Multi-area Economic Dispatch Problem Research Articles

Offline economic dispatch for multi-area power system via hierarchical reinforcement learning

In this paper, a novel hierarchical reinforcement learning (HRL) architecture is put forward to resolve the multi-area economic dispatch (MAED) problem in a fully off-line optimization manner, while the focus of MAED is to minimize the total generation cost of the entire multi-area power system by determining output power within area and the power transfer among areas. The original MAED problem is transformed into an augmented sub-MAED problem by exploring the relationship between power balance constraint and tie line capacity constraint in each area. This architecture first calculates the scheduled area load in the top layer through the primal–dual consensus-based distributed Q-learning, and then calculates load-power table assembled by the optimal output power within single area according to the multi-stage decision algorithm in the bottom layer. Acting as an underlying framework, the assigned load-power table is implemented with the combination of off-line calculation and on-line inquiry. It is capable of parallel and asynchronous optimization in each area while satisfying various constraints. Furthermore, a power-triggered algorithm is proposed to satisfy the power balance among areas, and its convergence is theoretically analyzed, which illustrates that the area power error will converge to zero in the limited iteration. Finally, the proposed approach is validated in three different cases: 20-unit, 40-unit, and 120-unit. The comparative results confirmed the superiority of the proposed HRL architecture with high real-time performance and less computation burden. Specifically, the HRL architecture reduces the fuel cost in the range of 0.01656%–0.19173% and accelerates the speed more than 10 times than others.

Solving multi-area economic dispatch problem using hybrid exchange market algorithm with grasshopper optimization algorithm

Solving multi-area economic dispatch problem using hybrid exchange market algorithm with grasshopper optimization algorithm

Feedback Optimizing MPC for Load Frequency Control and Economic Dispatch

With increasing renewable generation, demand response, and deregulation, power networks are becoming more uncertain, time-varying, and strongly coupled. As a result, the conventional approach of performing separate economic dispatch (ED) and load-frequency control (LFC) operations may no longer guarantee smooth and cost-efficient regulation of frequency across interconnected power networks. To address this, we present a tracking model predictive control (MPC) algorithm which simultaneously achieves economic dispatch and secondary frequency control in a multi-area power network. A unique feature of the proposed algorithm is that it exploits the implicit feedback in MPC to regulate the interconnected power system towards steady-state equilibria that solve a multi-area economic dispatch problem, without explicitly computing the latter as a reference to be followed or estimating the unknown disturbances. This feedback-based optimization approach endows the algorithm with inherent robustness to uncertainty (such as unknown step changes in the demand). Simulation results for a two-area power network show improved steady-state economic performance compared to standard MPC-based frequency control schemes, and better dynamic performance compared to other feedback-based optimization schemes.

Multi-area economic emission dispatch for large-scale multi-fueled power plants contemplating inter-connected grid tie-lines power flow limitations

The purpose of this research is to investigate the multi-area economic emission dispatch problem (MEEDP) in the presence of renewable energy resources (RES) to improve the energy sustainability and climatic benefits. MEEDP is a multi-objective problem in smart grids, with the purpose of minimizing the operating costs and emissions of thermal units. RES have made a substantial contribution to greenhouse gases emission control and environmental sustainability. The integration of RES into conventional grids, which is becoming increasingly prevalent, spread the research scope of MEEDP and needs to be re-examined. This work considers two renewable sources (wind and solar) along with thermal plants subjected to significant number of previously uncombined system level limitations such as power capacity limit, prohibited zones, transmission network losses, dynamic ramp limits, tie-line limits and multiple fueling options. The operating cost is computed as summation of predictive and stochastic components. The predictive part is calculated by utilization of cumulative distribution function for each wind and solar system. A swarm intelligence-based crow search optimization algorithm (CSOA) is modeled to handle the complex constrained MEEDP with adjusted predictive part of RES. Six benchmark test systems with multi-dimensional constraints have been chosen to validate the adaptability and efficacy of the presented approach. Regardless of the complexity of the problem, the proposed approach provides the best feasible solution with a finer convergence rate. Finally, the simulation results depict that the integration of the corresponding system constraints gives legitimacy to the system and delivers reliable output.

