CN105975751B - Model parameter calculation method based on characterization renewable energy power probability distribution - Google Patents
Model parameter calculation method based on characterization renewable energy power probability distribution Download PDFInfo
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Abstract
The invention discloses a kind of general distributed models of truncation of characterization renewable energy power probability distribution.Compared to common normal state, beta and general distribution in current renewable energy power characterization, has other and be distributed the characteristic not having: bounded truncating.In terms of characterizing the distribution of renewable energy source power, on the one hand there is higher fitting precision, on the other hand ensure that the boundedness of distribution function, and, the CDF of its distribution function and its inverse function all have closure analytical expression, are more suitable for containing type power system of renewable energy economic load dispatchings such as wind-powered electricity generations.Relatively to demonstrate the advantage of proposed probability Distribution Model to the fitting effect of practical wind power plant wind power and photovoltaic plant photovoltaic power actual distribution with other common distributions.This method has good promotional value and application prospect.
Description
Technical field
The invention belongs to operation and control of electric power system fields, are related to a kind of for characterizing renewable energy power probability point
The general distributed model calculation method of parameters of the truncation of cloth.
Background technique
In recent years, Chinese renewable energy was fast-developing.In renewable energy, wind-powered electricity generation and photovoltaic power generation are accounted for mainly
Position.In by the end of June, 2015 by, national wind-powered electricity generation adds up 105,530,000 kilowatts of grid connection capacity, occupies first place in the world.Global wind-power electricity generation ability
Reach 432,420,000 kilowatts in the end of the year 2015, increase by 17% compared with the end of the year 2014, is for the first time more than nuclear energy power generation.National Energy Board 2015
Annual data is shown, by the end of the year 2015, China photovoltaic power generation adds up 43,180,000 kilowatts of installed capacity, becomes global photovoltaic power generation dress
The maximum country of machine capacity.Wherein, 37,120,000 kilowatts of photovoltaic plant, 6,060,000 kilowatts distributed, 39,200,000,000 kilowatt hour of annual electricity generating capacity.
With the large-scale development of renewable energy, the natural quality of renewable energy power output randomness is to electric power netting safe running and scheduling
Control etc. brings huge challenge.
In recent years, a large amount of scholar studied the probability distribution of wind power both at home and abroad, and photovoltaic power probability
Distribution is studied less at present.Therefore then this patent discusses that photovoltaic power is general mainly using wind power probability distribution as research object
Rate distribution.For the stochastic problems of wind power, most efficient method is exactly using wind power as a kind of probability distribution table
Show.Classics mode both domestic and external is mostly to be divided the historical data for containing wind power prediction and measured value (or measurement error)
Case counts measured value (or measurement error) histogram in pre- measuring tank herein first, in accordance with predicted value branch mailbox, after branch mailbox, then makes
It is fitted with mathematical distribution, obtains wind power measured value (or measurement error) probability distribution of this pre- measuring tank, pay attention to herein
Be distributed as under certain pre- measuring tank wind-powered electricity generation measured value (or measurement error) distribution, be essentially conditional probability distribution.It is general in wind-powered electricity generation
Rate density characterization aspect, domestic and foreign scholars have carried out a large amount of basic research, have been broadly divided into four classes.
(1) the wind power characterizing method based on histogram.I.e. by the measured data of the case after predicted value branch mailbox according to one
Fixed group characterizes the practical wind power in this pre- measuring tank using this histogram and is distributed away from production histogram.Such theoretical method
On it is the most accurate, because of histogram, that is, wind-powered electricity generation actual power actual distribution, but the method is counted there are an apparent defect
Calculate speed issue.Histogram essentially corresponds to the probability distribution of discrete random variable, and discrete calculation increases scheduling model
The quantity of middle variable, thereby reduces calculating speed, has very big answer in fields such as the very fast calculating speeds of the needs such as Real-Time Scheduling
Use limitation.It can not be usually only fitted with a certain distribution in wind-powered electricity generation probability density and calculating speed is not strict with
When, it just will use histogram and handled.
