Stochastic Modeling and Optimization under Uncertainty of a Hydro Power System
(2005) In Doctoral Theses in Mathematical Sciences 2005:6. Abstract
 Electricity bought and sold on the deregulated Nordic power market is dominated by hydro power. However, hydro power generation is restricted by the amount of water in reservoirs. The inflows to these reservoirs show a yearly cycle and seasonal planning of the production is necessary.
Seasonal planning up to 1.5 years for a power producer in a hydrothermal system with a regulated river is considered. For a pricetaking, riskaverse producer who wants to maximize his profit, the representation of the stochastic variables, i.e. inflows and power price, in the planning algorithm is crucial. The representation of the stochastic variables as scenario trees is the main subject of this thesis.
The inflows to... (More)  Electricity bought and sold on the deregulated Nordic power market is dominated by hydro power. However, hydro power generation is restricted by the amount of water in reservoirs. The inflows to these reservoirs show a yearly cycle and seasonal planning of the production is necessary.
Seasonal planning up to 1.5 years for a power producer in a hydrothermal system with a regulated river is considered. For a pricetaking, riskaverse producer who wants to maximize his profit, the representation of the stochastic variables, i.e. inflows and power price, in the planning algorithm is crucial. The representation of the stochastic variables as scenario trees is the main subject of this thesis.
The inflows to the reservoirs in a river are highly spatially correlated and show temporal autocorrelation, as well. These properties are used to construct scenario trees. By using time series models the autocorrelation is explained and principal component analysis reduce substantially the dimension of the stochastic variables. Since the available amount of water that can be used for power production varies between years due to meteorological reasons the spot price shows large fluctuations. This dependence is used for modeling the power price and power contracts. Altogether, this gives an efficient method to create scenario trees suitable for stochastic programming with few assumptions concerning stochastic properties of the underlying stochastic processes.
Scenario tree generation is the stochastic part in the solution to the seasonal planning problem. A multistage stochastic programming model with the inflows to different stations and the power price as stochastic elements has been constructed as well as a program system, SPOT, for obtaining the solution in practice. The different scenario tree generation methods have been evaluated as well as a comparison between the stochastic programming model and a deterministic model. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/24567
 author
 Halldin, Roger ^{LU}
 supervisor
 opponent

 Professor Römisch, Werner, Institut für Mathematik, HumboldtUniversität zu Berlin
 organization
 publishing date
 2005
 type
 Thesis
 publication status
 published
 subject
 keywords
 Statistik, actuarial mathematics, programming, operations research, Statistics, energy derivatives, multistage stochastic programs, electricity prices, principal component analysis, Scenario trees, inflow modeling, operationsanalys, programmering, aktuariematematik
 in
 Doctoral Theses in Mathematical Sciences
 volume
 2005:6
 pages
 194 pages
 publisher
 Mathematical Statistics, Centre for Mathematical Sciences, Lund University
 defense location
 Matematikcentrum, Sölvegatan 18, sal MH:A, Lunds Tekniska Högskola
 defense date
 20050603 09:15:00
 ISSN
 14040034
 ISBN
 9162865390
 language
 English
 LU publication?
 yes
 id
 46c7fafae56548078f1520777b0ae259 (old id 24567)
 date added to LUP
 20160401 16:11:17
 date last changed
 20190521 13:32:49
@phdthesis{46c7fafae56548078f1520777b0ae259, abstract = {Electricity bought and sold on the deregulated Nordic power market is dominated by hydro power. However, hydro power generation is restricted by the amount of water in reservoirs. The inflows to these reservoirs show a yearly cycle and seasonal planning of the production is necessary.<br/><br> <br/><br> Seasonal planning up to 1.5 years for a power producer in a hydrothermal system with a regulated river is considered. For a pricetaking, riskaverse producer who wants to maximize his profit, the representation of the stochastic variables, i.e. inflows and power price, in the planning algorithm is crucial. The representation of the stochastic variables as scenario trees is the main subject of this thesis.<br/><br> <br/><br> The inflows to the reservoirs in a river are highly spatially correlated and show temporal autocorrelation, as well. These properties are used to construct scenario trees. By using time series models the autocorrelation is explained and principal component analysis reduce substantially the dimension of the stochastic variables. Since the available amount of water that can be used for power production varies between years due to meteorological reasons the spot price shows large fluctuations. This dependence is used for modeling the power price and power contracts. Altogether, this gives an efficient method to create scenario trees suitable for stochastic programming with few assumptions concerning stochastic properties of the underlying stochastic processes.<br/><br> <br/><br> Scenario tree generation is the stochastic part in the solution to the seasonal planning problem. A multistage stochastic programming model with the inflows to different stations and the power price as stochastic elements has been constructed as well as a program system, SPOT, for obtaining the solution in practice. The different scenario tree generation methods have been evaluated as well as a comparison between the stochastic programming model and a deterministic model.}, author = {Halldin, Roger}, isbn = {9162865390}, issn = {14040034}, language = {eng}, publisher = {Mathematical Statistics, Centre for Mathematical Sciences, Lund University}, school = {Lund University}, series = {Doctoral Theses in Mathematical Sciences}, title = {Stochastic Modeling and Optimization under Uncertainty of a Hydro Power System}, volume = {2005:6}, year = {2005}, }