CN105512492A - Probability modeling method for output power of tide flow energy electric generator - Google Patents

Abstract

The invention discloses a probability modeling method for the output power of a tide flow energy electric generator. The method comprises the steps of firstly, inputting actually-measured data of the tide flow velocity, the number of clusters and parameters of the tide flow energy electric generator with a computer through a program, and then based on the k-class mean value clustering method, obtaining the clustering center of various data so that regularity of diurnal variation of the tide flow velocity can be represented; secondly, according to the clustering center, calculating actually-measured data samples of random components of the tide flow velocity at all moments so that random volatility of the tide flow velocity can be represented; then, based on the nonparametric kernel density estimation theory, sequentially estimating probability density functions of the random components of the tide flow velocity at all the moments, and generating random samples; subsequently, according to the clustering center and the random samples of the random components of the tide flow velocity at all the moments, generating daily random samples of the tide flow velocity; finally, according to the functional relationship between the tide flow velocity and the output power of the tide flow energy electric generator, obtaining daily samples of the output power of the tide flow energy electric generator.

Description

The modelling method of probabilistic of tide current energy generated output power

Technical field

The invention belongs to the probabilistic Modeling technical field of electric power system power source output power, be specifically related to the modelling method of probabilistic of tide current energy generated output power in electric system.

Background technology

Tide current can generate electricity as a kind of exploitation of marine energy mode of technology relative maturity, obtains in recent years and pays close attention to widely and develop fast, and be more and more linked in electric system.But can not be ignored, the output power that tide current can generate electricity depends critically upon the meteorologic factors such as tide flow velocity, has stronger uncertainty, therefore, will bring profound influence after access to the planning of electric system and operation.For quantize tide current can generate electricity, economical operation reliable on power system security impact, assess energy-saving and emission-reduction effect that tide current can generate electricity and the digestion capability etc. that electric system can generate electricity to tide current, need a probabilistic Modeling difficult problem for solution tide current energy generated output power badly.

The modelling method of probabilistic of existing tide current energy generated output power, as civilian in " Probabilisticmodelingoftidalgenerationpower " in 2015 " IEEEPower & EnergySocietyGeneralMeetingProceeding ", disclosed method is: first, adopts Wakeby distribution to set up the probability model of tide flow velocity; Secondly, based on the random variation of normal distribution simulated seawater density; Finally, both are combined, and according to the funtcional relationship between tide current energy generated output power and density of sea water, tide flow velocity, the probability distribution of tide simulation stream energy generated output power.The major defect of the method is: the regularity that 1) have ignored tide current energy generator day output power.Tide is a kind of spontaneous phenomenon impact of coastland, refers to the cyclical movement that seawater produces under Between Celestial Tide-generating Forces effect.So corresponding, in one day, the change of tide flow velocity and tide current energy generated output power all have stronger regularity.Therefore, in probabilistic Modeling, need the above-mentioned regularity of accurate simulation, otherwise comparatively big error will be caused; 2) when the randomness of tide simulation stream energy generated output power, the method needs hypothesis parameter distribution (as Wakeby distribution and normal distribution), but parameter distribution choose dependence subjective experience, theoretical foundation is insufficient, the result of calculation very likely led to errors.

Summary of the invention

The object of the invention is the deficiency for existing tide current energy generated output power modelling method of probabilistic, a kind of modelling method of probabilistic of tide current energy generated output power is provided, there is the regularity accurately taking into account tide current energy generator day output power, the random variation feature of each moment output power of accurate simulation tide current energy generator, thus realize the accurate simulation of each moment output power of tide current energy generator, and then the accuracy that can improve containing tide current energy generation power system dependent probability analysis, and there is general applicability.

The technical scheme realizing the object of the invention is a kind of modelling method of probabilistic of tide current energy generated output power, utilize computing machine, pass through program, first input the parameter of the measured data of tide flow velocity, cluster numbers and tide current energy generator, the cluster centre of Various types of data is obtained again, to characterize the regularity of tide flow velocity diurnal variation based on k means clustering method; Secondly, according to cluster centre, the measured data sample of each moment tide flow velocity random component is calculated, to characterize the stochastic volatility of tide flow velocity; Then, estimate the probability density function of each moment tide flow velocity random component based on nonparametric probability theory successively, and produce random sample; Then, according to the random sample of cluster centre and each moment tide flow velocity random component, the day random sample of tide flow velocity is produced; Finally, according to the funtcional relationship between tide flow velocity and tide current energy generated output power, obtain the day sample of tide current energy generated output power.The concrete steps of described method are as follows:

(1) parameter of measured data sample and tide current energy generator is inputted

The measured data sample v in input tide flow velocity d moment of n days every days _ij, wherein the tide flow velocity measured data sample of i-th day is V _i=[v _i1, v _i2..., v _id], i=1,2 ..., n, j=1,2 ..., d, d are moment day number; Input cluster numbers k; The capacitation coefficient C of input tide current energy generator _p, density of sea water ρ, the area A that tide current energy generator blade is inswept, the incision flow velocity V of tide current energy generator _cutin, nominal flow rate V _rated, output rating P _rated.

(2) cluster centre is produced

After (1) step completes, according to the measured data of (1) step input, classify based on the day sample of k means clustering method by tide flow velocity, and obtain all kinds of cluster centres, concrete steps are as follows:

I) initial cluster center is selected

According to the measured data sample v in tide flow velocity d the moment of n days every days of (1) step input _ijand cluster numbers k, wherein i=1,2 ..., n, j=1,2 ..., d, d are moment day number; By front k day sample V ₁, V ₂..., V _kbe set to the cluster centre S of k class respectively ₁, S ₂..., S _k.Wherein, the cluster centre of h class is S _h=[s _h1, s _h2..., s _hd], wherein i=1,2 ..., n, j=1,2 ..., d, d are moment day number.

II) each day sample distance to each cluster centre is calculated

I) after step completes, according to the measured data sample v in tide flow velocity d moment of n days every days _ij(i=1,2 ..., n, j=1,2 ..., d) with k initial cluster center V ₁, V ₂..., V _k, utilize formula (1) to calculate each day sample distance to each cluster centre successively.Formula (1) is:

$D_{hi}={\[\underset{j=1}{\overset{d}{\Σ}}{(s_{hj}-v_{ij})}^2\]}^{1/2}---\left(1\right)$

In formula: D _hifor the i-th day sample V of tide flow velocity _i=[v _i1, v _i2..., v _id] to the cluster centre S of h class _h=[s _h1, s _h2..., s _hd] distance, wherein i=1,2 ..., n, h=1,2 ..., k, d are moment day number.

