翻译-人工神经网络在短期负荷预测中的应用

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1、目 录外文文献翻译11 绪论12 各种影响负荷预测的因素23 混合神经网络33.1 线性神经网络33.2 非线性神经网络44 神经网络结构的确定54.1 自动校正54.2 遗传算法75 短期负荷预测系统76 仿真结果97 优化处理107.1 基于规则系统107.2 模式识别系统10结论11外文文献原文121.Introduction122.Variables Afferting Short-Term Load143. Hybrid Neurak Networks153.1 Linear Neutal Networks153.2 Non-Linear Neural Networks164. De

2、termination of Network Structure174.1 Autocorrelation184.2 Genetic Algorithm195. Short Term Load Forecasting System206. Simulation Result217.Enhancement227.1 Rule-Based System237.2 Pattern Recognition System23Conclusion24外文文献翻译人工神经网络在短期负荷预测中的应用摘要：在本文，我们将讨论如何利用人工神经网络对短期负荷进行预测。在这类系统中，有两种类型的神经网络：非线性和线性

3、神经网络。非线性神经网络是用来捕获负荷和各种输入参数之间的高度非线性关系。基于ARMA模型的神经网络，主要用来捕捉很短的时间期限内负载的变化。我们的系统可以实现准确性高的短期负荷预测。关键词：短期负荷预测，人工神经网络1 绪论短期（每小时）负荷预测对于电力系统的稳定运行是必要的。准确的负荷预测对于高效的发电调度，开停机计划，需求方的管理，短时维护安排或其他目的等是很必要的。改进短期负荷预测的准确性能为公共事业和联合发电节省很多开支。很多种电力系统负荷预测方法在学术界已经报导了。这些方法包括：多元线性回归法，时间序列法，一般指数平滑法，卡尔曼滤波法，专家系统法和人工神经网络预测法。由于电力负荷和

4、各种参数（天气的温度，湿度，风速等）之间的高度非线性的关系，无论在电力负荷预测建模或在预测中都有重要的作用。人工神经网络就是这种具有潜力的非线性技术的代表，但是由于电力系统的复杂性，神经网络的规模会较大，所以，当终端用户每天甚至每小时都在改变系统的运行时，训练这个网络将是一个重大的问题。在本文中，我们把这网络看作是建立在负荷预测系统上的混合神经网络。这类网络中包含两类网络：非线性神经网络和线性神经网络。非线性神经网络常用来捕获负荷与各种输入参数（如历史负荷值、气象温度、相关湿度等）间的高度非线性关系。我们常用线性神经网络来建立ARMA模型。这种基于ARMA模型的神经网络主要用来捕获负荷在很短时

5、间期限内的变化。最终的负荷预测系统是两种神经网络的组合。要用大量的历史数据来训练神经网络，以减小平均绝对误差百分比 (MAPE)。一种改进的反向传播学习算法已经用来训练非线性神经网络。我们使用Widrow -霍夫算法训练线性神经网络。当网络结构越简单，那整个系统的训练也就越快。为了说明这个基于实际情况的负荷预测系统的神经网络的性能，我们采用一个公共机构提供的实际需求数据来训练系统，利用三年（1989，1990，1991）中每小时的数据来训练这个神经网络，用1992年每小时的实际需求数据用来验证整个系统。这文章内容安排如下：第一部分介绍本文内容；第二部分描述了影响负荷预测结果的因素；第三部分介绍

6、了混合神经网络在系统中的应用；第四部分描述了找到最初网络结构的方法。第五部分详细介绍了负荷预测系统；第六部分给出了一些仿真结果；最后，第七部分介绍了系统的优化处理。2 各种影响负荷预测的因素以下是一些影响负荷预测的因素：温度湿度风速云层日照时间地理区域假期经济因素显然，这些因素的影响程度取决于负荷的类型。例如：温度变化对民用和商业负荷的影响大于它对工业负荷的影响。相对较多民用负荷的区域的短期负荷受气候条件影响程度大于工业负荷较多的区域。但是，工业区域对于经济因素较为敏感，如假期。如下一个例子，图2.1表示了午夜开始的一天中负荷的变化。图2.1 一天中负荷变化的示例3 混合神经网络我们所研究的负

