We propose a multiscale model predictive control (MPC) framework for stationary battery systems that exploits high-fidelity models to trade-off short-term economic incentives provided by energy and frequency regulation (FR) markets and long-term degradation effects. We find that the MPC framework can drastically reduce long-term degradation while properly responding to FR and energy market signals (compared to MPC formulations that use low-fidelity models). Our results also provide evidence that sophisticated battery models can be embedded within closedloop MPC simulations by using modern nonlinear programming solvers (we provide an efficient and easy-to-use implementation in Julia). We use insights obtained with our simulations to design a low-complexity MPC formulation that matches the behavior obtained with high-fidelity models. This is done by designing a suitable terminal penalty term that implicitly captures longterm degradation. The results suggest that complex degradation behavior can be accounted for in low-complexity MPC formulations by properly designing the cost function. We believe that our proof-of-concept results can be of industrial relevance, as battery vendors are seeking to participate in fast-changing electricity markets while maintaining asset integrity.

中文翻译：

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使用基于物理的模型对频率调节市场的电池系统进行多尺度模型预测控制

我们为固定电池系统提出了一个多尺度模型预测控制 (MPC) 框架，该框架利用高保真模型来权衡能源和频率调节 (FR) 市场提供的短期经济激励和长期退化效应。我们发现 MPC 框架可以显着减少长期退化，同时正确响应 FR 和能源市场信号（与使用低保真模型的 MPC 公式相比）。我们的结果还提供了证据，证明可以通过使用现代非线性规划求解器将复杂的电池模型嵌入到闭环 MPC 仿真中（我们在 Julia 中提供了一种高效且易于使用的实现）。我们使用通过模拟获得的见解来设计一个低复杂度的 MPC 公式，该公式与使用高保真模型获得的行为相匹配。这是通过设计一个合适的终端惩罚项来实现的，该惩罚项隐含地捕获长期退化。结果表明，通过适当设计成本函数，可以在低复杂度 MPC 配方中解释复杂的降解行为。我们相信，我们的概念验证结果可能具有行业相关性，因为电池供应商正在寻求参与快速变化的电力市场，同时保持资产完整性。