Round-Trip Energy Efficiency and Energy-Efficiency Fade Estimation for Battery Passport

TL;DR

This work addresses quantifying round-trip energy efficiency $\eta_{RT,e}$ and its fade for battery passports using real-world drive-cycle data. It defines $\eta_{RT,e}$ as the ratio of discharged to charged energy, propagates measurement uncertainty, and links efficiency to impedance via a Thévenin model, yielding a practical linear-regression approach. By extracting round trips from BEB data and evaluating $\eta_{RT,e}$ under two key conditions—RMS C-rate and temperature—the authors build a predictive plane $\hat{\eta}_{RT,e}=\beta_1 C_1 + \beta_2 C_2 + \beta_3$ and track its evolution over 3.5 years. The results show a modest average fade of about $0.46$ percentage points, with vehicle-specific variations, and a clear interpretation in terms of impedance growth, underscoring the relevance and challenges of incorporating fade metrics into battery passports. The study highlights condition-aware reporting and potential online implementations to support policy and lifecycle decision-making.

Abstract

The battery passport is proposed as a method to make the use and remaining value of batteries more transparent. The future EU Battery Directive requests this passport to contain the round-trip energy efficiency and its fade. In this paper, an algorithm is presented and demonstrated that estimates the round-trip energy efficiency of a battery pack. The algorithm identifies round trips based on battery current and SoC and characterizes these round trips based on certain conditions. 2D efficiency maps are created as a function of the conditions `temperature' and `RMS C-rate'. The maps are parameterized using multiple linear regression, which allows comparison of the efficiency under the same conditions. Analyzing data from three battery-electric buses over a period of 3.5 years reveals an efficiency fade of up to 0.86 percent point.

Figures (5)

• Figure 1: The $SoC$ of Vehicle A in October 2019 during 48 hours. The red lines indicate the identified round trips, the start and end of which are marked by the time instances $t_{\color{changed2}start}$, respectively $t_{\color{changed2}end}$, as defined by \ref{['eq:conditiont1']} and \ref{['eq:conditiont2']}. The $SoC$ decrease between $t = 36$ hours and $t = 41$ hours is due to a period of driving without intermittent charging events. This initiates several shorter round-trips at lower $SoC$ values, which are ended during the subsequent charging session between $t = 42$ hours and $t = 46$ hours.
• Figure 2: Round-trip energy efficiency $\eta_{RT}$ of Vehicle A in October 2019 as function of four different conditions defined by (\ref{['eq:conditionSoC']},...,\ref{['eq:conditionTemp']}). A trend line is visualized in combination with the Spearman correlation coefficient $\rho$. No trend line is visualized in the top-left figure, because no statistically relevant correlation could be found.
• Figure 3: The round-trip efficiency${\eta}_{RT,e}$ as function of temperature $T_{RT}$ and RMS C-rate$_{RT}$ for Vehicle A in October 2019, visualized as points. The plane representing the estimated efficiency$\hat{\eta}_{RT,e}$ is also shown.
• Figure 4: The estimated round-trip energy efficiency$\hat{\eta}_{RT,e}$ as function of temperature$T_{RT}$ and RMS C-rate$_{RT}$ for Vehicle A at different moments in time.
• Figure 5: The estimated round-trip energy efficiency$\hat{\eta}_{RT,e}$ at C-rate$_{RT}^*$ and $T_{RT}^*$ for all three vehicles as function of time. The error bars indicate the 95% confidence bounds. The black lines indicate the three-month moving average.