Solving high-dimensional multi-area economic dispatch problem by decoupled distributed crisscross optimization algorithm with population cross generation strategy

Multi-area economic dispatch (MAED) is a non-convex non-differentiable high-dimensional optimization problem, aiming to minimize the total fuel cost and meet the requirements of load balance. Current distributed mathematical programming methods are hard to solve the valve point effect in MAED. In addition, distributed meta-heuristic algorithms so far require a centralized controller. To address these issues, a decoupled distributed crisscross optimization with population cross generation (DDCSO-PCG) algorithm is proposed, which can 1) realize decentralization, 2) protect area data privacy, 3) reduce dimensions and improve convergence ability. First, the population cross generation (PCG) strategy is integrated into the crisscross optimization (CSO) algorithm to maintain population diversity and enhance exploitation ability. Second, the DDCSO-PCG algorithm is implemented to solve the MAED problem in a fully decentralized manner. Under the distributed framework, the proposed algorithm employs CSO-PCG independently to optimize the area dispatch in parallel. The total optimal cost is achieved by minimizing the cost of each area with no centralized controller required. The experimental results on multi-area static economic dispatch (MASED) and multi-area dynamic economic dispatch (MADED) problems show that the proposed DDCSO-PCG algorithm can not only provide a distributed solution, but also achieve the best economic cost compared with other state-of-the-art techniques.

Solving static and dynamic multi-area economic dispatch problems using an improved competitive swarm optimization algorithm

Multi-area economic dispatch (MAED) is an important non-linear optimization problem in power system operation. MAED involves multiple power generation areas, and minimizes the total fuel cost by determining the power generation within areas and the power interchange between areas. This paper proposes an improved competitive swarm optimization (ImCSO) algorithm to solve the MAED problems. The ImCSO algorithm introduces two improvements into competitive swarm optimization for performance enhancement. Firstly, a ranking paired learning strategy is adopted to enhance the learning efficiency of the loser particles; secondly, a differential evolution strategy is used to update and improve the winner particles. Combining a constraint repair technique, the proposed ImCSO algorithm is applied to solve 10-unit, 40-unit and 120-unit multi-area static economic dispatch and 40-unit multi-area dynamic economic dispatch problems. The solved MAED problems integrate comprehensive constraints such as valve point effect, multiple fuels, transmission loss, tie-line constraint, prohibited operating zone and ramp rate limit. Through comparison with other well-established optimization algorithms, it is observed that the ImCSO algorithm has superiority in terms of solution accuracy and reliability in solving the MAED problems.

Multi-area economic dispatch with stochastic wind power using Salp Swarm Algorithm

Abstract Salp Swarm Algorithm (SSA) is a newly developed swarm intelligence based optimization method. Its analytical model mimics self-organized swarming and foraging behavior of salps. Salps are found in the ocean and they form a swarm called salp chain for their organized movement and foraging. Since its inception in 2017, SSA has been applied to many engineering domains. This paper presents the solution of complex constrained multi-area economic dispatch problem of power system with and without stochastic wind integration using SSA. Simulation analysis has been carried on four different constrained test cases with diverse dimensions/complexity level. They are (i) four area system with sixteen thermal units (ii) four area system with forty thermal units (iii) two area system with forty thermal units and (iv) two area forty-unit system with wind integration. Comparison of simulation results obtained by SSA with other methods reported in the recent literature has proven SSA’s capability of constrained handling and offered promising and efficient solutions.

An Efficient New Hybrid ICA-PSO Approach for Solving Large Scale Non-convex Multi Area Economic Dispatch Problems

Multi-area economic dispatch (MAED) is one of the vital problems in economic operation of interconnected power systems. This paper proposes a novel hybrid approach based on combined imperialist competitive algorithm (ICA) and particle swarm optimization (PSO) methods in order to determine the feasible optimal solution of the non-convex economic dispatch (ED) problem considering valve loading effects. In the proposed algorithm we have defined new type of countries in ICA algorithm, namely independent countries. These types of countries improve their position using a PSO based search strategy. The proposed method benefits from the advantage of the both algorithms. The proposed hybrid approach based on ICA-PSO is applied on different test systems and compared with most of the recent methodologies. Also, a large scale multi-area economic dispatch (MAED) problem is solved using the proposed hybrid approach to minimize total fuel cost in all areas while satisfying power balance constraints, generating limits and tie-line capacity constraints. The results show the effectiveness of the proposed approach and prove that ICA-PSO is applicable for solving the power system economic load dispatch problem, especially in large scale power systems.

A Newton Method-Based Distributed Algorithm for Multi-Area Economic Dispatch

In this paper, we propose a novel Newton method-based distributed algorithm (NMDA), which is also effective in solving the general single-area EDP (SAEDP), to deal with the multi-area economic dispatch problem (MAEDP), of which the focus is to minimize the total generation cost in the presence of system and generator constraints. To develop the NMDA, we first introduce a virtual SAEDP formulation to fit the framework of Newton method (NM), and then employ the average consensus protocol to obtain the global information needed to execute the NM and backtracking line search algorithm in a distributed manner. Compared with the centralized methods that can yield the optimal solution, the proposed NMDA provides a suboptimal solution with a very small relative error. The NMDA ensures the instantaneous system power balance throughout the iteration process while the centralized methods compared in this paper cannot do so. We also provide a rigorous theoretical analysis for the convergence of NMDA. Moreover, the advantage of NMDA in terms of the convergence speed is validated by comparing with other distributed methods such as the gradient-based ADMM (G-ADMM) and quasi Newton-based primal dual interior point (QN-PDIP) method. Finally, case studies demonstrate the effectiveness and scalability of the proposed distributed algorithm.

