**5.2.1 Parallel self tuning fuzzy system**

First, we will look at improving our prediction results, based on our knowledge of the energy demand conditions, which could have been partially missed in the given historical operation data. We aim at using the self tuner fuzzy system to improve the prediction accuracy. Fig. 8 illustrates a main fuzzy system with its tuner fuzzy system combination.

Fig. 8. Self-Tuning fuzzy system (self tuning fuzzy system)

For this system, it is required to enhance the performance of the prediction model by using the knowledge of the system performance, safe operation estimations and actual important needed decisions. In this work, two of the model inputs are selected to develop the fuzzy rule-based system. The rule-based system is developed to have a smooth transition between the specified operation cases in the decision making. In this work generally, we investigate the use of a one rule based system the twelve-month models. Table 3 illustrates the propose rule based system in this investigation.


Table 3. Self tuning fuzzy rule-based system

To cope with the operation pattern changes through the twelve months of the year, different membership functions are proposed for every month models: all twelve-month models

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

First, we will look at improving our prediction results, based on our knowledge of the energy demand conditions, which could have been partially missed in the given historical operation data. We aim at using the self tuner fuzzy system to improve the prediction accuracy. Fig. 8 illustrates a main fuzzy system with its tuner fuzzy system combination.

For this system, it is required to enhance the performance of the prediction model by using the knowledge of the system performance, safe operation estimations and actual important needed decisions. In this work, two of the model inputs are selected to develop the fuzzy rule-based system. The rule-based system is developed to have a smooth transition between the specified operation cases in the decision making. In this work generally, we investigate the use of a one rule based system the twelve-month models. Table 3 illustrates the propose

Hour\Temperature V. Cold Cold L. Warm Room temp. Warm Hot V. hot Midnight S. low Normal Normal S. High High V. High V. High Dawn Normal S. High High V. High V. High Vv High Vv High Morning Low S. Low Normal Normal S. High High V. High Afternoon V. Low V. Low Low Low S. Low Normal Normal Sunset V. Low Low S. Low Normal S. High High V. High Evening Low S. Low S. Low Normal S. High High V. High Night S. Low Normal S. High High V. High V. High Vv. High

To cope with the operation pattern changes through the twelve months of the year, different membership functions are proposed for every month models: all twelve-month models

**5.2 The self-tuning fuzzy system** 

**5.2.1 Parallel self tuning fuzzy system** 

Fig. 8. Self-Tuning fuzzy system (self tuning fuzzy system)

rule based system in this investigation.

Table 3. Self tuning fuzzy rule-based system

real-time demand change:

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 prediction.

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

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


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

Fuzzy Inference System in Energy Demand Forecasting 371

Month\model ANFIS ISE Self-tuning fuzzy-ANFIS ISE Improvement January 29030 27230 6.2% February 23590 22080 6.4% March 42060 41040 2.5% April 45300 45160 0.3% May 27880 27760 0.4% June 21660 21390 1.2% July 19100 18760 1.7% August 25030 24930 0.3% September 24160 23760 1.6% October 29260 28920 1.1% November 27050 25060 7.3% December 32890 30490 7.2%

Table 5. The amount of ISE in each month with improvement rate made by fuzzy tuning

The Feedback Self-Tuning System FSTF is applied when any external effect variables such as the real load measures are fed to the model to adapt its prediction accuracy. With its adaptation mechanism, it adapts the model prediction to the external effects. The adaptation is developed based on an expert knowledge based system, which achieves successful and safe adaptation when the external effects are applied. The main principle of using this mechanism in our case study is to consider the actual instant demand change pattern change in the next subsequent prediction intervals, which provides flexibility to the model to correct its prediction path. The mechanism is built based on a feedback signal supply to allow the real demand change to enhance the prediction

Just like the parallel self-tuning fuzzy system, the adaptation may apply on the main fuzzy parameters e.g. membership function parameters, input-output universe of discourse or the output scale. For simplicity, we aim at utilising the output scale example in this chapter.

For the twelve different load change patterns in the targeted electric network, twelve different adaptation designs are required. For simplicity, one rule base system could be implemented to cope with twelve-month load change pattern. It is required therefore to tune the FSTFS input-output universe of discourse to fit its output with the load change patterns in every individual month. Out of this adaptation mechanism, different adaptation

Fig.11 illustrates the adaptation mechanism for the Feedback Self-Tuning System.

systems

output.

