CN103854073A - Method for comprehensively predicting generation capacity of multi-radial flow type small hydropower station group area - Google Patents

Method for comprehensively predicting generation capacity of multi-radial flow type small hydropower station group area Download PDF

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CN103854073A
CN103854073A CN201410108969.0A CN201410108969A CN103854073A CN 103854073 A CN103854073 A CN 103854073A CN 201410108969 A CN201410108969 A CN 201410108969A CN 103854073 A CN103854073 A CN 103854073A
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predicted value
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generated energy
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刘志坚
黄蓉
周术明
杨志华
宋琪
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Kunming University of Science and Technology
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Abstract

本发明涉及一种多径流式小水电群地区发电量综合预测方法，属于电力技术领域。本发明首先采用偏最小二乘模型，得到多径流式小水电群地区发电量和影响发电量的相关因素之间的线性多元回归方程；同时采用改进灰色预测模型对各相关因素数列进行建模，得到相关因素预测值；然后将得到的相关因素预测值代入偏最小二乘模型所得的线性多元回归方程中，得到多径流式小水电群地区发电量预测值；最后根据发电量预测值得出相对误差。本发明预测精度更高、预测效果显著。

The invention relates to a method for comprehensively predicting power generation in multi-runoff small hydropower groups, and belongs to the technical field of electric power. The present invention first uses the partial least squares model to obtain the linear multiple regression equation between the power generation in the multi-runoff small hydropower group area and the relevant factors affecting the power generation; at the same time, the improved gray prediction model is used to model the series of relevant factors, Obtain the predicted value of relevant factors; then substitute the obtained predicted value of relevant factors into the linear multiple regression equation obtained by the partial least squares model to obtain the predicted value of power generation in the area of multi-runoff small hydropower clusters; finally get the relative error according to the predicted value of power generation . The invention has higher prediction precision and remarkable prediction effect.

Description

一种多径流式小水电群地区发电量综合预测方法A method for comprehensive forecasting of power generation in multi-runoff small hydropower clusters

技术领域 technical field

本发明涉及一种多径流式小水电群地区发电量综合预测方法，属于电力技术领域。 The invention relates to a method for comprehensively predicting power generation in multi-runoff small hydropower groups, and belongs to the technical field of electric power.

背景技术 Background technique

在电力市场环境下一般都会要求参加电力市场运营的相当规模地方小电厂根据电力公司计划部门下达的年、月发电上网计划，参加负荷预测和调峰发电计划。其中月度预测是电力计划部门、用电营销部门的重要工作，预测精度直接关系电力市场的经济运行。然而，在地方小电厂中以小水电居多，由于没有天然库容，其中的大部分均是不具备调节能力的径流式小水电，其发电能力受多种因素的制约和影响，丰水期间小水电电量无法在地方电网网内消耗，大量富余电量上省网，而枯水期因小电出力不足，需从省网下网补给电量，因此对多径流式小水电群地区发电量的预测精度直接关系到售电量和下省网电量等电力电量指标的预测精度，而这些预测值精度均作为电力营销部门电力需求侧管理中的考核指标。 In the electricity market environment, local small power plants of considerable scale that participate in the operation of the electricity market are generally required to participate in load forecasting and peak-shaving power generation plans according to the annual and monthly grid-connected power generation plans issued by the planning department of the power company. Among them, the monthly forecast is an important task of the power planning department and the power marketing department, and the prediction accuracy is directly related to the economic operation of the power market. However, most of the local small power plants are small hydropower plants. Since there is no natural storage capacity, most of them are run-of-the-river small hydropower plants without adjustment capabilities. Their power generation capacity is restricted and affected by various factors. The electricity cannot be consumed in the local power grid, and a large amount of surplus electricity is connected to the provincial grid. In the dry season, due to insufficient output of small electricity, it is necessary to supply electricity from the provincial grid. Therefore, the prediction accuracy of the power generation of multi-runoff small hydropower clusters is directly related to The prediction accuracy of power quantity indicators such as electricity sales and electricity in the lower provincial grid, and the accuracy of these prediction values are used as assessment indicators in the power demand side management of the power marketing department.

影响径流式小水电发电量的因素众多，且众多因素与小水电发电量之间存在多重共线性的问题，传统线性回归方法难以精确描述变量之间的关系。对于影响因素的处理，由于径流式小水电大多地处偏远山区，获取收集水文气象资料存在很大难度，并且由于运行人员素质及管理制度的落后，导致历史资料的匮乏。针对小样本数据问题，传统的统计学方法很难发现其变化规律。 There are many factors that affect the power generation of run-of-river small hydropower, and there is a problem of multicollinearity between many factors and the power generation of small hydropower. It is difficult for traditional linear regression methods to accurately describe the relationship between variables. As for the treatment of influencing factors, since run-of-river small hydropower is mostly located in remote mountainous areas, it is very difficult to obtain and collect hydrometeorological data, and due to the lack of historical data due to the backward quality of operating personnel and management systems. For the problem of small sample data, traditional statistical methods are difficult to find its changing law.

