The Exact Solution of the Environmental/Economic Dispatch Problem

Bayón, L.; Grau, J. M.; Ruiz, M. M.; Suárez, P. M.

doi:10.1109/tpwrs.2011.2179952

Cited by 57 publications

(23 citation statements)

References 15 publications

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“…EED [13][17]is a typical two-objective MOPF with several constraints, in which a lower generation cost often relates to a higher emission magnitude, and similarly a lower emission usually relates to a higher generation cost. In this paper, transmission loss is adopted as the third objective function to demonstrate a comprehensive decision making using a trade-off strategy over more than two objectives.…”

Section: B Objective Functions Of Mopf and Constraintsmentioning

confidence: 99%

“…The system for the investigation is based on the IEEE 30-bus test system [26], which has 30 buses, 6 generators and the total load demand is 189.2MW. The fuel cost and the emission coefficients corresponding to each generation unit (i.e., , … , ) are extracted from [13] and listed in Table I . Each sub-problem is based on the AOF of the weighted sum as given in (12), and the linear combination of the cost and the emission via the weighted sum AOF, as well as constraints can be combined into a Lagrange function which can be solved by optimal power flow of Newton method [14].…”

Section: A Case Studymentioning

confidence: 99%

“…The mathematical programming methods [ 13 ] are often computationally fast even when dealing with a large scale MOPF and generally the optimal solution can be obtained stably each time. However, such methods are based on the use of derivatives, and can be easily trapped into local optima.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Judicious Decision-Making Approach for Power Dispatch in Smart Grid Using a Multiobjective Evolutionary Algorithm Based on Decomposition

Xiao

Sutanto

Muttaqi

et al. 2020

IEEE Trans. on Ind. Applicat.

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Multiobjective evolutionary algorithm based on decomposition (MOEA/D) is an efficient mathematical strategy for solving multiobjective optimization problems. However, the MOEA/D algorithm has not yet been widely used on the multiobjective optimal power flow (MOPF) problems, which consider several conflicting objectives with varying tradeoff levels. This article proposes a novel differential evolution (DE) strategy based on the MOEA/D framework to quickly determine a set of optimal solutions of MOPFs, in the objective space formed from the different objectives, such as the most optimal economic dispatch, the least environmental emission objectives, and the minimum transmission losses, while considering the power system constraints. A judicious decision can be made by the user from the set of optimal solutions of the MOPF associated with the weight vectors representing the tradeoff levels of the different objectives. For improved performance, two aggregate objective functions, a load flow operator and a selfadaptive DE strategy work cooperatively: 1) to improve the weak convergence of the MOEA/D and to achieve a better decision speed; 2) to obtain more accurate optimal solutions even under non-convex conditions; 3) to ensure that the power system constraints are taken into account; 4) to integrate the above features into a fast and efficient algorithm. The proposed algorithm has been validated using the IEEE 30-bus system and a revised 33-bus radial system added to one node of the 30-bus system. The simulation results show that the proposed algorithm can provide a good accuracy and can converge to a set of optimal solutions of the MOPFs. Disciplines Disciplines Engineering | Science and Technology StudiesAbstract-Multi-objective evolutionary algorithm based on decomposition (MOEA/D) is an efficient mathematical strategy for solving multi-objective optimization problems. However, the MOEA/D algorithm has not yet been widely used on the multiobjective optimal power flow (MOPF) problems, which considers several conflicting objectives with varying trade-off levels. This paper proposes a novel differential evolution (DE) strategy based on the MOEA/D framework to quickly determine a set of optimal solutions of MOPFs, in the objective space formed from the different objectives, such as the most optimal economic dispatch, the least environmental emission objectives, and the minimum transmission losses, while considering the power system constraints. A judicious decision can be made by the user from the set of optimal solutions of the MOPF associated with the weight vectors representing the trade-off levels of the different objectives. For improved performance, two aggregate objective functions, a load flow operator and a self-adaptive DE strategy work cooperatively: 1) to improve the weak convergence of the MOEA/D and to achieve a better decision speed; 2) to obtain more accurate optimal solutions even under non-convex conditions; 3) to ensure that the power system constraints are taken into account; 4) to integrate the ab...

