**2. Fuzzy modelling**

Fuzzy modelling is a widely utilised and targeted modelling method. It attracts attention from academic and industrial research sectors because of its applicability and flexibility in interpreting the human decision in many complex computer controlled applications. Despite that its complexity has been mainly considered in modelling, as the number of developed fuzzy rules affects the modelling performance, fuzzy modelling is still one of the most efficient modelling techniques. Its main modelling concept is the same as that used in other modelling techniques, which is building mathematical expressions based on historical operation data for the modelled system. It is considered an effective technique to establish an FIS from a given nonlinear input-output set of data, when in fuzzy modelling, the data is partitioned in the input space and an optimal fuzzy rule table and membership functions are developed.

The data partition is performed using data clustering methods. A data clustering method is applied to partition the input-output set of data into a set of clusters. Depending on the type of clustering method, different type and number of clusters can be identified.

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

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

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

Fuzzy modelling is a widely utilised and targeted modelling method. It attracts attention from academic and industrial research sectors because of its applicability and flexibility in interpreting the human decision in many complex computer controlled applications. Despite that its complexity has been mainly considered in modelling, as the number of developed fuzzy rules affects the modelling performance, fuzzy modelling is still one of the most efficient modelling techniques. Its main modelling concept is the same as that used in other modelling techniques, which is building mathematical expressions based on historical operation data for the modelled system. It is considered an effective technique to establish an FIS from a given nonlinear input-output set of data, when in fuzzy modelling, the data is partitioned in the

detailing learning, training and verification for different type of demand patterns.

input space and an optimal fuzzy rule table and membership functions are developed.

of clustering method, different type and number of clusters can be identified.

The data partition is performed using data clustering methods. A data clustering method is applied to partition the input-output set of data into a set of clusters. Depending on the type

transport systems, etc.

and electronic market applications.

**2. Fuzzy modelling** 

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 by all research communities.

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 output tuning in most of the modelling cases.

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

#### **3. Self tuning fuzzy systems**

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

Fuzzy Inference System in Energy Demand Forecasting 359

the energy demand may depend on several independent variables, each having different weightings. Accept when it comes to a university type load profile, a few extra variables may affect the load change patterns. So, it is highly advantageous to analyse the historical operation data of the modelled system to indentify the effective variables. The ECU's electric network has nine substations serving 32 buildings. The minimum daily demand in this university does not drop below 500 kWh at any time, while the maximum daily demand may go up to 3500 kWh in summer daytime. Identifying the critical issues in the network is very important before proceeding in modelling. Fig. 1 shows Load changes in the ECU's

Fig. 1. Load changes in the ECU's Joondalup campus in January 2009.

By monitoring the load change in Fig.1, several load change patterns have been indentified including the weekdays, weekends and hours correlation. In addition, we can identify other important modelling factors e.g. weather, date, hours, order of the day (Monday, Tuesday,...,etc.) and type of the day (working day or weekends/holidays). It has also been noticed that big load changes are infrequent. In this modelling strategy, these big load change events are ignored. It is assumed that such big load changes need to be predefined or have warning settings assigned in order to avoid system overloads. From analysing these effective factors, we could draw a correlation picture about the load change in the ECU's Joondalup Campus and other effective parameters. For more details about load change analysis, Fig. 2 shows the correlation between a 30 minutes interval load change and other identified factors in the ECU's Joondalup campus in January 2009. Fig.2 includes 1500 entry

Joondalup campus in January 2009.

of the correlated information data.

tuner and main systems may share the same input parameters, or they may receive two different types of inputs from external sources depending on nature of operation. Selftuning systems have practically unlimited applications, and they have been widely utilised in academic and industrial applications.

Basically, a STFS is an on-line adaptive output fuzzy system, where its output is changed depending on the type of input and the pre-defined knowledge in the fuzzy tuning system. Generally speaking, a fuzzy system is called tuneable when any of its parameters (input/output scaling factors, membership functions shape and type or fuzzy rules) are changed instantly. It is a combination of general and tuner fuzzy, where the tuner FIS tunes the general system' parameters. Although sometimes both systems have the same input parameters, but they still perform different independent jobs. The main reason using STFS in modelling is to perform a short term prediction and to add the safe prediction estimations to the predicted output. This can be achieved by adapting the prediction to the external effects through a pre-defined knowledge based system.