(2) it is based on the wind power characterizing method of normal distribution (also referred to as Gaussian Profile).Normal distribution is as a kind of classics
Distribution, is widely used, but there are many obvious shortcomings for the method early stage wind-powered electricity generation probability distribution research.Normal distribution curve is
It is symmetrical centered on mean value, in the case where practical wind power probability distribution curve is distorted, normal distribution without
Method characterizes this distortion；Wind power distribution for certain time scales, such as the wind power prediction of minute grade, practical wind
Spike is presented in electrical power probability distribution curve near predicted value, and normal distribution is unable to characterize this spike；Normal distribution is not
Bounded distribution, actual wind power section is often exceeded when characterizing wind power, causes large error；Normal distribution
Cumulative Distribution Function (Cumulative Distribution Function, CDF) and its inverse function do not have closure resolution table
Up to form, therefore calculating speed is nothing like some probability distribution for having closure parsing expression-form.
(3) the wind power characterizing method based on beta distribution.In terms of newest wind power probability distribution research, shellfish
Tower distribution gradually replaces normal distribution.Compared to normal distribution, beta distribution have can off-axis considerable advantage, i.e. its probability is close
Spending function (Probability Density Function, PDF) curve can be asymmetric.Also, since wind power is surveyed
Value section is zero to installed capacity, therefore the independent variable bounded characteristic of beta distribution becomes the big advantage of one.But it is same, it is similar to just
State distribution is distributed the wind power of certain time scales, such as the wind power prediction of minute grade, practical wind power are general
Spike is presented in rate distribution curve near predicted value, and beta distribution is unable to characterize this spike；The CDF of beta distribution and its against letter
Number does not have closure parsing expression-form still, therefore calculating speed is nothing like some probability point for having closure parsing expression-form
Cloth.
(4) based on the wind power characterizing method of general distribution.With the further research of wind-powered electricity generation probability distribution problem, remove
Above-mentioned normal state and two kinds of beta classical distributions is outer, and doctor Zhang Zhaosui proposes a kind of completely new distribution form, entitled general
Distribution, to characterize wind power distribution.It is distributed compared to normal distribution and beta, general distribution curve is more flexible, and logical
Can have more accurate fitting effect with distribution curve with off-axis, can accurately be fitted the distribution of various time scales；It is more important
, the CDF of general distribution and its inverse function have closure parsing expression-form, can greatly improve calculating in many application fields
Speed.However, general distribution also has the shortcomings that certain, i.e., non-bounded.When characterizing the actual distribution of certain pre- measuring tanks, often
As normal distribution, probability density curve can be more than practical wind power distributed area.
Generally speaking, the common probability distribution that relatively characterization wind-powered electricity generation is distributed both at home and abroad at present, the fitting effect of general distribution
It is distributed better than beta, the two is better than normal distribution, however is distributed compared to the beta of bounded, and there are non-bounded to lack for general distribution
It falls into, constrains its further genralrlization.And in terms of practical wind-powered electricity generation prediction, wind power output predicted value is close to power interval endpoint
Data are often more, such as cover 46709 groups of predictions and the actual measurement Value Data of certain eastern wind power plant about time a year and a half, wherein measured value
The data for falling into 0-0.02p.u. installed capacity account for the 28.67% of total data.This rule directly result in pre- measuring tank close to 0 reality
, can be higher in the actual measurement value histogram at 0 in measured value distribution, the non-bounded distribution such as normal distribution at this time and general distribution is often
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 distribution, but the characteristic of its non-bounded restricts its application, and this patent proposes a kind of new distribution form as background,
Fitting effect, boundedness and mathematics properties have more outstanding effect.