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Section: B Objective Functions Of Mopf and Constraintsmentioning

confidence: 99%

Section: A Case Studymentioning

confidence: 99%

See 1 more Smart Citation

A Judicious Decision-Making Approach for Power Dispatch in Smart Grid Using a Multiobjective Evolutionary Algorithm Based on Decomposition

Xiao

Sutanto

Muttaqi

et al. 2020

IEEE Trans. on Ind. Applicat.

View full text Add to dashboard Cite

show abstract

“…F. Z. Gherbi et al [4] considered carbon emissions as an additional constraint to optimize the generation costs. The emissions and costs were also optimized separately as a single objective function, before weighted evaluating for each objective [5], [6]. Nonetheless, it would be more useful to apply multiobjective optimization problem (MOP) into EED for the purpose of fairly and effectively evaluating the interests of both costs and carbon emissions.…”

Section: Introductionmentioning

confidence: 99%

Stochastic environmental and economic dispatch of power systems with virtual power plant in energy and reserve markets

Hua¹,

Li²,

Sun³

et al. 2018

IJSGCE

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In order to alleviate the effects of greenhouse gas emissions, the environmental and economic dispatch (EED) is formulated as multiobjective optimization problem (MOP) solved by multiobjective immune algorithm (MOIA). Building on this model, the virtual power plant (VPP) is proposed involving distributed generation (DG), interruptible load (IL), and energy storage (ES) to participate in joint energy and reserve markets. The uncertainties of load prediction, DG, and IL are treated as an interval-based optimization in this study. The static and real-time simulations are conducted to demonstrate the validity of proposed stochastic EED model through the IEEE 30-bus test system.

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“…Abido (2006) compared three heuristic algorithms for the direct solution of the EEDP: non-dominated sorting genetic algorithms, niched Pareto genetic algorithms, and strength Pareto evolutionary algorithms. Bayón et al (2012), for the first time, presented the exact analytical solution for the EEDP. Jubril et al (2013) solved the WS strategy using semidefinite programming.…”

Section: Introductionmentioning

confidence: 99%

Solving the Multiobjective Environmental/Economic Dispatch Problem using Weighted Sum and $$\upvarepsilon $$ ε -Constraint Strategies and a Predictor-Corrector Primal-Dual Interior Point Method

Stanzani¹,

Balbo²,

Nepomuceno³

et al. 2014

J Control Autom Electr Syst

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This paper proposes a technique for solving the multiobjective environmental/economic dispatch problem using the weighted sum and ε-constraint strategies, which transform the problem into a set of single-objective problems. In the first strategy, the objective function is a weighted sum of the environmental and economic objective functions. The second strategy considers one of the objective functions: in this case, the environmental function, as a problem constraint, bounded above by a constant. A specific predictorcorrector primal-dual interior point method which uses the modified log barrier is proposed for solving the set of singleobjective problems generated by such strategies. The purpose of the modified barrier approach is to solve the problem with relaxation of its original feasible region, enabling the method to be initialized with unfeasible points. The tests involving the proposed solution technique indicate i) the efficiency of the proposed method with respect to the initialization with unfeasible points, and ii) its ability to find a set of efficient solutions for the multiobjective environmental/economic dispatch problem.

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The Exact Solution of the Environmental/Economic Dispatch Problem

Cited by 57 publications

References 15 publications

A Judicious Decision-Making Approach for Power Dispatch in Smart Grid Using a Multiobjective Evolutionary Algorithm Based on Decomposition

A Judicious Decision-Making Approach for Power Dispatch in Smart Grid Using a Multiobjective Evolutionary Algorithm Based on Decomposition

Stochastic environmental and economic dispatch of power systems with virtual power plant in energy and reserve markets

Solving the Multiobjective Environmental/Economic Dispatch Problem using Weighted Sum and $$\upvarepsilon $$ ε -Constraint Strategies and a Predictor-Corrector Primal-Dual Interior Point Method

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