Multi-area Economic Dispatch Research Articles

A reliable deterministic method for multi-area economic dispatch considering power losses

This paper offers a reliable deterministic method for solving multi-area economic dispatch (MAED). The proposed method can handle nonlinear power losses in electrical networks and discrete and nonlinear characteristics in power plants, such as fuel change facilities and nonconvex cost functions. To this end, the presented method reformulates the products of two variables in the power loss terms as one-dimensional expressions. Then, it converts all nonlinear terms in the MAED into linear segments. Moreover, it handles discrete decisions in fuel selection through binary variables. We assess the performance of the proposed method by some MAED test systems. The results show that the method can reliably obtain accurate solutions in the adopted test systems. It converges to costs of 10604.7, 654.7, 121592.7, 124628.4, and 169528.9 respectively in 2-area 4-unit, 3-area 10-unit, 4-area 40-unit, 2-area 40-unit, and 10-area 130-unit. These findings reproduce or outperform results found in earlier optimization algorithms. Moreover, the computational time evaluations indicate that the method can solve the adopted MAED problems in less than one minute, showing its efficiency. Overall, the obtained results confirm the efficacy of the method’s efficacy in handling the MAED with discrete and nonlinear terms.

Decentralized Multi-Area Economic Dispatch in Power Systems Using the Consensus Algorithm

A multi-area power system requires coordination to enhance reliability and reduce operating costs. Economic dispatch in such systems is crucial because of the uncertainties associated with variable loads and the increasing penetration of renewable energy sources. This paper presents a hierarchical consensus algorithm designed to determine the economic dispatch in a multi-area power system, accounting for the uncertainties in load and renewable generation. The proposed algorithm, which utilizes distributed agents, operates across three levels. Level 1 coordinates all areas, while levels 2 and 3 form a leader–follower consensus algorithm for overall economic dispatch. Breadth-first search is employed to identify the leader agent within each area. To address the uncertainties in loads and renewable generation, Monte Carlo simulations are performed. The efficacy of the proposed method is validated using the IEEE 39-bus and 118-bus systems, as well as a realistic 1968-bus power system in Taiwan. The traditional equal lambda method is employed to verify that the proposed approach is suitable for multi-area power systems using distributed computation.

Large-scale power system multi-area economic dispatch considering valve point effects with comprehensive learning differential evolution

The role of multi-area economic dispatch (MAED) in power system operation is increasingly significant. It is a non-linear and multi-constraint problem with many local extremes when considering the valve point effects, posing challenges in obtaining a globally optimal solution, especially for large-scale systems. In this study, an improved variant of differential evolution (DE) called CLDE based on comprehensive learning strategy (CLS) is proposed to solve this problem. Three improved strategies are employed to enhance the performance of CLDE. (1) A CLS-based guided mutation strategy is proposed, in which learning exemplars constructed by competent individuals are used to generate mutant vectors to prevent the searching away from global optimum and speed up convergence. (2) A time-varying increasing crossover rate is devised. It can endow CLDE with a larger probability at the later stage to help individuals escape from local extremes. (3) A CLS-based crossover strategy is presented. Trial vectors directly utilize the information from learning exemplars for evolving, which can ensure the search efficiency and population diversity. CLDE is applied to six MAED cases. Compared with DE, it approximately consumes 32 %, 35 %, 10 %, 22 %, 62 %, and 20 % of evaluations to attain comparable results, saves 126.2544$/h, 81.8173$/h, 152.0660$/h, 360.7907$/h, 65.5757$/h, and 1732.8544$/h in fuel costs on average, and exhibits improvements of 34.77 %, 1.80 %, 0.00 %, 76.09 %, 95.15 %, and 16.76 % in robustness, respectively. Moreover, it also outperforms other state-of-the-art algorithms significantly in statistical analysis. Furthermore, the effects of improved strategies on CLDE are thoroughly investigated.

