-γ))^-β (5)

Wherein, 0 < k < 1；

After introducing generalized constant, formula (3) (4) can be abbreviated as respectively:

$F\left(x\right)=\left\{\begin{array}{cc}0& x<m\\ \frac{1}{k}\&CenterDot;\&lsqb;{(1+e^{-\mathrm{\&alpha;}(x-\mathrm{\&gamma;})})}^{-\mathrm{\&beta;}}-{(1+e^{-\mathrm{\&alpha;}(m-\mathrm{\&gamma;})})}^{-\mathrm{\&beta;}}\&rsqb;& m\&le;x\&le;n\\ 1& x>n\end{array}\right.---\left(7\right)$

For giving a certain confidence level c, its inverse function:

$F^{-1}\left(c\right)=\mathrm{\&gamma;}-\frac{1}{\mathrm{\&alpha;}}ln({\left(k\&CenterDot;c+{\left(1+e^{-\mathrm{\&alpha;}(m-\mathrm{\&gamma;})}\right)}^{-\mathrm{\&beta;}}\right)}^{-1/\mathrm{\&beta;}}-1)---\left(8\right)$

Parameter calculates and comprises the following steps:

Step 1: input wind energy turbine set or photovoltaic plant historical statistical data, historical statistical data include sufficient amount of predictive value and Measured value combines；

Step 2: to every pair of data, carrying out branch mailbox according to predictive value, case number is set to M1；

Step 3: for the data of i case, carry out branch mailbox according to measured value, case number is set to M2, draws rectangular histogram；

Step 4: use and block the rectangular histogram that each the pre-measuring tank described in general fitting of distribution step 3 is corresponding, obtains blocking logical Three parameters with distribution: α, β, γ.