Power Economic Dispatch Research Articles

Genetic Algorithm-based Cost Optimization Model for Power Economic Dispatch Problem

Genetic Algorithm-based Cost Optimization Model for Power Economic Dispatch Problem

A nonlinear fractional programming approach for environmental–economic power dispatch

Abstract A nonlinear fractional programming approach is provided for addressing the environmental–economic power dispatch problems in the thermal power dispatch systems. The objective of this study is to simultaneously minimize the total fuel cost and total emissions of the power dispatch systems, which is realized by two simultaneous models with nonlinear constraints. The first model is to minimize the quotient of two competing and conflicting functions (i.e. [total emission function]/[total fuel cost function]), and the second one is to minimize the total fuel cost expressed by a quadratic objective function. In particular, the process of solving the first model uses Dinkelbach’s algorithm to convert the minimization problem with the nonlinear fractional objective function into a sequence of non-fractional minimization problems. The effectiveness of this approach is demonstrated through applying to the standard IEEE 30-bus test system. Comparison between the present approach and other existing approaches shows that the proposed approach can generate superior decision alternatives from the view point of realizing a more environmentally friendly and cost-effective scheme and/or considering the power transmission loss rate in the power dispatch systems.

Group search optimization for combined heat and power economic dispatch

Abstract This paper presents group search optimization to solve the complex non-smooth non-convex combined heat and power economic dispatch (CHPED) problem. Valve-point loading and prohibited operating zones of conventional thermal generators are taken into account. The effectiveness of the proposed method has been verified on four test systems. The results of the proposed approach have been compared with those obtained by other evolutionary methods. It is found that the proposed group search optimization based approach is able to provide better solution.

Applications of Harmony Search Algorithms in Engineering

In a recent article the authors reviewed the principles of harmony search and journal articles on harmony search algorithm (HSA). This article presents a review of applications of HSA including structural design, hydrologic model design, water distribution network design, water pump switching problem, transmission network expansion planning problem, job shop scheduling problem, university timetable and rosterering problem, training neural networks, clustering, combined heat and power economic dispatch problem, economic load dispatch problem, and economic and emission dispatch problem.

Cuckoo optimization algorithm with penalty function for combined heat and power economic dispatch problem

The CHPED (combined heat and power economic dispatch) is a complex engineering optimization problem. The goal is to minimize the system production costs by taking into consideration different kind of constraints. This research investigates the first implementation of a prevailing bio-inspired metaheuristic called the cuckoo optimization algorithm which is powered by a penalty function (PFCOA) for solving the CHPED problem. Two case studies of the CHPED are presented and the results are compared to those obtained by several other optimization techniques applied in the literature. It has been proven that the implemented PFCOA is superior.

Population Games Methods for Distributed Control of Microgrids

We illustrate the potential of applying population games in two key related problems in microgrids management: 1) economic dispatch of active and reactive power; and 2) demand response. For the dynamic economic dispatch problem, we present a hierarchical microgrid energy management algorithm able to dispatch active and reactive power dynamically. In the second case, we use an opinion dynamics model, including the market in which the network agents interact. Opinion dynamics considers individuals who shape their beliefs based on information they receive from a subset of the society and offers tools to analyze the outcome of collective decision processes, which apparently can be considered arbitrary. We propose an opinion dynamics model including some desired characteristics, such as prominent agents and environmental incentives.

Distributed Bisection Method for Economic Power Dispatch in Smart Grid

In this paper, we present a fully distributed bisection algorithm for the economic dispatch problem (EDP) in a smart grid scenario, with the goal to minimize the aggregated cost of a network of generators, which cooperatively furnish a given amount of power within their individual capacity constraints. Our distributed algorithm adopts the method of bisection, and is based on a consensus-like iterative method, with no need for a central decision maker or a leader node. Under strong connectivity conditions and allowance for local communications, we show that the iterative solution converges to the globally optimal solution. Furthermore, two stopping criteria are presented for the practical implementation of the proposed algorithm, for which sign consensus is defined. Finally, numerical simulations based on the IEEE 14-bus and 118-bus systems are given to illustrate the performance of the algorithm.

Modified Particle Swarm Optimization for Non-smooth Non-convex Combined Heat and Power Economic Dispatch

This article presents modified particle swarm optimization to solve the 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. Particle swarm optimization performs well for small-dimensional and less complicated problems but fails to locate global minima for complex multi-minima functions. This article proposes Gaussian random variables in the velocity term, which improves search efficiency and guarantees a high probability of obtaining the global optimum without significantly impairing the speed of convergence and the simplicity of the structure of particle swarm optimization. The effectiveness of the proposed method has been verified on two test systems. The results of the proposed approach are compared with those obtained by other evolutionary methods. It is found that the proposed modified particle swarm optimization based approach is able to provide a better solution.

