# Limitations and Characterization of Energy Storage Devices for Harvesting Applications

^{*}

## Abstract

**:**

## 1. Introduction

#### State of Art with Respect to the Self-Discharge Phenomenon in SCs and Lithium Batteries

_{n}capacity. To charge the C

_{n}capacitor, i.e., each activated carbon layer, two resistors are required as described in Figure 2c; through the R

_{1}resistor, which indicates the resistance between the single grains, the ions move, while through the R

_{S}resistor the layers are charged. The equivalent circuit used for conventional capacitor can also be applied to a super-capacitor as shown in Figure 2d.

_{1}, R

_{2}and R

_{n}are the internal resistances of the activated carbon layers, C

_{1}, C

_{2}and C

_{n}the electrostatic capacities, while R

_{L}is the insulation resistance of the whole SC device. If a voltage V is applied to the equivalent electrical circuit shown in Figure 2d, then the total current (${i}_{tot}$) can be calculated as the sum of the individual currents flowing in each single small capacitor (${C}_{i}$) related to i-th activated carbon layer:

_{SD}given by the combination of R

_{L}and the internal resistances R

_{i}(i = 1, 2 … n) related to the pore impedances (internal activated carbon layers); therefore, the self-discharge resistance R

_{SD}can be derived by the open-circuit voltage time behavior V(t) by using the following expression:

_{start}and V

_{final}) on a given time period Δt, an even more accurate estimation of R

_{SD}can be obtained through the following equation:

_{2}crystalline structure. SEI formation (solid-electrolyte interphase) at the negative electrode also competes with the Li-ions intercalation leading to a capacity loss of both Li-ion and LiPo batteries [39,40]. Seong et al. demonstrated that a Li-ion cell can suffer from abnormally accelerated self-discharging with thermal exposure (at 60 °C or 80 °C), even a short exposition time intervals [41]. The authors demonstrated that the self-discharging is ascribable to a thin layer of Li

_{3}P, created as consequence of the thermal exposition, that induces a chemical cathode lithiation; in fact, by transmission electron microscopy (TEM) imaging, it is evident the creation of a Li

_{3}P thin film on the charged Li

_{0.9}CoO

_{2}electrode, just after the thermal treatment, which is then converted to LiP during the self-discharge process [41].

## 2. Materials and Methods

- Nominal capacity: 380 mAh;
- Standard charge: constant current 0.5 C (i.e., it is fully charged with a constant current of 190 mA in 2 h);
- Nominal voltage: 3.7 V (maximum achievable voltage: 4.2 V);
- Maximum constant charging current: 1 C (380 mA);
- Standard discharge: 0.2 C (it supplies the load with a current of 76 mA for 5 h);
- Maximum continuous discharging current: 1.5 C (C-rate).

_{SD}resistance by using the relations (3) and (4), on the basis of the SC open-circuit voltage values (${V}_{start}$ and ${V}_{final}$ refer to different time intervals) measured during the self-discharge phase, as detailed in the following section. Additionally, in Section 4, the data acquired for each SC is approximated over the whole observation time interval (120 h) through the sum of two exponential trends featured by different time constants, and the related fitting performances are analyzed.

## 3. Results

#### 3.1. Characterization of SC Self-Discharge Phenomenon

_{SD}resistance is much higher than the type-B SCs one, probably due to a much higher manufacturing quality. Furthermore, it should be assumed that the measured self-discharge, related to the series of two 4 F type-C SCs, is the sum of the voltage percentage reduction of the two SCs and, at the same time, each type-C SC was charged to 2.5 V, initial voltage value that heavily affects the self-discharge rate [22]. In addition, the 1F type-A SC shows a higher self-discharge rate respect to the other ones obviously due to its lower capacity, which implies a lower time constant of self-discharge phenomenon and thus a greater reduction of the SC open circuit voltage for a given time interval.

_{SD}resistance on the three time intervals was calculated, considering the parameter Δt expressed in seconds.

_{DS}resistance in the three considered observation intervals are reported in the following Table 3.

