| In this thesis we present algorithms for the valuation and optimal operation of natural gas storage facilities, hydro-electric power plants and thermal power generators in competitive markets. Real options theory is used to derive nonlinear partial-integro-differential equations (PIDEs) for the valuation and optimal operating strategies of all types of facilities. The equations are designed to incorporate a wide class of spot price models that can exhibit the same time-dependent, mean-reverting dynamics and price spikes as those observed in most energy markets. Particular attention is paid to the operational characteristics of real energy assets. For natural gas storage facilities these characteristics include: working gas capacities, variable deliverability and injection rates and cycling limitations. For thermal power plants relevant operational characteristics include variable start-up times and costs, control response time lags, minimum generating levels, nonlinear output functions, structural limitations on ramp rates, and minimum up/down time restrictions. For hydro-electric units, head effects and environmental constraints are addressed. We illustrate the models with numerical examples of a gas storage facility, a hydro-electric pump storage facility and a thermal power plant. This PIDE framework is the first in the literature to achieve second order accuracy in characterizing the operating states of hydro-electric and hydro-thermal power plants. The continuous state space representation derived in this thesis can therefore achieve far greater realism in terms of operating state specification than any other method in the literature to date. This thesis is also the first and only to allow for any continuous time jump diffusion processes in order to account for price spikes. |