7、荷预测系统由两类网络组成：ARMA模型的线性神经网络和前馈非线性神经网络。非线性神经网络常用来捕获负荷与各种输入参数间的高度非线性关系。我们常用线性神经网络来建立ARMA模型，这种基于ARMA模型的神经网络主要用来捕获负荷在很短时间期限（一个小时）内的变化。3.1 线性神经网络一般的多元线性的调整参数p和独立变量x的关系是：其中： -时刻的电力负荷 -时刻的独立变量 -时刻的随机干扰量 -系数线性神经网络能成功地学习历史负荷数据和独立变量中的系数和，Widrow-Hoff已经决定了这些系数。这个模型包括了先前所以数据高达p的延迟，如上所示，这些数据不是独立的，它与负荷有不用程度的相关性。相关性

8、学习用来决定模型中包含的最重要的参数，决定了许多参数会被去掉。这样就减少了给定精度模型的大小和运算时间或是提高了给定规模大小的模型的精度。3.2 非线性神经网络为了能进行非线性预测，要建立一个类似线性模型的非线性模型，如下表示：其中：是由人工神经网络决定的非线性函数前馈神经网络用层来表示，通常有一个隐含层（在某些情况下有2层），层和层之间是充分联系的，每一层有一个偏置单元（输出层除外）。输出是每个单元的加权输入的总和（包括偏置），中间是通过指数激活函数来传递。我们已经应用了修正的反向神经网络。错误的是定义了输出单元的计数值和实际值或理想值之间的偏差的平方，这个定义使函数在微分的时候发生错误。不

9、像线性的时间序列模型那样在每个滞后变量有一个装有系数，非线性神经网络滞后输入变量的选择和装有系数的数量是独立的，而网络的规模，是有由层数和隐含层单元的数目决定的。此外，在线性回归模型中，如果输入变量是无关的，那么它的回归系数是零。但是在非线性神经网络中者不一定是真实的；一个输入变量可能不重要但是仍可能有权重；这些权重将会影响到下层的传递，对于隐含单元来说也是重要的。所以，在传统的反向传播神经网络中，没有自动消除无关输入节点和隐含节点的功能。但是，在实际预测中有必要建立一个简约模型，它能解决实际问题，但不会太简单也不会太复杂。如果神经网络太小（输入端少或是隐含单元少），就不够灵活来捕获电力系统的

10、动态需求变化。这就是我们所知的“欠拟合”现象。相反地，如果神经网络太大，它不仅可以容纳基本信号，还可以容纳训练时的噪声，这就是我们所知的“过拟合”现象。“过拟合”模型可能在训练时显示较低的错误率，但不能以偏概全，可能在实际预测时会有较高的错误率。非线性模型可以产生比线性规划更高的准确度，但是要更长的训练时间。较大的神经网络容易出现“过拟合”，预测需要简约模型的一般化概括。非线性神经网络的大小可以通过检查相关性系数或是通过遗传算法来选择最优的输入变量来减小。线性模型相对于非线性模型来说是一个令人满意的模型，而非线性模型是用来决定输入参数的。用反向传播来训练大型的人工神经网络是很耗费时间的，很多用

11、来减少训练时间的方法已经通过评估，已经找到一个减少训练时间的方法来取代使用最小二乘法来修改网络权重而达到速下降搜索的技术。每一步的计算量大了，但是迭代次数却大大减少。减少训练时间是我们希望达到的，不仅可以通过减少计算消耗，也可以通过研究考虑更多的可取的输入变量来达到，从而达到优化预测的精度。4 神经网络结构的确定4.1 自动校正一阶线性自动校正就是校正负荷在两个不同时间之间的校正系数，可以用下式表示：其中：是在时的自动校正系数 是期望值 是在时刻的电力负荷值图4.1显示了滞后于某个特殊电力用户的电力需求自动校正系数的每小时负荷变化。这个图证实了常识经验，就是在任何时候的负荷与前几天同一时刻的负

12、荷有高度相关性。这很有趣，并且对负荷预测很多帮助，另外，滞后的自动校正在24小时中比前整个一周都高出许多。除了前4天，负荷的相关峰值下降到0.88外，第7天又上升了。图4.1电力负荷自动校正系数与滞后时间的比较我们也分析了样本负荷在时间序列上的偏自相关函数（PACF）。这衡量去除了干扰变量后和之间的依赖关系。图4.2显示了负荷序列的PACF。可以观测到，负荷变化与之前的负荷有很大影响，这就表明一个小时后的负荷预测将会变得简单。图4.2 上午1点负荷的PACF4.2 遗传算法在时间序列模型中重要系数可以通过遗传算法自动鉴定出，不像反向传播模型的最小平方误差那样，遗传算法可以直接将MAPE减到最小