#### 3.2. Characterization of LiPo Batteries’ Self-Discharge Phenomenon

## 4. Discussion

_{SD}resistance, normalized with respect to the capacitance value, so determining a parameter dependent just from the device manufacturing quality.

_{SD}resistance is much greater in the last time interval (from the eighteenth hour to the one hundred and twentieth hour) compared to the previous ones (red and green font respectively in Table 2 and Table 3). This observation indicates the presence of two distinct phases in the SCs’ self-discharge: a first short-term behavior covering the first 15–18 h, followed by a long-term one valid for the whole subsequent time, with gradually increasing values of R

_{SD}resistance. The behavior in the initial time interval can be explained with an ions redistribution inside the electrodes’ pores; in fact, at the end of charging phase, the ions aren’t uniformly distributed along the pores depth of each electrode, and thus when the SCs are no longer under charge, the charge will redistribute inside the electrode material causing an initial voltage drop, which does not correspond to any charge loss, as detailed in [22]. This mechanism is in agreement with the equivalent circuit reported in Figure 2d; in fact, for shorter charging processes (up to a few hours) of the SCs, only the opening of the pores is involved in the charge distribution mechanism during the charging phase. Therefore, wanting to find a relationship between this physical behavior to the SC equivalent circuital model shown in Figure 2d, only the first equivalent capacitors (e.g., C

_{1}and C

_{2}), related to the shallower layers of the electrodes featured by a low internal series resistance (R

_{1}and R

_{2}, respectively), are charged. In this way, after the end of charging, the charge accumulated on C

_{1}and C

_{2}is redistributed to the other equivalent capacitors, related to deeper layers of the electrodes and thus featured by higher internal series resistances, leading to a voltage variation with time constant dependent by the series resistances of the other circuit branches (R

_{i}, for i = 3,…, n).

_{L}insulation resistor placed in parallel to the pores contributions.

_{SD}resistance featuring the self-discharge trends for the tested SCs (Table 2 and Table 3), taking into account that for the 2 F SC_C storage device the reported R

_{SD}resistance values are related to the sum of two resistors in series; however, the R

_{SD}value of each 4 F type-C SC is greater than those related to the other SCs typologies. Since the self-discharge R

_{SD}resistance is independent of the SC capacitance value, but related to the device manufacturing quality, relative to the characterized storage devices, the 1 F type-A SC is characterized by a higher R

_{SD}resistance with respect to the 4 F type-B SCs (Table 2 and Table 3).

_{SD}equivalent resistance (in the three considered time intervals) for the two different experimental cases, i.e., charging the SCs at 5 V and then kept under charge for one hour or five hours. As already highlighted, the self-discharge rate values related to the C-type cylindrical SCs are the smallest (red font in Table 4), although the series equivalent capacitance is only 2 F; even more so, the corresponding R

_{SD}resistance values are the highest by far (green font). Furthermore, the improvement in the case of SCs five hours under-charging after being charged at 5 V is evident for all SCs typologies; in particular, for the type-C SCs, the self-discharge rates are reduced of about 65%, 46% and 41% (for the time intervals 1, 2 and 3, respectively), as well as the R

_{SD}values increase by 204%, 49% and 104%, respectively (reported values in the orange and blue font for the self-discharge rate and R

_{SD}resistance, respectively).

_{3}, C

_{4}… C

_{n}), featured by higher time constants, are fully or partially charged and therefore, when the supply voltage is removed from the energy storage device, a lower redistribution in the high-index not-completely-charged capacitors is obtained.

^{2}) and the root mean square error (defined as $\sqrt{{{\displaystyle \sum}}_{i=1}^{N}{(\widehat{{V}_{i}}-{V}_{i})}^{2}/N,}RMSE$) of each determined approximation.

