A parallel genetic algorithm approach to solving the unitcommitment problem: implementation on the transputer networks

Through a constraint handling technique, this paper proposes a parallel genetic algorithm (GA) approach to solving the thermal unit commitment (UC) problem. The developed algorithm is implemented on an eight-processor transputer network, processors of which are arranged in master-slave and dual-direction ring structures, respectively. The proposed approach has been tested on a 38-unit thermal power system over a 24-hour period. Speed-up and efficiency for each topology with different number of processor are compared to those of the sequential GA approach. The proposed topology of dual-direction ring is shown to be well amenable to parallel implementation of the GA for the UC problem     

Short-term hydrothermal scheduling using clonal selection algorithm

An efficient optimization procedure based on the clonal selection algorithm (CSA) is proposed for the solution of short-term hydrothermal scheduling problem. CSA, a new algorithm from the family of evolutionary computation, is simple, fast and a robust optimization tool for real complex hydrothermal scheduling problems. Hydrothermal scheduling involves the optimization of non-linear objective function with set of operational and physical constraints. The cascading nature of hydro-plants, water transport delay and scheduling time linkage, power balance constraints, variable hourly water discharge limits, reservoir storage limits, operation limits of thermal and hydro units, hydraulic continuity constraint and initial and final reservoir storage limits are fully taken into account. The results of the proposed approach are compared with those of gradient search (GS), simulated annealing (SA), evolutionary programming (EP), dynamic programming (DP), non-linear programming (NLP), genetic algorithm (GA), improved fast EP (IFEP), differential evolution (DE) and improved particle swarm optimization (IPSO) approaches. From the numerical results, it is found that the CSA-based approach is able to provide better solution at lesser computational effort.     

Security constrained economic load dispatch using improved particle swarm optimization suitable for utility system

The objective of this paper is to evolve simple and effective methods for the economic load dispatch (ELD) problem with security constraints in thermal units, which are capable of obtaining economic scheduling for utility system. In the proposed improved particle swarm optimization (IPSO) method, a new velocity strategy equation is formulated suitable for a large scale system and the features of constriction factor approach (CFA) are also incorporated into the proposed approach. The CFA generates higher quality solutions than the conventional PSO approach. The proposed approach takes security constraints such as line flow constraints and bus voltage limits into account. In this paper, two different systems IEEE-14 bus and 66-bus Indian utility system have been considered for investigations and the results clearly show that the proposed IPSO method is very competent in solving ELD problem in comparison with other existing methods.     

A genetic algorithm solution to the optimal short-term hydrothermal scheduling

This paper presents an algorithm for solving the hydrothermal scheduling through the application of genetic algorithm (GA). The hydro subproblem is solved using GA and the thermal subproblem is solved using lambda iteration technique. Hydro and thermal subproblems are solved alternatively. GA based optimal power flow (OPF) including line losses and line flow constraints are applied for the best hydrothermal schedule obtained from GA. A 9-bus system with four thermal plants and three hydro plants and a 66-bus system with 12 thermal plants and 11 hydro plants are taken for investigation. This proposed GA reduces the complexity, computation time and also gives near global optimum solution.     

Using immune genetic algorithm based hybrid techniques for short-term unit commitment problem

This paper presents a hybrid chaos search (CS), immune algorithm (IA)/genetic algorithm (GA), and fuzzy system (FS) method (CIGAFS) for solving short-term thermal generating unit commitment (UC) problems. The UC problem involves determining the start-up and shut-down schedules for generating units to meet the forecasted demand at the minimum cost. The commitment schedule must satisfy other constraints such as the generating limits per unit, reserve, and individual units. First, we combined the IA and GA, then we added the CS and the FS approach. This hybrid system was then used to solve the UC problems. Numerical simulations were carried out using three cases: 10, 20, and 30 thermal unit power systems over a 24 h period. The produced schedule was compared with several other methods, such as dynamic programming (DP), Lagrangian relaxation (LR), standard genetic algorithm (SGA), traditional simulated annealing (TSA), and traditional Tabu search (TTS). A comparison with an immune genetic algorithm (IGA) combined with the CS and FS was carried out. The results show that the CS and FS all make substantial contributions to the IGA. The result demonstrated the accuracy of the proposed CIGAFS approach.     

Quantum-Inspired Particle Swarm Optimization for Valve-Point Economic Load Dispatch

Economic load dispatch (ELD) is an important topic in the operation of power plants which can help to build up effective generating management plans. The ELD problem has nonsmooth cost function with equality and inequality constraints which make it difficult to be effectively solved. Different heuristic optimization methods have been proposed to solve this problem in previous study. In this paper, quantum-inspired particle swarm optimization (QPSO) is proposed, which has stronger search ability and quicker convergence speed, not only because of the introduction of quantum computing theory, but also due to two special implementations: self-adaptive probability selection and chaotic sequences mutation. The proposed approach is tested with five standard benchmark functions and three power system cases consisting of 3, 13, and 40 thermal units. Comparisons with similar approaches including the evolutionary programming (EP), genetic algorithm (GA), immune algorithm (IA), and other versions of particle swarm optimization (PSO) are given. The promising results illustrate the efficiency of the proposed method and show that it could be used as a reliable tool for solving ELD problems.      

