CN104933315B - A kind of method of photovoltaic generation output joint probability distribution modeling - Google Patents

A kind of method of photovoltaic generation output joint probability distribution modeling Download PDF

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CN104933315B
CN104933315B CN201510378794.XA CN201510378794A CN104933315B CN 104933315 B CN104933315 B CN 104933315B CN 201510378794 A CN201510378794 A CN 201510378794A CN 104933315 B CN104933315 B CN 104933315B
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施涛
朱凌志
王湘艳
于若英
陈宁
曲立楠
葛路明
赵亮
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State Grid Corp of China SGCC
China Electric Power Research Institute Co Ltd CEPRI
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Abstract

The present invention provides a kind of method of photovoltaic generation output joint probability distribution modeling, the described method includes：Initialize each photovoltaic plant output sample data；Sunlight irradiation degree according to where photovoltaic plant in space obeys Beta distributions within certain period, draws probabilistic model and Beta distributed constants that each photovoltaic plant is contributed；It is vectorial that the corresponding probability distribution sample space of each sampled point of each photovoltaic plant is calculated according to the probabilistic model that each photovoltaic plant is contributed and Beta distributed constants；Choose contiguous function of the polynary Standard Normal Distribution as each photovoltaic plant joint probability distribution characteristic；Based on probability distribution sample space vector, parameter identification is carried out to the related coefficient of polynary Standard Normal Distribution；The probabilistic model that photovoltaic plant is contributed is updated to the joint probability distribution model that polynary Standard Normal Distribution draws photovoltaic plant.The present invention can reflect that each photovoltaic plant is contributed and the otherness in probability distribution and consider their mutual correlations.

