Medium-Term Planning in Deregulated Energy Markets with Decision Rules
Author(s)
Martins da Silva Rocha, Paula Cristina
Type
Thesis
Abstract
The ongoing deregulation of energy markets has greatly impacted the power industry. In this
new environment, firms shift their focus from cost-efficient energy supply to more profit-oriented
goals, trading energy at the price set by the market. Consequently, traditional management
approaches based on cost minimisation disregarding market uncertainties and financial risk are
no longer applicable.
In this thesis, we investigate medium-term planning problems in deregulated energy markets.
These problems typically involve taking decisions over many periods and are affected by significant
uncertainty, most notably energy price uncertainty. Multistage stochastic programming
provides a flexible framework for modelling this type of dynamic decision-making process: it
allows for future decisions to be represented as decision rules, that is, as measurable functions
of the observable data.
Multistage stochastic programs are generally intractable. Instead of using classical scenario tree-based
techniques, we reduce their computational complexity by restricting the set of decision
rules to those that exhibit an affine or quadratic data dependence. Decision rule approaches
typically lead to polynomial-time solution schemes and are therefore ideal to tackle industry-size
energy problems. However, the favourable scalability properties of the decision rule approach
come at the cost of a loss of optimality. Fortunately, the degree of suboptimality can be
measured efficiently by solving the dual of the stochastic program under consideration in linear
or quadratic decision rules. The approximation error is then estimated by the gap between the
optimal values of the primal and the dual decision rule problems. We develop this dual decision
rule technique for general quadratic stochastic programs.
Using these techniques, we solve a mean-variance portfolio optimisation problem faced by an
electricity retailer. We observe that incorporating adaptivity into the model is beneficial in a
risk minimisation framework, especially in the presence of high spot price variability or large
market prices of risk. For a problem instance involving six electricity derivatives and a monthly
planning horizon with daily trading periods, the solution time amounts to a few seconds. In
contrast, scenario tree methods result in excessive run times since they require a prohibitively
large number of scenarios to preclude arbitrage.
Moreover, we address the medium-term scheduling of a cascaded hydropower system. To reduce
computational complexity, we partition the planning horizon into hydrological macroperiods,
each of which accommodates many trading microperiods, and we account for intra-stage variability
through the use of price duration curves. Using linear decision rules, a solution to a
real-sized hydro storage problem with a yearly planning horizon comprising 52 weekly macroperiods
can be located in a few minutes, with an approximation error of less than 10%.
new environment, firms shift their focus from cost-efficient energy supply to more profit-oriented
goals, trading energy at the price set by the market. Consequently, traditional management
approaches based on cost minimisation disregarding market uncertainties and financial risk are
no longer applicable.
In this thesis, we investigate medium-term planning problems in deregulated energy markets.
These problems typically involve taking decisions over many periods and are affected by significant
uncertainty, most notably energy price uncertainty. Multistage stochastic programming
provides a flexible framework for modelling this type of dynamic decision-making process: it
allows for future decisions to be represented as decision rules, that is, as measurable functions
of the observable data.
Multistage stochastic programs are generally intractable. Instead of using classical scenario tree-based
techniques, we reduce their computational complexity by restricting the set of decision
rules to those that exhibit an affine or quadratic data dependence. Decision rule approaches
typically lead to polynomial-time solution schemes and are therefore ideal to tackle industry-size
energy problems. However, the favourable scalability properties of the decision rule approach
come at the cost of a loss of optimality. Fortunately, the degree of suboptimality can be
measured efficiently by solving the dual of the stochastic program under consideration in linear
or quadratic decision rules. The approximation error is then estimated by the gap between the
optimal values of the primal and the dual decision rule problems. We develop this dual decision
rule technique for general quadratic stochastic programs.
Using these techniques, we solve a mean-variance portfolio optimisation problem faced by an
electricity retailer. We observe that incorporating adaptivity into the model is beneficial in a
risk minimisation framework, especially in the presence of high spot price variability or large
market prices of risk. For a problem instance involving six electricity derivatives and a monthly
planning horizon with daily trading periods, the solution time amounts to a few seconds. In
contrast, scenario tree methods result in excessive run times since they require a prohibitively
large number of scenarios to preclude arbitrage.
Moreover, we address the medium-term scheduling of a cascaded hydropower system. To reduce
computational complexity, we partition the planning horizon into hydrological macroperiods,
each of which accommodates many trading microperiods, and we account for intra-stage variability
through the use of price duration curves. Using linear decision rules, a solution to a
real-sized hydro storage problem with a yearly planning horizon comprising 52 weekly macroperiods
can be located in a few minutes, with an approximation error of less than 10%.
Date Issued
2012
Date Awarded
2013-02
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Kuhn, Daniel
Rustem, Berc
Sponsor
Fundacao para a Ciencia e a Tecnologia
Grant Number
SFRH/BD/43250/2008
Publisher Department
Computing
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)