CN110807508B - Bus Peak Load Forecasting Method Considering Complicated Meteorological Effects - Google Patents
Bus Peak Load Forecasting Method Considering Complicated Meteorological Effects Download PDFInfo
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Abstract
Description
技术领域technical field
本发明属于母线峰值负荷预测技术领域,特别是涉及到一种计及复杂气象影响的母线峰值负荷预测方法。The invention belongs to the technical field of busbar peak load forecasting, and in particular relates to a busbar peak load forecasting method considering complex meteorological influences.
背景技术Background technique
母线峰值负荷历史数据有限、波动剧烈且呈现非线性和随机性特点,预测精度低且预测困难问题成为亟待解决的难题,如何提高母线峰值负荷预测精度已经成为亟待解决的课题。母线峰值负荷预测是电力系统保障可靠稳定运行的重要依据,分析和研究提高母线峰值负荷预测精度的方法具有十分重要的意义。The historical data of busbar peak load is limited, fluctuates violently and presents nonlinear and random characteristics, and the problem of low forecasting accuracy and difficult forecasting has become an urgent problem to be solved. How to improve the forecasting accuracy of busbar peak load has become an urgent problem to be solved. Bus peak load forecasting is an important basis for ensuring reliable and stable operation of power systems. It is of great significance to analyze and study methods to improve the accuracy of bus peak load forecasting.
目前,对于母线负荷预测,已有很多研究,分别针对母线负荷特点,优化了母线负荷预测,但是没有充分分析自然气象、社会等多种因素对母线负荷的影响,考虑众多因素时,没有进行特征选择,而且也没有考虑到不同母线影响因素的不同,没有对不同母线负荷的影响因素开展针对性特征选择,并且也没有在此基础上,建立针对性母线负荷预测模型。现有涉及峰荷预测研究多针对城市级电网峰值负荷的影响因素和预测方法开展,虽然现有研究一定程度上提高了峰荷预测精度,但尚未有针对峰值负荷预测中,历史数据有限的小样本问题开展针对性分析。At present, there have been many studies on the bus load forecasting, which optimized the bus load forecast according to the characteristics of the bus load, but did not fully analyze the influence of various factors such as natural weather and society on the bus load. When considering many factors, there is no characteristic selection, and did not take into account the different influencing factors of different busbars, did not carry out targeted feature selection for the influencing factors of different busbar loads, and did not establish a targeted busbar load forecasting model on this basis. Existing research on peak load forecasting is mostly carried out on the influencing factors and forecasting methods of peak load in city-level power grids. Although the existing research has improved the accuracy of peak load forecasting to a certain extent, there is no research on peak load forecasting with limited historical data. Carry out targeted analysis of sample questions.
因此现有技术当中亟需要一种新型的技术方案来解决这一问题。Therefore, there is an urgent need for a novel technical solution in the prior art to solve this problem.
发明内容Contents of the invention
本发明所要解决的技术问题是:提供一种计及复杂气象影响的母线峰值负荷预测方法用于解决现有技术中尚未有针对峰值负荷预测中,峰值负荷波动剧烈和历史数据有限的小样本问题开展针对性分析的技术问题。The technical problem to be solved by the present invention is to provide a bus peak load forecasting method that takes into account the influence of complex weather to solve the problem of small samples that have not yet been addressed in peak load forecasting, peak load fluctuations and limited historical data in the prior art Conduct targeted analysis of technical issues.