III) by the day sample clustering of tide flow velocity

II) after step completes, carry out cluster according to each day sample to the distance size of each cluster centre, the i-th day sample V of tide flow velocity _i=[v _i1, v _i2..., v _id], wherein i=1,2 ..., n, d are moment day number, V _idistance to each cluster centre is respectively D _1i, D _2i..., D _ki, wherein k is cluster numbers.Day sample is belonged in the classification nearest with it, works as D _cifor [D _1i, D _2i..., D _ki] in minimum value, wherein 1≤c≤k, i=1,2 ..., n, then by V _ibelong to c class; According to cluster result, the day number of samples n in statistics Various types of data _h, wherein h=1,2 ..., k.

IV) all kinds of cluster centres is recalculated

III) after step completes, utilize formula (2) to recalculate all kinds of cluster centre S _h=[s _h1, s _h2..., s _hd] (h=1,2 ..., k, j=1,2 ..., each element d), k is cluster numbers, and d is moment day number.Formula (2) is:

$s_{hj}=\frac{\underset{l=1}{\overset{n_h}{\Σ}}{v}_{lj}}{n_h}---\left(2\right)$

In formula, s _hjbe h class cluster centre S _hin a jth element, wherein j=1,2 ..., d; n _hbe the day number of samples in h class, wherein h=1,2 ..., k, j=1,2 ..., d, k are cluster numbers; v _ljbe the tide flow velocity in a jth moment in l day sample in h class, wherein l=1,2 ..., n _h, j=1,2 ..., d.

Then, turn back to Step II), so circulate, until the cluster centre that adjacent twice circulation obtains remains unchanged, jump to step (3).

(3) the day random sample of tide flow velocity is produced

(2)-III) after step completes, according to the measured data v in tide flow velocity d the integral point moment of n days every days of (1) step input _ij(i=1,2 ..., n, j=1,2 ..., cluster centre S d) calculated with (2) step _h=[s _h1, s _h2..., s _hd] (h=1,2 ..., k, j=1,2 ..., d), k is cluster numbers.Estimate the probability density function of each hour tide flow velocity random component based on nonparametric probability theory, and produce the day random sample obtaining tide flow velocity, concrete steps are as follows:

I) classification of Stochastic choice tide flow velocity measured data

According to the cluster result of (2) step, formula (3) and (4) are utilized to calculate all kinds of cumulative probabilities.Formula (3) and (4) are respectively:

$P_h=\frac{n_h}{n}---\left(3\right)$

$F_h=\underset{i=1}{\overset{h}{\Σ}}{P}_h---\left(4\right)$

In formula, n is the day sample number of tide flow velocity measured data, n _hbe the day number of samples in h class, P _hbe probability, the F of h class _hbe the cumulative probability of h class, wherein h=1,2 ..., k, k are cluster numbers.

Then, utilize computing machine, produce in [0,1] is interval and obey equally distributed random number r _p, and utilize formula (5) to select the classification of measured data.Formula (5) is:

F _h-1＜r _p≤F _h(5)

In formula, F _h-1be the cumulative probability of h-1 class, F _hit is the cumulative probability of h class.The classification h meeting condition shown in formula (5) is selected classification.

Ii) the measured data sample of each hour tide flow velocity random component is calculated

I-th) after step completes, according to the cluster centre S of h class _h=[s _h1, s _h2..., s _hd] and h class in day sample V _l=[v _l1, v _l2..., v _ld], wherein l=1,2 ..., n _h, h=1,2 ..., k, k are cluster numbers, and d is moment day number, utilize formula (6) to calculate each hour tide flow velocity random component r in h class _j(j=1,2 ..., measured data sample r d) _lj(l=1,2 ..., n _h, j=1,2 ..., d).Formula (6) is:

r _lj＝v _lj-s _hj(6)

In formula, r _ljbe a jth moment tide flow velocity random component in h class l measured data sample (l=1,2 ..., n _h, j=1,2 ..., d), s _hjbe h class cluster centre S _hin a jth element (j=1,2 ..., d), n _hbe the number of the Sino-Japan sample of h class, wherein h=1,2 ..., k _,k is cluster numbers; v _ljbe the measured data of a jth moment tide flow velocity in l day sample in h class, wherein l=1,2 ..., n _h, j=1,2 ..., d, d are moment day number.

Iii) probability density function of each moment tide flow velocity random component is estimated

I-th after i) step completes, according to each hour tide flow velocity random component r in h class _j(j=1,2 ..., measured data sample r d) _lj(l=1,2 ..., n _h, j=1,2 ..., d), utilize formula (7) to calculate each hour tide flow velocity random component r in h class successively _j(j=1,2 ..., nonparametric probability bandwidth parameter b d) _hj(j=1,2 ..., d).Formula (7) is:

b _hj＝1.06σ _jn _h ^-1/5(7)

In formula, b _hjfor the nonparametric probability bandwidth parameter of moment j tide flow velocity random component, σ _jbe in h class, the standard deviation of a jth moment tide flow velocity random component measured data sample, n _hbe the number of the Sino-Japan sample of h class, d is moment day number.

Then, each hour tide flow velocity random component r in h class is estimated successively based on nonparametric probability theory _j(j=1,2 ..., probability density function f (r d) _j), computing formula is:

$f\left(r_j\right)=\frac{1}{n_h{b}_{hj}}\underset{l=1}{\overset{n_h}{\Σ}}G\left(\frac{r_j-r_{lj}}{n_h}\right)---\left(8\right)$

In formula, r _jbe the random component of a jth moment tide flow velocity in h class, r _ljbe l measured data sample of moment j tide flow velocity random component in h class, n _hbe the number of the Sino-Japan sample of h class, b _hjbe the nonparametric probability bandwidth parameter of a jth moment tide flow velocity random component in h class, G is Standard Normal Distribution; Wherein h=1,2 ..., k, j=1,2 ..., d, l=1,2 ..., n _h, k is cluster numbers, and d is moment day number.