Based on general distributed model, this patent proposes a kind of new distribution form, the entitled general distribution of truncation
(Truncated Versatile distribution), this is distributed the fitting accuracy and mathematics for inheriting general distributed model
Analyticity, it is prior, have the characteristic that current normal state, beta and general distributed model do not have --- bounded truncation
Property, in terms of characterizing the distribution of renewable energy source power, especially when more measured value close to distributed area boundary (0p.u. and
When 1p.u.), the bounded of distribution on the one hand ensure that, it is prior, it is more bonded the rule of renewable energy source power distribution, greatly
Fitting precision is improved greatly.
Summary of the invention
The present invention in view of the drawbacks of the prior art, provides a kind of for characterizing the truncation of renewable energy power probability distribution
General distributed model.
Technical solution provided by the invention is a kind of to characterize renewable energy source power measured value (or measurement error) point
It is outstanding to renewable energy measured power (or measurement error) histogram quasi- to be mainly characterized by it for the mathematical distribution model of cloth
Close characteristic, boundedness and CDF and its reversible mathematical characteristic of inverse function.
A kind of general distributed model of truncation based on characterization renewable energy power probability distribution, which is characterized in that be based on
It is defined below:
If random variable of continuous type X obeys the general distribution of truncation that a form parameter is α, β and γ, it is denoted as:
X~V (α, β, γ) (1)
Wherein, form parameter α, β and γ meets:
α > 0, β > 0 ,-∞ < γ <+∞ (2)
The probability density function (Probability Density Function, PDF) of general distribution is truncated is defined as:
Wherein m, n represent standardization section, that is, the section of the general distribution stringent non-zero of PDF is truncated, in characterization wind-powered electricity generation actual measurement
When value, m=0, n=1；
Cumulative distribution function (Cumulative Distribution Function, the CDF) definition of general distribution is truncated
Are as follows:
Generalized constant k is defined to be 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 write a Chinese character in simplified form respectively are as follows:
For giving a certain confidence level c, inverse function:
Parameter calculate the following steps are included:
Step 1: inputting wind power plant or photovoltaic plant historical statistical data, historical statistical data include sufficient amount of prediction
Value and measured value combination；
Step 2: to each pair of data, carrying out branch mailbox according to predicted value, case number is set to M1；
Step 3: for the data of i case, carrying out branch mailbox according to measured value, case number is set to M2, draws histogram；
Step 4: using the corresponding histogram of M2 branch mailbox described in general fitting of distribution step 3 is truncated, obtaining being truncated general
Three parameters of distribution: α, β, γ.
The present invention by the various different distributions of analysis and summary to the actual measurement Distribution value of the pre- measuring tank of renewable energy source power, than
The advantages of compared with various distributions are absorbed, proposes a kind of probability Distribution Model of new characterization renewable energy source power distribution, claims truncation
General distribution.The present invention compares the general distribution of truncation and both at home and abroad other common characterizations renewable energy (by taking wind-powered electricity generation as an example)
The distribution function of power distribution, analyzes the mathematics advantage that general distribution is truncated.It is verified, it is known that technical solution of the present invention has
Effect property has good promotional value and application prospect.
Detailed description of the invention
Fig. 1 is influence of the alpha parameter of the general distribution of truncation of the embodiment of the present invention to general distribution PDF curve is truncated.
Fig. 2 is influence of the β parameter of the general distribution of truncation of the embodiment of the present invention to general distribution PDF curve is truncated.
Fig. 3 is influence of the γ parameter of the general distribution of truncation of the embodiment of the present invention to general distribution PDF curve is truncated.
Fig. 4 be the pre- measuring tank normal distribution of Irish wind power plant 0.00-0.02p.u. of the embodiment of the present invention, beta distribution,
General distribution is truncated for the fitting result chart of histogram in general distribution.
Fig. 5 is the pre- measuring tank normal distribution of illiteracy east wind electric field 0.02-0.04p.u. of the embodiment of the present invention, beta distribution, leads to
Be distributed, be truncated it is general distribution for histogram fitting result chart.
Fig. 6 is the pre- measuring tank normal distribution of illiteracy east wind electric field 0.04-0.06p.u. of the embodiment of the present invention, beta distribution, leads to
Be distributed, be truncated it is general distribution for histogram fitting result chart.
