Saumil Navalbhai Patel B.E., Gujarat University, India, 2007 PROJECT. Submitted in partial satisfaction of the requirements for the degree of

POWER LOAD BALANCING USING FUZZY LOGIC Saumil Navalbhai Patel B.E., Gujarat University, India, 2007 PROJECT Submitted in partial satisfaction of the requirements for the degree of MASTER OF SCIENCE in ELECTRICAL AND ELECTRONIC ENGINEERING at CALIFORNIA STATE UNIVERSITY, SACRAMENTO SUMMER 2010

POWER LOAD BALANCING USING FUZZY LOGIC A Project by Saumil Navalbhai Patel Approved by:, Committee Chair John C. Balachandra, Ph.D., Second Reader Fethi Belkhouche, Ph.D. Date ii

Student: Saumil Navalbhai Patel I certify that this student has met the requirements for format contained in the University format manual, and that this project is suitable for shelving in the Library and credit is to be awarded for the project., Graduate Coordinator Preetham Kumar, Ph.D. Date Department of Electrical and Electronic Engineering iii

Abstract of POWER LOAD BALANCING USING FUZZY LOGIC by Saumil Navalbhai Patel Overloading is a major problem as there is no any system to ensure the consumer power usage. For example, weather conditions can change the consumer usage and extreme weather conditions can cause overloading. So when there is no way to determine consumer usage, the one alternative is load balancing. Load balancing is very important feature that keeps the system safe from overloading. When one area is overloaded, the loads can be transferred to the less loaded areas using switches. And load balancing provides how much load has to be transferred to maintain system within limits. The other way is to control using automatic generation control (AGC). Load balancing is implemented at the substation side at the power distribution level, while AGC is implemented at power station side at power generation level. Because implementation of AGC is very costly, load balancing provides good alternative. In this project, the design and implementation of Power Load Balancing will be done using Fuzzy logic toolbox of MATLAB. Fuzzy logic provides easy way using graphical user interface to implement fuzzy system. A set of rules can determine the fuzzy system. iv

My focus in this project is on understanding the background of power system and importance of load balancing in power system. The designing part will give the hands-on experience on MATLAB fuzzy logic toolbox., Committee Chair John C. Balachandra, Ph.D. Date v

DEDICATION I would like to dedicate this work to my wife, Dhara, without whose caring support it would not have been possible. I would like to dedicate my Master of Science degree to my Mom and Dad, for their unending support and love throughout my life. vi

ACKNOWLEDGEMENTS Here, I take the opportunity to thank all the people who have been involved in successful completion of this project. With sincere respect, I would like to thank my project advisor Dr. John C. Balachandra for his valuable time, efforts, help and moral support. His continuous support and guidance led this project to a successful completion. I would like to thank Dr. Fethi Belkhouche for being my second reader and spending his valuable time for reviewing this report and giving feedback. I would like to thank Dr. Preetham Kumar for his time to check the format of the report. Finally, I would like to thank my family and friends for their continuous support and encouragement. vii

TABLE OF CONTENTS Page Dedication... vi Acknowledgements... vii List of Tables... x List of Figures... xi Chapter 1. INTRODUCION... 1 1.1 Background... 1 1.2 Purpose of Project... 2 1.3 Overview of the Document... 2 2. TOOL USED FOR LOAD BALANCING... 3 2.1 Fuzzy Logic Toolbox... 3 3. BACKGROUND OF POWER SYSTEM AND LOAD BALANCING... 8 3.1 Power Generation...8 3.2 Power Transmission... 9 3.3 Electrical Distribution... 10 3.4 Load Profile... 11 3.5 Automatic Generation Control (AGC)... 11 viii

3.6 Line Loss... 12 3.7 Load Balancing... 13 3.7.1 Introduction of Power Load Balancing... 13 3.7.2 Load Balancing Using Geometric Technique... 14 4. LOAD BALANCING USING FUZZY LOGIC...17 4.1 Introduction of Fuzzy Logic... 17 4.1.1 Set Theory... 18 4.1.2 Fuzzy System Design... 22 4.1.3 Pros and Cons... 24 4.1.4 Applications... 24 4.2 Implementation of Load Balancing Using Fuzzy Logic... 25 4.2.1 Load Balancing... 26 5. SIMULATION RESULTS... 37 5.1 Results... 37 5.2 Error Correction... 42 6. CONCLUSION AND FUTURE EXPANSION... 46 6.1 Conclusion... 46 6.2 Future Expansion... 47 Appendix A Source Code for Load Balancing... 48 Bibliography... 51 ix

LIST OF TABLES Page 1. Table 4.1 Meaning of Typical Linguistic Terms in Fuzzy Logic... 18 2. Table 4.2 Ranges for Input Load Variable... 30 3. Table 4.3 Ranges for Output Change Variable... 31 4. Table 4.4 Rules Used to Design Load Balancing Fuzzy System... 34 x

LIST OF FIGURES Page 1. Figure 2.1 Creating Basic Fuzzy Logic System Step 1...4 2. Figure 2.2 Creating Basic Fuzzy Logic System Step 2...5 3. Figure 2.3 Creating Basic Fuzzy Logic System Step 3...6 4. Figure 2.4 Creating Basic Fuzzy Logic System Step 4...7 5. Figure 3.1 Loop Associated with Tie-Line... 14 6. Figure 4.1 Set Theory Representation... 20 7. Figure 4.2 Basic Fuzzy Logic Controller (FLC)... 22 8. Figure 4.3 Feeder Distribution... 26 9. Figure 4.4 Load Balancing Algorithm... 27 10. Figure 4.5 Initialization of Load Balancing System... 29 11. Figure 4.6 Specifying the Input Variable as Load (kw)... 32 12. Figure 4.7 Specifying the Output Variable as Change (kw)... 33 13. Figure 4.8 Rule Editor from Fuzzy Logic Toolbox... 35 14. Figure 5.1 Result 1... 38 15. Figure 5.2 Result 2... 40 16. Figure 5.3 Result 3... 41 xi

