Economic dispatch with valve point effect using iteration particle swarm optimization

Economical dispatch of power is a significant real time optimization problem in the operation of power system, which allocates the loads on the committed generating units to reduce the generation cost, while meeting all the inequality and equality constraints. Traditionally, economic load dispatch problems have been formulated as convex optimization problem and various classical methods such as gradient methods, base-point participation factor method, etc. have been used for solving them. The traditional formulation is a quadratic input-output curve or piece wise linear cost curve, which are continuous and convex, however, real generating units have valve loading effects, which make the cost curve discontinuous and non-convex and hence the economic dispatch problem is no longer simple to handle. Thus, the classical methods cannot be employed for non-convex problems. The non-convex, non-linear and discontinuous economic dispatch (ED) problem can be better solved by metaheuristic approaches. Such approaches often require tuning of their respective evolutionary parameters. Although, solution to such type of problem have already been solved by different metaheuristic optimization techniques in previous studies as well, however, the algorithm employed in this paper to solve Power Economic Load Dispatch (PELD) problem is adaptive real coded quantum-inspired evolutionary algorithm, which does not require tuning of evolutionary parameters and performs better than some of the existing techniques on standard 6-bus 3 machine system and IEEE 14 bus 5 unit system.

This paper proposes a new differential evolution optimization (DE) strategy namely, Self-Realized Differential Evolution (SRDE) for solving the economic dispatch (ED) problem with non-smooth cost functions in power systems. The proposed SRDE is in the structure of differential evolution owning new mutation operation and selection mechanism. An effective constraint handling method is presented in the suggested stochastic search technique. The proposed approach has been examined and tested with the numerical results of ED problems with forty-generation units including ramp rate limits, prohibited operating zones and valve-point loading effects also ten-generation units with multiple fuel options. The results of the proposed technique are compared with that of other techniques reported in the literature. For both the cases, the proposed algorithm outperforms the solution reported for the existing algorithms. In addition, the promising results show the robustness, fast convergence and efficiency of the proposed technique.

This paper presents an efficient approach for solving economic dispatch(ED) problem with non-convex cost functions using particle swarm optimization with time varying acceleration coefficients. PSO_TVAC is applied to 3, 13, & 14 unit test system with and without valve point loading effects. The results of PSO_TVAC are compared with PSO From simulation results, it is clear that PSO_TVAC performance is better than many well settled nature inspired algorithms.Economic dispatch is one of the key functions of the modern energy management system. Classical particle swarm optimization (PSO) algorithm is capable of achieving near global solutions for such problems but it tends to converge prematurely. The practical Non Convex Economic Dispatch problem is solved here using PSO with a novel parameter automation strategy in which time varying acceleration coefficients (TVAC) are employed to efficiently control the local and global search, such that premature convergence is avoided and global solutions are achieved.

The Economic Dispatch (ED) is one of the most important optimization problems in power systems the ultimate goal of the ED is to minimize the cost of operations in a power generation. In this paper, the Woodpecker Mating Algorithm (WMA) is used to solve the ED problem considering the nonlinear properties of generators such as valve point effects (VPE), prohibited operating zones (POZ), ramp rate limits, multiple fuel options, and transmission loss. The WMA algorithm is a novel metaheuristic algorithm inspired by the mating behavior of woodpeckers and sound intensity (a physical quantity). The WMA is implemented on six test systems of different operational dimensions and characteristics to show its capacity for solving the ED problem. The results are compared with the latest and most efficient methods introduced in the literature. Proving the efficiency of the WMA to solve the ED problem, simulation results are promising and offer the optimal fuel cost of production.

This paper presents a particle swarm optimization (PSO) to solve hard combinatorial constrained optimization problems such as nonconvex and discontinuous economic dispatch (ED) problem of large thermal power plants. Several measures have been suggested in the control equation of the classical PSO by modifying its operators for better exploration and exploitation. The inertia operator of the PSO is modulated by introducing a new truncated sinusoidal function. The cognitive and social behaviors are dynamically controlled by suggesting new exponential constriction functions. The overall methodology effectively regulates the velocity of particles during their flight and results in substantial improvement in the classical PSO. The effectiveness of the proposed method has been tested for economic load dispatch of three standard test systems considering various operational constraints like valve-point loading effect, prohibited operating zones (POZs), network power loss, and so forth. The application results show that the proposed PSO method is very promising.

Economic load dispatch (ELD) performs an important part in the economic operation of power system. The ELD problem is considered as a non-linear constrained optimisation problem. The problem becomes non-convex and non-smooth when the generators’ prohibited zones and valve-point effect are considered. The purpose of this work is to present a solution strategy to solve ELD problem in an efficient way while considering several aspects of ELD. The strategy employs a hybrid mechanism involving a quantum mechanics inspired particle swarm optimisation (PSO). The conventional PSO is modified by integrating quantum mechanics theory that redefines the particles positions and velocities in more diverse manner and therefore explores more search space. The PSO is further upgraded from a single population-based to a multi-population one. Such feature of the method delivers a fine balance between the local and global searching abilities. The simulations are carried by considering several cases of thermal units by varying different combinations of system configurations such as with/without valve-point effect, with/without network loss and for one or several hours of load demand. The results are quite promising and effective compared with several benchmark methods.

