Data-driven Direct Diagnosis of PV Connected Batteries

Data-driven Direct Diagnosis of PV Connected Batteries | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Data-driven Direct Diagnosis of PV Connected Batteries Matthieu Dubarry, Nahuel Costa Cortez, Dax Matthews This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2058155/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract Photovoltaic systems are providing a growing share of power to the electric grid worldwide. To mitigate resource intermittency issues, new systems are increasingly being paired with battery energy storage for which ensuring long and safe operation is critical. Unlike more typical battery applications, these batteries will undergo sporadic usage which will prevent the application of traditional diagnosis methods. This work proposes a new methodology for opportunistic diagnosis using machine learning algorithms trained directly on photovoltaic battery charging data. The training was performed on synthetic voltage data under different degradations calculated from clear-sky model irradiance data. Validation was performed on synthetic voltage responses calculated from plane of array irradiance observations for a photovoltaic system located in Maui, HI, USA. An average RMSE of 2.75% was obtained for more than 10,000 different degradation paths with 25% or less degradation on the cells. Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 1. Introduction In recent years solar photovoltaic (PV) technologies provided the most additional generating capacity to the United States grid [ 1 ]. In 2021, a record 23.6 GW of solar capacity was installed and, over the next 10 years, it is predicted that 324 GW of new solar capacity will be added to the electric grid, quadrupling current levels [ 1 ]. New solar systems are increasingly being paired with battery energy storage systems at multiple grid levels. While some of the storage will be performed by grid-scale batteries, the percentage of residential storage installations has also been steadily increasing, reaching 8.1% in 2020 [ 2 ]. It is estimated that by 2025, one in three residential solar systems will be paired with small scale energy storage [ 1 ], most likely provided by Lithium-ion batteries [ 3 ]. To ensure long, safe, and continuous operation, batteries must be maintained and controlled properly, which includes regular estimation of their state of health. This can be problematic for batteries paired with PV because of sporadic usage in both charge and discharge. As a result of this unpredictability, diagnosis might only be performable under lengthy maintenance cycles. An alternative to avoid downtime could be to identify and take advantage of auspicious conditions to perform state estimation. With batteries supposed to last a decade or more, this opens the gates for different approaches such as using batteries response under clear-sky conditions under which PV power production is predictable on time-scales of up to twelve hours. Even if the PV power output offered by clear-sky conditions is predictable, state estimation will still be complex and requiring robust methodologies for Li-ion battery diagnosis. Because the duty-cycles of batteries paired with PV will not be under constant current (CC), the traditionally used features [ 4 ] to estimate SOH might difficult to interpret. This favors data-driven methods, and in particular machine learning (ML) methods. However, to be applicable, ML algorithms need to be trained on a wide variety of data covering the sporadicity of the application. Unfortunately, while some market data are beginning to be available publicly [ 5 , 6 ], actual PV connected battery data is not to the best of our knowledge. Few studies are available with battery testing associated with PV duty cycles [ 7 , 8 ], with most of the studies being modeling centered and using constant current testing [ 9 – 15 ]. Looking at CC data, the lack-of-data problem was recently solved with the introduction of synthetic datasets that enabled the emulation of every possible battery degradation [ 16 – 19 ]. While the duty cycle for clear-sky irradiance will be more complex, recent work suggest that the methodology used to generate the synthetic data could be applied outside of CC [ 20 ] and thus be applicable to irradiance. This work proposes a new method for diagnosis PV connected batteries using synthetic datasets that would allow for SOH estimation during normal battery operations. The method uses periods of clear-sky conditions, where charging from PV generation is relatively stable and predictable, for diagnosis. This paper describes a framework for (1) generating synthetic datasets of the voltage response of cells charged by PV systems, (2) synthetic dataset training of state-of-the-art ML algorithms, and (3) algorithm validation using synthesized data. This framework is summarized in Fig. 1 with a branch for training and a branch for validation. The training branch uses irradiance data from a clear-sky model, PV system information (longitude, tilt, orientation), and battery information (chemistry and W/Ah) to generate synthetic cycles consisting of the voltage response of the cells for specific duty cycles under tens of thousands of different degradations. This dataset is then used to train, test, and compare selected ML algorithms for diagnosis, including a Random Forest regressor (RF) [ 21 ], an Extreme Gradient Boosting regressor (XGB) [ 22 ], a Feed-forward neural network (FNN) [ 23 ], a 1 dimensional Convolutional Neural Network (1D-Conv) [ 16 ], and a dynamic time warping 2-D Convolutional Neural Network (DTW)-CNN [ 24 ]. While the validation would ideally be performed on data from deployed batteries, no deployed PV linked batteries dataset is publicly available to the best of our knowledge. Even if data was available, the actual degradation of each individual system would not likely be, making validation impossible. In anticipation of data becoming available, we examined the applicability of our approach to real systems by replacing the deployed data by synthetic datasets generated for various sky-clearness levels, Fig. 1 . These synthetic datasets are used to validate the applicability of the clear-sky irradiance trained ML algorithms for diagnosis under cloudy conditions. To further emulate realistic conditions, each dataset was calculated on a cell with slightly different parameters to account for cell-to-cell variations and inhomogeneities [ 25 ]. A selection of the data generated from this work is available in [ 26 , 27 ]. 2. Results 2.1 Irradiance data selection The output of a PV system is dependent on irradiance which is the power of the solar radiation striking the panels. Irradiance variability is driven by extraterrestrial and atmospheric effects and is also dependent on panel orientation [ 28 , 29 ]. The latter has become more varied in recent years [ 3 ], but panels are nominally oriented toward the equator at a tilt angle near to the latitude of the installation in order to maximize solar energy yield [ 30 ]. Clear-sky irradiance occurs during clear-sky conditions, defined as an absence of visible clouds across the entire sky dome [ 31 ]. Clear-sky irradiance is estimated using a clear-sky model (CSM) which calculates solar geometry and accounts for variations in air mass and variations in optical depth [ 32 ]. In this work, we used the CSM proposed by Ineichen and Perez [ 32 ] for a horizontal surface extended to estimate clear-sky irradiance on a tilted surface in the plan of array (POA) of a PV panel. The extended CSM recomputes the solar angle of incidence, accounts for the reduction of diffuse irradiance received [ 33 ], and adds a new ground reflected irradiance source [ 34 ]. Figure 2 (a) presents diurnal and seasonal variations in horizontal (top) and POA (bottom) clear-sky irradiance estimated by the CSM over a two-year period for a PV test site located at the Maui Economic Development Board (MEDB) office on the southwestern coast of the island of Maui, Hawaiʻi, USA, Fig. 3 (a), with PV panels oriented at a 20° tilt with a 197° N azimuth. Due to Hawaiʻi’s proximity to the Northern Tropic, clear-sky irradiance levels incident on a horizontal surface remained high from April to September, but drop during winter. Seasonal variations of clear-sky irradiance incident on the POA of PV panels located at the site are reduced, with peak levels found in spring and summer months. POA irradiance also peaks later in the day (by around 1 hour) relative to horizontal values, due to the panels facing slightly westward instead of due south. To further illustrate seasonal fluctuations, data at solstice and equinoxes are presented in Fig. 2 (b) and Fig. 2 (c) for horizontal and POA irradiances respectively. The CSM fails to account for several factors driving real irradiance variability. While the most obvious is cloud cover, fluctuations in atmospheric turbidity, shading, soiling, and reflection losses also affect the amount of irradiance available for a PV system. In this work, clear-sky conditions were identified using an algorithm that applies a series of threshold criteria tests to compare the smoothness, shape, and magnitude of observed values within a moving window to corresponding clear-sky values from the CSM [ 35 , 36 ]. The algorithm is assigning a daily “clearness” value, determined using the number of observations identified as clear-sky over the total number of observations during daytime conditions. The distribution of daily clearness per season for the whole dataset is shown in Fig. 3 (b). For almost half of the 2-year dataset, clear-sky conditions were found in less than 20% of the daily observations, however, in nearly one in five days, more than 50% of observations were identified as clear-sky. Moreover, the distribution of daily clearness values indicates only slight seasonal variations at the test site. To assess how the accuracy of the diagnosis was affected by irradiance variability, 18 days from the 2-year dataset were selected to encompass a range of irradiance conditions, Fig. 3 (c). The conditions range from a minimum clearness of 4% to a maximum of 84%, with cloud cover occurring at different times. Cloud effects range from small perturbations, likely due to high cirrus clouds, to significant attenuation and cloud enhancement, due to more opaque cloud cover. Shading effects caused by the construction of a nearby building can also be seen in the afternoon hours of the two days in October 2017. 2.2. Cell emulation & Duty cycle emulation As presented in Fig. 1 , a digital twin was used to generate the battery data needed to assess the impact of the different duty cycles on battery performance. The battery model included in the twin was based on the ‘alawa mechanistic model [ 37 , 38 ]. To parameterize the model and emulate the electrochemical response of the selected commercial Li-ion battery, the half-cell data for both the positive and negative electrodes (PE and NE respectively) were imported into the ‘alawa toolbox. The half-cell data was fitted to the full-cell by scanning different values for the loading ratio (LR), offset (OFS), resistance (R), and rate degradation factor (RDF) for the PE and the NE. Because the duty cycles simulated in this work were not CC, the ‘alawa model needed to be calibrated to correctly simulate rates within the range used by the duty cycles of batteries paired with PV. This calibration required emulations at different rates and verification of continuity between the rate-dependent emulation parameters to enable interpolation and extrapolation to other rates. Figure 4 (a,b,c) presents the results of the full-cell emulation of the C/15, C/8.5, and C/4 cycles, respectively, based on the half-cell data gathered from the harvested electrodes. The best fit had a LR of 1.2 with a 4% offset and a -0.1 resistance correction for the rate-independent parameters. Looking at the rate-dependent parameters, as the simulated rate increased, the RDFs for both electrodes were found to decrease from 0.6 to 0.2 for the PE and from 0.8 to 0.6 for the NE. An additional resistance correction was needed to compensate for peak movements for the RDF PE (RDF corrPE ). This correction ensured that the electrochemical response at different rates overlapped correctly when kinetics is adjusted, which cannot currently be done automatically by the model. The equation for this additional resistance correction is provided in Figure S1 with an explanatory schematic. No correction was needed for the RDF NE . The evolution of the three varying rate-dependent parameters could be fitted with power laws y = a*rate b with R 2 ≥0.997 vs. R 2 ~ 0.97 for linear regressions, Fig. 4 (d). Using the best fit parameters and equations, the synthetic cell voltage response under the different duty cycles was generated using the method proposed in [ 20 ] using solar panel power output as a duty cycle instead of CC. An example of clear-sky solar panel power output is presented in Fig. 5 (a). The power is 0 at sunrise, ramps up to its maximum around solar noon, then ramps down to 0 at sunset. As proposed in [ 20 ], and in order to simulate this duty cycle, a set of 100 voltage responses were simulated between the lowest rate (minimum power at maximum voltage) and the highest rate (maximum power at minimum voltage), Fig. 5 (b). The correct [voltage, rate] couple to match the required power was calculated for each 0.1% state of charge until full charge. Overall, the maximum rate was chosen to be C/6 so that around 95% of the