1 Chapter 1 INTRODUCTION 1.1 Background The steps for the power system are generation of power, transmission of power and distribution of power. Once power transmission to the subsystem is done, the next thing is to distribute the power among all the consumers. The faulty distribution can lead some areas overloaded and some areas with less loaded. So to avoid these conditions, controlling of power and hence controlling of load is required in those areas. It leads to the load balancing technique. Load balancing is the process to prevent the system from overloading situation. This project explains the details of load balancing and steps for how to design and implement a load balancing in power distribution. Consumption of the power at consumer side is highly unpredictable. Consumption varies at each time of the day and each day of a year. Now as we know that it is hard to save large amount of electricity using buffers, to avoid such problems, power controlling is desirable. Automatic generation control (AGC) is the one way to control power. It is implemented at the power station side and it controls the generation of power as requirement or load changes. If the power usage is very small, it is costly to implement such a system. So load balancing is the easy way to control power. Load balancing is implemented at the power distribution side. The basic action the system will take during overloading situation is to balance the load from over loaded area to the less loaded areas. The transfer is done through open/closed switches. In this

2 project, I have designed the load balancing system for three phase assuming that the total load remains same. Load balancing can be designed by many ways, but here I have designed and explained load balancing using fuzzy logic toolbox. Fuzzy logic has advantages of simple to understand and cheaper to implement. 1.2 Purpose of Project Main purposes of this project are to understand the concept of load balancing, need of it in real world and design and development of it using fuzzy logic tool of MATLAB. This project also gives good understanding of overall power system like power generation, transmission, distribution of power, automatic generation control and load profile. MATLAB covers very wide range of toolboxes, but this project gives better understanding and hands-on experience of fuzzy logic toolbox. 1.3 Overview of the Document As basic introduction of the project is explained, next chapter is about introducing of software tool used. In this project I have used fuzzy logic toolbox. It is the inbuilt tool from MATLAB. Chapter 3 explains about basic power system and load balancing. It includes power generation, power transmission, distribution, load profiles and automatic generation control. It also explains the basics of load balancing and geometric approach for balancing the load. Chapter 4 explains the fuzzy logic in details and load balancing using fuzzy logic. Simulation results are included in chapter 5 with error correction for the fuzzy logic technique. Chapter 6 provides the conclusion of this project and it is followed by the appendix.

3 Chapter 2 TOOL USED FOR LOAD BALANCING In this project, I have used fuzzy logic toolbox provided by MATLAB. MATLAB is an abbreviation of matrix laboratory. It was developed in late 1970s by the MathWorks Incorporation and provided to users. MATLAB covers different areas of real time implementation like matrix manipulation, data algorithms, user interfaces with languages like C and C++, data analysis and graphical implementations. MATLAB provides separate tools for applications. For example, it provides toolboxes for signal processing, fuzzy logic, neural networks and many other real time applications. In this project, I am using fuzzy logic for load balancing. So how to build a simple fuzzy logic system and how to simulate it, is explained in details below. [1] 2.1 Fuzzy Logic Toolbox MATLAB provides inbuilt fuzzy logic toolbox that provides Graphical User Interface (GUI) based implementation of fuzzy systems. In this project, this inbuilt function of MATLAB is used for load balancing. The example below shows the process steps for building a simple model using fuzzy logic. It is based on our visit to a restaurant. In this example, the tip is determined depending upon service and food quality from the restaurant. So service and food are two input variables and tip is the output variable.

4 To start fuzzy logic in MATLAB, open the MATLAB and type fuzzy in the command window. The FIS editor browser will be opened. Figure 2.1 Creating Basic Fuzzy Logic System Step 1 Now as you can see that by default there is one input and one output but you can add two or more inputs as well outputs in the system. To add input/output, click on edit and then add variable input/output.

5 Now as you can see in above figure 2.1, the default name of the input is input1. So we will have to give an appropriate name by typing in that window. Let us say our inputs are Service and Food, and output is tip. Now the system is untitled. So we have to save the file to determine fuzzy logic system. So, to save a file, go to File menu, click on Export to file and give appropriate name. Now next step is to define membership functions. To define membership functions of any input/output, double click on that particular input/output. As shown in below figure, the membership function editor is used to provide parameters, range and type. Figure 2.2 Creating Basic Fuzzy Logic System Step 2

6 Now after editing all membership function, the next step is to define rules for the system. Rules can be defined by double clicking on the fuzzy logic medium that is tipper in this case. It will open the rule editor window. Rules for any fuzzy logic can be set using this rule editor. Consider rules for the tip in this example are, 1. If service is bad and food is bad, tip is cheap. 2. If service is bad and food is good, tip is average 3. If service is good and food is bad, tip is average 4. if service is good and food is good, tip is generous It is shown below, Figure 2.3 Creating Basic Fuzzy Logic System Step 3

7 Now the fuzzy logic is ready to simulate. So go to view menu and click on rules will open a rule viewer window. Here, as per rules defined the tip amount changes. We can also apply own input variables and check the output value. Figure 2.4 Creating Basic Fuzzy Logic System Step 4 The above steps describe the implementation of a fuzzy system using fuzzy logic toolbox in MATLAB.

