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1、精选优质文档-倾情为你奉上 ARTIFICIAL NEURAL NETWORK FOR LOAD FORECASTING IN SMART GRIDHAO-TIAN ZHANG, FANG-YUAN XU, LONG ZHOUEnergy System Group,City University London,Northampton Square ,London,UKE-MAIL: abhbcity.ac.uk, abcx172city.ac.uk, long.zhou.1city.ac.ukAbstract: It is an irresistible trend of the electr

2、ic power 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 pla

3、ys a significant 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 fo

4、recast based on practical situation in Ontario Province, Canada.Keywords:Load forecast; Artificial Neuron Network; back propagation training; Matlab1. Introduction Load forecasting is vitally beneficial to the power system industries in many aspects. As an essential part in the smart grid, high accu

5、racy of 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,

6、weekends 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 ma

7、ssively 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 conce

8、rns about the behaviors of artificial neural network in load forecasting. Analysis of the factors affectingthe load demand in Ontario, Canada is made to give aneffective way for load forecast in Ontario.2. Back Propagation Network2.1. Background Because the outstanding characteristic of the statisti

9、cal 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 target is non-linear and very complicated. ANN is an appropriate method to apply into the problem to forecast t

10、he 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 date, Back propagation is widely used in neural networks, which is a feed-forward network with continuously v

11、alued 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 with some previous data in the same manner of the input.2.2. Architecture of back propagation algorithm Figu

12、re 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 activationfunction could be any kinds of functions. However, the generated output is different. Owing to the feed-forward network, in general

13、, 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 discontinuities. The architecture with three layers is shown in Figure 2 below: Figure 1. Neuron model of back

14、 propagation algorithm Figure 2. Architecture of three-layer feed-forward network 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 belo

15、w. Figure.3. Activation functions applied in back propagation (a)Log-sigmoid (b)Tan-sigmoid (c)linear function2.3. Training function selectionAlgorithms of training function employed based on back propagation approach are used and the function was integrated in the Matlab Neuron network toolbox. TAB

16、LE.I. TRAINING FUNCTIONS IN MATLABS NN TOOLBOX3. Training Procedures3.1. 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 divided into three parts which

17、 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 AcquisitionThe required training data can be divided into two

18、 parts: input vectors and output targets. For load forecasting, input vectors for training include all the information of factorsaffecting the load demand change, such as weather information, holidays or working days, fault occurring in the network and so on. Output targets are the real time loadsce

19、narios, 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 loadstatus. In this paper, factors affecting the loa

20、d changing are listed below:(1). Temperature ()(2). Dew Point Temperature ()(3). Relative Humidity (%)(4). Wind speed (km/h)(5). Wind Direction (10)(6). Visibility (km)(7). Atmospheric pressure (kPa)(8). Logical adjustment of weekday or weekend According to the information gathered above, the weathe

21、r information in Toronto taken place of the whole Ontario province is chosen to provide data acquisition. The data was gathered hourly according to the historical weather conditions remained in the weather stations. Load demand data also needs to be gathered hourly and correspondingly. In this paper

22、, 2 years weather data and load data is collected to train and test the created network.3.3. Data NormalizationOwing to prevent the simulated neurons 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 tar

23、get data are required to be divided by the maximum absolute value in corresponding factor. Each value of the normalized data is within the range 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 net

24、work creating Toolbox in Matlab is used for training and simulating the neuron network. The layout of the neural network consists of number of neurons and layers, connectivity of layers, activation functions, and error goal and so on. It depends on the practical situation to set the framework and pa

25、rameters of the network. The architecture of the ANN could be selected to achieve the optimized result. Matlab is one of the best simulationtools 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 arbi

26、trary 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 the 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 line

27、ar function, which is a linear function to calculate a layers output from its net input. There is one advantage for the linear output transfer 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 targe

28、t. The next step is the neurons and training functions selection. Generally, Trainbr and Trainlm are the best choices around all of the training functions in Matlab toolbox Trainlm (Levenberg-Marquardt algorithm) is the fastest training algorithm for networks with moderate size. However, the big pro

29、blem appears that it needs the storage 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 w

30、ill occur when the number of the 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 w

31、ell so that the optimal network architecture 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

32、. The trianbr algorithm has the best 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 availa

33、ble in Matlab neural network toolbox. 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 ch

34、ances will the algorithm such as 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 fin

35、al local minimum, but also affecting 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 a

36、s training target. The training performances 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. Figure 4 trainlm algorithm performance plotFigure 5. trainbr a

37、lgorithm performance plotFor both training algorithms, namely, trainbr and trainlm, the procedure will stop when any of the conditions occurs: (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

38、exceeds mu_max(6). Validation performance has increased more than max_fail times since the last time it decreased (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 stopp

39、ed owingto the validation check times is more than the max_fail times. Figure 6. Training result and training 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

40、. It is obvious that the training result meet the target in general. The network test simulation should be made in order to find out the performance in a real problem.3.6. Neural network simulationThe network is required to check whether it can achieve the expectation after training. Another set of

41、input vectors and demand scenarios are needed to test the network. Comparison needs to be made to check out 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 in

42、put, and the load demand scenarios in 2008 hourly in Ontario are used as the simulation target. After the 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 o

43、f succeed with neural network application. Mean squared error could be calculated as: MSEMean (se)max (test 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.Figure 7. The simulation

44、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 industry

45、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 trainl

46、m 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 training alg

47、orithms 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 havent been taken into account, such as disasters,

48、 failure of the electric network or some national holidays which is not mentioned on input vectors.Figure 8. the simulation result of the trainlm algorithm with 8 neuronsFigure 9. The simulation result of the trainbr algorithm with 10 neurons Figure 10 aims to compare the two algorithms with the same number of neurons applied into the networks. The blue track is the test simulation target, the red one is the result simulated by trainlm, and the green one is the result simulated by trainbr. The simulation result of trainbr is much closer to the test target than that of trainlm, a