How clustering approaches affect the optimal design of future multi-energy systems

This paper focuses on the correct assessment of the total cost and sizes of the energy conversion and storage units of multi-energy systems operating under uncertain energy market conditions. The objectives are to: i) find the best set of representative days of uncertain electricity and natural gas prices, global solar irradiance and air temperature, with a special focus on prices, influenced by unpredictable socio-economic events; ii) assess the impact of the representative days, including the extreme ones, on the optimal total cost and unit sizes of a multi-energy system. An available historical dataset (2010-2022) of time series is divided by shifting the “present” moment back to 2018 to use the previous period as “past” training dataset (2010-2018) and the subsequent period as two (independent) “future” testing datasets, featured with different price stability, corresponding to a pre- (2019-2020) and a post- (2021-2022) Russia-Ukraine war scenario, respectively. The novel methodology consists in comparing the “annual” and “seasonal” clustering approaches to obtain, respectively, sets of representative days of the uncertain variables in the entire training dataset or in the training dataset divided into seasons, also considering different criteria to evaluate the extreme days of electricity price and thermal demand. A Mixed-Integer Linear Programming model of the system is used to optimize the sizes and operation of its units, minimizing the total investment and operational costs in the training dataset. Subsequently, the optimal sizes are fixed to optimize the operation in the two testing datasets. The optimal total cost and sizes are compared with “perfect knowledge” solutions obtained considering all the time series really occurred in the two testing datasets. Key results highlight that the error of the optimal total cost with respect to the “perfect knowledge” solutions is about 2.5-4% with clustering, compared to 9-17% with the “state-of-the-art” hourly profiles averaged on months or seasons, respectively. This error is higher using seasonal clustering than annual clustering for a number of representative days higher than 12. Moreover, the extreme days of electricity price do not bring a relevant gain in the solution accuracy because they are very similar to the typical ones in the pre-war scenario and their weight is small in the post-war scenario, given the higher values of the real prices in the period 2021-2022. In contrast, the extreme days of thermal demand are necessary to guarantee a feasible solution.