发明内容 Contents of the invention

本发明提供了一种多径流式小水电群地区发电量综合预测方法，以用于解决在小样本容量下难以发现事物的统计规律、影响因素多重共线性时难以精确描述自变量与因变量之间的关系、径流式小水电来水即发等偶然性导致多小水电地区发电量预测精度不高等不足。 The present invention provides a method for comprehensive forecasting of power generation in a multi-runoff small hydropower group area, which is used to solve the problem that it is difficult to find the statistical laws of things under a small sample size, and it is difficult to accurately describe the relationship between the independent variable and the dependent variable when the influencing factors are multi-collinear. The relationship between the small hydropower station and the randomness of the run-of-the-river small hydropower station lead to low prediction accuracy of power generation in areas with many small hydropower stations.

本发明的技术方案是：一种多径流式小水电群地区发电量综合预测方法，首先采用偏最小二乘模型，得到多径流式小水电群地区发电量和影响发电量的相关因素之间的线性多元回归方程；同时采用改进灰色预测模型对各相关因素数列进行建模，得到相关因素预测值；然后将得到的相关因素预测值代入偏最小二乘模型所得的线性多元回归方程中，得到多径流式小水电群地区发电量预测值；最后根据发电量预测值得出相对误差。 The technical solution of the present invention is: a method for comprehensive prediction of power generation in multi-runoff small hydropower group areas. First, the partial least squares model is used to obtain the relationship between the power generation in the multi-runoff small hydropower group area and the relevant factors affecting the power generation. Linear multiple regression equation; at the same time, the improved gray prediction model is used to model the series of relevant factors to obtain the predicted value of relevant factors; Predicted value of power generation in the area of runoff small hydropower group; finally, the relative error is obtained based on the predicted value of power generation.

所述方法的具体步骤如下： The concrete steps of described method are as follows:

A、根据多径流式小水电群地区发电量y和m个影响发电量的相关因素变量x 1,x 2,…,x m ，选取n个样本观测点，得到X=[x 1,x 2,…,x m ] n×m ，Y=[y] n×1，根据偏最小二乘模型，建立线性多元回归方程为： A. According to the power generation y of the multi-runoff small hydropower group area and m related factor variables x 1 , x 2 ,…, x m that affect the power generation, select n sample observation points, and get X =[ x 1 , x 2 ,…, x m ] n × m , Y =[ y ] n ×1 , according to the partial least squares model, the linear multiple regression equation is established as:

Figure 2014101089690100002DEST_PATH_IMAGE002
                                                          （1）
Figure 2014101089690100002DEST_PATH_IMAGE002
                                                          (1)

其中，i=1,…m，m为假设的相关因素的个数；c 0为回归方程的误差系统，c 1,c 2,…c m 为回归系数；

Figure 2014101089690100002DEST_PATH_IMAGE004
,
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,…,
Figure 2014101089690100002DEST_PATH_IMAGE008
为X中各参数标准化逆过程的取值；
Figure DEST_PATH_IMAGE010
为Y中各参数标准化逆过程的取值； Among them, i =1,... m , m is the number of assumed related factors; c 0 is the error system of the regression equation, c 1 , c 2 ,... c m are the regression coefficients;
Figure 2014101089690100002DEST_PATH_IMAGE004
,
Figure DEST_PATH_IMAGE006
,…,
Figure 2014101089690100002DEST_PATH_IMAGE008
Standardize the value of the inverse process for each parameter in X ;
Figure DEST_PATH_IMAGE010
Standardize the value of the inverse process for each parameter in Y ;

B、采用改进灰色预测模型对各相关因素数列进行建模，得到相关因素预测值：所述改进灰色预测模型的具体步骤如下： B. Adopting the improved gray prediction model to model each relevant factor sequence, and obtaining the predicted value of the relevant factors: the specific steps of the improved gray prediction model are as follows:

B1、对原始数列进行滑动平均处理，得到经滑动平滑处理之后的数列； B1. Carry out sliding average processing on the original sequence to obtain the sequence after sliding and smoothing;

B2、对经滑动平滑处理之后的数列进行一次累加生成一次累加数列，运用一次累加数列构建一阶微分方程并确定数据矩阵； B2. Carry out an accumulation of the sequence after sliding and smoothing to generate an accumulation sequence, use the accumulation sequence to construct a first-order differential equation and determine the data matrix;

B3、采用最小二乘估计一阶线性微分方程的待估参数； B3. Using least squares to estimate the parameters to be estimated of the first-order linear differential equation;