By looking at our modelled case study, it has been noticed that the model has highly nonlinear characteristics. So, developing a model for a high precision prediction is a major challenge. Hence it is required to focus on the model prediction accuracy to consider its weak-points. By considering the energy demand in the targeted case study, modelling knowledge could be added regardless of its availability in the supplied operation data. Using the self-tuning fuzzy system will help in adding the missing knowledge to the operation history data. For such kind of systems, a possible design with external input parameters from external data sources to tune the main fuzzy model output based on a knowledge base could be implemented. In this chapter we aim at utilising the real-time demand change measure to investigate the FIS ability to adapt the prediction output to the actual demand change. Alternatively, in our modelling discussion we also use the main fuzzy system's input parameters to tune the prediction based on a knowledge base system. Similarly, the tuning part may use different mechanisms, e.g. rules, membership functions or output scale tuning. The Weights Adjusting Method (WAM), which is the method that adjusts the output of the main system, is derived from the process needs for adaptation. WAM is set to adjust the weights of the output of the main system and its tuner based on the needed amount of adaptation. Depending on the tuner's fuzzy rule base, a suitable WAM can be derived. Although even when different types of models are discussed in our modelled electric network, only one WAM is applied. For simplicity, we aim at utilising an output scale adaptation design. The full design details are explained in the Modelling Methodology section, whereas the results will be discussed from the prediction improvement point of view and the adaptation performance in the Summary section. In the next two sections, the details about modelling twelve-month load patterns in a real electric network are presented. Additionally, the twelve models are equipped with twelve different tuner fuzzy systems to improve their prediction accuracy or to adapt their prediction to the external effects, depending on the purpose of the modelling.

### **4. Case study**

The electrical energy use of the power network of the Joondalup campus of Edith Cowan University (ECU) in Western Australia has been selected in this study to evaluate the robustness of the proposed modelling technique. Just like most commercial buildings that

tuner and main systems may share the same input parameters, or they may receive two different types of inputs from external sources depending on nature of operation. Selftuning systems have practically unlimited applications, and they have been widely

Basically, a STFS is an on-line adaptive output fuzzy system, where its output is changed depending on the type of input and the pre-defined knowledge in the fuzzy tuning system. Generally speaking, a fuzzy system is called tuneable when any of its parameters (input/output scaling factors, membership functions shape and type or fuzzy rules) are changed instantly. It is a combination of general and tuner fuzzy, where the tuner FIS tunes the general system' parameters. Although sometimes both systems have the same input parameters, but they still perform different independent jobs. The main reason using STFS in modelling is to perform a short term prediction and to add the safe prediction estimations to the predicted output. This can be achieved by adapting the

prediction to the external effects through a pre-defined knowledge based system.

external effects, depending on the purpose of the modelling.

**4. Case study** 

By looking at our modelled case study, it has been noticed that the model has highly nonlinear characteristics. So, developing a model for a high precision prediction is a major challenge. Hence it is required to focus on the model prediction accuracy to consider its weak-points. By considering the energy demand in the targeted case study, modelling knowledge could be added regardless of its availability in the supplied operation data. Using the self-tuning fuzzy system will help in adding the missing knowledge to the operation history data. For such kind of systems, a possible design with external input parameters from external data sources to tune the main fuzzy model output based on a knowledge base could be implemented. In this chapter we aim at utilising the real-time demand change measure to investigate the FIS ability to adapt the prediction output to the actual demand change. Alternatively, in our modelling discussion we also use the main fuzzy system's input parameters to tune the prediction based on a knowledge base system. Similarly, the tuning part may use different mechanisms, e.g. rules, membership functions or output scale tuning. The Weights Adjusting Method (WAM), which is the method that adjusts the output of the main system, is derived from the process needs for adaptation. WAM is set to adjust the weights of the output of the main system and its tuner based on the needed amount of adaptation. Depending on the tuner's fuzzy rule base, a suitable WAM can be derived. Although even when different types of models are discussed in our modelled electric network, only one WAM is applied. For simplicity, we aim at utilising an output scale adaptation design. The full design details are explained in the Modelling Methodology section, whereas the results will be discussed from the prediction improvement point of view and the adaptation performance in the Summary section. In the next two sections, the details about modelling twelve-month load patterns in a real electric network are presented. Additionally, the twelve models are equipped with twelve different tuner fuzzy systems to improve their prediction accuracy or to adapt their prediction to the

