Introduction
According to Moore and McCabe, 1999, an outlier, in fuzzy systems, is a reflexion that lies a peculiar distance from other values in a random sample from a population. When an outlier is present in a dataset, it is an indicator of a problem or concern in the results. They can be easily spotted in histograms and in scatter plots. They are evident when two datasets are being compared to determine a relationship among the data. These outliers need to be discarded before finding the line of best fit using the least squares fitting methods on the data. It is very important to perform the electricity price forecasting so as to improve the performance of key market players in the electricity market. There is need to create an economical environment in the electricity market for many countries so as to achieve goals such as increase in efficacy and need to invest.
The Matlab simulation approach enables one to create a classic of the system to compute the cost of the electricity based on the generation cost using an prime distribution of the lead. The algorithm used requires extensive data entry (Bastian, Zhu, Banunaryan, & Mukherji, 1999; KavousiFard, Niknam, & Golmaryami, 2014). The calculations used in the modelling of time forecasts are a bit complex. For the time series approach, the past data is used to model and forecast current trends and future prices within a set period of time. The new methods of predicting values for the electricity trends employ intelligent approaches. An example is such as artificial neural networks (ANN). The technique has the ability in data forecasting and pattern recognition. The Neural Network processes the input and output data provided for a specific area of research. The forecasting process is based on predicting the time series of the electricity using the past data provided. A clustering algorithm is mainly utilized in the process of determining the fuzzy sets using constants of the model which are optimized. They are referred to as Teaching-Learning-Based optimization algorithm.
Several models are used to forecast electricity. There are several mathematical models used to provide a forecasting step forward for time series such as the ARMA or ARIMA, fuzzy inference systems, and SARIMAX. ARIMA is the most widely used model in determine and forecasting for time series. We seek to predict the occurrence of electricity prices in the near future based on the economic trends. Fuzzy logic is a term that refers to computational intelligence skill that aims at modelling the like way of thinking as of man. One can make decisions in an environment of ambiguity and imprecision which does not occur with discrete logic. This report uses the Mamdani inference system and sets some rules to link the inputs to the outputs.
The average relative error is a metric used to measure the forecasting system’s performance. It is defined by,
Where N- is the cardinality of the data set under testing
The system inputs and outputs
Temperature and total demand of electricity at time instant, t, be T(t) and D(t) respectively. The goal of the fuzzy forecasting system is to predict the RRP price by using some historical data as system inputs. The historical data set used for building the fuzzy system at time instant t is composed of a subset of the set
M={T(t-2),T(t-1),T(t),D(t-2),D(t-1),D(t)}
The output of the system at the time instant is a forecasting value of the recommended retail price of electricity at the next time instant t+1 denoted by P(t+1).
- Removing outliers from the output variable from the datasets and give a list of the outlier
- The appropriate values or fuzzy subsets for linguistic variables
- The fuzzy rules generated by using statistical analysis or correlation coefficients with heuristics
- Matlab implementation of the fuzzy system using Matlab with appropriate plots.
- The system performance in terms of the average relative error for both training and testing datasets, and analyse the effects of membership functions and defuzzification methods.
The plot of the testing dataset
There are many outliers in the dataset.
The Matlab simulation of the fuzzy implementation,
The training and testing data is loaded to the system. The FIS is initialized and generated. The data is analysed and viewed on the FIS GUI. The system performs an ANFIS training. The data is tested against the trained data in the FIS.
To evaluate, the mean average percentage error also known as MAPE and the standard deviation, SD, are used. The MAPE measures in utter terms, the deviation from the original series with the output of the model series. The standard deviation, on the other hand, is the dissimilarity between the original series and the series predicted by the archetypal. It is denoted as
The rules provided for the Mandani Fuzzy inference rule are,
There are eight rules in the ANFIS
The surface view of the rules for the fuzzy time series system for the data provided is
The quiver representation of the modelled system is
Conclusion
The attempt to obtain a model for the prices for Queensland data on electricity market trends showed a slight increase in the prices. A number of factor come into play with regards to electricity. The generation of electricity is a key component. The government agencies in charge of the regulation should regularly come up with better energy harnessing methods to ensure steady supply of electricity. New forms of energy are expensive to maintain such as the nuclear and the solar power grids. Some of the costs may be pushed down to the consumer at the end of the line. The regulation or provision of incentives in such a situation would subsidize the costs and ensure better pricing for electricity.
References
Azadeh V. N. A., Pazhouheshfar, P.; Saberic, M. An Adaptive-Network-Based Fuzzy Inference System for Long-Term Electric Consumption Forecasting (2008-2015): A Case Study of the Group of Seven (G7) Industrialized Nations: U.S.A, Canada, Germany, United Kingdom, Japan, France and Italy. IEEE. 2010.
Conejo, A. J.; Contreras, J.; Espínola, R.; Plazas, M. A. Forecasting electricity prices for a day-ahead pool-based electric energy market. International Journal of Forecasting 2005;21:435-65.
J.S.R. Jang, N. GulleyThe FuzzyLogic Toolbox for use with MATLAB. The MathWorks, Inc, Natick, Massachusetts (1995).
Gooijer, de; Jan,G.; Hydman, R. J. 25 years of time series forecasting.International Journal of Forecasting 2006;22(3):443-473