B4、计算无偏

Figure DEST_PATH_IMAGE012
模型的参数
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，
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； B4. Calculation is unbiased
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model parameters
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,
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;

B5、根据

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，A的估计值
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，
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建立原始数据序列模型： B5. According to
Figure DEST_PATH_IMAGE018
, an estimate of A
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,
Figure 420136DEST_PATH_IMAGE016
Model the original data sequence:

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                           （2）
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(2)

其中，0≤k≤n-1时

Figure DEST_PATH_IMAGE022
为原始数据序列的拟合值，k≥n时
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为原始数据序列的预测值； Among them, when 0≤ k ≤ n -1
Figure DEST_PATH_IMAGE022
is the fitting value of the original data sequence, when k ≥ n
Figure 466852DEST_PATH_IMAGE022
is the predicted value of the original data sequence;

C、将得到的相关因素预测值代入偏最小二乘模型所得的线性多元回归分析式中，得到多径流式小水电群地区发电量预测值； C. Substituting the predicted value of relevant factors obtained into the linear multiple regression analysis formula obtained by the partial least squares model, and obtaining the predicted value of power generation in the area of multi-runoff small hydropower groups;

D、将发电量的真实值与发电量预测值的差值的绝对值除以发电量的真实值得到相对误差。 D. Divide the absolute value of the difference between the actual value of power generation and the predicted value of power generation by the actual value of power generation to obtain the relative error.

本发明的工作原理是： The working principle of the present invention is:

1、设已知径流式小水电群地区发电量y和m个相关影响因素变量x 1,x 2,…,x m 。X=[x 1,x 2,…,x m ] n×m ，Y=[y] n×1，为了研究小水电群发电量与相关影响因素之间的统计关系，选取n个样本观测点，按下述方法进行标准化处理： 1. It is assumed that the power generation y in the runoff small hydropower cluster area and m related influencing factor variables x 1 , x 2 ,…, x m are known. X =[ x 1 , x 2 ,…, x m ] n × m , Y =[ y ] n ×1 , in order to study the statistical relationship between the power generation of small hydropower groups and related influencing factors, n sample observation points are selected, Standardize as follows:

Figure DEST_PATH_IMAGE024
,i=1,2,…n；j=1,2,…m
Figure DEST_PATH_IMAGE024
, i =1,2,… n ; j =1,2,… m

Figure DEST_PATH_IMAGE026
,i=1,2,…n
Figure DEST_PATH_IMAGE026
, i =1,2,… n

式中，x ij 表示自变量矩阵X中第j个变量第i个样本值，y i 表示矩阵Y的第i个样本值，

Figure DEST_PATH_IMAGE028
为矩阵X中第j列所有元素的平均值，为列向量矩阵Y中所有元素的均值，s j 为矩阵X中第j列所有元素的标准差、s y 为列向量矩阵Y中所有元素的标准差。因此经标准化之后得到： In the formula, x ij represents the i -th sample value of the j -th variable in the independent variable matrix X , and y i represents the i -th sample value of the matrix Y ,
Figure DEST_PATH_IMAGE028
is the average value of all elements in column j of matrix X , is the mean value of all elements in column vector matrix Y , s j is the standard deviation of all elements in column j of matrix X , and s y is the standard deviation of all elements in column vector matrix Y. So after normalization we get:

Figure DEST_PATH_IMAGE032
Figure DEST_PATH_IMAGE032

式中，i=1,2,…n；j=1,2,…m。 In the formula, i =1,2,... n ; j =1,2,... m .

对影响因素矩阵E 0进行主成分分析，提取第一主导因素t 1=E 0 w 1，t 1是各影响因子

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,,…,
Figure 414320DEST_PATH_IMAGE008
的线性组合，w 1为E 0的第一主轴，其中，
Figure DEST_PATH_IMAGE034
。要求t 1尽可能大的携带E 0中的变异信息，且与F 0的相关程度最大。这样既能很好地代表E 0，又能对F 0有最强的解释能力。 Conduct principal component analysis on the influencing factor matrix E 0 to extract the first dominant factor t 1 = E 0 w 1 , t 1 is each influencing factor
Figure 811858DEST_PATH_IMAGE004
, ,…,
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A linear combination of , w 1 is the first principal axis of E 0 , where,
Figure DEST_PATH_IMAGE034
. It is required that t1 carries the variation information in E0 as large as possible, and has the greatest correlation with F0 . This can not only represent E 0 well, but also have the strongest explanatory power for F 0 .

