Santiago Cerisola

A medium-term integrated risk management model for a hydrothermal generation company

This paper presents a methodology to manage the market risk faced by a hydrothermal generation company in the medium-term (one year). This risk is due to uncertainty in fuel prices, power demand, water inflows, and electricity prices. The proposed methodology includes three steps: the generation of scenarios for these random parameters, the approximation of these scenarios by a multivariate scenario tree, and the optimization of the companys operational and financial hedging decisions under a stochastic programming framework. The optimization model permits the representation of a diversified generation portfolio and measures risk exposure by means of conditional value-at-risk. A realistic numerical example is solved to illustrate the possibilities of our approach.

Stochastic Power Generation Unit Commitment in Electricity Markets: A Novel Formulation and a Comparison of Solution Methods

We propose a stochastic unit commitment model for a power generation company that takes part in an electricity spot market. The relevant feature of this model is its detailed representation of the spot market during a whole week, including seven day-ahead market sessions and the corresponding adjustment market sessions. The adjustment market sessions can be seen as an hour-ahead market mechanism. This representation takes into account the influence that the companys decisions exert on the market-clearing price by means of a residual demand curve for each market session. We introduce uncertainty in the form of several possible spot market outcomes for each day, which leads to a weekly scenario tree. The model also represents in detail the operation of the companys generation units. The model leads to large-scale mixed linear-integer problems that are hard to solve with commercial optimizers. This suggests the use of alternative solution methods. We test four solution approaches with a realistic numerical example in the context of the Spanish electricity spot market. The first is a direct solution with a commercial optimizer, which illustrates the mentioned limitations. The second is a standard Lagrangean relaxation algorithm. The third and fourth methods are two original variants of Benders decomposition for multistage stochastic integer programs. The first Benders decomposition algorithm builds approximations for the recourse function relaxing the integrality constraints of the subproblems. The second variant strengthens these cuts by performing one iteration of the Lagrangean of each subproblem. We analyze the advantages of these four methods and compare the results.

Stochastic dual dynamic programming applied to nonconvex hydrothermal models

In this paper we apply stochastic dual dynamic programming decomposition to a nonconvex multistage stochastic hydrothermal model where the nonlinear water head effects on production and the nonlinear dependence between the reservoir head and the reservoir volume are modeled. The nonconvex constraints that represent the production function of a hydro plant are approximated by McCormick envelopes. These constraints are split into smaller regions and the McCormick envelopes are used for each region. We use binary variables for this disjunctive programming approach and solve the problem with a decomposition method. We resort to a variant of the L-shaped method for solving the MIP subproblem with binary variables at any stage inside the stochastic dual dynamic programming algorithm. A realistic large-scale case study is presented.

Clustering algorithms for scenario tree generation: Application to natural hydro inflows

In stochastic optimization problems, uncertainty is normally represented by means of a scenario tree. Finding an accurate representation of this uncertainty when dealing with a set of historical series is an important issue, because of its influence in the results of the above mentioned problems. This article uses a procedure to create the scenario tree divided into two phases: the first one produces a tree that represents accurately the original probability distribution, and in the second phase that tree is reduced to make it tractable. Several clustering methods are analysed and proposed in the paper to obtain the scenario tree. Specifically, these are applied to an academic case and to natural hydro inflows series, and comparisons amongst them are established according to these results.

Modeling Risk Management in Oligopolistic Electricity Markets: A Benders Decomposition Approach

This paper presents a model for addressing the market risk management problem faced by a hydrothermal generation company trading in an oligopolistic market. The risk is due to uncertainty in fuel prices, power demand, water inflows, and electricity prices. The model permits the representation of a diversified generation portfolio and measures risk exposure by means of conditional value at risk. The model is formulated and solved as a stochastic linear complementarity problem. In order to deal with realistically sized problems, Benders decomposition technique is adapted to solve equilibrium models. A numerical example illustrates the possibilities of the algorithm we propose.