Multi-Area Load Dispatch with Emission and Fuel Cost Constraints Using Deep Recurrent Lstm Under Stochastic Pv and Wind Power Integration

An interconnected power system must employ multi-area economic load dispatch (MAELD) to keep generation dispatch efficient, satisfy load demands, and stay within technological limits. The goal of MAELD's operational constraints is to reduce fuel costs and emissions from multi-area power production facilities. Consequently, optimization solutions that successfully tackle MAELD problems are highly sought after. By merging an alternative model with the Deep Recurrent Neural Network (DRNN) one, this paper suggests a fresh approach to addressing MAELD problems. This paper provides a detailed account of the various optimization methodologies used to address the issue of load dispatch when non-conventional energy sources are present. Four domains utilizing 3-, 13-, and 40-unit systems were used to test the suggested DRNN and LSTM approach. Comparing this method to various optimization algorithms as firefly, Salp Swarm, Squirrel search, Particle Swarm, and Gross Hopper, results produced from the MATLAB/Simulink environment show that it delivers superior trade-off solutions without breaching limitations.

A novel derivative search political optimization algorithm for multi-area economic dispatch incorporating renewable energy

Multi-area economic dispatch (MAED) incorporating renewable energy has become an important issue in the power system optimization. Existing intelligent optimization algorithms often suffer from poor solution accuracy or slow convergence when dealing with MAED problems. In this paper, a novel derivative search-based political optimization (DSPO) algorithm is proposed to handle the MAED problem incorporating renewable energy including wind and solar energy. In the renewable energy modeling, the Weibull and log-normal probability density functions are used to calculate available wind and solar power respectively. In order to improve the search performance, DSPO adopts two strategies: leader guide strategy and derivative search mechanism. The former adds the leader’s global optimal information which can direct candidate solutions to more promising regions and speed up convergence. The latter derives neighborhood solutions around some high-quality solutions to improve the exploitation ability. The DSPO algorithm is applied to solve four MAED problems which take into account valve point effect, prohibited operating zone, power loss and so on. The simulation results show that the DSPO algorithm achieves the overall best results in terms of convergence speed, solution accuracy and stability when compared with several well-established algorithms.

Continuous power imbalance assessment from multi-area economic dispatch models

To be able to efficiently maintain a continuous balance between supply and demand in power systems with high shares of variable renewable energy (VRE) sources, a variety of studies related to the topic are needed. A fundamental input parameter for such studies is an assessment of the power system’s physical needs for balancing power, in form of power imbalances. This article presents a new model for simulating physical power imbalances with a 1-minute time resolution based on multi-area economic dispatch simulations. Compared to existing models with the same purpose, the new model includes the combination of simulating power imbalances with 1-minute time resolution, simulating forecast uncertainty, simulating the continuous behaviour of all power system components and simulating the transmission for netting of power imbalances between balancing areas. By applying the model to a case study of the Nordic synchronous power system in year 2045, the impact of including these features in the model is highlighted. Case study results also show that the size and pattern of power imbalances much depends on the characteristics of a balancing area, in terms of electricity demand, available generation technologies and interconnections to other balancing areas.

Performance comparison of dynamically controlled particle swarm optimization and grey wolf optimizer for dynamic power reserve scheduling in multi areas problems

The primary goal of Multi-Area Economic Dispatch (MAED) is to effectively meet the dynamic power demands of multiple interconnected regions while optimizing the economical generation dispatch strategy. This paper introduces a comprehensive investigation into the application of two advanced optimization techniques, namely Dynamically Controlled Particle Swarm Optimization (DCPSO) and thereafter Grey Wolf Optimizer (GWO), and their variant adaptations to address the complex challenges posed by MAED issue. The performance and efficacy of these strategies are rigorously assessed in three distinct scenarios: (a) Single-Area Power System with Three Generation Units: This scenario represents a fundamental single-area power network comprising three generation units. (b) Two-Area System with Four Generating Units: In this case, a two-area system with four generating units is analyzed. (c) Four-Area System with Forty Generation Units and Six Tie Lines. In the most intricate scenario, a four-area interconnected power system is scrutinized, featuring a total of forty generation units. GWO technique produces the cost saving of $ 0.1 for single area, 2 area cost saving is $ 0.11 likewise for 4 area the cost saving is $ 474.10 over the PSO. The execution time taken by GWO is 12.7 sec. less compared to DPSO.