cell capacity is used through an average day (03/21). C/6 is below the highest rate for the which the emulation parameters were deciphered (C/4). This will allow high confidence in the simulation of high loss of active material (LAM), because, with at most 50% degradation, the local rate would at worst double from C/6 to C/3 [ 20 , 37 ], which is still close to the range of experimentally tested rates. Thermodynamic battery degradation can be decomposed in three degradation modes, the loss of lithium inventory (LLI) and LAM on both the PE and the NE [ 20 , 37 ], because independent of what mechanism is inducing degradation, what will change is how much of each electrode is available to host lithium and how much lithium is able to go back and forth. Each combination of LLI, LAM PE , and LAM NE corresponds to a unique degradation and has a unique voltage signature. Diagnosis of a battery then corresponds to the quantification of the three degradation modes. As proposed in [ 17 – 19 ], the different degradations were simulated by scanning the entire range of possible combinations for loss of lithium inventory (LLI) and LAMs. Once generated, the data was used to train and validate ML algorithms. More details on the synthetic data generation and the training are provided in the method section. All the selected ML algorithms used in this work were developed to use features from a derivative of the voltage response under CC as input. In order to determine if these algorithms could be applied to irradiance duty cycles, it was necessary to verify that the associated derivative voltage response still showcased the expected features. Figure 6 (a-c) presents simulations of the voltage response of a cell, plotted as incremental capacity curves (IC, dQ/dV = f(V)), for individual degradation modes as calculated using the ‘alawa model from the clear-sky irradiance on March 21st. This degradation map is useful to assess the impact of degradation on the voltage response. The voltage evolutions in Fig. 6 (a-c) closely resemble the one observed for a traditional GIC/NMC cell tested under CC [ 17 ]. This provide confidence that the diagnosis algorithms developed under CC can be used on the data generated from PV irradiance. Since the simulations were not performed under CC, the voltage response versus time is different than the voltage response versus capacity. This is because capacity corresponds to time multiplied by current, capacity and time are thus only directly correlated if the current is constant. The time vs. voltage data offer a different dataset that could be available for training and validation if features are identifiable. Figure 6 (d-f) presents the t-based equivalent to the IC degradation maps (IT, dt/dV = f(V)). Despite some deformations, the t-based curves showcase significant similarities to their capacity counterparts and are therefore also perfectly suited for degradation mode quantification using the selected algorithms. In this work, both the capacity (Q) and time (t) based datasets will be generated and analyzed to determine if a t-based method could be as accurate as a Q-based one. 2.3 Diagnosability Three sets of experiments were performed for this work. More details can be found in the method section. Training for the first two sets of experiments was performed on synthetic data generated from clear-sky irradiance for the spring equinox (3/21). The spring equinox was selected because its POA clear-sky irradiance is close to the yearly average. For the initial set of experiments, representing an ideal case, validation was performed using the same data as the training. For the second set of experiments, aimed at quantifying the impact of seasonal variability on diagnosis accuracy, validation was performed using synthetic data generated from clear-sky irradiance for the 1st of each month. Finally, for the third set of experiments, to test the impact of cloud cover, training was performed on synthetic data generated from clear-sky irradiance for the 18 cloudy days detailed in section 2.1 and validation was performed using synthetic data generated from observed irradiance for those specific days. 2.3.1 First set, same day training & validation on clear-sky irradiance In order to test if the ML algorithms trained on clear-sky irradiance were able to diagnose different battery degradations, they were first validated using the same clear-sky irradiance. The only difference between the training and validation datasets were the cell parameters that were slightly varied to take cell-to-cell variations into consideration (cells 1 and 2 in Table S1, see methods for more details). The first 4 rows of Table 1 present average root-mean-square deviation (RMSE) between the real and predicted values for more than 100,000 different combinations of the three degradation modes. The algorithms were all able to quantify each degradation mode properly with RMSEs of 2.1%, at worst. Since smaller RMSEs were observed for lower degradations, Figure S2(a-e), Table 1 presents the average RMSEs for the Q- and t-diagnosis for degradations with at most 25% and 50% of each degradation mode. Statistics for the full dataset with additional metrics such as the mean absolute error (MAE) and Pearson’s correlation coefficient (ρ) are provided in Table S2. Overall, RMSEs below 0.85% for 25% or less degradation and 1.66% for 50% or less degradation were observed. Looking at the Q-diagnosis (top two rows), all algorithms performed nearly identically with average RMSEs around 0.70% for 25% or less degradation and 1.5% for 50% or less degradation. The average RMSEs of t-based data (rows 3 and 4) were similar but the individual algorithm performance varied. XGB, FNN, and 1DConv showed similar RMSEs, 1DConv showed a lowest average RMSE at 0.37%, and DTW-CNN RMSE nearly doubled compared to its Q-based counterpart. From the complete statistics in Table S2, it can be seen that LLI seems the easiest to diagnose before LAM PE for Q-based diagnosis while the opposite holds true for t-based ones. In both cases LAM NE was the hardest to decipher. In general, all the calculated RMSEs were small, below or near 2.1% at worst, for more than 100,000 tested degradations up to 50% degradation, demonstrating that data from irradiance duty cycles can be successfully diagnosed for the ideal case of a single day with no cloud coverage at all. The next sections will quantify the diagnosability cost associated with irradiance variability on time scales longer than one day and cloud coverage. Table 1 RMSE summary statistics for diagnosis from perfect irradiance data for March 21st (top four rows) and for every 1st day of the month (bottom four rows). Associated full statistics are available in Table S2. RF XGB FNN 1DConv DTW-CNN Q-based, same day, < 25% deg. 1.09 0.70 0.62 0.50 0.49 Q-based, same day, < 50% deg. 2.08 1.88 1.15 1.15 1.10 t-based, same day, < 25% deg. 1.27 0.81 0.64 0.45 1.00 t-based, same day, < 50% deg. 2.11 1.96 1.64 1.08 1.51 Q-based, different day, < 25% deg. 1.53 1.24 0.84 0.66 0.79 Q-based, different day, < 50% deg. 2.80 3.15 1.71 1.73 1.53 t-based, different day, < 25% deg. 3.30 3.24 3.56 3.25 5.75 t-based, different day, < 50% deg. 4.43 4.42 5.43 4.45 7.62 2.3.2. Second set, impact of seasonal irradiance variability In the baseline case presented above, training and validation were performed on the same clear-sky data. The second set of experiments was used to decipher the impact of training on one day and validate on another one. The impact of seasonal fluctuations in clear-sky irradiance was examined by validating the 03/21 trained algorithms on 43,000 degradation paths generated from clear-sky irradiance on the 1st day of each month for a year, Fig. 2 (a). This was done twice with two different set of cell parameters (details are in Table S1, cells 5 to 28) to investigate the impact of cell-to-cell variations at the same time. This impact will be assessed by comparing the diagnosis statistics for the two different batches of cells (12x43,000 data points). The impact of irradiance variations was significant as the average RMSE increased by 1.6% for Q- diagnosis and by more than 2% for the t-diagnosis compared to the ideal scenario, Table 1 bottom 4 rows. The three NN methods were the best performing for Q-diagnosis, with RMSE below 1% for 25% or less degradation and below 2% for 50% or less degradation. For the t-diagnosis, all the algorithms but DTW-CNN performed similarly, with RMSE slightly over 3% for 25% or less degradation (around 5% for 50% or less degradation). LAM NE diagnosis still had the highest RMSE with LLI and LAM PE RMSEs being very close. LAM PE RMSEs were lower for Q-diagnosis and the LLI ones for t-diagnosis. Cell-to-cell variations were negligeable with on average 0.4% MAE with a 0.7% standard deviation between the two sets, Figure S2(f). 2.3.3. Third set, impact of cloud coverage The third set of experiments examined the impact of different cloud coverages. This corresponds to the validation using observations. To remove the effects of a time difference between training and validation data (see section 2.3.2 ), training and validation data correspond in time. For each of the 18 cloudy days detailed in section 2.1 , validation of algorithms trained on clear-sky irradiance was performed using irradiance observations for that day which included cloud effects. Table 2 presents the average statistics for all 18 days, for days with at least 50% clear skies (10/18 days), and for days with at least 75% clear skies (3/18 days). Complete statistics with MAE and ρ are available in Table S3 and S4. Overall, for degradation paths with less than 25% of each degradation modes, the RMSEs were in the 1.75 to 3.6% range for all algorithms for Q- diagnosis and in the 4.4 to 5.2% range for t-diagnosis. Focusing on clearer days reduced the RMSE significantly, to below 1% (FNN, 1DConv, DTW-CNN) for Q-diagnosis and 2.5% (XGB, RF, 1DConv) for t-diagnosis. This highlights the validity of diagnosis for days with cloud coverage. Table 2 RMSE summary statistics for diagnosis on 11,000 voltage vs. capacity curves generated for degradation below 25% for all days, days with 50% of more clear sky, and days with 75% or more clear sky. Algorithms were trained on the same day clear-sky irradiance. Associated full statistics are available in Table S3 and S4. RF XGB FNN 1DConv DTW-CNN Q-based, all days, < 25% deg. 3.55 3.25 2.30 2.33 1.76 Q-based, all days, < 50% deg. 4.89 4.84 3.92 4.19 2.91 t-based, all days, < 25% deg. 4.46 5.01 5.20 4.70 5.17 t-based, all days, 50% clear-sky, 50% clear-sky, 50% clear-sky, 50% clear-sky, 75% clear-sky, 75% clear-sky, 75% clear-sky, 75% clear-sky, < 50% deg. 3.14 4.07 7.43 5.03 4.78 3. Discussion This study provides the first application of synthetic datasets for non-CC simulations. Because current was not constant, capacity and time were uncorrelated, which offered an opportunity to study two different datasets, V vs. Q and V vs. t.. While using voltage versus capacity is more traditional, it might not be the best solution for deployed systems because the V vs. t dataset should be less error-prone than the V vs. Q one as capacity is not directly measurable, but derived from time and current [ 39 ]. The V vs. Q dataset is however expected to be easier to diagnose because the area under a dQ/dV peak corresponds to capacity and, at low rates, it is independent of the applied current because it has a finite value. Therefore, current variations should have a limited impact on the overall peak shape and intensity. This is why the voltage responses showcased in Fig. 6 (a-c) are really similar to the signature under CC [ 17 ] despite the current varying. This is not the case for dt/dV peaks, because, while capacity stays the same with varying current, the time taken to complete the peak will be different. Therefore dt/dV peaks are much more sensitive to changes of current than dQ/dV ones. This sensibility explains the differences observed between Fig. 6 (d-f) and Fig. 6 (a-c) and why the t-diagnoses average errors were on average more than double the Q-based ones. The increased error was especially visible when the validation was done on a duty cycle different from the one used for training. Figure 7 (a) plots the RMSE variations as a function of the month of the year for algorithms trained on one day only (second set of experiments). The Q-based RMSE showcased little to no effect of the month of the year whereas the t-based ones varied significantly with a minimum close to the training day (March and April) and in fall (September and October) when irradiances are the most similar to the one used for training (03/21), Fig. 2 (b). The difference was also much more pronounced for cloudy days and aged cells. Therefore, although t-diagnosis is more interesting on paper, it might not be the best solution where clear-sky did not significantly dominate, at least for the tested algorithms. Figure S2, Table 1 and Table 2 , showed the performance degradation with increasing degradation percentage. This decline in performance can be explained by multiple factors. Although data imbalance during training could be a possible factor, as 2/3rds of the training data has a degradation below 25%, the main factor seems to come from the fact that small variations in one of the three degradation modes are hard to quantify when at least one of the other two modes has large variations. This is exemplified in Fig. 7 (b,c) where a distribution of the estimated vs. true values for LLI and the DTW-CNN algorithms are plotted for 