| 1. |
- Granfeldt, Caroline, 1991, et al.
(författare)
-
A Lagrangian relaxation approach to an electricity system investment model with a high temporal resolution
- 2023
-
Ingår i: OR Spectrum. - 1436-6304 .- 0171-6468. ; 45:4, s. 1263-1294
-
Tidskriftsartikel (refereegranskat)abstract
- The global production of electricity contributes significantly to the release of carbon dioxide emissions. Therefore, a transformation of the electricity system is of vital importance in order to restrict global warming. This paper proposes a modelling methodology for electricity systems with a large share of variable renewable electricity generation, such as wind and solar power. The model developed addresses the capacity expansion problem, i.e. identifying optimal long-term investments in the electricity system. Optimal investments are defined by minimum investment and production costs under electricity production constraints—having different spatial resolutions and technical detail—while meeting the electricity demand. Our model is able to capture a range of strategies to manage variations and to facilitate the integration of variable renewable electricity; it is very large due to the high temporal resolution required to capture the variations in wind and solar power production and the chronological time representation needed to model energy storage. Moreover, the model can be further extended—making it even larger—to capture a large geographical scope, accounting for the trade of electricity between regions with different conditions for wind and solar power. Models of this nature thus typically need to be solved using some decomposition method to reduce solution times. In this paper, we develop a decomposition method using so-called variable splitting and Lagrangian relaxation; the dual problem is solved by a deflected subgradient algorithm. Our decomposition regards the temporal resolution by defining 2-week periods throughout the year and relaxing the overlapping constraints. The method is tested and evaluated on some real-world cases containing regions with different energy mixes and conditions for wind power. Numerical results show shorter computation times as compared with the non-decomposed model, and capacity investment options similar to the optimal solution provided by the latter model.
|
|
| 2. |
- Granfeldt, Caroline, 1991
(författare)
-
Mathematical modelling and methodology for cost optimization of variable renewable electricity integration
- 2021
-
Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The global production of electricity contributes significantly to the release of carbon dioxide 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 an electricity system which contains a large share of variable renewable electricity generation, such as wind and solar power. The 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. Furthermore, they are able to capture some of the variation management strategies necessary for electricity systems that include a large share of variable renewable electricity. These models are very large in nature due to the high temporal resolution needed to capture the wind variations, and thus different decomposition methods are applied to reduce solution times. We develop two different decomposition methods: 1) Lagrangian relaxation combined with variable splitting solved using a subgradient algorithm, and 2) a heuristic decomposition approach using a consensus algorithm. In both 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 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.
|
|
| 3. |
- Granfeldt, Caroline, 1991
(författare)
-
Optimization of low-cost integration of wind and solar power in multi-node electricity systems: Mathematical modelling and dual solution approaches
- 2023
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- 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.
|
|
| 4. |
- Göransson, Lisa, 1982, et al.
(författare)
-
Management of Wind Power Variations in Electricity System Investment Models. A Parallel Computing Strategy
- 2021
-
Ingår i: Operations Research Forum. - : Springer Science and Business Media LLC. - 2662-2556. ; 2
-
Tidskriftsartikel (refereegranskat)abstract
- Accounting for variability in generation and load and strategies to tackle variability cost-efficiently are key components of investment models for modern electricity systems. This work presents and evaluates the Hours-to-Decades (H2D) model, which builds upon a novel approach to account for strategies to manage variations in the electricity system covering several days, the variation management which is of particular relevance to wind power integration. The model discretizes the time dimension of the capacity expansion problem into 2-week segments, thereby exploiting the parallel processing capabilities of modern computers. Information between these segments is then exchanged in a consensus loop. The method is evaluated with regard to its ability to account for the impacts of strategies to manage variations in generation and load, regional resources and trade, and inter-annual linkages. Compared to a method with fully connected time, the proposed method provides solutions with an increase in total system cost of no more than 1.12%, while reducing memory requirements to 1/26’th of those of the original problem. For capacity expansion problems concerning two regions or more, it is found that the H2D model requires 1–2% of the calculation time relative to a model with fully connected time when solved on a computer with parallel processing capability.
|
|
