2022年神经网络英文文献 .pdf

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1、 ARTIFICIAL NEURAL NETWORK FOR LOAD FORECASTING IN SMART GRID HAO-TIAN ZHANG, FANG-YUAN XU, LONG ZHOU Energy System Group ,City University London,Northampton Square ,London,UK E-MAIL: abhbcity.ac.uk, abcx172city.ac.uk, long.zhou.1city.ac.uk Abstract: It is an irresistible trend of the electric power

2、 improvement for developing the smart grid, which applies a large amount of new technologies in power generation, transmission, distribution and utilization to achieve optimization of the power configuration and energy saving. As one of the key links to make a grid smarter, load forecast plays a sig

3、nificant role in planning and operation in power system. Many ways such as Expert Systems, Grey System Theory, and Artificial Neural Network (ANN) and so on are employed into load forecast to do the simulation. This paper intends to illustrate the representation of the ANN applied in load forecast b

4、ased on practical situation in Ontario Province, Canada. Keywords:Load forecast; Artificial Neuron Network; back propagation training; Matlab 1. Introduction Load forecasting is vitally beneficial to the power system industries in many aspects. As an essential part in the smart grid, high accuracy o

5、f the load forecasting is required to give the exact information about the power purchasing and generation in electricity market, prevent more energy from wasting and abusing and making the electricity price in a reasonable range and so on. Factors such as season differences, climate changes, weeken

6、ds and holidays, disasters and political reasons, operation scenarios of the power plants and faults occurring on the network lead to changes of the load demand and generations. Since 1990, the artificial neural network (ANN) has been researched to apply into forecasting the load. “ANNs are massivel

7、y parallel networks of simple processing elements designed to emulate the functions and structure of the brain to solve very complex problems”. Owing to the transcendent characteristics, ANNs is one of the most competent methods to do the practical works like load forecasting. This paper concerns ab

8、out the behaviors of artificial neural network in load forecasting. Analysis of the factors affectingthe load demand in Ontario, Canada is made to give an effective way for load forecast in Ontario. 2. Back Propagation Network 名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - -

9、 - - 第 1 页，共 11 页 - - - - - - - - - 2.1. Background Because the outstanding characteristic of the statistical and modeling capabilities, ANN could deal with non-linear and complex problems in terms of classification or forecasting. As the problem defined, the relationship between the input and targe

10、t is non-linear and very complicated. ANN is an appropriate method to apply into the problem to forecast the load situation. For applying into the load forecast, an ANN needs to select a network type such as Feed-forward Back Propagation, Layer Recurrent and Feed-forward time-delay and so on. To dat

11、e, Back propagation is widely used in neural networks, which is a feed-forward network with continuously valued functions and supervised learning. It can match the input data and corresponding output in an appropriate way to approach a certain function which is used for achieving an expected goal wi

12、th some previous data in the same manner of the input. 2.2 . Architecture of back propagation algorithm Figure 1 shows a single Neuron model of back propagation algorithm. Generally, the output is a function of the sum of bias and weight multiplied by the input. The activation function could be any

13、kinds of functions. However, the generated output is different. Owing to the feed-forward network, in general, at least one hidden layer before the output layer is needed. Three-layer network is selected as the architecture, because this kind of architecture can approximate any function with a few d

14、iscontinuities. The architecture with three layers is shown in Figure 2 below: Figure 1. Neuron model of back propagation algorithm Figure 2. Architecture of three-layer feed-forward network 名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 2 页，共 11 页 - - - - - - - - -

15、Basically, there are three activation functions applied into back propagation algorithm, namely, Log-Sigmoid, Tan-Sigmoid, and Linear Transfer Function. The output range in each function is illustrated in Figure 3 below. Figure.3. Activation functions applied in back propagation (a)Log-sigmoid (b)Ta

16、n-sigmoid (c)linear function2.3. Training function selection Algorithms of training function employed based on back propagation approach are used and the function was integrated in the Matlab Neuron network toolbox. 名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 3 页，