进行

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、对第一主导因素
Figure DEST_PATH_IMAGE040
的回归： conduct
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, to the first dominant factor
Figure DEST_PATH_IMAGE040
The return of:

Figure DEST_PATH_IMAGE042
Figure DEST_PATH_IMAGE042

上式中，E 1、F 1为残差矩阵： In the above formula, E 1 and F 1 are the residual matrix:

b 1、a 1是回归系数向量为： b 1 and a 1 are regression coefficient vectors:

Figure DEST_PATH_IMAGE046
Figure DEST_PATH_IMAGE046

式中，

Figure DEST_PATH_IMAGE048
表示的是矩阵E 0的转置矩阵，
Figure DEST_PATH_IMAGE050
表示的是矩阵F 0的转置矩阵。 In the formula,
Figure DEST_PATH_IMAGE048
Represents the transpose matrix of matrix E 0 ,
Figure DEST_PATH_IMAGE050
Represents the transpose matrix of matrix F 0 .

进行收敛性判断，如果y对t 1的回归精度已达要求，则结束对成分的提取。否则用残差矩阵E 1和F 1取代E 0和F 0，然后重复上述步骤，提取第二主导因素t 2=E 1 w 2，如此循环提取成分。假设当满足精度要求时一共提取了k个成分t 1,t 2,…, t k ，对F 0在t 1,t 2,…, t k 上进行回归，有： Carry out convergence judgment, if the regression accuracy of y to t 1 has reached the requirement, then end the extraction of components. Otherwise, replace E 0 and F 0 with the residual matrix E 1 and F 1 , then repeat the above steps to extract the second dominant factor t 2 = E 1 w 2 , and extract components in this way. Assuming that a total of k components t 1 , t 2 ,…, t k are extracted when the accuracy requirements are met, and F 0 is regressed on t 1 , t 2 ,…, t k , there are:

Figure DEST_PATH_IMAGE052
Figure DEST_PATH_IMAGE052

由于

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是X=[x 1,x 2,…,x m ]的线性组合，而
Figure 573381DEST_PATH_IMAGE036
是X标准化处理之后的矩阵,因此上式可表达为： because
Figure DEST_PATH_IMAGE054
is a linear combination of X = [ x 1 , x 2 ,…, x m ], while
Figure 573381DEST_PATH_IMAGE036
is the matrix after X is standardized, so the above formula can be expressed as:

Figure DEST_PATH_IMAGE056
Figure DEST_PATH_IMAGE056

式中，

Figure DEST_PATH_IMAGE058
，I为单位矩阵，1≤h≤k，
Figure DEST_PATH_IMAGE060
是列向量矩阵b j 的转置矩阵，w h 的推导同
Figure 260977DEST_PATH_IMAGE034
。 In the formula,
Figure DEST_PATH_IMAGE058
, I is the identity matrix, 1≤ h ≤ k ,
Figure DEST_PATH_IMAGE060
is the transpose matrix of the column vector matrix b j , the derivation of w h is the same as
Figure 260977DEST_PATH_IMAGE034
.

将上式标准化还原逆过程，还原为

Figure DEST_PATH_IMAGE062
对
Figure DEST_PATH_IMAGE064
的回归方程为： The inverse process of normalizing the above formula can be reduced to
Figure DEST_PATH_IMAGE062
right
Figure DEST_PATH_IMAGE064
The regression equation for is:

Figure DEST_PATH_IMAGE066
Figure DEST_PATH_IMAGE066

式中，回归系数

Figure DEST_PATH_IMAGE068
，k为最终提取成分的个数，为列向量的第j行分量，1≤j≤m，而1≤h≤k。 In the formula, the regression coefficient
Figure DEST_PATH_IMAGE068
, k is the number of final extracted components, is a column vector The j -th row component of , 1≤ j ≤ m , and 1≤ h ≤ k .

通常，需要在回归方程中引入一个误差系数，记为c 0，原方程变为： Usually, it is necessary to introduce an error coefficient into the regression equation, denoted as c 0 , and the original equation becomes:

Figure DEST_PATH_IMAGE074
Figure DEST_PATH_IMAGE074

由以上分析可知，偏最小二乘回归方程并不需要选用全部的成分进行回归建模，在偏最小二乘回归建模中，要选取多少个成分为宜，可通过考察增加一个新的成分后，能否对模型的预测功能有明显的改进来考虑。基于此，定义了交叉有效性原则，即： From the above analysis, it can be seen that the partial least squares regression equation does not need to select all the components for regression modeling. In the partial least squares regression modeling, how many components should be selected can be determined by adding a new component. , whether it can significantly improve the predictive function of the model to consider. Based on this, the principle of cross validity is defined, namely:

Figure DEST_PATH_IMAGE076
Figure DEST_PATH_IMAGE076

其中，

Figure DEST_PATH_IMAGE078
，
Figure DEST_PATH_IMAGE080
；y i 表示第i个样本的真实值，
Figure DEST_PATH_IMAGE082
表示用除第i个样本外的所有样本拟合得到的模型在第i个样本上的预测值，表示所有样本拟合得到的模型在第i个样本上的预测值。当
Figure DEST_PATH_IMAGE086
时，t h 成分的边际贡献是显著的。这时增加成分t h 使预测模型得到显著改善。 in,
Figure DEST_PATH_IMAGE078
,
Figure DEST_PATH_IMAGE080
; y i represents the true value of the i- th sample,
Figure DEST_PATH_IMAGE082
Indicates the predicted value of the model on the i- th sample fitted by all samples except the i- th sample, Indicates the predicted value of the model fitted to all samples on the i- th sample. when
Figure DEST_PATH_IMAGE086
When , the marginal contribution of the t h component is significant. At this time, adding the component t h can significantly improve the prediction model.

2、设水文气象原始数据序列为： 2. Suppose the original hydrometeorological data sequence is:

Figure DEST_PATH_IMAGE088
Figure DEST_PATH_IMAGE088

经滑动平均处理得： After moving average processing:

Figure DEST_PATH_IMAGE090
Figure DEST_PATH_IMAGE090

其中： in:

Figure DEST_PATH_IMAGE092
Figure DEST_PATH_IMAGE092

考虑到水文气象数据的随机波动性，滑动平均可以减弱原始数据波动对于预测模型精度的影响。对经滑动平滑处理之后的水文气象数据进行一次累加生成后，形成数列： Considering the random fluctuation of hydrometeorological data, moving average can reduce the impact of raw data fluctuation on the accuracy of prediction model. After the hydrometeorological data after sliding and smoothing are accumulated and generated once, a sequence is formed:

Figure DEST_PATH_IMAGE094
Figure DEST_PATH_IMAGE094

式中，。 In the formula, .

确定数据矩阵B，Y N （这里之所以需要确定这两个系数矩阵是为了求一阶线性微分方程的待估参数

Figure DEST_PATH_IMAGE098
，。因为应用经过滑动平均和一次累加生成的数列
Figure 815103DEST_PATH_IMAGE094
建模，来描述事情的发展过程，构建下述一阶微分方程
Figure DEST_PATH_IMAGE102
）： Determine the data matrix B , Y N (the reason why these two coefficient matrices need to be determined here is to find the estimated parameters of the first-order linear differential equation
Figure DEST_PATH_IMAGE098
, . Because the application of the sequence generated by moving average and one accumulation
Figure 815103DEST_PATH_IMAGE094
Modeling, to describe the development process of things, construct the following first-order differential equation
Figure DEST_PATH_IMAGE102
):

Figure DEST_PATH_IMAGE104
Figure DEST_PATH_IMAGE104

Figure DEST_PATH_IMAGE106
Figure DEST_PATH_IMAGE106

采用最小二乘估计一阶线性微分方程的待估参数

Figure 916045DEST_PATH_IMAGE098
，
Figure 944044DEST_PATH_IMAGE100
： Estimate parameters to be estimated for first-order linear differential equations using least squares
Figure 916045DEST_PATH_IMAGE098
,
Figure 944044DEST_PATH_IMAGE100
:

Figure DEST_PATH_IMAGE108
Figure DEST_PATH_IMAGE108

计算无偏

Figure 187944DEST_PATH_IMAGE012
模型的参数： Calculations are unbiased
Figure 187944DEST_PATH_IMAGE012
Model parameters:

Figure DEST_PATH_IMAGE110
Figure DEST_PATH_IMAGE110

建立原始数据序列模型： Model the original data sequence:

Figure DEST_PATH_IMAGE112
Figure DEST_PATH_IMAGE112

式中，0≤k≤n-1时

Figure 502251DEST_PATH_IMAGE022
为原始数据序列的拟合值，k≥n时
Figure 962925DEST_PATH_IMAGE022
为原始数据序列的预测值。 In the formula, when 0≤ k ≤ n -1
Figure 502251DEST_PATH_IMAGE022
is the fitted value of the original data sequence, when k ≥ n
Figure 962925DEST_PATH_IMAGE022
is the predicted value of the original data series.

本发明的有益效果是： The beneficial effects of the present invention are:

1、在未事先假定的情况下，精确描述了径流式小水电群出力与其影响因素之间的复杂关系，与单纯线性拟合二者关系，预测精度更高。 1. Without prior assumptions, it accurately describes the complex relationship between the output of the run-of-river small hydropower group and its influencing factors. Compared with the simple linear fitting of the relationship between the two, the prediction accuracy is higher.

2、处理水文气象等相关影响因素时，改进灰色预测解决了样本容量有限且随机波动较大的问题，提高了预测精度。 2. When dealing with relevant influencing factors such as hydrology and meteorology, the improved gray prediction solves the problem of limited sample size and large random fluctuations, and improves the prediction accuracy.