## 5. Conclusions

_{SD}resistance. Based on the analysis of acquired self-discharge time-domain trends, two distinct physical mechanisms with different time constants are evident: a short-term behavior due to the charge redistribution in the electrodes’ pores and a long-term one ascribable to both charge leakages through the SC separator layer and parasitic charges transfer between electrodes and electrolyte. By comparing the voltage drop acquired values as function of time, relatively to the characterized SCs for different charging durations (i.e., one and five hours under charge at 5 V), a significant reduction of the self-discharge rate is obtained for all tested SCs by increasing the duration of charge, a justifiable result with a better charge distribution and penetration in the electrodes pores in case of longer charging time durations. Finally, the self-discharge trends of commercial LiPo batteries (LW 752035 model) were also acquired and analyzed; the obtained results show an open-circuit voltage drop of 0.59% in the first 24 h and only 1.43% after just over 5 days (124 h), an experimental result in agreement with other ones already reported in literature (6–10% for each month) [37].

_{SD}resistance) for each device model can be determined.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Weddell, A.S.; Magno, M.; Merrett, G.V.; Brunelli, D.; Al-Hashimi, B.M.; Benini, L. A survey of multi-source energy harvesting systems. In Proceedings of the 2013 Design, Automation Test in Europe Conference Exhibition (DATE), Grenoble, France, 18–22 March 2013; IEEE: Piscataway, NJ, USA; pp. 905–908. [Google Scholar]
- Visconti, P.; Primiceri, P.; Orlando, C. Solar Powered Wireless Monitoring System of Environmental Conditions for Early Flood Prediction or Optimized Irrigation in Agriculture. J. Eng. Appl. Sci.
**2016**, 11, 4623–4632. [Google Scholar] - Visconti, P.; Ferri, R.; Pucciarelli, M.; Venere, E. Development and Characterization of a solar-based energy harvesting and power management system for a WSN node applied to optimized goods transport and storage. Int. J. Smart Sens. Intell. Syst.
**2016**, 9, 1637–1667. [Google Scholar] - Visconti, P.; Primiceri, P.; Ferri, R.; Pucciarelli, M.; Venere, E. An Overview on State-of-Art Energy Harvesting Techniques and Choice Criteria: A WSN Node for Goods Transport and Storage Powered by a Smart Solar- Based EH System. Int. J. Renew. Energy Res.
**2017**, 7, 1281–1295. [Google Scholar] - Afif, A.; Rahman, S.M.; Tasfiah Azad, A.; Zaini, J.; Islan, M.A.; Azad, A.K. Advanced materials and technologies for hybrid supercapacitors for energy storage—A review. J. Energy Storage
**2019**, 25, 1–24. [Google Scholar] [CrossRef] - Hajiaghasi, S.; Salemnia, A.; Hamzeh, M. Hybrid energy storage system for microgrids applications: A review. J. Energy Storage
**2019**, 21, 543–570. [Google Scholar] [CrossRef] - Habibzadeh, M.; Hassanalieragh, M.; Ishikawa, A.; Soyata, T.; Sharma, G. Hybrid Solar-Wind Energy Harvesting for Embedded Applications: Supercapacitor-Based System Architectures and Design Tradeoffs. IEEE Circ. Syst. Magaz.
**2017**, 17, 29–63. [Google Scholar] [CrossRef] - Zhu, M.; Hassanalieragh, M.; Chen, Z.; Fahad, A.; Shen, K.; Soyata, T. Energy-Aware Sensing in Data-Intensive Field Systems Using Supercapacitor Energy Buffer. IEEE Sens. J.
**2018**, 18, 3372–3383. [Google Scholar] [CrossRef] - Vračar, L.; Prijić, A.; Nešić, D.; Dević, S.; Prijić, Z. Photovoltaic Energy Harvesting Wireless Sensor Node for Telemetry Applications Optimized for Low Illumination Levels. Electronics
**2016**, 5, 26. [Google Scholar] [CrossRef][Green Version] - Toh, W.Y.; Tan, Y.K.; Koh, W.S.; Siek, L. Autonomous Wearable Sensor Nodes with Flexible Energy Harvesting. IEEE Sens. J.
**2014**, 14, 2299–2306. [Google Scholar] [CrossRef] - Chen, X.; Villa, N.S.; Zhuang, Y.; Chen, L.; Wang, T.; Li, Z.; Kong, T. Stretchable Supercapacitors as Emergent Energy Storage Units for Health Monitoring Bioelectronics. Adv. Energy Mater.