Iv) interval of each moment tide flow velocity random component is calculated

I-th ii) after step completes, according to moment tide flow velocity random component r each in h class _j(j=1,2 ..., measured data sample d), utilizes formula (9) and (10) to calculate its interval [a _j, b _j].Formula (9) and (10) are:

$a_j=min\{r_{1j},r_{2j},...,r_{n_{h}j}\}---\left(9\right)$

$b_j=max\{r_{1j},r_{2j},...,r_{n_{h}j}\}---\left(10\right)$

In formula, b _j, a _jbe respectively a jth moment tide flow velocity random component r in h class _j(j=1,2 ..., value upper and lower limit d); r _1j, r _2j, be respectively a jth moment tide flow velocity random component r in h class _jthe the 1st, the 2nd, n-th _hindividual measured data sample, wherein j=1,2 ..., d, d are moment day number, n _hit is the number of the Sino-Japan sample of h class.

V) the probability density function maximal value of each moment tide flow velocity random component is calculated

I-th after v) step completes, according to tide flow velocity random component r in h class _j(j=1,2 ..., measured data sample d), utilizes formula (8), calculates f (r _j) functional value f (r at each measured data place _1j), f (r _2j) ..., then, formula (11) is utilized to calculate r _jprobability density function maximal value f _rjmax.Formula (11) is:

$f_{rjmax}=max\{f\left(r_{1j}\right),f\left(r_{2j}\right),...,f\left(r_{n_{h}j}\right)\}---\left(11\right)$

In formula, r _1j, r _2j, be respectively a jth moment tide flow velocity random component r in h class _jthe the 1st, the 2nd, n-th _hindividual measured data sample, f (r _1i), f (r _2i), be respectively r _1j, r _2j, probability density function values, n _hit is the number of the Sino-Japan sample of h class.

Vi) random sample of each moment tide flow velocity random component is produced

The after v) step completes, and utilizes computing machine, produces and obey equally distributed random number R in [0,1] is interval _rj, R _pj, calculate random sample r according to formula (12) _pj.Formula (12) is:

r _pj＝R _pj(b _j-a _j)+a _j(12)

Then, r is calculated according to formula (8) _pjprobability density function values f (r _pj), wherein, j=1,2 ..., d, d are moment day number, and p is a label symbol.When meeting condition shown in formula (13), by r _pjas the random sample r of a jth moment tide flow velocity random component _sj, and make r _sj=r _pj; Otherwise, utilize computing machine, in [0,1] interval, regenerate random number R _rj, R _pj, and calculate r _pjwith f (r _pj), till the condition shown in formula (13) meets.Formula (13) is:

R _rj≤f(r _pj)/f _rjmax(13)

In formula, f _rjmaxfor r _pjprobability density function maximal value.

The random sample R of each moment tide flow velocity random component is generated successively according to formula (12) and (13) _s=[r _s1, r _s2..., r _sd], wherein s is identifier, and d is moment day number.

Vii) the day sample of tide current energy generated output power is produced

Vi) after step completes, according to the cluster centre S of h class _h=[s _h1, s _h2..., s _hd] and the random sample R of each moment tide flow velocity random component _s=[r _s1, r _s2..., r _sd], utilize formula (14), calculate the day sample of tide flow velocity.Formula (14) is:

v _sj＝s _hj+r _sj(14)

In formula, v _sjfor the random sample of a jth moment tide flow velocity, s _hjbe a jth element of h class cluster centre, r _sjfor a jth moment tide flow velocity random component random sample (j=1,2 ..., d), d is moment day number.The day random sample of tide flow velocity is V _s=[v _s1, v _s2..., v _sd].

Then, according to the day random sample V of tide flow velocity _s=[v _s1, v _s2..., v _sd], utilize formula (15) to calculate the output power of each moment tide current energy generator successively.Formula (15) is:

$P_j=\left\{\begin{array}{cc}0& 0<v_{sj}<V_{cutin}\\ 0.5C_p{\mathrm{\&rho;Av}}_{sj}^3& V_{cutin}<v_{sj}<V_{rated}\\ P_{rated}& V_{rated}<v_{sj}\end{array}\right.---\left(15\right)$

In formula, P _jfor the output power of a jth moment tide current energy generator, v _sjfor tide flow velocity day random sample V _s=[v _s1, v _s2..., v _sd] in a jth element (j=1,2 ..., d), d is moment day number, C _pfor the capacitation coefficient of tide current energy generator, ρ is density of sea water, the area that A tide current energy generator blade is inswept, V _cutin, V _rated, P _ratedbe respectively incision flow velocity, nominal flow rate, the output rating of tide current energy generator.

So far, modeling terminates, and the day sample obtaining tide current energy generated output power is P=[P ₁, P ₂..., P _d].

After the present invention adopts technique scheme, mainly contain following effect:

1, the inventive method can not only the randomness of accurate simulation tide current energy generated output power, and fully can reflect the regularity of tide current energy generator day power stage, and then can realize the accurate modeling of tide current energy generated output power.

2, the inventive method adopts k means clustering method, carries out cluster analysis, thus can obtain the regularity of tide current energy generator day power stage easily and accurately to the measured data of tide flow velocity.

3, the inventive method is based on the random component of nonparametric probability theoretical modeling each moment tide flow velocity, without any need for assumed condition, therefore, and not only high, the highly versatile of accuracy, and strong adaptability.

4, the inventive method is only according to the measured data of tide flow velocity and the parameter of tide current energy generator, by k means clustering method and nonparametric probability theory, utilize computer program just can set up the probability model of tide current energy generated output power exactly, method is simple, practical, easy to utilize.

The present invention can be widely used in the probabilistic Modeling of tide current energy generated output power in Power System Analysis, for providing basis containing the probability analysis of tide current energy generation power system, reliable basis has been laid in the digestion capability that also can generate electricity to tide current for assessment electric system and correlation analysis calculating.

Accompanying drawing explanation

Fig. 1 is the program flow chart of the inventive method;

Fig. 2 is histogram and the probability density curve figure of China X local tide flow velocity moment random component;

In figure: the histogram carving random component when curve a is the tide flow velocity obtained based on measured data, when curve b is the tide flow velocity adopting the inventive method to obtain, carve the probability density curve of random component.

