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Due to the continuous increase of the population and the perpetual progress of industry, the energy management presents nowadays a relevant topic that concerns researchers in electrical engineering.
- NEURAL NETWORKS, FUZZY LOGIC AND GENETIC ALGORITHM: SYNTHESIS AND ...
- Soft Computing: Fuzzy Logic, Neural Networks, and Genetic Algorithms
- Advances in Fuzzy Logic, Neural Networks and Genetic Algorithms
NEURAL NETWORKS, FUZZY LOGIC AND GENETIC ALGORITHM: SYNTHESIS AND ...
Due to the continuous increase of the population and the perpetual progress of industry, the energy management presents nowadays a relevant topic that concerns researchers in electrical engineering. Indeed, in order to establish a good exploitation of the electrical grid, it is necessary to solve technical and economic problems. This can only be done through the resolution of the Unit Commitment Problem.
However, each production unit has some constraints that make this problem complex, combinatorial, and nonlinear. This paper presents a comparative study between a strategy based on hybrid gradient-genetic algorithm method and two strategies based on metaheuristic methods, fuzzy logic, and genetic algorithm, in order to predict the combinations and the unit commitment scheduling of each production unit in one side and to minimize the total production cost in the other side.
To test the performance of the optimization proposed strategies, strategies have been applied to the IEEE electrical network 14 busses and the obtained results are very promising. According to human activities, the electrical energy consumption is still increasing. Indeed, during one day the electricity demand is higher compared to the end of the night and this change is not related only to the day but also to the change of seasons, weekends, and so forth. In addition, the production of electricity must be compatible with the consumption considering the impossibility to store electricity.
For this reason, the electric company must plan the operations of the production units and organize their moments of connection to the network and the duration of each operation. The unit commitment UC is the best solution in the field of modern power systems planning since the main objective is to schedule the production units to respond to the consumers demand with minimum cost.
In fact, it allows both the optimization of the daily operational planning of electrical grids and the reduction of the total production cost through improving units while guaranteeing the continuity of service. The generation scheduling involves the determination of the commissioning and the quantity of power that should be generated by each unit during a specified planning period. Moreover, as each unit has its own production limits and its minimum start-up and shut-down times, it is the case of a complex, combinatorial, and nonlinear optimization problem [ 1 ].
Generally, the unit commitment problem depends directly on the unit production scheduling and on the economic dispatch, knowing that our system is subject to several constraints: power balance, spinning reserve, generation limits, and minimum start-up and shut-down times. Nevertheless, this problem concedes a multitude of problems such as the big size of the studied grid, the presence of coupling constraints, the presence of the operational constraints, and the time constraint which have to be low with respect to the size of the problem [ 2 ].
In this context, unit commitment scheduling has been established in order to make the best choice of production units that will be available to supply the forecasted load over a future period.
Therefore, a study of the literature on methods, which focus on unit commitment UC problem resolution, shows that various numerical optimization techniques have examined this subject such as dynamic programming [ 3 , 4 ], Lagrangian relaxation method [ 5 — 8 ], mixed integer programming [ 9 ], and branch-and-bound method [ 10 — 12 ].
It is worth mentioning that the dynamic programming method is simple but the calculation time required to converge to the optimal solution is quite long. Regarding the branch-and-bound method, it adopts a linear function to represent the fuel and start-up costs during a time horizon.
The disadvantage of this method is that the required execution time increases rapidly for UC problem having larger scales. The mixed integer programming uses linear programming to attain optimal solution.
Nevertheless, this method was applied to small problems of unit commitment and they required major assumptions [ 9 ] that limit the margin of solutions. For the Lagrangian relaxation method, we note that the convergence time is an advantage, but the obtained solution is not ideal because of the complexity of the problem especially when the optimization problem contains a great number of production units.
In addition to the methods previously mentioned, there is another category of digital techniques applied to the UC problem. Specifically, there are the fuzzy logic [ 13 , 14 ], the artificial neural network [ 15 ], the simulated annealing [ 16 — 18 ], the Tabu search [ 19 ], and the genetic algorithm [ 20 — 23 ]. These methods which can take into account more complex constraints are claimed to improve the quality of solutions. In this context, the works [ 24 , 25 ] have presented a new strategy based on genetic algorithm to determine the priority order of the production units.
The proposed strategy has presented an optimized unit commitment scheduling and the computation time taken through this strategy is promising.
