Application of Artificial Neural Network for Short Term Load Forecasting N. Amral
D. King
C.S. Rzveren
PT PLN (Persero) Indonesia
[email protected]
University of Abertay Dundee, UK
[email protected]
University of Abertay Dundee, UK
[email protected]
models are applied to the South Sulawesi Electricity System
Abstract- As accurate regional load forecasting is very important and the comparative summary of their performances are
for improvement of the management performance of the electric industry, various regional loads forecasting methods have been developed. In this paper we present the development of short term load forecaster using artificial neural network (ANN) models. Three approaches have been undertaken to forecast the load demand up to 24 hours ahead. The first model is a model that has 24 output nodes to forecast a sequence of 24 hourly loads at a time. The second ANN model forecasts the peak and valley load and the result is used to forecast the load profile, and finally a system with 24 separate ANNs in parallel, one for each hour of the days is used to forecast the load demand. These models are applied to the South Sulawesi Electricity System and the comparative summary of their performances are evaluated through simulation.
I. INTRODUCTION Fundamental functions of modern Energy Management systems (EMS) rely on accurate short term load forecasting (STLF) that result in economic cost savings and increased system security. Significant forecasting errors can lead to either overly conservative or overly risky scheduling, which in turn can result in economic and operational penalties. Various forecasting techniques have been employed by several authors to approach the forecasting problems. Traditionally, statistical methods, such as exponential smoothing, linear regression and the Box-Jenkins method have been frequently applied [1]. In the past few years, computational intelligence techniques have also been applied to the problem where the earlier works made use of expert systems [2]; subsequent studies employed artificial neural networks [3]. Since 1990s, most of the literature in STLF was on the application of various neural network techniques and models, with all the papers reporting good results [4]. The attraction of the methods lies in the assumption that neural networks are able to learn properties of the load, which would otherwise require careful highly sophisticates statistical and time series analysis to discover. In contrast ANNs are able to perform a nonlinear mapping of the load series, which allows the extraction of more complex relationships. These characteristic often make it possible to obtain more accurate forecasts [5]. This paper describes and evaluates the performance of the neural networks that employed to forecast the hourly (short term) electric load forecasting 24 steps ahead (1 day). Three models of neural networks were tested and compared. These
evaluated through simulation. Most of the literature surveyed proposed multilayer perceptron (MLP) that might be classified into two groups, according to the number of output nodes. In the first group are the ones that have several output nodes to forecast a sequence of hourly loads, typically 24 nodes, to forecast next day’s 24 hourly loads (this is called the load profile) [5,6,7,8]. In the second group are the ones that have only one output node, used to forecast next hour’s load, next day’s peak load or next day’s total load [9, 10, 11, and 12]. There are also many other factors considered as input to the neural network that distinguish one model to other. These different can be viewed from: the use of the weather data, the network architecture, the training algorithm, selection of the training data and the other input variables. The remaining of this paper has been organized as follows: section 2 contains a description about the South Sulawesi condition. Section 3 presents the implementation of neural networks models, section IV discuss the result and observation and section V conclusions II. SOUTH SULAWESI CONDITION 2.1. Demographical Condition South Sulawesi is one of the provinces in Indonesia, located on the western southern peninsula of Sulawesi island. Geographically South Sulawesi lies between 0o 12’ to 8o South Latitude and 116o 48’ to 122o 36’ East Longitude, the area of South Sulawesi province is 72,781 kilometer square, and has about 7.5 millions inhabitants in 2005 and the climate in South Sulawesi is wet-tropical with two (dry and rainfall) seasons. Most of the rainfall season is between October to March and the rest of the year is dry season, and the day-night temperature differential of 5-7 0C with the variability of the temperature is almost homogenous in the whole of the area. The variability of relative humidity is between 66 to 86 %. 2.2. Electricity Condition South Sulawesi electricity system is an isolated system, and a part of Indonesian state electricity company. This system supplies the electricity in South Sulawesi. The system peak load in 2005 was about 400 MW and the energy sales were