Embodiment

Below in conjunction with drawings and Examples, the invention will be further described, but should not be construed the above-mentioned subject area of the present invention and be only limitted to following embodiment.Without departing from the idea case in the present invention described above, according to ordinary skill knowledge and customary means, make various replacement and change, all should be included in protection scope of the present invention.

As shown in Figure 1, the concrete steps of the modelling method of probabilistic of a kind of tide current energy generated output power in China X area are as follows:

(1) parameter of measured data sample and tide current energy generator is inputted

The measured data sample v in input China X local tide flow velocity 24 moment of 365 day every day _ij(i=1,2 ..., n, j=1,2 ..., d), n=365, d=24, wherein, the tide flow velocity measured data sample of i-th day is V _i=[v _i1, v _i2..., v _id]; Input cluster numbers k=2; The capacitation coefficient C of input tide current energy generator _p=0.5, density of sea water ρ=1025kg/m ³, area A=314m that tide current energy generator blade is inswept ², the incision flow velocity V of tide current energy generator _cutin=1.2m/s, nominal flow rate V _rated=2.5m/s, output rating P _rated=1MW.

(2) cluster centre is produced

After (1) step completes, according to the measured data of (1) step input, classify based on the day sample of K means clustering method by tide flow velocity, and obtain all kinds of cluster centres, concrete steps are as follows:

I) initial cluster center is selected

According to the measured data v in tide flow velocity d=24 the moment of n=365 days every days of (1) step input _ij(i=1,2 ..., n, j=1,2 ..., d) and cluster numbers k=2, by front k=2 day sample V ₁, V ₂be set to the cluster centre S of k=2 class respectively ₁, S ₂.Wherein, the cluster centre of h class is S _h=[s _h1, s _h2..., s _hd] (h=1,2 ..., k, j=1,2 ..., d).

Calculate result:

S ₁＝[1.0736,0.5297,0.2531,0.8835,1.3994,1.1684,0.5526,0.5670,1.5908,1.8954,1.7576,1.5457,1.1154,0.5979,0.2298,1.0341，1.6404,1.6181,1.5130,0.7427,0.4461,1.4007,2.0340,1.6853]；

S2＝[1.5560,1.0907,0.5293,0.2601,1.0937,1.3692,0.9517,0.3557,0.6195,1.4776,1.8593,1.9049,1.5432,1.1035,0.6076,0.2606,1.1614,1.8087,1.6077,1.5488,0.8914,0.5917,1.4734,2.0175]

II) each day sample distance to each cluster centre is calculated

I) after step completes, according to the measured data v in tide flow velocity d=24 moment of n=365 days every days _ij(i=1,2 ..., n, j=1,2 ..., d) with k=2 initial cluster center V ₁, V ₂, utilize formula (1) to calculate each day sample distance to each cluster centre successively.Formula (1) is:

$D_{hi}={\&lsqb;\underset{j=1}{\overset{d}{\&Sigma;}}{(s_{hj}-v_{ij})}^2\&rsqb;}^{1/2}---\left(1\right)$

In formula, D _hifor the i-th day sample V of tide flow velocity _i=[v _i1, v _i2..., v _id] to the cluster centre S of h class _h=[s _h1, s _h2..., s _hd] distance, d=24 is moment day number.

Calculate result: with i=3, h=1 for example, tide flow velocity the i-th=3 day sample to the distance D of the cluster centre of h=1 class _hi=21.9381.

III) by the day sample clustering of tide flow velocity

II) after step completes, carry out cluster according to each day sample to the distance size of each cluster centre, day sample is belonged in the classification nearest with it.With the i-th=3 of tide flow velocity the day sample V _i=[v _i1, v _i2..., v _id] (d=24 is moment day number) be example, V _idistance to each cluster centre is respectively D _1i=13.3968, D _2i=21.9381 (k=2 is cluster numbers), D _ci(c=1) be [D _1i, D _2i] in minimum value, then Vi is belonged to c=1 class; According to cluster result, the day number of samples n in statistics Various types of data _h(h=1,2 ..., k=2).

Calculate result n ₁=190, n ₂=175.

IV) all kinds of cluster centres is recalculated

III) after step completes, utilize formula (2) to recalculate all kinds of cluster centre S _h=[s _h1, s _h2..., s _hd] (h=1,2 ..., k, j=1,2 ..., each element d), k=2 is cluster numbers, and d=24 is moment day number.Formula (2) is:

$s_{hj}=\frac{\underset{l=1}{\overset{n_h}{\&Sigma;}}{v}_{lj}}{n_h}---\left(2\right)$

In formula, s _hjbe h class cluster centre S _hin a jth element (j=1,2 ..., d), n _hbe the day number of samples in h class, v _ljfor the tide flow velocity for a jth moment in l day sample in h class.

Then, turn back to Step II), so circulate, until the cluster centre that adjacent twice circulation obtains remains unchanged, jump to step (3).

Calculate result, after 12 circulations, obtain cluster centre:

S ₁＝[1.5480,1.0680,0.8909,1.2284,1.7391,1.9017,1.5854,1.0959,0.8972,1.0901,1.5455,1.8691,1.7344,1.2560,0.9197,1.0368,1.5124,1.9067,1.8123,1.3308,0.9130,0.9293,1.3486,1.8165]；

S ₂＝[1.2025,1.6996，1.8797，1.5755，1.0372，0.8476，1.1310，1.5900，1.8073，1.6053，1.1360，0.8502，1.0058，1.4762，1.8216，1.7356，1.2614，0.8626，0.9502，1.4034，1.8212，1.7748，1.3911，0.9494]

(3) the day random sample of tide flow velocity is produced

After (2) step completes, according to the measured data v in tide flow velocity d=24 the integral point moment of n=365 days every days of (1) step input _ij(i=1,2 ..., n, j=1,2 ..., cluster centre S d) calculated with (2) step _h=[s _h1, s _h2..., s _hd] (h=1,2 ..., k=2, j=1,2 ..., d), estimate the probability density function of each hour tide flow velocity random component based on nonparametric probability theory, and produce the day random sample obtaining tide flow velocity, concrete steps are as follows:

I) classification of Stochastic choice tide flow velocity measured data

According to the cluster result of (2) step, formula (3) and (4) are utilized to calculate all kinds of cumulative probabilities.Formula (3) and (4) are:

$P_h=\frac{n_h}{n}---\left(3\right)$

$F_h=\underset{i=1}{\overset{h}{\&Sigma;}}{P}_h---\left(4\right)$

In formula, n _hbe the day number of samples in h class, P _hbe probability, the F of h class _hit is the cumulative probability of h class.