50% or less and 25% or less degradation. For the 50% or less degradation, there is a haze around the 1:1 line below 20% LLI that disappears when the maximum degradation is set at 25%. This indicates that the error mostly comes from degradation paths with low LLI but at least one LAM above 25%. This will be investigated further in future work. Looking at the detailed statistics, it can be seen from Table 2 , S3 and S4 that, although the algorithms performance was really close, some differences were noticeable. Overall, the DTW-CNN algorithm offers the best performance for Q-diagnosis while 1DConv is significantly better for t-diagnosis for degradations below 25%. Moreover, the algorithms are not all affected the same by the change of duty cycles. This is especially visible on Fig. 7 (a) were the performance of the t-diagnosis much more affected for winter days than of summer days for RF while the opposite is true or DTW-CNN. The other three algorithms being impacted the same. Future work will investigate in details the parameterization of the algorithms to improve performance. Looking in more details, it appears that the largest errors were always observed for LAM NE estimation (Tables S2-S4). This could be explained by the fact that LAM NE cannot be directly inferred from any feature of interest of the IC or IT curves. For the other two degradation modes, and as showcased in [ 17 ], the intensity of high voltage shoulder is in most cases directly proportional to LAM PE and the intensity of the main peak to LLI. This is NMC specific and different results are expected for non-layered oxides such as batteries based on LiFePO 4, where LAM PE should be much harder to quantify than the other two. A possible solution to improve the accuracy of LAM NE estimation for the current algorithms could be to train the algorithms on DV curves on top of the IC curves as LAM NE is, in most cases, directly decipherable from the DV curves. Figure 8 presents the RMSE variation for all the cloudy days tested in this work sorted by their clear-sky percentage with the associated actual irradiance vs. time curve as inset. Overall, clear-sky percentage is a useful indicator of diagnosability, although some other parameters also come into play. In general, the RMSE increases as clear-sky percentage decrease. However, there were some duty cycles that showed abnormal high (e.g., 34% clearness and 59% clearness) or low (e.g., 27% clearness) RMSE, indicating that the intensity and time of the cloud coverage could also play a major role in diagnosability. Together with cloud coverage, the type of diagnosis, Q-based or t-based also has a role. For example, for a day with 59% clear-sky, Q-diagnosis was better than normal and the t-based one far worse, while for a day with 34% clear-sky, the opposite was true. Finding the right set of parameters to identify which days are more auspicious for diagnosis will require more work but, from these results, it is clear that the use of synthetic data will be instrumental in testing the impact of different classification schemes. 5. Conclusions & Outlook This paper proposes and validates a new approach for the diagnosis of batteries paired with PV using synthetic data. This approach allows the degradation of PV-connected batteries to be diagnosed without the need for maintenance cycles by using state-of-art machine learning algorithms. Diagnoses have an average RMSE of 2.75% for more than 10,000 different degradation paths with 25% or less of the three thermodynamic degradation modes. Because diagnosis was done outside of constant current, the capacity- and time-based information could be decorrelated and compared. Time-based diagnosis was shown to be less accurate than its capacity counterpart for the tested algorithms. However, the accuracy of the both types of diagnosis is satisfactory for days where clear-sky dominates. For days with lower clear-sky conditions, accuracy depends on the clear-sky percentage, but additional factors such as the time and duration of cloud coverage also come into play. These factors will be investigated further in future work. The framework presented here proved that opportunistic diagnosis of PV connected battery is possible from auspicious cloud coverages. Based on our results, and for the studied system and location, diagnosis could be possible one out of every five days independent of the season which is more than frequent enough for batteries supposed to last 3,500 days or more. This number might be different in other locations where shadowing or snow could play a significant role but it could be easily assessed using the framework presented here. This highlights the significant benefits of using synthetic data to understand the expected variations of voltage response for different cloud coverage and to develop adapted diagnosis tools, particularly as real photovoltaic battery degradation data is not yet available. Despite promising results, there is still a significant amount of work to be done before this technique can be applied to deployed systems. There is a need for training under a wide array of different conditions, as PV systems in the field will have varying orientation, tilt, location, cleanliness, etc… Moreover, this work was performed on single cells and without considering any additional usage on the cells. Real systems will be composed of battery packs, which will have varying voltage response due to inhomogeneities and imbalance. Furthermore, these batteries will likely be used at the same time they are charged, which will further modify the duty cycles. The validation framework provided here can be applied to study these case figures and future work that addresses the complexity of different locations, modules, and possible additional load on batteries. The proposed framework might even be applicable to other types of intermittent renewable power systems for which storage could be considered, such as wave or tidal energy. Methods 5.1 PV data acquisition The PV testbed used in this work includes instrumentation for high-frequency PV and solar resource monitoring, including a Kipp & Zonen SMP21-A secondary standard pyranometer, which is installed in the POA of the testbed PV panels. The data was collected at 1 second intervals and averaged to 1 minute for 2 years. 5.2 Battery testing The commercial cells used in this work were provided by an industrial partner and are composed of a graphite intercalation compound (GIC) based negative electrode (NE) and a Nickel Manganese Cobalt oxide (NMC) positive electrode (NE) with a 1:1:1 stoichiometry. The industrial partner also provided the full cell cycling data with C/15, C/8.5 and C/4 cycles performed on a pristine cell. The half-cell data was harvested by opening a commercial cell from the same batch. The cell was slowly discharged to 2.0V before being opened in a glove box. The double-sided electrodes were rinsed with dimethyl carbonate and one side was scrubbed using N-Methylpyrrolidone before 1.8mm diameter electrodes were cut using an EL-CUT punching tool (EL-CELL, Hamburg, Germany). Half-cells were assembled in PAT-CELLs (EL-CELL, Hamburg, Germany) using a standard polypropylene sleeve, a borosilicate glass fiber separator, a metallic Li NE, as well as an electrolyte composed of ethylene carbonate and propylene carbonate in a 1:1 ratio with 1M Lithium hexafluorophosphate and 2% vinylene carbonate (all Sigma-Aldrich USA). For the testing, the cell formation consisted of 8 cycles at C/10 followed by 1 cycle at C/25 between 3.2V and 4.3V for the PE and 0.02 and 1.2V for the NE. After the formation cycles, the cells were tested at C/50, C/25, C/15, C/8, C/4, C/2, and C/1 with residual capacity measurements at C/50 for each regime following the protocol described in [40]. 5.3 Synthetic data generation The synthetic data used in this work, both for training and validation, was generated using the method described in [17-19] by scanning the entire range of possible combinations for loss of lithium inventory (LLI) and LAMs. Because the duty cycles have maximum currents below C/6, only the thermodynamic degradation parameters will be considered in this work. The maximum value for the degradation modes was set at 50%. For the main training dataset, the composition resolution was set at 1% (5,000 triplet tested) with at most a simulation every 0.5% for each degradation modes (>125 simulations per triplet from 0 to 50%). This resulted in around 700,000 unique voltage response for training. Additional training on different duty cycles was done with a 2.5% resolution with 1% steps to limit file sizes. This corresponds to more than 850 different triplets and 43,000 unique voltage curves. For the validation datasets, the resolution was decreased to 5% (225 triplets) with 1% steps (50 simulations per triplet) resulting in around 11,000 curves per condition. Finally, to avoid any overfitting error by training and validating on the same data, each simulation will be performed on a slightly different cell, i.e., a cell with emulation parameters (LR, OFS, R, and RDFs) randomly varied by ±1% to be in the same range as observed cell-to-cell variations in commercial cells [41]. The overall parameters for each simulation with the associated duty cycles are summarized in Table S1. 5.4 Diagnosis algorithms In this work, the leading machine learning algorithms for degradation modes quantification were used to validate our approach. A thermodynamic degradation modes diagnosis corresponds to the quantification of LLI, and LAMs for the positive and negative electrodes (PE and NE respectively) [37,42]. Such quantification provides more information than a simple capacity estimation and enables prognosis [17]. The selected algorithms can be divided into two categories, decision tree ensemble methods and neural networks. Decision trees are deterministic models that rely on multiple conditionals while neural networks follow a probabilistic approach in which they seek to learn by activating artificial neurons. For this work, Random Forest (RF) [21] and Gradient Boosting Trees (XGB) [22] algorithms were selected for the decision trees and Feed-forward neural network (FNN) [23], 1D-CNN (1DConv) [16], and the DTW-CNN approach [24] were selected as neural networks. It is important to note that in all cases the models use the raw derivative voltage curves as input except for DTW-CNN, which uses images created from the DTW matrix between the pristine and the degraded derivative curves. This allows to transform voltage changes into images that reflect the degradation and enables the use of 2D CNNs, which are widely known in the literature to work remarkable well with images [24]. In terms of implementation, and for the decision tree ensemble methods: The sklearn library [43] was used to implement the Random Forrest, specifically the ensemble module with the RandomForestRegressor algorithm, the hyperparameters were max_depth , and n_estimators . For the XGBoost model, the xgboost library [44] was used, specifically the XGBRegressor algorithm, the hyperparameters were max_depth=max_depth , and eta=eta . For the neural networks, all the models were implemented in TensorFlow [45]. The models configurations were as follows: FFN: 3 fully connected layers with 64 neurons in the first layer, 32 in the second and 3 in the third. CNN-1D: 5 layers of which 2 are CNN-1D layers with 32 neurons each and 3 are fully connected layers with 128, 64 and 3 neurons each. CNN-DTW: 4 convolution layers with 64 neurons in the first two layers and 128 in the next two, followed by two fully connected layers with 512 and 3 neurons each. The hyperparameters to be set in these three cases were the batch size and learning rate. The WandB framework [46] was used for hyperparameter tuning and callbacks were used during training to relegate the training stop condition to the validation error instead of the number of epochs. In this work, validation comprised varying initial conditions for the ML algorithms to produce model output that is compared against some truth to generate error statistics, which are used to quantify the experiments. Further details regarding the experimental setup and the source code to reproduce the experimental results are available in the following public git repository: https://github.com/NahuelCostaCortez/PVDiagnosis . All the sharable data from this work is available here [26,27] with the actual PV data and the synthetic cycles for perfect irradiance and cloud coverage. Declarations Author Contributions: Conceptualization, M.D..; methodology, M.D., D.M., and N.C.; software, M.D., D.M., and N.C.; validation, M.D., D.M., and N.C.; formal analysis, M.D., D.M., and N.C.; investigation, M.D. and N.C.; resources, M.D.; data curation, M.D.; writing—original draft preparation, M.D. and D.M.; writing—review and editing, M.D., D.M., and N.C.; visualization, M.D.; supervision, M.D.; project administration, M.D.; funding acquisition, M.D. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Office of Naval Research (ONR), grant numbers N00014-19-1-2159 and N00014-22-1-2045. Nahuel Costa has been partially supported by the Ministry of Economy, Industry and Competitiveness (“Ministerio de Economía, Industria y Competitividad”) from Spain/FEDER under grant PID2020-112726-RB-I00 and by Principado de Asturias, grant SV-PA-21-AYUD/2021/50994. Acknowledgments: The authors are thankful to ONR for funding the deployment and monitoring of the PV system used in this work with the help of HNEI’s Severine Busquet, Jonathan Kobayashi, and Richard Rocheleau. The authors are also thankful to Thomas Nemeth and Matthias Kuipers (ACCURE, Germany) for fruitful discussions. Finally, the authors would also like to thank Sara Matthews for her insightful comments. Conflicts of Interest: The authors declare no conflict of interest. References Mackenzie/SEIA, W. US Solar Market Insight ; Wood Mackenzie/SEIA 2021. 