## Operation, Investment and Hedging in Electricity Markets

Publikation: Bog/antologi/afhandling/rapport › Ph.d.-afhandling › Forskning

This thesis consists of an introduction as well as four papers. The papers

concern different problems associated to future electricity markets and the

topics include risk management, investment strategies, valuation and model

calibration. Each paper is presented in a separate chapter and hence the

chapters are self-contained and may be read individually. A more thorough

overview is presented in Chapter 1.

In Chapter 2 we consider a hedging problem for a power distributor delivering

electricity on fixed price contracts in the Nordic electricity market and

thereby being exposed to volume risk. We develop time series models for the

electric load, system price and deviation from system price. The model is

designed such that for independent electric load, system price and deviations

from system price, the minimal variance hedge coincide with the standard

practice of the industry. We extend the model to include price and load correlation

which results in an explicit strategy that reduces the variance. To

further improve the strategy we include autocorrelation and solve the hedging

problem numerically and show that there is a large potential in changing risk

measure and utilizing the skewness in the payoff distribution.

In Chapter 3 we consider an investment problem for a strategic investor

and a social planner with the opportunity to invest in inflexible and flexible

generation. We study the impact of market power and conjectured market

changes with a simple price model based on linear demand response. We show

that the strategic investor invests later and in less capacity than the socially

optimal and that with increased market ownership investment is delayed further

and capacity increased slightly. Furthermore, we find that an increase in

market share for the strategic investor delays inflexible generation more than

flexible generation due to the exposure to potential low prices.

In Chapter 4 we study the valuation of three representative generation

types, an inflexible wind turbine, a flexible gas fired power plant and a hydroelectric

plant that allows for storage. We account for the special characteristics

of each technology and include uncertainty in both price and volume

through diffusion or jump diffusion models. We find explicit expressions for

the expected instantaneous value of wind generation as a function of electricity

price and wind speed. We include startup and shutdown costs for the gas

fired power plant determine the startup and shutdown triggers as well as the

value of the plant by maximizing the value of shutting down. This is done analytically

in the diffusion models and numerically in the jump diffusion model.

For the hydroelectric power plant we relax storage level and discharge constraints

using penalty functions and linearize the optimal strategy from the

Hamilton-Jacobi-Bellman equation. This allows for closed form expressions of

the value in terms of the expected price, the second moment of the price and

the autovariance of the price. We calibrate the models to 7 years of hourly

price and wind data, determine the value and study the impact of anticipated

market changes on the value of the three types of generation.

In Chapter 5 we develop an EM-algorithm with two jump components

such that the jump density of the compound Poisson process is a mixture

of two normal distributions. We show that each step of the EM-algorithm

increases the log-likelihood of the observed data by maximizing the expectation

of the log-likelihood for the complete data conditional on the observed

data. We determine explicit expressions for the maximization step in terms

of simple conditional expectations and present an approach for determining

the conditional expectations. Finally, by applying the algorithm to calibrate

the jump diffusion model from Chapter 4, we demonstrate that the additional

jump component provides a significantly better model of the observed data

than a model without jumps and with only a single jump component.

concern different problems associated to future electricity markets and the

topics include risk management, investment strategies, valuation and model

calibration. Each paper is presented in a separate chapter and hence the

chapters are self-contained and may be read individually. A more thorough

overview is presented in Chapter 1.

In Chapter 2 we consider a hedging problem for a power distributor delivering

electricity on fixed price contracts in the Nordic electricity market and

thereby being exposed to volume risk. We develop time series models for the

electric load, system price and deviation from system price. The model is

designed such that for independent electric load, system price and deviations

from system price, the minimal variance hedge coincide with the standard

practice of the industry. We extend the model to include price and load correlation

which results in an explicit strategy that reduces the variance. To

further improve the strategy we include autocorrelation and solve the hedging

problem numerically and show that there is a large potential in changing risk

measure and utilizing the skewness in the payoff distribution.

In Chapter 3 we consider an investment problem for a strategic investor

and a social planner with the opportunity to invest in inflexible and flexible

generation. We study the impact of market power and conjectured market

changes with a simple price model based on linear demand response. We show

that the strategic investor invests later and in less capacity than the socially

optimal and that with increased market ownership investment is delayed further

and capacity increased slightly. Furthermore, we find that an increase in

market share for the strategic investor delays inflexible generation more than

flexible generation due to the exposure to potential low prices.

In Chapter 4 we study the valuation of three representative generation

types, an inflexible wind turbine, a flexible gas fired power plant and a hydroelectric

plant that allows for storage. We account for the special characteristics

of each technology and include uncertainty in both price and volume

through diffusion or jump diffusion models. We find explicit expressions for

the expected instantaneous value of wind generation as a function of electricity

price and wind speed. We include startup and shutdown costs for the gas

fired power plant determine the startup and shutdown triggers as well as the

value of the plant by maximizing the value of shutting down. This is done analytically

in the diffusion models and numerically in the jump diffusion model.

For the hydroelectric power plant we relax storage level and discharge constraints

using penalty functions and linearize the optimal strategy from the

Hamilton-Jacobi-Bellman equation. This allows for closed form expressions of

the value in terms of the expected price, the second moment of the price and

the autovariance of the price. We calibrate the models to 7 years of hourly

price and wind data, determine the value and study the impact of anticipated

market changes on the value of the three types of generation.

In Chapter 5 we develop an EM-algorithm with two jump components

such that the jump density of the compound Poisson process is a mixture

of two normal distributions. We show that each step of the EM-algorithm

increases the log-likelihood of the observed data by maximizing the expectation

of the log-likelihood for the complete data conditional on the observed

data. We determine explicit expressions for the maximization step in terms

of simple conditional expectations and present an approach for determining

the conditional expectations. Finally, by applying the algorithm to calibrate

the jump diffusion model from Chapter 4, we demonstrate that the additional

jump component provides a significantly better model of the observed data

than a model without jumps and with only a single jump component.

Originalsprog | Engelsk |
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Forlag | Department of Mathematical Sciences, Faculty of Science, University of Copenhagen |
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Status | Udgivet - 2016 |

ID: 170700609