The electrical energy use of the power network of the Joondalup campus of Edith Cowan University (ECU) in Western Australia has been selected in this study to evaluate the robustness of the proposed modelling technique. Just like most commercial buildings that

utilised in academic and industrial applications.

the energy demand may depend on several independent variables, each having different weightings. Accept when it comes to a university type load profile, a few extra variables may affect the load change patterns. So, it is highly advantageous to analyse the historical operation data of the modelled system to indentify the effective variables. The ECU's electric network has nine substations serving 32 buildings. The minimum daily demand in this university does not drop below 500 kWh at any time, while the maximum daily demand may go up to 3500 kWh in summer daytime. Identifying the critical issues in the network is very important before proceeding in modelling. Fig. 1 shows Load changes in the ECU's Joondalup campus in January 2009.

Fig. 1. Load changes in the ECU's Joondalup campus in January 2009.

By monitoring the load change in Fig.1, several load change patterns have been indentified including the weekdays, weekends and hours correlation. In addition, we can identify other important modelling factors e.g. weather, date, hours, order of the day (Monday, Tuesday,...,etc.) and type of the day (working day or weekends/holidays). It has also been noticed that big load changes are infrequent. In this modelling strategy, these big load change events are ignored. It is assumed that such big load changes need to be predefined or have warning settings assigned in order to avoid system overloads. From analysing these effective factors, we could draw a correlation picture about the load change in the ECU's Joondalup Campus and other effective parameters. For more details about load change analysis, Fig. 2 shows the correlation between a 30 minutes interval load change and other identified factors in the ECU's Joondalup campus in January 2009. Fig.2 includes 1500 entry of the correlated information data.

Fuzzy Inference System in Energy Demand Forecasting 361

two modelling systems: the main FIS which is developed from modelling the input-output data using FSCM and ANFIS, and the second FIS system which is either developed by using the correlation between the energy demand and the temperature throughout the day, or by using the knowledge about the real-time demand change with its ability to achieve safe

To improve the prediction accuracy and reduce the model complexity, the annual energy demand of the ECU's Joondalup Campus has been proposed to be split into twelve monthly models, represented by twelve different demand pattern models. Each model represents a one month demand model. Fig. 3 illustrates the proposed annual energy demand prediction structure for ECU's Joondalup campus, it also illustrates the possible extra added input to

Fig. 3. The energy annual demand prediction structure of ECU's Joondalup campus

Splitting the annual demand model into twelve spilt sub-models gives the prediction the ability to cope with the twelve different load change patterns. In addition, it reduces the computation resources, when only one month model is active at a time. Thus the modelling uses twelve separate modelling methodologies depending on the load change analyses for the individual months. Regarding building the two FIS, their methodology is explained in

adaptation to the main model's output.

the following subsections:

improve the prediction accuracy when possible.

Fig. 2. Load change correlation with the effective factors for ECU's Joondalup campus in January 2009.

By spotting at the critical load change correlation among the identified parameters in Fig.2, several ideas about the energy use scenarios can be obtained. It is also noticeable that there is a big correlation between the daylight time, temperature, type of the day and the monthly order of the day. In Fig.2, only the effective load change parameters mentioned previously are illustrated. Theoretically, other load change parameters could be identified by analysing the university work hours, the nature of activities and the weekly time table in the university. From analysing the university weekly time-table, we could introduce another variable, which is the weekly order of the day. Although this parameter would have an effective load change contribution to the university's energy usage for a certain time of the year, namely the teaching period, but it rarely affects the load change in the remaining times of the year. On an average, it would require higher computation resources and would not indicate the load change effectively throughout the whole year. Therefore, it has been concluded not to consider this parameter among the modelling parameters. The next section details the modelling process and illustrates some hints about the fuzzy modelling.

