CN105846425A - Economic dispatching method based on general wind power forecasting error model - Google Patents

Abstract

The invention discloses an economic dispatching method based on a general wind power forecasting error model. General distribution is employed for fitting of PDF and CDF of practical wind power powers on different wind power forecasting intervals, the method is relatively suitable for wind power forecasting error modeling at any time scale and any amplitude, the model fitting precision is higher than conventional Gauss distribution and beta distribution, moreover, an improved linear sequence algorithm taking consideration of wind power forecasting nondeterminacy is employed and provides new thinking for calculating an economic dispatching problem containing wind power field nondeterminacy, as the general distribution CDF and the corresponding inverse function have specific analysis expressions, a general wind power forecasting model is employed to make differential operation have the specific analysis expression, and difficulty in solving an economic dispatching problem containing undetermined wind power access is solved.

Description

A kind of economic load dispatching method based on general wind-powered electricity generation forecast error model

Technical field

The present invention relates to the field of new energy generation of power system, be specifically related to one and predict based on general wind-powered electricity generation The economic load dispatching method of error model.

Background technology

Owing to being affected by factors such as natural characteristic, geographical environment, wind energy turbine set self-conditions, wind power output has There is a stochastic volatility, and this wind-powered electricity generation basic reason on accessing electrical network and produce impact just.Wind power prediction (wind power forecasting, WPF) as ensure power grid security, improve wind-powered electricity generation benefit important tool, Obtain studying widely and applying.It is upper that wind power prediction by mistake extent and distribution influence needed for system Adjust/lower the discharge and recharge plan etc. of energy-accumulating power station in spare capacity, system, for operation of power networks safety, Economy has great significance.

Conventional wind-powered electricity generation Predicting Technique is broadly divided into physical method and statistical method two class.Physical method passes through Use numerical weather forecast (numerical weather prediction, NWP) at the model of different spaces span (global models, regional model etc.) obtains the weather condition of wind energy turbine set region；Again by terrain analysis, The method such as wake analysis and spatial coherence obtains wind energy turbine set periphery and the relevant weather number of internal minute yardstick According to, such as wind speed, wind direction, temperature, atmospheric density etc.；The power finally combining wind energy turbine set or Wind turbines is special Linearity curve obtains the power prediction value of correspondence.The method is generally used for the short-term forecast of a day to a week.System Meter method be with two groups of sequences (NWP provide forecasting wind speed time series and wind energy turbine set actual exert oneself go through History measures time series) based on, by using different statistical models, such as neutral net, support vector Machine, kernel regression etc. are trained, and obtain the wind power value of prediction time, are generally used for 1h to 12 The ultra-short term prediction of h.Both Forecasting Methodologies are combined by the wind-powered electricity generation forecasting software of current practice mostly Come, to obtain predicting the outcome and more preferable precision of prediction of different time span.Although wind power prediction warp Cross research and practice achieves bigger progress, but its forecast error is the biggest.As a example by predicting a few days ago, Average absolute percent error (the mean of the actual wind-powered electricity generation forecasting software put into commercial operation in global range Absolute percentage error, MAPE) it is about 14%～20%.Divide in the trend considering wind power integration In the problems such as analysis, Unit Combination, economic load dispatching, the order of accuarcy that wind power prediction error describes can be to excellent Change result and produce significant impact.Actual wind-powered electricity generation forecast error a few days ago presents bigger kurtosis and the degree of bias, makes Bigger error can be produced with normal distribution description, therefore have scholar to propose new error distribution.Have document with Persistence model (persistence model) predicts the outcome as reference, proposition use beta fitting of distribution prediction mistake Difference, and the distributed constant of each wind speed section is fitted；Document is had to propose to use Discrete Distribution and continuous function The mode combined describes forecast error；Document is had to establish with present period actual measurement wind speed and subsequent period pre- Survey the prediction error probability statistics model that wind speed is combination condition, have employed the tabular form method of discrete probabilistic.

Summary of the invention

Goal of the invention: the defect existed for above-mentioned prior art, it is desirable to provide one is based on general The economic load dispatching method of wind-powered electricity generation forecast error model.

Technical scheme: a kind of economic load dispatching method based on general wind-powered electricity generation forecast error model, including walking as follows Rapid:

S1: obtained wind-powered electricity generation forecasting sequence by wind-powered electricity generation prediction algorithm, and it is pre-to be divided into uniform wind power Survey interval；

S2: determine the form parameter of general distribution on each wind-powered electricity generation forecast interval, sets up the logical of wind-powered electricity generation prediction Use distributed model；

The fitting precision of the general distributed model of S3: quantitative analysis, sets up corresponding forecast error evaluation index；

S4: set up and consider wind-powered electricity generation probabilistic economic load dispatching model；

S5: according to the general distributed model of wind-powered electricity generation prediction, obtain corresponding CDF and inverse function thereof；Obtain again The linear order algorithm considering wind-powered electricity generation uncertainty in traffic improved；

S6: obtain system wind energy turbine set and the planned dispatching power of conventional power plant under different wind-powered electricity generation predictive value.

