Christos Nakos, NTUA, Postgraduate Student Optimal Management of the Dynamic Systems of the Economy and the environment THALES RESEARCH WORKSHOP

This presentation mainly follows the developments produced in : Gahungu, J and Y. Smeers (2011), A Real Options Model for Electricity Capacity Expansion, CORE discussion paper, Universite Catholique de Louvain, Belgium

Why use such kind of model for the capacity expansion of the power system? Better representation of risks (economic, regulatory) Traditional capacity expansion models of the optimization type become intractable when extended to a stochastic setting Provide an intuitive financial representation It offers a complementary field of investment analysis compared to the well known evaluation method of NPV.

Real option capacity expansion models for the power sector should take into account the following crucial particularities: Electricity is a differentiated product, i.e. cannot be stored Technologies differ by both operation and investment cost, a fact inconsonant with the assumptions considered by the majority of the real options capacity expansion models Profits accruing from new capacities are not given in a closed form but need to be computed numerically by an optimization problem

Assumption 1 : A competitive electricity market is considered, where a portfolio of k different generation technologies, candidates for investment, is introduced. These technologies have different technoeconomic characteristics(investment cost, fuel and VAROM costs, FIXOM costs) Assumption 2: The annual load demand is modelled as a decreasing step function (annual load curve), meaning that a certain (fixed) level of load is activated for each load segment respectively.

In reality, the annual load curve is non-linear and generally follows the form shown in figure. However, it is a well-known technique to approach the annual load curve as a step function under the condition that the area under the line, i.e the annual energy consumed remains equal in both cases.

Stochastic control problems may be transformed in a succession of optimal stopping problems The classical Dynamic Programming Techniques fail to apply when the control variable has to be non-decreasing The equivalence between the two formulations (SCP OSP) has been proved, only when certain conditions are met. Baldursson and Karatzas(1997)

The situation when the equivalence holds is often stated as optimality of myopia The term myopia is used to reflect the fact that each agent in the market acts assuming that a new capacity addition will be the last to be made in the horizon of the study. The sufficient and necessary conditions for the existence of myopia optimality, are : Investments should be defined in an incremental way The economy should be convex The agents should be homogenous The profit should be additively separable for each technology, or else each technology should have the same investment costs

Investment trigger with average growth of Y Investment trigger with volatility of Y

Investment trigger for nuclear technology with capital stock vectors Investment trigger for a coal power- generation technology with capital stock vectors

Develop this setting also for renewable technologies Investigate robustness of the optimality of myopia under violation of additive separability condition Realize synergies with other models or methodologies that deal with the same problem

THANK YOU!