Teaching learning based optimization for economic load dispatch problem considering valve point loading effect

This paper presents a novel teaching learning based optimization (TLBO) technique to solve economic load dispatch (ELD) of the thermal unit without considering transmission losses. The proposed methodology can take care of ELD considering nonlinearity such as valve point loading. The objective of economic load dispatch is to determine the optimal power generation of the units to meet the load demand, such that the overall cost of generation is minimized, while satisfying different operational constraints. TLBO is a recently developed evolutionary algorithm based on two basic concepts of education namely teaching phase and learning phase. At first, learners improve their knowledge through the teaching methodology of teacher and finally learners increase their knowledge by interactions among themselves. The effectiveness of the proposed algorithm has been verified on three different test systems with equality and inequality constraints. Compared with the other existing techniques demonstrates the superiority of the proposed algorithm.     

Improved parameters for economic dispatch problems by teaching learning optimization

The solution of Economic Dispatch (ED) problems mainly depends on the modelling of thermal generators. The physical variations such as aging and ambient temperature affect the modelling parameters and are unavoidable. As these parameters are the backbone of ED solution, the periodical estimation of these characteristics coefficients is necessary for accurate dispatch. The process is formulated as an error minimization problem and a nature inspired algorithm namely Teaching Learning Based Optimization (TLBO) is proposed as an estimator. This work provides a frame work for the computation of coefficients for quadratic and cubic cost functions, valve point loading, piece-wise quadratic cost and emission functions. The effectiveness of TLBO is demonstrated on 5 standard test systems and a practical Indian utility system, involving varying degree of complexity. TLBO yields better results than benchmark Least Error Square (LES) method and other evolutionary algorithms. The economic deviation is also tested with existing systems.     

Optimal reactive power dispatch using quasi-oppositional teaching learning based optimization

This paper presents a newly developed teaching learning based optimization (TLBO) algorithm to solve multi-objective optimal reactive power dispatch (ORPD) problem by minimizing real power loss, voltage deviation and voltage stability index. To accelerate the convergence speed and to improve solution quality quasi-opposition based learning (QOBL) concept is incorporated in original TLBO algorithm. The proposed TLBO and quasi-oppositional TLBO (QOTLBO) approaches are implemented on standard IEEE 30-bus and IEEE 118-bus test systems. Results demonstrate superiority in terms of solution quality of the proposed QOTLBO approach over original TLBO and other optimization techniques and confirm its potential to solve the ORPD problem.     

Multi-objective quasi-oppositional teaching learning based optimization for economic emission load dispatch problem

This paper proposes an efficient optimization approach, namely quasi-oppositional teaching learning based optimization (QOTLBO) for solving non-linear multi-objective economic emission dispatch (EED) problem of electric power generation with valve point loading. In this article, a non-dominated sorting QOTLBO is employed to approximate the set of Pareto solution through the evolutionary optimization process. The proposed approach is carried out to obtain EED solution for 6-unit, 10-unit and 40-unit systems. For showing the superiority of this optimization technique, numerical results of the four test systems are compared with several other EED based recent optimization methods. The simulation results show that the proposed algorithm gives comparatively better operational fuel cost and emission in less computational time compared to other optimization techniques.     

Kinetic gas molecule optimization for nonconvex economic dispatch problem

This paper presents kinetic gas molecule optimization (KGMO) algorithm to solve economic dispatch problems with non-smooth/non-convex cost functions. KGMO is based on kinetic energy and the natural motion of gas molecules. The effectiveness of the proposed method has been verified on four different non-convex economic dispatch problems with valve-point effects, prohibited operating zones with transmission losses, multiple fuels with valve point effects and the large-scale Korean power system with valve-point effects and prohibited operating zones. The results of the proposed approach are compared with those obtained by other evolutionary methods. It is found that the proposed KGMO based approach is able to provide better solution.     

A new rooted tree optimization algorithm for economic dispatch with valve-point effect

This work proposes a new optimization method called root tree optimization algorithm (RTO). The robustness and efficiency of the proposed RTO algorithm is validated on a 23 standard benchmark nonlinear functions and compared with well-known methods by addressing the same problem. Simulation results show effectiveness of the proposed RTO algorithm in term of solution quality and convergence characteristics. In order to evaluate the effectiveness of the proposed method, 3-unit, 30 Bus IEEE, 13-unit and 15-units are used as case studies with incremental fuel cost functions. The constraints include ramp rate limits, prohibited operating zones and the valve point effect. These constraints make the economic dispatch (ED) problem a non-convex minimization problem with constraints. Simulation results obtained by the proposed algorithm are compared with the results obtained using other methods available in the literature. Based on the numerical results, the proposed RTO algorithm is able to provide better solutions than other reported techniques in terms of fuel cost and robustness.     