**2019**, 1902769, 1–27. [Google Scholar] [CrossRef] - Kamal, T.; Karabacak, M.; Hassan, S.Z.; Fernández-Ramírez, L.M.; Riaz, M.H.; Riaz, M.T.; Khan, M.A.; Khan, L. Energy Management and Switching Control of PHEV Charging Stations in a Hybrid Smart Micro-Grid System. Electronics
**2018**, 7, 156. [Google Scholar] [CrossRef][Green Version] - Aravindan, V.; Gnanaraj, J.; Lee, Y.-S.; Madhavi, S. Insertion-Type Electrodes for Nonaqueous Li-Ion Capacitors. Chem. Rev.
**2014**, 114, 11619–11635. [Google Scholar] [CrossRef] - Technical Data-Sheet, Panasonic Industrial Company Electric Double Layer Capacitors (Gold Capacitors)-Technical Guide. 2005. Available online: https://industrial.panasonic.com/content/data/CP/PDF/Electric_Double/EDLC_TechnicalGuide_e.pdf (accessed on 25 December 2019).
- Jiya, I.N.; Gurusinghe, N.; Gouws, R. Electrical Circuit Modelling of Double Layer Capacitors for Power Electronics and Energy Storage Applications: A Review. Electronics
**2018**, 7, 268. [Google Scholar] [CrossRef][Green Version] - Helseth, L.E. Modelling supercapacitors using a dynamic equivalent circuit with a distribution of relaxation times. J. Energy Storage
**2019**, 25, 1–7. [Google Scholar] [CrossRef] - Yang, H.; Zhang, Y. Self-discharge analysis and characterization of supercapacitors for environmentally powered wireless sensor network applications. J. Power Sour.
**2011**, 196, 8866–8873. [Google Scholar] [CrossRef] - Sedlakova, V.; Sikula, J.; Majzner, J.; Sedlak, P.; Kuparowitz, T.; Buergler, B.; Vasina, P. Supercapacitor equivalent electrical circuit model based on charges redistribution by diffusion. J. Power Sour.
**2015**, 286, 58–65. [Google Scholar] [CrossRef] - Buller, S.; Karden, E.; Kok, D.; De Doncker, R.W. Modeling the dynamic behavior of supercapacitors using impedance spectroscopy. IEEE Trans. Ind. Appl.
**2002**, 38, 1622–1626. [Google Scholar] [CrossRef] - Ricketts, B.W.; Ton-That, C. Self-discharge of carbon-based supercapacitors with organic electrolytes. J. Power Sour.
**2000**, 89, 64–69. [Google Scholar] [CrossRef] - Diab, Y.; Venet, P.; Gualous, H.; Rojat, G. Self-Discharge Characterization and Modeling of Electrochemical Capacitor Used for Power Electronics Applications. IEEE Trans. Power Electron.
**2009**, 24, 510–517. [Google Scholar] [CrossRef] - Kowal, J.; Avaroglu, E.; Chamekh, F.; Šenfelds, A.; Thien, T.; Wijaya, D.; Sauer, D.U. Detailed analysis of the self-discharge of supercapacitors. J. Power Sour.
**2011**, 196, 573–579. [Google Scholar] [CrossRef] - Miniguano, H.; Barrado, A.; Fernández, C.; Zumel, P.; Lázaro, A. A General Parameter Identification Procedure Used for the Comparative Study of Supercapacitors Models. Energies
**2019**, 12, 1776. [Google Scholar] [CrossRef][Green Version] - Sibi Krishnan, K.; Pathiyil, P.; Sunitha, R. Generic Battery model covering self-discharge and internal resistance variation. In Proceedings of the 2016 IEEE 6th International Conference on Power Systems (ICPS), New Delhi, India, 4–6 March 2016; pp. 1–5. [Google Scholar]
- La Rosa, R.; Livreri, P.; Trigona, C.; Di Donato, L.; Sorbello, G. Strategies and Techniques for Powering Wireless Sensor Nodes through Energy Harvesting and Wireless Power Transfer. Sensors
**2019**, 19, 660. [Google Scholar] [CrossRef] [PubMed][Green Version] - Houbbadi, A.; Trigui, R.; Pelissier, S.; Redondo-Iglesias, E.; Bouton, T. Optimal Scheduling to Manage an Electric Bus Fleet Overnight Charging. Energies
**2019**, 12, 2727. [Google Scholar] [CrossRef][Green Version] - Dąbrowska, A.; Greszta, A. Analysis of the Possibility of Using Energy Harvesters to Power Wearable Electronics in Clothing. Adv. Mater. Sci. Eng.
**2019**, 2019, 1–13. [Google Scholar] [CrossRef][Green Version] - Korthauer, R. (Ed.) Lithium-Ion Batteries: Basics and Applications; Springer: Berlin/Heidelberg, Germany, 2018; ISBN 978-3-662-53069-6. [Google Scholar]
- Nitta, N.; Wu, F.; Lee, J.T.; Yushin, G. Li-ion battery materials: Present and future. Mater. Today