#### **5. Modelling methodology**

This section covers the methodology to model the energy demand measured at 30 minute intervals in the ECU's Joondalup Campus. Basically, the model is developed by combining

Fig. 2. Load change correlation with the effective factors for ECU's Joondalup campus in

details the modelling process and illustrates some hints about the fuzzy modelling.

This section covers the methodology to model the energy demand measured at 30 minute intervals in the ECU's Joondalup Campus. Basically, the model is developed by combining

By spotting at the critical load change correlation among the identified parameters in Fig.2, several ideas about the energy use scenarios can be obtained. It is also noticeable that there is a big correlation between the daylight time, temperature, type of the day and the monthly order of the day. In Fig.2, only the effective load change parameters mentioned previously are illustrated. Theoretically, other load change parameters could be identified by analysing the university work hours, the nature of activities and the weekly time table in the university. From analysing the university weekly time-table, we could introduce another variable, which is the weekly order of the day. Although this parameter would have an effective load change contribution to the university's energy usage for a certain time of the year, namely the teaching period, but it rarely affects the load change in the remaining times of the year. On an average, it would require higher computation resources and would not indicate the load change effectively throughout the whole year. Therefore, it has been concluded not to consider this parameter among the modelling parameters. The next section

January 2009.

**5. Modelling methodology** 

two modelling systems: the main FIS which is developed from modelling the input-output data using FSCM and ANFIS, and the second FIS system which is either developed by using the correlation between the energy demand and the temperature throughout the day, or by using the knowledge about the real-time demand change with its ability to achieve safe adaptation to the main model's output.

To improve the prediction accuracy and reduce the model complexity, the annual energy demand of the ECU's Joondalup Campus has been proposed to be split into twelve monthly models, represented by twelve different demand pattern models. Each model represents a one month demand model. Fig. 3 illustrates the proposed annual energy demand prediction structure for ECU's Joondalup campus, it also illustrates the possible extra added input to improve the prediction accuracy when possible.

Fig. 3. The energy annual demand prediction structure of ECU's Joondalup campus

Splitting the annual demand model into twelve spilt sub-models gives the prediction the ability to cope with the twelve different load change patterns. In addition, it reduces the computation resources, when only one month model is active at a time. Thus the modelling uses twelve separate modelling methodologies depending on the load change analyses for the individual months. Regarding building the two FIS, their methodology is explained in the following subsections:

Fuzzy Inference System in Energy Demand Forecasting 363

membership functions, thus influencing the complexity of the developed network. Table 1

illustrates the full details about r� settings for the investigated cases.

Fig. 4. Selecting suitable FSCM parameters in ANFIS modelling

#### **5.1 Main fuzzy system**

In this subsection, we discuss the use of FIS in modelling. In this investigation, we aim at utilising data clustering methods to perform the fuzzy modelling. Data clustering methods divide the supplied data into different groups based on identified common characteristics in each group. However, these characteristics are identified based on the type of data clustering method. In literature, several types of data clustering methods have been discussed including the on-line and off-line methods. In our investigation, we aim at utilising off-line data clustering methods in modelling.

We aim at clustering the historical operation data of the targeted electric network to develop the demand prediction models. At the end of clustering, a fuzzy reasoning system will be developed. We aim at using ANFIS for developing our targeted fuzzy models. The complete modelling process is illustrated in Fig. 4.

In our modelling example, we use Fuzzy Subtractive Clustering Method (FSCM) (Chiu 1994). It is a method where each of the supplied data is tested under the condition that it has the highest density among the tested individuals. Every individual data is considered to be a candidate for the cluster centring. The individual density is evaluated as follow:

$$P\_l = \Sigma\_{f=1}^n e^{-a\left\|\mathbf{x}\_l - \mathbf{x}\_f\right\|^2} \tag{1}$$

