A stochastic flexibility calculus for uncertainty-aware energy flexibility management

The increasing share of volatile renewables in power systems requires more reserves to balance forecast errors in renewable generation and power fluctuations. In contrast, common reserves such as gas-fired power plants are phased out, impeding the procurement of sufficient reserves. Alternative reserves, particularly on the demand side, such as battery storage systems, also exhibit some degree of freedom to deviate from their scheduled operating point to supply or consume more or less power, thus providing a flexibility potential. However, demand-side flexibility potentials are generally subject to uncertainties, and so is the generation of volatile renewables. The challenge is incorporating the uncertainties on both sides to procure sufficient (uncertain) flexibility potential in advance. Considering uncertainty is important to avoid additional, drastic measures in real-time to balance generation and demand, such as curtailing renewable generation or load shedding. This work presents a stochastic flexibility calculus that provides an indicator for computing the risk of insufficient flexibility potentials or, conversely, guarantees for sufficient flexibility potentials. Thus, the stochastic flexibility calculus contributes to overcoming the challenge of procuring sufficient flexibility potentials in renewable-based systems. An evaluation based on real data is performed using an example of a renewable energy community consisting of households equipped with photovoltaic power plants and battery storage systems. The newly introduced stochastic flexibility calculus computes the number of households that must operate their battery storage systems flexibly to balance forecast errors locally. The results show that the forecast method significantly influences this number. Some numerical results appear unexpected, as too many flexibility-friendly households can negatively impact the aggregated household flexibility potential.