计及复杂气象影响的母线峰值负荷预测方法,包括以下步骤,并且以下步骤顺次进行,The bus peak load forecasting method considering complex meteorological influences includes the following steps, and the following steps are carried out in sequence,
步骤一、基于自然气象和社会因素对母线峰值负荷预测精度的影响,根据自然气象和社会因素构建母线峰值负荷预测的原始特征集合,通过条件互信息(ConditionalMutual Information,CMI)分析原始特征集合中各特征与母线峰值负荷间的相关性,获得特征重要度排序;
步骤二、通过改进粒子群算法优化极限学习机的输入权和阈值获得改进粒子群优化的极限学习机(Improved Particle Swarm Optimization-Extreme Learning Machine,IPSO-ELM),然后以IPSO-ELM的预测精度为决策变量,根据步骤一中获得的特征重要度排序结果开展针对性前向特征选择,获得母线峰值负荷预测的最优特征子集,根据获得的最优特征子集重新训练IPSO-ELM得到最优母线峰值负荷预测模型;Step 2. Optimize the input weight and threshold of the extreme learning machine by improving the particle swarm optimization algorithm to obtain the improved particle swarm optimization extreme learning machine (Improved Particle Swarm Optimization-Extreme Learning Machine, IPSO-ELM), and then take the prediction accuracy of IPSO-ELM as Decision variables, according to the feature importance ranking results obtained in
步骤三、将历史数据中设定时间段内的测试集数据代入步骤二中获得的最优母线峰值负荷预测模型中,获得母线峰值负荷的预测值;Step 3. Substituting the test set data within the set time period in the historical data into the optimal bus peak load prediction model obtained in step 2 to obtain the predicted value of the bus peak load;
步骤四、通过线型模型分别对极端高温条件下母线峰值负荷和极端低温条件下母线峰值负荷进行统计,根据统计结果得知母线峰值负荷与极端高温和极端低温均具有线性关系;
步骤五、利用最小二乘法对极端高温和极端低温与母线峰值负荷进行线性拟合,分别获得极端温度条件下母线1和母线2的峰值负荷预测的线性模型如下:
极端高温条件下,母线1峰值负荷预测的线性模型为:Under extreme high temperature conditions, the linear model for
极端低温条件下,母线1峰值负荷预测的线性模型为:Under extreme low temperature conditions, the linear model of
极端高温条件下,母线2峰值负荷预测的线性模型为:Under extreme high temperature conditions, the linear model for busbar 2 peak load prediction is:
极端低温条件下,母线2峰值负荷预测的线性模型为:Under extreme low temperature conditions, the linear model for bus 2 peak load prediction is:
公式中:为极端高温条件下母线1的峰值负荷;/>为极端高温条件下母线2的峰值负荷;/>为极端低温条件下母线1的峰值负荷;/>为极端低温条件下母线2的峰值负荷;T为极端温度。formula: is the peak load of
所述自然气象包括经度、纬度、温度、气压、湿度、风向和风速。The natural weather includes longitude, latitude, temperature, air pressure, humidity, wind direction and wind speed.
所述社会因素包括日期和节假日。The social factors include dates and holidays.
所述步骤二中的预测精度为预测值与实际值的平均绝对百分比误差(MeanAbsolute Percent Error,MAPE),MAPE的计算公式为:The prediction precision in described step 2 is the average absolute percentage error (MeanAbsolute Percent Error, MAPE) of predicted value and actual value, and the calculation formula of MAPE is:
公式中,Yi为母线峰值负荷实测值;为母线峰值负荷预测值;N为预测样本数。In the formula, Y i is the measured value of bus peak load; is the bus peak load forecast value; N is the number of forecast samples.
所述步骤二中通过改进粒子群算法优化极限学习机的输入权和阈值获得IPSO-ELM的具体方法为:In said step 2, the specific method for obtaining IPSO-ELM by improving the particle swarm optimization algorithm to optimize the input weight and threshold of the extreme learning machine is as follows:
1)基于原始特征集合构建母线峰值负荷预测的ELM模型,并随机产生ELM的输入权值ω和隐层单元偏置阈值b;1) Construct the ELM model of bus peak load forecasting based on the original feature set, and randomly generate the input weight ω and hidden layer unit bias threshold b of ELM;
2)确定输入母线峰值负荷预测所需原始特征集合的数据,设置迭代次数;2) Determine the data of the original feature set required for input bus peak load prediction, and set the number of iterations;
3)针对母线峰值负荷预测原始特征集合数据,进行归一化处理;3) Normalize the original feature set data for bus peak load prediction;
4)根据ELM的母线峰荷预测的平均绝对百分误差值获得适应度值,并获得当前个体适应度值和群体最佳适应度值;4) Obtain the fitness value according to the average absolute percentage error value of the bus peak load prediction of the ELM, and obtain the current individual fitness value and the group best fitness value;
5)在粒子群算法PSO基础上,根据非线性动态惯性权重系数的计算公式和学习因子计算公式,更新粒子速度与位置;5) On the basis of the particle swarm optimization algorithm PSO, according to the calculation formula of the nonlinear dynamic inertia weight coefficient and the calculation formula of the learning factor, the particle velocity and position are updated;
6)计算并获得当前粒子适应度值,当前粒子适应度值与历史最优个体粒子适应度值比较,当前粒子适应度值更优,则更新粒子最优解;否则维持个体最佳适应度值;6) Calculate and obtain the current particle fitness value, compare the current particle fitness value with the historical optimal individual particle fitness value, if the current particle fitness value is better, then update the particle optimal solution; otherwise maintain the individual optimal fitness value ;
7)当前粒子的适应度值比群体最优解更优,则更新群体最优解;否则,维持群体最优解不变;7) If the fitness value of the current particle is better than the swarm optimal solution, update the swarm optimal solution; otherwise, keep the swarm optimal solution unchanged;
8)未达到步骤2)中设定的迭代次数,返回步骤3),直至达到设定的迭代次数,将最优解输入权值ω和隐层单元偏置阈值b代入ELM,构建母线峰值负荷预测模型。8) If the number of iterations set in step 2) is not reached, return to step 3) until the set number of iterations is reached, and then substitute the optimal solution input weight ω and hidden layer unit bias threshold b into the ELM to construct the bus peak load predictive model.