where

$$a = \frac{4}{r\_a^2} \tag{2}$$

The data density for a specific cluster centre candidate is evaluated from the number of nearer individuals that contribute to the cluster centre. The highest density is identified to become a first cluster centre. The cluster size is decided when FSCM parameters are set to cover a range of data individuals in the cluster's neighbourhood. The radius �� , which is also referred by Range of Influence (ROI), defines the range of neighbourhood for the clusters extraction. Each of the developed clusters is a basis of a fuzzy rule that describes the system attitude, when the number of these clusters is the number of the fuzzy rules in the modelled network. When the first cluster centre is found, the next highest density is evaluated. Let the new investigated cluster centre to be ��, and �� be its density measure. When every data individuals is ��, the next cluster centre is identified as follow:

$$P\_l = P\_l - P\_{c1}e^{-\beta \| \mathbf{x}\_l - \mathbf{x}\_{c1} \|^2} \tag{3}$$

$$
\beta = \frac{4}{r\_b^2} \tag{4}
$$

$$r\_b = 1.5r\_a \tag{5}$$

Where P�� is the next density point to be examined, and x��is the next data point to be examined. where r� is a constant, which has the influence of reducing the density measure. r� is defined based on the experience of data clustering. Usually, it is larger than r� to avoid closely placed clusters. Sometimes, trial and error is used to select the best value of r�. However, the value of r� is set to 1.5r� as illustrated in literature (Chiu 1994), and r� is set based on the experience about the data clustering. In our investigated cases different values were applied depending on the type of the problem. It is clearly noticed that ROI value decides the number of

In this subsection, we discuss the use of FIS in modelling. In this investigation, we aim at utilising data clustering methods to perform the fuzzy modelling. Data clustering methods divide the supplied data into different groups based on identified common characteristics in each group. However, these characteristics are identified based on the type of data clustering method. In literature, several types of data clustering methods have been discussed including the on-line and off-line methods. In our investigation, we aim at

We aim at clustering the historical operation data of the targeted electric network to develop the demand prediction models. At the end of clustering, a fuzzy reasoning system will be developed. We aim at using ANFIS for developing our targeted fuzzy models. The complete

In our modelling example, we use Fuzzy Subtractive Clustering Method (FSCM) (Chiu 1994). It is a method where each of the supplied data is tested under the condition that it has the highest density among the tested individuals. Every individual data is considered to be

> �� � ∑ ���������� � �

> > ��

The data density for a specific cluster centre candidate is evaluated from the number of nearer individuals that contribute to the cluster centre. The highest density is identified to become a first cluster centre. The cluster size is decided when FSCM parameters are set to cover a range of data individuals in the cluster's neighbourhood. The radius �� , which is also referred by Range of Influence (ROI), defines the range of neighbourhood for the clusters extraction. Each of the developed clusters is a basis of a fuzzy rule that describes the system attitude, when the number of these clusters is the number of the fuzzy rules in the modelled network. When the first cluster centre is found, the next highest density is evaluated. Let the new investigated cluster centre to be ��, and �� be its density measure.

> � � � ��

Where P�� is the next density point to be examined, and x��is the next data point to be examined. where r� is a constant, which has the influence of reducing the density measure. r� is defined based on the experience of data clustering. Usually, it is larger than r� to avoid closely placed clusters. Sometimes, trial and error is used to select the best value of r�. However, the value of r� is set to 1.5r� as illustrated in literature (Chiu 1994), and r� is set based on the experience about the data clustering. In our investigated cases different values were applied depending on the type of the problem. It is clearly noticed that ROI value decides the number of

��� (1)

� (2)

(3)

� (4)

�� � 1.5�� (5)

a candidate for the cluster centring. The individual density is evaluated as follow:

When every data individuals is ��, the next cluster centre is identified as follow:

�� � �� � ������‖������‖�

**5.1 Main fuzzy system** 

where

utilising off-line data clustering methods in modelling.

� � �

modelling process is illustrated in Fig. 4.

membership functions, thus influencing the complexity of the developed network. Table 1 illustrates the full details about r� settings for the investigated cases.

Fig. 4. Selecting suitable FSCM parameters in ANFIS modelling

Fuzzy Inference System in Energy Demand Forecasting 365

Fig. 5. Modelling data utilization for the ECU's Joondalup Campus energy consumption

representation have the same property as well.