8 Chapter 3 BACKGROUND OF POWER SYSTEM AND LOAD BALANCING In this chapter, the basics of power system like power generation at power station, power transmission to the subsystem and power distribution to the user are discussed. The other alternative of load balancing that is automatic generation control is also discussed. The basic steps of power system are as below, 3.1 Power Generation None of us can ever imagine a world without electricity. The very first step is the generation of power. Companies generally use load curve to measure the approximate amount of power that has to be generated at a given time. This provides only an approximate value and to make it precise automatic generation control or load balancing is implemented for power control. But these curves give good information for selection of generator units. Power is generated at power stations with the generators running by heat, nuclear, gas, water flow, wind or other natural source of energy. Generators convert one form of energy into electrical energy that is transmitted over the lines. Most of the commercial power is generated from electromagnetic induction that uses mechanical energy to produce electrical energy. However, power generated from natural resources is much cheaper and eco friendly than the conventional sources. It includes water flow, wind energy, solar energy or biomass. That is the reason many countries are now implementing more and more power plants using natural resources. Very less power requirements like a small building or a small area is provided with a small electricity

9 generator that uses reciprocating engines. The resources generally include diesel or gas in reciprocating engines. Once power is generated, the next step is to transmit it over the lines. [2] 3.2 Power Transmission Power transmission and power distribution are two totally different scenarios. Power transmission deals with the bulk transfer of electricity from power plants to the power substations located near consumer s place. And power distribution deals with the affective distribution of the power within all consumers to avoid overloading or less loading conditions. Transmission lines are generally called grid lines, uses three phase AC power signals. However DC signals are also be used and transmitted for a small distance. Most of the losses are occurred during transmission. So to reduce the losses, power is transmitted at a very high voltage range. Overloading of the power at the destination area can cause the entire transmission interrupted. [3] Transmission can be done by overhead lines or underground lines. Overhead transmission is done through an aluminum conductor above the ground level. As overhead transmission is not insulated, it requires extra cautions for safety and also it has higher power loss in extreme weather conditions. Underground transmission is easier for highly populated urban areas. Also power transmission is not affected due to weather conditions. But complexity for installation and repair are the main disadvantages of underground transmission. [3]

10 3.3 Electrical Distribution Once power is generated at the power station, and reaches to the substations, the next thing comes is the proper distribution network to different areas. The effective distribution uses load profile technique. Depending upon the load profile values, the transformers and power carrying conductors are designed. Many countries uses single phase 220-230 V, and few regions also use split phase. Split phase provides both 120 V and 240 V power. Small transformers are used to downgrade the voltage to 120V for household use and 240V is used for heavy appliances in industry. Generally many countries use only two frequencies of 50 Hz and 60 Hz with the accuracy of less than 0.1 Hz. Size of the transformer is decided from the frequency being used. For example smaller transformer is needed for 60 Hz frequency. 120 V is generally associated with 60 Hz frequency and 240 V is associated with 50 Hz. [4] There are two types of distribution networks: radial and interconnected. Radial: No normal connection is required for radial network for the transmission from the generator to the user. It is generally implemented in isolated areas where it is hard to transfer electricity. [4] Interconnected: One distribution network is connected to multiple other networks at a given point that leads to a complex distribution network. It is generally implemented in urban areas to provide proper power distribution. The advantage of interconnected network is, if fault is found it can be repaired without disturbing the area power supply. [4]

11 3.4 Load Profile Load profile is a graphical representation of the electrical usage versus time. It gives the approximate load usage for a given area. Direct meter can be used to determine load profile, however easy way is to use customer billing for the usage. For example evaluating all energy bills from a given area determines the load usage and put it as a graphical representation gives load balancing that will be used as reference for the power generation. [5] 3.5 Automatic Generation Control (AGC) In urban areas where load varies all the time through out a year, it is desired to implement such system that is capable of handling such big variations in load. Automatic generation control (AGC) provides the solution. When the load is drastically changing, the reactive and real power at the generation side must change accordingly. Also it is necessary to maintain tie-line power within limits. Automatic generation control provides controlling of power with maintaining tie-line power. The technique of controlling the power at the generation side is known as automatic generation control. AGC regulates the power output of generators to meet the system requirements for power load variations. AGC can be implemented using industrial controllers like PI controller, PID controller or fuzzy controller. Implementing if AGC is very costly as it requires the controlling of generator and turbine. So it is generally preferred to implement AGC in large power stations that provide electricity to many urban areas. And small power stations uses load balancing for power controlling. [6]

12 Objectives of AGC: 1. Each area must be capable of controlling its own load demands. [6] 2. Tie-line flows should remain in limits. [6] 3. System frequency swings must be within limits for better controlling. [6] 4. If one area is unexpectedly overloaded, the nearby areas must provide power. [6] 3.6 Line Loss Loss reduction is the main concern in power generation and transmission. After many observations, it has been concluded that during transmission of the power, large portion of the generated power goes as losses. So to reduce the power cost, losses should be minimized. Losses generally depend upon the length of transmission as losses are high during long transmission of electricity. Transmission line conductors also play an important role determining the losses. The conductors can carry power only it is capable of, and rest power is lost during transmission to ensure that system is not overloaded. Hence, power distribution with proper conductor cables is very critical in determining the system protection. [7] Line loss is the final step after all the load flow analysis is done. As described above, it could be due to conductor inertia or due to faulty tap ratio of the transformer or due to long transmission lines without substations at regular intervals. It is calculated from the active and reactive powers of the transmission network. Capacitive components can be added to reduce reactive part and thus to reduce losses. [7]