所述非线性动态惯性权重系数的表达式为:The expression of the nonlinear dynamic inertia weight coefficient is:
式中:w为惯性权重,wmin为惯性权重最小值,wmax为惯性权重最大值;f为粒子适应度;favg为平均适应度;fmin为最小适应度。In the formula: w is the inertia weight, w min is the minimum value of the inertia weight, w max is the maximum value of the inertia weight; f is the particle fitness; f avg is the average fitness; f min is the minimum fitness.
所述学习因子的表达式为:The expression of the learning factor is:
式中:c1和c2为学习因子,c1s为c1的初值,c2s为c2的初值,c1c为c1的终值,c2c为c2的终值;iter是当前迭代的次数;itermax是总迭代的次数。In the formula: c 1 and c 2 are learning factors, c 1s is the initial value of c 1 , c 2s is the initial value of c 2 , c 1c is the final value of c 1 , c 2c is the final value of c 2 ; iter is The number of current iterations; iter max is the number of total iterations.
所述迭代次数为200次。The number of iterations is 200.
通过上述设计方案,本发明可以带来如下有益效果:Through the above design scheme, the present invention can bring the following beneficial effects:
本发明以条件互信息对原始特征集合中待选特征的特征重要度结果为依据,结合IPSO-ELM作为预测器,开展前向特征选择,确定母线峰值负荷预测的最优特征集合,降低了母线峰值负荷预测时特征冗余对预测精度的影响,且针对不同母线分别构建最优预测模型有效提高了不同母线预测精度,又引入IPSO-ELM与线性方法结合,开展不同场景下峰荷预测,满足小样本或无样本场景下预测需要。The present invention is based on the conditional mutual information on the feature importance results of the features to be selected in the original feature set, and combines IPSO-ELM as a predictor to carry out forward feature selection to determine the optimal feature set for bus peak load prediction, reducing the bus load. The impact of feature redundancy on prediction accuracy during peak load forecasting, and the construction of optimal forecasting models for different buses can effectively improve the forecasting accuracy of different buses, and the combination of IPSO-ELM and linear methods is introduced to carry out peak load forecasting under different scenarios to meet Prediction needs in small-sample or no-sample scenarios.
附图说明Description of drawings
以下结合附图和具体实施方式对本发明作进一步的说明:The present invention will be further described below in conjunction with accompanying drawing and specific embodiment:
图1是本发明计及复杂气象影响的母线峰值负荷预测方法的实施例中极端高温条件下母线1峰值负荷平均值散点图和拟合曲线图。Fig. 1 is a scatter diagram and a fitting curve diagram of the peak load average value of
图2是本发明计及复杂气象影响的母线峰值负荷预测方法的实施例中极端高温条件下母线2峰值负荷平均值散点图和拟合曲线图。Fig. 2 is a scatter diagram and a fitting curve diagram of the peak load average value of bus 2 under extremely high temperature conditions in the embodiment of the bus peak load forecasting method considering complex weather effects of the present invention.
图3是本发明计及复杂气象影响的母线峰值负荷预测方法的实施例中极端低温条件下母线1峰值负荷平均值散点图和拟合曲线图。Fig. 3 is a scatter diagram and a fitting curve diagram of the peak load average value of
图4是本发明计及复杂气象影响的母线峰值负荷预测方法的实施例中极端低温条件下母线2峰值负荷平均值散点图和拟合曲线图。Fig. 4 is a scatter diagram and a fitting curve diagram of the peak load average value of bus 2 under extremely low temperature conditions in the embodiment of the bus peak load forecasting method considering complex meteorological influences of the present invention.
图5是本发明计及复杂气象影响的母线峰值负荷预测方法的实施例中母线1峰值负荷特征重要度分析图。Fig. 5 is an analysis diagram of the importance degree of peak load characteristics of
图6是本发明计及复杂气象影响的母线峰值负荷预测方法的实施例中母线2峰值负荷特征重要度分析图。Fig. 6 is an analysis diagram of the importance degree of peak load characteristics of bus 2 in the embodiment of the bus peak load prediction method considering complex meteorological influences in the present invention.
图7是本发明计及复杂气象影响的母线峰值负荷预测方法的实施例中条件互信息结合不同预测器的最优特征集合选择图。Fig. 7 is an optimal feature set selection diagram of conditional mutual information combined with different predictors in an embodiment of the bus peak load forecasting method considering complex meteorological influences in the present invention.
图8是本发明计及复杂气象影响的母线峰值负荷预测方法的实施例中针对性模型和统一模型母线峰值负荷预测对比图。Fig. 8 is a comparison chart of bus peak load forecasting between the targeted model and the unified model in the embodiment of the bus peak load forecasting method considering complex meteorological influences in the present invention.