**5.2.2 Feedback Self-Tuning Fuzzy System** 

The twelve-month models have different self-tuning fuzzy designs. From the twelve designs, different prediction improvements are carried out. Conservatively, we would like to spot on the weakest prediction region throughout January in Fig. 10, which shows the demand prediction for the 17th to the 21st of January 2009 using ANFIS and Self-Tuning Fuzzy System. The amount of prediction improvement is calculated by evaluating the Integral Square of Error (ISE). ISE is evaluated as follow:

$$ISE = \frac{1}{n} \sum\_{t=1}^{n} (\mathfrak{y}\_t - \widehat{\mathfrak{y}}\_t)^2$$

where � is the number of entries, � is the time at each entry, �� is the actual demand and ��� is the predicted value. From the equation above, the results show that the self-tuning fuzzy system has an enhanced prediction accuracy error. Table 5 shows the amount of ISE in each month and the percentage of improvement achieved by the fuzzy tuning systems.

Fig. 10. Self tuning and ANFIS prediction for the 17th to the 21st of January 2009

The twelve-month models have different self-tuning fuzzy designs. From the twelve designs, different prediction improvements are carried out. Conservatively, we would like to spot on the weakest prediction region throughout January in Fig. 10, which shows the demand prediction for the 17th to the 21st of January 2009 using ANFIS and Self-Tuning Fuzzy System. The amount of prediction improvement is calculated by evaluating the

�

��� where � is the number of entries, � is the time at each entry, �� is the actual demand and ��� is the predicted value. From the equation above, the results show that the self-tuning fuzzy system has an enhanced prediction accuracy error. Table 5 shows the amount of ISE in each month and the percentage of improvement achieved by the fuzzy tuning

����� � �� �� �

��� � 1

Fig. 10. Self tuning and ANFIS prediction for the 17th to the 21st of January 2009

Integral Square of Error (ISE). ISE is evaluated as follow:

systems.


Table 5. The amount of ISE in each month with improvement rate made by fuzzy tuning systems

### **5.2.2 Feedback Self-Tuning Fuzzy System**

The Feedback Self-Tuning System FSTF is applied when any external effect variables such as the real load measures are fed to the model to adapt its prediction accuracy. With its adaptation mechanism, it adapts the model prediction to the external effects. The adaptation is developed based on an expert knowledge based system, which achieves successful and safe adaptation when the external effects are applied. The main principle of using this mechanism in our case study is to consider the actual instant demand change pattern change in the next subsequent prediction intervals, which provides flexibility to the model to correct its prediction path. The mechanism is built based on a feedback signal supply to allow the real demand change to enhance the prediction output.

Just like the parallel self-tuning fuzzy system, the adaptation may apply on the main fuzzy parameters e.g. membership function parameters, input-output universe of discourse or the output scale. For simplicity, we aim at utilising the output scale example in this chapter. Fig.11 illustrates the adaptation mechanism for the Feedback Self-Tuning System.

For the twelve different load change patterns in the targeted electric network, twelve different adaptation designs are required. For simplicity, one rule base system could be implemented to cope with twelve-month load change pattern. It is required therefore to tune the FSTFS input-output universe of discourse to fit its output with the load change patterns in every individual month. Out of this adaptation mechanism, different adaptation

Fuzzy Inference System in Energy Demand Forecasting 373

To show the adaptation performance of the investigated systems, a conservative result is shown in Fig. 13, which illustrates the weakest prediction accuracy region throughout the

Fig. 12. FSTFS membership function design for the proposed demand prediction model

year for the investigated electric power network.

ranges may come from the twelve-month models. Table 6 illustrates the used rule based system for the proposed FSTFS.

Fig. 11. Feedback Self-Tuning Fuzzy System


Table 6. FSTFS Rule Based System

Fig. 12 illustrates the FSTFS membership function design for the proposed demand prediction model.

The feedback prediction mechanism can be safely utilised in generation scheduling application or any other energy management system applications. For a safe use of prediction output, a safety margin value is added to the prediction results, which allows a flexible utilisation for the predicted demand.

ranges may come from the twelve-month models. Table 6 illustrates the used rule based

Error Degree of Change

Vvery Low Vvery High Very Low Very High Low High Zero Normal High Low Very High Very Low Vvery High Vvery Low

Fig. 12 illustrates the FSTFS membership function design for the proposed demand

The feedback prediction mechanism can be safely utilised in generation scheduling application or any other energy management system applications. For a safe use of prediction output, a safety margin value is added to the prediction results, which allows a

system for the proposed FSTFS.