**2015**, 18, 252–264. [Google Scholar] [CrossRef] - Hannan, M.A.; Hoque, M.M.; Hussain, A.; Yusof, Y.; Ker, P.J. State-of-the-Art and Energy Management System of Lithium-Ion Batteries in Electric Vehicle Applications: Issues and Recommendations. IEEE Access
**2018**, 6, 19362–19378. [Google Scholar] [CrossRef] - Zhu, F.; Liu, G.; Tao, C.; Wang, K.; Jiang, K. Battery management system for Li-ion battery. J. Eng.
**2017**, 2017, 1437–1440. [Google Scholar] [CrossRef] - Madani, S.S.; Swierczynski, M.J.; Kær, S.K. A review of thermal management and safety for lithium ion batteries. In Proceedings of the 2017 Twelfth International Conference on Ecological Vehicles and Renewable Energies (EVER), Monte Carlo, Monaco, 11–13 April 2017; pp. 1–20. [Google Scholar]
- Riviere, E.; Sari, A.; Venet, P.; Meniere, F.; Bultel, Y. Innovative Incremental Capacity Analysis Implementation for C/LiFePO4 Cell State-of-Health Estimation in Electrical Vehicles. Batteries
**2019**, 5, 37. [Google Scholar] [CrossRef][Green Version] - Liu, K.; Li, K.; Yang, Z.; Zhang, C.; Deng, J. An advanced Lithium-ion battery optimal charging strategy based on a coupled thermoelectric model. Electrochim. Acta
**2017**, 225, 330–344. [Google Scholar] [CrossRef] - Omariba, Z.B.; Zhang, L.; Sun, D. Review on Health Management System for Lithium-Ion Batteries of Electric Vehicles. Electronics
**2018**, 7, 72. [Google Scholar] [CrossRef][Green Version] - Dai, Q.; Kelly, J.C.; Gaines, L.; Wang, M. Life Cycle Analysis of Lithium-Ion Batteries for Automotive Applications. Batteries
**2019**, 5, 48. [Google Scholar] [CrossRef][Green Version] - Chen, X.; Vereecken, P.M. Solid and Solid-Like Composite Electrolyte for Lithium Ion Batteries: Engineering the Ion Conductivity at Interfaces. Adv. Mater. Interf.
**2019**, 6, 1–31. [Google Scholar] [CrossRef][Green Version] - Julien, C.; Nazri, G.-A. Solid State Batteries: Materials Design and Optimization; Springer US Science & Business Media: New York, NY, USA, 2013; ISBN 978-1-4615-2704-6. [Google Scholar]
- Palacín, M.R.; de Guibert, A. Why do batteries fail? Science
**2016**, 351, 1–7. [Google Scholar] [CrossRef] [PubMed][Green Version] - Kong, L.; Li, C.; Jiang, J.; Pecht, M.G. Li-Ion Battery Fire Hazards and Safety Strategies. Energies
**2018**, 11, 2191. [Google Scholar] [CrossRef][Green Version] - Seong, W.M.; Park, K.-Y.; Lee, M.H.; Moon, S.; Oh, K.; Park, H.; Lee, S.; Kang, K. Abnormal self-discharge in lithium-ion batteries. Energy Environ. Sci.
**2018**, 11, 970–978. [Google Scholar] [CrossRef] - Redondo-Iglesias, E.; Venet, P.; Pelissier, S. Global Model for Self-Discharge and Capacity Fade in Lithium-Ion Batteries Based on the Generalized Eyring Relationship. IEEE Trans. Vehic. Technol.
**2018**, 67, 104–113. [Google Scholar] [CrossRef] - Saha, P.; Khanra, M. Equivalent circuit model of supercapacitor for self-discharge analysis—A comparative study. In Proceedings of the 2016 International Conference on Signal Processing, Communication, Power and Embedded System (SCOPES), Paralakhemundi, India, 3–5 October 2016; pp. 1381–1386. [Google Scholar]
- Kularatna, N. Rechargeable batteries and their management. IEEE Instrument. Measure. Magaz.
**2011**, 14, 20–33. [Google Scholar] [CrossRef] - Berrueta, A.; Ursúa, A.; Martín, I.S.; Eftekhari, A.; Sanchis, P. Supercapacitors: Electrical Characteristics, Modeling, Applications, and Future Trends. IEEE Access
**2019**, 7, 50869–50896. [Google Scholar] [CrossRef] - Kurzweil, P.; Shamonin, M. State-of-Charge Monitoring by Impedance Spectroscopy during Long-Term Self-Discharge of Supercapacitors and Lithium-Ion Batteries. Batteries
**2018**, 4, 35. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**Ragone graph of common ESDs; the dotted lines indicate the device characteristic time (figure derived from [13]).

