Depreciation Cost is a Poor Proxy for Revenue Lost to Aging in Grid Storage Optimization

Abstract

Dispatch of a grid energy storage system for arbitrage is typically formulated into a rolling-horizon optimization problem that includes a battery aging model within the cost function. Quantifying degradation as a depreciation cost in the objective can increase overall profits by extending lifetime. However, depreciation is just a proxy metric for battery aging; it is used because simulating the entire system life is challenging due to computational complexity and the absence of decades of future data. In cases where the depreciation cost does not match the loss of possible future revenue, different optimal usage profiles result and this reduces overall profit significantly compared to the best case (e.g., by 30-50%). Representing battery degradation perfectly within the rolling-horizon optimization does not resolve this - in addition, the economic cost of degradation throughout life should be carefully considered. For energy arbitrage, optimal economic dispatch requires a trade-off between overuse, leading to high return rate but short lifetime, vs. underuse, leading to a long but not profitable life. We reveal the intuition behind selecting representative costs for the objective function, and propose a simple moving average filter method to estimate degradation cost. Results show that this better captures peak revenue, assuming reliable price forecasts are available.

Figures (8)

• Figure 1: Maximizing the returns of grid energy storage requires a trade-off between overuse, resulting in limited revenue because of early end-of-life, and underuse, resulting in limited revenue because of missed opportunities. Dots indicate end-of-life returns for each case.
• Figure 2: Net present values and corresponding profitability indices for different degradation cost weights and interest rates; firstly where only $\lambda_\text{cal}$ is changed and $\lambda_\text{cyc}=1$ (blue line with circle markers); secondly where only $\lambda_\text{cyc}$ is changed and $\lambda_\text{cal}=1$ (red line with diamond markers); thirdly, with $\lambda_\text{both} = \lambda_\text{cal} = \lambda_\text{cyc}$ and both are changed together (yellow line with square markers).
• Figure 3: Change in profitability index (PI) as a function of $\lambda_\text{both}$ for various interest rates. Solid lines represent yearly interest rates of 0%, 1%, 2%, 3%, 5%, 8%, 12%, and 20% respectively, top to bottom. Dashed line is PI = $\lambda_\text{both}$.
• Figure 4: Evolution of estimated $\lambda$ using moving mean over historical data, with a window size of one year. Zoomed section (grey) shows performance in the first year.
• Figure 5: Estimated $\lambda$ based on weekly revenue and $Q_\text{loss}$, colors denote the closeness of the data point to end of life.