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.

中文翻译：

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带存储的频率调节：关于损失和利润

低碳社会需要储存大量电力，以平衡风能和太阳能的间歇性发电，例如通过频率调节。在这里，我们针对向电网运营商出售调频电力并在日前市场上进行电力交易的存储运营商的决策问题得出了一个分析解。在数学上，我们将未来的频率偏差轨迹视为后退鲁棒优化问题中的函数不确定性。我们将预期的终端充电状态限制为等于某个目标，以便存储运营商不仅可以为当前而且可以为未来做出正确的决策。由于这一限制，日前市场上的交易电量是出售给电网运营商的调节电力的隐含函数。隐式函数量化了需要购买的电量，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增加而减少，并随着频率偏差离散度的增加而增加。我们发现，在能量受限的存储设备的整个生命周期中，频率调节的利润大致与必须投入调节功率的时间长度成反比。