13 3.7 Load Balancing In general, balancing is the process to maintain the outputs in certain limits and load balancing is to maintain the system load in specific limits or as per the system requirements. Load balancing is used in many fields like power, computer, internet and telecommunication. The topics below provide an in depth analysis of power load balancing in electrical field. 3.7.1 Introduction of Power Load Balancing The load or power consumption is always varying everyday of a year and every time of a day. So it is necessary to handle the varying loads to ensure that system is not overloaded or less loaded. In urban areas, where the load demand is very high and load changes are very drastic, power plants generally use automatic generation control (AGC) as explained above. AGC controls the generation of the power at the power station side, depending upon the load variation in particular area. So consider if load consumption in one area is 100 loads and due to weather or any other reason it goes to 200 loads, the area is using double loads than the regular usage. So AGC controls the generation of the power and provides the necessary power for that area. But AGC implementation is generally very costly. So for rural areas or the areas with small power plants, load balancing is used rather than AGC. Load balancing provides substations to meet extra load demands. [8] Load balancing of power is done by open/close tie-switches in the distribution feeders. Overloading of network is maintained by transferring load from heavily loaded feeders to the less loaded feeders. Reconfiguring system is one of the main techniques for

14 load balancing. It allows smoothening the load demands by distribution, reduced feeder losses and increased network reliability. [8] 3.7.2 Load Balancing Using Geometric Technique One approach for load balancing is to use of geometric technique. Network reconfiguration provides the switching options for specific loads. It is used to relieve overload situation in a 3-phase system. Now let us consider each loop in a network is represented as circle. If the load is perfectly balanced then all circles touches at (0, 0) coordinate. The largest circle gives the maximum improvement of balanced load. To identify that circle, it is compared with the zero load balanced change circles. Here the circles in which no load balancing is required are called zero load balanced change circles. Now the next step is to execute tie-line switching in that loop so that maximum load balancing can be achieved. As I described, the largest circle does require load balancing to prevent overloading, thus reducing the size of the circle determines the improvisation in load balancing. [8] Common node (0) l-2 l-1 l h h-1 (m) (k) (t) P m P k-1 P k P h Lower voltage side Higher voltage side Figure 3.1 Loop Associated with Tie-Line

15 The above figure 3.1 is taken from [8]. Considering figure 3.1, there are two sides of loop as shown above. The lower voltage side is represented by l and higher voltage side represented by h. Here the change in load balancing formula calculations below starting from equation 3.1 to equation 3.7 are taken from [8], [P m A/C] 2 + [Q m B/C] 2 = [A/C] 2 + [B/C] 2 - ΔLB S tm/c (3.1) Where, A = Σ K l P l - Σ K h P h (3.2) B = Σ K l Q l - Σ K h Q h (3.3) C = K loop (3.4) ΔLB S tm = change in load balancing P m and Q m = real and reactive power flows K loop = sum of K value from each branch From equation 3.1, Center of the circle = (A/C, B/C) (3.5) And, Radius = [(A 2 + B 2 )/ C 2 - ΔLB S tm / C] 1/2 (3.6) Now as discussed above, in zero load balancing change ΔLB S tm = 0. So from equation 3.1, [P m A/C] 2 + [Q m B/C] 2 = [A/C] 2 + [B/C] 2 (3.7) Load balancing depends on the values of ΔLB S tm, that is if it is positive means load balancing is improved from the last value and negative represents that load balancing is more worse than last value. [8]

16 Here the technique is first to identify the maximum loop and then to identify the switching options for maximum balancing. So from equation 3.6 and ΔLB S tm, we can determine the maximum load balancing loop. Now next step is to determine the switching options. The switching can be tie switching that is normally closed and sectionalizing switching that is normally opened switches. As shown in figure 3.1, the load transfers from low voltage side to the high voltage side in the loop. That load transfer is done by switching operation. The main disadvantage of this technique for load balancing is it is a two stage searching approach as described above. So it provides slow results compare to fuzzy logic that is described in next chapter.

17 Chapter 4 LOAD BALANCING USING FUZZY LOGIC As we discussed in previous chapter, load balancing refers to the release of power or maintaining of power as per consumer demand. In this project, I have used fuzzy logic technique to determine load balancing. In this chapter, I will discuss basics of fuzzy logic, how fuzzy logic is used for load balancing and steps to design and implement of load balancing. 4.1 Introduction of Fuzzy Logic Fuzzy control was introduced in 1970s and it is classified as intelligent controller. Fuzzy logic is derived from fuzzy set theory to deal with reasoning that is approximate rather than precise. But in many scenarios, rough practical answer comes out as more effective than complex precision. It was developed for control operations to develop knowledge based systems and allows values to be defined like true/false and yes/no. It is simple to implement and hence it is becoming more favorite for knowledge based system implementations. It can be used where the traditional controllers like PI or PID controllers in use. These controllers use linear control action while fuzzy logic provides controlling action with fuzzy set and rules. Conventional controllers depend on mathematical modeling while fuzzy controller depends on information provided by membership functions from domain experts. There are many software available in market that is capable of designing such systems, but in this project, I have used MATLAB fuzzy logic toolbox. [9]

18 In fuzzy logic, some of the typical linguistic terms used are shown in table below, Linguistic term Meaning PL PM PS ZE NS NM NL Positive large Positive medium Positive small Zero Negative small Negative medium Negative large Table 4.1 Meaning of Typical Linguistic Terms in Fuzzy Logic The above table data is taken from [9]. The above linguistic variables are just a representation of the knowledge. And fuzzy set theory is used to manipulate those variables. 4.1.1 Set Theory To describe fuzzy set theory, let us consider U as a collection of objects that is universe of discourse and F is the fuzzy set. So the fuzzy set is defined as the set F in a U and characterized by μ F. It takes values within [0, 1] interval. [9][10] So, fuzzy sets can be defined depending on if universe of discourse is discrete or continuous. And two methods are used to define fuzzy sets.

