模式識別作業(yè)—人工神經(jīng)網(wǎng)絡(luò).doc

模式識別大作業(yè)外文翻譯Artificial Neural Networks in Short Term load Forecasting人工神經(jīng)網(wǎng)絡(luò)在短期負(fù)荷預(yù)測中的應(yīng)用姓 名： 劉德龍 學(xué) 號： 03081413 班 級： 030814 日 期： 2011.05 外文文獻(xiàn)原文:Artificial Neural Networks in Short Term load ForecastingK.F. Reinschmidt, 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 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 accuracy 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 commitment, 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 literature. 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 techniques, 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 system. 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 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 neural 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 modified 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-based 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 follows: 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 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 speedCloud 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 loads 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, starting 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 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 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 coefficient.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 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 network.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 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 everywhere.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 determined 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 necessarily 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 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 flexible 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 error 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 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 for 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 replaces 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 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., 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 the 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 utility. 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 week 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 the 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 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 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 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 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 strings.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 individuals 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 combinatiori 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 linear and non-linear neural networks, respectively. The output of linear neural network is fed into the non-linear neural network as input. With historical data and output of linear neural network as input, the non-linear neural network generates forecasted load values over one day to one week. The initial network structure for both networks are based on statistical analysis and genetic algorithm. As shown in Figure 4.2, the load value at tiime t is largely dependent upon the historical load at f-1. Therefore, accurate onehour ahead forecast will improve the short term load forecast.However, for one-day (24 hours) and/or one week (168 hours) ahead forecast, the load value at the previous hour is also a forecasted value. For example, suppose we want to forecast the load at 10 a.m. tomorrow. Obviously, the load at 9 a.m. tomorrow is not available. What we have is the forecasted load value at 9 a.m. tomorrow. Since the load at 10 a.m. is very sensitive with respect to the load at 9 a.m., accurate forecast of load at 9 a.m. will improve the forecast of load at 10 a.m. In our system, the linear neural network (ARMA model) is used for one-hour ahead load forecastFor the non-linear network, the input layer consists of variables at Werent time lags. Although the load at time t is sigmlicantly aEected by the load at f-1, the load at f-1 itself is not sufficient in order to forecast load at f accurately. This is mainly due to the long term variation (see Figure 4.1).6、Simulation Result We have been able to access the historical load data and various weather data at a utility company. The data we choose for simulation is the historical hourly load values in 1989, 1990 and 1991; the hourly temperatures in the same years. The non-linear neural network consists of 24 subnets, each represents one particular hour in one day. Similarly, there are 24 subnet for the linear neural network. All of these 48 subnets have multiple input nodes, but only ONE output node. At any moment, only one non-linear subnet and one linear subnet is activated (total only two nets). This unique structure has the following advantages:(1) Fast to generate load forecast;(2) Fast to re-train the system;(3) Modularization. Updating system is determined by the forecasting accuracyat particular hours.(4) High accuracy.Note that these advantages are important in the commercial application of our system. Speed and accuracy are essential for utilities to use load forecasting system at hourly/daily basis. We use historical load and temperature data in 1989 and 1990 for training; load and temperature in 1991 for testing. During training and testing, the actual future temperatures are used. Figure 6.1 shows the 24-hour ahead MAPE of our system in testing case with data in the first quarter of 1991. Figure 6.1 MAPE of testing result for the first quarter of 19917、EnhancementFrom our experience, we find that a system with ONLY traditional neural networks is not sufficient to handle with various situations which utilities encounter quite often, For example, the system trained with regular data will not be able to produce good load forecast when there are some whether sudden changes. These problems can not be solved by simply adding similar historical data points into training data set since these points are not enough for the system to learn.We are adding two additional subsystems to our short term load forecasting system, namely,rule-based system and pattern recognition system. These two subsystems perform different task and are activated under certain situation such as those mentioned above.7.1 Rule-Based SystemNeural networks for pattern recognition, genetic algorithms, and artificial neural network models of time series produce usable short-term electric load forecasts. However, to obtain the minimum forecasting error with acceptable model complexity and training time requires tuning of the model parameters to the conditions of specific utilities.Particularly for reg