Fig. 7 is the pre- measuring tank normal distribution of illiteracy east wind electric field 0.00-0.02p.u. of the embodiment of the present invention, beta distribution, leads to
Be distributed, be truncated it is general distribution for histogram fitting result chart.
Fig. 8 be the pre- measuring tank normal distribution of Irish wind power plant 0.18-0.20p.u. of the embodiment of the present invention, beta distribution,
General distribution is truncated for the fitting result chart of histogram in general distribution.
Fig. 9 be the pre- measuring tank normal distribution of Irish wind power plant 0.42-0.44p.u. of the embodiment of the present invention, beta distribution,
General distribution is truncated for the fitting result chart of histogram in general distribution.
Figure 10 is Ireland and the illiteracy east wind electric field normal distribution, beta distribution, general distribution, truncation of the embodiment of the present invention
The error of fitting of histogram is compared in general distribution.
Figure 11 is Ireland and the illiteracy east wind electric field normal distribution, beta distribution, general distribution, truncation of the embodiment of the present invention
General distribution area out-of-limit for the matched curve of histogram compares.
Figure 12 is the pre- measuring tank normal distribution of Shandong photovoltaic plant 0.00-0.05p.u. of the embodiment of the present invention, beta point
General distribution is truncated for the fitting result chart of histogram in cloth, general distribution.
Figure 13 is the pre- measuring tank normal distribution of Shandong photovoltaic plant 0.05-0.10p.u. of the embodiment of the present invention, beta point
General distribution is truncated for the fitting result chart of histogram in cloth, general distribution.
Figure 14 is the pre- measuring tank normal distribution of Shandong photovoltaic plant 0.30-0.35p.u. of the embodiment of the present invention, beta point
General distribution is truncated for the fitting result chart of histogram in cloth, general distribution.
Figure 15 is the pre- measuring tank normal distribution of Shandong photovoltaic plant 0.70-0.75p.u. of the embodiment of the present invention, beta point
General distribution is truncated for the fitting result chart of histogram in cloth, general distribution.
Figure 16 be the Shandong photovoltaic plant normal distribution of the embodiment of the present invention, beta distribution, it is general distribution, be truncated it is general
The error of fitting of histogram is compared in distribution.
Figure 17 be the Shandong photovoltaic plant normal distribution of the embodiment of the present invention, beta distribution, it is general distribution, be truncated it is general
Area out-of-limit for the matched curve of histogram is distributed to compare.
Figure 18 is method flow schematic diagram of the invention.
Specific embodiment
In order to be more clear the purpose, technical solution, advantage of the embodiment of the present invention, below in conjunction with the embodiment of the present invention
Technical solution of the present invention is introduced with attached drawing.
Technical solution provided by the invention is a kind of for being fitted the new probability distribution of renewable energy source power, and principle is such as
Under:
The prediction of wind power plant or photovoltaic plant historical power and measured data mark are changed, it is pre- according to renewable energy source power
The difference of measured value carries out branch mailbox to historical power data, quasi- using general distribution function is truncated under different capacity prediction level
The distribution for closing measured power under different pre- measuring tanks obtains the corresponding general distribution parameter of truncation.
1, proposition and the Parameter analysis of general distributed model is truncated.
The 1.1 general distributed models of truncation.
If random variable of continuous type X obeys the general distribution of truncation that a form parameter is α, β and γ, it is denoted as:
X~V (α, β, γ) (1)
Wherein, form parameter α, β and γ meets:
α > 0, β > 0 ,-∞ < γ <+∞ (2)
The probability density function (Probability Density Function, PDF) of general distribution is truncated is defined as:
Wherein m, n represent standardization section, that is, the section of the general distribution stringent non-zero of PDF is truncated, in characterization wind-powered electricity generation actual measurement
When value, m=0, n=1.