Further, the partition process that wind power prediction described in step S1 is interval specifically includes:

Wind-powered electricity generation forecasting sequence is normalized and is transformed on interval [0,1], be divided into M uniformly interval [0,1/M], [1/M, 2/M] ..., [(M-1)/M, 1], each length of an interval degree is 1/M, interval m I.e. m=1,2 ..., M, corresponding prediction power bracket is [(m-1)/M, m/M]；In each moment, Prediction power sequence matches one by one with actual wind power output power, for each predictive value in interval m, all There is an actual value corresponding；Thus obtain the one group actual merit corresponding with each predictive value in interval m Rate point；M is the integer defined according to the scale of historical data by user.

Further, M=25.

Further, set up described in step S2 wind-powered electricity generation prediction general distributed model particularly as follows:

By discrete probability density rectangular histogram and the cumulative distribution table of the actual power point of m interval in S1, use Method of least square determines three form parameters of general distributed model；The general profile shape parameter in each interval Different, M wind-powered electricity generation forecast interval there are M PDF and CDF with general fitting of distribution；Logical With PDF and CDF of distributed model respectively as shown in formula (1), formula (2):

$f\left(x\right|\mathrm{\α},\mathrm{\β},\mathrm{\γ})=\frac{{\mathrm{\α\βe}}^{-\mathrm{\α}(x-\mathrm{\γ})}}{{(1+e^{-\mathrm{\α}(x-\mathrm{\γ})})}^{\mathrm{\β}+1}}---\left(1\right)$

F (x | α, β, γ)=(1+e^-α(x-γ))^-β (2)

In formula, x is stochastic variable, α, and beta, gamma is all form parameter；The inverse function form of CDF is as follows:

$F^{-1}\left(c\right|\mathrm{\α},\mathrm{\β},\mathrm{\γ})=\mathrm{\γ}-\frac{1}{\mathrm{\α}}ln(c^{1/\mathrm{\β}}-1)---\left(3\right)$

In formula, c is level of confidence.

Further, described step S3 is particularly as follows: with the matching of the general distributed model of RMSE quantitative analysis Precision, root-mean-square value such as formula (4) institute between the CDF and the CDF of general distribution of actual wind power Show:

${\mathrm{RMSE}}_m=\sqrt{\frac{1}{N}\underset{n=1}{\overset{N}{\Σ}}{\left(F_{act,m}\right(x_n)-F_{sim,m}(x_n\left)\right)}^2}---\left(4\right)$

In formula, subscript m is interval sequence number, x_nIt is the n-th corresponding for wind-powered electricity generation real output PDF cylindricality, N is cylindricality quantity total for actual PDF, F_act,m(x_n) it is that wind-powered electricity generation output is less than x_nActual CDF value, F_sim,m(x_n) it is that wind-powered electricity generation output is less than x_nThe CDF value of general distribution.

Further, described in step S4 set up consider wind-powered electricity generation probabilistic economic load dispatching model particularly as follows:

$\begin{array}{c}\min \underset{i=1}{\overset{I}{\Σ}}{C}_i\left(p_i\right)+\underset{j=1}{\overset{J}{\Σ}}{C}_{w,j}\left(w_j\right)\\ +\underset{j=1}{\overset{J}{\Σ}}{C}_{p,j}(w_{av,j}-w_j)\\ +\underset{j=1}{\overset{J}{\Σ}}{C}_{r,j}(w_j-w_{av,j})\end{array}---\left(5\right)$

$\begin{array}{cc}s.t.& \underset{i=1}{\overset{I}{\Σ}}{p}_i+\underset{j=1}{\overset{J}{\Σ}}{w}_j=L\end{array}---\left(6\right)$

p_min,i≤p_i≤p_max,i (7)

0≤w_j≤w_r,j (8)

0≤r_u,i≤min{p_max,i-p_i,r_u,max,i} (9)

0≤r_d,i≤min{p_i-p_min,i,r_d,max,i} (10)

$\underset{i=1}{\overset{I}{\Σ}}{r}_{u,i}\≥\underset{j=1}{\overset{J}{\Σ}}(w_j-w_{av,j})---\left(11\right)$

$\underset{i=1}{\overset{I}{\Σ}}{r}_{u,i}\≥\underset{j=1}{\overset{J}{\Σ}}(w_j-w_{av,j})---\left(12\right)$

In formula: I is total conventional power plant quantity, J is total wind energy turbine set quantity, C_iIt is that i-th is conventional The cost function in power plant, C_w,jIt is the cost function of jth wind energy turbine set, C_p,jIt is above planning wind-power electricity generation The cost function of amount part, C_r,jIt is the cost function not up to planning wind-power electricity generation amount part, p_iIt is conventional The plan output of power plant i, p_min,iAnd p_max,iIt is respectively the upper and lower bound of conventional power plant i, w_jFor plan wind-power electricity generation amount, w_av,jPower, w can be obtained for jth Fans reality_r,jFor jth Fans Installed capacity, L is system demand, r_u,iAnd r_d,iIt is respectively the upper limit of i-th conventional power plant spare capacity And lower limit, r_u,max,iAnd r_d,max,iIt is respectively the maximum that i-th conventional power plant can be provided by within a certain period of time Capacity and minimum capacity.

Further, the cost function containing uncertain variables in formula (5) is rewritten into average form:

$\begin{array}{c}{C}_{p,j}(w_{av,j}-w_j)=k_p(w_{av,j}-w_j)\\ =k_p{\∫}_{w_j}^{w_{r,j}}(x-w_j)g_{j,m}\left(x\right)dx\end{array}---\left(13\right)$

$\begin{array}{c}{C}_{r,j}(w_j-w_{av,j})=k_r(w_j-w_{av,j})\\ =k_r{\∫}_0^{w_j}(w_j-x)g_{j,m}\left(x\right)dx\end{array}---\left(14\right)$

In formula: k_pAnd k_rFor power beyond the cost coefficient with insufficient section, g_j,mDefeated for wind energy turbine set in interval m Go out the PDF of power.