3、将偏最小二乘算法与改进灰色预测综合，二者取长补短，预测效果显著。 3. Combining the partial least squares algorithm and the improved gray prediction, the two learn from each other, and the prediction effect is remarkable.

附图说明 Description of drawings

图1为本发明的预测步骤框图； Fig. 1 is the prediction step block diagram of the present invention;

图2为本发明中实施例2的预测效果图。 Fig. 2 is a prediction effect diagram of embodiment 2 of the present invention.

具体实施方式 Detailed ways

实施例1：如图1-2所示，一种多径流式小水电群地区发电量综合预测方法，首先采用偏最小二乘模型，得到多径流式小水电群地区发电量和影响发电量的相关因素之间的线性多元回归方程；同时采用改进灰色预测模型对各相关因素数列进行建模，得到相关因素预测值；然后将得到的相关因素预测值代入偏最小二乘模型所得的线性多元回归方程中，得到多径流式小水电群地区发电量预测值；最后根据发电量预测值得出相对误差。 Example 1: As shown in Figure 1-2, a comprehensive forecasting method for the power generation in a multi-runoff small hydropower group area. First, the partial least squares model is used to obtain the power generation in the multi-runoff small hydropower group area and the influence on the power generation. The linear multiple regression equation between relevant factors; at the same time, the improved gray prediction model is used to model the series of relevant factors to obtain the predicted value of relevant factors; In the equation, the predicted value of power generation in the multi-runoff small hydropower group area is obtained; finally, the relative error is obtained according to the predicted value of power generation.

所述方法的具体步骤如下： The concrete steps of described method are as follows:

A、根据多径流式小水电群地区发电量y和m个影响发电量的相关因素变量x 1,x 2,…,x m ，选取n个样本观测点，得到X=[x 1,x 2,…,x m ] n×m ，Y=[y] n×1，根据偏最小二乘模型，建立线性多元回归方程为： A. According to the power generation y of the multi-runoff small hydropower group area and m related factor variables x 1 , x 2 ,…, x m that affect the power generation, select n sample observation points, and get X =[ x 1 , x 2 ,…, x m ] n × m , Y =[ y ] n ×1 , according to the partial least squares model, the linear multiple regression equation is established as:

Figure DEST_PATH_IMAGE114
                                          （1）
Figure DEST_PATH_IMAGE114
(1)

其中，i=1,…m，m为假设的相关因素的个数；c 0为回归方程的误差系统，c 1,c 2,…c m 为回归系数；

Figure DEST_PATH_IMAGE116
,
Figure DEST_PATH_IMAGE118
,…,
Figure DEST_PATH_IMAGE120
为X中各参数标准化逆过程的取值；
Figure DEST_PATH_IMAGE122
为Y中各参数标准化逆过程的取值； Among them, i =1,... m , m is the number of assumed related factors; c 0 is the error system of the regression equation, c 1 , c 2 ,... c m are the regression coefficients;
Figure DEST_PATH_IMAGE116
,
Figure DEST_PATH_IMAGE118
,…,
Figure DEST_PATH_IMAGE120
Standardize the value of the inverse process for each parameter in X ;
Figure DEST_PATH_IMAGE122
Standardize the value of the inverse process for each parameter in Y ;

B、采用改进灰色预测模型对各相关因素数列进行建模，得到相关因素预测值：所述改进灰色预测模型的具体步骤如下： B. Adopting the improved gray prediction model to model each relevant factor sequence, and obtaining the predicted value of the relevant factors: the specific steps of the improved gray prediction model are as follows:

B1、对原始数列进行滑动平均处理，得到经滑动平滑处理之后的数列； B1. Carry out sliding average processing on the original sequence to obtain the sequence after sliding and smoothing;

B2、对经滑动平滑处理之后的数列进行一次累加生成一次累加数列，运用一次累加数列构建一阶微分方程并确定数据矩阵； B2. Carry out an accumulation of the sequence after sliding and smoothing to generate an accumulation sequence, use the accumulation sequence to construct a first-order differential equation and determine the data matrix;

B3、采用最小二乘估计一阶线性微分方程的待估参数； B3. Using least squares to estimate the parameters to be estimated of the first-order linear differential equation;

B4、计算无偏

Figure DEST_PATH_IMAGE124
模型的参数
Figure DEST_PATH_IMAGE126
，
Figure DEST_PATH_IMAGE128
； B4. Calculation is unbiased
Figure DEST_PATH_IMAGE124
model parameters
Figure DEST_PATH_IMAGE126
,
Figure DEST_PATH_IMAGE128
;