**Figure 2.**Cross-section of a button-type super-capacitor (

**a**); nanometer-scale operating principle of a SC (

**b**); circuital model related to the physical structure of a SC for overlapped carbon layers (

**c**); equivalent electrical circuit of a SC (

**d**) [14].

**Figure 3.**Type-A and -B button-shape super-capacitors (

**a**) and (

**b**) respectively and type-C cylindrical supercapacitors (

**c**).

**Figure 5.**Image of the experimental setup for the charging of all employed SCs (specifically type-A and -B SCs indicated as device 3).

**Figure 6.**Experimental setup for charging the LiPo batteries by using the LinkMan LK-1008D adapter (in the inset).

**Figure 7.**Self-discharge time-domain patterns for two different type-B SCs (indicated as SC_B1 and SC_B2), a type-A SC (SC_A) and a 2F type-C SC (indicated as SC_C), charged at 5 V and then kept under charge for one hour.

**Figure 8.**Self-discharge time-domain trends for two different type-B SCs (indicated as SC_B1 and SC_B2), a type-A SC (SC_A) and a 2 F type-C SC (indicated as SC_C), charged at 5 V and kept under charge for five hours.

**Figure 10.**Exponential fitting functions determined in order to approximate the self-discharge voltage values acquired for tested SCs, kept in charge at 5 V for 1 h.

**Table 1.**Self-discharge rate of LiPo batteries for the first month [42].

State of Charge | Charge Loss at T = 0 °C for the First Month | Charge Loss at T = 25 °C for the First Month | Charge Loss at T = 60 °C for the First Month |
---|---|---|---|

Full charge | 6% | 20% | 35% |

40–60% charge | 2% | 4% | 15% |

**Table 2.**Summarizing table with SCs’ self-discharge rates, expressed in mV/h, and self-discharge R

_{SD}resistance calculated for the three considered time intervals (SCs charged at 5 V and then kept under charge for one hour).