Active power based distance protectionscheme in the presence of seriescompensators

This paper presents opposition-based differential evolution to determine the optimal hourly schedule of power generation in a hydrothermal system. Differential evolution (DE) is a population-based stochastic parallel search evolutionary algorithm. Opposition-based differential evolution has been used here to improve the effectiveness and quality of the solution. The proposed opposition-based differential evolution (ODE) employs opposition-based learning (OBL) for population initialization and also for generation jumping. The effectiveness of the proposed method has been verified on two test problems, two fixed head hydrothermal test systems and three hydrothermal multi-reservoir cascaded hydroelectric test systems having prohibited operating zones and thermal units with valve point loading. The results of the proposed approach are compared with those obtained by other evolutionary methods. It is found that the proposed opposition-based differential evolution based approach is able to provide better solution.     

Opposition-based differential evolution for hydrothermal power system

This paper presents opposition-based differential evolution to determine the optimal hourly schedule of power generation in a hydrothermal system. Differential evolution (DE) is a population-based stochastic parallel search evolutionary algorithm. Opposition-based differential evolution has been used here to improve the effectiveness and quality of the solution. The proposed opposition-based differential evolution (ODE) employs opposition-based learning (OBL) for population initialization and also for generation jumping. The effectiveness of the proposed method has been verified on two test problems, two fixed head hydrothermal test systems and three hydrothermal multi-reservoir cascaded hydroelectric test systems having prohibited operating zones and thermal units with valve point loading. The results of the proposed approach are compared with those obtained by other evolutionary methods. It is found that the proposed opposition-based differential evolution based approach is able to provide better solution     

Comparative performance analysis of teaching learning based optimization for automatic load frequency control of multi-source power systems

This paper presents a new population based parameter free optimization algorithm as teaching learning based optimization (TLBO) and its application to automatic load frequency control (ALFC) of multi-source power system having thermal, hydro and gas power plants. The proposed method is based on the effect of the influence of teacher on the output of learners and the learners can enhance their knowledge by interactions among themselves in a class. In this extensive study, the algorithm is applied in multi area and multi-source realistic power system without and with DC link between two areas in order to tune the PID controller which is used for automatic generation control (AGC). The potential and effectiveness of the proposed algorithm is compared with that of differential evolution algorithm (DE) and optimal output feedback controller tuning performance for the same power systems. The dynamic performance of proposed controller is investigated by different cost functions like integral of absolute error (IAE), integral of squared error (ISE), integral of time weighted squared error (ITSE) and integral of time multiplied absolute error (ITAE) and the robustness of the optimized controller is verified by its response toward changing in load and system parameters. It is found that the dynamic performance of the proposed controller is better than that of recently published DE optimized controller and optimal output feedback controller and also the proposed system is more robust and stable to wide changes in system loading, parameters, size and locations of step load perturbation and different cost functions.     

An intelligent θ-Modified Bat Algorithm to solve the non-convex economic dispatch problem considering practical constraints

This paper proposes a practical formulation for the non-convex economic dispatch problem to consider multi-fuel options, ramp rate limits, valve loading effect, prohibited operating zones and spinning reserve. A new optimization algorithm based on the θ-bat algorithm (θ-BA) is suggested to solve the problem. The θ-BA converts the Cartesian search space into the polar coordinates such that more search ability would be achieved. According to the complex, nonlinear, and constrained nature of the problem, a new self-adaptive modification method is proposed. The proposed modified θ-BA (θ-MBA) is constructed based on the roulette wheel mechanism to effectively increase the convergence of the algorithm. The high ability and satisfying performance of the proposed optimization method is examined on IEEE 15-unit, 40-unit and 100-unit test systems.     