Calculate result: P ₁=0.5205, P ₂=0.4795, F ₁=0.5205, F ₂=1.

Then, utilize computing machine, produce in [0,1] is interval and obey equally distributed random number r _p=0.3121, and utilize formula (5) to select the classification of measured data.Formula (5) is:

F _h-1＜r _p≤F _h(5)

In formula, F _h-1be the cumulative probability of h-1 class, F _hit is the cumulative probability of h class.The classification h meeting condition shown in formula (5) is selected classification.

Calculate result: h=1.

Ii) the measured data sample of each hour tide flow velocity random component is calculated

I-th) after step completes, according to the cluster centre S of h=1 class _h=[s _h1, s _h2..., s _hd] (j=1,2 ..., d=24) and h=1 class in day sample V _l=[v _l1, v _l2..., v _ld] (l=1,2 ..., n _h=190) formula (6), is utilized to calculate each hour tide flow velocity random component r in h class _j(j=1,2 ..., d=24) measured data sample r _lj(l=1,2 ... .n _h=190, j=1,2 ..., d=24).Formula (6) is:

r _lj＝v _lj-s _hj(6)

In formula, r _ljbe a jth moment tide flow velocity random component in h class l measured data sample (l=1,2 ..., n _h=190, j=1,2 ..., d=24), s _hjbe h class cluster centre S _hin a jth element (j=1,2 ..., d=24), n _h=190 is the number of the Sino-Japan sample of h=1 class, v _ljbe a jth moment tide flow velocity in l day sample in h class measured data (l=1,2 ..., n _h, j=1,2 ..., d), d=24 is moment day number.

Calculate result: with l=3, j=1 for example, r _lj=0.6329.

Iii) probability density function of each moment tide flow velocity random component is estimated

I-th after i) step completes, according to each hour tide flow velocity random component r in h=1 class _j(j=1,2 ..., measured data sample r d) _lj(l=1,2 ..., n _h=190, j=1,2 ..., d=24), utilize formula (7) to calculate each hour tide flow velocity random component r in h class successively _j(j=1,2 ..., d=24) nonparametric probability bandwidth parameter b _hj(j=1,2 ..., d=24).Formula (7) is:

b _hj＝1.06σ _jn _h ^-1/5(7)

In formula, b _hjfor the nonparametric probability bandwidth parameter of moment j tide flow velocity random component, σ _jin h class, the standard deviation of a jth moment tide flow velocity random component measured data sample, n _h=190 is the number of the Sino-Japan sample of h=1 class, and d=24 is moment day number.

Calculate result: b _hj=0.2342.

Then, each hour tide flow velocity random component r in h class is estimated successively based on nonparametric probability theory _j(j=1,2 ..., d=24) probability density function f (r _j), computing formula is:

$f\left(r_j\right)=\frac{1}{n_h{b}_{hj}}\underset{l=1}{\overset{n_h}{\&Sigma;}}G\left(\frac{r_j-r_{lj}}{n_h}\right)---\left(8\right)$

In formula, r _j(j=1,2 ..., d=24) be the random component of a jth moment tide flow velocity in h class, r _ljbe l measured data sample of moment j tide flow velocity random component in h class, n _hbe the number of the Sino-Japan sample of h=1 class, b _hjbe the nonparametric probability bandwidth parameter of a jth moment tide flow velocity random component in h class, G is Standard Normal Distribution.

Iv) interval of each moment tide flow velocity random component is calculated

I-th ii) after step completes, according to moment tide flow velocity random component r each in h class _j(j=1,2 ..., d=24) measured data sample, utilize formula (9) and (10) to calculate its interval [a _j, b _j].Formula (9) and (10) are:

$a_j=min\{r_{1j},r_{2j},...,r_{n_{h}j}\}---\left(9\right)$

$b_j=max\{r_{1j},r_{2j},...,r_{n_{h}j}\}---\left(10\right)$

In formula, b _j, a _jbe respectively a jth moment tide flow velocity random component r in h class _j(j=1,2 ..., d=24) value upper and lower limit; r _1j, r _2j, be respectively a jth moment tide flow velocity random component r in h class _jthe the 1st, the 2nd, n-th _h=190 measured data samples.

Calculate result: for j=1, a _j=-1.0071, b _j=1.7227.

V) the probability density function maximal value of each moment tide flow velocity random component is calculated

I-th after v) step completes, according to tide flow velocity random component r in h class _j(j=1,2 ..., d=24) measured data sample, utilize formula (8), calculate f (r _j) functional value f (r at each measured data place _1j), f (r _2j) ..., then, formula (11) is utilized to calculate r _jprobability density function maximal value f _rjmax.Formula (11) is:

$f_{rjmax}=max\{f\left(r_{1j}\right),f\left(r_{2j}\right),...,f\left(r_{n_{h}j}\right)\}---\left(11\right)$

In formula, r _1j, r _2j, be respectively a jth moment tide flow velocity random component r in h class _jthe the 1st, the 2nd, n-th _h=190 measured data samples, f (r _1i), f (r _2i), be respectively r _1j, r _2j, probability density function values.

Calculate result: for j=1, f _rjmax=0.4933.

Vi) random sample of each moment tide flow velocity random component is produced

The after v) step completes, and utilizes computing machine, produces and obey equally distributed random number R in [0,1] is interval _rj=0.2153, R _pj=0.5101, calculate random sample r according to formula (12) _pj.Formula (12) is:

r _pj＝R _pj(b _j-a _j)+a _j(12)

Then, r is calculated according to formula (8) _pjprobability density function values f (r _pj), when meeting condition shown in formula (13), by r _pj=0.3854 as the random sample r of a jth moment tide flow velocity random component _sj, and make r _sj=r _pj; Otherwise, utilize computing machine, in [0,1] interval, regenerate random number R _rj, R _pj, and calculate r _pjwith with f (r _pj), till the condition shown in formula (13) meets.Formula (13) is:

R _rj≤f(r _pj)/f _rjmax(13)

In formula, f _rjmaxfor r _pjprobability density function maximal value;

Calculate result: for j=1, r _pj=0.3854.