V_{1,start} (V) | V_{1,final} (V) | V_{2,start} (V) | V_{2,final} (V) | V_{3,start} (V) | V_{3,final} (V) | ${\left(\frac{\mathbf{\Delta}\mathit{V}}{\mathbf{\Delta}\mathit{t}}\right)}_{1}$ [mV/h] | ${\left(\frac{\mathbf{\Delta}\mathit{V}}{\mathbf{\Delta}\mathit{t}}\right)}_{2}$ [mV/h] | ${\left(\frac{\mathbf{\Delta}\mathit{V}}{\mathbf{\Delta}\mathit{t}}\right)}_{3}$ [mV/h] | R_{SD1} [kΩ)] | R_{SD2} [kΩ] | R_{SD3} [kΩ] | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

SC_A | 4.46 | 3.64 | 3.64 | 2.87 | 2.87 | 1.51 | −164.0 | −85.6 | −14.3 | 88.6 | 181.8 | 571.8 |

SC_B1 | 4.73 | 4.29 | 4.29 | 3.90 | 3.90 | 3.15 | −88.0 | −43.3 | −7.9 | 46.1 | 113.3 | 429.8 |

SC_B2 | 4.71 | 4.14 | 4.14 | 3.74 | 3.74 | 3.01 | −114.0 | −44.4 | −7.7 | 34.9 | 106.3 | 422.7 |

SC_C | 4.78 | 4.49 | 4.49 | 4.31 | 4.31 | 3.74 | −58.0 | −20.0 | −6.0 | 143.8 | 527.9 | 1294.3 |

**Table 3.**Summarizing table with SCs’ self-discharge rates, expressed in mV/h, and self-discharge R

_{SD}resistance calculated for the three considered time intervals (SCs charged at 5 V and kept under charge for five hours).

V_{1,start} (V) | V_{1,final} (V) | V_{2,start} (V) | V_{2,final} (V) | V_{3,start} (V) | V_{3,final} (V) | ${\left(\frac{\mathbf{\Delta}\mathit{V}}{\mathbf{\Delta}\mathit{t}}\right)}_{1}$ [mV/h] | ${\left(\frac{\mathbf{\Delta}\mathit{V}}{\mathbf{\Delta}\mathit{t}}\right)}_{2}$ [mV/h] | ${\left(\frac{\mathbf{\Delta}\mathit{V}}{\mathbf{\Delta}\mathit{t}}\right)}_{3}$ [mV/h] | R_{SD}_{1} [kΩ)] | R_{SD}_{2} [kΩ] | R_{SD}_{3} [kΩ] | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

SC_A | 4.55 | 4.05 | 4.05 | 3.37 | 3.37 | 2.43 | −100.0 | −56.7 | −9.2 | 154.6 | 235.0 | 1122.9 |

SC_B1 | 4.90 | 4.67 | 4.67 | 4.40 | 4.40 | 3.87 | −46.0 | −22.5 | −5.2 | 93.6 | 181.3 | 715.2 |

SC_B2 | 4.82 | 4.45 | 4.45 | 4.09 | 4.09 | 3.40 | −74.0 | −30.0 | −6.8 | 56.3 | 128.0 | 496.8 |

SC_C | 4.92 | 4.82 | 4.82 | 4.69 | 4.69 | 4.33 | −20.0 | −10.8 | −3.5 | 438.3 | 790.0 | 2298.9 |

**Table 4.**Comparison of self-discharge rate and R

_{SD}resistance values for the characterized SCs relatively to the one hour and five hours under charge cases at 5 V.

${\left(\frac{\mathbf{\Delta}\mathit{V}}{\mathbf{\Delta}\mathit{t}}\right)}_{1}$ [mV/h] | R_{SD}_{1}[kΩ)] | ${\left(\frac{\mathbf{\Delta}\mathit{V}}{\mathbf{\Delta}\mathit{t}}\right)}_{2}$ [mV/h] | R_{SD}_{2}[kΩ] | ${\left(\frac{\mathbf{\Delta}\mathit{V}}{\mathbf{\Delta}\mathit{t}}\right)}_{3}$ [mV/h] | R_{SD}_{3}[kΩ)] | ||
---|---|---|---|---|---|---|---|

