Solving the multiobjective environmental/economic dispatch problem using weighted sum and ε-constraint strategies and a predictor-corrector primal-dual interior point method

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 predictor-corrector primal-dual interior point method which uses the modified log barrier is proposed for solving the set of single-objective 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.

Non-convex dynamic economic/environmental dispatch with plug-in electric vehicle loads

Electric vehicles are a key prospect for future transportation. A large penetration of electric vehicles has the potential to reduce the global fossil fuel consumption and hence the greenhouse gas emissions and air pollution. However, the additional stochastic loads imposed by plug-in electric vehicles will possibly introduce significant changes to existing load profiles. In his paper, electric vehicles loads are integrated into an 5-unit system using a non-convex dynamic dispatch model. The actual infrastructure characteristics including valve-point effects, load balance constrains and transmission loss have been included in the model. Multiple load profiles are comparatively studied and compared in terms of economic and environmental impacts in order o identify patterns to charge properly. The study as expected shows ha off-peak charging is the best scenario with respect to using less fuels and producing less emissions.

A self-learning teaching-learning based optimization for dynamic economic/environmental dispatch considering multiple plug-in electric vehicle loads

Economic and environmental load dispatch aims to determine the amount of electricity generated from power plants to meet load demand while minimizing fossil fuel costs and air pollution emissions subject to operational and licensing requirements. These two scheduling problems are commonly formulated with non-smooth cost functions respectively considering various effects and constraints, such as the valve point effect, power balance and ramp rate limits. The expected increase in plug-in electric vehicles is likely to see a significant impact on the power system due to high charging power consumption and significant uncertainty in charging times. In this paper, multiple electric vehicle charging profiles are comparatively integrated into a 24-hour load demand in an economic and environment dispatch model. Self-learning teaching-learning based optimization (TLBO) is employed to solve the non-convex non-linear dispatch problems. Numerical results on well-known benchmark functions, as well as test systems with different scales of generation units show the significance of the new scheduling method.

Reinforcement Learning approaches to Economic Dispatch problem

This paper presents Reinforcement Learning (RL) approaches to Economic Dispatch problem. In this paper, formulation of Economic Dispatch as a multi stage decision making problem is carried out, then two variants of RL algorithms are presented. A third algorithm which takes into consideration the transmission losses is also explained. Efficiency and flexibility of the proposed algorithms are demonstrated through different representative systems: a three generator system with given generation cost table, IEEE 30 bus system with quadratic cost functions, 10 generator system having piecewise quadratic cost functions and a 20 generator system considering transmission losses. A comparison of the computation times of different algorithms is also carried out.

An effortless hybrid method to solve economic load dispatch problem in power systems

This paper proposes a new approach and coding scheme for solving economic dispatch problems (ED) in power systems through an effortless hybrid method (EHM). This novel coding scheme can effectively prevent futile searching and also prevents obtaining infeasible solutions through the application of stochastic search methods, consequently dramatically improves search efficiency and solution quality. The dominant constraint of an economic dispatch problem is power balance. The operational constraints, such as generation limitations, ramp rate limits, prohibited operating zones (POZ), network loss are considered for practical operation. Firstly, in the EHM procedure, the output of generator is obtained with a lambda iteration method and without considering POZ and later in a genetic based algorithm this constraint is satisfied. To demonstrate its efficiency, feasibility and fastness, the EHM algorithm was applied to solve constrained ED problems of power systems with 6 and 15 units. The simulation results obtained from the EHM were compared to those achieved from previous literature in terms of solution quality and computational efficiency. Results reveal that the superiority of this method in both aspects of financial and CPU time. (C) 2011 Elsevier Ltd. All rights reserved.

Designing a modified Hopfield network to solve an Economic Dispatch problem with nonlinear cost function

Economic Dispatch (ED) problems have recently been solved by artificial neural networks approaches. In most of these dispatch models, the cost function must be linear or quadratic. Therefore, functions that have several minimum points represent a problem to the simulation since these approaches have not accepted nonlinear cost function. Another drawback pointed out in the literature is that some of these neural approaches fail to converge efficiently towards feasible equilibrium points. This paper discusses the application of a modified Hopfield architecture for solving ED problems defined by nonlinear cost function. The internal parameters of the neural network adopted here are computed using the valid-subspace technique, which guarantees convergence to equilibrium points that represent a solution for the ED problem. Simulation results and a comparative analysis involving a 3-bus test system are presented to illustrate efficiency of the proposed approach.