Further, the uncertain constraint of formula (11) and formula (12) is changed into chance constraint:

$\mathrm{Pr}\{\underset{i=1}{\overset{I}{\Σ}}{r}_{u,i}\≥\underset{j=1}{\overset{J}{\Σ}}(w_j-w_{av,j})\}\≥c_u---\left(15\right)$

$\mathrm{Pr}\{\underset{i=1}{\overset{I}{\Σ}}{r}_{d,i}\≥\underset{j=1}{\overset{J}{\Σ}}(w_{av,j}-w_j)\}\≥c_d---\left(16\right)$

In formula: c_uAnd c_dIt is to provide the confidence level of enough bound spare capacities respectively.

Further, the linear order algorithm (SLP) of wind-powered electricity generation uncertainty in traffic is considered described in step S5 Specifically include following sub-step:

S5.1: object function carries out at benchmark operating point Taylor expansion, use of differentiating is specific to be solved Analysis expression formula:

$\begin{array}{c}\frac{\∂C_{p,j}}{\∂w_j}=-k_p{\∫}_{w_j}^{w_{r,j}}{g}_{j,m}\left(x\right)dx\\ =k_p\·\left(G_{j,m}\right(w_j)-G_{j,m}(w_{r,j}\left)\right)\end{array}---\left(17\right)$

$\begin{array}{c}\frac{\∂C_{r,j}}{\∂w_j}=-k_r{\∫}_0^{w_j}{g}_{j,m}\left(x\right)dx\\ =k_r\·\left(G_{j,m}\right(w_j)-G_{j,m}(0\left)\right)\end{array}---\left(18\right)$

In formula: G_j,m() is the CDF of the pre-power scale of jth wind energy turbine set on interval m；

S5.2: formula (15), the chance constraint of (16) are converted into linear deterministic expression:

$\underset{j=1}{\overset{J}{\Σ}}{w}_j-\underset{i=1}{\overset{I}{\Σ}}{r}_{u,i}\≤G_{\mathrm{\Σ}}^{-1}(1-c_u)---\left(19\right)$

$\underset{j=1}{\overset{J}{\Σ}}{w}_j+\underset{i=1}{\overset{J}{\Σ}}{r}_{d,i}\≥G_{\mathrm{\Σ}}^{-1}\left(c_d\right)---\left(20\right)$

In formula: G_∑() is the CDF that all Power Output for Wind Power Field are total；

S5.3: with SLP by object function at benchmark operating point

(w₁(k),w₂(k),…,w_J(k),p₁(k),p₂(k),…,p_I(k)) place carries out Taylor expansion, by kth time iteration mesh The expression formula of scalar functions is write as:

$\begin{array}{cc}\min & H\mathrm{\Δ}L+\underset{i=1}{\overset{I}{\Σ}}{h}_{i\left(k\right)}(p_i-p_{i\left(k\right)})+\underset{j=1}{\overset{J}{\Σ}}{h}_{w,j\left(k\right)}(w_j-w_{j\left(k\right)})\end{array}---\left(21\right)$

In formula: H Δ L is penalty term, Δ L is load reduction, and H is penalty coefficient, takes H ＞ 100； Wherein conventional power generation usage optimization object function coefficient h_i(k)Wind-power electricity generation amount optimization object function h with blower fan_w,j(k)Meter Calculate as follows:

$\left\{\begin{array}{c}{h}_{i\left(k\right)}=\frac{\∂C_i}{\∂p_i}{|}_{p_i=p_{i\left(k\right)}}\\ h_{w,j\left(k\right)}=(\frac{\∂C_{w,j}}{\∂w_j}+\frac{\∂C_{p,j}}{\∂w_j}+\frac{\∂C_{r,j}}{\∂w_j})\end{array}\right.---\left(22\right)$

For the linear objective function of kth time iteration, conventional interior point method or reduced gradient method is used to solve.

Further, described step S6 includes: utilize improvement SLP to carry out k iterative computation, until |(w_1(k+1),w_2(k+1),…,w_J(k+1),p_1(k+1),p_2(k+1),…,p_I(k+1))-(w_1(k),w_2(k),…,w_J(k),p_1(k),p_2(k),…,p_I(k))|≤ε , wherein ε is convergence criterion parameter；Obtain different conventional power plant corresponding to the pre-power scale of wind-powered electricity generation and wind-powered electricity generation The planned dispatching power of field.

Beneficial effect: the invention provides a kind of economic load dispatching side based on general wind-powered electricity generation forecast error model Method, this method uses general distribution to carry out the PDF of actual wind power on matching difference wind-powered electricity generation forecast interval (probability density function) and CDF (cumulative distribution function), can preferably be suitable for random time yardstick and width The wind-powered electricity generation forecast error modeling of value, its models fitting precision is higher than conventional Gauss distribution and β distribution；And And, the linear order algorithm (SLP) considering wind-powered electricity generation uncertainty in traffic of the improvement that the present invention uses, this The method of kind is to calculate the uncertainty Economic Dispatch Problem Han wind energy turbine set to provide novel thinking, due to general point The CDF of cloth and inverse function thereof have specific analytical expression, use general wind-powered electricity generation forecast model that differential can be made to transport Calculator has specific analytical expression, thus solves conventional SLP and be difficult to process containing uncertain wind power integration The difficulty of Economic Dispatch Problem.

