Steffen Rebennack

Optimal Bidding Strategies for Hydro-Electric Producers: A Literature Survey

In a competitive environment with bid-based markets, power generation companies desire to develop bidding strategies that maximize their revenue. In this paper we ask: What approaches and methodologies have been used to model the bidding problem for hydro-electric producers? We present the problems developments over time and, through reviewing different variants of the problem, progressively build to the case in which the agent is a price-maker hydro-electric producer. In each variant of the bidding problem, we examine how the approaches used to solve it may or may not be applicable to other variants. Last, for the price-maker hydro-electric producers bidding problem, we recognize the most recent developments and illuminate a path for future efforts.

Stochastic Hydro-Thermal Scheduling Under

Despite the uncertainty surrounding the design of a mechanism which is ultimately accepted by nations worldwide, the necessity to implement regulations to curb emissions of greenhouse gases on a global scale is consensual. The electricity sector plays a fundamental role in this puzzle and countries may soon have to revise their operating policy directives in order to make them compatible with additional constraints imposed by such regulations. We present a modeling approach for greenhouse gas emissions quotas which can be incorporated into a stochastic dual dynamic programming algorithm, commonly used to solve the hydro-thermal scheduling problem. Our approach is flexible and capable of accommodating a detailed representation of emissions and related constraints. A case study based on the Guatemalan power system exemplifies the potential effects of considering these restrictions.

{\rm CO}_{2}

This paper deals with the cutting-plane approach to the maximum stable set problem. We provide theoretical results regarding the facet-defining property of inequalities obtained by a known project-and-lift-style separation method called edge-projection, and its variants. An implementation of a Branch and Cut algorithm is described, which uses edge-projection and two other separation tools which have been discussed for other problems: local cuts (pioneered by Applegate, Bixby, Chvátal and Cook) and mod-k cuts. We compare the performance of this approach to another one by Rossi and Smiriglio (Oper. Res. Lett. 28:63–74, 2001) and discuss the value of the tools we have tested.

Emissions Constraints

With the surge of the global energy demand, natural gas plays an increasingly important role in the global energy market. To meet the demand, optimization techniques have been widely used in the natural gas industry, and has yielded a lot of promising results. In this chapter, we give a detailed discussion of optimization models in the natural gas industry, with the focus on the natural gas production, transportation, and market.

A Branch and Cut solver for the maximum stable set problem

Nested Benders decomposition is a widely used and accepted solution methodology for multi-stage stochastic linear programming problems. Motivated by large-scale applications in the context of hydro-thermal scheduling, in 1991, Pereira and Pinto introduced a sampling-based variant of the Benders decomposition method, known as stochastic dual dynamic programming (SDDP). In this paper, we embed the SDDP algorithm into the scenario tree framework, essentially combining the nested Benders decomposition method on trees with the sampling procedure of SDDP. This allows for the incorporation of different types of uncertainties in multi-stage stochastic optimization while still maintaining an efficient solution algorithm. We provide an illustration of the applicability of our method towards a least-cost hydro-thermal scheduling problem by examining an illustrative example combining both fuel cost with inflow uncertainty and by studying the Panama power system incorporating both electricity demand and inflow uncertainties.

Optimization Models in The Natural Gas Industry

AbstractWe provide a comprehensive study on network flow problems with arc reversal capabilities. The problem is to identify the arcs to be reversed in order to achieve a maximum flow from source(s) to sink(s). The problem finds its applications in emergency transportation management, where the lanes of a road network could be reversed to enable flow in the opposite direction. We study several network flow problems with the arc reversal capability and discuss their complexity. More specifically, we discuss the polynomial time algorithms for the maximum dynamic flow problem with arc reversal capability having a single source and a single sink, and for the maximum (static) flow problem. The presented algorithms are based on graph transformations and reductions to polynomially solvable flow problems. In addition, we show that the quickest transshipment problem with arc reversal capability and the problem of minimizing the total cost resulting from arc switching costs are

Combining sampling-based and scenario-based nested Benders decomposition methods: application to stochastic dual dynamic programming

\mathcal{NP}

Complexity analysis for maximum flow problems with arc reversals

-hard.

Cutting ellipses from area-minimizing rectangles

A set of ellipses, with given semi-major and semi-minor axes, is to be cut from a rectangular design plate, while minimizing the area of the design rectangle. The design plate is subject to lower and upper bounds of its widths and lengths; the ellipses are free of any orientation restrictions. We present new mathematical programming formulations for this ellipse cutting problem. The key idea in the developed non-convex nonlinear programming models is to use separating hyperlines to ensure the ellipses do not overlap with each other. For small number of ellipses we compute feasible points which are globally optimal subject to the finite arithmetic of the global solvers at hand. However, for more than 14 ellipses none of the local or global NLP solvers available in GAMS can even compute a feasible point. Therefore, we develop polylithic approaches, in which the ellipses are added sequentially in a strip-packing fashion to the rectangle restricted in width, but unrestricted in length. The rectangle’s area is minimized in each step in a greedy fashion. The sequence in which we add the ellipses is random; this adds some GRASP flavor to our approach. The polylithic algorithms allow us to compute good, near optimal solutions for up to 100 ellipses.

Transmission-Capacity Expansion for Minimizing Blackout Probabilities

The objective of this paper is to determine an optimal plan for expanding the capacity of a power grid in order to minimize the likelihood of a large cascading blackout. Capacity-expansion decisions considered in this paper include the addition of new transmission lines and the addition of capacity to existing lines. We embody these interacting considerations in a simulation optimization model, where the objective is to minimize the probability of a large blackout subject to a budget constraint. The probability of a large-scale blackout is estimated via Monte Carlo simulation of a probabilistic cascading blackout model. Because the events of interest are rare, standard simulation is often intractable from a computational perspective. We apply a variance-reduction technique within the simulation to provide results in a reasonable time frame. Numerical results are given for some small test networks including an IEEE 14-bus test network. A key conclusion is that the different expansion strategies lead to different shapes of the tails of the blackout distributions. In other words, there is a tradeoff between reducing the frequency of small-scale blackouts versus reducing the frequency of large-scale blackouts.