Strategic bidding in electricity spot markets under uncertainty: a roadmap

The liberalization of the power industry and the creation of electricity spot markets throughout the world has triggered a significant research effort both by academic and practitioners. A part of this effort has been oriented to the development of methodologies and tools devoted to the optimization of bidding strategies for electricity spot markets. Uncertainty with respect to the behavior of the rest of participants is a major ingredient of this problem. After several years a vast literature has been produced on this particular topic. The purpose of this paper is to contribute to the definition of a general body of knowledge by characterizing the most relevant features of some of the lines of research that have been followed

Modeling the Major Overhaul Cost of Gas-Fired Plants in the Unit Commitment Problem

The operation and maintenance (O&M) costs of gas-turbine-based generation technologies have traditionally been introduced in unit commitment problems by means of simplified formulations (such as the approach of including an additional energy cost adder component). We argue that, in the new context characterized by the increasing need for cycling operation, such simplified approaches do not realistically reflect the impact that these new operation regimes have on the O&M costs for both open and combined cycle gas turbines. We first review the role of the so-called long-term service agreements (LTSA), which is a commonly used type of contract offered by gas-turbine manufacturers to plant owners. We analyze how these contracts implicitly determine the maintenance intervals as a function of the operating regime, and, as a consequence, determine the impact of cycling operation on O&M costs. Based on this analysis, we develop a formulation based on linear constraints that makes possible a realistic modeling of O&M costs (as defined in LTSA contracts) in the unit commitment problem. This formulation is then tested using some examples, so as to illustrate how a proper modeling of these contracts significantly changes the scheduling resulting from the traditional unit commitment problem formulation.

A Progressive Contingency Incorporation Approach for Stochastic Optimization Problems

Reliability is a key objective in many optimal design problems. Very often this criterion is incorporated into stochastic optimization problems by introducing contingency evaluation scenarios. This results in a special problem structure where the stochastic scenarios used to describe reliability are linked to the failure of specific individual elements. This paper presents a progressive contingency incorporation (PCI) approach that takes advantage of this structure to increase efficiency. The algorithm is applied to the design of an offshore wind farm, where the electrical layout is decided, as representative of the possible advantages of PCI within power systems. The problem must determine the placement and type of cables in a collector system. Results show that time savings achieved by the PCI approach can be remarkable, reaching two orders of magnitude for the case study.

Analysis of stochastic problem decomposition algorithms in computational grids

Stochastic programming usually represents uncertainty discretely by means of a scenario tree. This representation leads to an exponential growth of the size of stochastic mathematical problems when better accuracy is needed. Trying to solve the problem as a whole, considering all scenarios together, yields to huge memory requirements that surpass the capabilities of current computers. Thus, decomposition algorithms are employed to divide the problem into several smaller subproblems and to coordinate their solution in order to obtain the global optimum. This paper analyzes several decomposition strategies based on the classical Benders decomposition algorithm, and applies them in the emerging computational grid environments. Most decomposition algorithms are not able to take full advantage of all the computing power available in a grid system because of unavoidable dependencies inherent to the algorithms. However, a special decomposition method presented in this paper aims at reducing dependency among subproblems, to the point where all the subproblems can be sent simultaneously to the grid. All algorithms have been tested in a grid system, measuring execution times required to solve standard optimization problems and a real-size hydrothermal coordination problem. Numerical results are shown to confirm that this new method outperforms the classical ones when used in grid computing environments.

Coordinated Hydropower Plant Simulation for Multireservoir Systems

AbstractHydroreservoirs usually serve two main purposes: hydropower production and water consumption. The great flexibility, low operating costs, and low carbon impact of hydroturbines turns them into a desirable technology in the generator mix of power systems. In addition, sustainability and environmental concerns support their use in current power systems, along with other renewable energy sources like wind and solar energy. However, the stochastic nature of river inflows hinders their long-term use and hints at the need to use planning tools. Furthermore, it also requires the use of planning tools in order to balance present and future requirements. This work presents a simulation tool that is employed at Iberdrola to help in the preparation of medium-term hydroelectric production schedules. The main objective of the simulation is to follow the production guidelines given by a long-term hydrothermal problem, while avoiding spillages and failures to fulfill water release agreements. In order to achieve...