5 V charged and then one hour under charge | SC_A | −164.0 | 88.6 | −85.6 | 181.8 | −14.3 | 571.8 |

SC_B1 | −88.0 | 46.1 | −43.3 | 113.3 | −7.9 | 429.8 | |

SC_B2 | −114.0 | 34.9 | −44.4 | 106.3 | −7.7 | 422.7 | |

SC_C | −58.0 | 143.8 | −20.0 | 527.9 | −6.0 | 1294.3 | |

5 V charged and then five hours under charge | SC_A | −100.0 | 154.6 | −56.7 | 235.0 | −9.2 | 1122.9 |

SC_B1 | −46.0 | 93.6 | −22.5 | 181.3 | −5.2 | 715.2 | |

SC_B2 | −74.0 | 56.3 | −30.0 | 128.0 | −6.8 | 496.8 | |

SC_C | −20.0 | 438.3 | −10.8 | 790.0 | −3.5 | 2298.9 | |

Percentage difference | SC_A | −39.0% | 74.5% | −33.8% | 29.3% | −35.7% | 96.4% |

SC_B1 | −47.7% | 103.0% | −48.0% | 60.0% | −34.2% | 66.4% | |

SC_B2 | −35.1% | 61.3% | −32.4% | 20.4% | −11.7% | 17.5% | |

SC_C | −65.5% | 204.8% | −46.0% | 49.65% | −41.6% | 77.61% |

**Table 5.**Table with the parameters of the exponential fitting functions for the SCs kept in charge at 5 V for 1 h; the determination coefficient (R

^{2}) and root mean square error (RMSE) are also reported.

SC | $\mathit{a}$ | $\mathit{\tau}1\text{}\left[\mathbf{h}\right]$ | $\mathit{b}$ | $\mathit{\tau}2\text{}\left[\mathbf{h}\right]$ | R^{2} | RMSE |
---|---|---|---|---|---|---|

SC_A | 1.94 | 7.78 | 2.84 | 181.59 | 0.996 | 0.083 |

SC_B1 | 1.08 | 8.25 | 3.82 | 568.18 | 0.996 | 0.044 |

SC_B2 | 1.23 | 7.15 | 3.67 | 545.25 | 0.996 | 0.044 |

SC_C | 0.58 | 5.92 | 4.32 | 759.87 | 0.993 | 0.036 |

**Table 6.**Voltage percentage variations for the most performing tested SCs, kept under charging at 5 V for one and five hours, and for the LiPo batteries.

SC_B1 One Hour Under Charge at 5 V [V] | SC_C One Hour Under Charge at 5 V [V] | SC_B1 Five Hours Under Charge at 5 V [V] | SC_C Five Hours Under Charge at 5 V [V] | LiPo Battery LW 752035 [V] | |
---|---|---|---|---|---|

Initial value | 5.00 | 5.00 | 5.00 | 5.00 | 4.20 |

After 24 h | 3.76 | 4.22 | 4.33 | 4.66 | 4.175 |

After 120 h | 3.15 | 3.75 | 3.87 | 4.33 | 4.14 |

Self-discharge after 24 h | −24.80% | −15.60% | −13.40% | −6.80% | −0.59% ^{1} |

Self-discharge after 120 h | −37.00% | −25.00% | −22.60% | −13.40% | −1.43% ^{1} |

^{1}Values referred to 124 h instead of 120 h.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

de Fazio, R.; Cafagna, D.; Marcuccio, G.; Visconti, P. Limitations and Characterization of Energy Storage Devices for Harvesting Applications. *Energies* **2020**, *13*, 783.
https://doi.org/10.3390/en13040783

**AMA Style**

de Fazio R, Cafagna D, Marcuccio G, Visconti P. Limitations and Characterization of Energy Storage Devices for Harvesting Applications. *Energies*. 2020; 13(4):783.
https://doi.org/10.3390/en13040783

**Chicago/Turabian Style**

de Fazio, Roberto, Donato Cafagna, Giorgio Marcuccio, and Paolo Visconti. 2020. "Limitations and Characterization of Energy Storage Devices for Harvesting Applications" *Energies* 13, no. 4: 783.
https://doi.org/10.3390/en13040783