Privacy Protection Decentralized Economic Dispatch Over Directed Networks With Accurate Convergence

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.

This chapter discusses the application of linear programming (LP) techniques to find the optimal solution of the economic dispatch (ED) problem without considering transmission losses. The ED problem is concerned with optimizing the power generated by several generating units. The objective is to find the optimal power produced by each unit to supply the required load at minimum total cost. The generation cost associated with each unit is usually in the form of a quadratic or cubic function of the power produced. To apply LP, these nonlinear cost functions have to be linearized. The optimal solution is then determined by LP based on the approximate linear model. Piece-wise linearization methodology is adopted in this chapter. To evaluate the performance of the linearization method, a comprehensive set of benchmark test problems is used. LP solutions of linearized ED problems are compared with several other techniques from the literature. The LP technique with piece-wise linearization shows an overall competitive advantage in terms of total cost, solution time, and load satisfaction.

Optimizing multiple objectives is a common challenge in complex decision-making scenarios, where improving one objective often comes at the expense of another. In power system generation, two critical objectives must be simultaneously minimized: the total generation cost and the total emissions released. This study introduces a multi-objective optimization method developed to address these dual objectives. The proposed approach aims to identify the optimal solution to the economic dispatch problem, balancing the trade-off between minimizing generation costs and reducing environmental impact by lowering total emissions. Heuristic optimization is used to solve this multi-objective combined economic and emission dispatch (MOCEED) problems through the implementation of Multi-Objective Evolutionary Programming (MOEP). In this study, the Weighted Sum Method (WSM) is combined with the Evolutionary Programming (EP) technique to minimize both objectives. The developed approach is validated on the IEEE 30-Bus RTS, which consists of six generators. The effectiveness of the developed technique is evaluated and compared the results against scenarios without optimization. Simulations are performed using MATLAB software, and the results demonstrate that the proposed Multi-Objective Evolutionary Programming (MOEP) successfully identifies the optimal generator outputs, achieving significant reductions in both total generation cost and emissions. These results highlight the method's capability to provide superior solutions for multi-objective economic dispatch problems.

The Economic Dispatch (ED) is one of the most important optimization problems in power systems the ultimate goal of the ED is to minimize the cost of operations in a power generation. In this paper, the Woodpecker Mating Algorithm (WMA) is used to solve the ED problem considering the nonlinear properties of generators such as valve point effects (VPE), prohibited operating zones (POZ), ramp rate limits, multiple fuel options, and transmission loss. The WMA algorithm is a novel metaheuristic algorithm inspired by the mating behavior of woodpeckers and sound intensity (a physical quantity). The WMA is implemented on six test systems of different operational dimensions and characteristics to show its capacity for solving the ED problem. The results are compared with the latest and most efficient methods introduced in the literature. Proving the efficiency of the WMA to solve the ED problem, simulation results are promising and offer the optimal fuel cost of production.

This paper focuses on the design of an initialization-free distributed finite-time algorithm for the economic dispatch problem in smart grid, where the generation units only communicate with its neighbors to minimize the total cost cooperatively. Firstly, the optimal solution of the economic dispatch problem is analyzed in accordance with the saddle-point dynamics. Then, an initialization-free finite-time algorithm is presented to guarantee the active power generation and the incremental cost converge to the optimal solution in a distributed manner. At last, some numerical simulations are preformed to validate the proposed method.

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.

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

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.

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

Economic dispatch (ED) problem exhibits highly nonlinear characteristics, such as prohibited operating zone, ramp rate limits, and non-smooth property. Due to its nonlinear characteristics, it is hard to achieve the expected solution by the classical methods. To overcome the challenging difficulty, this paper proposes an improved firefly algorithm (FA) to solve economic dispatch (ED) problem. The improved FA employs two strategies to enhance the search ability and avoid the premature usually suffered from in standard FA. The first one is based on the distance information among the fireflies, and it adjusts the light absorption coefficient adaptively. The other one is a decreasing strategy for the randomization parameter. Additionally, a crossover operation is employed to create potential solution with high diversity. The designs are able to enhance the search ability and performance of FA, which have been demonstrated on six benchmark functions. To validate the proposed algorithm, we also use three different systems to demonstrate its efficiency and feasibility in solving ED problem. The experimental results show that the proposed FA method was capable of achieving higher quality solutions in ED problems.

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.

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.

Energy, building, and water networks are three interlinked critical infrastructures that need to be operated cooperatively to maximize the smart grid's economic benefits. In this paper, a mixed-integer linear programming (MILP) formulation is proposed to approach the economic dispatch (ED) problem for smart grids embedded with interdependent water and energy networks. Energy management of various building applications is considered by intelligently controlling the indoor temperature during occupied and unoccupied hours. To optimize the demand of water distribution system, pump's nonlinear scheduling and hydraulic factors and daily water usage of buildings are added to the proposed model. Piecewise linear approximation of univariate and bivariate nonlinear functions is used to convert the nonlinear problem to an MILP formulation. Several case studies were conducted to examine the impact of indoor temperature settings of the buildings, speed of pumps, battery efficiency, and end of day (EoD) battery and tank constraints on economic dispatch of the microgrid system.