17、共 11 页 - - - - - - - - - TABLE.I. TRAINING FUNCTIONS IN MATLABS NN TOOLBOX 3. Training Procedures 3.1. Background analysis The neural network training is based on the load demand and weather conditions in Ontario Province, Canada which is located in the south of Canada. The region in Ontario can be

18、divided into three parts which are southwest, central and east, and north, according to the weather conditions. The population is gathered around southeastern part of the entire province, which includes two of the largest cities of Canada, Toronto and Ottawa. 3.2. Data Acquisition The required train

19、ing data can be divided into two parts: input vectors and output targets. For load forecasting, input vectors for training include all the information of factors affecting the load demand change, such as weather information, holidays or working days, fault occurring in the network and so on. Output

20、targets are the real time load scenarios, which mean the demand presented at the same time as input vectors changing. Owing to the conditional restriction, this study only considers the weather information and logical adjustment of weekdays and weekends as the factors affecting the load status. In t

21、his paper, factors affecting the load changing are listed below: (1). Temperature () (2). Dew Point Temperature () (3). Relative Humidity (%) 名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 4 页，共 11 页 - - - - - - - - - (4). Wind speed (km/h) (5). Wind Direction (10) (

22、6). Visibility (km) (7). Atmospheric pressure (kPa) (8). Logical adjustment of weekday or weekend According to the information gathered above, the weather information in Toronto taken place of the whole Ontario province is chosen to provide data acquisition. The data was gathered hourly according to

23、 the historical weather conditions remained in the weather stations. Load demand data also needs to be gathered hourly and correspondingly. In this paper, 2 years weather data and load data is collected to train and test the created network. 3.3. Data Normalization Owing to prevent the simulated neu

24、rons from being driven too far into saturation, all of the gathered data needs to be normalized after acquisition. Like per unit system, each input and target data are required to be divided by the maximum absolute value in corresponding factor. Each value of the normalized data is within the range

25、between -1 and +1 so that the ANN could recognize the data easily. Besides, weekdays are represented as 1, and weekend are represented as 0. 3.4. Neural network creating Toolbox in Matlab is used for training and simulating the neuron network. The layout of the neural network consists of number of n

26、eurons and layers, connectivity of layers, activation functions, and error goal and so on. It depends on the practical situation to set the framework and parameters of the network. The architecture of the ANN could be selected to achieve the optimized result. Matlab is one of the best simulation too

27、ls to provide visible windows. Three-layer architecture has been chosen to give the simulation as shown in Figure 2 above. It is adequate to approximate arbitrary function, if the nodes of the hidden layer are sufficient . Due to the practical input value is from -1 to +1, the transfer function of t

28、he first layer is set to be tan sigmiod, which is a hyperbolic tangent sigmoid transfer function. The transfer function of the output layer is set to be linear function, which is a linear function to calculate a layer s output from its net input. There is one advantage for the linear output transfer

29、 function: because the linear output neurons lead to the output take on any value, there is no difficulty to find out the differences between output and target. The next step is the neurons and training functions selection. Generally, Trainbr and Trainlm are the best choices around all of the traini

30、ng functions in Matlab toolbox Trainlm (Levenberg-Marquardt algorithm) is the fastest training algorithm for networks with moderate size. However, the big problem 名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 5 页，共 11 页 - - - - - - - - - appears that it needs the st

31、orage of some matrices which is sometimes large for the problems. When the training set is large, trainlm algorithm will reduce the memory and always compute the approximate Hessian matrix with nn dimensions. Another drawback of the trainlm is that the over-fitting will occur when the number of the

32、neurons is too large. Basically, the number of neurons is not too large when the trainlm algorithm is employed into the network. Trainbr (Bayesian regularization) is a modified algorithm of the Levenberg-Marquardt training method to create networks which generalize well so that the optimal network a

33、rchitecture can be easily determined. Impacts from effectively used weights and biases of the network can be seen clearly by this algorithm. And the number of the effective weights and biases will not change too much when the dimension of the network is getting large. The trianbr algorithm has the b

