Multi-layered perceptron network for short-term load forecasting

The use of the multi-layer perceptron (MLP) network for short-term load forecasting is performed. Through weather and load data from the Hydro-Quebec database, capabilities, advantages, and limitations of this artificial intelligence method in load forecasting are investigated. Current management tools for energy systems are based on deterministic optimization methods, where supply, demand, and production are assumed to be known. Changes in electricity supply and demand have made their adjustment more complex. It is no longer a question of adjusting centralized production to demand, but rather of adjusting centralized production, decentralized production, and production from decentralized storage facilities. Our approach will be based on a predictive optimization method adapted to energy systems. An artificial neural network is applied to forecast load for Mascouche in Quebec, Canada. It is about a part of the Hydro-Quebec’s grid where the maximum capacity is 140 megawatts.


Introduction
Universal access to affordable, reliable, sustainable and modern energy -Sustainable Development Goal (SDG) 7 is a key element to increase access to electricity while reducing poverty.Load forecasting is one of the essential inputs to achieve this goal.Prediction uncertainty can arise due to measurement errors, lack of knowledge of input data, and model approximation errors (e.g.due to imperfections in the model formulation, the estimation process, etc.) [1], [2], [3].When not properly taken into account, data's stochastic aspect generates additional costs to power producers and customers.For the specific case of variable renewable energy (VRE) integrated power systems, the impact on system's reliable operation is a capital parameter to consider knowing a significant share of variable sources.The increasing share of intermittent sources within competitive and modern power grids implies the need of finding suitable techniques of load prediction for a sustainable and efficient energy market.Reliable and safe load forecasting allows power producers to balance demand and generation in order to serve load on the next day in a secure manner.The vast majority of the existing studies on power and load predictions only provide point predictions, without considering the uncertainties in the network structure and input data [4], [5].The prediction method we propose can fix uncertainty and its reliability is evidenced.

Load forecasting
The most important work in building an ANN (Artificial Neural Network) load forecasting is the selection of input variables [6].There is no particular process to consider.Indicators of hour and day, weather-related inputs, and historical loads are the types of variables used as inputs and the neural network is built by trial and error.

Hour indicator H (i)
Load changes every single hour with an hour indicator H (i) (1 hour to 24 hour) is capital in short-term load forecasting.

Day indicator D (i)
Electrical load changes every single day.For all seasons, the week-ends' power consumption is much less than it is on the weekdays.

Weather variables
Weather variables have an effect on the Hydro-Quebec load data.It is given in Table 1 following our investigation: L (load), T (temperature), W (wind velocity), and C (cloud cover).
The most determinant variable is the temperature.The wind velocity and cloud cover have a less significant impact on the load.The considered variable is the temperature.The correlation between these variables is shown in table 1 [7].

Historical loads
In this application, no load history is used.In load prediction, there is no load history in general, only the estimated data is essential.Hence, an error, even small, can propagate drastically creating issues in the prediction model.No load history is used in this work.

Proposed methodology
The MLP is used in this application.The used Artificial Neural Network (ANN) is composed of three layers (input, hidden, and output layers).L(k), the hour k load, is the output of the ANN, and the inputs are: Measured temperature at the designated site, Mascouche, is T. The resulting ANN is shown in figure 1.  ), columns 4 and 5 respectively.The desired output (target) of the network will be the load, column 1, in MW or per unit (pu).
The idea is that by knowing the temperature for the next three days, can we predict the hourly load for these three days.Here the trained neural network is tested for different Windows, namely Windows 1, 3, 5, and 7.For each window, the NN output is plotted and compared with the real (measured) load.Comparison is using the Root Mean Squared Error (RMSE): ( Where is the prediction, is the field recording true value, and n is the actual measurement points.

Results and discussion
We used the Levenberg-Marquardt training algorithm for the multi-layered perceptron (MLP).It generated a quick training with a significantly reduced error within few iterations.Using a set of data that were not part of the training set, the developed ANN model's performance for load profile prediction is evaluated.This allows us to appreciate the ANN's output with comparision to the Hydro-Quebec's load.
The Taylor expansion of the error, function of these weights, is given by the below equations, where W is the errors' vector and J the Jacobian: (2) The results on a period of 72h (3 days) from Nahi Kandil et al's [7] works on different locations, show that the average percentage error for ANN forecasting is eNN = 0.981, while for the traditional method used by Hydro-Quebec, the error is eHQ = 1.083 [8].In our special case of the Mascouche region, the ANN performance calculation gives an average percentage error eNN = 1.281.It resulted in a very good performing ANN and a very efficient load prediction approach.The average amount of input data for the neural network allows us to use the Levenberg-Marquardt as a training function of the network; the fact that seemingly accelerated the training and convergence process.On the above graph (figure 3) we remark clearly that the RMSE reached its minimum (10 -4 ) at the 331st epoch.We are also able, with Matlab, to generate the fineness graph between the actual data and the predicted data by the neural network as shown in figure 4. As we remark on the graph, this function allows us to evaluate the quality of the prediction following the distribution of the cloud of points and also via the correlation coefficient (R=1) which indicates the perfect fitting between predicted and actual data.

Conclusion
Operating a power system suitably needs a reliable and efficient load forecasting model.ANNs are a good fit for this type of application considering the flexibility between inputs and output.We investigated on the application of ANNs for short-term load forecasting for a part of the Hydro-Quebec's power grid.Then we have shown the advantages and limits of this tool.We also demonstrated ANNs' capabilities in load forecasting without using load history in the input set.Additionally, among the weather variables, only temperature is considered.Sky condition (cloud cover) and wind velocity have no serious effect and are not taken into account as inputs variables.Concerning the ANN, a multi-layered feed-forward ANN is used in Matlab environment, and results show that it can provide the future load pattern by fitting in the load and weather data during training phase.We could get better results by using: (i) more improved ANN, (ii) more qualitative choice of input parameters, (iii) improved architecture for the ANN, and (iv) better choice of the training set.Additionally, further works using historical loads are planned to show comparative advantages and limitations.

Figure 1 .
Figure 1.The model of ANN used with inputs and output (forecasted load).

3. 1 .
The neural network's training: data and algorithms Two files of data (Mascouche 1 and Mascouche 2) are provided having hourly real load (MW) for two months, one month in each file having only working days, i.e.: weekends are not included, and here the two months are in the wintertime.Mascouche 2, having the file (data 2), is used for training the neural network, and Mascouche 1, having the data file (data 1), is used for validating (testing) the neural network.Each of these two data files has 5 columns: Load, Days, Hours, Temperature, and the average of temperature over the last five hours.The data file Mascouche 2 (data 2) is used for training the neural network.Inputs of the network are temperature (T) and the average of the temperature (

Figure 2
Figure 2 illustrates the quality of the network's training with data 2 values reserved for the same.It compares the efficiency of the neural network for training and data presented as a target.

Figure 2 .
Figure 2. Validation with training set.Matlab tools allow us to visualize different steps of the neural networks' training.The performance of the number of epochs is defined by the Root Mean Square Error (RMSE) between predicted data by the network and data introduced as the expected output of the same network.This is clearly shown in figure 3.

Figure 3 .
Figure 3. Performance regarding the number of epochs.

Figure 4 .
Figure 4. Fineness of the prediction with training data for the neural network.