Accompanying drawing explanation

Fig. 1 is the algorithm flow chart of the present invention；

Fig. 2 is the economic load dispatching system frame structure figure that the present invention accesses wind-powered electricity generation.

Detailed description of the invention

Embodiment 1: a kind of economic load dispatching method based on general wind-powered electricity generation forecast error model, such as Fig. 1 institute Showing, the present embodiment specifically provides the application of a kind of economic load dispatching method based on general wind-powered electricity generation forecast error model Case, comprises the steps:

S1: obtained wind-powered electricity generation forecasting sequence by wind-powered electricity generation prediction algorithm, and it is pre-to be divided into uniform wind power Survey interval:

Wind-powered electricity generation forecasting sequence is normalized and is transformed on interval [0,1], be divided into M uniformly interval [0,1/M], [1/M, 2/M] ..., [(M-1)/M, 1], each length of an interval degree is 1/M, interval m I.e. m=1,2 ..., M, corresponding prediction power bracket is [(m-1)/M, m/M]；In each moment, Prediction power sequence matches one by one with actual wind power output power, for each predictive value in interval m, all There is an actual value corresponding；Thus obtain the one group actual merit corresponding with each predictive value in interval m Rate point；M is the integer defined according to the scale of historical data by user.The value of M can arbitrarily take, value Predicting the outcome the most greatly the best, in order to ensure that there is abundant power number strong point in each interval, M=25 is suitable for The situation of whole year operation.

S2: determine the form parameter of general distribution on each wind-powered electricity generation forecast interval, sets up the logical of wind-powered electricity generation prediction With distributed model:

By discrete probability density rectangular histogram and the cumulative distribution table of the actual power point of m interval in S1, use Method of least square determines three form parameters of general distributed model；The general profile shape parameter in each interval Different, M=25, therefore 25 wind-powered electricity generation forecast intervals there are the PDF of 25 general fittings of distribution of use And CDF；PDF and CDF of general distributed model is respectively as shown in formula (1), formula (2):

$f\left(x\right|\mathrm{\α},\mathrm{\β},\mathrm{\γ})=\frac{{\mathrm{\α\βe}}^{-\mathrm{\α}(x-\mathrm{\γ})}}{{(1+e^{-\mathrm{\α}(x-\mathrm{\γ})})}^{\mathrm{\β}+1}}---\left(1\right)$

F (x | α, β, γ)=(1+e^-α(x-γ))^-β (2)

In formula, x is stochastic variable, α, and beta, gamma is all form parameter；The inverse function form of CDF is as follows:

$F^{-1}\left(c\right|\mathrm{\α},\mathrm{\β},\mathrm{\γ})=\mathrm{\γ}-\frac{1}{\mathrm{\α}}ln(c^{1/\mathrm{\β}}-1)---\left(3\right)$

In formula, c is level of confidence.

General distributed model has two big characteristics, characteristic one: general distribution can preferably be suitable for random time chi The wind-powered electricity generation forecast error modeling of degree and amplitude, its models fitting precision is divided higher than conventional Gauss distribution and β Cloth.Characteristic two: the CDF of general distribution and inverse function thereof have specific analytical expression, as formula (2), (3) shown in, it is adaptable to consider the algorithm of the probabilistic Economic Dispatch Problem of wind-powered electricity generation.

The fitting precision of the general distributed model of S3: quantitative analysis, sets up corresponding forecast error evaluation index: With the fitting precision of the general distributed model of RMSE (root-mean-square error) quantitative analysis, actual wind power Shown in root-mean-square value between the CDF of CDF and general distribution such as formula (4):

${\mathrm{RMSE}}_m=\sqrt{\frac{1}{N}\underset{n=1}{\overset{N}{\Σ}}{\left(F_{act,m}\right(x_n)-F_{sim,m}(x_n\left)\right)}^2}---\left(4\right)$

In formula, subscript m is interval sequence number, x_nIt is the n-th corresponding for wind-powered electricity generation real output PDF cylindricality, N is cylindricality quantity total for actual PDF, F_act,m(x_n) it is that wind-powered electricity generation output is less than x_nActual CDF value, F_sim,m(x_n) it is that wind-powered electricity generation output is less than x_nThe CDF value of general distribution.

Root-mean-square value between the CDF and the CDF of general distribution of actual wind power is as shown in table 1:

The RMSEs value of table 1 different distributions model compares

As seen from table, with the RMSE value of the wind power of each forecast interval of general fitting of distribution much smaller than Gauss Distribution and β are distributed, and illustrate that general distribution is more suitable for the modeling of wind-powered electricity generation forecast error.

