Optimization of low-cost integration of wind and solar power in multi-node electricity systems: Mathematical modelling and dual solution approaches
Doctoral thesis, 2023
The global production of electricity contributes significantly to the release of CO2 emissions. Therefore, a transformation of the electricity system is of vital importance in order to restrict global warming. This thesis concerns modelling and methodology of electricity systems which contain a large share of variable renewable electricity generation (i.e. wind and solar power).
The two models developed in this thesis concern optimization of long-term investments in the electricity system. They aim at minimizing investment and production costs under electricity production constraints, using different spatial resolutions and technical detail, while meeting the electricity demand.
These models are very large in nature due to the 1) high temporal resolution needed to capture the wind and solar variations while maintaining chronology in time, and 2) need to cover a large geographical scope in order to represent strategies to manage these variations (e.g.\ electricity trade). Thus, different decomposition methods are applied to reduce computation times. We develop three different decomposition methods: Lagrangian relaxation combined with variable splitting solved using either i) a subgradient algorithm or ii) an ADMM algorithm, and iii) a heuristic decomposition using a consensus algorithm. In all three cases, the decomposition is done with respect to the temporal resolution by dividing the year into 2-week periods. The decomposition methods are tested and evaluated for cases involving regions with different energy mixes and conditions for wind and solar power. Numerical results show faster computation times compared to the non-decomposed models and capacity investment options similar to the optimal solutions given by the latter models. However, the reduction in computation time may not be sufficient to motivate the increase in complexity and uncertainty of the decomposed models.
The two models developed in this thesis concern optimization of long-term investments in the electricity system. They aim at minimizing investment and production costs under electricity production constraints, using different spatial resolutions and technical detail, while meeting the electricity demand.
These models are very large in nature due to the 1) high temporal resolution needed to capture the wind and solar variations while maintaining chronology in time, and 2) need to cover a large geographical scope in order to represent strategies to manage these variations (e.g.\ electricity trade). Thus, different decomposition methods are applied to reduce computation times. We develop three different decomposition methods: Lagrangian relaxation combined with variable splitting solved using either i) a subgradient algorithm or ii) an ADMM algorithm, and iii) a heuristic decomposition using a consensus algorithm. In all three cases, the decomposition is done with respect to the temporal resolution by dividing the year into 2-week periods. The decomposition methods are tested and evaluated for cases involving regions with different energy mixes and conditions for wind and solar power. Numerical results show faster computation times compared to the non-decomposed models and capacity investment options similar to the optimal solutions given by the latter models. However, the reduction in computation time may not be sufficient to motivate the increase in complexity and uncertainty of the decomposed models.
variable renewable electricity
Lagrangian relaxation
ADMM
electricity system modelling
variable splitting
capacity expansion
cost optimization
variation management
consensus algorithm
subgradient algorithm
Pascal, Chalmers Tvärgata 3, Göteborg
Opponent: Professor Asgeir Tomasgard, Department of Industrial Economics and Technology Management, NTNU, Trondheim, Norway
Author
Caroline Granfeldt
Chalmers, Mathematical Sciences, Applied Mathematics and Statistics
Granfeldt, C., Strömberg, A-B., Göransson, L. A Lagrangian relaxation approach to an electricity system investment model with a high temporal resolution
Granfeldt, C., Strömberg, A-B., Göransson, L. Managing the temporal resolution in a multi-node electricity system investment model: Parallel computations by variable splitting and Lagrangian relaxation
Granfeldt, C., Strömberg, A-B., Mattsson, N. An approximate consensus ADMM approach to a multi-node electricity system investment problem with a high temporal resolution
Management of Wind Power Variations in Electricity System Investment Models. A Parallel Computing Strategy
Operations Research Forum,;Vol. 2(2021)
Journal article
Computations for low-cost capacity expansion of renewables in the electricity system
The European electricity system is currently undergoing a major transition from carbon-emitting technologies (i.e., fossil fuels) to renewable electricity generation in order to curb global warming. This thesis models cost minimization of long-term investments in new production capacity to meet the future demand of electricity, while still reducing the system emissions of carbon dioxide.
If wind and solar power are used to meet a large share of our electricity demand, there is a need to account for their natural variations over the day. Variation management strategies accounted for include electricity trade between regions, flexible electricity production, and energy storage. Further, since the actual production can change from one hour to the next, mathematical optimization models describing the system need to include a fine temporal resolution. This, in turn, leads to huge-scale models, with billions of variables and constraints, thus being computationally extremely expensive to solve optimally.
This thesis examines solution approaches for decomposing these large-scale models into several smaller, more manageable, subproblems, which are then coordinated into good, feasible solutions. Our results show that for most of the investigated cases, our suggested methods provide shorter computation times while the resulting capacity investment options are similar to those resulting from the non-decomposed models.
The European electricity system is currently undergoing a major transition from carbon-emitting technologies (i.e., fossil fuels) to renewable electricity generation in order to curb global warming. This thesis models cost minimization of long-term investments in new production capacity to meet the future demand of electricity, while still reducing the system emissions of carbon dioxide.
If wind and solar power are used to meet a large share of our electricity demand, there is a need to account for their natural variations over the day. Variation management strategies accounted for include electricity trade between regions, flexible electricity production, and energy storage. Further, since the actual production can change from one hour to the next, mathematical optimization models describing the system need to include a fine temporal resolution. This, in turn, leads to huge-scale models, with billions of variables and constraints, thus being computationally extremely expensive to solve optimally.
This thesis examines solution approaches for decomposing these large-scale models into several smaller, more manageable, subproblems, which are then coordinated into good, feasible solutions. Our results show that for most of the investigated cases, our suggested methods provide shorter computation times while the resulting capacity investment options are similar to those resulting from the non-decomposed models.
Mathematical modelling of large scale integration of variable electricity generation - a new modelling paradigm
Swedish Energy Agency (39907-1), 2015-07-01 -- 2020-12-31.
Swedish Energy Agency (39907-1), 2015-07-01 -- 2018-12-31.
Driving Forces
Sustainable development
Subject Categories
Mathematics
Other Mathematics
Other Electrical Engineering, Electronic Engineering, Information Engineering
Areas of Advance
Energy
ISBN
978-91-7905-892-0
Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 5358
Publisher
Chalmers
Pascal, Chalmers Tvärgata 3, Göteborg
Opponent: Professor Asgeir Tomasgard, Department of Industrial Economics and Technology Management, NTNU, Trondheim, Norway