10,297 research outputs found
A probabilistic numerical method for optimal multiple switching problem and application to investments in electricity generation
In this paper, we present a probabilistic numerical algorithm combining
dynamic programming, Monte Carlo simulations and local basis regressions to
solve non-stationary optimal multiple switching problems in infinite horizon.
We provide the rate of convergence of the method in terms of the time step used
to discretize the problem, of the size of the local hypercubes involved in the
regressions, and of the truncating time horizon. To make the method viable for
problems in high dimension and long time horizon, we extend a memory reduction
method to the general Euler scheme, so that, when performing the numerical
resolution, the storage of the Monte Carlo simulation paths is not needed.
Then, we apply this algorithm to a model of optimal investment in power plants.
This model takes into account electricity demand, cointegrated fuel prices,
carbon price and random outages of power plants. It computes the optimal level
of investment in each generation technology, considered as a whole, w.r.t. the
electricity spot price. This electricity price is itself built according to a
new extended structural model. In particular, it is a function of several
factors, among which the installed capacities. The evolution of the optimal
generation mix is illustrated on a realistic numerical problem in dimension
eight, i.e. with two different technologies and six random factors
Gather-and-broadcast frequency control in power systems
We propose a novel frequency control approach in between centralized and
distributed architectures, that is a continuous-time feedback control version
of the dual decomposition optimization method. Specifically, a convex
combination of the frequency measurements is centrally aggregated, followed by
an integral control and a broadcast signal, which is then optimally allocated
at local generation units. We show that our gather-and-broadcast control
architecture comprises many previously proposed strategies as special cases. We
prove local asymptotic stability of the closed-loop equilibria of the
considered power system model, which is a nonlinear differential-algebraic
system that includes traditional generators, frequency-responsive devices, as
well as passive loads, where the sources are already equipped with primary
droop control. Our feedback control is designed such that the closed-loop
equilibria of the power system solve the optimal economic dispatch problem
Modeling highly volatile and seasonal markets: evidence from the Nord Pool electricity market
In this paper we address the issue of modeling spot electricity prices. After analyzing factors leading to the unobservable in other financial or commodity markets price dynamics we propose a mean reverting jump diffusion model. We fit the model to data from the Nord Pool power exchange and find that it nearly duplicates the spot price's main characteristics. The model can thus be used for risk management and pricing derivatives written on the spot electricity price.electricity price, mean reversion, wavelet transform, jump diffusion model
Joint Modelling of Gas and Electricity spot prices
The recent liberalization of the electricity and gas markets has resulted in
the growth of energy exchanges and modelling problems. In this paper, we
modelize jointly gas and electricity spot prices using a mean-reverting model
which fits the correlations structures for the two commodities. The dynamics
are based on Ornstein processes with parameterized diffusion coefficients.
Moreover, using the empirical distributions of the spot prices, we derive a
class of such parameterized diffusions which captures the most salient
statistical properties: stationarity, spikes and heavy-tailed distributions.
The associated calibration procedure is based on standard and efficient
statistical tools. We calibrate the model on French market for electricity and
on UK market for gas, and then simulate some trajectories which reproduce well
the observed prices behavior. Finally, we illustrate the importance of the
correlation structure and of the presence of spikes by measuring the risk on a
power plant portfolio
- …