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Jafari, S.; Shahbazi, Z.; Byun, Y.-C.; Lee, S.-J. Lithium-Ion Battery Estimation in Online Framework Using Extreme Gradient Boosting Machine Learning Approach. Mathematics 2022, 10 (6). Lee, S.; Kim, Y. Li-ion Battery Electrode Health Diagnostics using Machine Learning. In Proceedings of the 2020 American Control Conference, Denver, CO, 2020; pp. 1137–1142. Costa, N.; Sanchez, L.; Ansean, D.; Dubarry, M. Li-ion battery degradation modes diagnosis via Convolutional Neural Networks. Journal of Energy Storage 2022, Accepted. Beck, D.; Dechent, P.; Junker, M.; Sauer, D.U.; Dubarry, M. Inhomogeneities and Cell-to-Cell Variations in Lithium-Ion Batteries, a Review. Energies 2021, 14 (11), 3276. Dubarry, M.; Costa, N.; Matthews, D. GIC//NMC Solar Battery Synthetic Data 1–700,000 degradation for 03/21 clear-sky irradiance. 2022. Dubarry, M.; Costa, N.; Matthews, D. GIC//NMC Solar Battery Synthetic Data 2–45,000 x 18 degradation for clear-sky irradiance and cloudy days. 2022. 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Empirical validation of models to compute solar irradiance on inclined surfaces for building energy simulation. Solar Energy 2007, 81 (2), 254–267. Reno, M.J.; Hansen, C.W.; Stein, J.S. Global Horizontal Irradiance Clear Sky Models: Implementation and Analysis ; SANDIA: 2012. Reno, M.J.; Hansen, C.W. Identification of periods of clear sky irradiance in time series of GHI measurements. Renewable Energy 2016, 90 , 520–531. Dubarry, M.; Truchot, C.; Liaw, B.Y. Synthesize battery degradation modes via a diagnostic and prognostic model. J. Power Sources 2012, 219 , 204–216. HNEI. Alawa central. Available online: https://www.soest.hawaii.edu/HNEI/alawa/ (accessed on June 2022). Dubarry, M.; Tun, M.; Baure, G.; Matsuura, M.; Rocheleau, R.E. Battery Durability and Reliability under Electric Utility Grid Operations: Analysis of On-Site Reference Tests. Electronics 2021, 10 (13). Dubarry, M.; Baure, G. Perspective on Commercial Li-ion Battery Testing, Best Practices for Simple and Effective Protocols. Electronics 2020, 9 (1), 152. Devie, A.; Dubarry, M. Durability and Reliability of Electric Vehicle Batteries under Electric Utility Grid Operations. Part 1: Cell-to-Cell Variations and Preliminary Testing. Batteries 2016, 2 (3), 28. Birkl, C.R.; Roberts, M.R.; McTurk, E.; Bruce, P.G.; Howey, D.A. Degradation diagnostics for lithium ion cells. J. Power Sources 2017, 341 , 373–386. Pedregosa, F.; Varoquaux, G.; Gramfort, A.; Michel, V.; Thirion, B.; Grisel, O.; Blondel, M.; Prettenhofer, P.; Weiss, R.; Dubourg, V.; et al. Scikit-learn: Machine Learning in Python. Journal of Machine Learning Research 2011 , (12), 2825–2830. Chen, T.; Guestrin, C. XGBoost: A Scalable Tree Boosting System. In Proceedings of the Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2016; pp. 785–794. Abadi, M.; Barham, P.; Chen, J.; Chen, Z.; Davis, A.; Dean, J.; Devin, M.; Ghemawat, S.; Irving, G.; Isard, M.; et al. TensorFlow: A system for large-scale machine learning. In Proceedings of the 12th USENIX Symposium on Operating Systems Design and Implementation (OSDI ’16), Savannah, GA, USA, 2016. Biewald, L. Experiment Tracking with Weights and Biases. Available online: https://wandb.ai/ (accessed on Additional Declarations There is NO Competing Interest. Supplementary Files SupplementaryInformation.docx Cite Share Download PDF Status: Under Review Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-2058155","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":137233113,"identity":"f5688612-3e0a-4cf7-9e65-e3760ede54c8","order_by":0,"name":"Matthieu Dubarry","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0klEQVRIiWNgGAWjYJACZgYDBgZ+CRDTAEQmENTA2AzSIjmDNC0gxTfgIgS06LafP/64oMAmcfPt5mcSPwosGPjZcwzwajE7k8zYPMMgLXHbnWNmkj1Ah0n2vCGg5QBQC4/B4cRtNxLMbvAAtRjcIGTL+ccgLf8TN89I/3bzD1CLPUEtN8C2HEjcIJFjdhtsiwRBLY8NZ/MYJBvPuJFT/lvGQIJH4syzAgIOS3zwmeePnWz/jPTNhm/+1MnxtydvwKsFA/CQpnwUjIJRMApGAVYAAIWqRg9jgse0AAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-3228-1834","institution":"University of Hawaii at Manoa","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Matthieu","middleName":"","lastName":"Dubarry","suffix":""},{"id":137233114,"identity":"7f2ba5b4-1c63-4512-a91a-67e54d7151ce","order_by":1,"name":"Nahuel Costa Cortez","email":"","orcid":"https://orcid.org/0000-0002-9189-2192","institution":"University of Oviedo / Polytechnic School of Engineering","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Nahuel","middleName":"Costa","lastName":"Cortez","suffix":""},{"id":137233115,"identity":"db13c1af-aa58-449c-be40-eab8629bae07","order_by":2,"name":"Dax Matthews","email":"","orcid":"","institution":"University of Hawaii at Manoa / HNEI","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Dax","middleName":"","lastName":"Matthews","suffix":""}],"badges":[],"createdAt":"2022-09-12 20:35:47","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2058155/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2058155/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":26566997,"identity":"ea42356e-abe5-4dd7-9302-9002c2fab1dd","added_by":"auto","created_at":"2022-09-16 16:16:01","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":152303,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic representation of the proposed approach comprising a training branch and a validation branch.\u003c/p\u003e","description":"","filename":"f1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2058155/v1/34847cb3a7f0fb333e1e193d.jpg"},{"id":26567724,"identity":"d944a1d2-62ae-4b31-a7c5-596ab502c72b","added_by":"auto","created_at":"2022-09-16 16:26:02","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":135703,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Diurnal and seasonal variations in clear-sky irradiance from a CSM for a test site in Maui, HI, USA and irradiance at equinoxes and solstices for (b) horizontal and (c) POA.\u003c/p\u003e","description":"","filename":"f2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2058155/v1/e267fc7b79d73b3b24aba604.jpg"},{"id":26567002,"identity":"5d8a72b3-c6f0-4537-a1c0-35d03df202b6","added_by":"auto","created_at":"2022-09-16 16:16:01","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":164784,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Maui topographic map with system location and (b) seasonal distribution of clear-sky distributions. (c) Selected cloudy days with associated percentages of clear-sky in blue.\u003c/p\u003e","description":"","filename":"f3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2058155/v1/e0fa42b804825acd2baaa750.jpg"},{"id":26567305,"identity":"c12dc842-d5c5-4142-9075-6132a019c8db","added_by":"auto","created_at":"2022-09-16 16:21:01","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":111801,"visible":true,"origin":"","legend":"\u003cp\u003eEmulation for (a) the C/15, (b) the C/8.5, and (c) the C/4 cycles with associated parameters. (d) variations of RDFPE, RDFNE, and RDFcorrPE with rate.\u003c/p\u003e","description":"","filename":"f4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2058155/v1/bdae1ebf253bce977f0db597.jpg"},{"id":26567000,"identity":"8d9327ee-8ba1-4ccc-9616-289892df73ad","added_by":"auto","created_at":"2022-09-16 16:16:01","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":108244,"visible":true,"origin":"","legend":"\u003cp\u003e(a) example of a perfectly sunny day PV power generation and (b) associated voltage and rate variations versus SOC for the Li-ion battery to match the power input (in blue) from a fully discharged state.\u003c/p\u003e","description":"","filename":"f5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2058155/v1/72dd679502d4c177ce9a2a15.jpg"},{"id":26567309,"identity":"719227f5-9278-4270-9369-badba0fe2dc7","added_by":"auto","created_at":"2022-09-16 16:21:01","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":104873,"visible":true,"origin":"","legend":"\u003cp\u003e(a-c) IC and (d-f) IT degradation maps for the synthetic duty cycles generated from the perfect horizontal irradiance data at the MEDB site on March 21st.\u003c/p\u003e","description":"","filename":"f6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2058155/v1/19a9ca4811e41d721a926702.jpg"},{"id":26567723,"identity":"b11ec3d3-7664-43aa-86a8-b26321f3a96c","added_by":"auto","created_at":"2022-09-16 16:26:01","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":101757,"visible":true,"origin":"","legend":"\u003cp\u003e(a) RMSE dependency of the day of the year for algorithms trained on data from March 21st. Predicted vs. real LLI distribution for the DTW-CNN algorithm when trained and validated on the same day for (b) the entire dataset and (c) all degradation modes below 25%.\u003c/p\u003e","description":"","filename":"f7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2058155/v1/813a613f809a18e314de0703.jpg"},{"id":26567306,"identity":"a8b3372d-baaf-447f-b375-fb207a69dc36","added_by":"auto","created_at":"2022-09-16 16:21:01","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":156165,"visible":true,"origin":"","legend":"\u003cp\u003eRMSE dependency of clear-sky percentage and cloud distribution with actual irradiance data as inset (same color code as Figure 3(c) for seasonality).\u003c/p\u003e","description":"","filename":"f8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2058155/v1/7f8ea54fb14221712f42e937.jpg"},{"id":26567726,"identity":"7c0862e0-6fe7-4866-988f-e84254919bbb","added_by":"auto","created_at":"2022-09-16 16:26:08","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1351295,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2058155/v1/a7ce4d9f-e5b3-4642-8356-04ddca60f79d.pdf"},{"id":26566998,"identity":"4bc6b073-aff1-4d8d-9346-6af58f3e10dd","added_by":"auto","created_at":"2022-09-16 16:16:01","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":531562,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementaryInformation.docx","url":"https://assets-eu.researchsquare.com/files/rs-2058155/v1/901120e971d438ff19f26b1e.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Data-driven Direct Diagnosis of PV Connected Batteries","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eIn recent years solar photovoltaic (PV) technologies provided the most additional generating capacity to the United States grid [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. In 2021, a record 23.6 GW of solar capacity was installed and, over the next 10 years, it is predicted that 324 GW of new solar capacity will be added to the electric grid, quadrupling current levels [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. New solar systems are increasingly being paired with battery energy storage systems at multiple grid levels. While some of the storage will be performed by grid-scale batteries, the percentage of residential storage installations has also been steadily increasing, reaching 8.1% in 2020 [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. It is estimated that by 2025, one in three residential solar systems will be paired with small scale energy storage [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e], most likely provided by Lithium-ion batteries [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eTo ensure long, safe, and continuous operation, batteries must be maintained and controlled properly, which includes regular estimation of their state of health. This can be problematic for batteries paired with PV because of sporadic usage in both charge and discharge. As a result of this unpredictability, diagnosis might only be performable under lengthy maintenance cycles. An alternative to avoid downtime could be to identify and take advantage of auspicious conditions to perform state estimation. With batteries supposed to last a decade or more, this opens the gates for different approaches such as using batteries response under clear-sky conditions under which PV power production is predictable on time-scales of up to twelve hours.\u003c/p\u003e \u003cp\u003eEven if the PV power output offered by clear-sky conditions is predictable, state estimation will still be complex and requiring robust methodologies for Li-ion battery diagnosis. Because the duty-cycles of batteries paired with PV will not be under constant current (CC), the traditionally used features [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e] to estimate SOH might difficult to interpret. This favors data-driven methods, and in particular machine learning (ML) methods. However, to be applicable, ML algorithms need to be trained on a wide variety of data covering the sporadicity of the application. Unfortunately, while some market data are beginning to be available publicly [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e], actual PV connected battery data is not to the best of our knowledge. Few studies are available with battery testing associated with PV duty cycles [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], with most of the studies being modeling centered and using constant current testing [\u003cspan additionalcitationids=\"CR10 CR11 CR12 CR13 CR14\" citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Looking at CC data, the lack-of-data problem was recently solved with the introduction of synthetic datasets that enabled the emulation of every possible battery degradation [\u003cspan additionalcitationids=\"CR17 CR18\" citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. While the duty cycle for clear-sky irradiance will be more complex, recent work suggest that the methodology used to generate the synthetic data could be applied outside of CC [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] and thus be applicable to irradiance.