图9是本发明计及复杂气象影响的母线峰值负荷预测方法的实施例中三种方法的母线峰值负荷预测对比图。Fig. 9 is a comparison chart of bus peak load forecasting of three methods in the embodiment of the method for forecasting bus peak load considering complex meteorological influences in the present invention.
具体实施方式Detailed ways
如图所示,计及复杂气象影响的母线峰值负荷预测方法,包括以下步骤:As shown in the figure, the bus peak load forecasting method considering complex meteorological influences includes the following steps:
1、母线峰值负荷预测原始特征集合构建1. Construction of original feature set for bus peak load forecasting
(1)母线峰值负荷预测的原始特征集合(1) The original feature set of bus peak load forecasting
自然气象、社会等多种因素都会导致母线峰值负荷发生波动。通过对复杂气象因素分析和相关文献研究,构建的原始特征集合如表1所示。Various factors such as natural weather and society will cause the peak load of the bus to fluctuate. Through the analysis of complex meteorological factors and related literature research, the original feature set constructed is shown in Table 1.
表1母线峰值负荷预测原始特征集合Table 1 The original feature set of bus peak load forecasting
注:Note:
1)FT表示预测日当天温度峰值,FTave表示预测日当天温度平均值;FT(max,d-1)表示预测日前一天温度峰值,FT(ave,d-1)表示预测日前一天的平均温度;FA表示预测时刻的气压、FH表示预测时刻的湿度、FW表示预测时刻的风向、FW1表示预测时刻的风速,FA、FH、FW以及FW1等均为气象特征;1) FT represents the peak temperature on the forecast day, F Tave represents the average temperature on the forecast day; FT(max,d-1) represents the peak temperature on the day before the forecast day, and FT(ave,d-1) represents the day before the forecast day F A is the air pressure at the forecast time, F H is the humidity at the forecast time, F W is the wind direction at the forecast time, F W1 is the wind speed at the forecast time, F A , F H , F W and F W1 are all meteorological features;
2)FG1表示待预测母线的经度、FG2表示待预测母线的纬度;FT、FTave、FT(max,d-1)、FT(ave,d-1)、FA、FH、FW、FW1、FG1以及FG2等均为自然气象特征;2) F G1 represents the longitude of the bus to be predicted, F G2 represents the latitude of the bus to be predicted; F T , F Tave , F T(max,d-1) , F T(ave,d-1) , F A , F H , F W , F W1 , F G1 and F G2 are all natural meteorological features;
3)FD1到FD7为星期内日期;FJ1为标志工作日;FJ2为非工作日;FH1表示节假日;FH2表示正常日;FD1到FD7、FJ1、FJ2、FH1以及FH2均为社会因素;3) F D1 to F D7 are days of the week; F J1 is a working day; F J2 is a non-working day; F H1 is a holiday; F H2 is a normal day; F D1 to F D7 , F J1 , F J2 , F Both H1 and F H2 are social factors;
4)FL(max,d-1)表示预测日前一天的母线峰值负荷,FL(max,d-2)表示预测日前两天的母线峰值负荷,以此类推;FL(t-15)表示待测日前一天峰值负荷前15分钟的母线负荷,FL(t-30)表示待测日前一天母线峰值负荷前30分钟的母线负荷,依此类推。4) FL (max,d-1) represents the peak load of the bus one day before the forecast date, FL (max,d-2) represents the peak load of the bus two days before the forecast date, and so on; FL(t-15) FL (t-30) represents the
(2)条件互信息(2) Conditional mutual information
在母线峰值负荷预测中,设D为包含自然气象、社会等多种因素的原始特征集合;Q为实测母线峰值负荷值;Z集合是已选择的特征。D和Q间的互信息为:In bus peak load forecasting, let D be the original feature set including various factors such as natural weather and society; Q be the measured bus peak load value; Z set is the selected feature. The mutual information between D and Q is:
公式(1)中,F(D;Q)表示D和Q间的互信息,P(d)为D的边际密度函数,P(q)为Q的边际密度函数,P(d,q)为D和Q的联合概率密度。In formula (1), F(D; Q) represents the mutual information between D and Q, P(d) is the marginal density function of D, P(q) is the marginal density function of Q, and P(d,q) is Joint probability density of D and Q.