The cumulative distribution function (CDF) of general distribution is truncated is defined as:
For convenience of period, defines generalized constant k and be shown below, 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 write a Chinese character in simplified form respectively are as follows:
It can prove that 0 < k < 1 below.
For giving a certain confidence level c, due to c ∈ [0,1], therefore its inverse function:
The general distribution parameter analysis of 1.2 truncations.
M=0, n=1 are taken, is truncated in three parameters of general distribution, parameter γ can move horizontally distribution curve (horizontal parameters),
It notices when by proximal border, due to guarantee that in [0,1] interior PDF integral be 1, therefore curve will vary widely, such as Fig. 1 institute
Show；Parameter beta can change the deviation (being biased to 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 0 positive number, general distribution form is truncated levels off to and be uniformly distributed.
Be uniformly distributed, exponential distribution, normal distribution, beta distribution and it is general distribution etc. the PDF of common mathematical distribution and
CDF has following mathematical property, and the general distribution of the truncation that this patent is proposed is likewise supplied with these properties.Wherein, the mathematics of PDF
Matter includes:
(1)f(x)≥0；
(2)
(3) F (x) is continuous function；
(4) to any point x, perseverance has Pr { X=x }=0；
(5) in the continuity point of f (x), F (x) can be led, and have 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 property is truncated.
The 2.1 general distributed model engineering properties of truncation.
In terms of engineer application, general distribution, which is truncated, has following engineering properties:
(1) property 1: general distribution, which is truncated, can relatively accurately characterize any predicted time scale and any predicted value condition
Under pre- measuring tank in renewable energy power probability distribution.
General distribution is truncated 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 that general distribution is truncated is distributed better than normal distribution and beta.It cuts
It is open close why to there is very strong versatility with distribution, to be attributed to its three form parameters α, β and γ.By adjusting three
Form parameter, PDF the and CDF curve that general distribution is truncated can be deformed flexibly, make its farthest approaching to reality can be again
Raw energy power probability distribution, therefore general distribution is truncated being capable of the practical wind-powered electricity generation of more preferable simulation than common normal state and beta distribution
The probability density characteristics of power.
General distribution is truncated compared to general distribution, in the actual measurement of the pre- measuring tank close to renewable energy power interval endpoint
Effect is more preferable in Distribution value fitting, in the measured value fitting of distribution of the pre- measuring tank of non-close renewable energy power interval endpoint
It is almost the same with general distributed effect.
(2) property 2: the independent variable value range that general distribution is truncated is a finite interval that can be adjusted, and is more suitable for
Characterization is similarly the renewable energy source power distribution of finite interval.
The distribution unbounded for normal distribution and general this independent variable value of distribution, close to renewable energy source power area
Between endpoint pre- measuring tank measured value fitting of distribution in, PDF matched curve often or exceed renewable energy power interval endpoint.
Such situation can bring two problems:
1) bigger error of fitting, since the histogram area of pictural surface of actual distribution is 1, therefore when PDF matched curve exceeds section
When endpoint, it may appear that PDF curve matching area of the area less than 1 is equal to the case where 1 histogram, it is clear that can reduce fitting at this time
Effect；
2) scheduling error, when PDF matched curve exceed interval endpoint when, in Unit Combination and economic load dispatching may
Obtain the case where renewable energy schedule power is less than 0p.u. or greater than 1p.u., it is clear that this is unacceptable.
It is worth noting that, beta distribution is also a bounded distribution, but its fitting effect and mathematics analyticity are far from
General distribution is such as truncated, behind will do it detailed analysis discussion.
(3) property 3: the general distribution CDF of truncation and its inverse function have the closure expression formula (Closed Form) parsed,
The algorithm that can simplify Economic Dispatch Problem when the distribution of renewable energy power probability is characterized with general be distributed is truncated.
By taking wind-powered electricity generation as an example, in the probabilistic model of the economic load dispatching containing wind-powered electricity generation, for consider wind power uncertainty, usually
It is included in the expectation cost for underestimating and over-evaluating practical wind power output in objective function, is included in constraint condition and is gone out with practical wind-powered electricity generation
Power is the chance constraint of stochastic variable.In some such as equal incrementals and the solution procedure of the classical dispatching algorithm of successive linearization
It is generally necessary to the partial derivative of calculating target function and linearize constraint condition, the partial derivative and chance constraint of objective function are to close
In the contrafunctional expression formula of CDF or CDF of wind power probability distribution.If characterizing wind power probability with general distribution is truncated
Distribution, then corresponding CDF and its inverse function can be obtained by analytical Calculation, and then improve the efficiency of economic load dispatching algorithm.Phase
Than under, the CDF of normal state and beta distribution does not have such property, and the CDF of the two generally passes through artificial look-up table or passes through
The numerical integration of PDF obtains, and calculating speed is quick not as good as analytic method.
The relationship of 2.2 truncation general distributed models and general distributed model.
It is improvement and extension in general distributed basis that general distribution, which is truncated, when m and n takes negative infinite sum just infinite respectively
When, k=1, it is general distribution that general distribution, which is truncated, i.e., general distribution is the special case that general distribution is truncated.Also, work as general point
The PDF curve of cloth is in the case where meeting a certain error, and in the domain that such as entirely falls in the amount of being fitted, then k ≈ 1, is truncated general distribution
It can be reduced to general distribution.It is the clipped form of general distribution and a kind of application of truncated distribution that general distribution, which is truncated,.
By taking PDF as an example, formula (5) can also be write as formula form:
K=F (n)-F (m) (9)
Wherein F (m) and F (n) is the CDF for being truncated the i.e. general distribution of function, and generalized constant k is general is distributed in
The area that PDF on [m, n] is surrounded.As n>m, there is 0<k<1.
Therefore formula (7) can also 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, general distribution is truncated and characterizes wind power probability distribution.
3.1 fitting effects compare.
(1) the case where predicted value is close to renewable energy power interval endpoint 1:
Data 1: Irish wind-powered electricity generation field prediction and actual measurement Value Data, predicted value case: 0.00-0.02p.u. is surveyed in this case
It is worth branch mailbox M2=100, compares normal distribution, beta distribution, general distribution, the fitting effect that general distribution is truncated for histogram
Fruit, such as Fig. 4 and Figure 10,11.
Data 2: covering east prediction and survey Value Data, predicted value case: 0.02-0.04p.u., measured value branch mailbox M2 in this case
=50, compare normal distribution, beta distribution, general distribution, general distribution be truncated for the fitting effect of histogram, such as Fig. 5 and
Figure 10,11.
Data 3: covering east prediction and survey Value Data, predicted value case: 0.04-0.06p.u., measured value branch mailbox M2 in this case
=50, compare normal distribution, beta distribution, general distribution, general distribution be truncated for the fitting effect of histogram, such as Fig. 6 and
Figure 10,11.
When predicted value is close to renewable energy power interval endpoint, the actual measurement histogram close to 0p.u. still has certain height
Degree, when the histogram height near proximal border is not significantly larger than other histograms, i.e. data 1-3, beta distribution at this time can be through
(0,0) point is crossed, 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,
It is best that general distributed effect is truncated, general distribution is taken second place, and beta and normal distribution fitting effect are bad；From the point of view of boundedness,
Compare the out-of-limit area of Figure 11, normal distribution and general distribution have different degrees of out-of-limit, and general distribution and beta are truncated
Distribution ensure that the bounded of PDF curve.
(2) the case where predicted value is close to renewable energy power interval endpoint 2:
Data 4: covering east prediction and survey Value Data, predicted value case: 0.00-0.02p.u., measured value branch mailbox M2 in this case
=200, compare normal distribution, beta distribution, general distribution, general distribution be truncated for the fitting effect of histogram, such as Fig. 7 and
Figure 10,11.