19 The fuzzy set F for discrete U is, F = µf(x 1 )/x 1 + µf(x 2 )/x 2 +..+ µf(x n )/x n (4.1) F = (4.2) And fuzzy set F for continuous U is, F = µf(x)/x (4.3) Above equations 4.1, 4.2 and 4.3 are taken from [9]. There are two methods to define fuzzy set are numerical definition and functional definition explained below, Numerical definition: In this method, membership function is represented as a vector of numerical numbers. So the fuzzy set consists of range of numerical values for each input and the output is determined for those set of values only. [10] Functional definition: In this method, membership function is represented in a functional form. The functions can be bell shaped, triangular shaped, trapezoidal shaped, sigmoid shaped, sinusoidal shaped etc. It is easy to define membership function using this method than numerical method because the functions can be readily adapted to a change in normalization of universe. [10] Fuzzy set can be represented by Complement, Union, Intersection, Cartesian product and Sup-star composition.

20 There are some differences in classical set theory and fuzzy set theory. Consider an example below, Figure 4.1 Set Theory Representation The basic idea about above figure 4.1 is taken from [9]. Consider a classical set theory shown on left side in above figure 4.1. There is a sharp transaction from low to high at point 30. So the height 30 or above 30 would be considered as tall and height anything below 30 would be considered as short. Now in classical set theory, when range is defined as per above figure 4.1, the output value is defined by any one input value only. For example, what would be the answer if height is 29.99 in this case? In classical set theory, the system will consider it as a short, because the height tall is considered only for 30 or more. So the output is defined either by short or by tall inputs at a given time.

21 That is the main difference between classical set representation and fuzzy set representation. Now consider a fuzzy set theory representation on right side of above figure 4.1. Fuzzy set theory is defined by membership functions and the output does not depend on just one input but it is defined as a part of both the inputs in this case. A set of membership functions and rules define the output. Now as we can see in above figure, there is a slope starting from point 20 to point 30. Here height 30 and above is considered as 100% tall and 0% short. Height below 20 is considered as 100% short and 0% tall. And point between 20 and 30 depend upon both short and tall functions. Now depending upon how the weight is distributed while defining the rules, height 29.999 can be represented as 95% tall and 5% short or 97% tall and 3% short or other combinations of both the input functions. Here user has a control to define output function using fuzzy set rules. That is more realistic answer compare to classical set representation. Each input in the fuzzy set theory is represented by membership functions. It defines functional overlap regions between inputs, weights of each inputs and also output responses.

22 4.1.2 Fuzzy System Design Figure 4.2 Basic Fuzzy Logic Controller (FLC) The above figure is taken from the [10]. It shows the block diagram of basic fuzzy logic controller. The basic components of fuzzy logic controller are: Fuzzification interface: The functions of Fuzzification module are: - Measures input variables. [10] - Use to convert numerical values in the membership function related to a particular fuzzy set. [9]

23 Knowledge base: It consists of an application domain and also the control goals mainly data based and rule based. Data base provides definitions of fuzzy sets and rules define the control rules for domain. [10] Inference or decision making logic: It provides the control actions by defining set of rules. Rules are the graphical representation to manipulate the knowledge based system. Knowledge representations from previous step are examined in this step using fuzzy logic rules. [9] Defuzzification module: This module is the opposite of Fuzzification module. It gets the fuzzy set values from inference module and converts logic back to the scaled values. Defuzzification is a very important step in fuzzy system. It provides final output in terms of physical variables. Out of many methods, the most common methods for Defuzzification are CENTROID method and MAXIMUM method. [9] There are also other important blocks in the fuzzy system as below, Normalized module: The basic need for normalized module is to transform the physical values into scaled values. [9] Denormalization module: This module is opposite of normalized module. It converts scaled values back into physical values. [9]

24 4.1.3 Pros and Cons Pros: Fuzzy logic is easy to implement using MATLAB. [11] As shown in figure 4.1, it gives more realistic results than classical representation of set theory. [11] It is easy to handle nonlinear functions using fuzzy set theory and fuzzy rules. [11] It provides higher amount of tolerance for imprecise data. [11] It can also be used with conventional control logic. [11] It provides faster and cheaper operation. [9] Cons: Due to nonlinear effects, it is sometimes difficult to analyze the performance of the fuzzy system. [9] Handling and operating the physical system implemented with fuzzy logic with less experience in fuzzy systems can lead to inappropriate results. [9] In many systems, it is difficult to include fuzzy logic entirely. So it can be used as a second alternative. [9] 4.1.4 Applications Few of the industry application where fuzzy logic is widely used are mentioned below. The below applications are taken from [9] and [11] Consumer products - Dishwasher