2,170 GWH with the composition of 51% residential, 17% commercial, 25% industrial and 7% public. The operation of the integrated electric power system in the South Sulawesi supervised and controlled by a Load Dispatch Center (LDC) which is conducting energy management and supervising transmission system and managing switching operation of the 150,70 and 30 kV systems 2.3. Load Characteristic Following a pre-analysis of the load shapes of South Sulawesi electricity systems, it was decided that the days can be divided into four groups: weekdays (Monday to Friday), Saturday, Sunday and Holiday. Fig. 1 depicts the typical load of South Sulawesi system for weekday, weekend and holiday. From Fig. 1 it is clear the difference curve of weekday in rainy season ( Wed, Nov 23, 2005), weekday in dry season (Wed, May 18, 2005), and weekend, (Sat, Nov 19 2005), (Sun, Nov 2005), and holiday (Muslim festive day, Nov 3, 2005). III. DESCRIPTION OF THE MODEL APPROACH Many experiments with different ANN architectures were conducted in order to identify the architecture that gives the best results. In this paper we report the three approaches of ANN model that were implemented for the forecasting next day’s load profile of the South Sulawesi Electricity System. These three ANN approaches that mentioned above are: 1). The ANN model that has 24 output nodes to forecast a sequence of 24 hourly loads at a time. 2). The ANN model that forecast the peak and valley load and the result is used to forecast the load profile, and 3). A system with 24 separate ANN in parallel, one for each hour of the days is used to forecast the load demand. The load data were consisted of one series of hourly measurements of the load supplied by the utility in South Sulawesi for 2005 and 2006. The weather data are also available. All models used Multi Layer Perceptron (MLP) with one hidden layer between input and output layer. Typical Load Curve
L o ad (M W )
400 Wed, 23 Nov 05
300
Sat,19 Nov 05
200
Sun, 20 Nov 05
100
Tue, 01 Nov 05 Thu, 3 Nov 05
0 1
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9 11 13 15 17 19 21 23
Wed, 18 May 05
hour
Fig. 1 Typical load curve of South Sulawesi
The idea in using three layer MLP network in each model is to identify the assumed dependency of the forecast outcome on earlier load and temperature data. The network is trained on the past data and is hoped to learn to approximate this unknown dependency. The Levenbergh-Marquardt back propagation (LMBP) was used to train the MLP networks in this work [4]. A hyperbolic tangent function was used as the activation function in the hidden layer and linear activation function in the output layer by all feed forward neural networks of this work. These functions are mapping into the interval [-1, 1]. To enable the converging of the network training within a reasonable time, the desired output values should be scaled onto this interval. All load and temperature values are therefore normalized linearly between -1 and 1. The training process is carried out by sliding window process, which is input data for training are always renewed with the latest actual data before the target day. The idea of using this training process is based on the fact that the forecast load is affected dominantly by the recent correlated data [12]. In this paper, the forecasting process is only for weekday and weekend, since we are not interested in forecasting for “irregular” day such as holiday. As the neural network forecasters can give slightly different results with different training session, the training and forecasting was performed five times with each network. The error values are averages from these five test runs. In order to decide on the optimal number of neurons, the simulation with networks that had different number of hidden neurons is run. The process is carried out by trying 3, 6, 12, 18, 24, and 30 hidden layer neurons. 3.1 Neural Network with 24 Output Nodes The idea to use this approach is to forecast all loads at once so that each profile is represented by a 24 dimensional vector with one or two previous days are used as main inputs, and temperature factor and the day as addition inputs. To forecast the load profile at once, the first variable to be used is at least the load itself, as the load series is strongly correlated. Several different input were tested for this model such as either the load of one or two previous target day, the corresponding maximum and minimum temperature and the type of the day Input structure that gives the best performance for this model is as follow, Inputs: 34 Load L (d-1): 24 nodes Day (d-1), T max (d-1), T min (d-1): 5 nodes Day (d), T max (d), T min (d): 5 nodes Hidden layer neurons: 12 Outputs: 24 nodes 3.2 Peak and Valley load Forecasting Fig. 2 shows the block diagram of this forecaster. The separate network is used to forecast peak and valley load.