S4: set up and consider wind-powered electricity generation probabilistic economic load dispatching (ED) model:

$\begin{array}{c}\min \underset{i=1}{\overset{I}{\Σ}}{C}_i\left(p_i\right)+\underset{j=1}{\overset{J}{\Σ}}{C}_{w,j}\left(w_j\right)\\ +\underset{j=1}{\overset{J}{\Σ}}{C}_{p,j}(w_{av,j}-w_j)\\ +\underset{j=1}{\overset{J}{\Σ}}{C}_{r,j}(w_j-w_{av,j})\end{array}---\left(5\right)$

$\begin{array}{cc}s.t.& \underset{i=1}{\overset{I}{\Σ}}{p}_i+\underset{j=1}{\overset{J}{\Σ}}{w}_j=L\end{array}---\left(6\right)$

p_min,i≤p_i≤p_max,i (7)

0≤w_j≤w_r,j (8)

0≤r_u,i≤min{p_max,i-p_i,r_u,max,i} (9)

0≤r_d,i≤min{p_i-p_min,i,r_d,max,i} (10)

$\underset{i=1}{\overset{I}{\Σ}}{r}_{u,i}\≥\underset{j=1}{\overset{J}{\Σ}}(w_j-w_{av,j})---\left(11\right)$

$\underset{i=1}{\overset{I}{\Σ}}{r}_{u,i}\≥\underset{j=1}{\overset{J}{\Σ}}(w_j-w_{av,j})---\left(12\right)$

In formula: I is total conventional power plant quantity, J is total wind energy turbine set quantity, C_iIt is that i-th is conventional The cost function in power plant, C_w,jIt is the cost function of jth wind energy turbine set, C_p,jIt is above planning wind-power electricity generation The cost function of amount part, C_r,jIt is the cost function not up to planning wind-power electricity generation amount part, p_iIt is conventional The plan output of power plant i, p_min,iAnd p_max,iIt is respectively the upper and lower bound of conventional power plant i, w_j For plan wind-power electricity generation amount, w_av,jPower, w can be obtained for jth Fans reality_r,jDress for jth Fans Machine capacity, L is system demand, r_u,iAnd r_d,iBe respectively i-th conventional power plant spare capacity the upper limit and Lower limit, r_u,max,iAnd r_d,max,iIt is respectively the maximum appearance that i-th conventional power plant can be provided by within a certain period of time Amount and minimum capacity.

Formula (5), containing uncertain variables w in (11) and (12)_av,j, bring to Economic Dispatch Problem Huge challenge.Having two kinds of methods tackled at present, the first will contain the cost letter of uncertain variables in formula (5) Several average forms that are rewritten into:

$\begin{array}{c}{C}_{p,j}(w_{av,j}-w_j)=k_p(w_{av,j}-w_j)\\ =k_p{\∫}_{w_j}^{w_{r,j}}(x-w_j)g_{j,m}\left(x\right)dx\end{array}---\left(13\right)$

$\begin{array}{c}{C}_{r,j}(w_j-w_{av,j})=k_r(w_j-w_{av,j})\\ =k_r{\∫}_0^{w_j}(w_j-x)g_{j,m}\left(x\right)dx\end{array}---\left(14\right)$

In formula: k_pAnd k_rFor power beyond the cost coefficient with insufficient section, g_j,mDefeated for wind energy turbine set in interval m Go out the PDF of power.

It two is that the uncertain constraint of formula (11) and formula (12) changes into chance constraint:

$\mathrm{Pr}\{\underset{i=1}{\overset{I}{\Σ}}{r}_{u,i}\≥\underset{j=1}{\overset{J}{\Σ}}(w_j-w_{av,j})\}\≥c_u---\left(15\right)$

$\mathrm{Pr}\{\underset{i=1}{\overset{I}{\Σ}}{r}_{d,i}\≥\underset{j=1}{\overset{J}{\Σ}}(w_{av,j}-w_j)\}\≥c_d---\left(16\right)$

In formula: c_uAnd c_dIt is to provide the confidence level of enough bound spare capacities respectively.

Due to available wind power (w_av,j) uncertainty, the SLP of improvement adjusts economical in step S4 The degree formula (11) of model, (12) replace with constraints condition of opportunity, then can be obtained linear true by conversion Fixed expression formula.SLP needs to carry out object function at benchmark operating point Taylor expansion, uses general wind Electricity forecast model can make to differentiate and have specific analytical expression, thus solves conventional SLP and be difficult to locate The difficulty of the reason Economic Dispatch Problem containing uncertain wind power integration.

S5: according to the general distributed model of wind-powered electricity generation prediction, obtain corresponding cumulative distribution function and anti-letter thereof Number；Obtain the linear order algorithm considering wind-powered electricity generation uncertainty in traffic improved again；

Linear order algorithm (SLP) tool considering wind-powered electricity generation uncertainty in traffic of the improvement proposed in step S5 Body includes following sub-step:

S5.1: object function carries out at benchmark operating point Taylor expansion, use of differentiating is specific to be solved Analysis expression formula:

$\begin{array}{c}\frac{\∂C_{p,j}}{\∂w_j}=-k_p{\∫}_{w_j}^{w_{r,j}}{g}_{j,m}\left(x\right)dx\\ =k_p\·\left(G_{j,m}\right(w_j)-G_{j,m}(w_{r,j}\left)\right)\end{array}---\left(17\right)$

$\begin{array}{c}\frac{\∂C_{r,j}}{\∂w_j}=-k_r{\∫}_0^{w_j}{g}_{j,m}\left(x\right)dx\\ =k_r\·\left(G_{j,m}\right(w_j)-G_{j,m}(0\left)\right)\end{array}---\left(18\right)$

In formula: G_j,m() is the CDF of the pre-power scale of jth wind energy turbine set on interval m；