25 - Microwave oven - Air conditioner - Refrigerator Industrial controller - Microcontrollers and microprocessors - Medical instrumentation - Remote sensing - To replace PI or PID controller - For controlling operation in automobile as cruise control - Elevators - Process control Power engineering - Load balancing - Power system control - Automatic generation control 4.2 Implementation of Load Balancing Using Fuzzy Logic Let us consider in our case, the distribution feeder is a three phase structure. Each feeder is connected to specific amount of loads. So, to analyze the load balancing using fuzzy logic, it is considered that each feeder is connected to 100 domestic loads. So, 300 loads are connected to three feeders. In this project, I have kept loads constant to 300 but as for future expansion of this project, load balancing can also be designed for variable loads. When one feeder is overloaded and others are lightly loaded, the load transfer takes

26 place to balance the system. It is done by load balancing. Load balancing can also reduce the power loss during load transfer. As I have explained before, it uses switching operations to balance the load between multiple systems. The switching operations can be implemented using hardware system like combinatorial logic. Here I have implemented the fuzzy logic system using MATLAB software which later on can be implemented in hardware. 4.2.1 Load Balancing As I have mentioned in introduction of this chapter, feeder is a three phase structure and 100 domestic loads are connected to each feeder. As shown in figure below, each load can be connected to only one phase at a time through switches. So maximum of 300 loads can be connected to the system. ph1 ph2 ph3 L1 L300 Figure 4.3 Feeder Distribution

27 Above figure 4.3 is taken from [9]. So when one feeder is overloaded, the loads are transformed from overloaded branch to the lightly loaded branch without reconfiguring the system. Let us examine the total unbalance in the three feeder system. Figure 4.4 shows the flow chart steps of the load balancing technique. Figure 4.4 Load Balancing Algorithm

28 Above figure 4.4 is taken from [9]. Here the average unbalance is checked at defined time. If the unbalance is not over the defined limits, means the load is balanced within limits. So there is no need to balance the load. However, if the load is greater than the defined limits, load balancing using fuzzy logic is required. The negative value indicates that phase is overloaded and must release some load. And positive value indicates that phase is lightly loaded than limits and it can receive some load to get balanced. [9] Average unbalance is calculated by the equation, LoadPh1 - LoadPh2 + LoadPh2 - LoadPh3 + LoadPh3 LoadPh1 Average Unbalance/Phase = (4.4) 3 Above equation 4.4 is taken from [9]. As shown in equation 4.4, the unbalance depends on all three phase calculations. Once average unbalance is known, the only thing remains is to adjust that unbalance with another phase of the system to make system perfectly loaded. Now as we have gathered all the details about fuzzy logic, fuzzy logic toolbox and load balancing, let us start with designing of fuzzy controller using MATLAB. Our main aim is to keep the load within limits, so our system will have a load as input. Now if the system is not balanced then we will need to calculate an unbalance change. So our system will have change as output that will give an exact amount of unbalance in the

29 system. Once change is known, the exact amount of load transfer can be done using switching. Typing fuzzy on the MATLAB window starts the FIS editor. Now in our system, the input is named Load (kw) to indicate total phase load for each phase and the output is named Change (kw) to calculate the total change of load for each phase. First step is to provide input and output in FIS editor and save the system with an appropriate name. Here, I have given a name Load balancing. It is shown in figure 4.5 below, Figure 4.5 Initialization of Load Balancing System

30 Now the next step is to define the range of inputs. So to provide fuzzy membership functions, and represent input logic in a simple way, I have divided ranges in different regions shown in table 4.2 below. Input Load Description Fuzzy logic Linguistic term kw range Very Less Loaded VLL 0 to 100 Less Loaded LL 70 to 170 Medium Loaded ML 130 to 230 Perfect Loaded PL 200 to 300 Slightly Overloaded SOL 250 to 350 Medium Overloaded MOL 330 to 430 Overloaded OL 400 to 500 Heavily Overloaded HOL 470 to 600 Table 4.2 Ranges for Input Load Variable In our project, the total load is 300. So as shown in above table 4.2, the system below 200 loads is considered as less loaded. System between 200 to 300 loads is considered as balanced system where no load balancing is required. Now when any system goes above its defined limits, it is considered overloaded. Here also above 300 loads, the system is considered overloaded. And no system can handle double loads than defined. So once system goes over 600 loads, the entire system should be cutoff to prevent system damage.

31 The output changes of the fuzzy logic are related to the input. For example, if the system is medium loaded, changes should be such that the system again becomes perfectly loaded. So the output also should be divided in ranges same as input. It is shown in table 4.3 below, Output Change Description Fuzzy logic Linguistic term kw range High Subtraction HS -300 to -170 Subtraction S -200 to -100 Medium Subtraction MS -130 to -30 Slight Subtraction SS -100 to 50 Perfect Addition PA 0 to 100 Medium Addition MA 70 to 170 Large Addition LA 130 to 230 Very Large Addition VLA 200 to 300 Table 4.3 Ranges for Output Change Variable Consider table 4.3 above. Here if the system is very heavily loaded, means very high load must be subtracted. So, values above perfect addition give the amount of subtraction to make system within limits from overloading. Perfect addition determines the balanced system. And if the system is less loaded, more loads should be added. So variable below perfect addition give the amount of addition to make system within limits from less loaded.