Firefly Algorithm for solving non-convex economic dispatch problems with valve loading effect

Solving non-convex economic load dispatch problem via artificial cooperative search algorithm

In this paper, an effective and reliable variant of particle swarm optimization with time-varying acceleration coefficients (PSO-TVAC) technique is proposed for the economic load dispatch problem considering valve-point loading effect. Main objective of the economic load dispatch (ELD) problem is to minimize the fuel cost by allocating the generation of the committed units subjected to the equality and inequality constraints. Equation of the economic dispatch objective function gets modified with the addition of a new parameter which represents the effect of valve-point loading. While exploring the use of PSO and its other variants to the economic dispatch problem, a number of research works have not considered the transmission losses properly. This paper represents the usefulness of the proposed PSO-TVAC algorithm to significantly reduce the fuel cost while taking into account the effect of transmission losses along with the non-convex characteristic due to valve loading. The results have been demonstrated for three-generator and ten-generator test systems.

The objective of the economic dispatch problem of electrical power generation is to schedule the committed generating unit's output so as to meet the required load demand while satisfying the system equality and inequality constraints. This paper solves the combined economic emission dispatch problem by Min-Max and Max-Max price penalty factor approaches using Lagrange's method. The price penalty factor for the combined economic emission dispatch (CEED) is the ratio of fuel cost to emission value. The literature papers reported that most of them use Max-Max Price penalty factor for the CEED problem. This paper analyses Min-Max and Max-Max price penalty factors for CEED problem. This problem is solved for a five generator system by considering the valve point effect for both fuel cost and emission function. The total fuel cost by considering valve point effect of the combined economic emission dispatch problem is less when using Min-Max price penalty factor approach in comparison to Max-Max price penalty factor.

In the current scenario Economic Dispatch problem has taken a suitable twist as the public has become increasingly concerned with environmental matters. The dispatch of systems to minimise pollutants, as well as to achieve minimum cost are the two main constraints to be dealt with. In this paper, Global optimization techniques such as Honey Bee’s and Simulated Annealing techniques are employed together (HB-SA) to solve the Combined static Economic and Emission dispatch (CEED) problems in power system. This paper clearly is justified with the results, separately obtained for the above two techniques and is also provided with the results on applying both the algorithms separately. With practical consideration, Economic Dispatch will have non-smooth cost functions with equality and inequality constraints that make the problem, a large-scale highly constrained non linear optimization problem. As to demonstrate the effectiveness of the proposed method, it is subjected to the CEED problems considering (or) handling valve point loading effects. Comparison with other optimization techniques showed the superiority of the proposed HB-SA approach and confirmed its potential for solving nonlinear CEED problems.

An efficient optimization procedure based on oppositional chemical reaction optimization (OCRO) is proposed for the solution of economic load dispatch (ELD) problem with continuous and non-smooth cost function having valve point effect and multi-fuel options with various constraints. To accelerate the convergence speed and improve the simulation results, opposition based learning (OBL) is incorporated with the basic CRO algorithm. OCRO deals with the formation and breaking of chemical bonds in a chemical reaction. To show the potential of the proposed oppositional CRO algorithm, it has been applied to two different test systems namely, a 10-generator system along with multiple fuel options and 40 unit system having valve-point effects and transmission loss in the system. Comparing with the other existing techniques, the current proposal is found better than other techniques available in the literature. The proposed method is considered to be a promising alternative approach for solving the ELD problems in practical power system.

Due to growing concerns over environmental protection, economic and environmentally responsible power dispatching has become a hot topic in the field of power system control. Multi-objective optimization minimizes fuel costs and pollution emissions without violating operational constraints. To solve this problem, the MOP is decomposed into individual objects via the weighted sum method, and Newton’s method is used to tackle equality constraints iteratively. To this end, a hybrid algorithm (HKSOPSO-CP) based on kernel search optimization (KSO) and particle swarm optimization (PSO) with Cauchy perturbation is proposed in this paper. An experiment with 23 CEC benchmark functions shows that HKSOPSO-CP offers better performance compared with various popular algorithms proposed in recent years. When employed to solve the IEEE standard economic emission dispatch (EED) problems with 6, 10, 40, and 110 units, the proposed HKSOPSO-CP algorithm produces results indicating a better trade-off between the objectives relating to fuel costs and emissions compared to other algorithms that have recently been reported on in the literature.

Solving non-convex economic dispatch problem with valve point effects using modified group search optimizer method

Economic load dispatch is one of the vital purposes in electrical power system operation, management and planning. Economic dispatch problem is one of the most important problems in electric power system operation. In large scale system, the problem is more complex and difficult to find out optimal solution because it is nonlinear function and it contains number of local optimal. Combined economic emission dispatch (CEED) problem is to schedule the committed generating units outputs to meet the required load demand at minimum operating cost with minimum emission simultaneously. The main aim of economic load dispatch is to reduce the total production cost of the generating system and at the same time the necessary equality and inequality constraints should also be fulfilled. This leads to the development of CEED techniques. There are various techniques proposed by several researchers to solve CEED problem based on optimization techniques. But still some problems such as slower convergence and higher computational complexity exist in using the optimization techniques such as GA for solving CEED problem. This paper proposes an efficient and reliable technique for combined fuel cost economic optimization and emission dispatch using the Modified Ant Colony Optimization algorithm (MACO) to produce better optimal solution. The simulation results reveal the significant performance of the proposed MACO approach.