Description

A kind of method of photovoltaic generation output joint probability distribution modeling
Technical field
The present invention relates to a kind of method of probability distribution modeling, and in particular to a kind of photovoltaic generation output joint probability distribution The method of modeling.
Background technology
Photovoltaic generating system common at present is according to whether two classes can be divided into by being contacted with local power grid there are electric energy：Independent light Photovoltaic generating system and grid-connected photovoltaic power generation system.Angle of solar battery system refers to the power supply that load fully relies on photovoltaic battery array power supply System, the unique energy source of system are photovoltaic battery arrays by electric energy caused by illumination.Angle of solar battery system is typically provided Energy storage device, the electric energy of energy storage device storage can ensure that system runs well at night or cloudy day.Angle of solar battery system by Limited in by capacity of energy storing device, individual system installed capacity is smaller, and little Yi realizes centralization application.In order in Urban Roof Deng place large-scale application photovoltaic generation, photovoltaic generation cost is reduced, grid-connected photovoltaic power generation system is increasingly taken seriously.It is grid-connected Photovoltaic generating system refers to that load relies on the power-supply system of photovoltaic battery array and local power grid collaboration power supply.Sent out in grid-connected photovoltaic In electric system, the direct current that photovoltaic battery array produces is transformed into alternating current by gird-connected inverter, by step-up transformer and Local power grid is in parallel, on the premise of local load is met back to, excrescent electric power can be sent to local power grid.Grid-connected photovoltaic power generation System does not have energy storage device, meets workload demand by accessing the local power grid peak load synergic adjustment that disappears.Work as grid-connected photovoltaic power generation When system output power cannot meet burden requirement, required difference power is supplemented by local power grid：When grid-connected photovoltaic power generation system When system output power exceeds workload demand, unnecessary electric energy is sent back in local power grid by gird-connected inverter.Grid-connected photovoltaic is sent out Electric system is rapidly developed in recent years.
The probability statistics model that photovoltaic generation is contributed is to carry out the intermittent quantitative analysis with fluctuation of photovoltaic generation output Basis, while be also to carry out typical scene in photovoltaic power generation grid-connecting technical research to produce and definite precondition.Pin at present Description to photovoltaic generation output probabilistic statistical characteristics mainly uses single argument, single scene mode, i.e., for same geographic area Interior, the photovoltaic plant of diverse location carries out quantitative analysis using same probability statistics model and parameter, and have ignored difference Correlation in otherness of the position photovoltaic plant in model parameter, and each comfortable sequential.
The content of the invention
In order to overcome the above-mentioned deficiencies of the prior art, the present invention provides a kind of photovoltaic generation output joint probability distribution modeling Method, the present invention is in same geographic area, the photovoltaic plant of diverse location, between both having considered that each photovoltaic plant was contributed Correlation, it is further contemplated that each otherness of output probability distribution, proposes that a kind of multiple photovoltaic plant output joint probability distributions are special The modeling method of property.
In order to realize foregoing invention purpose, the present invention adopts the following technical scheme that：
A kind of method of photovoltaic generation output joint probability distribution modeling, described method includes following steps：
(1) each photovoltaic plant output sample data is initialized；
(2) the sunlight irradiation degree according to where photovoltaic plant in space obeys Beta distributions within certain period, draws The probabilistic model that each photovoltaic plant is contributed and Beta distributed constants；
(3) it is each with Beta distributed constants each photovoltaic plant to be calculated in the probabilistic model contributed according to each photovoltaic plant The corresponding probability distribution sample space vector of sampled point；
(4) contiguous function of the polynary Standard Normal Distribution as each photovoltaic plant joint probability distribution characteristic is chosen；
(5) based on probability distribution sample space vector, the related coefficient of polynary Standard Normal Distribution is carried out Parameter identification；
(6) probabilistic model that photovoltaic plant is contributed is updated to the connection that polynary Standard Normal Distribution draws photovoltaic plant Close probability Distribution Model.
Preferably, in the step (1), if [X1,…,Xi…,Xm] it is m light of diverse location in same geographic area Overhead utility is contributed sample data in same time scale, whereinN is sample number, and i represents i-th of photovoltaic plant, xinRepresent output sampled value of i-th of photovoltaic plant within n-th of period.
Preferably, in the step (2), the sunlight irradiation degree where the photovoltaic plant in space is within certain period Beta distributions are obeyed, its probability density function is as follows：
In formula, α, β be Beta distribution form parameter, rmaxFor the maximum of irradiation level, Γ () is gamma function,X is integration variable；
Light transfer characteristic based on photovoltaic generation, the output of photovoltaic generation equally obey Beta distributions：
