Risk and forward contracting in medium-term electricity generation planning

Resumen

The advent of liberalization in the electricity sector has changed many aspects of the decision making processes that occur in the different phases of electricity generation, distribution, and commercialization, Within the deregulated frameworks, generation and commercialization become decentralized processes where many agents interact by participating in wholesale electricity spot and forward markets. In this context, the agents' objective is maximization of the tradeoff between expected profit and minimization of operational decisions risks. There is a hierarchy of decisions in generation planning: long-term decisions may span over an horizon of several years and are mainly related to generation capacity expansion or obsolete plants replacement; medium-term planning where, by considering the in- place generation facilities and an horizon of a year or two, energy generation goals are set up by taking into account availability limits (in hydro power, in certain fuels, etc.) and operational limits (like emission caps); short-term planning goals are solving unit commitment and finding bidding policies for the primary and secondary markets. This top-down hierarchy of planning decisions is motivated by the fact that when considering longer planning horizons, it is not possible to describe the generation system behavior with the same detail used in short-term planning, but the information provided by the longer term models should always be included in shorter term models in order to avoid taking myopic decisions. The medium-term planning problem for a price maker generator company in a deregulated framework is the central aim of this thesis: in this context, in addition to technical and environmental factors, such as the availability of hydro resources and the possibility of unit outages, the complexity of the decision making problem is increased by the consideration of the competition with other companies, the uncertainty of electricity wholesale prices, and the presence of a price-responsive demand. Furthermore, in order to complement the wholesale spot markets, forward markets have been established to help companies to manage and share their risks. Our thesis proposes a Nash equilibrium conjectured-price model and extends it in order to cover modeling topics such as price elasticity, risk aversion and forward contracting. The proposed models contain the following peculiarities and contributions: the Bloom and Gallant (B&G) formulation for load matching has been combined with stochastic programming and equilibrium. The resulting model allows taking into account multiple uncertainty factors: from intra-period load and unit outage uncertainties, to stochastic hydro inflows and renewable energy availability. We consider price elasticity of demand by approximating elastic Load duration curves and considering cross elasticity effects (the most noticeable effects in today's markets). Risk aversion has been taken into account by considering the Conditional Value at Risk (CVaR). We calculated the CVaR both on absolute losses and on losses derived by using the concept of perfect information and we demonstrated the possibility of calculating multiple CVaR functionals for quadratic losses in equilibrium contexts. We model forward price by exploiting the relation between forward price and expected spot prices. We hence model forward prices starting from the expected endogenous spot prices and by considering a stochastic risk premium. We calculate equilibrium solutions by adapting the Nikaido-Isoda Relaxation Algorithm to our problems. The resulting relaxed mathematical programming models are convex quadratic or non-linear multi-stage stochastic programs. In order to speed up computation we adapted an existing heuristic (needed to avoid the generation of a large number of LMCs coming from the B&G formulation), and we used event tree reduction techniques in order to maintain tractability.