S5.2: at another, important improvement is that formula (15), the chance constraint of (16) are converted into and are linearly determined Property expression formula, as shown in formula (19), (20):

$\underset{j=1}{\overset{J}{\Σ}}{w}_j-\underset{i=1}{\overset{I}{\Σ}}{r}_{u,i}\≤G_{\mathrm{\Σ}}^{-1}(1-c_u)---\left(19\right)$

$\underset{j=1}{\overset{J}{\Σ}}{w}_j+\underset{i=1}{\overset{J}{\Σ}}{r}_{d,i}\≥G_{\mathrm{\Σ}}^{-1}\left(c_d\right)---\left(20\right)$

In formula: G_∑() is the CDF that all Power Output for Wind Power Field are total；

S5.3: with SLP by object function at benchmark operating point

(w₁(k),w₂(k),…,w_J(k),p₁(k),p₂(k),…,p_I(k)) place carries out Taylor expansion, by kth time iteration mesh The expression formula of scalar functions is write as:

$\begin{array}{cc}\min & H\mathrm{\Δ}L+\underset{i=1}{\overset{I}{\Σ}}{h}_{i\left(k\right)}(p_i-p_{i\left(k\right)})+\underset{j=1}{\overset{J}{\Σ}}{h}_{w,j\left(k\right)}(w_j-w_{j\left(k\right)})\end{array}---\left(21\right)$

In formula: H Δ L is penalty term, Δ L is load reduction, and H is penalty coefficient, takes H ＞ 100； Wherein conventional power generation usage optimization object function coefficient h_i(k)Wind-power electricity generation amount optimization object function h with blower fan_w,j(k)Meter Calculate as follows:

$\left\{\begin{array}{c}{h}_{i\left(k\right)}=\frac{\∂C_i}{\∂p_i}{|}_{p_i=p_{i\left(k\right)}}\\ h_{w,j\left(k\right)}=(\frac{\∂C_{w,j}}{\∂w_j}+\frac{\∂C_{p,j}}{\∂w_j}+\frac{\∂C_{r,j}}{\∂w_j})\end{array}\right.---\left(22\right)$

For the linear objective function of kth time iteration, interior point method or the reduced gradient method etc. of routine can be used It is easy to solve.

S6: obtain system wind energy turbine set and the planned dispatching power of conventional power plant under different wind-powered electricity generation predictive value: sharp K iterative computation is carried out with improving SLP, until

|(w_1(k+1),w_2(k+1),…,w_J(k+1),p_1(k+1),p_2(k+1),…,p_I(k+1))-(w_1(k),w_2(k),…,w_J(k),p_1(k),p_2(k),…,p_I(k))|≤ε , wherein ε is convergence criterion parameter；Obtain different conventional power plant corresponding to the pre-power scale of wind-powered electricity generation and wind-powered electricity generation The planned dispatching power of field.Each conventional power plant and wind energy turbine set is given, it is achieved economic benefit by transmitting scheduling information Maximize.Access the economic load dispatching system framework of wind-powered electricity generation as shown in Figure 2.

A kind of based on general wind-powered electricity generation forecast error model the economic load dispatching method that the present invention provides, for wind-powered electricity generation The modeling of forecast error and there is preferable accuracy and effectively containing solving of probabilistic economic load dispatching model Property.Below it is only the preferred embodiment of the present invention, it should be pointed out that: for the ordinary skill of the art For personnel, under the premise without departing from the principles of the invention, it is also possible to make some improvements and modifications, these Improvements and modifications also should be regarded as protection scope of the present invention.

Claims (10)

1. an economic load dispatching method based on general wind-powered electricity generation forecast error model, it is characterised in that include as Lower step:

S1: obtained wind-powered electricity generation forecasting sequence by wind-powered electricity generation prediction algorithm, and it is pre-to be divided into uniform wind power Survey interval；

S2: determine the form parameter of general distribution on each wind-powered electricity generation forecast interval, sets up the logical of wind-powered electricity generation prediction Use distributed model；

The fitting precision of the general distributed model of S3: quantitative analysis, sets up corresponding forecast error evaluation index；

S4: set up and consider wind-powered electricity generation probabilistic economic load dispatching model；

S5: according to the general distributed model of wind-powered electricity generation prediction, obtain corresponding CDF and inverse function thereof；Obtain again The linear order algorithm considering wind-powered electricity generation uncertainty in traffic improved；

S6: obtain system wind energy turbine set and the planned dispatching power of conventional power plant under different wind-powered electricity generation predictive value.

A kind of economic load dispatching side based on general wind-powered electricity generation forecast error model the most according to claim 1 Method, it is characterised in that the partition process in the interval of wind power prediction described in step S1 specifically includes:

Wind-powered electricity generation forecasting sequence is normalized and is transformed on interval [0,1], be divided into M uniformly interval [0,1/M], [1/M, 2/M] ..., [(M-1)/M, 1], each length of an interval degree is 1/M, interval m I.e. m=1,2 ..., M, corresponding prediction power bracket is [(m-1)/M, m/M]；In each moment, Prediction power sequence matches one by one with actual wind power output power, for each predictive value in interval m, all There is an actual value corresponding；Thus obtain the one group actual merit corresponding with each predictive value in interval m Rate point；M is the integer defined according to the scale of historical data by user.

A kind of economic load dispatching side based on general wind-powered electricity generation forecast error model the most according to claim 2 Method, it is characterised in that M=25.

