In recent years there has been an increased interest in finding cost efficient strategies to reduce the emissions of the building stock, in the effort to reach the climate goals outlined in the Paris Agreement [1]. The specific focus on the built environment is motivated by its significant energy footprint: in the EU, the energy demand of buildings makes up 40% of the total energy demand, and 35% of the total greenhouse gas emissions [2].
The strategies can typically be divided into two groups: strategies to reduce energy demand of buildings, through investments in retrofitting and heating systems, and strategies to increase the local energy supply of buildings, through investments in photo-voltaic systems and battery energy storage systems [3] .
Within the project Digital Twin for Positive Energy Districts—DT4PED, in a collaboration between the Department of Mathematical Sciences and the Department of Architecture and Civil Engineering, both at Chalmers, we approach the problem of reducing emissions by using a case study building district in Gothenburg, see figure below. The aim is to transform the area into a Positive Energy District, that is, a district with low energy demand and high utilization of renewable resources, and that ideally is a net supplier of energy [4].
Specifically, the problem considered is the optimization of investments in and operations of a mixed-use building district. Operations include local transmission and production of electricity, import and export of electricity, district heating, and battery management. The objectives are to find solutions in the form of investments and operation plans that minimize total system costs across the district, as well as total system emissions (both operational and embodied), over the planning horizon.
A key challenge in this optimization is to consider a long enough time horizon—reflecting the long payback period of investments (30+ years)—while maintaining the fine temporal resolution (of one hour) needed to capture fluctuations in energy demand, solar electricity production, and electricity prices. In many studies, this challenge is handled by reducing the time horizon into a few representative days that are assumed to occur a certain number of times in each year, see, for example, [3] [5] [6]. The representative days approach is, however, not compatible with battery energy storage, which would in such case be constrained to solely daily charging and discharging cycles. Furthermore, seasonal fluctuations in spot prices, electricity demand, etc., cannot be considered.
Another challenge is the connectedness of buildings in the spatial dimension, arising from (the possibility of) local electricity production that allows transmission of electricity between buildings, and from the usage of a shared battery energy storage system. Hence, investments and operations must be optimized at a district level as opposed to individually for each building.
We manage to solve this bi-objective optimization problem for a district with 24 buildings, over a planning horizon of ten years using a Benders decomposition [7]. In our formulation, the Benders’ master problem suggests values for the investment variables, and parallelized subproblems for each year find the corresponding optimal operations.
Two Pareto sets of optimal solutions are illustrated in the figure, reflecting the two scenarios of spot electricity prices that were used: one with moderate volatility (scenario 2023), and another one with high volatility (scenario 2022). For both scenarios, Pareto solutions with a higher weight on the emission objective include large investments in PV, but keep the buildings’ existing district heating system, and do not include building renovations, indicating that emissions savings from a reduced heat demand after retrofitting are unlikely to off-set the embodied emissions of the retrofit itself, especially when the local district heating system is already low carbon.
While no battery energy system investment is made in any of the Pareto solutions for scenario 2023, the solutions for scenario 2022 shows Pareto optima close to the cost-optimal solutions with investments in a local battery energy system and it achieves significantly lower system costs than the first scenario. This demonstrates that a battery energy system can be utilized at an economic profit in a scenario where a high price volatility can be exploited in a load-shift or for selling electricity back to the grid when prices are high.
Jenny Enerbäck was a Project Assistant within the project “Digital Twin for Positive Energy Districts–DT4PED” and is currently a PhD-student in Numerical Linear Algebra at the Department of Mathematical Sciences, Chalmers.
References
[1] W. K. Fong, M. Sotos, M. Doust, S. Schultz, A. Marques and C. Deng-Beck, “Global Protocol for Community-Scale Greenhouse Gas Inventories,” 2014. [Online]. Available: https://ghgprotocol.org/ghg-protocol-cities. [Accessed 01 May 2024].
[2] European Commission, “Energy Performance of Buildings Directive adopted to bring down energy bills and reduce emissions,” 2024. [Online]. Available: https://ec.europa.eu/commission/presscorner/detail/en/ip_24_1965.
| [3] A. Lerbinger, I. Petkov, G. Mavromatidis and C. Knoeri, “Optimal decarbonization strategies for existing districts considering energy systems and retrofits,” Applied Energy, vol. 352, 2023. Available: https://www.sciencedirect.com/science/article/pii/S0306261923012278?via%3Dihub |
[4] RI.SE, “Positive Energy District,” Research Institutes of Sweden, [Online]. Available: https://www.ri.se/en/expertise-areas/expertises/positive-energy-districts-ped. [Accessed 04 02 2025].
[5] G. Mavromatidis and I. Petkov, “MANGO: A novel optimization model for the long-term, multi-stage planning of decentralized multi-energy systems,” Applied Energy, vol. 288, 2021. Available: https://www.sciencedirect.com/science/article/pii/S030626192100129X?via%3Dihub
[6] I. Petkov, G. Mavromatidis, K. Christof, J. Allan and H. Volker H., “MANGOret: An optimization framework for the long-term investment planning of building multi-energy system and envelope retrofits,” Applied Energy, vol. 314, 2022. Available: https://www.sciencedirect.com/science/article/pii/S0306261922003269#b113
[7] R. Rahmaniani, T. G. Crainic, M. Gendreau and W. Rei, “The Benders decomposition algorithm: A literature review,” European Journal of Operational Research, vol. 259, no. 3, pp. 801-817, 2017. Available: https://www.sciencedirect.com/science/article/pii/S0377221716310244