B5、根据

Figure 342085DEST_PATH_IMAGE018
，A的估计值
Figure 706071DEST_PATH_IMAGE126
，建立原始数据序列模型： B5. According to
Figure 342085DEST_PATH_IMAGE018
, an estimate of A
Figure 706071DEST_PATH_IMAGE126
, Model the original data sequence:

Figure DEST_PATH_IMAGE130
                           （2）
Figure DEST_PATH_IMAGE130
(2)

其中，0≤k≤n-1时

Figure DEST_PATH_IMAGE132
为原始数据序列的拟合值，k≥n时
Figure 76933DEST_PATH_IMAGE132
为原始数据序列的预测值； Among them, when 0≤ k ≤ n -1
Figure DEST_PATH_IMAGE132
is the fitting value of the original data sequence, when k ≥ n
Figure 76933DEST_PATH_IMAGE132
is the predicted value of the original data sequence;

C、将得到的相关因素预测值代入偏最小二乘模型所得的线性多元回归分析式中，得到多径流式小水电群地区发电量预测值； C. Substituting the predicted value of relevant factors obtained into the linear multiple regression analysis formula obtained by the partial least squares model, and obtaining the predicted value of power generation in the area of multi-runoff small hydropower groups;

D、将发电量的真实值与发电量预测值的差值的绝对值除以发电量的真实值得到相对误差。 D. Divide the absolute value of the difference between the actual value of power generation and the predicted value of power generation by the actual value of power generation to obtain the relative error.

实施例2：如图1-2所示，一种多径流式小水电群地区发电量综合预测方法，所述方法的具体实施步骤如下： Embodiment 2: As shown in Figure 1-2, a method for comprehensive prediction of power generation in a multi-runoff type small hydropower group area, the specific implementation steps of the method are as follows:

选取某地区径流式小水电群2009年～2011年分月发电量数据作为历史数据，对2012年分月发电量进行预测。选取与发电量紧密相关的水文水流量、水文降水量、气象降水量作为自变量因素进行预测分析，可知，样本观测点为3，相关因素的个数为3。利用Matlab7.0仿真软件，以该小水电群2012年3月份预测为实例进行说明，原始数据如表1所示。 The monthly power generation data of runoff small hydropower groups in a certain area from 2009 to 2011 were selected as historical data, and the monthly power generation in 2012 was predicted. Hydrological water flow, hydrological precipitation, and meteorological precipitation, which are closely related to power generation, are selected as independent variable factors for prediction and analysis. It can be seen that the number of sample observation points is 3 and the number of related factors is 3. Using Matlab7.0 simulation software, the prediction of the small hydropower group in March 2012 is taken as an example to illustrate. The original data are shown in Table 1.

Figure DEST_PATH_IMAGE134
Figure DEST_PATH_IMAGE134

首先，选取以上三组数据进行PLS（偏最小二乘，Partial Least Square）建模，得到回归方程为： First, the above three sets of data are selected for PLS (Partial Least Square) modeling, and the regression equation is obtained as:

然后采用改进灰色预测算法对各相关因素分别进行处理，各因素预测数列如表2所示。 Then, the improved gray prediction algorithm is used to process each relevant factor separately, and the prediction sequence of each factor is shown in Table 2.

Figure DEST_PATH_IMAGE138
Figure DEST_PATH_IMAGE138

最后，将各相关因素的改进灰色预测值代入PLS线性回归方程，得到该地区径流式小水电群2012年3月份月度发电量预测值。以此类推，采用基于PLS与改进GM综合预测算法，可以得到2012年1～12月份月发电量预测值，与真实值对比预测效果如图2所示。预测相对误差分析如表3所示。 Finally, the improved gray forecast value of each relevant factor was substituted into the PLS linear regression equation to obtain the monthly power generation forecast value of the runoff small hydropower group in March 2012. By analogy, using the comprehensive forecasting algorithm based on PLS and improved GM, the forecasted value of monthly power generation from January to December 2012 can be obtained, and the predicted effect compared with the real value is shown in Figure 2. The prediction relative error analysis is shown in Table 3.

Figure DEST_PATH_IMAGE140
Figure DEST_PATH_IMAGE140

在2012年共12个月份月预测值中，最大误差为14.02%，最小误差为0.17%，平均预测误差为5.43%。显然本文所提出的针对径流式小水电群地区月度发电量的综合预测模型具有很高预测精度，且水文水流量、水文降水量等水文气象数据易于获取。通过仿真验证本发明正确有效。 In 2012, the maximum error is 14.02%, the minimum error is 0.17%, and the average forecast error is 5.43%. Obviously, the comprehensive prediction model for the monthly power generation in the area of runoff small hydropower clusters proposed in this paper has high prediction accuracy, and hydrometeorological data such as hydrological water flow and hydrological precipitation are easy to obtain. The correctness and effectiveness of the present invention are verified by simulation.

