Policy-based unit commitment problem: a case in a peaking power generation plant

Using suitable solution techniques to the unit commitment (UC) and economic load dispatch (ELD) problems play major role on finding an optimal power scheduling in electrical power system. The UC and ELD problems are to decide when and which generating units to commit and decommit, in order to minimize the total fuel cost over specified period subject to a large number of difficult constraints. Lagrangian relaxation (LR) has been widely used to solve UC and ELD. Recently bundling method (BM) has appeared to be one of the best multipliers updated techniques for LR. This method has promising and the fastest convergence characteristics for UC and ELD problems. For that reason, this paper is to solve the UC and ELD problems via LR, BM and interior point method. This paper explores also the best possible way of updating Lagrangian multipliers with minimum computation time using fast programming techniques.

A layered matrix encoding cascade genetic algorithm and particle swarm optimization approach (GA-PSO) for unit commitment and economic load dispatch problem in a thermal power system is presented in this paper. The tasks of determining and allocating power generation to different thermal units in a way that the total power production cost is at the minimum subject to equality and inequality constraints makes unit commitment and economic load dispatch challenging. A case study, based on the thermal power generation problem presented in [1], is used to demonstrate the effectiveness of the proposed method in generating a cost-effective power generation schedule. The schedule obtained is compared with that of Linear Programming (LP) as reported in [1]. The results show that the proposed GA-PSO approach outperforms LP in solving the unit commitment and economic load dispatch problem for thermal power generation system in this case study.

An optimal solution to the unit commitment (UC) and economic load dispatch (ELD) problems lead to remarkable saving in the power system operational cost. UC and ELD main problems are to find the maximum profit and fast computation simulation time for the scheduling program. Lagrangian relaxation (LR) has become one of the best solution methods in solving the UC and ELD problems. The approach is claimed to be more efficient and easier than other methods in solving large-scale problems. When applying LR, the dual function needed to be updated at the higher level. Lately, bundling method (BM) is one of the best solution methods to Lagrangian dual problem. This paper presents LR technique, BM and interior point method for solving the UC and ELD problems. It will also explore the best possible way of updating Lagrangian multipliers with minimum computation time using fast programming techniques.

This paper proposes an innovative genetic algorithm (GA) approach to solve the thermal unit commitment (UC) problem in power generation industry through a constraint satisfaction technique. Due to a large variety of constraints to be satisfied, the solution space of the UC problem is highly nonconvex, and therefore the UC problem can not be solved efficiently by the standard GA. To effectively deal with the constraints of the problem and greatly reduce the search space of the GA, the minimum up- and down-time constraints are embedded in the binary strings that are coded to represent the on-off states of the generating units. The violations of the other constraints are handled by integrating penalty factors into the cost function. Numerical results on the practical Taiwan Power (Taipower) system of 38 thermal units over a 24-hour period show that the features of easy implementation, fast convergence, and highly near-optimal solution in solving the UC problem can be achieved by the proposed GA approach. >

The Economic Load Dispatch (ELD) is considered to minimize the only fuel cost in power system planning and operation. Due to environmental issues, the emission amount released by thermal power generation should be considered in minimizing the total cost generation as well. This make the power dispatch problem become multi-objective problem that called Economic and Emission Load Dispatch (EELD). This paper investigates the performances of Artificial Bee colony (ABC) algorithm for determining optimal solution for EELD problem. In this paper, the EELD problem is formulated as a single objective problem by taking minimization of total cost and emission level as separated objective. The cost characteristic of thermal generator considered the effect of opening and closing of the valve for practical application. The ABC algorithm has been tested on standard test systems which is 10-generating unit test system in order to validate the effectiveness of proposed ABC algorithm. The results obtained have been compared with reported result by other methods in literature. From the result, it found that ABC algorithm is better than other methods for minimizing fuel cost of thermal power generation and obtained comparative results in reducing the emission level.

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

Fossil fuel is considered to be the primary power generation source. As this source is not that eco- and environmentally friendly, researchers are constantly searching for an alternative source for power generation. Renewable energy has drawn much attention in this regard in recent times. For solving economic load dispatch issues, numerous operational constraints must be considered. Due to the restructuring of the power sector, there is competition between different power systems organizations. Increasing fossil fuel costs drive power-producing utilities to adopt a cost-effective technique for dispatching actual power output. Due to the presence of nonlinearity and non-convexity in the fuel of cost function of generators, the economic load dispatch is often considered a complex optimization problem. Many researchers have been optimizing fuel costs to solve the economic power dispatch problem. This paper offers a critical analysis of ELD that takes into account both traditional and non-traditional energy sources. The review covers a variety of algorithms, including hybrid algorithms for integrating renewable energy sources (RES). The paper also focuses on several restricted optimization techniques and contemporary algorithms including PSO, Jaya, GWO, SMO, TLBO, Rao, MRao-2, and MFO to reduce the fuel cost of generation units using large-scale solar PV. Moreover, this paper provides a comprehensive overview of the current state of economic load dispatch and provides valuable insights for electricity researchers and practitioners. It also discusses future technologies and next steps in the field of ELD, emphasizing the need for more environmentally friendly and cost-effective power generation and distribution solutions. Overall, the paper demonstrates the benefits of renewable energy sources as well as optimization techniques for creating a more sustainable and efficient power generation system.

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.

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.