The random sample of each moment tide flow velocity random component is generated successively according to formula (12) and (13)

R _s=[r _s1, r _s2..., r _sd]=[-0.6688 ,-1.3291,0.4461,0.4390,1.5634 ,-0.5902,0.0738 ,-0.0170,0.1280,0.1655,0.2715,0.9338,-0.1201 ,-0.2393,0.1102 ,-0.7626,0.0861,0.5942 ,-0.4643,1.1099,-0.3094,0.4382 ,-0.0886 ,-0.6471] d=24 is moment day number.

Vii) the day sample of tide current energy generated output power is produced

Vi) after step completes, according to the cluster centre S of h=1 class _h=[s _h1, s _h2..., s _hd] and the random sample R of each moment tide flow velocity random component _s=[r _s1, r _s2..., r _sd], utilize formula (14), calculate the day sample of tide flow velocity.Formula (14) is:

v _sj＝sh _j+r _sj(14)

In formula, v _sjfor the random sample of a jth moment tide flow velocity, s _hjbe a jth element of h=1 class cluster centre, r _sjfor a jth moment tide flow velocity random component random sample (j=1,2 ..., d), d=24 is moment day number.The day random sample of tide flow velocity is V _s=[v _s1, v _s2..., v _sd].

Calculate result:

V _s＝[v _s1,v _s2,...,v _sd]＝[0.5338,0.3704,2.3259,2.0146,2.6006,0.2574,1.2048,1.5729,1.9353,1.7708,1.4076,1.7841,0.8856,1.2368,1.9318,0.9729,1.3475,1.4569,0.4858,2.5133,1.5117,2.2131,1.3025,0.3023]

Then, according to the day random sample V of tide flow velocity _s=[v _s1, v _s2..., v _sd], utilize formula (15) to calculate the output power of each moment tide current energy generator successively.Formula (15) is:

$P_j=\left\{\begin{array}{cc}0& 0<v_{sj}<V_{cutin}\\ 0.5C_p{\mathrm{\&rho;Av}}_{sj}^3& V_{cutin}<v_{sj}<V_{rated}\\ P_{rated}& V_{rated}<v_{sj}\end{array}\right.---\left(15\right)$

In formula, P _jfor the output power of a jth moment tide current energy generator, v _sjfor tide flow velocity day random sample V _s=[v _s1, v _s2..., v _sd] in a jth element (j=1,2 ..., d), d=24 is moment day number, C _p=0.5 is the capacitation coefficient of tide current energy generator, ρ=1025kg/m ³for density of sea water, A=314m ²for the area that tide current energy generator blade is inswept, V _cutin=1.2m/s, V _rated=2.5m/s, P _rated=1MW is respectively incision flow velocity, nominal flow rate, the output rating of tide current energy generator.

The day sample of tide current energy generated output power is P=[P ₁, P ₂..., P _d].

Calculate result:

P＝[P ₁,P ₂,...,P _d]＝[0,0,1,0.6579,1,0,0.1407,0.3131,0.5832,0.4468,0.2244,0.4569,0,0.1522,0.5801,0,0.1969,0.2488,0,1,0.2779,0.8721,0.1778,0]

Test effect:

To the tide current energy generator in embodiment 1 China X area, design following simulation example, the validity of checking the inventive method.

To the tide current energy generator in embodiment 1 China X area, the measured data sample v in input China X local tide flow velocity 24 moment of 365 day every day _ij(i=1,2 ..., n, j=1,2 ..., d), n=365, d=24, wherein, the tide flow velocity measured data sample of i-th day is V _i=[v _i1, v _i2..., v _id]; Input cluster numbers k=2; The capacitation coefficient C of input tide current energy generator _p=0.5, density of sea water ρ=1025kg/m ³, area A=314m that tide current energy generator blade is inswept ², the incision flow velocity V of tide current energy generator _cutin=1.2m/s, nominal flow rate V _rated=2.5m/s, output rating P _rated=1MW.The inventive method is adopted to set up the probability model of tide current energy generated output power, and random sampling.The average of each moment tide current energy generated output power is calculated respectively according to measured data and data from the sample survey, as shown in the table, and carve when drawing tide flow velocity based on measured data random component histogram, carve the probability density curve of random component when to draw tide flow velocity based on data from the sample survey, as shown in Figure 2.

From experimental result:

1. the inventive method can realize the accurate simulation of each moment output power of tide current energy generator, and accuracy is high;

2. the inventive method is based on the random component of nonparametric probability theoretical modeling each moment tide flow velocity, and without any need for assumed condition, and accuracy is high;

3. the inventive method is according to measured data, the probabilistic Modeling of tide current energy generated output power is carried out based on k average and nonparametric probability theory, without any need for assumed condition, computer program is utilized just to set up the probability model of tide current energy generated output power exactly, method is simple, practical, easy to utilize.

Claims (1)

1. the modelling method of probabilistic of a tide current energy generated output power, utilize computing machine, pass through program, first input the parameter of the measured data of tide flow velocity, cluster numbers and tide current energy generator, the cluster centre of Various types of data is obtained again, to characterize the regularity of tide flow velocity diurnal variation based on k means clustering method; Secondly, according to cluster centre, the measured data sample of each moment tide flow velocity random component is calculated, to characterize the stochastic volatility of tide flow velocity; Then, estimate the probability density function of each moment tide flow velocity random component based on nonparametric probability theory successively, and produce random sample; Then, according to the random sample of cluster centre and each moment tide flow velocity random component, the day random sample of tide flow velocity is produced; Finally, according to the funtcional relationship between tide flow velocity and tide current energy generated output power, obtain the day sample of tide current energy generated output power;

The concrete steps of described method are as follows;

(1) parameter of measured data sample and tide current energy generator is inputted;