A harmony-genetic based heuristic approach toward economic dispatching combined heat and power

The Combined Heat and Power Economic Dispatch (CHPED) problem seeks to determine the heat and power production to minimize the system production costs and satisfy the heat–power demands and capacity constraints. This study examines the combined heat and power dispatching needs of cogeneration plants, and investigates the performance of an evolutionary computing approach which is based on both genetic algorithm (GA) and harmony search (HS). Experimental results were conducted for an extensive comparison with GA and HS to confirm the superior performance of this hybrid approach in cost minimization and computation times. The output results indicate that the proposed algorithm is capable of managing the CHPED problem and yields high-quality solutions.     

Short-term hydrothermal generation scheduling by a modified dynamic neighborhood learning based particle swarm optimization

The main objective of the short-term hydrothermal generation scheduling (SHGS) problem is to determine the optimal strategy for hydro and thermal generation in order to minimize the fuel cost of thermal plants while satisfying various operational and physical constraints. Usually, SHGS is assumed for a 1 day or a 1 week planing time horizon. It is viewed as a complex non-linear, non-convex and non-smooth optimization problem considering valve point loading (VPL) effect related to the thermal power plants, transmission loss and other constraints. In this paper, a modified dynamic neighborhood learning based particle swarm optimization (MDNLPSO) is proposed to solve the SHGS problem. In the proposed approach, the particles in swarm are grouped in a number of neighborhoods and every particle learns from any particle which exists in current neighborhood. The neighborhood memberships are changed with a refreshing operation which occurs at refreshing periods. It causes the information exchange to be made with all particles in the swarm. It is found that mentioned improvement increases both of the exploration and exploitation abilities in comparison with the conventional PSO. The presented approach is applied to three different multi-reservoir cascaded hydrothermal test systems. The results are compared with other recently proposed methods. Simulation results clearly show that the MDNLPSO method is capable of obtaining a better solution.     

Considering Different Network Topologies in Optimal Overcurrent Relay Coordination Using a Hybrid GA

The directional overcurrent relays (DOCRs) coordination problem is usually studied based on a fixed network topology in an interconnected power system, and is formulated as an optimization problem. In practice, the system may be operated in different topologies due to outage of the transmission lines, transformers, and generating units. There are some situations for which the changes in the network topology of a system could cause the protective system to operate without selectivity. The aim of this paper is to study DOCRs coordination considering the effects of the different network topologies in the optimization problem. Corresponding to each network topology, a large number of coordination constraints should be taken into account in the problem formulation. In this situation, in addition to nonlinearity and nonconvexity, the optimization problem experiences many coordination constraints. The genetic algorithm (GA) is selected as a powerful tool in solving this complex and nonconvex optimization problem. In this paper, in order to improve the convergence of the GA, a new hybrid method is introduced. The results show a robust and optimal solution can be efficiently obtained by implementing the proposed hybrid GA method.     

Application embedded chaos search immune genetic algorithm for short-term unit commitment

This paper presents a Hybrid Chaos Search (CS) immune algorithm (IA)/genetic algorithm (GA) and Fuzzy System (FS) method (CIGAFS) for solving short-term thermal generating unit commitment (UC) problems. The UC problem involves determining the start-up and shutdown schedules for generating units to meet the forecasted demand at the minimum cost. The commitment schedule must satisfy other constraints such as the generating limits per unit, reserve and individual units. First, we combined the IA and GA, then we added the chaos search and the fuzzy system approach. This hybrid system was then used to solve the UC problems. Numerical simulations were carried out using three cases: 10, 20 and 30 thermal unit power systems over a 24 h period. The produced schedule was compared with several other methods, such as dynamic programming (DP), Lagrangian relaxation (LR), Standard genetic algorithm (SGA), traditional simulated annealing (TSA), and Traditional Tabu Search (TTS). A comparison with an IGA combined with the Chaos Search and FS was carried out. The results show that the Chaos Search and FS all make substantial contributions to the IGA. The result demonstrated the accuracy of the proposed CIGAFS approach.     

