### Calculation of a Power Price Equilibrium under Risk Averse Trading

- Series
- Other Talks
- Time
- Monday, October 26, 2015 - 13:30 for 1 hour (actually 50 minutes)
- Location
- Skiles 168
- Speaker
- Raphael Hauser – Mathematical Institute, University of Oxford

We propose a term structure power price model that, in contrast
to widely accepted no-arbitrage based approaches, accounts for the
non-storable nature of power. It belongs to a class of equilibrium game
theoretic models with players divided into producers and consumers. The
consumers' goal is to maximize a mean-variance utility function subject to
satisfying an inelastic demand of their own clients (e.g households,
businesses etc.) to whom they sell the power. The producers, who own a
portfolio of power plants each defined by a running fuel (e.g. gas, coal,
oil...) and physical characteristics (e.g. efficiency, capacity, ramp
up/down times...), similarly, seek to maximize a mean-variance utility
function consisting of power, fuel, and emission prices subject to
production constraints. Our goal is to determine the term structure of the
power price at which production matches consumption. We show that in such a
setting the equilibrium price exists and discuss the conditions for its
uniqueness. The model is then extended to account for transaction costs and
liquidity considerations in actual trading. Our numerical simulations
examine the properties of the term structure and its dependence on various
model parameters. We then further extend the model to account for the
startup costs of power plants. In contrast to other approaches presented in
the literature, we incorporate the startup costs in a mathematically
rigorous manner without relying on ad hoc heuristics. Through numerical
simulations applied to the entire UK power grid, we demonstrate that the
inclusion of startup costs is necessary for the modeling of electricity
prices in realistic power systems. Numerical results show that startup
costs make electricity prices very spiky. In a final refinement of the
model, we include a grid operator responsible for managing the grid.
Numerical simulations demonstrate that robust decision making of the grid
operator can significantly decrease the number and severity of spikes in
the electricity price and improve the reliability of the power grid.