# SOC Estimation of Lead Carbon Batteries Based on the Operating Conditions of an Energy Storage System in a Microgrid System

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Cell Model and Parameters

#### 2.1. Cell Model

#### 2.2. Experiments

#### 2.3. Parameters Identification

#### 2.3.1. Acquisition of OCV

#### 2.3.2. Acquisition of $\eta $

#### 2.3.3. Acquisition of Other Parameters

## 3. SOC Estimation

#### 3.1. Denoising Approach

#### 3.1.1. Decomposition of Original Signals

#### 3.1.2. Selecting Threshold for Denoising

#### 3.1.3. Denoised Signal Obtained by Wavelet Reconstruction

#### 3.2. Extend Kalman Filter

#### 3.3. A Compound SOC Estimation Algorithm Based on Wavelet Transform

**Step 1**Define the following variables, the minimum current ${I}_{\mathrm{min}}=0.5A$, the standing time ${T}_{st}=30\mathrm{min}$, the sampling time ${t}_{k}$, the $SO{C}_{k}$ of ${t}_{k}$, the ${I}_{k}$ of ${t}_{k}$, the ${V}_{k}$ of ${t}_{k}$, the SOC initial value $SO{C}_{0}$, the Coulomb efficiency $\eta $, and the current rate $\kappa $;

**Step 2**Establish the relationships between SOC and OCV, and between the Coulomb efficiency and the current rate;

**Step 3**Establish a mathematical model of the lead carbon battery;

**Step 4**If the batteries of BESS are in a static state (${I}_{k}\le {I}_{\mathrm{min}}$ and ${t}_{k}\le {T}_{st}$), the value of OCV is equal to ${V}_{k}$ of ${t}_{k}$, and the $SO{C}_{0}$ is obtained by Equation (4). If it is not in a static state, the value of $SO{C}_{0}$ is equal to $SO{C}_{k}$ of ${t}_{k}$;

**Step 5**The $SO{C}_{k+1}$ of ${t}_{k+1}$ is estimated by the EKF based on wavelet denoising algorithm;

**Step 6**The $SO{C}_{k+2}$ of ${t}_{k+2}$ is estimated through the Ah algorithm;

**Step 7**In a group of batteries, select the minimum SOC value as the final output value.

## 4. Algorithm Validations and Analysis

#### 4.1. Analysis and Verification of Experimental Data

- (1)
- Figure 9a shows the SOC result using the experimental data. The accuracy of the compound algorithm is very high, with the relative error within 0.6%.
- (2)
- Figure 9b displays the robustness of the algorithm. It is supposed that there is an initial deviation value ($SO{C}_{0}$ of the compound algorithm is 0.5 while $SO{C}_{0}$ of the Ah algorithm is 1). The combined algorithm can correct the initial error quickly, and the final estimated relative error is within 0.6%.