在已知Z集合的条件下,集合D与实测母线峰值负荷值Q的条件互信息为:Under the condition that the Z set is known, the conditional mutual information between the set D and the measured bus peak load value Q is:
公式(2)中,F(D,Q|Z)表示在Z条件下D和Q间的条件互信息,P(d|z)为在Z条件下D、Q的概率密度函数;P(q|z)为在Z条件下Q的概率密度函数;P(d,q|z)为在Z条件下D、Q的联合概率密度函数;P(d,q,z)为D、Q、Z的联合概率密度函数。In formula (2), F(D,Q|Z) represents the conditional mutual information between D and Q under Z condition, P(d|z) is the probability density function of D and Q under Z condition; P(q |z) is the probability density function of Q under Z condition; P(d,q|z) is the joint probability density function of D and Q under Z condition; P(d,q,z) is D, Q, Z The joint probability density function of .
母线峰值负荷影响因素众多,如果考虑全部影响因素,将会造成信息冗余,母线峰值负荷预测精度低。为提高母线峰值负荷预测精度,通过条件互信息分析各影响因素与不同母线峰值负荷间的相关性,获得原始特征集合中特征重要度排序。There are many factors affecting bus peak load. If all the influencing factors are considered, information redundancy will be caused, and the prediction accuracy of bus peak load will be low. In order to improve the prediction accuracy of bus peak load, the correlation between various influencing factors and different bus peak loads is analyzed through conditional mutual information, and the ranking of feature importance in the original feature set is obtained.
2、母线峰值负荷预测模型构建2. Construction of busbar peak load forecasting model
(2.1)基于改进粒子群优化的极限学习机原理(2.1) The principle of extreme learning machine based on improved particle swarm optimization
以有限的母线峰值负荷数据训练神经网络等预测器,难以获得理想的母线峰值负荷预测模型。因此,应用适用于小样本训练的极限学习机构建母线峰值负荷预测器。为避免参数选择不当影响预测效果,应用改进的粒子群算法优化极限学习机的输入权值和阈值,母线峰值负荷预测器,以进一步提高预测精度。It is difficult to obtain an ideal bus peak load forecasting model by training predictors such as neural networks with limited bus peak load data. Therefore, an extreme learning machine suitable for small-sample training is applied to build a bus peak load predictor. In order to avoid the influence of improper parameter selection on the prediction effect, the improved particle swarm optimization algorithm is applied to optimize the input weight and threshold of the extreme learning machine, bus peak load predictor, to further improve the prediction accuracy.
(2.1.1)极限学习机(2.1.1) Extreme Learning Machine
设有N个样本其中,输入数据为xi=[xi1,xi2,…,xin]T∈Rn,目标输出值为ti=[ti1,ti2,…,tim]T∈Rm。则隐层节点的数目为L的单隐层神经网络的ELM极限学习机网络模型可表示为With N samples Wherein, the input data is xi =[x i1 , xi2 ,…,x in ] T ∈ R n , and the target output value is t i =[t i1 ,t i2 ,…,t im ] T ∈ R m . Then the ELM extreme learning machine network model of the single hidden layer neural network whose number of hidden layer nodes is L can be expressed as
式中,oj表示网络输出值;g表示激活函数;ωi为输入权重;βi是输出权重;bi是第i个隐层单元的偏置;xj表示xi中的数据。In the formula, o j represents the network output value; g represents the activation function; ω i is the input weight; β i is the output weight; b i is the bias of the i-th hidden layer unit; x j represents the data in xi .
无误差时,激活函数无限接近任意N个样本,即When there is no error, the activation function is infinitely close to any N samples, that is
根据式(4)可得According to formula (4), we can get
式中,g表示激活函数;ωi为输入权重;βi是输出权重;bi是第i个隐层单元的偏置;tj表示激活函数能够零误差逼近任意N个样本时的网络输出值;In the formula, g represents the activation function; ω i is the input weight; β i is the output weight; b i is the bias of the i-th hidden layer unit; t j represents the network output when the activation function can approach any N samples with zero error value;
式(5)中N个方程矩阵形式为The matrix form of N equations in formula (5) is
Hβ=T (6)Hβ=T (6)
其中,in,
H表示隐含层节点输出;T为期望输出;β表示输出层和隐层之间的权值矩阵。H represents the hidden layer node output; T represents the desired output; β represents the weight matrix between the output layer and the hidden layer.
通过获得和/>实现对单隐层ELM训练,使得by obtaining and /> Realize the training of single hidden layer ELM, so that
式中,表示βi最优解;/>表示ωi的最优解;/>表示bi的最优解;H表示隐含层节点输出;T为期望输出;In the formula, Indicates the optimal solution of β i ; /> Indicates the optimal solution of ω i ; /> Represents the optimal solution of bi ; H represents the hidden layer node output; T is the expected output;
与(9)式等价的最小损失函数为The minimum loss function equivalent to (9) is
式中,E表示最小损失函数;g表示激活函数;ωi为输入权重;βi是输出权重;bi是第i个隐层单元的偏置。In the formula, E represents the minimum loss function; g represents the activation function; ω i is the input weight; β i is the output weight; b i is the bias of the ith hidden layer unit.
