# Mathematical modelling and methodology for cost optimization of variable renewable electricity integration Licentiate thesis, 2021

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.

cost optimization

variation management

variable renewable electricity

variable splitting

electricity system modelling

consensus algorithm

Lagrangian relaxation

wind power integration

long-term investment models

Pascal, Chalmers tvärgata 3, och online via Zoom
Opponent: Dr. Peter Lindroth, Andra AP-fonden (AP2), Göteborg

## Author

### Caroline Granfeldt

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

### Mathematical modelling of large scale integration of variable electricity generation - a new modelling paradigm

Swedish Energy Agency (39907-1), 2015-07-01 -- 2018-12-31.

Swedish Energy Agency (39907-1), 2015-07-01 -- 2020-12-31.

### Subject Categories

Mathematics

Energy Engineering

Energy Systems

Energy

### Publisher

Chalmers

Pascal, Chalmers tvärgata 3, och online via Zoom

Opponent: Dr. Peter Lindroth, Andra AP-fonden (AP2), Göteborg