32 To provide these ranges in input and output, double clicking on respective input or output signal box will open membership function editor. Now we have total of 8 membership functions for input Load and 8 membership functions for output Change. So we have to select 8 membership functions and give each membership function a name and a range as given in above table 4.2 and table 4.3. Below figure 4.6 shows 8 membership functions defined for input variable Load. Figure 4.6 Specifying the Input Variable as Load (kw)

33 Now, next step is to provide membership functions for output variable Change as defined in table 4.3. Here 8 membership functions are determined with the range of -300 kw to 300 kw. It is shown in figure 4.7 below, Figure 4.7 Specifying the Output Variable as Change (kw)

34 The above steps determine Fuzzification of the system. Now next step is fuzzy inference. As we discussed above, fuzzy inference provides set of rules that describe the control action of entire fuzzy system. The output changes depending upon the input and the rules defined in fuzzy inference system. So, to provide proper balancing, IF-THEN rule set is used in this project. It means, IF (input load is this) THEN (output changes to this). Fuzzy set rules are the very important criteria to provide the effective load balancing. [9] The rules I have used in this project are described as below, table 4.4 is taken from [9]. Rule No. Rule Description 1 If Load is VLL then Change is VLA 2 If Load is LL then Change is LA 3 If Load is ML then Change is MA 4 If Load is PL then Change is PA 5 If Load is SOL then Change is SS 6 If Load is MOL then Change is MS 7 If Load is OL then Change is S 8 If Load is HOL then Change is HS Table 4.4 Rules Used to Design Load Balancing Fuzzy System

35 To provide these rules in MATLAB, double clicking on fuzzy medium that is the medium between input and output in our case Load balancing, rule editor window opens. In rule window, we can provide and/or if we have multiple inputs. We also can provide different weights for different rule. In this project, all the rules have same weight. Now as per the table above, rules are included in fuzzy design as shown in figure 4.8 below. Figure 4.8 Rule Editor from Fuzzy Logic Toolbox

36 Once rules are defined, fuzzy system is ready to execute. So clicking on rules under view window in FIS editor, new window named rule viewer is opened. It shows results of the fuzzy system. Variations in output can be measured using those results. Results are shown in next chapter with error calculations.

37 Chapter 5 SIMULATION RESULTS 5.1 Results The results for the load balancing are shown below. We can adjust the input load value by moving the red line shown in figure and we can also apply input value in the box named input. Here in figure 5.1, the total load is 75 kw. So it means the system is less loaded (LL). So it can receive some load from other feeders. Now as the total load is 300, the change should be such that total of the received load and current load is around 300 kw. It means the change must be positive and it has to be added to the actual load value. So, here change indicated from fuzzy logic is 237 kw. So total system load goes to 75 kw + 237 kw = 312 kw. Hence, the system is balanced in this case. Now as per the control flow diagram in figure 4.4, the control logic checks the system again and finds that it is balanced now. So no further action will be needed until system goes off balance next time. It will continue checking the system at defined time intervals.

Figure 5.1 Result - 1 38

39 Here in figure 5.2, the total load is 481 kw. So it means the system is heavily over loaded (HOL) and it must release some load to other less loaded feeders. Now as the total load is 300, the release should be such that this heavily over loaded system comes back as a balanced system. it means the output change must be negative and it has to be added from the original load value. So here, change indicated from fuzzy logic is -184 kw. It means the system must release -184 kw load to become again a balanced system. So total system load goes to 481 kw + (-184 kw) = 297 kw. Now as per the control flow diagram in figure 4.4, the control logic checks the system again and finds that it is balanced now. So no further action is needed until system goes off balance next time.

Figure 5.2 Result - 2 40

41 Here in figure 5.3, the total load is 316 kw. So it means the system is slightly overloaded (SOL). So it has to release some load to other feeders. Here change is -25 kw. That indicates slightly subtraction (SS) needed. So after adding change to the original load value, we get 316 + (-25) = 291 kw. It is shown below, Figure 5.3 Result - 3

42 5.2 Error Correction Now the problem in above technique is, in figure 5.1, after adding a change value, the final load of the system in 312 kw. Same in figure 5.2, after reducing the change value, the final load is 297 kw. And in figure 5.3, the final value of load remains 291 kw. In all cases, the final load after adding or subtracting a change load is not equal to 300 kw exactly. It means the system load is not fixed and changes every time. That is not possible in our system as we have assumed that the final load remains constant every time. So this method will give erroneous results. So error correction is implemented to make a system entirely balanced. The error correction is explained below. This error correction and the equation 5.1, 5.2, 5.3 and 5.4 are taken from [9]. The average error AE is, AE = round (5.1) Here, ΔP fuzzy is the output change given by the fuzzy system. So, 237 So in our case, ΔP fuzzy = -184-25 kw Now, Σ Δ P fuzzy = 237 + (-184) + (-25) = 28 kw

43 Now, the error matrix ΔP error is calculated by, AE Δ P error = AE Σ Δ P fuzzy 2AE (5.2) The final load change after removing all the error components is given by ΔP, as shown in equation 5.3. ΔP = ΔP fuzzy - ΔP error (5.3) And as per the equation 5.1, Average error AE = round (28/3) = 9 kw. Applying above values or AE and Σ Δ P fuzzy in equation 5.2 we get, 9 ΔP error = 9 28 18 9 = 9 10 kw So from equation 5.3, and putting values for ΔP fuzzy and ΔP error in equation, we get 237 9 ΔP = -184-9 -25 10 kw

44 228 ΔP = -193-35 kw So, the final output of fuzzy logic P final is, P final = P in + ΔP, (5.4) Here, P in = input load of the system 75 = 481 320 kw So, from equation 5.4, the final output of the system is, 75 228 P final = 481 + -193 320-35 kw 303 = 288 285 kw Now applying equation 4.4 from previous chapter on P in and P final values we achieved from above calculations, we get

45 For P in value: Initial absolute average unbalance per phase = 270.66 kw For P final value: Final absolute average unbalance per phase = 12 kw So from above results, we can see that unbalance is reduced by a factor of 95% after implementation of fuzzy logic error correction. Hence, by performing this project I have successfully demonstrated the requirements and implementation of load balancing in real world.