\u003c/p\u003e \u003cp\u003eThis work proposes a new method for diagnosis PV connected batteries using synthetic datasets that would allow for SOH estimation during normal battery operations. The method uses periods of clear-sky conditions, where charging from PV generation is relatively stable and predictable, for diagnosis. This paper describes a framework for (1) generating synthetic datasets of the voltage response of cells charged by PV systems, (2) synthetic dataset training of state-of-the-art ML algorithms, and (3) algorithm validation using synthesized data. This framework is summarized in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e with a branch for training and a branch for validation.\u003c/p\u003e \u003cp\u003eThe training branch uses irradiance data from a clear-sky model, PV system information (longitude, tilt, orientation), and battery information (chemistry and W/Ah) to generate synthetic cycles consisting of the voltage response of the cells for specific duty cycles under tens of thousands of different degradations. This dataset is then used to train, test, and compare selected ML algorithms for diagnosis, including a Random Forest regressor (RF) [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e], an Extreme Gradient Boosting regressor (XGB) [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e], a Feed-forward neural network (FNN) [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e], a 1 dimensional Convolutional Neural Network (1D-Conv) [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e], and a dynamic time warping 2-D Convolutional Neural Network (DTW)-CNN [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eWhile the validation would ideally be performed on data from deployed batteries, no deployed PV linked batteries dataset is publicly available to the best of our knowledge. Even if data was available, the actual degradation of each individual system would not likely be, making validation impossible. In anticipation of data becoming available, we examined the applicability of our approach to real systems by replacing the deployed data by synthetic datasets generated for various sky-clearness levels, Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. These synthetic datasets are used to validate the applicability of the clear-sky irradiance trained ML algorithms for diagnosis under cloudy conditions. To further emulate realistic conditions, each dataset was calculated on a cell with slightly different parameters to account for cell-to-cell variations and inhomogeneities [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. A selection of the data generated from this work is available in [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"2. Results","content":"\u003cdiv class=\"Section2\" id=\"Sec3\"\u003e\n \u003ch2\u003e2.1 Irradiance data selection\u003c/h2\u003e\n \u003cp\u003eThe output of a PV system is dependent on irradiance which is the power of the solar radiation striking the panels. Irradiance variability is driven by extraterrestrial and atmospheric effects and is also dependent on panel orientation [\u003cspan class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e29\u003c/span\u003e]. The latter has become more varied in recent years [\u003cspan class=\"CitationRef\"\u003e3\u003c/span\u003e], but panels are nominally oriented toward the equator at a tilt angle near to the latitude of the installation in order to maximize solar energy yield [\u003cspan class=\"CitationRef\"\u003e30\u003c/span\u003e].\u003c/p\u003e\n \u003cp\u003eClear-sky irradiance occurs during clear-sky conditions, defined as an absence of visible clouds across the entire sky dome [\u003cspan class=\"CitationRef\"\u003e31\u003c/span\u003e]. Clear-sky irradiance is estimated using a clear-sky model (CSM) which calculates solar geometry and accounts for variations in air mass and variations in optical depth [\u003cspan class=\"CitationRef\"\u003e32\u003c/span\u003e]. In this work, we used the CSM proposed by Ineichen and Perez [\u003cspan class=\"CitationRef\"\u003e32\u003c/span\u003e] for a horizontal surface extended to estimate clear-sky irradiance on a tilted surface in the plan of array (POA) of a PV panel. The extended CSM recomputes the solar angle of incidence, accounts for the reduction of diffuse irradiance received [\u003cspan class=\"CitationRef\"\u003e33\u003c/span\u003e], and adds a new ground reflected irradiance source [\u003cspan class=\"CitationRef\"\u003e34\u003c/span\u003e].\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e(a) presents diurnal and seasonal variations in horizontal (top) and POA (bottom) clear-sky irradiance estimated by the CSM over a two-year period for a PV test site located at the Maui Economic Development Board (MEDB) office on the southwestern coast of the island of Maui, Hawaiʻi, USA, Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e(a), with PV panels oriented at a 20\u0026deg; tilt with a 197\u0026deg; N azimuth. Due to Hawaiʻi\u0026rsquo;s proximity to the Northern Tropic, clear-sky irradiance levels incident on a horizontal surface remained high from April to September, but drop during winter. Seasonal variations of clear-sky irradiance incident on the POA of PV panels located at the site are reduced, with peak levels found in spring and summer months. POA irradiance also peaks later in the day (by around 1 hour) relative to horizontal values, due to the panels facing slightly westward instead of due south. To further illustrate seasonal fluctuations, data at solstice and equinoxes are presented in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e (b) and Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e(c) for horizontal and POA irradiances respectively.\u003c/p\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n \u003cp\u003eThe CSM fails to account for several factors driving real irradiance variability. While the most obvious is cloud cover, fluctuations in atmospheric turbidity, shading, soiling, and reflection losses also affect the amount of irradiance available for a PV system. In this work, clear-sky conditions were identified using an algorithm that applies a series of threshold criteria tests to compare the smoothness, shape, and magnitude of observed values within a moving window to corresponding clear-sky values from the CSM [\u003cspan class=\"CitationRef\"\u003e35\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e36\u003c/span\u003e]. The algorithm is assigning a daily \u0026ldquo;clearness\u0026rdquo; value, determined using the number of observations identified as clear-sky over the total number of observations during daytime conditions. The distribution of daily clearness per season for the whole dataset is shown in Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e(b). For almost half of the 2-year dataset, clear-sky conditions were found in less than 20% of the daily observations, however, in nearly one in five days, more than 50% of observations were identified as clear-sky. Moreover, the distribution of daily clearness values indicates only slight seasonal variations at the test site.\u003c/p\u003e\n \u003cp\u003eTo assess how the accuracy of the diagnosis was affected by irradiance variability, 18 days from the 2-year dataset were selected to encompass a range of irradiance conditions, Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e(c). The conditions range from a minimum clearness of 4% to a maximum of 84%, with cloud cover occurring at different times. Cloud effects range from small perturbations, likely due to high cirrus clouds, to significant attenuation and cloud enhancement, due to more opaque cloud cover. Shading effects caused by the construction of a nearby building can also be seen in the afternoon hours of the two days in October 2017.\u003c/p\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv class=\"Section2\" id=\"Sec4\"\u003e\n \u003ch2\u003e2.2. Cell emulation \u0026amp; Duty cycle emulation\u003c/h2\u003e\n \u003cp\u003eAs presented in Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e, a digital twin was used to generate the battery data needed to assess the impact of the different duty cycles on battery performance. The battery model included in the twin was based on the \u003cem\u003e\u0026lsquo;alawa\u003c/em\u003e mechanistic model [\u003cspan class=\"CitationRef\"\u003e37\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e38\u003c/span\u003e]. To parameterize the model and emulate the electrochemical response of the selected commercial Li-ion battery, the half-cell data for both the positive and negative electrodes (PE and NE respectively) were imported into the \u003cem\u003e\u0026lsquo;alawa\u003c/em\u003e toolbox. The half-cell data was fitted to the full-cell by scanning different values for the loading ratio (LR), offset (OFS), resistance (R), and rate degradation factor (RDF) for the PE and the NE. Because the duty cycles simulated in this work were not CC, the \u003cem\u003e\u0026lsquo;alawa\u003c/em\u003e model needed to be calibrated to correctly simulate rates within the range used by the duty cycles of batteries paired with PV. This calibration required emulations at different rates and verification of continuity between the rate-dependent emulation parameters to enable interpolation and extrapolation to other rates. Figure \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e(a,b,c) presents the results of the full-cell emulation of the C/15, C/8.5, and C/4 cycles, respectively, based on the half-cell data gathered from the harvested electrodes. The best fit had a LR of 1.2 with a 4% offset and a -0.1 resistance correction for the rate-independent parameters. Looking at the rate-dependent parameters, as the simulated rate increased, the RDFs for both electrodes were found to decrease from 0.6 to 0.2 for the PE and from 0.8 to 0.6 for the NE. An additional resistance correction was needed to compensate for peak movements for the RDF\u003csub\u003ePE\u003c/sub\u003e (RDF\u003csub\u003ecorrPE\u003c/sub\u003e). This correction ensured that the electrochemical response at different rates overlapped correctly when kinetics is adjusted, which cannot currently be done automatically by the model. The equation for this additional resistance correction is provided in Figure S1 with an explanatory schematic. No correction was needed for the RDF\u003csub\u003eNE\u003c/sub\u003e. The evolution of the three varying rate-dependent parameters could be fitted with power laws \u003cem\u003ey\u0026thinsp;=\u0026thinsp;a*rate\u003c/em\u003e\u003csup\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sup\u003e with R\u003csup\u003e2\u003c/sup\u003e\u0026ge;0.997 vs. R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;~\u0026thinsp;0.97 for linear regressions, Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e(d).\u003c/p\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n \u003cp\u003eUsing the best fit parameters and equations, the synthetic cell voltage response under the different duty cycles was generated using the method proposed in [\u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e] using solar panel power output as a duty cycle instead of CC. An example of clear-sky solar panel power output is presented in Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e(a). The power is 0 at sunrise, ramps up to its maximum around solar noon, then ramps down to 0 at sunset. As proposed in [\u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e], and in order to simulate this duty cycle, a set of 100 voltage responses were simulated between the lowest rate (minimum power at maximum voltage) and the highest rate (maximum power at minimum voltage), Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e(b). The correct [voltage, rate] couple to match the required power was calculated for each 0.1% state of charge until full charge. Overall, the maximum rate was chosen to be C/6 so that around 95% of the cell capacity is used through an average day (03/21). C/6 is below the highest rate for the which the emulation parameters were deciphered (C/4). This will allow high confidence in the simulation of high loss of active material (LAM), because, with at most 50% degradation, the local rate would at worst double from C/6 to C/3 [\u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e37\u003c/span\u003e], which is still close to the range of experimentally tested rates.\u003c/p\u003e\n \u003cp\u003eThermodynamic battery degradation can be decomposed in three degradation modes, the loss of lithium inventory (LLI) and LAM on both the PE and the NE [\u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e37\u003c/span\u003e], because independent of what mechanism is inducing degradation, what will change is how much of each electrode is available to host lithium and how much lithium is able to go back and forth. Each combination of LLI, LAM\u003csub\u003ePE\u003c/sub\u003e, and LAM\u003csub\u003eNE\u003c/sub\u003e corresponds to a unique degradation and has a unique voltage signature. Diagnosis of a battery then corresponds to the quantification of the three degradation modes. As proposed in [\u003cspan class=\"CitationRef\"\u003e17\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e19\u003c/span\u003e], the different degradations were simulated by scanning the entire range of possible combinations for loss of lithium inventory (LLI) and LAMs. Once generated, the data was used to train and validate ML algorithms. More details on the synthetic data generation and the training are provided in the method section.