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

Black Widow Optimization for Multi Area Economic Emission Dispatch

The optimization field has grown tremendously, and new optimization techniques are developed based on statistics and evolutionary procedures. Therefore, it is necessary to identify a suitable optimization technique for a particular application. In this work, Black Widow Optimization (BWO) algorithm is introduced to minimize the cost functions in order to optimize the Multi-Area Economic Dispatch (MAED). The BWO is implemented for two different-scale test systems, comprising 16 and 40 units with three and four areas. The performance of BWO is compared with the available optimization techniques in the literature to demonstrate the strategy’s efficacy. Results show that the optimized cost for four areas with 16 units is found to be 7336.76$/h, whereas it is 121,589$/h for four areas with 40 units using BWO. It is also noted that optimization algorithms other than BWO require higher cost value. The best-optimized solution for emission is achieved at 9.2784e+06 tones/h, and it is observed that there is a considerable difference between the worst and the best values. Also, the suggested technique is implemented for large-scale test systems successfully with high precision, and rapid convergence occurs in MAED.

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.

Decentralized power economic dispatch by distributed crisscross optimization in multi-agent system

This paper proposes a high-efficient crisscross optimization (CSO) solution to the multi-area economic dispatch (MAED) in both centralized and decentralized optimization manners. First, the CSO is first employed to solve the complex MAED problem by using two powerful search operators including horizontal crossover and vertical crossover. Second, a unique distributed crisscross optimization (DCSO) is put forward to address the MAED problem in a fully decentralized optimization manner, aiming to protect the data privacy, reduce the solving dimensions, and alleviate the heavy communication burden. Under the decentralized framework, the proposed DCSO allows several separate CSOs across the network to optimize the operation of each generation area in parallel. Third, the CSOs assigned to different generation areas are all implemented by multi-agent system that provides the underlying framework of communication between generation areas, which contributes to achieving the independent and asynchronous optimization in each area while minimizing the total operational cost of the entire multi-area power system. Finally, the proposed approach is validated on three different cases. The experimental results verify the superiority of the CSO over other methods in solving the conventional MAED problem and confirm the effectiveness of the proposed DCSO in solving the decentralized MAED problem.

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.

Multiarea Economic Dispatch Using Evolutionary Algorithms

Multiarea economic dispatch (MAED) is a vital problem in the present power system to allocate the power generation through dispatch strategies to minimize fuel cost. In economic dispatch, this power generation distribution always needs to satisfy the following constraints: generating limit, transmission line, and power balance. MAED is a complex and nonlinear problem and cannot be solved with classical techniques. Many metaheuristic methods have been used to solve economic dispatch problems. In this study, the dynamic particle swarm optimization (DPSO) and grey wolf optimizer (GWO) have been used to solve the MAED problem for single-area 3 generation units, a two-area system with four generating units, and four areas with 40-unit system. The hunting and social behaviors of grey wolves are implemented to obtain optimal results. During the optimization search, this algorithm does not require any information regarding the objective function’s gradient. The tunable parameters of the original PSO that are three parameters are dynamically controlled in this work that provides the efficient cost values in less execution time although satisfying all the MAED problem’s diverse constraints. In this study, the authors also implemented the GWO algorithm with two tunable parameters, and its execution is straightforward to implement for the MAED problem.