According to our study, we found that it is possible to use genetic algorithms to optimize the production cost while providing effective results. In fact, solving the unit commitment problem by genetic algorithm promotes the dynamic operation scheduling of each unit taking into account the system parameters, the operating constraints, and the requested load during a definite time horizon.
We examined the works of Victoire and Jeyakumar [ 1 ] which consist of the integration of a hybrid optimization strategy to solve the unit commitment problem.
The combinatorial part of the UC problem was solved using the TS method. Moreover, [ 16 , 17 , 26 ] proposed a new technique using simulated annealing method. This technique increases the probability of generating feasible solutions and reduces significantly the time to research unfeasible solutions.
With regard to [ 27 ], the adopted method is based on fuzzy logic approach to produce a logical and feasible solution for each horizon time and to take into account many uncertainties involved in the power systems planning. Indeed, the load demand and reserve margin are treated as fuzzy variables in order to estimate the required generated power in the electrical grid and to schedule this quantity among the production units considering the reserve margin and the power production limits.
We have proposed three strategies applied to IEEE electrical network 14 buses to solve the UCP in general and in particular to find the optimized combination scheduling of the produced power for each unit production. The first strategy is based on the use of fuzzy logic approach, the second one relies on the use of genetic algorithm, and the third strategy uses a hybrid optimization method, gradient-genetic algorithm.
Throughout these three strategies, we arrived to develop an optimized scheduling plan of the generated power allowing a better exploitation of the production cost in order to bring the total operating cost to possible minimum when it is subjected to a series of constraints.
A comparison was made to test the performances of the proposed strategies and to prove their effectiveness in solving unit commitment problems. The paper is organized as follows; Section 2 is reserved to formulating the unit commitment problem. Next, in Section 3 , methodologies of resolution through fuzzy logic, genetic algorithm, and gradient-genetic algorithm methods are presented.
Section 4 deals with the discussion of simulation results and the main improvements of adopted strategies are highlighted. Finally, Section 5 resumes the main conclusions followed by references. Unit commitment is a highly constrained optimization problem. Different power systems have a different set of imposed constraints. The most common can be divided into two categories. The first, called unit constraints, represents the constraints that are applied to the single units; the second type, system constraints, contains those that are applied to the whole power system.
The real practical barrier in the unit commitment problem is the high dimensionality of the possible search space. The mentioned unit and system constraints present the main limits of the search space of the studied model.
Here, in order to transform the complex nonlinear constrained problem into a linear unconstrained problem, we consider the following Lagrangian function: Herein, is the Lagrangian coefficient.
The hypothesis tested in this paper is that the unit commitment dynamic can use both metaheuristic methods as hybrid methods to get the final commitment over the entire planning period.
For our case study, three optimization methods are used to solve the unit commitment problem; the first one uses the genetic algorithm. This strategy takes into account the advantage of the genetic algorithm speed in solving problems having a fairly complex architecture. The second method relies on the use of the fuzzy logic approach. The use of the fuzzy logic approach to solve this problem is depicted to the effectiveness of this optimization method in solving nonlinear difficult problems.
Besides, the third strategy is based on the combination of two calculations methods, the genetic algorithm and the gradient method. The resolution of the unit commitment problem through gradient-genetic algorithm method is provided by a specific adjustment of the Lagrangian multipliers of the Lagrangian function. The combined choice of these two methods is due to inquire about the rapidity of the genetic algorithm in the search for global minimum in first step and to operate the benefits the gradient method in a second step, since it is effective in terms of the quality of the obtained optimal solutions.
The fundamental principle of a genetic algorithm is to represent the natural evolution of organisms individuals. In each evolution stage, the genetic operators selection, crossover, and mutation operate based on the data structures in order to allow each individual to sweep the solutions horizon and to distinguish the global optimum among the local optima.
At first, from an initial population of individuals, the evaluation function satisfies the following relation: with : maximum of the function , : penalty coefficient, : scaling coefficient, and : constant defined as follows:. Genetic algorithm did not work on the real generator outputs themselves but on bit string encodings of them. For our case study, we have adopted the biased roulette wheel method in order to select the best chromosomes according to their performances obeying to the following equation: where is the length of a binary string.
After the selection of the parent chromosomes, recombination and mutation take place to produce the offspring chromosomes. Owing to the nature of our coding and the use of integers, we cannot use the crossover and mutation operators in their classic form. Crossover is a structured, yet randomized, mechanism of exchanging information between strings.