Fig. 6. ANFIS structure with its learning mechanism

After the rules which relate the input-output data have been developed, the developed clusters have been utilised in neuro-fuzzy networks to develop a zero-order Sugeno FIS, which will perform a 30 minutes ahead short-term prediction. In conventional fuzzy systems, trial and error is applied to tune the developed membership functions of the input-output universe of discourse of the fuzzy system. When ANN is used to tune the membership functions, an automated selection process based on the performance index is performed. The membership functions are trained to resemble the training data characteristics. In neuro-fuzzy networks, their networks structure is changed accordingly with the operation scenarios. Neuro-fuzzy networks however utilise the ability of learning of the neural networks to get the best tuning process with better performance and less time (Kandel 1993). Since the fuzzy systems have the property of universal approximation, it is expected that the equivalent neuro-fuzzy networks

Adaptive Neuro Fuzzy Inference System (ANFIS) is another candidate to perform the fuzzy membership functions tuning. ANFIS structure was firstly proposed by (Jang 1993), where other models of ANFIS were proposed by (Chin-Teng Lin 1996) and (Wang and Mendel

1992). Fig. 6 illustrates the ANFIS structure with its learning mechanism.

The next stage is to repeat the above estimation process to identify other cluster centres. The process of indentifying clusters is repeated until the amount of new identified density is equal of less to 0.15 of the highest identified density. More information about FSCM parameters details is found in (Chiu 1994).

The identified data clusters can be easily utilised as fuzzy rules' centres in the zero-order Sugeno fuzzy models. When a data individual is located within the cluster range, a membership function between that particular data individual and its cluster centre is derived. Data affiliation to the cluster centres is derived as follow:

$$\mu\_l = \exp(-\frac{\|\mathbf{x} - p\_l\|^2}{(r\_a/2)^2})\tag{6}$$

where x is the cluster centre and p� is the input set of data.

By clustering temperature, hour, day and load change data, random FSCM parameters values e.g. Influence Range, Squash, Accept Ratio and Reject Ratio are applied.

These values selection may have strong effects on the complexity of the developed models. Table 1 shows the number of membership functions and the selected ROI values for each of the twelve month models.


Table 1. ROI Values and Complexity of the 12 Month Models

After clustering is made, the developed membership functions are trained. Then, when the developed network is being trained, a simple test will be carried to verify the prediction accuracy of the developed models. To increase the range of prediction in the developed models, the historical operation of three years set of data (2007, 2008 and 2009) is used. The three years data has been divided into three different groups. The first set of data is used to extract the clusters, which is taken as a 90% of the 2007 and 2008 historical data. The second set of data, which is used to train the developed fuzzy systems, has been taken as a whole set of 2007 and 2008 data. Finally, the third set of data, which is used to verify the success of the developed model, has been taken as the 2009 operation data. Fig. 5 shows the data utilization in developing the demand models in this work.

The next stage is to repeat the above estimation process to identify other cluster centres. The process of indentifying clusters is repeated until the amount of new identified density is equal of less to 0.15 of the highest identified density. More information about FSCM

The identified data clusters can be easily utilised as fuzzy rules' centres in the zero-order Sugeno fuzzy models. When a data individual is located within the cluster range, a membership function between that particular data individual and its cluster centre is

�� � �xp��� ‖����‖�

By clustering temperature, hour, day and load change data, random FSCM parameters

These values selection may have strong effects on the complexity of the developed models. Table 1 shows the number of membership functions and the selected ROI values for each of

Functions ranges ROI Rules Membership Fctn. January 0.35 28 112 February 0.4 23 92 March 0.5 14 56 April 0.33 40 160 May 0.44 17 68 June 0.4 25 100 July 0.45 20 80 August 0.48 19 76 September 0.43 18 72 October 0.5 11 44 November 0.5 16 64 December 0.41 20 80

After clustering is made, the developed membership functions are trained. Then, when the developed network is being trained, a simple test will be carried to verify the prediction accuracy of the developed models. To increase the range of prediction in the developed models, the historical operation of three years set of data (2007, 2008 and 2009) is used. The three years data has been divided into three different groups. The first set of data is used to extract the clusters, which is taken as a 90% of the 2007 and 2008 historical data. The second set of data, which is used to train the developed fuzzy systems, has been taken as a whole set of 2007 and 2008 data. Finally, the third set of data, which is used to verify the success of the developed model, has been taken as the 2009 operation data. Fig. 5 shows the data

values e.g. Influence Range, Squash, Accept Ratio and Reject Ratio are applied.