上面结合附图对本发明的具体实施方式作了详细说明，但是本发明并不限于上述实施方式，在本领域普通技术人员所具备的知识范围内，还可以在不脱离本发明宗旨的前提下作出各种变化。 The specific implementation of the present invention has been described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned implementation, within the knowledge of those of ordinary skill in the art, it can also be made without departing from the gist of the present invention. Variations.

Claims (2)

1. the group of a multipath streaming small power station area generated energy Comprehensive Prediction Method, is characterized in that: first adopt partial least square model, obtain the multipath streaming group of small power station area generated energy and affect the linear multiple regression equation between the correlative factor of generated energy; Adopt improved grey model forecast model to carry out modeling to each correlative factor ordered series of numbers simultaneously, obtain correlative factor predicted value; Then by the linear multiple regression equation of the correlative factor predicted value substitution partial least square model gained obtaining, obtain the multipath streaming group of small power station area generated energy predicted value; Finally draw relative error according to generated energy predicted value.
2. the multipath streaming group of small power station according to claim 1 area generated energy Comprehensive Prediction Method, is characterized in that: the concrete steps of described method are as follows:
A, according to the multipath streaming group of small power station area generated energy ywith mthe individual correlative factor variable that affects generated energy x 1, x 2..., x m , choose nindividual sample observation station, obtains x=[ x 1, x 2..., x m ] n× m , y=[ y] n× 1 , according to partial least square model, set up linear multiple regression equation and be:
Figure 9568DEST_PATH_IMAGE001
（1）
Wherein, i=1, m, mfor the number of correlative factor of hypothesis; c 0for the error system of regression equation, c 1, c 2, c m for regression coefficient;
Figure 532953DEST_PATH_IMAGE002
,
Figure 25114DEST_PATH_IMAGE003
...,
Figure 329057DEST_PATH_IMAGE004
for xin the value of each standard parameter inverse process; for yin the value of each standard parameter inverse process;
B, employing improved grey model forecast model carry out modeling to each correlative factor ordered series of numbers, obtain correlative factor predicted value: the concrete steps of described improved grey model forecast model are as follows:
B1, original data series is carried out to running mean processing, obtain the ordered series of numbers after slipping smoothness is processed;
B2, the ordered series of numbers after slipping smoothness is processed is carried out to one-accumulate generate one-accumulate ordered series of numbers, use one-accumulate ordered series of numbers structure differential equation of first order specified data matrix;
The solve for parameter of B3, employing least-squares estimation linear first-order differential equation;
B4, calculating are without inclined to one side
Figure 811433DEST_PATH_IMAGE006
the parameter of model
Figure 146599DEST_PATH_IMAGE007
, ;
B5, basis
Figure 78969DEST_PATH_IMAGE009
, aestimated value
Figure 576947DEST_PATH_IMAGE007
,
Figure 410910DEST_PATH_IMAGE008
set up original data sequence model:
（2）
Wherein, 0≤ k≤ n-1 o'clock for the match value of original data sequence, k>= ntime
Figure 219707DEST_PATH_IMAGE011
for the predicted value of original data sequence;
C, by the linear multiple regression analysis formula of the correlative factor predicted value substitution partial least square model gained obtaining, obtain the multipath streaming group of small power station area generated energy predicted value;
D, the absolute value of the difference of the actual value of generated energy and generated energy predicted value is obtained to relative error divided by the actual value of generated energy.
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CN109102110A (en) * 2018-07-23 2018-12-28 云南电网有限责任公司临沧供电局 A kind of radial-flow type small power station goes out force prediction method and device in short term
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Cited By (7)

* Cited by examiner, † Cited by third party
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CN106548285A (en) * 2016-11-04 2017-03-29 广西电网有限责任公司电力科学研究院 The bulk sale power predicating method that meter and small power station exert oneself
CN108154268A (en) * 2017-12-25 2018-06-12 国网福建省电力有限公司 The method of quick estimation Small Hydropower Stations generated energy
CN108154268B (en) * 2017-12-25 2022-07-05 国网福建省电力有限公司 A method for quickly estimating the power generation of small hydropower stations
CN109102110A (en) * 2018-07-23 2018-12-28 云南电网有限责任公司临沧供电局 A kind of radial-flow type small power station goes out force prediction method and device in short term
CN109102110B (en) * 2018-07-23 2022-03-22 云南电网有限责任公司临沧供电局 Method and device for predicting short-term output of runoff small hydropower station
CN110969297A (en) * 2019-11-26 2020-04-07 国网浙江省电力有限公司 Power load prediction method and device based on backward interval partial least square method
CN113610288A (en) * 2021-07-28 2021-11-05 华北电力大学 Power demand prediction method, device and storage medium

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