Decentralized multi-area multi-agent economic dispatch model using select meta-heuristic optimization algorithms

This paper presents a decentralized multiarea multiagent economic dispatch (DMMED) model using select meta-heuristic optimization (MO) algorithms. The previous multiarea economic dispatch (MAED) studies that used MO algorithms were centrally planned and did not include multiple independent local agents in their decision-making framework. The proposed model allows to optimize the operation of the power systems involving the system operators (TSOs) and multiple independent local aggregators (LAs) in a decentralized manner. The objective of the model is to minimize the total operation cost of the system in a time-efficient manner by effectively coordinating the operation of the TSOs and LAs. Each area accounts for its operational uncertainties and power reserves considering the worst-case scenarios of the uncertainty sets of the individual agent in the area. To respect each area ownership, the solution algorithm utilizes separate population sets and a dependent bi-level operation approach to solve the DMMED model for each area in parallel, allowing the areas to achieve optimal operation, independently. Case studies with select MO algorithms are performed on a modified Nigerian 330 kV 39-bus transmission systems having three areas each with one TSO and three LAs to demonstrate the effectiveness of the proposed model.

Multi-area economic environmental dispatch using multi-objective squirrel search algorithm

The main objective of multi-area economic/environmental dispatch (MAEED) problems is the effective management of electrical energy generation by minimizing the total fuel cost and emissions of a multi-area power generation units, while satisfying various system and operating constraints. This paper bestows a new swarm intelligence approach, multi-objective squirrel search algorithm (MOSSA) to solve the MAEED problem. In the suggested approach, an exterior elitist vault system, crowding distance and fuzzy clustering principles are acquainted to procure a uniformly spaced Pareto optimal front curve. In addition, the MAEED problem is unraveled by squirrel search algorithm based weighted sum approach (SSA-WSA) with price penalty factors, artificial bee colony (ABC) and exchange market algorithm (EMA). The adequacy of the suggested strategy is approved on 40 generating units with single and multi-area power systems. The numeric results exhibit that the suggested MOSSA strategy accomplished much preferred trade-off solutions over the SSA-WSA, ABC, EMA and different strategies surfaced in the literature. The result transmuted evinces the desirability of MOSSA to solve the MAEED problem.

Solving power systems optimization problems in the presence of renewable energy sources using modified exchange market algorithm

This paper introduces a novel evolutionary algorithm namely modified exchange market algorithm (MEMA) to solve the various problems in the power system operation topics such as combined heat and power economic emission dispatch (CHPEED), and multi-area economic dispatch (MAED) in the presence of renewable energy sources (RESs). The MEMA is a new version of the EMA that has been modified to improve its performance and to find a better solution with high robustness. To scrutiny the applicability of the MEMA, it is employed to solve the different problems with considering RESs. Also, to prove the scalability and evaluate the performance of the proposed method, several large and small scale test systems are used in each case. Also, three different approaches are considered to investigate the impacts of RESs. In the first approach, RESs are assumed to be a negative load, while in the latter case, their cost impacts on the problem are also considered. Finally, in the last approach, the uncertainty of RES and its stochastic nature are considered. In all test systems, the results obtained by the proposed method are compared with the results of other suggested techniques in this era. Also, the robustness of the proposed method is investigated using parametric and non-parametric statistical tests. The comparative and statistical analysis confirm the superiority and robustness of the proposed method over the other methods in all test systems.

An Effective Algorithm for MAED Problems with a New Reliability Model at the Microgrid

This paper proposes a new framework for multi-area economic dispatch (MAED) in which the cost associated with the reliability consideration is taken into account together with the common operational and emission costs using expected energy not supplied (EENS) index. To improve the reliability level, the spinning reserve capacity is considered in the model as well. Furthermore, the MAED optimization problem and non-smooth cost functions are taken into account as well as other technical limitations such as tie-line capacity restriction, ramp rate limits, and prohibited operating zones at the microgrid. Considering all the above practical issues increases the complexity in terms of optimization, which, in turn, necessitates the use of a powerful optimization tool. A new successful algorithm inspired by phasor theory in mathematics, called phasor particle swarm optimization (PPSO), is used in this paper to address this problem. In PPSO, the particles’ update rules are driven by phase angles to essentially ensure a spread of variants across the population so that exploitation and exploration can be balanced. The optimal results obtained via simulations confirmed the capability of the proposed PPSO algorithm to find suitable optimal solutions for the proposed model.