A kind of economic load dispatching side based on general wind-powered electricity generation forecast error model the most according to claim 2 Method, it is characterised in that set up described in step S2 wind-powered electricity generation prediction general distributed model particularly as follows:

By discrete probability density rectangular histogram and the cumulative distribution table of the actual power point of m interval in S1, use Method of least square determines three form parameters of general distributed model；The general profile shape parameter in each interval Different, M wind-powered electricity generation forecast interval there are M PDF and CDF with general fitting of distribution；Logical With PDF and CDF of distributed model respectively as shown in formula (1), formula (2):

$f\left(x\right|\mathrm{\α},\mathrm{\β},\mathrm{\γ})=\frac{{\mathrm{\α\βe}}^{-\mathrm{\α}(x-\mathrm{\γ})}}{{(1+e^{-\mathrm{\α}(x-\mathrm{\γ})})}^{\mathrm{\β}+1}}---\left(1\right)$

F (x | α, β, γ)=(1+e^-α(x-γ))^-β (2)

In formula, x is stochastic variable, α, and beta, gamma is all form parameter；The inverse function form of CDF is as follows:

$F^{-1}\left(c\right|\mathrm{\α},\mathrm{\β},\mathrm{\γ})=\mathrm{\γ}-\frac{1}{\mathrm{\α}}ln(c^{1/\mathrm{\β}}-1)---\left(3\right)$

In formula, c is level of confidence.

A kind of economic load dispatching side based on general wind-powered electricity generation forecast error model the most according to claim 1 Method, it is characterised in that described step S3 is particularly as follows: by the plan of the general distributed model of RMSE quantitative analysis Close precision, root-mean-square value such as formula (4) institute between the CDF and the CDF of general distribution of actual wind power Show:

${\mathrm{RMSE}}_m=\sqrt{\frac{1}{N}\underset{n=1}{\overset{N}{\Σ}}{\left(F_{act,m}\right(x_n)-F_{sim,m}(x_n\left)\right)}^2}---\left(4\right)$

In formula, subscript m is interval sequence number, x_nIt is the n-th corresponding for wind-powered electricity generation real output PDF cylindricality, N is cylindricality quantity total for actual PDF, F_act,m(x_n) it is that wind-powered electricity generation output is less than x_nActual CDF value, F_sim,m(x_n) it is that wind-powered electricity generation output is less than x_nThe CDF value of general distribution.

A kind of economic load dispatching side based on general wind-powered electricity generation forecast error model the most according to claim 2 Method, it is characterised in that set up described in step S4 and consider that wind-powered electricity generation probabilistic economic load dispatching model is concrete For:

$\begin{array}{c}\min \underset{i=1}{\overset{I}{\mathrm{\Σ}}}{C}_i\left(p_i\right)+\underset{j=1}{\overset{J}{\mathrm{\Σ}}}{C}_{w,j}\left(w_j\right)\\ +\underset{j=1}{\overset{J}{\mathrm{\Σ}}}{C}_{p,j}\left(w_{av,j}-w_j\right)\\ +\underset{j=1}{\overset{J}{\mathrm{\Σ}}}{C}_{r,j}\left(w_j-w_{av,j}\right)\end{array}---\left(5\right)$

$\begin{array}{cc}s.t.& \underset{i=1}{\overset{I}{\Σ}}{p}_i+\underset{j=1}{\overset{J}{\Σ}}{w}_j=L\end{array}---\left(6\right)$

p_min,i≤p_i≤p_max,i (7)

0≤w_j≤w_r,j (8)

0≤r_u,i≤min{p_max,i-p_i,r_u,max,i} (9)

0≤r_d,i≤min{p_i-p_min,i,r_d,max,i} (10)

$\underset{i=1}{\overset{I}{\Σ}}{r}_{u,i}\≥\underset{j=1}{\overset{J}{\Σ}}(w_j-w_{av,j})---\left(11\right)$

$\underset{i=1}{\overset{I}{\Σ}}{r}_{u,i}\≥\underset{j=1}{\overset{J}{\Σ}}(w_j-w_{av,j})---\left(12\right)$

In formula: I is total conventional power plant quantity, J is total wind energy turbine set quantity, C_iIt is that i-th is conventional The cost function in power plant, C_w,jIt is the cost function of jth wind energy turbine set, C_p,jIt is above planning wind-power electricity generation The cost function of amount part, C_r,jIt is the cost function not up to planning wind-power electricity generation amount part, p_iIt is conventional The plan output of power plant i, p_min,iAnd p_max,iIt is respectively the upper and lower bound of conventional power plant i, w_jFor plan wind-power electricity generation amount, w_av,jPower, w can be obtained for jth Fans reality_r,jFor jth Fans Installed capacity, L is system demand, r_u,iAnd r_d,iIt is respectively the upper limit of i-th conventional power plant spare capacity And lower limit, r_u,max,iAnd r_d,max,iIt is respectively the maximum that i-th conventional power plant can be provided by within a certain period of time Capacity and minimum capacity.

