Short term load forecast by using Locally Linear Embedding manifold learning and a hybrid RBF-Fuzzy network

The aim of the short term load forecasting is to forecast the electric power load for unit commitment, evaluating the reliability of the system, economic dispatch, and so on. Short term load forecasting obviously plays an important role in traditional non-cooperative power systems. Moreover, in a restructured power system a generator company (GENCO) should predict the system demand and its corresponding price for efficient decision making. The task of a forecasting engine is to find the relation of the inputs and outputs of the system and also predicts the outputs for a given inputs. Therefore, the accuracy of forecasting is highly affected by the inputs of the forecasting engine. This effect can be studied from two points of view; First, extracting the more informative inputs and second, reducing the dimension of input space, both make it possible to learn the forecasting network via more simple models with more generalization. As a result, a reduced informative input space leads to lower prediction error. In many previous load forecasting methods, the inputs have been selected empirically. In this manner, the more correlative factors with the load in the forecasting day have been chosen as the inputs. They are generally a combination of load history and weather conditions. Several researches are focused on mathematical approaches of the input selection which are mainly based on principal component analysis (PCA) method as well as some intelligent algorithms. In this paper, a manifold learning method namely Locally Linear Embedding (LLE) is proposed, aiming to extract more informative inputs and to reduce the dimension of input space for short term load forecasting. Among all methods based on manifold learning, it can be seen that LLE performs very well in extracting the electric load curve features. The aim of this paper is to analyze the features of the load curve for estimating this curve in future. The extensive computational experiments show that the extracted features by LLE results in less prediction error than two other methods. Furthermore, LLE acts faster and makes input dimension lower than the two other methods. In the following section we will discuss the LLE method. The LLE method finds the nonlinear relationships among features by mapping a locally linear manifold in the feature space. Extracting the more informative inputs by extracting the combinational features by finding the nonlinear dependences of the features, results in reducing the dimension of input space. The resulted inputs from feature extraction and dimension reduction are utilized for load forecasting. To examine the effect of the proposed feature extraction method on load prediction error, a hybrid prediction system is proposed which is a combination of a radial basis function (RBF) network and a fuzzy system. The RBF network is the core of the prediction engine and works with historical load data as its inputs. The fuzzy inference system is combined with the RBF network to incorporate the impact of temperature on load. The case studies are carried out on the real data of electric power load of Mazandaran area in Iran. The efficiency of the proposed forecasting engine is compared with three benchmarks, the artificial neural network, time series and neuro-fuzzy methods. Furthermore, the proposed input selection method (LLE) is compared with principal component analysis (PCA) and empirical selection of inputs. Simulation results with statistical significance analysis show that the LLE method with the proposed forecasting engine is superior to other input selection methods and forecasting engines in sense of lower input dimension and lower prediction error.