13、。MAPE就是平均绝对误差百分比，它广泛用于衡量负荷预测的准确度。为了描述遗传算法里的负荷预测模型，要定义一根曲线，它包括滞后值和每个滞后的系数或是，那么这根曲线可以表示为：常数项 第一个滞后， 系数第二个滞后， 系数滞后， 系数第一个独立变量的滞后，系数第二个独立变量的滞后，系数 独立变量的滞后，系数这样一种曲线是随机产生的。然后两根曲线被随机选择（与它们的MAPEs的概率成反比）。两根曲线的交叉点被随机选择，而两条母曲线通过交叉点复制两条新的曲线。这个过程中产生了新一代的曲线。将会计算出每一条曲线的适应值（通过一组负荷数据训练而产生的预测MAPE的逆值）。这些低适应能力的将会被丢弃，高适应

14、能力的将会繁殖下一代。突变也用来随机修改下一代中独特的。结果就是经过多代的繁殖过程，曲线具有高度的适应性（低MAPE值），这就是用电力负荷通过训练后最好的预测值。5 短期负荷预测系统本文的短期负荷预测系统是一个线性神经网络（ARMA模型）和非线性神经网络的组合。整个系统的结构如图5.1示。图5.1 短期负荷预测系统的结构图在这个系统中，线性系统和非线性系统两者都有第二部分中提到的影响负荷预测的几种或全部因素作为历史数据的输入。数据处理器的数据是从线性和非线性神经网络的历史数据中提取出来的，分别地，线性神经网络的输出作为反馈，输入到非线性神经网络中。有历史数据和线性神经网络的输出作为输入，非线性

15、神经网络就会预测出一天或者一周的负荷值。这两个网络组成的最初的网络结构是基于统计分析和遗传算法。如图4.2所示，时刻的负荷值很大程度上取决于时刻的历史负荷值。所以，准确地预测1小时后负荷的会提高短期负荷预测准确度。但是，一天（24小时）后或在一个星期（168小时）后的预测，在之前的几个小时的负荷值仍然是预测值。例如，我们要预测明天上午10点的负荷值，显然，我们拥有的明天上午9点的负荷值不是实际值，我们只有明天上午9点的预测值。因为在9点的负荷对10点的负荷的影响较密切，准确的预测9点的负荷会提高预测10点负荷的准确度。在我们这个系统中，线性神经网络（ARMA模型）是用来预测一个小时后的负荷值的

16、。对于非线性神经网络来说，输入层包括不同时间滞后的变量。虽然时刻的负荷受到时刻的显著影响，但是时刻的负荷本身的准确度不足够以至影响预测时刻负荷的准确度。这主要受长期负荷变化的影响（见图4.1）6 仿真结果我们可以通过公共事业公司获得历史数据和各种天气数据。我们用来仿真的数据是1898，1990和1991年的每小时历史负荷数据和当年的每小时的温度数据。非线性神经网络由24个子网组成，没一个代表一天中一个特定的时间。相似的，线性神经网络也有24个子网。全部48个子网有很多个输入节点，但是只有一个输出节点。在任何时候，只有一个非线性子网和一个线性子网在工作（总共只有2个网）。这种独一无二的结构具有以

17、下优点：（1） 预测速度快（2） 重新训练系统快（3） 模块化。可以在特定时间根据预测精度更新系统（4） 预测精度高可以得出系统的这些优点对于商业应用来说是很重要的。根据每小时或每天预测的原则来说，预测速度很精度对于公共事业来说是非常需要的我们用1898和1990年的历史负荷数据和温度数据来训练；1991年的负荷和温度来作验证。在训练和验证期间，用到了未来的实际温度。图6.1显示了利用1991年第一季度的数据验证我们的系统预测24小时后的MAPE值曲线。图6.1 1991第一季度MAPE的验证结果7 优化处理 由经验可知，我们发现只有一个传统神经网络的系统不足够处理我们往往遇到的那些具有多种变