\u003c/p\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n \u003cp\u003eAll the selected ML algorithms used in this work were developed to use features from a derivative of the voltage response under CC as input. In order to determine if these algorithms could be applied to irradiance duty cycles, it was necessary to verify that the associated derivative voltage response still showcased the expected features. Figure \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e(a-c) presents simulations of the voltage response of a cell, plotted as incremental capacity curves (IC, dQ/dV\u0026thinsp;=\u0026thinsp;f(V)), for individual degradation modes as calculated using the \u003cem\u003e\u0026lsquo;alawa\u003c/em\u003e model from the clear-sky irradiance on March 21st. This degradation map is useful to assess the impact of degradation on the voltage response. The voltage evolutions in Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e(a-c) closely resemble the one observed for a traditional GIC/NMC cell tested under CC [\u003cspan class=\"CitationRef\"\u003e17\u003c/span\u003e]. This provide confidence that the diagnosis algorithms developed under CC can be used on the data generated from PV irradiance.\u003c/p\u003e\n \u003cp\u003eSince the simulations were not performed under CC, the voltage response versus time is different than the voltage response versus capacity. This is because capacity corresponds to time multiplied by current, capacity and time are thus only directly correlated if the current is constant. The time vs. voltage data offer a different dataset that could be available for training and validation if features are identifiable. Figure \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e(d-f) presents the t-based equivalent to the IC degradation maps (IT, dt/dV\u0026thinsp;=\u0026thinsp;f(V)). Despite some deformations, the t-based curves showcase significant similarities to their capacity counterparts and are therefore also perfectly suited for degradation mode quantification using the selected algorithms. In this work, both the capacity (Q) and time (t) based datasets will be generated and analyzed to determine if a t-based method could be as accurate as a Q-based one.\u003c/p\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv class=\"Section2\" id=\"Sec5\"\u003e\n \u003ch2\u003e2.3 Diagnosability\u003c/h2\u003e\n \u003cp\u003eThree sets of experiments were performed for this work. More details can be found in the method section. Training for the first two sets of experiments was performed on synthetic data generated from clear-sky irradiance for the spring equinox (3/21). The spring equinox was selected because its POA clear-sky irradiance is close to the yearly average. For the initial set of experiments, representing an ideal case, validation was performed using the same data as the training. For the second set of experiments, aimed at quantifying the impact of seasonal variability on diagnosis accuracy, validation was performed using synthetic data generated from clear-sky irradiance for the 1st of each month. Finally, for the third set of experiments, to test the impact of cloud cover, training was performed on synthetic data generated from clear-sky irradiance for the 18 cloudy days detailed in section \u003cspan class=\"InternalRef\"\u003e2.1\u003c/span\u003e and validation was performed using synthetic data generated from observed irradiance for those specific days.\u003c/p\u003e\n \u003cdiv class=\"Section3\" id=\"Sec6\"\u003e\n \u003ch2\u003e2.3.1 First set, same day training \u0026amp; validation on clear-sky irradiance\u003c/h2\u003e\n \u003cp\u003eIn order to test if the ML algorithms trained on clear-sky irradiance were able to diagnose different battery degradations, they were first validated using the same clear-sky irradiance. The only difference between the training and validation datasets were the cell parameters that were slightly varied to take cell-to-cell variations into consideration (cells 1 and 2 in Table S1, see methods for more details). The first 4 rows of Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e present average root-mean-square deviation (RMSE) between the real and predicted values for more than 100,000 different combinations of the three degradation modes. The algorithms were all able to quantify each degradation mode properly with RMSEs of 2.1%, at worst. Since smaller RMSEs were observed for lower degradations, Figure S2(a-e), Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e presents the average RMSEs for the Q- and t-diagnosis for degradations with at most 25% and 50% of each degradation mode. Statistics for the full dataset with additional metrics such as the mean absolute error (MAE) and Pearson\u0026rsquo;s correlation coefficient (\u0026rho;) are provided in Table S2. Overall, RMSEs below 0.85% for 25% or less degradation and 1.66% for 50% or less degradation were observed. Looking at the Q-diagnosis (top two rows), all algorithms performed nearly identically with average RMSEs around 0.70% for 25% or less degradation and 1.5% for 50% or less degradation. The average RMSEs of t-based data (rows 3 and 4) were similar but the individual algorithm performance varied. XGB, FNN, and 1DConv showed similar RMSEs, 1DConv showed a lowest average RMSE at 0.37%, and DTW-CNN RMSE nearly doubled compared to its Q-based counterpart. From the complete statistics in Table S2, it can be seen that LLI seems the easiest to diagnose before LAM\u003csub\u003ePE\u003c/sub\u003e for Q-based diagnosis while the opposite holds true for t-based ones. In both cases LAM\u003csub\u003eNE\u003c/sub\u003e was the hardest to decipher.\u003c/p\u003e\n \u003cp\u003eIn general, all the calculated RMSEs were small, below or near 2.1% at worst, for more than 100,000 tested degradations up to 50% degradation, demonstrating that data from irradiance duty cycles can be successfully diagnosed for the ideal case of a single day with no cloud coverage at all. The next sections will quantify the diagnosability cost associated with irradiance variability on time scales longer than one day and cloud coverage.\u003c/p\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003cdiv align=\"left\" class=\"colspec\"\u003e\u003cbr\u003e\u003c/div\u003e\n \u003cdiv align=\"char\" class=\"colspec\"\u003e\u003cbr\u003e\u003c/div\u003e\n \u003cdiv align=\"char\" class=\"colspec\"\u003e\u003cbr\u003e\u003c/div\u003e\n \u003cdiv align=\"char\" class=\"colspec\"\u003e\u003cbr\u003e\u003c/div\u003e\n \u003cdiv align=\"char\" class=\"colspec\"\u003e\u003cbr\u003e\u003c/div\u003e\n \u003cdiv align=\"char\" class=\"colspec\"\u003e\u003cbr\u003e\u003c/div\u003e\u0026nbsp;\u003ctable border=\"1\" id=\"Tab1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eRMSE summary statistics for diagnosis from perfect irradiance data for March 21st (top four rows) and for every 1st day of the month (bottom four rows). Associated full statistics are available in Table S2.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"6\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eRF\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eXGB\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eFNN\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e1DConv\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eDTW-CNN\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eQ-based, same day, \u0026lt;\u0026thinsp;25% deg.\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.62\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.49\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eQ-based, same day, \u0026lt;\u0026thinsp;50% deg.\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.88\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.10\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003et-based, same day, \u0026lt;\u0026thinsp;25% deg.\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.81\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.64\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.45\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.00\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003et-based, same day, \u0026lt;\u0026thinsp;50% deg.\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.64\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.51\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eQ-based, different day, \u0026lt;\u0026thinsp;25% deg.\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.53\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.84\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.66\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.79\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eQ-based, different day, \u0026lt;\u0026thinsp;50% deg.\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.71\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.73\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.53\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003et-based, different day, \u0026lt;\u0026thinsp;25% deg.\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.56\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.75\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003et-based, different day, \u0026lt;\u0026thinsp;50% deg.\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.42\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.45\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7.62\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv class=\"Section3\" id=\"Sec7\"\u003e\n \u003ch2\u003e2.3.2. Second set, impact of seasonal irradiance variability\u003c/h2\u003e\n \u003cp\u003eIn the baseline case presented above, training and validation were performed on the same clear-sky data. The second set of experiments was used to decipher the impact of training on one day and validate on another one. The impact of seasonal fluctuations in clear-sky irradiance was examined by validating the 03/21 trained algorithms on 43,000 degradation paths generated from clear-sky irradiance on the 1st day of each month for a year, Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e(a). This was done twice with two different set of cell parameters (details are in Table S1, cells 5 to 28) to investigate the impact of cell-to-cell variations at the same time. This impact will be assessed by comparing the diagnosis statistics for the two different batches of cells (12x43,000 data points).\u003c/p\u003e\n \u003cp\u003eThe impact of irradiance variations was significant as the average RMSE increased by 1.6% for Q- diagnosis and by more than 2% for the t-diagnosis compared to the ideal scenario, Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e bottom 4 rows. The three NN methods were the best performing for Q-diagnosis, with RMSE below 1% for 25% or less degradation and below 2% for 50% or less degradation. For the t-diagnosis, all the algorithms but DTW-CNN performed similarly, with RMSE slightly over 3% for 25% or less degradation (around 5% for 50% or less degradation). LAM\u003csub\u003eNE\u003c/sub\u003e diagnosis still had the highest RMSE with LLI and LAM\u003csub\u003ePE\u003c/sub\u003e RMSEs being very close. LAM\u003csub\u003ePE\u003c/sub\u003e RMSEs were lower for Q-diagnosis and the LLI ones for t-diagnosis. Cell-to-cell variations were negligeable with on average 0.4% MAE with a 0.7% standard deviation between the two sets, Figure S2(f).\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv class=\"Section3\" id=\"Sec8\"\u003e\n \u003ch2\u003e2.3.3. Third set, impact of cloud coverage\u003c/h2\u003e\n \u003cp\u003eThe third set of experiments examined the impact of different cloud coverages. This corresponds to the validation using observations. To remove the effects of a time difference between training and validation data (see section \u003cspan class=\"InternalRef\"\u003e2.3.2\u003c/span\u003e), training and validation data correspond in time. For each of the 18 cloudy days detailed in section \u003cspan class=\"InternalRef\"\u003e2.1\u003c/span\u003e, validation of algorithms trained on clear-sky irradiance was performed using irradiance observations for that day which included cloud effects. Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e presents the average statistics for all 18 days, for days with at least 50% clear skies (10/18 days), and for days with at least 75% clear skies (3/18 days). Complete statistics with MAE and \u0026rho; are available in Table S3 and S4.\u003c/p\u003e\n \u003cp\u003eOverall, for degradation paths with less than 25% of each degradation modes, the RMSEs were in the 1.75 to 3.6% range for all algorithms for Q- diagnosis and in the 4.4 to 5.2% range for t-diagnosis. Focusing on clearer days reduced the RMSE significantly, to below 1% (FNN, 1DConv, DTW-CNN) for Q-diagnosis and 2.5% (XGB, RF, 1DConv) for t-diagnosis. This highlights the validity of diagnosis for days with cloud coverage.