Fig. 11. Feedback Self-Tuning Fuzzy System

Table 6. FSTFS Rule Based System

flexible utilisation for the predicted demand.

prediction model.

To show the adaptation performance of the investigated systems, a conservative result is shown in Fig. 13, which illustrates the weakest prediction accuracy region throughout the year for the investigated electric power network.

Fig. 12. FSTFS membership function design for the proposed demand prediction model

Fuzzy Inference System in Energy Demand Forecasting 375

second fuzzy tuning mechanism, a real-time demand change has been added to the main fuzzy models to adapt their prediction to the real-time demand change through tuner fuzzy systems. From the twelve different demand changes throughout the year, different prediction adaptation ranges have been found. As a conclusion for these discussions, the FIS has a wide range of applications in modelling, especially when we deal with highly nonlinear multiple input-output systems we have also shown throughout this chapter that several simulation studies have proved the success of using FIS in modelling, which

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**7. References** 

Fig. 13. Actual and Feedback Self-Tuning System Demand Prediction in the ECU Power Network for the 17th to the 21st of January 2009

#### **6. Summary**

In this chapter, the art of using FIS in modelling energy demand prediction for a specific electric network has been discussed. The type and the size of the modelled electric network has been comprehensively analysed in terms of the input-output identified effective parameters and their correlation in changing the pattern of the energy use. The identified parameters, however, were used in developing the energy demand prediction models. Fuzzy modelling process has been discussed by looking at its applications and limitations for the selected case study. In our modelling, we have utilised Fuzzy Subtractive Clustering Method to show the tips about its use in modelling, where ANFIS has been applied to develop the zero-order Sugeno fuzzy models. The annual energy demand model for the selected case study has been developed for an individual monthly basis with a specific design applied to deal with the twelve-month patterns. However, certain modifications had to be applied on each month to account for the peculiar conditions to that month.

In addition, two fuzzy tuning mechanisms have been used to improve the fuzzy models prediction accuracy. The first mechanism was used to add the safe operation assumptions to reduce the missing knowledge in the decision making for the developed models. The results from the first mechanism showed that the added fuzzy systems improved the prediction accuracy with different rates throughout the twelve months of the year. In case of the second fuzzy tuning mechanism, a real-time demand change has been added to the main fuzzy models to adapt their prediction to the real-time demand change through tuner fuzzy systems. From the twelve different demand changes throughout the year, different prediction adaptation ranges have been found. As a conclusion for these discussions, the FIS has a wide range of applications in modelling, especially when we deal with highly nonlinear multiple input-output systems we have also shown throughout this chapter that several simulation studies have proved the success of using FIS in modelling, which brightens wider its range of mathematical and engineering applications.

#### **7. References**

374 Fuzzy Inference System – Theory and Applications

Fig. 13. Actual and Feedback Self-Tuning System Demand Prediction in the ECU Power

In this chapter, the art of using FIS in modelling energy demand prediction for a specific electric network has been discussed. The type and the size of the modelled electric network has been comprehensively analysed in terms of the input-output identified effective parameters and their correlation in changing the pattern of the energy use. The identified parameters, however, were used in developing the energy demand prediction models. Fuzzy modelling process has been discussed by looking at its applications and limitations for the selected case study. In our modelling, we have utilised Fuzzy Subtractive Clustering Method to show the tips about its use in modelling, where ANFIS has been applied to develop the zero-order Sugeno fuzzy models. The annual energy demand model for the selected case study has been developed for an individual monthly basis with a specific design applied to deal with the twelve-month patterns. However, certain modifications had

to be applied on each month to account for the peculiar conditions to that month.

In addition, two fuzzy tuning mechanisms have been used to improve the fuzzy models prediction accuracy. The first mechanism was used to add the safe operation assumptions to reduce the missing knowledge in the decision making for the developed models. The results from the first mechanism showed that the added fuzzy systems improved the prediction accuracy with different rates throughout the twelve months of the year. In case of the

Network for the 17th to the 21st of January 2009

**6. Summary** 


**Application to System Modeling and** 

**Control Problems** 

Yager, R. R. and D. P. Filev (1994). "Approximate clustering via the mountain method." *Systems, Man and Cybernetics, IEEE Transactions on* 24(8): 1279-1284. **Section 6** 