When predicted value is close to renewable energy power interval endpoint, if the histogram height near proximal border is significantly larger than
When other histograms, i.e., data 4, at this time beta distribution 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, compare the root-mean-square error value of Figure 10, is truncated that general distributed effect is best, and general distribution is taken second place, shellfish
Tower and normal distribution fitting effect are bad；From the point of view of boundedness, compare the out-of-limit area of Figure 11, normal distribution and general distribution
Have different degrees of out-of-limit, and general distribution is truncated and beta distribution ensure that the bounded of PDF curve.
(3) the case where predicted value is not close to renewable energy power interval endpoint:
Data 5: Irish wind-powered electricity generation field prediction and actual measurement Value Data, predicted value case: 0.18-0.20p.u. is surveyed in this case
It is worth branch mailbox M2=50, compares normal distribution, beta distribution, general distribution, the general fitting effect being distributed for histogram is truncated,
Such as Fig. 8 and Figure 10,11.
Data 6: Irish wind-powered electricity generation field prediction and actual measurement Value Data, predicted value case: 0.42-0.44p.u. is surveyed in this case
It is worth branch mailbox M2=100, compares normal distribution, beta distribution, general distribution, the fitting effect that general distribution is truncated for histogram
Fruit, such as Fig. 9 and Figure 10,11.
When pre- measuring tank is not close to renewable energy power interval endpoint, i.e. data 5,6 from the point of view of fitting effect, compare figure
10 root-mean-square error value, is truncated that general distributed effect is best, and general distribution is taken second place, and beta and normal distribution fitting effect are most
Difference.
The analysis of 3.2 fitting effects.
When predicted value is close to renewable energy power interval endpoint, the actual measurement histogram close to 0p.u. still has certain height
Degree, compared to normal distribution and general distribution, beta is distributed some superiority of withdrawing deposit out, ensure that boundedness, but its fitting effect
It is obvious to be not so good as that general distribution is truncated, the reason is as follows that:
When predicted value is close to renewable energy power interval endpoint, when beta is distributed in fitting, PDF near 0 or
(0,0) is converged to, such as situation 1, the histogram height near 0 is not significantly larger than other histograms at this time；Diffuse to (+
∞, 0), such as situation 2, the histogram height near 0 is significantly larger than other histograms at this time.And in fact, near 0 it is straight
Often its height can't be so extreme for side's figure, and the general distribution of truncation for having bounded truncating can be truncated to a conjunction at 0
Suitable value, more accurately fitting is fitted.On the other hand, the dropping characteristic of such as Fig. 7, beta distribution from+∞ are not flexible, in order to
The 2nd No. three case fitting effect in left side can be made more preferable, dramatic decrease occurs in beta distribution, greatly reduces fitting effect.When
So, it is in the nature beta distribution and the mathematics difference for being standardized function that general distribution is truncated, sees below discussion.
Standard beta is distributed (domain [0,1]) PDF:
Wherein, u and v is the parameter of beta distribution, they meet following calculate between sample average μ and standard deviation sigma and close
System:
When using beta distribution characterization wind power probability distribution, the way for seeking beta distribution parameter at present is: first
Calculate the average and standard deviation of the corresponding wind-powered electricity generation measured power original data set of i-th of prediction power grade, then by they
Substitution formula (13).
Notice that beta distribution form is truncation funcation form, being truncated function is xu-1(1-x)v-1, denominator is to be truncated letter
Number subtracts the CDF of left margin in the PDF area of domain namely the CDF of right margin.
General distribution is truncated and beta distribution is all standardized (truncation), expression formula is all the shape of truncated distribution
Formula, the difference is that its truncation funcation is different.As previously mentioned, the truncation funcation that general distribution is truncated is general distribution, spirit
Activity significantly larger than beta distribution is truncated function xu-1(1-x)v-1.Also, the general truncation interval endpoint that is distributed in can connect
The truncation funcation of continuous value, beta distribution can only take 0 and just infinite two kinds of values (not considering that it is uniformly distributed form), although bounded
But do not have truncating, therefore beta fitting of distribution effect is obviously not so good as that general distribution is truncated.