46 Chapter 6 CONCLUSION AND FUTURE EXPANSION 6.1 Conclusion Load balancing is a critical requirement of the power system to ensure that entire system works without overloading. This project gives us a good understanding of load balancing. Fuzzy logic toolbox provided by MATLAB is used in this project for design and development of load balancing. MATLAB is provided by MathWorks Incorporation and it covers areas of applications like data algorithm, matrix manipulation and data manipulation. Fuzzy logic is a toolbox that provides graphical user interface based implementation of fuzzy system. Before consumer usage of power, it has to be properly generated, transmitted and distributed. Power stations generate the power by converting one form of energy into electrical energy. Once power is generated, it should be transmitted to the subsystems near consumers. So proper power transmission network is required to reduce transmission losses. Transmission can be overhead or underground depending upon requirements. The critical stage is power distribution. Depending upon the consumer usage, the distribution should be such that it can avoid over loading situation. Load profile gives the graphical representation of the customer power usage. Automatic generation control is the one way to control the continuously changing load. It is implemented at the power station side and it controls the generation of power

47 depending upon the change in load. It is good alternative to load balancing, but it is very costly. So for rural areas where load fluctuations are not large, load balancing is employed. Fuzzy logic is the easy way to design load balancing. Using basic fuzzy rules and fuzzy blocks like normalized, Fuzzification, Defuzzification and Denormalized, we can design a load balancing system. In this project, the load balancing using 3-phase with 100 loads per phase system is designed successfully. But the fuzzy system balances the load with some error value that keep changing the final load. So to avoid that error value, error calculations are required. Hence this project elaborates the need of load balancing and provides the design concepts for the same. 6.2 Future Expansion In this project, it is assumed that for a 3-phase system, each phase has maximum of 100 loads. So, entire system can have total of 300 loads. Here, number of loads are assumed fix. And for load balancing, load can be transferred from overloaded system to less loaded system keeping total loads same. But this project can be expanded to design and implement of load balancing system for variable loads in future. Each subsystem can have some amount of buffer to store the electrical energy and when overloading occurs, it can provide power for balancing the load.

48 APPENDIX A Source Code for Load Balancing [System] Name='Load balancing' Type='mamdani' Version=2.0 NumInputs=1 NumOutputs=1 NumRules=8 AndMethod='min' OrMethod='max' ImpMethod='min' AggMethod='max' DefuzzMethod='centroid' [Input1] Name='Load(kW)' Range=[0 600] NumMFs=8 MF1='VLL':'trimf',[0 50 100] MF2='LL':'trimf',[70 120 170]

49 MF3='ML':'trimf',[130 180 230] MF4='PL':'trimf',[200 250 300] MF5='SOL':'trimf',[250 300 350] MF6='MOL':'trimf',[330 380 430] MF7='OL':'trimf',[400 450 500] MF8='HOL':'trimf',[470 535 600] [Output1] Name='Change(kW)' Range=[-300 300] NumMFs=8 MF1='HS':'trimf',[-300-235 -170] MF2='S':'trimf',[-200-150 -100] MF3='MS':'trimf',[-130-80 -30] MF4='SS':'trimf',[-100-25 50] MF5='PA':'trimf',[-0 50 100] MF6='MA':'trimf',[70 120 170] MF7='LA':'trimf',[130 180 230] MF8='VLA':'trimf',[200 250 300] [Rules] 1, 8 (1) : 1

50 2, 7 (1) : 1 3, 6 (1) : 1 4, 5 (1) : 1 5, 4 (1) : 1 6, 3 (1) : 1 7, 2 (1) : 1 8, 1 (1) : 1

51 BIBLIOGRAPHY [1] The MATH WORKS Inc. (2001). Learning MATLAB, Version 6 (Release 12). Retrieved from World Wide Web: http://courses.washington.edu/css457/matlab/learning_matlab.pdf [2] Wikipedia, the free encyclopedia, Electricity generation. Retrieved from World Wide Web: http://en.wikipedia.org/wiki/power_generation [3] Wikipedia, the free encyclopedia, Electric power transmission. Retrieved from World Wide Web: http://en.wikipedia.org/wiki/electric_power_transmission [4] Wikipedia, the free encyclopedia, Electricity distribution. Retrieved from World Wide Web: http://en.wikipedia.org/wiki/electrical_distribution [5] Wikipedia, the free encyclopedia, Load profile. Retrieved from World Wide Web: http://en.wikipedia.org/wiki/load_profile [6] Gaddam Mallesham, Akula Rajani (2006), Automatic Generation Control Using Fuzzy Logic. Retrieved from World Wide Web: http://www.dasconference.ro/papers/2006/b9.pdf [7] Mugdegem Tanrioven, Kayhan Gulez (1998), The determination and realization of compensation degrees in power control systems having load asymmetry by using fuzzy logic controller supported by artificial neural networks. Retrieved from World Wide Web: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=692496 [8] M. A. Kashem, V. Ganapathy, G. B. Jasmon (2000), A geometric approach for threephase load balancing in distribution networks. Retrieved from World Wide Web: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=900072