18、化情况的公共事业公司。例如，当天气突然变化时，利用常规的数据来训练系统不能得到较好的预测效果。当系统的历史数据点不足够系统来学习时，可以通过简单地增加相似的历史负荷点到训练数据中来解决上述问题。我们将增加两个附加的子系统到我们的短期负荷预测系统中，给它取名为：基于规则的系统和模式识别系统。这两个字子系统在遇到上述的一些情况下会起不同的作用和完成不同的任务。7.1 基于规则系统模式识别，遗传算法和人工神经网络的时间序列模型所构成的神经网络都可用作短期负荷预测。但是，为了获得最小的预测误差，且在可接受的复杂程度和训练时间，需要知道使用这个网络的特殊公共事业的使用范围。特别是对于区域的负荷预测，这些

19、特殊地理区域和服务场所或多或少受到诸如温度和假期的影响，取决于这个区域的负荷是工业负荷占重要部分，还是商业负荷，或是民用负荷，或取决于负荷是在夏季达到峰值还是冬季达到峰值等。为了使公共事业单位或其他没背景的公司能够成功使用人工智能的短期负荷预测系统，当它达到最佳性能的时候，有必要提供根据当地条件来设置变化参数的规则。7.2 模式识别系统这个系统被很多公共事业单位所用来作日常负荷预测的一种方法，它给出了一个小时为单位的负荷的大型数据库，只要找出与预测日相似的负荷记录，将它所在那天的数据作为预测的依据。这个系统的问题就是如何在历史负荷数据记录中找出相似的记录。有很多种可行的方式来定义相似，我们所用

20、的其中一种就是比较平均绝对误差百分比，我们概括为：（1） 神经网络可以用来识别模式或评估相似匹配程度。（2） 这些神经网络应该组合起来，如用时间序列法(利用延迟线) 那样单独来预测，就存在每一种方法矛盾错误的权重。结 论在本文中，我们介绍了以用线性和非线性网络组成的负荷预测系统为基础的混合神经网络。我们已经论证了这个系统是理想的，可为公共事业或是商业应用服务的。另外本文也描述两个子系统，它们作为优化处理我们现有的系统来处理各种不平常的情况。外文文献原文Artificial Neural Networks in Short Term load ForecastingK.F. Reinschmid

21、t, President B. LingStone h Webster Advanced Systems Development Services, Inc. 245 Summer Street Boston, U 0221 0Phone: 617-589-1 84 1Abstract：We discuss the use of artificial neural networks to the short term forecasting of loads. In this system, there are two types of neural networks: non-linear

22、and linear neural networks. The nonlinear neural network is used to capture the highly non-linear relation between the load and various input parameters. A neural networkbased ARMA model is mainly used to capture the load variation over a very short time period. Our system can achieve a good accurac

23、y in short term load forecasting.Key words: short-term load forecasting, artificial neural network1 IntroductionShort term (hourly) load forecasting is an essential hction in electric power operations. Accurate shoirt term load forecasts are essential for efficient generation dispatch, unit commitme

24、nt, demand side management, short term maintenance scheduling and other purposes. Improvements in the accuracy of short term load forecasts can result in significant financial savings for utilities and cogenerators. Various teclmiques for power system load forecasting have been reported in literatur

25、e. Those include: multiple linear regression, time series, general exponential smoothing, Kalman filtering, expert system, and artificial neural networks. Due to the highly nonlinear relations between power load and various parameters (whether temperature, humidity, wind speed, etc.), non-linear tec

26、hniques, both for modeling and forecasting, tend to play major roles in the power load forecasting. The artificial neural network (A) represents one of those potential non-linear techniques. However, the neural networks used in load forecasting tend to be large in size due to the complexity of the s

27、ystem. Therefore, training of such a large net becomes a major issue since the end user is expected to run this system at daily or even hourly basis. In this paper, we consider a hybrid neural network based load forecasting system. In this network, there are two types of neural networks: non-linear

28、and linear neural networks. The nonlinear neural network is used to capture the highly non-linear relation between the load and various input parameters such as historical load values, weather temperature, relative humidity, etc. We use the linear neural network to generate an ARMA model. This neura

29、l network based ARMA model will be mainly used to capture the load variation over a very short time period. The final load forecasting system is a combination of both neural networks. To train them, sigxuiicant amount of historical data are used to minimize MAPE (Mean Absolute Percentage Error). A m