Crisscross optimization algorithm for solving combined heat and power economic dispatch problem

As cogeneration plays an increasingly important role in energy utilization, the combined heat and power economic dispatch (CHPED) becomes an important task in power system operation. In this paper, a novel crisscross optimization (CSO) algorithm is implemented to solve the large scale CHPED problem, which is a challenging non-convex optimization problem with a large number of local minima. The feature of applying CSO to address the CHPED problem lies in two interacting operators, namely horizontal crossover and vertical crossover. The horizontal crossover searches for the new solutions within a half population of hyper-cubes with a large probability while in their respective peripheries with a decreasing probability. The vertical crossover provides a effective mechanism for those stagnant dimensions of a population to escape from premature convergence. The combination of both gifts CSO with a powerful global search ability. The effectiveness of the proposed method is validated on six cogeneration systems with different characteristics. The numeric results demonstrates that the proposed CSO method achieves much better results than other methods reported in the literature. To investigate the robustness and applicability of CSO in large power system, two new systems with 96 and 192 units by duplicating the system of case 4 two times and four times are also studied. The results obtained substantiates the suitability of CSO for large-scale constrained CHPED problem.

Economic dispatch optimization algorithm based on particle diffusion

Due to the widespread installation of emissions control equipment in fossil fuel-fired power plants, the cost of emissions control needs to be considered, together with the plant fuel cost, in providing economic power dispatch of those units to the grid. On the other hand, while using wind power decreases the overall power generation cost for the power grid, it poses a risk to a traditional grid, because of its inherent stochastic characteristics. Therefore, an economic dispatch optimization model needs to consider all of the fuel cost, emissions control cost and wind power cost for each of the generating unit conforming the fleet that meets the required grid power demand. In this study, an optimization algorithm referred as diffusion particle optimization (DPO) is proposed to solve such complex optimization problem. In this algorithm, Brownian motion theory is used to guide the movement of particles so that the particles can search for an optimal solution over the entire definition region. Several benchmark functions and power grid system data were used to test the performance of DPO, and compared to traditional algorithms used for economic dispatch optimization, such as, particle swarm optimization and artificial bee colony algorithm. It was found that DPO has less probability to be trapped in local optimums. According to results of different power systems DPO was able to find economic dispatch solutions with lower costs. DPO was also used to analyze the impact of wind power risk and fossil unit emissions coefficients on power dispatch. The result are encouraging for the use of DPO as a dynamic tool for economic dispatch of the power grid.

Power Line Losses of Energy for Power System with Micro-Grid Implementation

Micro-grid system is an integrated energy system as it consists of distributed energy resources (DERs) and multiple electrical loads operating in parallel or islanded grid. The primary objective of this project is to examine whether Micro-grid implementation can reduce the cost of energy. It can be determined through the modelling bus bar system; 26-Bus Test System. This application can be divided into three aspects which are modelling, simulation and analysis. The power system analysis was conducted under two conditions, steady state condition and contingencies condition using two different methods which are optimal power flow and economic dispatch. Newton-Raphson algorithm was introduced during the power flow analysis. The optimal power flow and economic dispatch for total generation cost was obtained through PowerWorld software simulation.

Backtracking search optimization based economic environmental power dispatch problems

Abstract This paper presents the solution for a nonlinear constrained multi objective of the economic and emission load dispatch (EELD) problem of thermal generators of power systems by means of the backtracking search optimization technique. Emission substance like NO X, power demand equality constraint and operating limit constraint are considered here. The aim of backtracking search optimization (BSA) is to find a global solution under the influence of two new crossover and mutation operations. BSA has capability to deal with multimodal problems due to its powerful exploration and exploitation capability. BSA is out of excessive sensitivity to control parameters as it has single control parameter. The performance of BSA is compared with existing newly developed optimization techniques in terms quality of solution obtained, computational efficiency and robustness for multi objective problems.

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

Abstract 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.

Analysis of electric vehicle charging using the traditional generation expansion planning analysis tool WASP-IV

Electric vehicles (EV) are proposed as a measure to reduce greenhouse gas emissions in transport and support increased wind power penetration across modern power systems. Optimal benefits can only be achieved, if EVs are deployed effectively, so that the exhaust emissions are not substituted by additional emissions in the electricity sector, which can be implemented using Smart Grid controls. This research presents the results of an EV roll-out in the all island grid (AIG) in Ireland using the long term generation expansion planning model called the Wien Automatic System Planning IV (WASP-IV) tool to measure carbon dioxide emissions and changes in total energy. The model incorporates all generators and operational requirements while meeting environmental emissions, fuel availability and generator operational and maintenance constraints to optimize economic dispatch and unit commitment power dispatch. In the study three distinct scenarios are investigated base case, peak and off-peak charging to simulate the impacts of EV’s in the AIG up to 2025.