The output of NLA is as follow PEAK AND VALLEY LOAD Predictor
Input ANN
FORECASTER
Normalized Load Averager
Historical Normalized Load data Fig. 2 Diagram of Peak and Valley Load Forecaster
The fundamental design of this model is using the prediction of peak and valley load with ANN techniques and the normalized load profile which is obtained by averaging the historical normalized load data and then scaling the normalized load profile by the forecasted peak and valley load. Here, a decision was made to use a separate network for weekday and weekend day types. Another possibility would have been to use one network for each day type, but this was considered unnecessary on the basis of some preliminary testing. Other features to be decided about the architecture of the network are the input variables and the number of hidden layer neurons. To forecast the maximum load of a certain day, at least the maximum load of the previous day and the corresponding day from the previous week, can be considered as potential input variables. Also the temperature data of those days may be useful if temperature forecasts for the target day are available. Maximum and minimum temperatures are considered for this purpose. The structure output and input listed below is for peak load forecasting. If the target is the valley load, all maximum load values are replaced by corresponding minimum load values. 3.2.1. Peak and Valley load predictor Output: L max (i) Input: 38 Lmax (i-1,…, i-12): 12 nodes Tmax (i-1,…, i-12): 12 nodes Tmin (i-1,…, i-12): 12 nodes Tmax (i), Tmin (i): 2 nodes Hidden layer neurons: 6 3.2.2 Normalized Load Averager (NLA) The inputs for this block are the latest 6 patterns of normalized load profile which is similar to the day to be predicted, the output is hourly averaged normalized of them. The shape of the load curve for a certain day contains 24 normalized load values. The normalized load values are calculated by using the equation below:
L nor ( d , h ) =
2 * [ L ( d , h ) − L min ( d )] −1 [ L max ( d ) − L min ( d )]
Lˆ (d , h) = 1 / 6 * [ L(d − 1, h) + ... + L(d − 6, h)] Where Lnor ( d , h) = normalized load at hour h on day d,
L(d , h) = load at hour h on day d, Lmin (d ) = valley load of day d, Lmax ( d ) = peak load of day d. 3.2.3 Forecaster The inputs to the forecaster are the predicted peak and valley loads and the outputs of NLA. Using the peak and valley load, the next day load is obtained by
Lˆ(d, h) = [0.5*(Lˆnor(d, h) +1) *(Lˆmax(d) − Lˆmin(d))]− Lˆmin(d) Where the hats indicate the values are forecasts. 3.3 Hourly Forecast Model The work principle of this approach, each hour of the load is forecasted by the separate ANN, hence to forecast the load profile, it is needed 24 ANN which forecast the load of hour 1 to hour 24. Fig.3 depicts the block diagram of this model. To forecast the load of a certain hour of the day, at least the load of the previous corresponding hour of the similar day, can be considered as potential input variables. The temperature data of those hours may be useful as well if temperature forecasts for the target hour are available. The temperature in the corresponding hour is considered for this purpose. Output: Load at hour h day d, L (d, h) Input structures: Input: 25 L (d-1, h)… L (d-12, h): 12 nodes T (d-1, h)… T (d-12, h): 12 nodes T (d, h): 1 node. Hidden layer neurons: 6 Where, d-1... d-12= the 12 latest previous similar day (i.e. Monday one week previous, Monday two week previous... Monday n week previous), h = the hour index, L=load, T=Temperature Output
CO MB INER
NN1
NN2
NN3
NN24
Input Fig.3 Diagram of Hourly Forecast Model