30、odified back propagation learning algorithm is carried out to train thenon-linear neural network. We use Widrow-Hoff algorithm to train the linear neural network.Since our network structure is simple, the overall system training is very fast. To illustrate the performance of this neural network-base

31、d load forecasting system in real situations, we apply the system to actual demand data provided by one utility. Three years of hourly data (1989, 1990 and 1991) are used to train the neural networks. The hourly demand data for 1992 are used to test the overall system. This paper is organized as fol

32、lows: Section I is the introduction of this paper; Section I1 describes the variables sigdicantly affecting short term load forecasting; in Section III, wepresent the hybrid neural network used in our system; in Section IV, we describe the way to find the initial network structure; we introduce our

33、load forecasting system in details in Section V; and in Section VI, some simulation result is given; finally, we describe the enhancement to our system in Section VII.2 Variables Afferting Short-Term LoadSome of the variables affecting short-term electxical load are:TemperatureHumidityWind speedClou

34、d coverLength of daylightGeographical regionHolidaysEconomic factorsClearly, the impacts of these variables depend on the type of load: variations in temperature, for example, have a larger effect on residential and commercial loads than on industrial load. Regions with relatively high residential l

35、oads will have higher variations in short-term load due to weather conditions than regions with relatively high industrial loads. Industrial regions, however, will have a greater variation due to economic factors, such as holidays.As an example, Figure 2.1 shows the loadvariation over one day, start

36、ing at midnight.Figure 2.1 Example of load variation during one day3 Hybrid Neurak NetworksOur short-term load forecasting system consists of two types of networks:linear neural network ARMA model and feedforward .Non-linear neural network.The non-linear neural network is used to capture the highly

37、non-linear relation between the load and various input parameters.We use the linear neural network to generate an ARMA model which will be mainly used to capture the load variation over a very short time period(one hour).3.1 Linear Neutal NetworksThe general multivariate linear model of order p with

38、 independent x,isWhere:-electrical load at time t -independent variable at time t-random disturbance at time t-coefficientsLinear neural networks can successfully learn the coefficient and from the historrcal load data,and the independent variables,Widrow-Hoff has been used to determine the coeffici

39、ent.This model includes all the previous data up to lag p.As shown above ,these data are not independent ,and have varying degrees of correlation with the load.Correlation studies can be used to determine the most significant parameters to be includes in the model,allowing many to be eliminated.This

40、 reduces the size and computer time for a model of given accuracy,or increases the accuracy for a model of given size.3.2 Non-Linear Neural NetworksFor non-linear forecasting,a nonlinear model analogous to the linear model is:where:f(.) is a nonlinear function determined by the artificial neural net

41、work.Layered, feed-forward neural networks are used, typically with one hidden layer (although in some cases with two). The layers are fully connected, with one bias unit in each layer (except the output layer). The output of each unit is the slum of the weighted inputs (including the bias), passed

42、through an exponential activation fiinction.Our modiked backpropagation method is applied. The errors are defined to be the sum of the squares of the deviations between the computed values at the output units and the actual or desired values; this definition makes the error function differentiable e

43、verywhere.Unlike the linear time series model, in which there is one fitted coefficient for each lagged variable, in the nonlinear neural network forecaster tlhe selection of lagged input variables is independent of the number of fitted coefficients, the network weights, the number of which is deter

44、mined by the number of layers and the number of hidden units. Also, in linear regression models, if an input variable is extraneous, then its regression coefficient is zero (or, more properly, is not significantly different from zero by a t-test). However, in nonlinear neural networks this is not ne

45、cessarily true; an input Variable may be unimportant but still have large weights; the effects of these weights cancel somewhere downstream. The same is true for the hidden units.Therefore, in conventional backpropagation for nonlinear neural networks, there is no automatic elimination of extraneous

46、 input nodes or hidden nodes. However, in practical forecasting it is necessary to achieve a parsimonious model, one which is neither too simple nor too complex for the problem at hand. If the neural network is chosen to be too small (to have too few input or hidden units), then it will not be flexi

47、ble enough to capture ithe dynamics of the electrical demand system; this is known as underfitting. Conversely, if the neural network is too large, then it can fit not only the underlying signal but also the noise in the training set; this is known as overfitting. Overfitted models may show low erro