在ELM中,输入权值ω和隐层单元的偏置阈值b一旦被随机确定,即可获得唯一隐含层节点输出H。由此,确定ELM结构。In ELM, once the input weight ω and the bias threshold b of the hidden layer unit are randomly determined, the unique hidden layer node output H can be obtained. From this, the ELM structure is determined.
(2.2)基于改进粒子群的极限学习机参数优化(2.2.1)改进粒子群原理(2.2) Parameter optimization of extreme learning machine based on improved particle swarm (2.2.1) Principle of improved particle swarm
为了优化在全局最优解周围粒子群算法易发生波动的问题,通过惯性权重对传统粒子群改进,其表达式为:In order to optimize the problem that the particle swarm algorithm is prone to fluctuations around the global optimal solution, the traditional particle swarm optimization is improved through the inertia weight, and its expression is:
式(11)中:w表示惯性权重,wmin为惯性权重最小值,wmax为惯性权重最大值;f为粒子适应度;favg为平均适应度;fmin为最小适应度。In formula (11): w represents inertia weight, w min is the minimum value of inertia weight, w max is the maximum value of inertia weight; f is particle fitness; f avg is average fitness; f min is minimum fitness.
为了使粒子群优化算法能快速确定全局最优解,通过式(12)传统粒子群进行动态调整,即In order to enable the particle swarm optimization algorithm to quickly determine the global optimal solution, the traditional particle swarm is dynamically adjusted through formula (12), namely
在(12)中:c1和c2均为学习因子,c1s为c1的初值,c2s为c2的初值,c1c为c1的终值;c2c为c2的终值;iter是当前迭代的次数;itermax是总迭代的次数。In (12): c 1 and c 2 are learning factors, c 1s is the initial value of c 1 , c 2s is the initial value of c 2 , c 1c is the final value of c 1 ; c 2c is the final value of c 2 Value; iter is the number of current iterations; iter max is the total number of iterations.
(2.2.2)基于改进粒子群的ELM参数优化(2.2.2) ELM parameter optimization based on improved particle swarm
以原始特征集合构建母线峰值负荷预测模型最优过程为例,展示IPSO优化ELM过程如下:Taking the optimal process of constructing the bus peak load forecasting model with the original feature set as an example, the IPSO optimization ELM process is shown as follows:
1)基于原始特征集合构建母线峰值负荷预测ELM,并随机产生ELM的输入权值ω和隐层单元偏置阈值b;1) Construct busbar peak load prediction ELM based on the original feature set, and randomly generate ELM input weight ω and hidden layer unit bias threshold b;
2)确定输入母线负荷峰值预测所需原始特征集合的数据,设置迭代次数;2) Determine the data of the original feature set required for input bus load peak prediction, and set the number of iterations;
3)针对母线峰值负荷预测原始特征集合的数据,开展归一化处理;3) Carry out normalization processing for the data of the original feature set of bus peak load prediction;
4)根据ELM的母线峰荷预测的平均绝对百分误差获得适应度值,并确定当前个体和群体最佳适应值;4) Obtain the fitness value according to the average absolute percentage error of the peak load prediction of the ELM, and determine the best fitness value of the current individual and group;
5)在传统PSO基础上,并根据式(11)、(12),更新粒子速度与位置;5) On the basis of traditional PSO, and according to equations (11) and (12), update particle velocity and position;
6)首先,计算当前粒子适应度值,然后与历史最优值比较,如更优,则更新粒子最优解;否则维持个体最佳适应度值;6) First, calculate the current particle fitness value, and then compare it with the historical optimal value. If it is better, update the particle optimal solution; otherwise, maintain the individual optimal fitness value;
7)如果当前粒子的适应度值比群体最优解更优,则更新群体最优解;否则,维持群体最优解不变;7) If the fitness value of the current particle is better than the swarm optimal solution, update the swarm optimal solution; otherwise, keep the swarm optimal solution unchanged;
8)如未达到迭代次数,则返回3),否则,将最优解ω和b代入ELM,构建母线峰值负荷预测模型。8) If the number of iterations is not reached, return to 3), otherwise, substitute the optimal solution ω and b into the ELM to construct a bus peak load forecasting model.
后文特征选择环节,对不同维度特征集合构建针对性最优ELM预测器,均采用以上方法。In the following feature selection link, the above methods are used to construct targeted optimal ELM predictors for feature sets of different dimensions.