������� � (6)

parameters details is found in (Chiu 1994).

the twelve month models.

Months\Membership

derived. Data affiliation to the cluster centres is derived as follow:

where x is the cluster centre and p� is the input set of data.

Table 1. ROI Values and Complexity of the 12 Month Models

utilization in developing the demand models in this work.

Fig. 5. Modelling data utilization for the ECU's Joondalup Campus energy consumption

After the rules which relate the input-output data have been developed, the developed clusters have been utilised in neuro-fuzzy networks to develop a zero-order Sugeno FIS, which will perform a 30 minutes ahead short-term prediction. In conventional fuzzy systems, trial and error is applied to tune the developed membership functions of the input-output universe of discourse of the fuzzy system. When ANN is used to tune the membership functions, an automated selection process based on the performance index is performed. The membership functions are trained to resemble the training data characteristics. In neuro-fuzzy networks, their networks structure is changed accordingly with the operation scenarios. Neuro-fuzzy networks however utilise the ability of learning of the neural networks to get the best tuning process with better performance and less time (Kandel 1993). Since the fuzzy systems have the property of universal approximation, it is expected that the equivalent neuro-fuzzy networks representation have the same property as well.

Adaptive Neuro Fuzzy Inference System (ANFIS) is another candidate to perform the fuzzy membership functions tuning. ANFIS structure was firstly proposed by (Jang 1993), where other models of ANFIS were proposed by (Chin-Teng Lin 1996) and (Wang and Mendel 1992). Fig. 6 illustrates the ANFIS structure with its learning mechanism.

Fig. 6. ANFIS structure with its learning mechanism

Fuzzy Inference System in Energy Demand Forecasting 367

Fig. 7. The developed input membership functions for the four inputs zero-order Sugeno fuzzy system of January's operation of the ECU's Joondalup Campus power network.

where f is the output of the net, x and y are the inputs to this net. The weights of layer 3 are represented by (w��, w��), and the weights of layer 4 are represented by (w��f�,w��f�), where the used rules of Sugeno ANFIS in this model are expressed in the following form:

> 1 1 11 1 1 *If x is A and y is B THEN f p x q y r* 2 2 22 2 2 *If x is A and y is B THEN f p x q y r*

Where ( , , *i ii p q r* ) are the parameters that are determined and referred to as the consequent parameters. More details about ANFIS parameters can be found in (Jang 1993).

In conventional neuro-fuzzy networks, back-propagation algorithm is used to adjust the network parameters, while in ANFIS the adjusting mechanism is performed by the Hybrid Learning Algorithm (HLA). HLA is basically combined of two identification methods, the least-squares method to identify consequent parameters for the forward pass in layer 4 and the back-propagation method for the backward pass to identify the premise parameters by the gradient descent in layer 2. This combination achieves faster convergence than that of the original back-propagation method. Table 2 illustrates the hybrid learning passes with their identified parameters:


Table 2. Two passes in the hybrid learning procedure for ANFIS (J. S. R. Jang 1997).

Finally, when verification result is within an acceptable error bound, the modelling procedure is concluded. Fig. 7 illustrates the developed input membership functions for the four inputs zero-order Sugeno fuzzy system of January's operation of the ECU's Joondalup Campus power network.

From Fig 7, and from the developed Sugeno-fuzzy system for January demand prediction, the developed rules are explained as following:

**If** *(Temperature is Temperature in Cluster n) and (Hour is Hour in Cluster n) and (Day is Day in Cluster n) and (Day-type is Day-type in Cluster n)* **Then** *(Demand is Demand in Cluster n)*

#### Where 0 <*n* ≤ number of developed rules.

Finally, for the other 11 months of the year, their developed models have different inputoutput ranges based on the pattern of operation and weather change throughout the four seasons of the year in city of Joondalup. Although other effective modelling parameters have been nominated for the proposed models, experimental investigations have been applied to use three-, four- and five-input modelling parameters for the demand prediction performance improvement, we stick to choosing the four-input modelling parameters, which has been successfully approved to be an optimal selection, from the prediction complexity and prediction improvement point of view, for the developing demand prediction models for the targeted power network.

