Measuring Performance of Long-Term Power Generating Portfolios - Green Energy and Efficiency: An Economic Perspective - page 392

policy makers commit themselves to a certain future path of the allowance price by
setting a oor (i.e. carbon price evolves stochastically but always above a minimum

threshold level). We run the model to assess the overall impact (both absolute and
relative to the case without a

oor price). Besides, we try different time-varying
portfolios of generation facilities. This way the model can assist decision makers
when confronted with challenging strategic choices.
We aim to evaluate the performance of long-term portfolios through the resulting
electricity price and its volatility alongside the abatement of CO 2 emissions. Since
the probability distribution of these impacts can be asymmetric, we go beyond
average values and derive whole distributions of effects. The electricity prices in
particular can be used to check whether they are high enough to get a fair return on
investments in any particular type of power technology.
The optimal power

ow (OPF) algorithm dispatches generation assets in merit
(least-cost) order subject to physical constraints. The economic dispatch problem is
to nd output for each available technology so as to minimize total (system) costs

while meeting load plus line losses. At every time demand and supply must be
balanced, and the Laws of Physics must apply in the network.

2.1 Physical Environment

Load . Load is assumed inelastic and stochastic while showing seasonality.
D denotes the net demand for electricity from consumers. Pumped storage is a
power technology that effectively consumes electricity; its contribution, P , has a
negative sign. Therefore, the gross demand d is the sum of the realizations of two
different stochastic processes computed as:

d ¼ D þ P :

Depending on the infrastructure available, load can be fully served or not.
The electricity actually served is denoted by s .
Future demand dispalys seasonality and is uncertain. We assume that the des-
easonalized load evolves over time according to the following Inhomogeneous
geometric Brownian motion (IGBM):

d D t ¼ kðL D t Þ d t þ rD t d V t ;

D is assumed to show mean reversion. L is the long-term equilibrium level
toward which the present deseasonalized load tends. k is the speed of reversion
toward that

level. The instantaneous volatility of this load is denoted by r .
d V t is the increment to a standard Wiener process; it is normally distributed with
mean zero and variance d t .

“ normal ”