In formula, PMContribute for photovoltaic generation, PmaxThe maximum contributed for photovoltaic generation, f (PM) it is that photovoltaic generation output is PMWhen corresponding probability density；F(PM) contribute for photovoltaic generation in 0~PMBetween probability, choose the sample number in the period According to drawing the Beta distributed constants in each photovoltaic plant period by parameter identification：
Preferably, in the step (3), the probabilistic model that each photovoltaic plant is contributed is expressed as：
In formula：XiFor the output of i-th of photovoltaic plant；UiFor the probability of i-th of photovoltaic plant output distribution；Fi() is The corresponding probability-distribution function of i-th of photovoltaic plant output, xinThe output for being i-th of photovoltaic plant within n-th of period sampling Value；uinIt is output of i-th of photovoltaic plant within n-th of period in 0~xinBetween probability.
Preferably, in the step (4), expression formula is：
C(u1 … ui … um；ρ)=Φm(u1 … ui … um；ρ) (6)
In formula, C (u1 … ui … um；ρ) it is Copula contiguous functions to be solved；Φm() is that related coefficient is ρ M members standard multiple normal distyribution function, uiFor i-th of photovoltaic plant output distribution probability.
Preferably, in the step (6), the joint probability distribution model expression of the photovoltaic plant is：
In formula：Fmx(x1 … xi … xm；ρ) represent the Joint Distribution probability that m photovoltaic plant is contributed, xiFor i-th of light The output of overhead utility, ρ are related coefficient, Fi() represents the corresponding probability-distribution function of i-th of photovoltaic plant output.
Compared with prior art, the beneficial effects of the present invention are：
The present invention provides a kind of for multiple photovoltaic plant output joint probability distribution characteristics in same geographic area Quantify modeling means, than univariate probability statistics model, can reflect difference of each photovoltaic plant output in probability distribution Property, and can consider their mutual correlations, it is that a kind of photovoltaic plant output probabilistic statistical characteristics more to become more meticulous quantify Modeling method.
Brief description of the drawings
Fig. 1 is a kind of method flow diagram of photovoltaic generation output joint probability distribution modeling provided by the invention
Embodiment
The present invention is described in further detail below in conjunction with the accompanying drawings.
As shown in Figure 1, a kind of method of photovoltaic generation output joint probability distribution modeling, this method comprises the following steps：
Step S101, each photovoltaic plant output sample data is initialized；
Step S102, the sunlight irradiation degree according to where photovoltaic plant in space obeys Beta points within certain period Cloth, draws probabilistic model and Beta distributed constants that each photovoltaic plant is contributed；
Step S103, each photovoltaic is calculated with Beta distributed constants in the probabilistic model contributed according to each photovoltaic plant The corresponding probability distribution sample space vector of each sampled point in power station；
Step S104, connection of the polynary Standard Normal Distribution as each photovoltaic plant joint probability distribution characteristic is chosen Function；
Step S105, based on probability distribution sample space vector, the phase relation to polynary Standard Normal Distribution Number carries out parameter identification；
Step S106, the probabilistic model that photovoltaic plant is contributed is updated to polynary Standard Normal Distribution and draws photovoltaic electric The joint probability distribution model stood.
Below by taking two photovoltaic plants as an example, application of the present invention in binary combination probabilistic Modeling is introduced, step is as follows：
A, two photovoltaic plant PV are assumed1,PV2It is (α that output in period t obeys parameter respectively1,β1), (α2,β2) Beta probability distribution.Then by the sequential output sample X of photovoltaic plant1,X2, photovoltaic plant PV can be obtained1,PV2Going out in period t Power distribution probability is：
In formula：x1：Photovoltaic plant PV1Output sampled value；
x2：Photovoltaic plant PV2Output sampled value；
u1：Photovoltaic plant PV1Contribute in 0~x1Between probability；
u2：Photovoltaic plant PV2Contribute in 0~x2Between probability；
F1(·)：Photovoltaic plant PV1Output probability-distribution function；
F2(·)：Photovoltaic plant PV2Output probability-distribution function；
Parameter is α1,β1Beta distribution probability density functions；
Parameter is α2,β2Beta distribution probability density functions.
Due to sample X1,X2Also corresponded in sequential, therefore, U1,U2Also corresponded in sequential.(α is taken herein1 =2.3253, β1=6.4217；α2=2.0550, β2=6.0966).
B, binary Standard Normal Distribution is chosen as the connection letter between two photovoltaic plant output probability-distribution functions Number,
Then have
In formula：u1：Photovoltaic plant PV1Contribute in 0~x1Between probability；
u2：Photovoltaic plant PV2Contribute in 0~x2Between probability；
ρ：Related coefficient
C, based on [U1,U2] sample data, parameter Estimation is carried out to binary Standard Normal Distribution, obtains ρ=0.9966
D, two photovoltaic plant PV1,PV2Corresponding joint probability distribution function in period t can be expressed as：
ρ=0.9966 in formula.
E, due toThen two photovoltaic electrics Stand PV1,PV2Sequential contribute combination (X1,X2) joint probability distribution function can be expressed as：
Finally it should be noted that：The above embodiments are merely illustrative of the technical scheme of the present invention and are not intended to be limiting thereof, to the greatest extent Pipe is described in detail the present invention with reference to above-described embodiment, those of ordinary skills in the art should understand that：Still Can be to the embodiment technical scheme is modified or replaced equivalently of the present invention, and without departing from any of spirit and scope of the invention Modification or equivalent substitution, it should all cover among scope of the presently claimed invention.