3、无训练样本母线峰值负荷预测模型3. No training sample bus peak load forecasting model
ELM等预测器虽然适用于小样本预测,但其构建仍然依赖历史样本。如在预测日出现历史未曾出现过的极端温度(极端高温和极端低温),则无法保证预测效果。为提高无训练样本母线峰值负荷预测精度,引入线型模型单独对无训练样本极端高、低温场景母线峰值负荷开展预测。Although predictors such as ELM are suitable for small-sample forecasting, their construction still relies on historical samples. If there are extreme temperatures (extreme high temperature and extreme low temperature) that have not occurred in history on the forecast date, the forecast effect cannot be guaranteed. In order to improve the prediction accuracy of bus peak load without training samples, a linear model is introduced to predict the peak load of bus in extreme high and low temperature scenarios without training samples.
实施例:Example:
对东北某市2018年的极端高温和极端低温的极端气象条件下的多条母线峰值负荷进行统计分析。在本实施例中设定极端高温为日最高温度高于30度,极端低温为日最低温度低于零下20度。由统计结果知母线峰值负荷与最高温度具有明显的线性关系,因此,利用最小二乘法对极端温度与母线峰值负荷进行线性拟合。Statistical analysis was carried out on the peak loads of multiple buses under the extreme weather conditions of extreme high temperature and extreme low temperature in a certain city in Northeast China in 2018. In this embodiment, the extreme high temperature is set as the daily maximum temperature higher than 30 degrees, and the extreme low temperature is set as the daily minimum temperature lower than minus 20 degrees. According to the statistical results, there is an obvious linear relationship between the peak load of the busbar and the maximum temperature. Therefore, the linear fitting between the extreme temperature and the peak load of the busbar is carried out by using the least square method.
图1至图4分别给出了东北某城市2018年的母线1和母线2的极端高温和极端低温的极端气象条件下,母线峰值负荷平均值的散点图和对应的拟合曲线。通过图1至图4以及两条母线极端气象条件下的母线峰值负荷预的线性模型可知,极端气象对不同母线的峰值负荷的影响不同。因此,极端气象条件时,对于不同母线,需要针对性建模分析,提高母线峰值负荷的预测精度。Figures 1 to 4 respectively show the scatter diagrams and corresponding fitting curves of the bus peak load average under the extreme high temperature and extreme low temperature weather conditions of
通过利用最小二乘法对极端温度与母线峰值负荷线性拟合得到的极端气象条件下母线1和母线2的峰值负荷预测的线性模型如下:The linear model of the peak load prediction of
极端高温条件下,母线1峰值负荷预测的线性模型为:Under extreme high temperature conditions, the linear model for
极端低温条件下,母线1峰值负荷预测的线性模型为:Under extreme low temperature conditions, the linear model of
采用相同方法,得到母线2线性预测模型。Using the same method, get the bus 2 linear prediction model.
极端高温条件下,母线2峰值负荷预测的线性模型为:Under extreme high temperature conditions, the linear model for busbar 2 peak load prediction is:
极端低温条件下,母线2峰值负荷预测的线性模型为:Under extreme low temperature conditions, the linear model for bus 2 peak load prediction is:
公式中:和/>分别为极端高温条件下母线1和母线2的峰值负荷;/>和/>分别为极端低温条件下母线1和母线2的峰值负荷;T为极端温度。formula: and /> are the peak loads of
研究中应用2018年东北某市母线峰值负荷和气象信息数据,其中1、4、8、10月份数据作为验证集,7月份数据作为测试集,其余7个月为训练集,对不同母线开展针对性特征选择。为证明新方法先进性,以IPSO-ELM与ELM和BP神经网络(Back Propagation NeuralModel,BPNN)作对比实验。以平均绝对百分比误差(Mean Absolute Percent Error,MAPE)、均方根误差(Root Mean Square Error,RMSE)评估模型预测效果,指标计算方法如下:In the study, the busbar peak load and meteorological information data of a city in Northeast China in 2018 were used. The data in January, April, August, and October were used as the verification set, the data in July was used as the test set, and the remaining 7 months were used as the training set. Sexual selection. In order to prove the advanced nature of the new method, IPSO-ELM, ELM and BP neural network (Back Propagation NeuralModel, BPNN) were used as comparative experiments. The prediction effect of the model is evaluated by mean absolute percentage error (Mean Absolute Percent Error, MAPE) and root mean square error (Root Mean Square Error, RMSE). The index calculation method is as follows:
在式(17)和(18):Yi为母线峰值负荷实测值;为母线峰值负荷预测值;N为预测样本数。In formulas (17) and (18): Y i is the measured value of bus peak load; is the bus peak load forecast value; N is the number of forecast samples.