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003cdiv align=\"char\" class=\"colspec\"\u003e\u003cbr\u003e\u003c/div\u003e\n \u003cdiv align=\"char\" class=\"colspec\"\u003e\u003cbr\u003e\u003c/div\u003e\n \u003cdiv align=\"char\" class=\"colspec\"\u003e\u003cbr\u003e\u003c/div\u003e\u0026nbsp;\u003ctable border=\"1\" id=\"Tab2\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eRMSE summary statistics for diagnosis on 11,000 voltage vs. capacity curves generated for degradation below 25% for all days, days with 50% of more clear sky, and days with 75% or more clear sky. Algorithms were trained on the same day clear-sky irradiance. Associated full statistics are available in Table S3 and S4.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"6\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eRF\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eXGB\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eFNN\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e1DConv\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eDTW-CNN\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eQ-based, all days, \u0026lt;\u0026thinsp;25% deg.\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.55\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.76\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eQ-based, all days, \u0026lt;\u0026thinsp;50% deg.\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.89\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.84\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.92\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.91\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003et-based, all days, \u0026lt;\u0026thinsp;25% deg.\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.46\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.17\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003et-based, all days, \u0026lt;\u0026thinsp;50% deg.\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.84\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e6.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8.53\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8.59\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7.67\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eQ-based, \u0026gt; 50% clear-sky, \u0026lt;\u0026thinsp;25% deg.\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.91\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.75\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.78\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eQ-based, \u0026gt; 50% clear-sky, \u0026lt;\u0026thinsp;50% deg.\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.91\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.67\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003et-based, \u0026gt; 50% clear-sky, \u0026lt;\u0026thinsp;25% deg.\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.61\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.34\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.59\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.20\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003et-based, \u0026gt; 50% clear-sky, \u0026lt;\u0026thinsp;50% deg.\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.67\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7.14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e6.67\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eQ-based, \u0026gt; 75% clear-sky, \u0026lt;\u0026thinsp;25% deg.\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.37\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.72\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.58\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eQ-based, \u0026gt; 75% clear-sky, \u0026lt;\u0026thinsp;50% deg.\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.56\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.59\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.65\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.16\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003et-based, \u0026gt; 75% clear-sky, \u0026lt;\u0026thinsp;25% deg.\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.45\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.45\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.06\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003et-based, \u0026gt; 75% clear-sky, \u0026lt;\u0026thinsp;50% deg.\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.07\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7.43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.78\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cdiv class=\"gridtable\"\u003e\u003cbr\u003e\u003c/div\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n \u003c/div\u003e\n\u003c/div\u003e"},{"header":"3. Discussion","content":"\u003cp\u003eThis study provides the first application of synthetic datasets for non-CC simulations. Because current was not constant, capacity and time were uncorrelated, which offered an opportunity to study two different datasets, V vs. Q and V vs. t.. While using voltage versus capacity is more traditional, it might not be the best solution for deployed systems because the V vs. t dataset should be less error-prone than the V vs. Q one as capacity is not directly measurable, but derived from time and current [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]. The V vs. Q dataset is however expected to be easier to diagnose because the area under a dQ/dV peak corresponds to capacity and, at low rates, it is independent of the applied current because it has a finite value. Therefore, current variations should have a limited impact on the overall peak shape and intensity. This is why the voltage responses showcased in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(a-c) are really similar to the signature under CC [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e] despite the current varying. This is not the case for dt/dV peaks, because, while capacity stays the same with varying current, the time taken to complete the peak will be different. Therefore dt/dV peaks are much more sensitive to changes of current than dQ/dV ones. This sensibility explains the differences observed between Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(d-f) and Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(a-c) and why the t-diagnoses average errors were on average more than double the Q-based ones. The increased error was especially visible when the validation was done on a duty cycle different from the one used for training. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e(a) plots the RMSE variations as a function of the month of the year for algorithms trained on one day only (second set of experiments). The Q-based RMSE showcased little to no effect of the month of the year whereas the t-based ones varied significantly with a minimum close to the training day (March and April) and in fall (September and October) when irradiances are the most similar to the one used for training (03/21), Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(b). The difference was also much more pronounced for cloudy days and aged cells. Therefore, although t-diagnosis is more interesting on paper, it might not be the best solution where clear-sky did not significantly dominate, at least for the tested algorithms.\u003c/p\u003e \u003cp\u003eFigure S2, Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, showed the performance degradation with increasing degradation percentage. This decline in performance can be explained by multiple factors. Although data imbalance during training could be a possible factor, as 2/3rds of the training data has a degradation below 25%, the main factor seems to come from the fact that small variations in one of the three degradation modes are hard to quantify when at least one of the other two modes has large variations. This is exemplified in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e(b,c) where a distribution of the estimated vs. true values for LLI and the DTW-CNN algorithms are plotted for 50% or less and 25% or less degradation. For the 50% or less degradation, there is a haze around the 1:1 line below 20% LLI that disappears when the maximum degradation is set at 25%. This indicates that the error mostly comes from degradation paths with low LLI but at least one LAM above 25%. This will be investigated further in future work.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eLooking at the detailed statistics, it can be seen from Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, S3 and S4 that, although the algorithms performance was really close, some differences were noticeable. Overall, the DTW-CNN algorithm offers the best performance for Q-diagnosis while 1DConv is significantly better for t-diagnosis for degradations below 25%. Moreover, the algorithms are not all affected the same by the change of duty cycles. This is especially visible on Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e(a) were the performance of the t-diagnosis much more affected for winter days than of summer days for RF while the opposite is true or DTW-CNN. The other three algorithms being impacted the same. Future work will investigate in details the parameterization of the algorithms to improve performance. Looking in more details, it appears that the largest errors were always observed for LAM\u003csub\u003eNE\u003c/sub\u003e estimation (Tables S2-S4). This could be explained by the fact that LAM\u003csub\u003eNE\u003c/sub\u003e cannot be directly inferred from any feature of interest of the IC or IT curves. For the other two degradation modes, and as showcased in [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e], the intensity of high voltage shoulder is in most cases directly proportional to LAM\u003csub\u003ePE\u003c/sub\u003e and the intensity of the main peak to LLI. This is NMC specific and different results are expected for non-layered oxides such as batteries based on LiFePO\u003csub\u003e4,\u003c/sub\u003e where LAM\u003csub\u003ePE\u003c/sub\u003e should be much harder to quantify than the other two. A possible solution to improve the accuracy of LAM\u003csub\u003eNE\u003c/sub\u003e estimation for the current algorithms could be to train the algorithms on DV curves on top of the IC curves as LAM\u003csub\u003eNE\u003c/sub\u003e is, in most cases, directly decipherable from the DV curves.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e presents the RMSE variation for all the cloudy days tested in this work sorted by their clear-sky percentage with the associated actual irradiance vs. time curve as inset. Overall, clear-sky percentage is a useful indicator of diagnosability, although some other parameters also come into play. In general, the RMSE increases as clear-sky percentage decrease. However, there were some duty cycles that showed abnormal high (e.g., 34% clearness and 59% clearness) or low (e.g., 27% clearness) RMSE, indicating that the intensity and time of the cloud coverage could also play a major role in diagnosability. Together with cloud coverage, the type of diagnosis, Q-based or t-based also has a role. For example, for a day with 59% clear-sky, Q-diagnosis was better than normal and the t-based one far worse, while for a day with 34% clear-sky, the opposite was true. Finding the right set of parameters to identify which days are more auspicious for diagnosis will require more work but, from these results, it is clear that the use of synthetic data will be instrumental in testing the impact of different classification schemes.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"5. Conclusions \u0026 Outlook","content":"\u003cp\u003eThis paper proposes and validates a new approach for the diagnosis of batteries paired with PV using synthetic data. This approach allows the degradation of PV-connected batteries to be diagnosed without the need for maintenance cycles by using state-of-art machine learning algorithms. Diagnoses have an average RMSE of 2.75% for more than 10,000 different degradation paths with 25% or less of the three thermodynamic degradation modes. Because diagnosis was done outside of constant current, the capacity- and time-based information could be decorrelated and compared. Time-based diagnosis was shown to be less accurate than its capacity counterpart for the tested algorithms. However, the accuracy of the both types of diagnosis is satisfactory for days where clear-sky dominates. For days with lower clear-sky conditions, accuracy depends on the clear-sky percentage, but additional factors such as the time and duration of cloud coverage also come into play. These factors will be investigated further in future work.\u003c/p\u003e \u003cp\u003eThe framework presented here proved that opportunistic diagnosis of PV connected battery is possible from auspicious cloud coverages. Based on our results, and for the studied system and location, diagnosis could be possible one out of every five days independent of the season which is more than frequent enough for batteries supposed to last 3,500 days or more. This number might be different in other locations where shadowing or snow could play a significant role but it could be easily assessed using the framework presented here. This highlights the significant benefits of using synthetic data to understand the expected variations of voltage response for different cloud coverage and to develop adapted diagnosis tools, particularly as real photovoltaic battery degradation data is not yet available.