Comparison between Harmony Search Algorithm, Genetic Algorithm and Particle Swarm Optimization in Economic Power Dispatch

This paper presents a solution of economic power dispatch problem using Harmony Search (HS) algorithm. The method easily takes care of equality and inequality constraints of the power dispatch problem to find the optimal solution. To show its efficiency, the algorithm is applied to IEEE 118-bus power system having 54 generating units. The problem is also solved by Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) techniques. Results have shown that Harmony Search method gives minimum cost of production of real power and minimum power loss in the system as compared to Genetic Algorithm and Particle Swarm Optimization. This shows the robustness and effectiveness of this method. Moreover, cost of real power generation in dollar per hour per megawatt output of each generator is calculated to identify the least to most expensive generator in the system.

Fast economic power dispatch method for power system planning studies

This study describes a method for solving the optimal economic power dispatch problem. The method proposed here uses linear programming, because linear programming-based formulations tend to be flexible, reliable and faster than their non-linear counterparts. The proposed linear programming-based method is developed based on a linearised network model, in which voltage magnitudes and reactive power flows have both been accounted for, unlike traditional linearised power flow methods. A piecewise linear model is developed to handle the thermal capacities of transmission lines. Piecewise linear models are also developed to deal with the exponential loads, cost functions of generators and total power losses. The effectiveness of the proposed method is demonstrated on numerous standard test systems, including the IEEE 300-bus system. Further, a comparison with some other methods, which are available in the literature, is held to validate the consistency of the proposed method in finding the optimal or near-optimal global solution. The results show that the proposed method could lead to optimal or near-optimal global solution, and is appropriate to use for power system planning studies.

Dynamic Economic Dispatch for Combined Heat and Power Units using Particle Swarm Algorithms

In this paper, combined heat and power units are incorporated in dynamic economic dispatch to minimize total production costs considering realistic constraints such as ramp rate and spinning reserve limits effects over a short time span. Four evolutionary approaches, namely particle swarm optimization (PSO), particle swarm optimization with constriction factor (PSOCFA), particle swarm optimization with inertia weight factor (PSOIWA) and particle swarm optimization with both constriction factor and inertia weight factor (PSOCFIWA) are successfully implemented to solve the combined heat and power economic dispatch (CHPED) problem. These approaches have been tested on 12-generation units system with two steam, four gas and six cogeneration units. In addition, the performance tests are applied to measure the actual power output and the fuel consumption in every point tests for achieving different curves such as input/output, incremental heat rate and heat rate curves for the twelve units. The results of the four approaches are compared with those obtained using existing performance testing method. The results show that the particle swarm optimization with improved inertia weight is able to achieve a better solution at less computational time.

Game-Theoretic Formulation of Power Dispatch With Guaranteed Convergence and Prioritized BestResponse

This paper formulates and solves the economic power dispatch (ED) problem with practical operation constraints using potential games. Each generator operates as an independent player in a self-optimizing manner with marginal contribution utility functions to minimize the total generation cost. The proposed distributed formulation converts inequality constraints into feasible action sets, incorporates equality constraints by penalty functions, and extends to practical cases that exhibit non-convex or non-smooth objective functions. Two learning algorithms with guaranteed convergence to Nash equilibria and/or optima are applied to solve the proposed formulation. How generators react as best responses to others is analyzed to capture the reasoning of operations. As a numerical example, the solutions obtained using the proposed ED method in a benchmark system are analyzed. Examples are provided to emphasize how priority for renewable sources are incorporated.

Opposition-based gravitational search algorithm applied to economic power dispatch problems consisting of thermal units with emission constraints

In this study, a multiobjective environmental economic power dispatch problem has been converted into a single-objective optimization problem using the weighted sum method. For the solution of the converted problem, the gravitational search algorithm (GSA), which is one of the latest algorithms, has been used. In order to increase the performance of the GSA, opposite positioning quality has been added to the structure of the algorithm (OGSA). The obtained results show that the proposed algorithm has obtained better results and has provided a faster convergence. The 30-bus 6-generator test system has been selected for application of the OGSA. The transmission line losses have been added to the problem by using a B loss matrix. Optimum solutions of the problem have been obtained for different weights and the results have been veried.

Coordination of combined heat and power-thermal-wind-photovoltaic units in economic load dispatch using chance-constrained and jointly distributed random variables methods

CHP (Combined heat and power) generation or cogeneration has been considered worldwide as the major alternative to traditional systems in terms of significant energy saving and environmental conservation. Furthermore, the wind power generators and photovoltaic units have vastly speared over the power systems due to their free inputs. However, there are many challenges for power system operators because of uncertain characteristics of renewable units and load demands. Therefore, a new multi-objective stochastic framework based on chance constrained programming is developed to handle combined heat and power economic load dispatch considering the stochastic characteristics of wind and photovoltaic power outputs, customer's electrical and heat load demands. The proposed technique makes use of a jointly distributed random variables method to calculate chance of meeting the electrical and heat load requirement using the target decision variables while maintaining the electrical energy cost below a scheduled value. The framework benefits from a new method named hybrid modified cuckoo search algorithm and differential evolution to extract the Pareto optimal surface for minimum cost and maximum probability of meeting the target cost and applies them as the objective functions. Applying to 6 and 40 unit test systems, the ability of the suggested framework is confirmed.