Title: Frequency Regulation with Storage: On Losses and Profits Show Chinese title

Title: 储能在频率调节中的收益与损耗

Abstract: Low-carbon societies will need to store vast amounts of electricity to balance intermittent generation from wind and solar energy, for example, through frequency regulation. Here, we derive an analytical solution to the decision-making problem of storage operators who sell frequency regulation power to grid operators and trade electricity on day-ahead markets. Mathematically, we treat future frequency deviation trajectories as functional uncertainties in a receding horizon robust optimization problem. We constrain the expected terminal state-of-charge to be equal to some target to allow storage operators to make good decisions not only for the present but also the future. Thanks to this constraint, the amount of electricity traded on day-ahead markets is an implicit function of the regulation power sold to grid operators. The implicit function quantifies the amount of power that needs to be purchased to cover the expected energy loss that results from providing frequency regulation. We show how the marginal cost associated with the expected energy loss decreases with roundtrip efficiency and increases with frequency deviation dispersion. We find that the profits from frequency regulation over the lifetime of energy-constrained storage devices are roughly inversely proportional to the length of time for which regulation power must be committed. Show Chinese abstract

Abstract: 低碳社会需要存储大量的电力，以平衡来自风能和太阳能的间歇性发电，例如，通过频率调节实现这一点。 在这里，我们推导出了解决储能运营商决策问题的解析解，这些运营商向电网运营商出售频率调节电力，并在日前市场交易电力。 从数学上讲，我们将未来的频率偏差轨迹视为滚动时域鲁棒优化问题中的函数不确定性。 我们约束预期的终端荷电状态等于某个目标值，以便储能运营商不仅能够为当前做出良好的决策，也能为未来做出良好决策。 由于这一约束，日前市场上交易的电量是隐式地由提供给电网运营商的调节电力量决定的。 隐式函数量化了需要购买的电力量，以弥补因提供频率调节而导致的预期能量损失。 我们展示了与预期能量损失相关的边际成本如何随着往返效率的提高而降低，随着频率偏差分散度的增加而提高。 我们发现，受能量限制的储能设备在整个使用寿命内从频率调节中获得的利润大致与必须承诺的调节功率持续时间成反比。