Crossover begins by selecting at random two members previously placed in the mating pool during reproduction. A crossover point is then selected at random, and information from one parent, up to the crossover point, is exchanged with the other parent. The probability of crossover is given by the following expression [ 31 , 32 ]: where is the larger of the fitness values of the solutions to be crossed, is the average of the fitness function, and is the constant of proportionality.
Mutation is generally considered a secondary operator. Mutation ensures that no string position will ever be fixed at a certain value for all the time. Mutation operates by toggling, in a binary code, any given string position with probability of mutation. The expression of the probability of mutation is given as follows [ 31 , 32 ]: where is the constant of proportionality. GA terminates the evolution only when the generation reaches its maximum number.
The process of solving the unit commitment problem by genetic algorithm method is performed according to Figure 1. This step is important because it determines the degree of exploitation and advancement of the optimal solution search. This research is based on saving the best solution until the optimization progresses. Fuzzy logic provides not only a meaningful and powerful representation for measurement of uncertainties but also a meaningful representation of blurred concept expressed in normal language.
Fuzzy logic is a mathematical theory, which encompasses the idea of vagueness when defining a concept or a meaning.
Such ideas are readily applicable to the unit commitment problem. The application of fuzzy logic allows a qualitative description of the behavior of a certain system, the characteristics of the system, and its response without the need for exact mathematical formulation [ 13 , 14 , 33 , 34 ].
To establish our strategy, we have considered the partial derivatives of the Lagrange function 9 with respect to each of the controllable variables equal to zero:.
Equations 15 represent the optimality conditions necessary to solve equation systems 1 and 5 without using inequality constraints 5 and 6. Hence, 9 can be written as follows: The term represents the incremental cost IC of each unit and represents the incremental losses IL. These terms occur as fuzzy variables associated to our strategy in order to solve the unit commitment problem. It should be noted that the strategy is based on the integration of a fuzzy controller to optimize the cost of the production unit while ensuring proper planning of the production units.
In the current formulation, the fuzzy input variables associated to the unit commitment problem are the load capacity of the generator LCG , the incremental cost IC , and the incremental losses IL. The output variable is the cost of production. The following is a brief description and explanation of the main choice of the mentioned fuzzy variables.
The fuzzy system consists of three principle components: fuzzification, fuzzy rules, and defuzzification which are described as follows [ 14 , 33 ]. Three inputs are considered, load capacity of generator LCG , incremental losses IL , and incremental cost IC and the output vector is represented by the amount of the production cost.
The triangular membership functions are considered for the fuzzification of the input variables. However, the output variable is presented in five fuzzy sets of linguistic values: low L , below average BAV , average AV , above average AAV , and high H with associated triangular membership functions, as shown in Figure 2.
The Mamdani-type fuzzy rules are used to formulate the conditional statements that comprise fuzzy logic. According to the fuzzy sets of linguistic value related to each input variable, 45 rules are designed as shown in Table 1. Each rule represents a mapping from the input space to the output space. Based on the aforementioned fuzzy sets, membership functions are selected for each fuzzy input and the fuzzy output variables.
Soft Computing: Fuzzy Logic, Neural Networks, and Genetic Algorithms
PHI Learning Pvt. This book provides comprehensive introduction to a consortium of technologies underlying soft computing, an evolving branch of computational intelligence. The constituent technologies discussed comprise neural networks, fuzzy logic, genetic algorithms, and a number of hybrid systems which include classes such as neuro-fuzzy, fuzzy-genetic, and neuro-genetic systems. The book also gives an exhaustive discussion of FL-GA hybridization. Every architecture has been discussed in detail through illustrative examples and applications. The algorithms have been presented in pseudo-code with a step-by-step illustration of the same in problems.
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Skip to Main Content. A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. Use of this web site signifies your agreement to the terms and conditions. It provides an easy to use graphical user interface to design, construct and execute neural networks. The most important design goals were easy extensibility, good performance and the ability to solve real world problems.
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Search this site. The constituent technologies discussed comprise neural network NN , fuzzy system FS , evolutionary algorithm EA , and a number of hybrid systems, which include classes such as neuro-fuzzy, evolutionary-fuzzy, and neuro-evolutionary systems. The algorithms have been presented in pseudo-code with a step-by-step illustration of the same in problems. The applications, demonstrative of the potential of the architectures, have been chosen from diverse disciplines of science and engineering. This book, with a wealth of information that is clearly presented and illustrated by many examples and applications, is designed for use as a text for the courses in soft computing at both the senior undergraduate and first-year postgraduate levels of computer science and engineering. It should also be of interest to researchers and technologists desirous of applying soft computing technologies to their respective fields of work.
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