The short-term hydro generation scheduling (STHGS) decomposed into unit commitment (UC) and economic load dispatch (ELD) subproblems is complicated problem with integer optimization, which has characteristics of high dimension, nonlinear and complex hydraulic and electrical constraints. In this study, the improved binary-real coded shuffled frog leaping algorithm (IBR-SFLA) is proposed to effectively solve UC and ELD subproblems, respectively. For IB-SFLA, the new grouping strategy is applied to overcome the grouping shortage of SFLA, and modified search strategies for each type of frog subpopulation based on normal cloud model (NCM) and chaotic theory are introduced to enhance search performance. The initialization strategy with chaos theory and adaptive frog activation mechanism are presented to strengthen performance of IR-SFLA on ELD subproblem. Furthermore, to solve ELD subproblem, the optimal economic operation table is formed using IR-SFLA and invoked from database. Moreover, reserve capacity supplement and repair, and minimum on and off time repairing strategies are applied to handle complex constraints in STHGS. Finally, the coupled external and internal model corresponding to UC and ELD subproblems is established and applied to solve STHGS problem in Three Gorges hydropower station. Simulation results obtained from IBR-SFLA are better than other compared algorithms with less water consumption. In conclusion, to solve STHGS optimization problem, the proposed IBR-SFLA presents outstanding performance on solution precision and convergence speed compared to traditional SFLA effectively and outperforms the rivals to get higher precision solution with improving the utilization rate of waterpower resources.

Stochastic Hopfield artificial neural network for unit commitment and economic power dispatch

The growing incidence of thermal power generation plants and strict environmental laws have constituted the Economic Emission Load Dispatch (EELD) issue into a challenging problem in contemporary power systems operation. This issue comprises the strategy of reducing the cost of fuel and pollutant emission at the same time and meeting the power balance within the system and the operating limits of the generator as well as the transmission losses. Due to the nonlinearity and conflict of these aims, the traditional single-objective optimization methods do not give flexible and environmentally sustainable solutions. An Interactive Fuzzy Goal Programming (IFGP) methodology is suggested in this work to be used to solve the multi-objective EELD problem. The technique converts the economic and emission targets to fuzzy target in terms of linear membership functions based on the ideal and anti-ideal solutions. This is an interactive decision-making mechanism, which enables the levels of aspiration to be updated stochastically until a satisfying compromise solution has been reached. The approach suggested is verified on three generators thermal power system where the transmission losses are modeled using B-coefficients. Extensive graphical explanations such as cost and emission change with demand of load, trade-off properties, and relative comparison with classical Economic Load Dispatch (ELD), are given. The findings indicate a high level of emission reduction by the IFGP approach at a small cost addition to fuel as opposed to traditional ELD. The suggested framework has increased flexibility, clear sightedness, and decision support and is thus a great fit to sustainable and viable power system planning and operation.

A multi-objective particle swarm optimization (MOPSO) approach for multi-objective economic load dispatch problem in power system is presented in this paper. The economic load dispatch problem is a non-linear constrained multi-objective optimization problem. The proposed MOPSO approach handles the problem as a multi-objective problem with competing and non-commensurable fuel cost, emission and system loss objectives and has a diversity-preserving mechanism using an external memory (call “repository”) and a geographically-based approach to find widely different Pareto-optimal solutions. In addition, fuzzy set theory is employed to extract the best compromise solution. Several optimization runs of the proposed MOPSO approach were carried out on the standard IEEE 30-bus test system. The results revealed the capabilities of the proposed MOPSO approach to generate well-distributed Pareto-optimal non-dominated solutions of multi-objective economic load dispatch. Comparison with Multi-objective Evolutionary Algorithm (MOEA) showed the superiority of the proposed MOPSO approach and confirmed its potential for solving multi-objective economic load dispatch.

Economic Load Dispatch (ELD) optimization is an important and difficult task in power system planning. Previously, most of the research mainly focused on proposing various evolutionary algorithms (EAs) to pursue better results of ELD problems. However, few comprehensive analysis of the effects of various constraint handling techniques (CHTs) on the performance of EA-based techniques are available so far. In this paper, we try to fill this gap by experimentally testing the algorithmic variants of combining four effective and widely used EAs with three CHTs. From the experimental results on the ELD problems with valve-point and those problems with both valve-point and multiple-fuel effect, several important conclusions can be achieved, including 1) for the low scale ELD problem with valve-point only, the selection of EAs is more important than CHTs; 2) for the large scale problems, CHTs play crucial roles; 3) the appropriate combination of EA and CHT is helpful to achieve better performance. This study is also expected to provide solid basis for further strengthening the robustness of EAs for ELD optimization. It is also interesting to observe that the experimental results obtained in this paper are much better than those of the previous effective ELD optimization algorithms.

Unit commitment is an efficient method to lower the total cost of the power plant by scheduling units' generation and meeting the constraint condition. However, in practice, few power plants implement the algorithm for fear that the load response in the power plant would not be fast enough to track the unscheduled load demand from the power grid if some units of the power plant are shut down. This paper proposes a new unit commitment method that tries to solve this problem effectively. The proposed method guarantees the desired speed limit by setting the plant-level load tracking speed. In this method a ‘one-at-a-time’ unit commitment is accomplished. The most expensive unit (which is determined by computing its cost) is optimized, the unit commitment schedule is updated, and the load dispatch result is re-computed. The result will be repeatedly optimized until the spinning reserve or load tracking speed is lack. The optimization loop will breaks out as well if the unit schedules of two consecutive iterations over the time period remain unchanged. The test results from 10-machine system shows that the proposed method is easy to understand and quick to solve, and is of practical use.