where f is the output of the net, x and y are the inputs to this net. The weights of layer 3 are represented by (w��, w��), and the weights of layer 4 are represented by (w��f�,w��f�), where the

1 1 11 1 1 *If x is A and y is B THEN f p x q y r*

2 2 22 2 2 *If x is A and y is B THEN f p x q y r*

Where ( , , *i ii p q r* ) are the parameters that are determined and referred to as the consequent

In conventional neuro-fuzzy networks, back-propagation algorithm is used to adjust the network parameters, while in ANFIS the adjusting mechanism is performed by the Hybrid Learning Algorithm (HLA). HLA is basically combined of two identification methods, the least-squares method to identify consequent parameters for the forward pass in layer 4 and the back-propagation method for the backward pass to identify the premise parameters by the gradient descent in layer 2. This combination achieves faster convergence than that of the original back-propagation method. Table 2 illustrates the hybrid learning passes with

Parameters\Direction Forward pass Backward Pass Premise parameters Fixed Gradient descent

Finally, when verification result is within an acceptable error bound, the modelling procedure is concluded. Fig. 7 illustrates the developed input membership functions for the four inputs zero-order Sugeno fuzzy system of January's operation of the ECU's Joondalup

From Fig 7, and from the developed Sugeno-fuzzy system for January demand prediction,

**If** *(Temperature is Temperature in Cluster n) and (Hour is Hour in Cluster n) and (Day is Day in Cluster n) and (Day-type is Day-type in Cluster n)* **Then** *(Demand is Demand in Cluster n)*

Where 0 <*n* ≤ number of developed rules. Finally, for the other 11 months of the year, their developed models have different inputoutput ranges based on the pattern of operation and weather change throughout the four seasons of the year in city of Joondalup. Although other effective modelling parameters have been nominated for the proposed models, experimental investigations have been applied to use three-, four- and five-input modelling parameters for the demand prediction performance improvement, we stick to choosing the four-input modelling parameters, which has been successfully approved to be an optimal selection, from the prediction complexity and prediction improvement point of view, for the developing demand

Signals Node outputs Error signals

Consequent parameters Least-square estimator Fixed

Table 2. Two passes in the hybrid learning procedure for ANFIS (J. S. R. Jang 1997).

used rules of Sugeno ANFIS in this model are expressed in the following form:

parameters. More details about ANFIS parameters can be found in (Jang 1993).

their identified parameters:

Campus power network.

the developed rules are explained as following:

prediction models for the targeted power network.

Fig. 7. The developed input membership functions for the four inputs zero-order Sugeno fuzzy system of January's operation of the ECU's Joondalup Campus power network.

Fuzzy Inference System in Energy Demand Forecasting 369

have the same membership functions shape, but with different input/output ranges. Fig. 9 shows the proposed membership function design for the tuning fuzzy system of the January

Fig. 9. Membership functions design for the tuning fuzzy system of January demand

Table 4 illustrates the membership function design for the twelve monthly prediction fuzzy

January [-10 30] [0 24] [-75 75] February [-10 35] [0 24 ] [-75 75] March [-10 20] [0 24] [-50 50] April [15 35] [0 24] [-30 30] May [0 20] [0 24] [-40 40] June [0 25] [0 24] [-50 50] July [-20 20] [0 24] [-50 50] August [5 20] [0 24] [-30 30] September [-20 20] [-4 24] [-30 30] October [30 70] [0 18] [-200 200] November [10 50] [-4 18] [-100 100] December [-10 20] [-4 18] [-100 100]

Months\Membership Functions ranges Temperature Hour Output

Table 4. Membership function design ranges for the 12 monthly demand prediction tuning

prediction.

prediction model

systems.

fuzzy systems

#### **5.2 The self-tuning fuzzy system**

In this subsection, we aim at discussing two tuning mechanisms which have the ability to improve the prediction accuracy and adapt the prediction to the external effects such as the real-time demand change:
