Optimal Scheduling Of Large Hydrothermal Power Systems

In this paper the operation of small isolated island grids is investigated with the presence of centrally managed battery energy storage (BES) facilities. A mixed integer linear programming (MILP) unit commitment and economic dispatch (UC-ED) method is utilized to evaluate the impact from the introduction of BES on system operation. Two small non-interconnected island (NII) power systems with diversified characteristics are examined under high renewable energy source (RES) penetration conditions and the anticipated benefits for the system from the presence of storage are quantified in terms of security, economics and achievable renewable energy penetration levels in each case.

This study presents a multi-objective based on a hybrid methodology to apply the problem of economic emission dispatch that is incorporated with hydro, thermal and wind power units. The hybrid method is the combination of both the modified quantum-behaviour lightning search algorithm (MQLSA) and artificial intelligence technique with the help of PSNN. To determine the optimal amounts of the generated powers from the thermal, wind farms and hydro units, the proposed approach is introduced by minimising the cost of generation and the emission level simultaneously. MQLSA is utilised to generate the optimal combination of thermal power with the objective of the minimum error function to minimise the fuel and emission cost of the system with wind speed factor. To capture the optimised wind power with the objective of minimum speed factor, the PSO-artificial neural network technique is utilised. The algorithm is integrated with the feasible solution constraint handling techniques. To validate the effectiveness of the proposed method, the six and ten generating thermal system with wind power is studied. The proposed hybrid technique is implemented in MATLAB/Simulink platform and the simulation result demonstrates the superiority of the proposed method compared to the various existing techniques.

Economic dispatch in wind-integrated power systems is a critical challenge, yet many recent metaheuristics suffer from premature convergence, heavy parameter tuning, and limited ability to escape local optima in non-smooth valve-point landscapes. This study proposes a new hybrid optimization framework, the Fractional Grasshopper Optimization algorithm (FGOA), which integrates fractional-order calculus into the standard Grasshopper Optimization algorithm (GOA) to enhance its search efficiency. The FGOA method is applied to the economic load dispatch (ELD) problem, a nonlinear and nonconvex task that aims to minimize fuel and wind-generation costs while satisfying practical constraints such as valve-point loading effects (VPLEs), generator operating limits, and the stochastic behavior of renewable energy sources. Owing to the increasing role of wind energy, stochastic wind power is modeled through the incomplete gamma function (IGF). To further improve computational accuracy, FGOA is hybridized with Sequential Quadratic Programming (SQP), where FGOA provides global exploration and SQP performs local refinement. The proposed FGOA-SQP approach is validated on systems with 3, 13, and 40 generating units, including mixed thermal and wind sources. Comparative evaluations against recent metaheuristic algorithms demonstrate that FGOA-SQP achieves more accurate and reliable dispatch outcomes. Specifically, the proposed approach achieves fuel cost reductions ranging from 0.047% to 0.71% for the 3-unit system, 0.31% to 27.25% for the 13-unit system, and 0.69% to 12.55% for the 40-unit system when compared with state-of-the-art methods. Statistical results, particularly minimum fitness values, further confirm the superior performance of the FGOA-SQP framework in addressing the ELD problem under wind power uncertainty.

Optimal economic emission dispatch of hydrothermal power systems

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.

New metaheuristic methodology for solving security constrained hydrothermal unit commitment based on adaptive genetic algorithm

To ensure minimization of power losses as well as economic feasibility of electrical power generation, economic load dispatch happens to be one of the most challenging optimization problems which is faced in electrical engineering. With the advent of distributed power systems, an interconnection of power systems generating from different sources have come into consideration. However, all sources do not operate in the same manner and hence the generation cost for different sources varies significantly. Economic Load Dispatch (ELD) can be defined as a technique to schedule the power generator outputs with respect to the load demands, and to operate the power system in the most economical way. This paper presents a neural network model for implementing economic load dispatch for a three as well as six generation system. The load is also varied for both the 3 and 6 generations systems. The results clearly indicate that the cost of generation increases with the increase in load, which is also intuitive and hence gets tested. Thus the proposed model can be used to implement an optimized economic load dispatch mechanism for multi-unit power systems which is a typical characteristic of distributed power systems.

A rule based economic dispatch (ED) has been proposed for the daily and weekly operation planning of thermal units. The proposed ED scheme is based on the well known equal incremental cost method to determine the load dispatch among thermal units in the study system considering several constraints. A simple rule base has also been proposed for the unit commitment according to a ranking considering the startup cost of each thermal unit. To demonstrate the efficiency of the proposed ED scheme, a weekly planning of 23 thermal units has been performed with highly good reduction of the total fuel cost compared with that in the actual operation.

Chapter 8 - Economic dispatch of large-scale integrated heat and power systems by application of a novel harmony search approach

This paper presents using the Bees algorithm approach to multi-objective optimal economic dispatch of electrical power systems. The generation of electricity from the fossil fuel releases several contaminants, such as sulfur oxides, nitrogen oxides and carbon dioxide, into the atmosphere. Genetic algorithmic approach to power system optimization, as reported here for a case of economic power dispatch, consists essentially of minimizing the objective function while gradually satisfying the constraint relations. In the Multi-objective problem formulation, four important non-commensurable objectives in an electrical thermal power system are considered. These are economy and environmental impacts because of NOx, SO2, CO2 emissions. The suitability of the proposed approach is described to multiobjective optimal economic dispatch of electrical power systems.

This paper proposes a two-tiered approach to solving multi-area security constrained economic dispatch (SCED) in large interconnected power systems while preserving inter-area power exchange schedules. The multi-area SCED problem is decomposed into a higher-level master problem and regional sub-problems. The master problem optimizes equivalent power injection at tie-line buses in each area, in order to preserve the scheduled power flow of inter-area interfaces. In the subproblems, a regional SCED with all the detailed parameters of internal generators/loads will be performed with fixed tie-line power flow. Ward equivalencing-based network reduction is employed to perform power flow computation at the higherlevel dispatch. A novel virtual supply function is introduced based on the locational marginal price (LMP) for each tie-line bus. This virtual supply function internalizes the detailed supply and demand information within each area, and provides key information for faster convergence to global optimality. The proposed approach is shown to have good trade-off between global economic optimality and power exchange controllability. Furthermore, this approach allows fully autonomous dispatch of internal resources within each area. Experimental results of 3-area IEEE RTS are presented to verify the economic optimality and computational speed of this method.

By integrating simulated annealing and the interactive best-compromise approach, a method to determine economic dispatch in power systems, while accounting for carbon emissions, is proposed in this study. To satisfy load demands and operational constraints, traditional economic dispatches are determined by minimizing total power generation costs based on the power output of the generating units in a system. In the proposed method, carbon emissions are taken into consideration. A carbon dioxide (CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ) equivalent model that accounted for the various fuel types (e.g., coal, oil, and natural gas) used in power generation was created. The correlation between power generation costs and carbon emission was determined according to CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> emission equivalent tradeoff and incremental cost CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> reduction curves. The proposed method was applied to the Taiwan Power Company system. The results indicated that the method was effective at determining the influence of CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> emissions on power generation costs during off-peak, semi-peak, and peak hours, as well as daily load demands. The system allows economic and environmental benefits to be considered simultaneously.

Economic Dispatch is an important optimization problem in power system planning. This article presents an overview of the economic dispatch problem, its formulation, and a comparison of addressing the problem between the vertically integrated market and the liberalized market environments.

Solutions to optimal control problems obtained via direct methods are usually of low resolution. As the desired resolution becomes higher, the number of parameters in the resulting parameter optimization problem increases nonlinearly. A concatenated approach to trajectory optimization previously introduced by the authors to obtain high resolution optimal solutions with low storage requirements is applicable only to a specific class of problems, such as minimum time and minimum energy optimal control problems. The hodograph ballooning approach introduced in this paper generalizes the concatenated approach to the most general optimal control problem. Introduction The development of powerful nonlinear programming software [1, 2] has made direct approaches to trajectory optimization the method of choice for most practical applications [3-5]. The discretization of an optimal control problem to a finite dimensional parameter optimization problem avoids many of the troublesome pathologies that are typical for the optimization over infinite dimensional function spaces [6-8]. Furthermore, direct approaches usually do not. require guessing the switching structure, and the dynamical system is devoid of the nonintuitive costate variables. However, to achieve good resolution it is usually necessary to refine some type of discretization mesh, and, ultimately, to use a large number of design parameters. For typical gradient search methods, this increase in the dimension of the optimization problem has nearly always a negative effect on the convergence rate and the robustness. Additionally, CPU time and RAM requirements for each iteration increase with the second power of the number of parameters (third power for non-sparse solvers) so that direct optimization approaches can become quite expensive. In [9], a method was introduced that achieves excellent resolution without solving high-dimensional nonlinear programming problems. This was achieved by lo'Senior Engineer, Member AIAA. t Supervising Engineer, Member AIAA. 117 Research Drive, Hampton, VA 23666. Copyright ©1996 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved cally optimizing the trajectory on an iterative sequence of short, partly overlapping subarcs. However, this approach is not applicable to the most general problem formulation. Loosely sneaking, it was required in [9] that the cost state does not appear explicitly in the right-hand side of the equations of motion. The present paper introduces a method through which the approach introduced in [9] becomes applicable to the most general problem formulation. Application of this method, however, requires a priori knowledge of the optimal cost. In practice it is observed that the optimal cost can be obtained with very high precision with reasonably low order discretizations. Once a good guess for the optimal cost is obtained presented in this paper can be applied to refine the trajectory, or, if the optimal cost value is not known a priori with sufficient precision, it can be applied iteratively with the prescribed cost value adjusted in an outer loop. Problem Formulation Let us consider the following simple optimal control problem stated in Mayer form: ^ 4 ( x ( t f ) , t f ) (1 )

Considering different character between hydroelectric power and thermal power contributed to tie-line, as well as the cost function of the whole interconnected system under electric power market environments, this paper presents a new optimization strategy based on benefit analysis to solve the power regulation on tie-line in hydro-thermal interconnected power system. The units relating to tie-line can be procured by an electrical dissection algorithm in the sending and receiving network and matched with different correlative coefficient, while the other units are also due to be coordinated with diverse regulating power capacity at the same time. The effectiveness of the proposed method is demonstrated on IEEE 57-bus system comprising of hydro and thermal units and compared with some conventional approaches. The experimental results show that the proposed new strategy approaches is able to obtain higher quality solutions efficiently than the conventional approaches.