This paper discusses using real options to value power plants with unit commitment constraints over a short-term period. We formulate the problem as a multistage stochastic problem and propose a solution procedure that integrates forward-moving Monte Carlo simulation with backward-moving dynamic programming. We assume that the power plant operator maximizes expected profit by deciding in each hour whether or not to run the unit, that a certain lead time for commitment and decommitment decisions is necessary to start up and shut down a unit, and that these commitment decisions, once made, are subject to physical constraints such as minimum uptime and downtime. We also account for the costs associated with starting up and shutting down a unit. Last, we assume that there are hourly markets for both electricity and the fuel used by the generator and that their prices follow Ito processes. Using numerical simulation, we show that failure to consider physical constraints may significantly overvalue a power plant.

Abstract. In order to overcome the drawbacks of mathematical optimization techniques, soft computing algorithms have been vigorously introduced during the past decade. However, there are still some possibilities of devising new algorithms based on analogies with natural phenomena. A nature-inspired algorithm, mimicking the improvisation process of music players, has been recently developed and named Harmony Search (HS). The algorithm has been successfully applied to various engineering optimization problems. In this paper, the HS was applied to a TSP-like NP-hard Generalized Orienteering Problem (GOP) which is to find the utmost route under the total distance limit while satisfying multiple goals. Example area of the GOP is eastern part of China. The results of HS showed that the algorithm could find good solutions when compared to those of artificial neural network.

Infrastructure facilities are generally heavy, fixed, and normally irreversible once construction has been completed. As existing facilities, they may confront economic competition of an increased space demand and the need for future expansion. Due to economic-based irreversibility, the expansion of a constructed facility requires the foundation and, to a lesser degree, columns to be enhanced and options for expansion to be accounted for at the very beginning of construction. Enhancing the foundation and columns represents an up-front cost, but has a return in flexibility for future expansion. This trade-off can be viewed as an investment problem, in that a premium has to be paid first for an option that can be exercised later. A model of the foundations versus flexibility trade-off enables the competing options to be optimized by balancing the expected profits that may arise from future expansion, i.e., the value of flexibility, and the cost of enhancing the foundation. Use of the model is demonstrated for the construction of a public parking garage, with the optimal foundation size determined. The evolution of parking demand is modeled with a trinomial lattice. Stochastic dynamic programming is used to determine the optimal expansion process. A model that does not consider the value of flexibility is compared with two value-flexible models. The value of flexibility in this case study is so significant that failure to account for flexibility is not economical. Valuation modeling such as discounted cash flow analysis with uncertainty modeling is important to capitalize on the worth of flexibility.

Absiract-This paper describes a Lagrangian relaxation based method to solve the short-term resource scheduling (STRS) problem with ramp constraints. Instead of discretizing the generation levels, the ramp rate constraints are relaxed with the system demand constraints using Lagrange multipliers. Three kinds of ramp constraints, startup, operating and shutdown ramp constraints are considered. The proposed method has been applied to solve the hydro-thermal generation scheduling problem at, PG&E. An example along with numerical results is also presented.

In this paper, we use a real-options framework to value a power plant. The real option to commit or decommit a generating unit may be exercised on an hourly basis to maximize expected profit while subject to intertemporal operational constraints. The option-exercising process is modeled as a multistage stochastic problem. We develop a framework for generating discretetime price lattices for two correlated Ito processes for electricity and fuel prices. We show that the proposed framework exceeds existing approaches in both lattice feasibility and computational efficiency. We prove that this framework guarantees existence of branching probabilities at all nodes and all stages of the lattice if the correlation between the two Ito processes is no greater than 4/ √ 35 ≈ 0 676. With price evolution represented by a lattice, the valuation problem is solved using stochastic dynamic programming. We show how the obtained power plant value converges to the true expected value by refining the price lattice. Sensitivity analysis for the power plant value to changes of price parameters is also presented.