Parallel Augmented Lagrangian Relaxation for Multi- Period Economic Dispatch Using Diagonal Quadratic Approximation Method

One of the surface mining methods is open-pit mining, by which a pit is dug to extract ore or waste downwards from the earth’s surface. In the mining industry, one of the most significant difficulties is long-term production scheduling (LTPS) of the open-pit mines. Deterministic and uncertainty-based approaches are identified as the main strategies, which have been widely used to cope with this problem. Within the last few years, many researchers have highly considered a new computational type, which is less costly, i.e., meta-heuristic methods, so as to solve the mine design and production scheduling problem. Although the optimality of the final solution cannot be guaranteed, they are able to produce sufficiently good solutions with relatively less computational costs. In the present paper, two hybrid models between augmented Lagrangian relaxation (ALR) and a particle swarm optimization (PSO) and ALR and bat algorithm (BA) are suggested so that the LTPS problem is solved under the condition of grade uncertainty. It is suggested to carry out the ALR method on the LTPS problem to improve its performance and accelerate the convergence. Moreover, the Lagrangian coefficients are updated by using PSO and BA. The presented models have been compared with the outcomes of the ALR-genetic algorithm, the ALR-traditional sub-gradient method, and the conventional method without using the Lagrangian approach. The results indicated that the ALR is considered a more efficient approach which can solve a large-scale problem and make a valid solution. Hence, it is more effectual than the conventional method. Furthermore, the time and cost of computation are diminished by the proposed hybrid strategies. The CPU time using the ALR-BA method is about 7.4% higher than the ALR-PSO approach.

This paper deals with dynamic combined economic emission dispatch problem of an electric power system consisting of thermal, hydro and photovoltaic (PV) power plants. Mathematical models of these plants as well as the model of dynamic combined economic-environmental nonlinear optimization problem are given. The proposed optimization model was implemented in publicly available GAMS software, and the result is the optimal load distribution among the plants during a one-day optimization period. The software is applied to the power system without PV power plants and with a number of new PV plants added to the existing hydrothermal system. The results quantify the positive effects of PV power plants on both fuel cost and greenhouse gas reduction and recommendations are given related to the application of PV generation in modern systems. Software efficiency in solving both dynamic economic dispatch (DED) and dynamic combined economic emission dispatch (DCEED) problems is discussed, and the conclusions are drawn about its application possibilities.

Enhanced physics-informed neural networks with Augmented Lagrangian relaxation method (AL-PINNs)

Enhanced sequential approximate programming using second order reliability method for accurate and efficient structural reliability-based design optimization

The dynamic economic dispatch (DED) problem is an extension of the conventional static load dispatch problem in the context of electrical power generation. In this paper, issues related to the implementation of the several soft computing techniques are highlighted for a successful application to solve dynamic economic dispatch (DED) problem, which is a constrained optimization problem in power systems. First of all, a survey covering the basics of the techniques is presented and then implementation of the techniques in the DED problem is discussed. The soft computing techniques, namely multi-layered perceptron neural network (MLP NN), genetic algorithm (GA), Imperialist Competitive Algorithm(ICA), particle swarm (PSO) and are applied to solve the DED problem. The Evolutionary Algorithms are tested on power system consisting 3 generating units and the results are compared together. Suggestion is presented to improve techniques.

The robust optimization based dynamic economic dispatch (DED) model has been extensively studied to address uncertainties of net loads induced by renewable energy resource variabilities and demand fluctuations. However, the robust DED model is computationally expensive, when solved by the column-and-constraint generation (CCG) approach that iterates between a master problem and a max-min subproblem. This letter proposes a feasible region projection-based approach to equivalently reformulate the robust DED as a single-level linear programming (LP) model that can be effectively solved while guaranteeing solution optimality. Numerical studies show the proposed approach is one order of magnitude faster than CCG.

We present in this paper new results on the existence of saddle points of augmented Lagrangian functions for constrained nonconvex optimization. Four classes of augmented Lagrangian functions are considered: the essentially quadratic augmented Lagrangian, the exponential-type augmented Lagrangian, the modified barrier augmented Lagrangian, and the penalized exponential-type augmented Lagrangian. We first show that under second-order sufficiency conditions, all these augmented Lagrangian functions possess local saddle points. We then prove that global saddle points of these augmented Lagrangian functions exist under certain mild additional conditions. The results obtained in this paper provide a theoretical foundation for the use of augmented Lagrangians in constrained global optimization. Our findings also give new insights to the role played by augmented Lagrangians in local duality theory of constrained nonconvex optimization.

Multi-objective dynamic economic emission dispatch of electric power generation integrated with game theory based demand response programs

Dynamic economic emission dispatch considering renewable energy generation: A novel multi-objective optimization approach

Duality in nonlinear programs using augmented Lagrangian functions

Estimation of Optimal Well Controls Using the Augmented Lagrangian Function with Approximate Derivatives

Dynamic economic dispatch problem in power system considering valve‐point effects of generators is a non‐smooth, non‐convex and multi‐dimensional constrained optimisation problem. In allusion to those characteristics, this study proposes a hybrid algorithm which integrates low‐discrepancy sequences, improved shuffled frog leaping algorithm and sequential quadratic programming. The effectiveness of the proposed method has been verified by using case studies based on 5‐unit, 10‐unit and 30‐unit test systems over a period of 24 h. The results show that the proposed method has improved solution quality and computation efficiency, compared with most current approaches.

Dynamic economic dispatch (DED) that considers valve-point effects is a complex nonconvex and nonsmooth optimization problem in power systems. Over the past few decades, multiple approaches have been developed to solve this problem. In this paper, an adaptive differential evolution based on simulated annealing algorithm is proposed to solve the DED problem with valve-point effects. Simulated annealing (SA) algorithm is employed to carry out an adaptive selection mechanism in which the mutation operators of differential evolution (DE) are selected adaptively based on their historical performance. A mutation operator pool consisting of five operators is built to make each operator show its strength at different stages of the evolutionary process. Moreover, a heuristic strategy is introduced to transform infeasible solutions towards feasible ones to enhance the convergence rate of the proposed algorithm. The effectiveness of the proposed methods is demonstrated first on 10 popular benchmark functions with 100 dimensions, in comparison with the classic DE and five variants. Then, it is used to solve four DED problems with 10, 15, 30, and 54 units, which consider the valve-point effects, transmission loss, and prohibited operating zones. The simulation results are compared with those of state-of-the-art algorithms to clarify the significance of the proposed method and verify its performance. Three systems with 100-500 generators are also tested to confirm the advantages of the proposed method on large-scale DED problem.

Look ahead dynamic security-constrained economic dispatch considering frequency stability and smart loads

A dynamic economic emission dispatch considering wind power uncertainty incorporating energy storage system and demand side management