Investigação e aplicação de métodos primal - dual pontos interiores em problemas de despacho econômico e ambiental

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Métodos híbridos de pontos interiores/exteriores e de aproximantes de funções em problemas multiobjetivo de despacho econômico e ambiental

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A Reinforcement Learning Algorithm to Economic Dispatch Considering Transmission Losses

Reinforcement Learning (RL) refers to a class of learning algorithms in which learning system learns which action to take in different situations by using a scalar evaluation received from the environment on performing an action. RL has been successfully applied to many multi stage decision making problem (MDP) where in each stage the learning systems decides which action has to be taken. Economic Dispatch (ED) problem is an important scheduling problem in power systems, which decides the amount of generation to be allocated to each generating unit so that the total cost of generation is minimized without violating system constraints. In this paper we formulate economic dispatch problem as a multi stage decision making problem. In this paper, we also develop RL based algorithm to solve the ED problem. The performance of our algorithm is compared with other recent methods. The main advantage of our method is it can learn the schedule for all possible demands simultaneously.

An efficient neural approach to economic load dispatch in power systems

A neural approach to solve the problem defined by the economic load dispatch in power systems is presented in this paper, Systems based on artificial neural networks have high computational rates due to the use of a massive number of simple processing elements and the high degree of connectivity between these elements the ability of neural networks to realize some complex nonlinear function makes them attractive for system optimization the neural networks applyed in economic load dispatch reported in literature sometimes fail to converge towards feasible equilibrium points the internal parameters of the modified Hopfield network developed here are computed using the valid-subspace technique These parameters guarantee the network convergence to feasible quilibrium points, A solution for the economic load dispatch problem corresponds to an equilibrium point of the network. Simulation results and comparative analysis in relation to other neural approaches are presented to illustrate efficiency of the proposed approach.

Optimal reactive power dispatch using stochastic chance-constrained programming

Deterministic Optimal Reactive Power Dispatch problem has been extensively studied, such that the demand power and the availability of shunt reactive power compensators are known and fixed. Give this background, a two-stage stochastic optimization model is first formulated under the presumption that the load demand can be modeled as specified random parameters. A second stochastic chance-constrained model is presented considering uncertainty on the demand and the equivalent availability of shunt reactive power compensators. Simulations on six-bus and 30-bus test systems are used to illustrate the validity and essential features of the proposed models. This simulations shows that the proposed models can prevent to the power system operator about of the deficit of reactive power in the power system and suggest that shunt reactive sourses must be dispatched against the unavailability of any reactive source. © 2012 IEEE.

Penalty-based nonlinear solver for optimal reactive power dispatch with discrete controls

The optimal reactive dispatch problem is a nonlinear programming problem containing continuous and discrete control variables. Owing to the difficulty caused by discrete variables, this problem is usually solved assuming all variables as continuous variables, therefore the original discrete variables are rounded off to the closest discrete value. This approach may provide solutions far from optimal or even unfeasible solutions. This paper presents an efficient handling of discrete variables by penalty function so that the problem becomes continuous and differentiable. Simulations with the IEEE test systems were performed showing the efficiency of the proposed approach. © 1969-2012 IEEE.

Método previsor-corretor primal-dual de pontos interiores em problemas multiobjetivo de despacho econômico e ambiental

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Particle Swarm Optimization Based Reactive Power Dispatch for Power Networks with Distributed Generation

Reactive power is critical to the operation of the power networks on both safety aspects and economic aspects. Unreasonable distribution of the reactive power would severely affect the power quality of the power networks and increases the transmission loss. Currently, the most economical and practical approach to minimizing the real power loss remains using reactive power dispatch method. Reactive power dispatch problem is nonlinear and has both equality constraints and inequality constraints. In this thesis, PSO algorithm and MATPOWER 5.1 toolbox are applied to solve the reactive power dispatch problem. PSO is a global optimization technique that is equipped with excellent searching capability. The biggest advantage of PSO is that the efficiency of PSO is less sensitive to the complexity of the objective function. MATPOWER 5.1 is an open source MATLAB toolbox focusing on solving the power flow problems. The benefit of MATPOWER is that its code can be easily used and modified. The proposed method in this thesis minimizes the real power loss in a practical power system and determines the optimal placement of a new installed DG. IEEE 14 bus system is used to evaluate the performance. Test results show the effectiveness of the proposed method.

A genetic algorithm based method for deregulated electricity market dispatch

In a deregulated electricity market, optimizing dispatch capacity and transmission capacity are among the core concerns of market operators. Many market operators have capitalized on linear programming (LP) based methods to perform market dispatch operation in order to explore the computational efficiency of LP. In this paper, the search capability of genetic algorithms (GAs) is utilized to solve the market dispatch problem. The GA model is able to solve pool based capacity dispatch, while optimizing the interconnector transmission capacity. Case studies and corresponding analyses are performed to demonstrate the efficiency of the GA model.