\u003c/p\u003e \u003cp\u003eDespite promising results, there is still a significant amount of work to be done before this technique can be applied to deployed systems. There is a need for training under a wide array of different conditions, as PV systems in the field will have varying orientation, tilt, location, cleanliness, etc\u0026hellip; Moreover, this work was performed on single cells and without considering any additional usage on the cells. Real systems will be composed of battery packs, which will have varying voltage response due to inhomogeneities and imbalance. Furthermore, these batteries will likely be used at the same time they are charged, which will further modify the duty cycles. The validation framework provided here can be applied to study these case figures and future work that addresses the complexity of different locations, modules, and possible additional load on batteries. The proposed framework might even be applicable to other types of intermittent renewable power systems for which storage could be considered, such as wave or tidal energy.\u003c/p\u003e"},{"header":"Methods","content":"\u003ch2\u003e5.1 PV data acquisition\u003c/h2\u003e\n\u003cp\u003eThe PV testbed used in this work includes instrumentation for high-frequency PV and solar resource monitoring, including a Kipp \u0026amp; Zonen SMP21-A secondary standard pyranometer, which is installed in the POA of the testbed PV panels. The data was collected at 1 second intervals and averaged to 1 minute for 2 years.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003e5.2 Battery testing\u003c/h2\u003e\n\u003cp\u003eThe commercial cells used in this work were provided by an industrial partner and are composed of a graphite intercalation compound (GIC) based negative electrode (NE) and a Nickel Manganese Cobalt oxide (NMC) positive electrode (NE) with a 1:1:1 stoichiometry. The industrial partner also provided the full cell cycling data with C/15, C/8.5 and C/4 cycles performed on a pristine cell. The half-cell data was harvested by opening a commercial cell from the same batch. The cell was slowly discharged to 2.0V before being opened in a glove box. The double-sided electrodes were rinsed with dimethyl carbonate and one side was scrubbed using N-Methylpyrrolidone before 1.8mm diameter electrodes were cut using an EL-CUT punching tool (EL-CELL, Hamburg, Germany). Half-cells were assembled in PAT-CELLs (EL-CELL, Hamburg, Germany) using a standard polypropylene sleeve, a borosilicate glass fiber separator, a metallic Li NE, as well as an electrolyte composed of ethylene carbonate and propylene carbonate in a 1:1 ratio with 1M Lithium hexafluorophosphate and 2% vinylene carbonate (all Sigma-Aldrich USA). For the testing, the cell formation consisted of 8 cycles at C/10 followed by 1 cycle at C/25 between 3.2V and 4.3V for the PE and 0.02 and 1.2V for the NE. After the formation cycles, the cells were tested at C/50, C/25, C/15, C/8, C/4, C/2, and C/1 with residual capacity measurements at C/50 for each regime following the protocol described in [40].\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003e5.3 Synthetic data generation\u003c/h2\u003e\n\u003cp\u003eThe synthetic data used in this work, both for training and validation, was generated using the method described in [17-19]\u0026nbsp;by scanning the entire range of possible combinations for loss of lithium inventory (LLI) and LAMs.\u0026nbsp;Because the duty cycles have maximum currents below C/6, only the thermodynamic degradation parameters will be considered in this work. \u0026nbsp; \u0026nbsp; \u0026nbsp;The maximum value for the degradation modes was set at 50%. For the main training dataset, the composition resolution was set at 1% (5,000 triplet tested) with at most a simulation every 0.5% for each degradation modes (\u0026gt;125 simulations per triplet from 0 to 50%). This resulted in around 700,000 unique voltage response for training. Additional training on different duty cycles was done with a 2.5% resolution with 1% steps to limit file sizes. This corresponds to more than 850 different triplets and 43,000 unique voltage curves. For the validation datasets, the resolution was decreased to 5% (225 triplets) with 1% steps (50 simulations per triplet) resulting in around 11,000 curves per condition.\u003c/p\u003e\n\u003cp\u003eFinally, to avoid any overfitting error by training and validating on the same data, each simulation will be performed on a slightly different cell, i.e., a cell with emulation parameters (LR, OFS, R, and RDFs) randomly varied by \u0026plusmn;1% to be in the same range as observed cell-to-cell variations in commercial cells [41]. The overall parameters for each simulation with the associated duty cycles are summarized in Table S1.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003e5.4 Diagnosis algorithms\u003c/h2\u003e\n\u003cp\u003eIn this work, the leading machine learning algorithms\u0026nbsp;for degradation modes quantification were used to validate our approach. A thermodynamic degradation modes diagnosis corresponds to the quantification of LLI, and LAMs for the positive and negative electrodes (PE and NE respectively)\u0026nbsp;[37,42]. Such quantification provides more information than a simple capacity estimation and enables prognosis\u0026nbsp;[17]. The selected algorithms can be divided into two categories, decision tree ensemble methods and neural networks. Decision trees are deterministic models that rely on multiple conditionals while neural networks follow a probabilistic approach in which they seek to learn by activating artificial neurons. For this work, Random Forest (RF)\u0026nbsp;[21]\u0026nbsp;and Gradient Boosting Trees (XGB)\u0026nbsp;[22]\u0026nbsp;algorithms were selected for the decision trees and Feed-forward neural network (FNN)\u0026nbsp;[23], 1D-CNN (1DConv)\u0026nbsp;[16], and the DTW-CNN approach\u0026nbsp;[24]\u0026nbsp;were selected as neural networks. It is important to note that in all cases the models use the raw derivative voltage curves as input except for DTW-CNN, which uses images created from the DTW matrix between the pristine and the degraded derivative curves. This allows to transform voltage changes into images that reflect the degradation and enables the use of 2D CNNs, which are widely known in the literature to work remarkable well with images\u0026nbsp;[24].\u003c/p\u003e\n\u003cp\u003eIn terms of implementation, and for the decision tree ensemble methods:\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003eThe sklearn library [43] was used to implement the Random Forrest, specifically the ensemble module with the RandomForestRegressor algorithm, the hyperparameters were \u003cem\u003emax_depth\u003c/em\u003e, and \u003cem\u003en_estimators\u003c/em\u003e.\u003c/li\u003e\n \u003cli\u003eFor the XGBoost model, the xgboost library [44] was used, specifically the XGBRegressor algorithm, the hyperparameters were \u003cem\u003emax_depth=max_depth\u003c/em\u003e, and \u003cem\u003eeta=eta\u003c/em\u003e.\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eFor the neural networks, all the models were implemented in TensorFlow [45]. The models configurations were as follows:\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003eFFN: 3 fully connected layers with 64 neurons in the first layer, 32 in the second and 3 in the third.\u003c/li\u003e\n \u003cli\u003eCNN-1D: 5 layers of which 2 are CNN-1D layers with 32 neurons each and 3 are fully connected layers with 128, 64 and 3 neurons each.\u003c/li\u003e\n \u003cli\u003eCNN-DTW: 4 convolution layers with 64 neurons in the first two layers and 128 in the next two, followed by two fully connected layers with 512 and 3 neurons each.\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThe hyperparameters to be set in these three cases were the batch size and learning rate.\u003c/p\u003e\n\u003cp\u003eThe WandB framework [46] was used for hyperparameter tuning and callbacks were used during training to relegate the training stop condition to the validation error instead of the number of epochs.\u003c/p\u003e\n\u003cp\u003eIn this work, validation comprised varying initial conditions for the ML algorithms to produce model output that is compared against some truth to generate error statistics, which are used to quantify the experiments.\u003c/p\u003e\n\u003cp\u003eFurther details regarding the experimental setup and the source code to reproduce the experimental results are available in the following public git repository: \u003ca href=\"https://github.com/NahuelCostaCortez/PVDiagnosis\"\u003ehttps://github.com/NahuelCostaCortez/PVDiagnosis\u003c/a\u003e.\u003c/p\u003e\n\u003cp\u003eAll the sharable data from this work is available here [26,27] with the actual PV data and the synthetic cycles for perfect irradiance and cloud coverage.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAuthor Contributions:\u003c/strong\u003e Conceptualization, M.D..; methodology, M.D., D.M., and N.C.; software, M.D., D.M., and N.C.; validation, M.D., D.M., and N.C.; formal analysis, M.D., D.M., and N.C.; investigation, M.D. and N.C.; resources, M.D.; data curation, M.D.; writing\u0026mdash;original draft preparation, M.D. and D.M.; writing\u0026mdash;review and editing, M.D., D.M., and N.C.; visualization, M.D.; supervision, M.D.; project administration, M.D.; funding acquisition, M.D. All authors have read and agreed to the published version of the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding:\u003c/strong\u003e This research was funded by the Office of Naval Research (ONR), grant numbers N00014-19-1-2159 and N00014-22-1-2045. Nahuel Costa has been partially supported by the Ministry of Economy, Industry and Competitiveness (\u0026ldquo;Ministerio de Econom\u0026iacute;a, Industria y Competitividad\u0026rdquo;) from Spain/FEDER under grant PID2020-112726-RB-I00 and by Principado de Asturias, grant SV-PA-21-AYUD/2021/50994.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgments:\u003c/strong\u003e The authors are thankful to ONR for funding the deployment and monitoring of the PV system used in this work with the help of HNEI\u0026rsquo;s Severine Busquet, Jonathan Kobayashi, and Richard Rocheleau. The authors are also thankful to Thomas Nemeth and Matthias Kuipers (ACCURE, Germany) for fruitful discussions. Finally, the authors would also like to thank Sara Matthews for her insightful comments.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflicts of Interest:\u003c/strong\u003e The authors declare no conflict of interest.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eMackenzie/SEIA, W. \u003cem\u003eUS Solar Market Insight\u003c/em\u003e; Wood Mackenzie/SEIA 2021.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBolinger, M.; Seel, J.; Warner, C.; Robson, D. \u003cem\u003eUtility-Scale Solar, 2021 Edition\u003c/em\u003e; Lawrence Berkeley National Laboratory: 2021.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eEIA. \u003cem\u003eBattery Storage in the United States: An Update on Market Trends\u003c/em\u003e; 2021.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhao, H.; Lam, W.-Y.A.; Wang, L.; Xu, H.; Daoud, W.A.; He, X. 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Available online: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://wandb.ai/\u003c/span\u003e\u003cspan address=\"https://wandb.ai/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (accessed on\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-2058155/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2058155/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003ePhotovoltaic systems are providing a growing share of power to the electric grid worldwide. To mitigate resource intermittency issues, new systems are increasingly being paired with battery energy storage for which ensuring long and safe operation is critical. Unlike more typical battery applications, these batteries will undergo sporadic usage which will prevent the application of traditional diagnosis methods. This work proposes a new methodology for opportunistic diagnosis using machine learning algorithms trained directly on photovoltaic battery charging data. The training was performed on synthetic voltage data under different degradations calculated from clear-sky model irradiance data. Validation was performed on synthetic voltage responses calculated from plane of array irradiance observations for a photovoltaic system located in Maui, HI, USA. An average RMSE of 2.75% was obtained for more than 10,000 different degradation paths with 25% or less degradation on the cells.\u003c/p\u003e","manuscriptTitle":"Data-driven Direct Diagnosis of PV Connected Batteries","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2022-09-16 16:15:59","doi":"10.21203/rs.3.rs-2058155/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-communications","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"NCOMMS","sideBox":"Learn more about [Nature Communications](http://www.nature.com/ncomms/)","snPcode":"","submissionUrl":"https://mts-ncomms.nature.com/","title":"Nature Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Communications","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"81c59037-59dd-4180-8c26-2385e6a055be","owner":[],"postedDate":"September 16th, 2022","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2023-05-20T08:50:40+00:00","versionOfRecord":[],"versionCreatedAt":"2022-09-16 16:15:59","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-2058155","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2058155","identity":"rs-2058155","version":["v1"]},"buildId":"WrCJVZZCHTDjtuVLN7oU0","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}