Hybrid Optimization Algorithm to Solve the Nonconvex Multiarea Economic Dispatch Problem

In this paper, multiarea economic dispatch (MAED) problems are solved by a novel straightforward process. The solved MAED problems include transmission losses, tie-line constraints, multiple fuels, valve-point effects, and prohibited operating zones in which small, medium, and large scale test systems are involved. The methodology of tackling the problems consists in a new hybrid combination of JAYA and TLBO algorithms simultaneously to take the advantages of both to solve even nonsmooth and nonconvex MAED problems. In addition, a new and simple process is used to tackle with the interaction between areas. The objective is to economically supply demanded loads in all areas while satisfying all of the constraints. Indeed, by combining JAYA and TLBO algorithms, the convergence speed and the robustness have been improved. The computational results on small, medium, and large-scale test systems indicate the effectiveness of our proposed algorithm in terms of accuracy, robustness, and convergence speed. The obtained results of the proposed JAYA–TLBO algorithm are compared with those obtained from ten well-known algorithms. The results depict the capability of the proposed JAYA–TLBO based approach to provide a better solution.

Robust and effective parallel process to coordinate multi‐area economic dispatch (MAED) problems in the presence of uncertainty

Considering the independency of areas as a challenge in multi-area economic dispatch (MAED) problems, this study presents a novel parallel process MAED to preserve independency in MAED problems and, at the same time, supply the demanded power in each area. Although distributed power networks are physically connected to each other to improve the financial and technical aspects of the operation, they have to operate with few information about other areas. In addition, utilising renewable energies, especially wind turbines, are unavoidable in the future to supply the demanded power. However, the uncertainty that arises from wind behaviour makes the MAED problems more complicated, meaning that the exact amount of output power in each time instant is not known. Hence, the authors analyse the wind and load uncertainty effect on the MAED cost function using the unscented transformation (UT) method. Moreover, the applicability of the UT method in terms of accuracy and speed is evaluated with Monte–Carlo simulation method. Finally, four different cases, both small and large, are studied to evaluate the effectiveness of the proposed parallel process and UT method in MAED problems.

Risk-Oriented Multi-Area Economic Dispatch Solution With High Penetration of Wind Power Generation and Compressed Air Energy Storage System

This paper investigates the risk-oriented multi-area economic dispatch (MAED) problem with high penetration of wind farms (WFs) combined with compressed air energy storage (CAES). The main objective is to help system operators to minimize the operational cost of thermal units and CAES units with an appropriate level of security through optimized WF power generation curtailment strategy and CAES charging/discharging control. In the obtained MAED model, several WFs integrated with CAES units are considered in different generation zones, and the probability to meet demand by available spinning reserve during N - 1 security contingency is characterized as a risk function. Furthermore, the contribution of CAES units in providing the system spinning reserve is taken into account in the MAED model. The proposed framework is demonstrated by a case study using the modified IEEE 40-generator system. The numerical results reveal that the proposed method brings a significant advantage to the efficient scheduling of thermal units' power generation, WF power curtailment, and CAES charging/discharging control in the power system.

A multi-objective framework for multi-area economic emission dispatch

Economic dispatch seeks for the most economical combination of generation units in power system while satisfying bunch of physical and operational constraints. Finding the most economical generation strategy in power markets with several generation zones is crucial for power system operation. Conventional economic dispatch models cannot find the most economical generation schedule in power system with different generation zones. Moreover, the most economical schedule of generation cannot satisfy the environmental expectations. Therefore, compromising between generation cost and environmental issues is unavoidable. In this connection, total emission produces by generation units is taken into consideration as an objective function in concert with generation cost function. Furthermore, different operational constraints including valve-point effect, prohibited operating zones and multi-fuel operation are considered to make the proposed approach more realistic. Considering all these restrictions necessitate solving the proposed problem, i.e. multi-objective multi-area economic dispatch problem, by a reliable and strong optimization algorithm. In this regard, a hybrid evolutionary algorithm based on the shuffle frog leaping algorithm and the particle swarm optimization is proposed to solve the proposed problem. Effectiveness of the proposed hybrid algorithm is verified on different test systems.