IV. RESULT AND OBSERVATIONS The performance of the three developed models for load profile forecasting has been tested using one year (2005) of load and temperature data. The load profiles of all days of 2006 (holidays are excluded) are forecasted using each developed ANN which is trained with data available prior to the forecasting day. The load profile forecast is then compared with the actual load profile and the deviation was calculated by mean absolute percentage error (MAPE), defined by 1 n y − yˆ t * 100 % MAPE = ∑ t n t =1 yt Where, y t is actual load, yˆ t is predicted load and n is number of the forecasted target. A summary of the MAPE is given in Table 1. All figures given are percentages of absolute forecasting error. By comparing the errors in Table 1, we can see that the model # 3 performed much better than others. However, those results are not truly out of sample, since they were computed over the same database. The input structure and the number of hidden layer that yield the best performance for model #1 had 24 output nodes, 12 hidden layer neurons and 34 input, which mean it had 732 weights and biases as the parameters and compare to the model #2 and model #3 that had 241 and 163 parameters respectively. One of the factors that influence the performance of the model is the model structure. The selection of the input variables, the number of neurons in the hidden layer and the number of neurons in the output layer, determine the capability of the model to forecast future load based on the historical data. The parameters in the model which are connecting the relation between input and output are determined by the number of nodes in the input and the number of neurons in the hidden and output layer
Each neuron brings a certain free parameters in the model. We observe the larger the number of parameters in the model, the more likely the model less accurate due to overfitting. The training aims at minimizing the errors of the network outputs with regard to the input-output patterns of the training set. The success in this does not, however, prove anything about the performance of the network after training. More important is the success in generalization. A network is said to generalize well, when the output is correct or close enough for an input, which has not been included in training set. While the load forecasting model as described in the previous section is acceptably most of the time, there are a significant number of days when it yields forecasts which are to inaccurate to be acceptable. Taking a closer look at the errors produced by each method, we found that the largest MAPE, above 8 %, were always produced on Sunday, December 31, 2006. Fig.4 shows the frequency histogram of MAPE for all of the models, over the same period. It can be observed that the errors produced by the model #3 were not only smaller than those of the other models, on average, but also were less spread and this is also shown in the table I that the standard deviation of model 3 always smaller than the others. Fig. 5 depicts the comparison of forecasted load of each models and actual load profiles for the ordinary weekday. One of the improved forecast accuracy impacts is economic saving from better scheduling result either from avoiding unnecessary start up cost (due to over forecast) that are not actually needed, or avoiding costly combustion turbine generation or purchases of spot power when too little capacity has been committed (due to under forecast). The economic cost of inaccurate forecasts have been reported in [13], which declare that the reduction of 1 % in MAPE decreases the variable generation cost by approximately 0.1 % to 0.3 % depending upon the utility.
350
TABLE I Monthly absolute error statistics load forecast for 2006 (all figures are percentages)
300
Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec yearly
Model #1 Mean stdev 4,56 2,27 3,96 1,79 4,44 1,96 4,74 1,57 4,45 1,71 2,83 0,87 3,55 1,41 3,08 0,95 4,06 1,19 3,70 1,17 3,36 1,48 3,63 2,13 3,87 1,72
Model #2 Mean stdev 3,14 0,97 2,85 0,94 2,51 0,68 3,35 0,97 3,09 0,96 2,46 0,62 2,52 0,74 2,67 1,10 2,45 0,69 2,89 0,68 2,75 0,79 3,09 2,16 2,81 1,08
Model # 3 Mean stdev 1,51 0,44 1,38 0,44 1,37 0,30 1,37 0,43 1,41 0,32 1,13 0,28 1,33 0,36 1,34 0,39 1,55 0,43 1,45 0,27 1,23 0,33 1,56 1,50 1,38 0,56
F req u en cy
250
200 method 1 method 2 method 3
150
100
50
0
e