Claims (1)

  1. A kind of 1. method of photovoltaic generation output joint probability distribution modeling, it is characterised in that described method includes following steps：
    (1) each photovoltaic plant output sample data is initialized；
    (2) the sunlight irradiation degree according to where photovoltaic plant in space obeys Beta distributions within certain period, draws each light The probabilistic model that overhead utility is contributed and Beta distributed constants；
    (3) probabilistic model contributed according to each photovoltaic plant is calculated each photovoltaic plant with Beta distributed constants and respectively samples The corresponding probability distribution sample space vector of point；
    (4) contiguous function of the polynary Standard Normal Distribution as each photovoltaic plant joint probability distribution characteristic is chosen；
    (5) based on probability distribution sample space vector, parameter is carried out to the related coefficient of polynary Standard Normal Distribution Identification；
    (6) probabilistic model that photovoltaic plant is contributed is updated to polynary Standard Normal Distribution and show that the joint of photovoltaic plant is general Rate distributed model；
    In the step (1), if [X1,…,Xi…,Xm] in same geographic area, m photovoltaic plant of diverse location is same Output sample data in one time scale, whereinFor sample number, i represents i-th of photovoltaic plant, xinRepresent Output sampled value of i-th of photovoltaic plant within n-th of period；
    In the step (2), the sunlight irradiation degree where the photovoltaic plant in space obeys Beta points within certain period Cloth, its probability density function are as follows：
    <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>&amp;Gamma;</mi> <mrow> <mo>(</mo> <mi>&amp;alpha;</mi> <mo>+</mo> <mi>&amp;beta;</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>&amp;Gamma;</mi> <mrow> <mo>(</mo> <mi>&amp;alpha;</mi> <mo>)</mo> </mrow> <mi>&amp;Gamma;</mi> <mrow> <mo>(</mo> <mi>&amp;beta;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <msup> <mrow> <mo>(</mo> <mfrac> <mi>r</mi> <msub> <mi>r</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <mrow> <mi>&amp;alpha;</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mfrac> <mi>r</mi> <msub> <mi>r</mi> <mi>max</mi> </msub> </mfrac> <mo>)</mo> </mrow> <mrow> <mi>&amp;beta;</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
    In formula, α, β be Beta distribution form parameter, rmaxFor the maximum of irradiation level, Γ () is gamma function,X is integration variable；
    Light transfer characteristic based on photovoltaic generation, the output of photovoltaic generation equally obey Beta distributions：
    <mrow> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mi>M</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>&amp;Gamma;</mi> <mrow> <mo>(</mo> <mi>&amp;alpha;</mi> <mo>+</mo> <mi>&amp;beta;</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>&amp;Gamma;</mi> <mrow> <mo>(</mo> <mi>&amp;alpha;</mi> <mo>)</mo> </mrow> <mi>&amp;Gamma;</mi> <mrow> <mo>(</mo> <mi>&amp;beta;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <msup> <mrow> <mo>(</mo> <mfrac> <msub> <mi>P</mi> <mi>M</mi> </msub> <msub> <mi>P</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <mrow> <mi>&amp;alpha;</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mfrac> <msub> <mi>P</mi> <mi>M</mi> </msub> <msub> <mi>P</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <mrow> <mi>&amp;beta;</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <mi>F</mi> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mi>M</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <msub> <mi>P</mi> <mi>M</mi> </msub> </msubsup> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>x</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
    In formula, PMContribute for photovoltaic generation, PmaxThe maximum contributed for photovoltaic generation, f (PM) it is that photovoltaic generation output is PMWhen Corresponding probability density；F(PM) contribute for photovoltaic generation in 0~PMBetween probability, choose the sample data in the period, lead to Cross parameter identification and draw Beta distributed constants in each photovoltaic plant period：
    <mrow> <mi>&amp;alpha;</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>&amp;alpha;</mi> <mn>1</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;alpha;</mi> <mi>m</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>&amp;beta;</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>&amp;beta;</mi> <mn>1</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;beta;</mi> <mi>m</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
    In the step (3), the probabilistic model that each photovoltaic plant is contributed is expressed as：
    <mrow> <msub> <mi>U</mi> <mi>i</mi> </msub> <mo>=</mo> <msub> <mi>E</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>u</mi> <mrow> <mi>i</mi> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>u</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>F</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>F</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
    In formula：XiFor the output of i-th of photovoltaic plant；UiFor the probability of i-th of photovoltaic plant output distribution；Fi() is i-th The corresponding probability-distribution function of photovoltaic plant output, xinThe output sampled value for being i-th of photovoltaic plant within n-th of period；uin It is output of i-th of photovoltaic plant within n-th of period in 0~xinBetween probability；
    In the step (4), expression formula is：
    C(u1 … ui … um；ρ)=Φm(u1 … ui … um；ρ) (6)
    In formula, C (u1 … ui … um；ρ) it is Copula contiguous functions to be solved；Φm() is the m members that related coefficient is ρ Standard multiple normal distyribution function, uiFor i-th of photovoltaic plant output distribution probability；
    In the step (6), the joint probability distribution model expression of the photovoltaic plant is：
    Fmx(x1 … xi … xm；ρ)=C (u1 … ui … um；ρ)
    =Φm(u1 … ui … um；ρ) (7)
    =Φm(F1(x1) … Fi(xi) … Fm(xm)；ρ)
    In formula：Fmx(x1 … xi … xm；ρ) represent the Joint Distribution probability that m photovoltaic plant is contributed, xiFor i-th of photovoltaic electric The output stood, ρ are related coefficient, Fi() represents the corresponding probability-distribution function of i-th of photovoltaic plant output.
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