Combined heat and power economic dispatch using opposition-based group search optimization

This paper presents opposition-based group search optimization to solve non-smooth non-convex combined heat and power economic dispatch problem. Valve-point loading and prohibited operating zones of conventional thermal generators are taken into account. Group search optimization inspired by the animal searching behavior is a biologically realistic algorithm. Opposition-based group search optimization has been used here to improve the effectiveness and quality of the solution. The proposed opposition-based group search optimization employs opposition-based learning for population initialization and also for iteration wise update operation. The effectiveness of the proposed method has been verified on four test systems. The results of the proposed approach are compared with those obtained by other evolutionary methods. It is found that the proposed opposition-based group search optimization based approach is able to provide better solution.     

求解非光滑燃料费用函数的基于进化规划的机组最优潮流

提出求解具有非光滑燃料费用函数的存在爬坡率限制的最优潮流方法。针对两次、阶梯形、联合循环机组的非光滑燃料费用函数,介绍一个基于进化规划的算法。在该算法中,为避免早熟,交叉操作随后代的数目非线性变化。介绍了所提出的进化算法应用于有线路约束的IEEE30节点系统和印度62节点系统的情况。以MVA为单位的线路潮流直接采用牛顿-拉夫逊法计算。算例证明所提出的进化算法简单,对求解具有非光滑燃料费用函数的存在很多约束的最优潮流问题有效。     

An improved PSO technique for short-term optimal hydrothermal scheduling

This paper presents a new approach to the solution of optimal power generation to short-term hydrothermal scheduling problem, using improved particle swarm optimization (IPSO) technique. The practical hydrothermal system is highly complex and possesses nonlinear relationship of the problem variables, cascading nature of hydraulic network, water transport delay and scheduling time linkage that make the problem of finding global optimum difficult using standard optimization methods. In this paper an improved PSO technique is suggested that deals with an inequality constraint treatment mechanism called as dynamic search-space squeezing strategy to accelerate the optimization process and simultaneously, the inherent basics of conventional PSO algorithm is preserved. To show its efficiency and robustness, the proposed IPSO is applied on a multi-reservoir cascaded hydro-electric system having prohibited operating zones and a thermal unit with valve point loading. Numerical results are compared with those obtained by dynamic programming (DP), nonlinear programming (NLP), evolutionary programming (EP) and differential evolution (DE) approaches. The simulation results reveal that the proposed IPSO appears to be the best in terms of convergence speed, solution time and minimum cost when compared with established methods like EP and DE.     

Modified particle swarm optimization for nonconvex economic dispatch problems

This paper presents modified particle swarm optimization to solve economic dispatch problems with non-smooth/non-convex cost functions. Particle swarm optimization performs well for small dimensional and less complicated problems but fails to locate global minima for complex multi-minima functions. This paper proposes Gaussian random variables in velocity term which improves search efficiency and guarantees a high probability of obtaining the global optimum without considerably worsening the speed of convergence and the simplicity of the structure of particle swarm optimization. The efficacy of the proposed method has been demonstrated on four test problems and four different non-convex economic dispatch problems with valve-point effects, prohibited operating zones with transmission losses, multiple fuels with valve point effects and the large-scale Korean power system with valve-point effects and prohibited operating zones. The results of the proposed approach are compared with those obtained by other evolutionary methods reported in the literature. It is found that the proposed modified particle swarm optimization based approach is able to provide better solution.     

Chaotic self-adaptive differential harmony search algorithm based dynamic economic dispatch

Dynamic economic dispatch (DED) is one of the main optimization problems in electrical power system operation and control. DED problem is a non-smooth and non-convex problem when valve point effect, ramp-rate limits and prohibited operating zones of generation units are taken into account. This paper proposes an efficient chaotic self-adaptive differential harmony search (CSADHS) algorithm to solve the complicated DED problem in the presence of valve point effect, ramp-rate limits and prohibited operating zones constraints. In the proposed algorithm, chaotic self-adaptive differential mutation operator is used instead of pitch adjustment operator in the harmony search (HS) algorithm, to enhance the searching performance to find the quality solution. The effectiveness of the proposed algorithm is demonstrated on 10, 15 and 30 unit systems for a period of 24 h. The simulation results obtained by the proposed algorithm are compared with the results obtained, using differential harmony search (DHS) algorithm, chaotic differential harmony search (CDHS) algorithm, and also with the results of other methods available in the literature. In terms of solution quality, the proposed algorithm is found to be better than other algorithms and in terms of speed of convergence, standard deviation of generation cost, and computational time, the proposed algorithm is better than DHS and CDHS algorithm.     