Reliability based generator maintenance scheduling using hybrid evolutionary approach

With the growth of electrical energy demand, providing reliable energy without interruption has become very important nowadays. Maintenance scheduling of generating units is one of the crucial factors in delivering reliable electrical energy to the vital industrial and urban loads. As number of generating units and constraints over their operation is increasing, there is growing need for developing new methods for planning optimal outage of generating units for maintenance. This paper presents a hybrid evolutionary algorithm to tackle the reliability based generator maintenance scheduling problem. Uncertainties in the generating units and the load variations are included so that a more realistic scheduling is obtained. Maintenance scheduling problem is a large scale constrained optimization problem with a large number of variables which needs novel methods to cope with it. A new local search method which is derived from Extremal Optimization (EO) and Genetic Algorithm (GA) is presented to tackle the problem. The proposed method can be used as a local optimizer to further improve the potential solutions in the GA. The proposed method, Hill Climbing Technique (HCT), GA and their hybrid approaches are applied to the IEEE Reliability Test System (RTS) and the obtained results are discussed.     

A hybrid firefly algorithm and pattern search technique for automatic generation control of multi area power systems

In this paper, a novel hybrid Firefly Algorithm and Pattern Search (hFA–PS) technique is proposed for Automatic Generation Control (AGC) of multi-area power systems with the consideration of Generation Rate Constraint (GRC). Initially a two area non-reheat thermal system with Proportional Integral Derivative (PID) controller is considered and the parameters of PID controllers are optimized by Firefly Algorithm (FA) employing an Integral Time multiply Absolute Error (ITAE) objective function. Pattern Search (PS) is then employed to fine tune the best solution provided by FA. The superiority of the proposed hFA–PS based PID controller has been demonstrated by comparing the results with some recently published modern heuristic optimization techniques such as Bacteria Foraging Optimization Algorithm (BFOA), Genetic Algorithm (GA) and conventional Ziegler Nichols (ZN) based PI/PID controllers for the same interconnected power system. Furthermore, sensitivity analysis is performed to show the robustness of the optimized controller parameters by varying the system parameters and operating load conditions from their nominal values. Finally, the proposed approach is extended to multi area multi source hydro thermal power system with/without considering the effect of physical constraints such as time delay, reheat turbine, GRC, and Governor Dead Band (GDB) nonlinearity. The controller parameters of each area are optimized under normal and varied conditions using proposed hFA–PS technique. It is observed that the proposed technique is able to handle nonlinearity and physical constraints in the system model.     

Multiple tabu search algorithm for economic dispatch problem considering valve-point effects

This paper presents a multiple tabu search (MTS) algorithm to solve the economic dispatch (ED) problem by taking valve-point effects into consideration. The practical ED problem with valve-point effects is represented as a non-smooth optimization problem with equality and inequality constraints that make the problem of finding the global or near global optimum difficult. The proposed MTS algorithm is the sequential execution of individual tabu search (TS) algorithm simultaneously by only one personal microcomputer. The MTS algorithm introduces additional techniques for improvement of search process, such as initialization, adaptive searches, multiple searches, replacing and restarting process. To show its effectiveness, the MTS is applied to test two studied systems consisting of 13 and 40 power generating units with valve-point effects. The optimized results by MTS are compared with those of conventional approaches, such as simulated annealing (SA), genetic algorithm (GA), TS algorithm and particle swarm optimization (PSO). Studied results confirm that the proposed MTS approach is capable of obtaining higher quality solution efficiently and lowest computational time.     

Short-term hydrothermal scheduling through evolutionary programming technique

An efficient short-term hydrothermal scheduling algorithm based on the evolutionary programming (EP) technique is proposed. In the algorithm, the thermal generating units in the system are represented by an equivalent unit. The power balance constraints, total water discharge constraint, reservoir volume constraints and the constraints on the operation limits of the equivalent thermal and hydro units are fully taken into account. The effectiveness of the proposed algorithm is demonstrated through an example system and the results are compared with those obtained by the classical gradient search and simulated annealing (SA) approaches. Numerical results show that the proposed EP approach provides a cheaper schedule even than the SA approach and hence, has more powerful ability to achieve the global optimum solution than the SA approach.     

A novel hybrid PSO-PS optimized fuzzy PI controller for AGC in multi area interconnected power systems

In this paper, a novel hybrid Particle Swarm Optimization (PSO) and Pattern Search (PS) optimized fuzzy PI controller is proposed for Automatic Generation Control (AGC) of multi area power systems. Initially a two area non-reheat thermal system is used and the gains of the fuzzy PI controller are optimized employing a hybrid PSO and PS (hPSO-PS) optimization technique. The superiority of the proposed fuzzy PI controller has been shown by comparing the results with Bacteria Foraging Optimization Algorithm (BFOA), Genetic Algorithm (GA), conventional Ziegler Nichols (ZN), Differential Evolution (DE) and hybrid BFOA and PSO based PI controllers for the same interconnected power system. Additionally, the proposed approach is further extended to multi source multi area hydro thermal power system with/without HVDC link. The superiority of the proposed approach is shown by comparing the results with some recently published approaches such as ZN tuned PI, Variable Structure System (VSS) based ZN tuned PI, GA tuned PI, VSS based GA tuned PI, Fuzzy Gain Scheduling (FGS) and VSS based FGS for the identical power systems. Further, sensitivity analysis is carried out which demonstrates the ability of the proposed approach to wide changes in system parameters, size and position of step load perturbation The proposed approach is also extended to a non-linear power system model by considering the effect of governor dead band non-linearity and the superiority of the proposed approach is shown by comparing the results of hybrid BFO-PSO and craziness based PSO approach for the identical interconnected power system. Finally, the study is extended to a three area system considering both thermal and hydro units with different controllers in each area and the results are compared with hybrid BFO-PSO and ANFIS approaches.     

