This work is devoted to study optimization problems arising in energy distribution systems with storage. We consider a simplified network topology organized around four nodes: the load aggregator, the external grid, the consumption and the storage. The imported power from the external grid should balance the consumption and the storage variation. The merit function to minimize is the total price the load aggregator has to pay in a given time interval to enforce this balance.
Two optimization problems are considered. The first one is linear and standard. It can be solved through classical optimization methods. The second problem is obtained from the previous one by taking into account a power subscription, which makes it piecewise linear. We establish mathematical properties on both these models.
Finally, a new method based on a sliding window algorithm is derived. It allows to reduce drastically the computational time and makes feasible real time simulations. Numerical results are performed on real data to highlight both models and to illustrate the performance of the sliding window algorithm.
Citation: Jean-Paul Chehab, Vivien Desveaux, Marouan Handa. A sliding window algorithm for energy distribution system with storage[J]. AIMS Mathematics, 2021, 6(11): 11815-11836. doi: 10.3934/math.2021686
This work is devoted to study optimization problems arising in energy distribution systems with storage. We consider a simplified network topology organized around four nodes: the load aggregator, the external grid, the consumption and the storage. The imported power from the external grid should balance the consumption and the storage variation. The merit function to minimize is the total price the load aggregator has to pay in a given time interval to enforce this balance.
Two optimization problems are considered. The first one is linear and standard. It can be solved through classical optimization methods. The second problem is obtained from the previous one by taking into account a power subscription, which makes it piecewise linear. We establish mathematical properties on both these models.
Finally, a new method based on a sliding window algorithm is derived. It allows to reduce drastically the computational time and makes feasible real time simulations. Numerical results are performed on real data to highlight both models and to illustrate the performance of the sliding window algorithm.
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Jean-Paul Chehab, Vivien Desveaux, Marouan Handa. A sliding window algorithm for energy distribution system with storage[J]. AIMS Mathematics, 2021, 6(11): 11815-11836. doi: 10.3934/math.2021686
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