Energy-Optimal Allocation of Storage in Transmission Grid Networks

Abstract

The deployment of renewable energy technologies supposes the connection to the power grid of many new, distributed, and variable electricity production facilities. Among the investments deeply needed for a successful shift to clean energy, electricity storage systems are key to provide power reliably, continuously and economically. Here, we are concerned with the energy that must be invested and embodied in storage devices and in production oversizing to cope with natural variations of renewable electricity production, and compensate for any gap between production and consumption. We developed a model to analyze the variation of energy expenses with the location in the grid, capacity of storage and production oversizing. We apply it to a time scale of fluctuations of a few hours that can be taken care of by Li-ion batteries to calculate the optimal storage capacity and production oversizing yielding a maximum value of the ESOI ratio [Energy Stored On energy Invested] at a given satisfaction rate of customer demand. We evaluate these values for a rescaled present-time French power mix and two idealized zero-emission mixes (100% PV and 100% wind). In parallel, using a recently developed model of French transmission grid, a centrality-based analysis shows that locating storage at nodes of maximal installed power minimizes additional Joule losses. These results generalize existing grid-level energy return frameworks to incorporate storage sizing, placement, and transmission losses into a unified assessment of future power grid configurations.

Figures (7)

• Figure 1: Variation over the year 2021 of the power discrepancy in the raw data in red. The blue signal is obtained by removing carbonized production and multiplying renewable production by $\alpha$.
• Figure 2: Example of a simple power evolution obtained by the dynamical storage model. Here we take $P(t) = P_0 (1+\sin(\omega t)) + P_1$ and $C(t) = P_0$. We have $P_0$ as the instantaneous average power produced and consumed, and $P_1$ is the oversizing that is needed to compensate the fact that $\eta_{\mathrm{st}}$ is lower than 1. The total value correspond to the sum $P(t)+P_{\mathrm{st}}(t)-C(t)$. Bottom right: Schematic picture of an energy system including storage.
• Figure 3: Variation over 50 hours of the Haar reconstructed power discrepancy in blue. The orange signal is obtained by adding the storage power to $\tilde{P}_\Delta(t)$.
• Figure 4: Characterizations of 10000 iterations of the model for 100 values of $S_\text{max}$ and 100 values of $P_1$. Upper left: Values of satisfaction rate. Upper right: Values of ESOI. Lower panel: Projection of the ESOI values on the subset of parameters corresponding the 95% satisfaction rate.
• Figure 5: Difference between the total Joule losses with and without storage for various scenarios and centrality functions. The power centrality ranking corresponds to the production ranking of the nodes. The differences are integrated over 250 hours. The main figure represent the strategies focusing on minimum or maximum centralities in the case of the present French mix ("RTE mix"). The inset figure focuses on the maximum centrality case only but with 100% PV and 100% Wind energy mixes.