The measured data sample v in input tide flow velocity d moment of n days every days _ij, the tide flow velocity measured data sample of i-th day is V _i=[v _i1, v _i2..., v _id], wherein i=1,2 ..., n, j=1,2 ..., d, d are moment day number; Input cluster numbers k; The capacitation coefficient C of input tide current energy generator _p; Density of sea water ρ; The area A that tide current energy generator blade is inswept; The incision flow velocity V of tide current energy generator _cutin, nominal flow rate V _rated, output rating P _rated;

(2) cluster centre is produced;

After (1) step completes, according to the measured data of (1) step input, classify based on the day sample of k means clustering method by tide flow velocity, and obtain all kinds of cluster centres, concrete steps are as follows;

I) initial cluster center is selected;

According to the measured data sample v in tide flow velocity d the moment of n days every days of (1) step input _ijand cluster numbers k, wherein i=1,2 ..., n, j=1,2 ..., d, d are moment day number; By front k day sample V ₁, V ₂..., V _kbe set to the cluster centre S of k class respectively ₁, S ₂..., S _k; Wherein, the cluster centre of h class is S _h=[s _h1, s _h2..., s _hd], wherein h=1,2 ..., k, d are moment day number;

II) each day sample distance to each cluster centre is calculated;

I) after step completes, according to the measured data sample v in tide flow velocity d moment of n days every days _ij, wherein i=1,2 ..., n, j=1,2 ..., d, d are moment day number, and k initial cluster center V ₁, V ₂..., V _k, utilize formula (1) to calculate each day sample distance to each cluster centre successively;

$D_{hi}={\&lsqb;\underset{j=1}{\overset{d}{\&Sigma;}}{(s_{hj}-v_{ij})}^2\&rsqb;}^{1/2}---\left(1\right)$

In formula, D _hifor the i-th day sample V of tide flow velocity _i=[v _i1, v _i2..., v _id] to the cluster centre S of h class _h=[s _h1, s _h2..., s _hd] distance, wherein i=1,2 ..., n, h=1,2 ..., k, d are moment day number;

III) by the day sample clustering of tide flow velocity;

II) after step completes, carry out cluster according to each day sample to the distance size of each cluster centre, the i-th day sample V of tide flow velocity _i=[v _i1, v _i2..., v _id], wherein i=1,2 ..., n, d are moment day number, V _idistance to each cluster centre is respectively D _1i, D _2i..., D _ki, wherein k is cluster numbers; Day sample is belonged in the classification nearest with it, works as D _cifor [D _1i, D _2i..., D _ki] in minimum value, wherein 1≤c≤k, i=1,2 ..., n, then by V _ibelong to c class; According to cluster result, the day number of samples n in statistics Various types of data _h, wherein h=1,2 ..., k;

IV) all kinds of cluster centres is recalculated;

III) after step completes, utilize formula (2) to recalculate all kinds of cluster centre S _h=[s _h1, s _h2..., s _hd] in each element, wherein h=1,2 ..., k, j=1,2 ..., d, k are cluster numbers, and d is moment day number;

$s_{hj}=\frac{\underset{l=1}{\overset{n_h}{\&Sigma;}}{v}_{lj}}{n_h}---\left(2\right)$

In formula, s _hjbe h class cluster centre S _hin a jth element, wherein j=1,2 ..., d; n _hbe the day number of samples in h class, wherein h=1,2 ..., k, j=1,2 ..., d, k are cluster numbers; v _ljbe the tide flow velocity in a jth moment in l day sample in h class, wherein l=1,2 ..., n _h, j=1,2 ..., d;

Then, turn back to Step II), so circulate, until the cluster centre that adjacent twice circulation obtains remains unchanged, jump to step (3);

(3) the day random sample of tide flow velocity is produced;

(2)-III) after step completes, according to the measured data v in tide flow velocity d the integral point moment of n days every days of (1) step input _ij, wherein i=1,2 ..., n, j=1,2 ..., d, and the cluster centre S that (2) step calculates _h=[s _h1, s _h2..., s _hd], wherein h=1,2 ..., k, j=1,2 ..., d, k are cluster numbers, estimate the probability density function of each hour tide flow velocity random component, and produce the day random sample obtaining tide flow velocity based on nonparametric probability theory; Concrete steps are as follows;

I) classification of Stochastic choice tide flow velocity measured data;

According to the cluster result of (2) step, formula (3) and (4) are utilized to calculate all kinds of cumulative probabilities;

$P_h=\frac{n_h}{n}---\left(3\right)$

$F_h=\underset{i=1}{\overset{h}{\&Sigma;}}{P}_h---\left(4\right)$

In formula, n is the day sample number of tide flow velocity measured data, n _hbe the day number of samples in h class, P _hbe probability, the F of h class _hbe the cumulative probability of h class, wherein h=1,2 ..., k, k are cluster numbers;

Then, utilize computing machine, produce in [0,1] is interval and obey equally distributed random number r _p, and utilize formula (5) to select the classification of measured data;

F _h-1＜r _p＜F _h(5)

In formula, F _h-1be the cumulative probability of h-1 class, F _hit is the cumulative probability of h class; The classification h meeting condition shown in formula (5) is selected classification;

Ii) the measured data sample of each hour tide flow velocity random component is calculated;

I-th) after step completes, according to the cluster centre S of h class _h=[s _h1, s _h2..., s _hd] and h class in day sample V _l=[v _l1, v _l2..., v _ld], wherein l=1,2 ..., n _h, h=1,2 ..., k, k are cluster numbers, and d is moment day number; Formula (6) is utilized to calculate each hour tide flow velocity random component r in h class _jmeasured data sample r _lj, wherein l=1,2 ..., n _h, j=1,2 ..., d, d are moment day number;

r _lj＝v _lj-s _hj(6)

In formula, r _ljbe l measured data sample of a jth moment tide flow velocity random component in h class, wherein l=1,2 ..., n _h, j=1,2 ..., d, d are moment day number; s _hjbe h class cluster centre S _hin a jth element, wherein j=1,2 ..., d; n _hbe the number of the Sino-Japan sample of h class, wherein h=1,2 ..., k, k are cluster numbers; v _ljbe the measured data of a jth moment tide flow velocity in l day sample in h class, wherein l=1,2 ..., n _h, j=1,2 ..., d;

Iii) probability density function of each moment tide flow velocity random component is estimated;

