Solution to economic dispatch problem with valve-point loading effect using IPSO algorithm
Sadegh Khaleghi1, Reihane Kardehi Moghaddam2, Amir Ebrahimi Mousavi3, Elnaz Ghahremani4
1,2,3Department of Electrical Engineering, Mashhad branch, Islamic Azad University, Mashhad, Iran
4Department of Computer Engineering and Information, Amirkabir University of Technology
1Pen.khaleghi@gmail.com
2R_k_moghaddam@mshdiau.ac.ir
3 Amir.e.musavi@gmail.com
4El.ghahremani@aut.ac.ir
Abstract— This paper involves a novel application of the improved particle swarm optimization (IPSO) in an economic dispatch problem (EDP) that consists influence of valve-point loading, power balance, and generators constraints. This method is able to improve the best value of the cost function with a slight increase in the average time trials. This procedure is suitable for solving large-scale and complex economic dispatch problems. In this report, IPSO algorithm is tested on three systems and experimental results are compared with other efficient methods. Simulation results demonstrate the efficiency of proposed algorithms for solving economic dispatching problems.
Keywords: IPSO, Economic dispatch, Optimization, Valve point loading
Introduction
The main object of EDPs for generating the electricity is to adjust the output of generator unit for minimizing the final cost of them to establish a balance between demand load and generator production. Beside this numerous cases, all equal and
Government has introduced many schemes, policies and incentives in order to enhance the use of electric
One of the most significant devices that control the cost of transporting and supplying power to these units is the idea of peak units and off-peak units; where a load factor is produced and prepares the supplier based on an estimate of prospective demand. It helps the supplier to have a rough evaluation of what the demand may be or when the demand is high and when it is low. This will give the supplier better control level on supply; including
The energy industry has seen some changes by way of deregulation in the supply of energy for both businesses and residential. Giving the power to owners to choose who supplies them electric and natural gas and at what rate they want it supplied because of the competition from suppliers, some supplier offering rate as low as $0.0619 per KWH. These new regulations policy has initiated changes in the mode of operation of American electric power (AEP) with the supply of energy.
For the purpose of this discussion, the specifics of the electrical energy system in the United States are not important, rather an introduction to the basic elements of the system, who they serve, how they relate the larger whole and how they are regulated will suffice. On a most basic level the electrical grid, or system, in the United States is comprised of three basic components; the generation of electrical energy, transmission of this energy, and the distribution of this energy to end consumers.
Dispatched generator real power output should not exceed the maximum real power capability of the unit (Pgen = Pmin). Note: Although small violations of this Pmin rule appear trivial, the result is same for all violations – the case will not initialize in dynamics.
Firstly, due to the increase in automation; there are improvements to programming logic controllers (PLC’s), instrumentation devices, and emergency shut down (ESD) devices (Payne, 2014). Therefore, these improvements all contribute to a safer operation of a nuclear power plant, since there are more process feedback devices, and methods to control the process. Which, give the operator more information at the panel, allowing them to make more informed decisions when operating the plant (Payne, 2014).
iv. LP&L’s generation is not necessary for the Planning Coordinator or Transmission Provider as per Criterion 2.3.
Multi-swarm optimization is a variant of particle swarm optimization (PSO) based on the use of multiple sub-swarms instead of one (standard) swarm. The general approach in multi-swarm optimization is that each sub-swarm focuses on a specific region while a specific diversification method decides where and when to launch the sub-swarms. The multi-swarm framework is especially fitted for the optimization on multi-modal problems, where multiple (local) optima exist.
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. In order to verify the feasibility and efficiency of the proposed algorithm, RTO algorithm was applied on two set of case studies. The first set includes a 23 standard benchmark functions. The second set includes four test systems (i.e., 3, 6, 13 and 15-units systems) for solving ED problem considering various constraints.
They compared their annealing scheme leads to results with ω=1 obtained by Angeline [89], and concluded a significant performance improvement on four tested functions. The reducing ω -strategy is a near-optimum setting for many problems, as it allows the swarm to explore the search-space in the beginning of the run, and still manages to shift towards a local search when fine-tuning is required. This was named PSO-TVIW method (PSO with Time-Varying-Inertia-Weight) [90]. At the end, Eberhart and Shi devised an adaptive fuzzy PSO, where a fuzzy controller was employed to control ω over time [91]. This approach is very interesting, as it potentially lets the PSO self-adapt ω to the problem and therefore optimizes and eliminates a parameter of
PSO algorithm is developed by the social behavior patterns of the organisms that exist and interact within large groups. As, it converges at a faster rate than the global optimization algorithms, the PSO algorithm is applied for solving various optimization problems easily. In the PSO technique, a population called as a swarm of candidate solutions are encoded as particles in the search space. Initially, PSO begins with the random initialization of the population. These particles move iteratively through the D-dimensional search space to search the optimal solutions, by updating the position of each particle. During the movement of the swarm, a vector Xi=(Xi1, Xi2,…., XiD) represents the current position of the particle ‘i’. Vi=(Vi1, Vi2,…., ViD) represents the velocity of the particle which is in the range of [−vmax, vmax]. The best previous position of a particle is denoted as personal best Pbest. The global best position obtained by the population is denoted as Gbest. The PSO searches for the optimal solution by updating the velocity and position of each particle, based on the Pbest and Gbest. The next position of the particle in the search space is calculated by using the new velocity value. This process is repeated for a fixed number of times or until a minimum error is achieved. The rate of the change in the velocity and position of the particle is given as
Abstract— There is a pressing need to accelerate the development of advanced clean energy technologies in order to control the usage of the fossil fuels which are going to get diminished with in a few span of years due to the present usage.With the upcoming new technologies the demand for energy is increasing rapidly which makes us to seek the more importance towards renewable sources of energy .A methodology for optimized economy optimization of a stand-alone hybrid PV/diesel energy system is addressed in this paper .The main aim is to find the optimal selection of number of units. So that the total system cost is minimized subject to the constraint that the load energy necessities are met. The system is optimized using Particle swarm optimization. The optimization focuses on the total system cost for the given hybrid system .The deciding variables that are being considered for this optimization process are number of PV panels (NPV) and number of Diesel generators (Nd).
As the real world problems are getting complex and intricate day by day, the need of fast, simple (with few control parameters) and effective optimization algorithms is increasing among the researchers from various fields. New algorithms are required to cope up with the existing problems. SMO is a new meta-heuristic nature-inspired algorithm and is a hit and trial based mutual iterative strategy for global optimization over discrete and continuous spaces. It has performed superior to other evolutionary and swarm intelligence based algorithms which is clear from the fact that it gave better results when tested on various benchmark problems. As few control parameters are involved in SMO, so it becomes easy to implement SMO in various types of optimization problems. It is exceptionally evident that some inborn disadvantages are likewise there in each algorithm. To overcome these, various modifications have been made in the original SMO. These modifications has enhanced the basic algorithm and also improved its efficiency due to which, it can be applied to solve various other real world complex optimization problems.
The framework of the fuzzy multi-objective particle swarm optimization (FMOPSO) for solving the fuzzy TCQT problem will be presented. The PSO simulates a social behavior scenario such as bird flocking to certain position. A particle is assigned attributes of velocity and position and defined as a point in multi-dimensional space. The particle position depicts a candidate solution to the task at hand. A swarm of particles (birds) fly toward an optimal defined position according to the evolving method that utilizes the best experience (or position) of a particle (called local best) and the best experience (or position) ever identified by any particle (called global best). To show how effective is the proposed fuzzy multi-objective particle swarm optimization
To whom is it important-- especially industries, people living mostly in the rural and urban areas get affected by shortage of electricity