Differential evolution algorithm for emission constrained economic power dispatch problem

In this paper, a differential evolution (DE) algorithm is developed to solve emission constrained economic power dispatch (ECEPD) problem. Traditionally electric power systems are operated in such a way that the total fuel cost is minimized regardless of emissions produced. With increased requirements for environmental protection, alternative strategies are required. The proposed algorithm attempts to reduce the production of atmospheric emissions such as sulfur oxides and nitrogen oxides, caused by the operation of fossil-fueled thermal generation. Such reduction is achieved by including emissions as a constraint in the objective of the overall dispatching problem. A simple constraint approach to handle the system constraints is proposed. The performance of the proposed algorithm is tested on standard IEEE 30-bus system and is compared with conventional methods. The results obtained demonstrate the effectiveness of the proposed algorithm for solving the emission constrained economic power dispatch problem.     

A solution method using neural networks for the generator commitment problem

This paper studies the feasibility of applying the Hopfield-type neural network to unit commitment problems in a large power system. The unit commitment problem is to determine an optimal schedule of what thermal generation units must be started or shut off to meet the anticipated demand; it can be formulated as a complicated mixed integer programming problem with a number of equality and inequality constraints. In our approach, the neural network gives the on/off states of thermal units at each period and then the output power of each unit is adjusted to meet the total demand. Another feature of our approach is that an ad hoc neural network is installed to satisfy inequality constraints which take into account standby reserve constraints and minimum up/down time constraints. The proposed neural network approach has been applied to solve a generator scheduling problem involving 30 units and 24 time periods; results obtained were close to those obtained using the Lagrange relaxation method.     

Unit Commitment solution using an optimized genetic system

This paper presents an investigation into the application of an optimized Genetic Algorithm (GA) to solve the Thermal Unit Commitment (UC) problem. A Parallel structure was first developed to handle the infeasibility problem in a structured and improved GA which provides an effective search process and therefore greater economy. The proposed methodology resulted in a better performance with faster operation by using both computational methods and classification of unit characteristics. Typical constraints such as system power balance, minimum up and down times, start-up and shut-down ramps, have also been considered. A number of important parameters (standard and new parameters) of the UC problem have been identified. The proposed method is implemented and tested using a C# program. The tests are carried out using two systems including 10 and 20 units during a scheduling period of 24 h. The results are finally compared with those obtained from genetic schemes in other similar investigations through which the effectiveness of the proposed scheme is affirmed.     

Reliability constrained generation expansion planning by a modified shuffled frog leaping algorithm

This paper introduces a modified shuffled frog leaping algorithm (MSFLA) to solve reliability constrained generation expansion planning (GEP) problem. GEP, as a crucial issue in power systems, is a highly constrained non-linear discrete dynamic optimization problem. To solve this complicated problem by MSFLA, a new frog leaping rule, associated with a new strategy for frog distribution into memeplexes, is proposed to improve the local exploration and performance of the SFLA. Furthermore, integer encoding, mapping procedure and penalty factor approach are implemented to improve the efficiency of the proposed methodology. To show the effectiveness of the method, it is applied to a test system for two planning horizon of 12 and 24 years. For the sake of methodology validation, an ordinary SFLA as well as a Genetic Algorithm (GA) are both applied to solve the same problem. Simulation results show the advantages of the proposed MSFLA over the SFLA and GA.     

Short-term hydro-thermal dispatch detailed model and solutions

An efficient method is described for the solution of the short-term hydro-thermal dispatch problem including optimal power flow (OPF) as the mathematical model of the thermal subsystem. This approach has the capability of taking into account the following effects: coupling of cascaded multichannel reservoirs, water time delays, reservoir head variations, load flow, and other constraints due to security and environmental considerations. The problem is decomposed into hydro and thermal subproblems which are then solved iteratively. An effective adjustment has been proposed to take into account the nonlinear relation between the two subproblems to speed up the convergence of the iterative process. In this adjustment, as well as in solving the thermal subproblem, equations of coordination and OPF are combined for better computational efficiency. On the basis of the proposed approach, four different methods, which differ in the degree of details in modeling the thermal system, have been tested and investigated. Numerical examples are included to demonstrate the advantages of the approach