**1. Introduction**

354 Fuzzy Inference System – Theory and Applications

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Fuzzy Inference Systems (FIS) have been widely used in many applications including image processing, optimization, control and system identification. Among these applications, we would like to investigate energy demand modelling. Generally, developing an energy demand model is the challenge of interpreting the historical use of energy in an electric power network into equations which approximate the future use of energy. The developed model's equations are coded and embedded into a processor based system, which predicts the output when a certain type of input occurs. However, the range and quality of prediction is still limited within the knowledge supplied to the model. The major concern about the energy demand modelling is to categorize the type of prediction in short or longterm prediction. In addition, it is crucial to categorize the type of the power network to be modelled. Since identifying the useful historical operation data for setting the model parameters is crucial in modelling, the operation history of the modelled systems must to be analysed. In simple terms, modelling energy demand is the art of identifying the right modelling technique and system's operation parameters. The operation parameters differ based on the type and size of the modelled system. So, taking into consideration why the system is modelled will justify the selection of modelling techniques. Among the reasons for modelling energy demand is managing the use of energy through an Energy Management System (EMS).

For EMS, most of the Artificial Intelligence (AI) methods will lack robustness in terms of their programming and their required computation resources, especially when the EMS is designed to perform on-line quick response tasks. Artificial Neural Network (ANN) might be good candidate among modelling techniques, as there has to be a compromise between robustness of the method and its required computation resources for a specific type of modelling. However, there are a few reasons why ANNs are not suitable for our proposed discussion: their limited adaptability within limited computation resources, their training time and their models' complexity, especially when we deal with highly non-linear systems. Looking at our case study and the reasons this scenario is modelled, we have found that Fuzzy Inference Systems (FIS) are the most appropriate for modelling the energy demand in this specific system, since model development, model parameters, model adaptation capability and computation resources requirements are met. The reason behind choosing FIS

Fuzzy Inference System in Energy Demand Forecasting 357

A range of data clustering methods have been illustrated in literature such as the nearest neighbourhood clustering method (Wang 1994), Gustafson-Kessel clustering method(Donald and William 1978), Gath-Geva clustering method (Gath and Geva 1989), fuzzy c-means (FCM) clustering method (Frank Höppner 1999), the mountain clustering method (Yager and Filev 1994) (Yager and Filev 1994), and Fuzzy Subtractive Clustering Method (FSCM) (Chiu 1994). However, the main problem of fuzzy modelling comes from the difficulties of choosing the right range of parameters which leads to the number of rules. In other words, the inaccurate parameter settings would deteriorate the prediction accuracy. Good fuzzy modelling parameter settings come from a good understanding of the modelled system and its modelling problems. The main justification for this problem is that when the number of clusters is increased, the prediction output will have strong alignment with the modelled data. As when the number of clusters equals to the number of data, the developed clusters will specifically resemble the training data characteristics, and lose the generality of resembling the system operation characteristics. Consequently, the clusters will mostly resemble a part of the operation data. Therefore, the prediction will miss other kind of operation data that differ from data modelled despite their availability within the modelled data range, which will result in a high prediction error. In contrast, when the number of clusters is reasonable, the prediction will cover the training data regions, as well as any other types of operation data, as far as they are located within the range of the training data. The prediction however will result in an acceptable range of error, which is fairly accepted

In other terms, a suitable parameters choice is the key solution for a successful fuzzy modelling, which will be based on an optimized number of rules and prediction accuracy level. This problem can be solved by analysing the modelled system operation history and indentifying suitable modelling parameters. In addition, having experience about fuzzy modelling will help the modelling process. However, trial and error may be applied for

In comparing fuzzy modelling with ANN, it has been concluded that to select the right modelling method, it is crucial to consider the type and the size of the system, the amount of system's historical operation data and the required computation resources. Regarding the type and the size of our case study, it has been found that fuzzy modelling will suit the modelling process. More details about the case study and data analysis are explained in the case study section in this chapter. Full details about the fuzzy modelling process are also explained in modelling methodology section in this chapter. In this chapter we aim at discussing the use FIS as a tuner fuzzy system. The next section describes the main operation principles of Self-Tuning Fuzzy Systems STFS and the use of FIS to improve the

In modern automation, adaptability has become crucial in implementing smart applications. In the way, that they resemble the human sense of adaptive thinking. Usually, ANN is highly utilised in implementing adaptive systems. However, self tuning and adaptive algorithms are not restricted to ANN, they can also be implemented through fuzzy logic and other optimization techniques. The specific tuning mechanism implementation is subject to the type of the problem or the system to be processed. The

prediction accuracy or to adapt the prediction to the external effects.

by all research communities.

output tuning in most of the modelling cases.

**3. Self tuning fuzzy systems** 

to model the energy demand is the flexibility to control the prediction performance and the complexity of the model. Fuzzy modelling and reasoning systems have been widely utilised in literature because of their applicability and modelling performance. The use of Adaptive Neuro Fuzzy Inference Systems (ANFIS) gives the fuzzy modelling two extra valuable advantages: the training time and prediction accuracy compared to other modelling techniques. Fuzzy modelling has been successfully applied in different types of applications including electricity and gas demands, economics and finance, weather and meteorology studies, health and population growth, geographic information systems, traffic and transport systems, etc.

In the recent years, energy demand prediction modelling has been widely investigated, especially when its smartgrid applications have been rapidly grown, and energy price change has been rapidly correlated to the energy demand prediction. Different smart prediction mechanisms have been introduced in literature. (McSharry 2007) has developed a day-ahead demand prediction models, and (Alireza Khotanzad 2002) has introduced a new short-term energy demand prediction modelling technique which integrates the real-time energy price change in the prediction models. (Amir-Hamed Mohsenian-Rad 2010) have also introduced the real-time price environment modelling to perform an optimised residential load control, where a fundamental bid-based stochastic model is presented to predict electricity hourly prices and average price in a given period by (Mazumdar 2008). Among the prediction mechanisms we aim at addressing the use of Fuzzy Inference systems in developing short-term demand prediction models, which can be applied in SmartGrid and electronic market applications.

The objective of this chapter is to review the use of fuzzy logic in modelling the energy demand in a specific electric network after analysing its demand characteristics. This chapter will also discuss the use of FIS to improve the prediction performance and adapt the prediction to the real time effects. We consider a real electric power system by modelling its energy demand and verifying the prediction output results. The next section will consider the system's operation data while selecting the most effective modelling parameters, highlighting the use of FIS in modelling, choosing the suitable data clustering method and detailing learning, training and verification for different type of demand patterns.