I-th after i) step completes, according to each hour tide flow velocity random component r in h class _jmeasured data sample r _lj, wherein l=1,2 ..., n _h, j=1,2 ..., d, d are moment day number; Formula (7) is utilized to calculate each hour tide flow velocity random component r in h class successively _jnonparametric probability bandwidth parameter b _hj, wherein h=1,2 ..., k, j=1,2 ..., d, k are cluster numbers;

b _hj＝1.06σ _jn _h ^-1/5(7)

In formula, σ _jbe in h class, the standard deviation of a jth moment tide flow velocity random component measured data sample, n _hbe the number of the Sino-Japan sample of h class, wherein h=1,2 ..., k, j=1,2 ..., d, k are cluster numbers, and d is moment day number;

Then, each hour tide flow velocity random component r in h class is estimated successively based on nonparametric probability theory _jprobability density function f (r _j), wherein j=1,2 ..., d, computing formula is:

$f\left(r_j\right)=\frac{1}{n_h{b}_{hj}}\underset{l=1}{\overset{n_h}{\&Sigma;}}G\left(\frac{r_j-r_{lj}}{n_h}\right)---\left(8\right)$

In formula, r _jbe the random component of a jth moment tide flow velocity in h class, r _ljbe l measured data sample of moment j tide flow velocity random component in h class, n _hbe the number of the Sino-Japan sample of h class, b _hjbe the nonparametric probability bandwidth parameter of a jth moment tide flow velocity random component in h class, G is Standard Normal Distribution; Wherein h=1,2 ..., k, j=1,2 ..., d, l=1,2 ..., n _h, k is cluster numbers, and d is moment day number;

Iv) interval of each moment tide flow velocity random component is calculated;

I-th ii) after step completes, according to moment tide flow velocity random component r each in h class _jmeasured data sample, wherein j=1,2 ..., d, d are moment day number, utilize formula (9) and (10) to calculate its interval [a _j, b _j];

$a_j=min\{r_{1j},r_{2j},...,r_{n_{h}j}\}---\left(9\right)$

$b_j=max\{r_{1j},r_{2j},...,r_{n_{h}j}\}---\left(10\right)$

In formula, b _j, a _jbe respectively a jth moment tide flow velocity random component r in h class _jvalue upper and lower limit; r _1j, r _2j, be respectively a jth moment tide flow velocity random component r in h class _jthe the 1st, the 2nd, n-th _hindividual measured data sample, wherein j=1,2 ..., d, d are moment day number, n _hit is the number of the Sino-Japan sample of h class;

V) the probability density function maximal value of each moment tide flow velocity random component is calculated;

I-th after v) step completes, according to tide flow velocity random component r in h class _jmeasured data sample, wherein j=1,2 ..., d, utilizes formula (8), calculates f (r _j) functional value f (r at each measured data place _1j), f (r _2j) ..., then, formula (11) is utilized to calculate r _jprobability density function maximal value f _rjmax;

$f_{rjmax}=max\{f\left(r_{1j}\right),f\left(r_{2j}\right),...,f\left(r_{n_{h}j}\right)\}---\left(11\right)$

In formula, r _1j, r _2j, be respectively a jth moment tide flow velocity random component r in h class _jthe the 1st, the 2nd, n-th _hindividual measured data sample, f (r _1i), f (r _2i), be respectively r _1j, r _2j, probability density function values, n _hit is the number of the Sino-Japan sample of h class;

Vi) random sample of each moment tide flow velocity random component is produced;

The after v) step completes, and utilizes computing machine, produces and obey equally distributed random number R in [0,1] is interval _rj, R _pj, calculate random sample r according to formula (12) _pj;

r _pj＝R _pj(b _j-a _j)+a _j(12)

Then, r is calculated according to formula (8) _pjprobability density function values f (r _pj), wherein j=1,2 ..., d, d are moment day number, and p is a label symbol; When meeting condition shown in formula (13), by r _pjas the random sample r of a jth moment tide flow velocity random component _sj, and make r _sj=r _pj; Otherwise, utilize computing machine, in [0,1] interval, regenerate random number R _rj, R _pj, and calculate r _pjwith f (r _pj), till the condition shown in formula (13) meets;

R _rj≤f(r _pj)/f _rjmax(13)

In formula, f _rjmaxfor r _pjprobability density function maximal value;

The random sample R of each moment tide flow velocity random component is generated successively according to formula (12) and (13) _s=[r _s1, r _s2..., r _sd], wherein s is marker character, and d is moment day number;

Vii) the day sample of tide current energy generated output power is produced;

Vi) after step completes, according to the cluster centre S of h class _h=[s _h1, s _h2..., s _hd] and the random sample R of each moment tide flow velocity random component _s=[r _s1, r _s2..., r _sd], wherein d is moment day number, utilizes formula (14), calculates the day sample of tide flow velocity;

v _sj＝s _hj+r _sj(14)

In formula, v _sjfor the random sample of a jth moment tide flow velocity, s _hjbe a jth element of h class cluster centre, r _sjfor the random sample of a jth moment tide flow velocity random component, wherein j=1,2 ..., d, d are moment day number; The day random sample V of tide flow velocity _s=[v _s1, v _s2..., v _sd];

Then, according to the day random sample V of tide flow velocity _s=[v _s1, v _s2..., v _sd], utilize formula (15) to calculate the output power of each moment tide current energy generator successively;

$P_j=\left\{\begin{array}{cc}0& 0<v_{sj}<V_{cutin}\\ 0.5C_p{\mathrm{\&rho;Av}}_{sj}^3& V_{cutin}<v_{sj}<V_{rated}\\ P_{rated}& V_{rated}<v_{sj}\end{array}\right.---\left(15\right)$

In formula, P _jfor the output power of a jth moment tide current energy generator; v _sjfor tide flow velocity day random sample V _s=[v _s1, v _s2..., v _sd] in a jth element, wherein j=1,2 ..., d, d are moment day number; C _pfor the capacitation coefficient of tide current energy generator, ρ is density of sea water, the area that A tide current energy generator blade is inswept, V _cutin, V _rated, P _ratedbe respectively incision flow velocity, nominal flow rate, the output rating of tide current energy generator;

So far modeling terminates, and the day sample of tide current energy generated output power is P=[P ₁, P ₂..., P _d], d is moment day number.