When predicted value is not close to renewable energy power interval endpoint, general distributed effect is truncated and general distribution is basic
Unanimously, it is slightly good that general distribution is truncated, as previously mentioned, fitting effect is superior to beta distribution.
Conclusion:
Since the bounded truncating of general distribution is truncated, the general distribution of truncation is close in predicted value compared to general distribution
Fitting effect is obviously dominant when renewable energy power interval endpoint, when predicted value is not close to renewable energy power interval endpoint
It is almost the same, and general distribution CDF and its inverse function are inherited in the presence of the advantage of closure expression formula.Be truncated it is general distribution compared to
Beta distribution, all has apparent advantage under any predicted value.
Therefore compared to currently used normal distribution, beta distribution and general distribution, the general distribution of truncation has more excellent
Fitting effect and mathematics advantage, be more suitable for describe renewable energy power probability distribution.
4, general distribution is truncated and characterizes photovoltaic power probability distribution.
By national energy office data, it is similar to wind-power electricity generation, China's photovoltaic power generation is at present largely using centralization access
Form, i.e. photovoltaic plant, research photovoltaic power probability distribution are of great significance.Photovoltaic power probability distribution research at present compared with
It is few, it is similar to wind power, this patent is fitted photovoltaic power probability distribution using general distribution is truncated, and compares normal state
The fitting effect of distribution, beta distribution and general distribution.
Data use the predicted value in Shandong photovoltaic plant in March, 2016 and measured value rolling forecast information, resolution ratio are
15min pays attention to being different from wind-powered electricity generation data, information at the time of photovoltaic data only record photovoltaic predicted value non-zero a few days ago, predicted value case
Number M1 takes 20.
As Figure 12-17 is truncated general be distributed in and characterizes photovoltaic function compared to normal distribution, beta distribution and general distribution
Effect is more excellent in terms of rate probability distribution.It is noted that due in daily early morning and dusk, photovoltaic power predicted value and reality
Measured value is lower, and when predicted value is close to interval endpoint, the actual measurement histogram close to 0p.u. is easier the height for having certain, right
The requirement of distributed model boundedness is higher compared to wind-powered electricity generation, and the bounded truncation sexual clorminance that general distribution is truncated is bigger.
Claims (1)
1. the model parameter calculation method based on characterization renewable energy power probability distribution, which is characterized in that based on following fixed
Justice:
If random variable of continuous type X obeys the general distribution of truncation that a form parameter is α, β and γ, it is denoted as:
X~V (α, β, γ) (1)
Wherein, form parameter α, β and γ meets:
α > 0, β > 0 ,-∞ < γ <+∞ (2)
The probability density function (Probability Density Function, PDF) of general distribution is truncated is defined as:
Wherein m, n represent standardization section, that is, the section of the general distribution stringent non-zero of PDF is truncated, when characterizing wind-powered electricity generation measured value,
M=0, n=1；
The cumulative distribution function (Cumulative Distribution Function, CDF) of general distribution is truncated is defined as:
Generalized constant k is defined to be 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 write a Chinese character in simplified form respectively are as follows:
For giving a certain confidence level c, inverse function:
Parameter calculate the following steps are included:
Step 1: input wind power plant or photovoltaic plant historical statistical data, historical statistical data include sufficient amount of predicted value and
Measured value combination；
Step 2: to each pair of data, carrying out branch mailbox according to predicted value, case number is set to M1；
Step 3: for the data of i case, carrying out branch mailbox according to measured value, case number is set to M2, draws histogram；
Step 4: using the corresponding histogram of M2 branch mailbox described in general fitting of distribution step 3 is truncated, obtaining being truncated general point
Three parameters of cloth: α, β, γ.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| 计及风电功率不确定性的经济调度问题求解方法;张昭遂 等;《电力系统自动化》;20111125;第35卷(第22期);第125-130页 |
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