Combined economic and emission dispatch problems using biogeography-based optimization

In this work, biogeography-based optimization (BBO) is presented for solving different constrained economic load dispatch (ELD) problems combined with economic emission aspects in power system. Nonlinear characteristics of generators like valve point discontinuities, ramp rate limits and prohibited operating zones are considered in the problem. The simulation results show that the proposed BBO algorithm based solutions prove to be the best near-global optimal as compared to the solutions based on Newton–Raphson, Tabu search, genetic algorithm (GA), non-dominated sorting genetic algorithm (NSGA), fuzzy logic controlled genetic algorithm (FCGA), particle swarm optimization (PSO) and differential evolution (DE).     

Security constrained optimal power flow considering detailed generator model by a new robust differential evolution algorithm

This paper presents a new multiobjective model, including two objective functions of generation cost and voltage stability margin, for optimal power flow (OPF) problem. Moreover, the proposed OPF formulation contains a detailed generator model including active/reactive power generation limits, valve loading effects, multiple fuel options and prohibited operating zones of units. Furthermore, security constraints, including bus voltage limits and branch flow limits in both steady state and post-contingency state of credible contingencies, are also taken into account in the proposed formulation. To solve this OPF problem a novel robust differential evolution algorithm (RDEA) owning a new recombination operator is presented. The proposed RDEA has a minimum number of adjustable parameters. Besides, a new constraint handling method is also presented, which enhances the efficiency of the RDEA to search the solution space. To show the efficiency and advantages of the proposed solution method, it is applied to several test systems having complex solution spaces and compared with several of the most recently published approaches.     

Non-convex economic dispatch with heuristic load patterns, valve point loading effect, prohibited operating zones, ramp-rate limits and spinning reserve constraints using harmony search algorithm

This paper attempts to investigate the applicability of harmony search algorithm (HSA) to solve extremely challenging non-convex economic load dispatch problem with valve point loading effect, prohibited operating zones, ramp-rate limits, spinning reserve constrains and transmission losses involving variations of consumer load patterns. The performance of the proposed approach HSA has been tested successfully on the standard 6-bus, IEEE-14 bus and IEEE-30 bus system with several heuristic load patterns. The results of this study reveals that the proposed approach is able to find appreciable economical load dispatch solutions than those of improved fast evolutionary program and particle swarm optimization. Besides this, the transmission line losses are also considerably reduced and the computation time is reasonably even and less when compared to other methods.     

Solving dynamic economic dispatch problem with security constraints using bacterial foraging PSO-DE algorithm

This paper presents a heuristic optimization methodology, namely, Bacterial foraging PSO-DE (BPSO-DE) algorithm by integrating Bacterial Foraging Optimization Algorithm (BFOA), Particle Swarm Optimization (PSO) and Differential Evolution (DE) for solving non-smooth non-convex Dynamic Economic Dispatch (DED) problem. The DED problem exhibits non-smooth, non-convex nature due to valve-point loading effects, ramp rate limits, spinning reserve capacity, prohibited operating zones and security constraints. The proposed hybrid method eliminates the problem of stagnation of solution with the incorporated PSO and DE operators in original bacterial foraging algorithm. It achieves global cost by selecting the bacterium with good foraging strategies. The bacteria with good foraging strategies are obtained in the updating process of every chemo-tactic step by the PSO operator. The DE operator fine tunes the solution obtained through bacterial foraging and PSO operator. A 3- and 7-unit systems for static economic dispatch, a 26-bus, 6-generator test system and an IEEE 39-bus, 10-unit New England test systems are considered to show the effectiveness of the proposed method over other methods reported in the literature.     

An improved harmony search algorithm to solve economic load dispatch problems with generator constraints

This paper presents a new improved harmony search (IHS) algorithm to solve non-convex economic load dispatch problems in the power system. In the proposed IHS algorithm, multiple harmony memory consideration rates and dynamic pitch adjusting rate are used to generate a new harmony/solution vector with enhanced solution quality. The effectiveness of the proposed IHS algorithm has been successfully tested in the test systems which consists of six units with ramp rate limits, prohibited operating zones and transmission loss, thirteen units with valve point effect, and ten units with multiple fuel options and valve point effect. The results obtained using the proposed IHS algorithm are compared with the results of other techniques reported in the literature. The comparative results reveal that the proposed IHS algorithm has good searching capacity to find the global optimal solution, than the other methods reported in the literature and also has good convergence characteristic.