DECOMPOSITION METHOD FOR SOLUTION OF A MULTI-AREA POWER DISPATCH PROBLEM

Large interconnected power systems are decomposed into areas or zones based on the size of the electric power system, network topology and geographical location. Multi-area economic emission dispatch (MAEED) problem is an optimisation task in power system operation for allocating amount of generation to the committed units within these areas. Its objective is to minimise the fuel cost subject to the power balance, generators limits, transmission lines, and tie-line constraints. The solution of the MAEED problem in the conditions of deregulation is difficult, due to the model size, nonlinearity, and interconnections. It determines the amount of power that can be economically generated in the areas and transferred to other areas if it is needed without violating tie-line capacity constraints. High-performance computing (HPC) gives possibilities for reduction of the problem complexity and the time for calculation by the use of parallel processing for running advanced application programs efficiently, reliably and quickly.

Fast Convergence Evolutionary Programming for Multi-area Economic Dispatch

This paper develops and suggests fast convergence evolutionary programming (FCEP) for solving multi-area economic dispatch problem with tie-line constraints, transmission losses, multiple fuels, valve point effect, and disallowed operating region. Evolutionary programming (EP), a class of evolutionary algorithm, is based on the basic genetic operation of human chromosomes. EP has the ability to seek out the global or close to the global optima. FCEP has been developed to boost convergence speed and solution quality. The efficacy of the developed technique has been tested on three different types of test systems. Test results have been compared with those acquired from improved fast evolutionary programming, EP and other stated evolutionary techniques. It has been observed from the comparison that the developed FCEP has the ability to offer superior solution.

Water Wave Optimization Algorithm for Solving Multi-Area Economic Dispatch Problem

Water Wave Optimization Algorithm for Solving Multi-Area Economic Dispatch Problem

Equal Incremental Fuel Cost Approach for Multi Area Operation of Power System

This paper presents a novel approach, Equal Incremental fuel cost (λ-Concept) approach, for solving Multi Area Economic Dispatch (MAED) problem. It is a simple approach and developed from the basic observation of incremental fuel cost of an area. The proposed approach has been tested on 4-area system with four generators in each area and a large 2-area system consists of 120 generators. The suggested algorithm has been tested extensively by considering the different tie line power transfer limits and useful recommendations are provided. Further, the impact of tie line power transfer limits on total fuel cost is also discussed. It is found from the test cases that the proposed method is shown to be robust, very fast and extensible to include a large class of problems. The simulation results of the proposed method have been compared with the existing methods.

Multi-Area Economic Dispatch Performance Using Swarm Intelligence Technique Considering Voltage Stability

Economic dispatch is one of the important issues in power system operation and planning. Economic dispatch requires reliable technique to achieve minimal cost; otherwise, a non-optimal solution may cause non-economic electricity generation to the utility. Single area economic dispatch does not make complete electricity generation of the whole system on the electrical transmission network. Thus, multi-area economic dispatch implementation leads to complete consideration for power transmission system. This paper presents multi-area economic dispatch performance using swarm intelligence technique. In this study, swarm intelligence technique, namely the particle swarm optimization technique (PSO) is employed for solving multi-area economic dispatch problems. The algorithm is tested on a 2-area 48-bus power system with different case studies. Variation in active power loading in achieving an optimal solution is also considered in this study. Several trials were taken into consideration to assess the consistency of results. Comparative studies were performed with respect to evolutionary programming (EP) and revealed that PSO yields better results as compared to the EP.

Practical multi‐area bi‐objective environmental economic dispatch equipped with a hybrid gradient search method and improved Jaya algorithm

Generation dispatch decision making integrated into a centralised wholesale electricity market has been always a challenging concern for transmission system operators. The reason lies mainly in the complex and highly-interconnected structure of the grid, escalated demand, and the crisis of the amount and price of energy. For the dispatch solutions to be highly reliable with an acceptable level of accuracy, several factors need to be taken into account, among which one can mention the valve-point effect, multiple fuel options, disjoint prohibited zones, up/down ramp rate requirements of units, as well as the spinning reserve constraints which, in turn, intensify the non-smoothness, non-convexity, non-linearity, and dynamic restriction of such combinatorial problems. This study proposes a new optimization toolset for the bi-objective multi-area economic dispatch problem to determine the transmission power flow and power output of units while satisfying system demand and security constraints at each area. The proposed architecture builds on an improved gradient-based Jaya algorithm to generate a feasible set of Pareto-optimal solutions corresponding to the operation cost and emission calculated through a new robust bi-objective gradient-based method. The projected algorithm is proved to be capable of finding the robust global or near-global Pareto solutions fast and accurate.

On the O(1/n) Convergence Rate of the Auxiliary Problem Principle for Separable Convex Programming and Its Application to the Power Systems Multi-Area Economic Dispatch Problem

The auxiliary problem principle has been widely applied in power systems to solve the multi-area economic dispatch problem. Although the effectiveness and correctness of the auxiliary problem principle method have been demonstrated in relevant literatures, the aspect connected with accurate estimate of its convergence rate has not yet been established. In this paper, we prove the O ( 1 / n ) convergence rate of the auxiliary problem principle method.