A kind of economic load dispatching side based on general wind-powered electricity generation forecast error model the most according to claim 6 Method, it is characterised in that average form will be rewritten into containing the cost function of uncertain variables in formula (5):

$\begin{array}{c}{C}_{p,j}(w_{av,j}-w_j)=k_p(w_{av,j}-w_j)\\ =k_p{\∫}_{w_j}^{w_{r,j}}\left(x-w_j\right)g_{j,m}\left(x\right)dx\end{array}---\left(13\right)$

$\begin{array}{c}{C}_{r,j}(w_j-w_{av,j})=k_r(w_j-w_{av,j})\\ =k_r{\∫}_0^{w_j}\left(w_j-x\right)g_{j,m}\left(x\right)dx\end{array}---\left(14\right)$

In formula: k_pAnd k_rFor power beyond the cost coefficient with insufficient section, g_j,mDefeated for wind energy turbine set in interval m Go out the PDF of power.

A kind of economic load dispatching side based on general wind-powered electricity generation forecast error model the most according to claim 6 Method, it is characterised in that the uncertain constraint of formula (11) and formula (12) is changed into chance constraint:

$\mathrm{Pr}\{\underset{i=1}{\overset{I}{\Σ}}{r}_{u,i}\≥\underset{j=1}{\overset{J}{\Σ}}(w_j-w_{av,j})\}\≥c_u---\left(15\right)$

$\mathrm{Pr}\{\underset{i=1}{\overset{I}{\Σ}}{r}_{d,i}\≥\underset{j=1}{\overset{J}{\Σ}}(w_{av,j}-w_j)\}\≥c_d---\left(16\right)$

In formula: c_uAnd c_dIt is to provide the confidence level of enough bound spare capacities respectively.

A kind of economic load dispatching side based on general wind-powered electricity generation forecast error model the most according to claim 8 Method, it is characterised in that consider the linear order algorithm of wind-powered electricity generation uncertainty in traffic described in step S5

(SLP) following sub-step is specifically included:

S5.1: object function carries out at benchmark operating point Taylor expansion, use of differentiating is specific to be solved Analysis expression formula:

$\begin{array}{c}\frac{\∂C_{p,j}}{\∂w_j}=-k_p{\∫}_{w_j}^{w_{r,j}}{g}_{j,m}\left(x\right)dx\\ =k_p\·\left(G_{j,m}\left(w_j\right)-G_{j,m}\left(w_{r,j}\right)\right)\end{array}---\left(17\right)$

$\begin{array}{c}\frac{\∂C_{r,j}}{\∂w_j}=-k_r{\∫}_0^{w_j}{g}_{j,m}\left(x\right)dx\\ =k_r\·\left(G_{j,m}\left(w_j\right)-G_{j,m}\left(0\right)\right)\end{array}---\left(18\right)$

In formula: G_j,m() is the CDF of the pre-power scale of jth wind energy turbine set on interval m；

S5.2: formula (15), the chance constraint of (16) are converted into linear deterministic expression:

$\underset{j=1}{\overset{J}{\Σ}}{w}_j-\underset{i=1}{\overset{I}{\Σ}}{r}_{u,i}\≤G_{\mathrm{\Σ}}^{-1}(1-c_u)---\left(19\right)$

$\underset{j=1}{\overset{J}{\Σ}}{w}_j+\underset{i=1}{\overset{J}{\Σ}}{r}_{d,i}\≥G_{\mathrm{\Σ}}^{-1}\left(c_d\right)---\left(20\right)$

In formula: G_∑() is the CDF that all Power Output for Wind Power Field are total；

S5.3: with SLP by object function at benchmark operating point

(w₁(k),w₂(k),…,w_J(k),p₁(k),p₂(k),…,p_I(k)) place carries out Taylor expansion, by kth time iteration mesh The expression formula of scalar functions is write as:

$\begin{array}{cc}\min & H\mathrm{\Δ}L+\underset{i=1}{\overset{I}{\Σ}}{h}_{i\left(k\right)}(p_i-p_{i\left(k\right)})+\underset{j=1}{\overset{J}{\Σ}}{h}_{w,j\left(k\right)}(w_j-w_{j\left(k\right)})\end{array}---\left(21\right)$

In formula: H Δ L is penalty term, Δ L is load reduction, and H is penalty coefficient, takes H ＞ 100；

Wherein conventional power generation usage optimization object function coefficient h_i(k)Wind-power electricity generation amount optimization object function h with blower fan_w,j(k)Meter Calculate as follows:

$\left\{\begin{array}{c}{h}_{i\left(k\right)}=\frac{\∂C_i}{\∂p_i}{|}_{p_i=p_{i\left(k\right)}}\\ h_{w,j\left(k\right)}=\left(\frac{\∂C_{w,j}}{\∂w_j}+\frac{\∂C_{p,j}}{\∂w_j}+\frac{\∂C_{r,j}}{\∂w_j}\right)\end{array}\right.---\left(22\right)$

For the linear objective function of kth time iteration, conventional interior point method or reduced gradient method is used to solve.

A kind of economic load dispatching side based on general wind-powered electricity generation forecast error model the most according to claim 1 Method, it is characterised in that described step S6 includes: utilize improvement SLP to carry out k iterative computation, until |(w_1(k+1),w_2(k+1),…,w_J(k+1),p_1(k+1),p_2(k+1),…,p_I(k+1))-(w_1(k),w_2(k),…,w_J(k),p_1(k),p_2(k),…,p_I(k))|≤ε , wherein ε is convergence criterion parameter；Obtain different conventional power plant corresponding to the pre-power scale of wind-powered electricity generation and wind-powered electricity generation The planned dispatching power of field.