34、est performance after the network input and output normalized into the range from -1 to +1. An important thing when using trainbr should be mentioned is that the algorithm should not stop until the effective number of parameters has converged. More details are available in Matlab neural network tool

35、box. Number of neurons in the first layer also can be selected to optimize the network so that an expected result can be made. Generally speaking, the more complicated architecture of the network is, the more accurate the output result will be, however, the higher chances will the algorithm such as

36、trainlm with over-fitting. In this paper, the number of neurons is 8 in trainlm algorithm, and 30 in trainbr algorithm. 3.5. Neural network training Before training, the network needs to be initialized first. The network initialization is not only influencing the final local minimum, but also affect

37、ing the speed of convergence, the convergence probability and generalization . The information on weather conditions in 2007 hourly and weekday and weekend logic in Ontario are defined as training input; the load demand changes in 2007 hourly in Ontario are defined as training target. The training p

38、erformances of trainlm algorithm and trainbr algorithm are shown in Figure 4 and 5, respectively. As can be seen in these plots, the mean squared error is decreasing from a large value to a smaller value. 名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 6 页，共 11 页 - -

39、- - - - - - - Figure 4 trainlm algorithm performance plot Figure 5. trainbr algorithm performance plot For both training algorithms, namely, trainbr and trainlm, the procedure will stop when any of the conditions occurs: 名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第

40、 7 页，共 11 页 - - - - - - - - - (1). Epochs reached the maximum value (2). Time approaches to the preinstalled value (3). Goal error is minimized (4). Gradient is decreased to min_grad (5). Mu exceeds mu_max (6). Validation performance has increased more than max_fail times since the last time it decr

41、eased (when usingvalidation). There is no difficult to find out that the trainlm performance plot stopped because of meeting the error goal which is set as 0.001; the trainbr performance stopped owing to the validation check times is more than the max_fail times. Figure 6. Training result and traini

42、ng target by trainbr algorithm with 8 neurons From Figure 6, comparison of training result and training target are made to check out the performance of the algorithm applied on load forecasting. It is obvious that the training result meet the target in general. The network test simulation should be

43、made in order to find out the performance in a real problem. 3.6. Neural network simulation The network is required to check whether it can achieve the expectation after training. Another set of input vectors and demand scenarios are needed to test the network. Comparison needs to be made to check o

44、ut the difference between the test output and real demand. In this project, the information on weather conditions in 2008 hourly and weekday and weekend logic in Ontario are used as simulation input, and the load demand scenarios in 2008 hourly in Ontario are used as the simulation target. After the

45、 simulation, a set of output could be obtained through the trained neural network. The simulation output and the simulation target are used to check the mean squared error to analyze the extent of succeed with neural network application. Mean squared error could be calculated as: MSEMean (se) max (t

46、est target) Where Mean(se) is the mean value of the difference between the simulation output and the test target; Max(test target) is the maximum value of the test target. 名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 8 页，共 11 页 - - - - - - - - - Figure 7. The simul

47、ation result of the trainbr algorithm with 8 neurons Figure 7 shows a sample of the simulation results which is applying the same network as the training simulation in Figure 6. The green track is the test simulation result and the blue track is the real load demand which is provided by electric ind

48、ustry in Ontario. The horizontal is presenting time, and ordinate is presenting the load which has been normalized. The less the mean squared error is, the better the created neuron network can perform. 4. result comparison Table 2 illustrates the MSE of the trainoss algorithm, trainbr algorithm and

49、 trainlm algorithm when the number of the neurons in the hidden layer is increasing. Each network has been trained 10 times to achieve the global minimum. It is obvious that trainlm and trainbr have better performance than trainoss. Figure 8-9 demonstrate two of the best results with different train

50、ing algorithms and different neuron number. As can be seen in both figures, most of the test simulation results could meet the target very well. However, there are still some simulation part didnt follow the real target. It may be because the factors which haven t been taken into account, such as di