(1)基于条件互信息特征选择分析(1) Feature selection analysis based on conditional mutual information
图5和图6为不同母线峰值负荷特征重要度分析图,由图可知,不同母线峰值负荷与特征间相关性存在差异。图7给出了CMI分别结合IPSO-ELM、BPNN、ELM对母线1最优特征集合选择后,最优特征集合包含的特征个数和对应的MAPE值;表2给出最优特征集合包含特征。由图7可知,母线峰值负荷预测时,选择的特征集合不同,预测误差不同。当IPSO-ELM、BPNN、ELM分别作为预测器,且特征子集特征维度分别为25、28、34时,母线峰值负荷预测的误差最小。且由图7可知,根据最优特征集合,用BPNN、ELM、IPSO-ELM分别作为预测器时,母线1峰值负荷预测的MAPE值分别为,4.54%、3.75%、3.04%,在三种预测器中,IPSO-ELM母线峰值负荷预测的MAPE值最小,表明了IPSO-ELM预测精度高的优点。同理,可确定母线2最优特征子集。Figure 5 and Figure 6 are the analysis diagrams of the importance of peak load characteristics of different buses. It can be seen from the figure that there are differences in the correlation between peak load and characteristics of different buses. Figure 7 shows the number of features contained in the optimal feature set and the corresponding MAPE values after CMI combines IPSO-ELM, BPNN, and ELM to select the optimal feature set for
表2最优特征集合Table 2 Optimal feature set
(2)母线峰值负荷预测结果分析(2) Analysis of busbar peak load forecast results
为证明提出的母线峰值负荷预测方法精度高的优点,列出2018年7月东北某市母线1和母线2的峰值负荷预测结果。图8中给出了两条母线针对性建模和采用原始特征集合构建预测模型的母线峰值负荷预测结果;表3对应图8中母线峰值负荷预测误差。当最优模型下,两条母线峰值负荷预测的MAPE分别为3.04%和2.98%;原始特征集合建模时,两条母线峰值负荷预的MAPE分别3.89%和4.01%。通过对比可以看出,针对不同母线开展针对性特征选择,根据特征选择结果,针对性建立母线峰值负荷预测模型,预测精度高。In order to prove the advantages of the proposed bus peak load forecasting method with high accuracy, the peak load forecast results of
图9给出了IPSO-ELM、ELM和BPNN分别作为母线峰值负荷预测器时,对2018年东北某市母线1的7月份母线峰值负荷预测结果,表4对应图9中三种母线峰值负荷预测方法的预测误差。从表4中可以看出,应用BPNN、ELM和IPSO-ELM预测母线峰值负荷的MAPE分别为4.23%,3.93%、3.04%,IPSO-ELM母线峰值负荷预测的MAPE最小。因此,对于复杂气象因素导致母线峰值负荷剧烈波动的问题,本发明提出的方法预测精度高。Figure 9 shows the bus peak load forecast results of
表3母线峰值负荷预测误差Table 3 Bus Peak Load Prediction Error
表4三种方法的峰值负荷预测误差Table 4 Peak load forecasting errors of the three methods
为进一步验证无训练样本极端高温、极端低温场景下新方法预测有效性,将东北某市2018年度最高、最低气温日从训练样本中剔除,并将该最高、最低气温日作为待预测日,以该气温日之前的历史数据作为训练数据。分别以改进粒子群优化极限学习机与线性模型预测该日不同母线峰值负荷,结果如表5所示。由表5可知,以线性模型预测无历史温度样本母线峰荷时具有更高精度,证明新方法能够有效避免无训练样本极端温度下历史数据缺失导致的峰荷预测误差。新方法具有更好的可应用性。In order to further verify the effectiveness of the new method in extreme high temperature and extreme low temperature scenarios without training samples, the highest and lowest temperature days in a certain city in Northeast China in 2018 were removed from the training samples, and the highest and lowest temperature days were used as the days to be predicted. The historical data before the temperature day is used as training data. The improved particle swarm optimization extreme learning machine and linear model were used to predict the peak load of different buses on that day, and the results are shown in Table 5. It can be seen from Table 5 that the linear model has higher accuracy in predicting the bus peak load of samples without historical temperature, which proves that the new method can effectively avoid the peak load prediction error caused by the lack of historical data under extreme temperatures without training samples. The new method has better applicability.
表5极端气象日母线峰值负荷预测Table 5 Bus Peak Load Forecast on Extreme Weather Days
综上,以条件互信息值为依据,开展母线峰值负荷预测特征选择,降低了母线峰值负荷预测时特征冗余对预测精度的影响,且针对不同母线分别构建最优预测模型有效提高了不同母线预测精度,又引入改进粒子群优化极限学习机与线性方法结合,开展不同场景下峰荷预测,满足小样本或无样本场景下预测需要。In summary, based on the conditional mutual information value, the feature selection of bus peak load forecasting is carried out, which reduces the influence of feature redundancy on the prediction accuracy of bus peak load forecasting, and the optimal forecasting models for different buses are constructed to effectively improve the performance of different busbars. In order to improve the prediction accuracy, the combination of improved particle swarm optimization extreme learning machine and linear method is introduced to carry out peak load prediction in different scenarios to meet the prediction needs in small sample or no sample scenarios.
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