48、r rates on the training set but do not generalize; they may then have high error rates in actual prediction. The nonlinear model can yield greater accuracy than the linear formulation, but takes much longer to train. Large nonlinear neural networks are also prone to overfitting. Forecasting requires

49、 parsimonious models capable of generalization. The size of the nonlinear neural network can be reduced by examining the correlation coefficients, or by using the genetic algorithm to select the optimum set of input variables. The linear model is a satisfactory approximation to the nonlinear model f

50、or the purpose of selecting the input terms. Large artificial neural networks trained using backpropagation are notoriously time-consuming, and a number of methods to reduce training time have been evaluated. One method that has been found to yield orders of magnitude reductions in training time rep

51、laces the steepest descent search by techniques that model the network weights using a least-squares approach; the computations in each step are greater but the number of iterations is greatly reduced. Reductions in training time are desirable not only to reduce computation costs, but to allow more

52、alternative input variables to be investigated, and hence to optimize forecast accuracy.4 Determination of Network StructureAs we stated above, the neural network used in load forecasting tends to be large in size, which results in longer training time. By carefully choosing network structure (i.e.,

53、 input nodes, output nodes), one will be able to build a relatively small network. In our system, we apply statistical analysis and genetic algorithm to find the network optimal structure which is used as a base for further network turning.4.1 Autocorrelation First-order linear autocorrelation is th

54、e correlation coefficient between the loads at two different times, and is given by: where: is the autocorrelation at lag zE is the expected valuez(f) is the electrical load at time t.Figure 4.1 shows the hourly variation in the lagged autocorrelation of electrical demand for a particular electric u

55、tility. This plot confirms common sense experience, that the load at any hour is very highly correlated with the load at the same hour of previous days. It is interesting, and useful for forecasting, that the autocorrelation for lags at multiples of 24 hours remains high for the entire preceding wee

56、k the peak correlation falls to about 0.88 for loads four days apart, but rises again for loads seven days apnpart. Figure 4.1 Autocorrelation of utility electrical load vs.lag hoursWe also analyze the sample partial autocorrelation function (PACF) of the time series of load. This is a measure of th

57、e dependence between zt+h and z, after removing the effect of the intervening variables zt+ , Z 2, . Zt+h-l . Figure 4.2 shows the PACF of load series. It can be observed that load variation is largely affected by one at previous hour. This indicates that one-hour ahead forecast would be relatively

58、easy. 4.2 Genetic Algorithm The most significant coefficients in the time series model can be identified automatically byusing the genetic algorithm. Unlike the back propagation method, which minimizes the sum of squares of the errors,the genetic algorithm can minimize the MAPE directly.MAPE stands

59、for Mean Absolute Percentage Error which is widely used as a measure in load forecasting.To represent the forecasting model in the genetic algorithm, a string is defined ,consisting of the lag values,I,and the coefficients at each lag, a, or c,. Then a string would be as follows:constant term first

60、lag,i1ai1,coefficient of zsecond lag,i2ai2,coefficient of zp-th lag,ipaip,coefficient of zlag j1 of the first independent variablecj1,coefficient of xlag j2 of the second indepent variablecj2,coefficient of xlag jp of the p-th independent variablecjp coefficient of xA population of these strings is

61、generated randomly. Then pairs of strings are selected randomly (with probabilities inversely proportional to their respective MAPEs);a crossover point in both strings is selected randomly; and the two parent strings reproduce two new strings by crossover.This processproduces a new generation of str

62、ings.The fitness (the inverse of the MAPE of the forecasts generated by the string across the training set of load data) is computed for each strings,those with low fitness are discarded and those with high fitness survive to reproduce in the next generation. Mutation is also used to modify individu

63、als randomly in each generation. The result of ai number of generations of this selection process is a string with high fitness (low MAPE) that is the best predictor of the electrical load over the training set.5 Short Term Load Forecasting SystemOur short term load forecasting system is a combinati

64、ori of linear neural network (ARMA model) ancl non-linear neural network. The overall system structure is shown in Figure 5.1. Figure 5.1 Structure of our short term load forecasting systemIn this system, both linear and non-linear systems have historical data as input which include all or some of the variables listed in Section 11. The data processor is used to extract data from Ihe historical data set for linea