In this chapter, you will see how the simplex method simplifies when it is applied to a class of optimization problems that are known as “network flow models.” You will also see that if a network flow model has “integer-valued data,” the simplex method finds an optimal solution that is integer-valued.

Flows in Networks

Spot Pricing of Electricity

We give the reader a tour of good energy optimization models that explicitly deal with uncertainty. The uncertainty usually stems from unpredictability of demand and/or prices of energy, or from resource availability and prices. Since most energy investments or operations involve irreversible decisions, a stochastic programming approach is meaningful. Many of the models deal with electricity investments and operations, but some oil and gas applications are also presented. We consider both traditional cost minimization models and newer models that reflect industry deregulation processes. The oldest research precedes the development of linear programming, and most models within the market paradigm have not yet found their final form.

https://www.pogc.ir/Portals/0/maghalat/890812.13.pdf

Stochastic Programming Models in Energy

This article presents a review of the state of the art of the Wind Farm Design and Optimization (WFDO) problem. The WFDO problem refers to a set of advanced planning actions needed to extremize the performance of wind farms, which may be composed of a few individual Wind Turbines (WTs) up to thousands of WTs. The WFDO problem has been investigated in different scenarios, with substantial differences in main objectives, modelling assumptions, constraints, and numerical solution methods. The aim of this paper is: (1) to present an exhaustive survey of the literature covering the full span of the subject, an analysis of the state-of-the-art models describing the performance of wind farms as well as its extensions, and the numerical approaches used to solve the problem; (2) to provide an overview of the available knowledge and recent progress in the application of such strategies to real onshore and offshore wind farms; and (3) to propose a comprehensive agenda for future research.

/pdf/a-review-of-methodological-approaches-for-the-design-and-2jexgpua4r.pdf

A Review of Methodological Approaches for the Design and Optimization of Wind Farms

The layout scheme of wind farms is a challenging job having many design objectives and constraints due to the multiple wake phenomenon. Wake effect calculation is one of the significant problems in the wind farms and needs to be modeled to decrease the power loss due to near and far wake effect. This paper reviews the wake models in general and far wake models in particular. The comparison of different far wake models shows that the Jensen׳s far wake model is a good choice to solve the wind farm layout problem due to its simplicity and relatively high degree of accuracy. This research also focuses on the studies carried out on wind farm layout optimization problem and the current state of the art of fitness functions used for the optimization of wind farms using Jensen׳s wake model. It is found that there is a need of more optimization techniques to be applied to solve the layout problem. In addition, future advancements have been identified for better positioning of wind turbines in larger wind farms.

Wake effect modeling: A review of wind farm layout optimization using Jensen׳s model

http://www.optimization-online.org/DB_FILE/2010/10/2767.pdf

Solving shortest path problems with a weight constraint and replenishment arcs

Hydro-electric unit commitment subject to uncertain demand

This paper applies recently developed mixed-integer programming (MIP) tools to the problem of optimal siting and sizing of distributed generators in a distribution network. We investigate the merits of three MIP approaches for finding good installation plans: a full AC power flow approach, a linear DC power flow approximation, and a nonlinear DC power flow approximation with quadratic loss terms, each augmented with integer generator placement variables. A genetic algorithm-based approach serves as a baseline for the comparison. A simple knapsack problem method involving generator selection is presented for determining lower bounds on the optimal design objective. Solution methods are outlined, and computational results show that the MIP methods, while lacking the speed of the genetic algorithm, can find improved solutions within conservative time requirements and provide useful information on optimality.

/pdf/comparison-of-mixed-integer-programming-and-genetic-31u0ezvqkp.pdf

Comparison of Mixed-Integer Programming and Genetic Algorithm Methods for Distributed Generation Planning

This work develops a wind intensity interference coefficient which captures the interference caused by an upwind turbine on a downwind turbine in the same wind flow. This coefficient includes the use of a Weibull distribution to handle variability in the wind velocity, and also accounts for the geometric relationship between the turbines and the boundaries of the wind sector. This interference coefficient then forms part of a mixed integer linear program (MILP) which is used to optimise the locations of wind turbines within a wind farm site. The MILP approach is an exact method that can guarantee that the turbine locations determined by the model are optimal with respect to an a priori chosen set of possible turbine locations. Tests on an example data set (based on a demonstration case in the WindFarmer software) show, for the particular wind resource used, that interference results in a loss of power of approximately 4.2% when compared to the power production which would be predicted without accounting f...

/pdf/wind-turbine-interference-in-a-wind-farm-layout-optimization-edxasgqsk5.pdf

Hamish Waterer

Papers

Solving shortest path problems with a weight constraint and replenishment arcs

Hydro-electric unit commitment subject to uncertain demand

Comparison of Mixed-Integer Programming and Genetic Algorithm Methods for Distributed Generation Planning

Wind Turbine Interference in a Wind Farm Layout Optimization Mixed Integer Linear Programming Model

Integer programming methods for large-scale practical classroom assignment problems