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Table 2 Performance of solving the global optimization problem (1): The heuristic candidates with different fchar/dischar models are compared to the optimal solution from solving the global optimization problem as a linear program

From: Scaling: managing a large number of distributed battery energy storage systems

Algorithms Revenue [Euro] average violations discharging
Global Optimization 7949 0%
Heuristic 1: without function 4749 21.6%
Heuristic 2: bounded SoC 2859 9.8%
Heuristic 3: linear 6694 12.2%
Heuristic 4: concave piece-wise linear 7311 13.2%
Heuristic 5: non-concave piece-wise linear 7473 6.0%
  1. The heuristic without a function modeled approximates this daily deterministic problem quite poorly, resulting in trying to schedule more charging or discharging than what is available. This leads to a bad policy since on average 21.6% of the control (relative to maximum VPP discharging power) is not possible to be implemented by the individual BESS. In order to avoid critical operation where some individual BESS may be full or depleted, heuristic 2 bounds the SoC of the VPP. This leads to much less violations, however, at the costs of using only a fraction of the energy storage of the VPP. Having more complicated models leads to better results up to the non-concave piece-wise linear model with a difference from the optimal value of only 6% and average violations of also 6%