A distributed finite-time economic dispatch algorithm in smart grid

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

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.

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

The capability of economic dispatch (ED) algorithms to address the power dispatch problem with unknown cost functions and switching network topology is an important feature for practical applications of power dispatch algorithms in smart grid. Inspired by distributed fast consensus technique and reinforcement learning (RL) approach, this research presents a kind of ED strategy consisting of a fixed-time consensus tracking (FCT) algorithm and a distributed RL-based power dispatch algorithm to address the economic dispatch problem (EDP) with unknown cost functions and switching network topology. Different with existing results on EDP of smart grid where the feasible power outputs are calculated from centralized algorithm, a distributed FCT algorithm is utilised to balance the power demand and output for each dispatch duration, where the achievement of such a consensus leads to feasible power outputs and secures the system performance against switching interaction topology. Then, a distributed RL-based power dispatch algorithm is developed to train a policy for solving EDP with unknown cost functions through the technique of distributed training with distributed execution (DTDE). Finally, case studies are presented to demonstrate the effectiveness of the proposed ED algorithms.

In this paper, a consensus based fully distributed optimization algorithm is proposed for solving economic dispatch problem (EDP) in smart grid. Since the incremental cost of all buses reach consensus when the optimal solution is achieved, it is selected as a consensus variable. An additional variable at each bus, called “surplus” is added to record the local power mismatch, which is used as a feedback variable to purse the balance between power supply and demand. Different from most of the existing distributed methods which require the communication network to be balanced, the algorithm uses a row random matrix and a column random matrix to precisely steer all the agents to asymptotically converge to a global optimal solution over a time‐varying directed communication network. Due to the use of a fixed step size, the proposed algorithm also outperforms other algorithms in terms of convergence speed. The graph and eigenvalue perturbation theories are employed for the algorithm convergence analysis, and the upper bound of the parameters required for convergence is given theoretically. Finally, the performance and scalability of the proposed distributed algorithm are verified by several case studies conducted on the IEEE 14‐bus power system and a 200‐node test system.

Decentralized algorithms to solve the economic dispatch problem (EDP) in smart grids have been a significant focus within engineering research due to their advantages in scalability, robustness, and flexibility. Its purpose is to optimize the generation power of each generator to jointly achieve the minimal total generation cost on the premise of satisfying the total demand and generation capacity. Recently, the emergence of data security and the requirement for complex computing have led to a resurgence of activity in this area. To address EDP while considering the issues of private security and computation efficiency, we propose a novel privacy-protected decentralized random sleep algorithm over an unbalanced directed network. On the one hand, the proposed algorithm can effectively protect sensitive information by adding conditional noises in the state exchange. On the other hand, it can also promote computation efficiency over an unbalanced directed network by incorporating the random sleep strategy into the decentralized inexact gradient method with the gradient rescaling technique. It is proved that the proposed algorithm is able to achieve the optimal solution of the EDP. Furthermore, we also provide theoretical proof to guarantee the convergence and privacy properties of the proposed algorithm. Finally, two simulation examples of EDP in smart grids are provided to demonstrate the effectiveness of the proposed algorithm.

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.

A hybrid optimization framework for the non-convex economic dispatch problem via meta-heuristic algorithms

The increased complexity of modern energy network raises the necessity of flexible and reliable methods for smart grid operation. To this end, this article is centered on the economic dispatch problem (EDP) in smart grids, which aims at scheduling generators to meet the total demand at the minimized cost. This article proposes a fully distributed algorithm to address the EDP over directed networks and takes into account communication delays and noisy gradient observations. In particular, the rescaling gradient technique is introduced in the algorithm design and the implementation of the distributed algorithm only resorts to row-stochastic weight matrices, which allows each generator to locally allocate the weights on the messages received from its in-neighbors. It is proved that the optimal dispatch can be achieved under the assumptions that the nonidentical constant communication delays inflicting on each link are uniformly bounded and the noises embroiled in gradient observation of every generator are bounded variance zero mean. Simulations are provided to validate and testify the effectiveness of the presented algorithm.

The major issue in power system is economic dispatch (ED) problem. The Economic dispatch problem is aim to distribute electrical power generators in some active electrical system to minimize the total of cost of generators. Here, the purpose of this paper is to achieve the combination of power output, maximum total of demand with the transmission losses, minimum the total cost of generating unit and design web based application to simplify the calculation of economic dispatch problem for user at PT. Indonesia Power. This paper introduces a solution to ED problem using Dr. Xin She Yang developed firefly algorithm. The result obtained by the proposed algorithm have been compared with the result from the data source and that results is more optimal using firefly algorithm than the results of the data source. Based on the result, it can be concluded that this web based application is very useful to user in calculating the economic dispatch problem with transmission losses at PT. Indonesia Power.

In India Electrical Energy is generated mainly Coal based Thermal Power stations and hydro Electric Power Stations. The main aim of power generating company is to provide good quality and reliable power to consumers at minimum cost. The problem of Combined Economic and Emission Dispatch deals with the minimization of both fuel cost and emission of pollutants such as oxides of Nitrogen and Oxides of Sulphur. In our power system the emission is major problem created that’s why in now a days we move from green energy source or renewable energy such as Sunlight, Wind, Tides, Wave, and Geothermal Heat Energy. The Emission constrained Economic Dispatch problem treats the emission limit as an additional constraint and optimizes the fuel cost. In this paper we optimizes the Combined Economic and Emission Dispatch problem by using two different optimization method such as Artificial Bee Colony (ABC) and Genetic Algorithm (GA).The proposed ABC Algorithm has been successfully implemented is to IEEE 30 bus and Indian Utility sixty two Bus System The simulation result are compare and found the effective algorithm for Combined Economic and Emission Dispatch problem.

This paper focuses on the economic power dispatch problem in a smart grid by using the distributed consensus with event‐triggered communication mechanism based on continuous‐time multi‐agent systems over balanced directed networks, where there are many generation units working cooperatively to achieve an optimal solution. The event‐triggered communication mechanism means that the information transmission between agents is triggered by event instead of time. The triggering condition and algorithm for each agent are fully decentralized. At each instant time, each agent updates its state by employing the states collected from itself and its neighboring agents at their last triggering time. Finally, two examples are given to analyze the feasibility of above proposed algorithm.

Event-triggered scheme for finite-time distributed economic dispatch in smart grids

A new gumption approach for economic dispatch problem with losses effect based on valve-point active power

The aim of the current paper is to present a mimetic algorithm called the chaotic evolutionary programming Powell’s pattern search (CEPPS) algorithm for the solution of the multi-fuel economic load dispatch problem. In the CEPPS algorithm, the exploration process is maintained by chaotic evolutionary programming, whereas exploitation is taken care off by a pattern search. The proposed CEPPS has two variants based on the Gauss map and the tent map. Seven generalized benchmark test functions and six cases of the multi-fuel economic load dispatch problem are considered for the performance analysis. It is observed from the analysis that the CEPPS solution procedure based on the tent map exhibits superiority to obtain an excellent solution and better convergence characteristics than traditional chaotic evolutionary programming. Further, the performance investigation for the considered economic load dispatch shows that the Gauss map CEPPS solution procedure performs better than the tent map based CEPPS to obtain the solution of the multi-fuel economic dispatch problem.