#### 4.2. Verification and Analysis of ESS Operation Data

## 5. Conclusions

- In this study, three algorithms were used to estimate SOC. The EKF algorithm estimates the SOC accurately, but it does not eliminate system noise, while the EKF based on the wavelet transform algorithm estimates the SOC accurately by eliminating system noise. The above two algorithms are based on accurate identification of the parameters of the battery model. If the parameters are not identified accurately in the process of iterative correction, the precision of SOC estimation is significantly affected. The proposed composite algorithm, in this study, has many advantages. The OCV-SOC method is used to determine the initial value of SOC. There is a simple correction link when the initial value is determined. Then, in the process of denoising and EKF estimation, the SOC estimation is combined with the Ah method. In this way, one step of estimation is carried out without relying on the battery model, and the precision of estimation is increased.
- The composite algorithm suppresses the system noise and satisfies the needs of engineering applications in the ESS of the microgrid system.
- Compared with other methods, it is relatively accurate in the frequent high-current charge and discharge conditions, especially the complex and changeable operating conditions.
- This research demonstrates that the proposed composite method has the characteristics of robustness.
- The battery model used, in this study, does not consider the influence of temperature, and the accuracy of estimation needs to be improved.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Grillo, S.; Marinelli, M.; Massucco, S.; Silvestro, F. Optimal management strategy of a battery-based storage system to improve renewable energy integration in distribution networks. IEEE Trans. Smart Grid
**2012**, 3, 950–958. [Google Scholar] [CrossRef] - Jiang, Q.; Gong, Y.; Wang, H. A battery energy storage system dual layer control strategy for mitigating wind farm fluctuations. IEEE Trans. Power Syst.
**2013**, 28, 3263–3273. [Google Scholar] [CrossRef] - Guo, L.D.; Lei, M.Y.; Yang, Z.L.; Wang, Y.B.; Xu, H.H.; Chen, Y.Y. Research on control strategy of the energy storage system for photovoltaic and storage combined system. In Proceedings of the IECON 2017-43rd Annual Conference of the IEEE Industrial Electronics Society, Beijing, China, 29 October–1 November 2017; pp. 2813–2817. [Google Scholar]
- Dan, W.; Fen, T.; Dragicevic, T.; Vasquez, J.C.; Guerrero, J.M. Autonomous active power control for islanded AC microgrids with photovoltaic generation and energy storage system. IEEE Trans. Energy Convers.
**2014**, 29, 882–892. [Google Scholar] - Kim, J.Y.; Jeon, J.H.; Kim, S.K.; Cho, C.; Park, J.H.; Kim, H.M.; Nam, K.Y. Cooperative control strategy of energy storage system and microsources for stabilizing the microgrid during islanded operation. IEEE Trans. Power Electron.
**2010**, 25, 3037–3048. [Google Scholar] - Sebastián, R. Application of a battery energy storage for frequency regulation and peak shaving in a wind diesel power system. IET Gener. Transm. Dist.
**2016**, 10, 764–770. [Google Scholar] [CrossRef] - Anderson, J.L.; Frankhouser, J. Advanced lead carbon batteries for partial state of charge operation in stationary applications. In Proceedings of the 2015 IEEE International Telecommunications Energy Conference (INTELEC), Osaka, Japan, 18–22 October 2015; IEEE: Piscataway, NJ, USA, 2016. [Google Scholar]
- Yang, Z.; Zhang, J.; Kintner-Meyer, M.C.; Lu, X.; Choi, D.; Lemmon, J.P.; Liu, J. Electrochemical energy storage for green grid. Chem. Rev.
**2011**, 111, 3577–3613. [Google Scholar] [CrossRef] - Tong, P.; Zhao, R.; Zhang, R.; Yi, F.; Shi, G.; Li, A.; Chen, H. Characterization of lead (II)-containing activated carbon and its excellent performance of extending lead-acid battery cycle life for high-rate partial-state-of-charge operation. J. Power Sources
**2015**, 286, 91–102. [Google Scholar] [CrossRef] - Xiang, J.; Ding, P.; Zhang, H.; Wu, X.; Chen, J.; Yang, Y. Beneficial effects of activated carbon additives on the performance of negative lead-acid battery electrode for high-rate partial-state-of-charge operation. J. Power Sources
**2013**, 241, 150–158. [Google Scholar] [CrossRef] - Lawder, M.T.; Suthar, B.; Northrop, P.W.; De, S.; Hoff, C.M.; Leitermann, O.; Crow, M.L. Battery Energy Storage System (BESS) and Battery Management System (BMS) for Grid-Scale Applications. Proc. IEEE
**2014**, 102, 1014–1030. [Google Scholar] [CrossRef] - Elsayed, A.T.; Lashway, C.R.; Mohammed, O.A. Advanced Battery Management and Diagnostic System for Smart Grid Infrastructure. IEEE Trans. Smart Grid
**2016**, 7, 897–905. [Google Scholar] - Dang, X.; Yan, L.; Xu, K.; Wu, X.; Jiang, H.; Sun, H. Open-Circuit Voltage-Based State of Charge Estimation of Lithium-ion Battery Using Dual Neural Network Fusion Battery Model. Electrochim. Acta
**2015**, 188, 356–366. [Google Scholar] [CrossRef] - Yang, N.; Zhang, X.; Li, G. State of charge estimation for pulse discharge of a LiFePO4 battery by a revised Ah counting. Electrochim. Acta
**2015**, 151, 63–71. [Google Scholar] [CrossRef] - Chen, Z.; Fu, Y.; Mi, C.C. State of Charge Estimation of Lithium-Ion Batteries in Electric Drive Vehicles Using Extended Kalman Filtering. Veh. Technol.
**2013**, 62, 1020–1030. [Google Scholar] [CrossRef] - Chen, J.; Ouyang, Q.; Xu, C.; Su, H. Neural Network-Based State of Charge Observer Design for Lithium-Ion Batteries. IEEE Trans. Control Syst. Technol.
**2017**, 26, 313–320. [Google Scholar] [CrossRef] - Anton, J.C.A.; Nieto, P.J.G.; Viejo, C.B.; Vilán, J.A.V. Support Vector Machines Used to Estimate the Battery State of Charge. IEEE Trans. Power Electron.
**2013**, 28, 5919–5926. [Google Scholar] [CrossRef] - Plett, G.L. Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs. J. Power Sources
**2004**, 134, 262–276. [Google Scholar] [CrossRef] - Chen, M.; Rincon-Mora, G.A. Accurate electrical battery model capable of predicting runtime and I-V performance. IEEE Trans. Energy Convers.
**2006**, 21, 504–511. [Google Scholar] [CrossRef] - Chen, Y.; Yang, Z.; Guo, L.; Huang, X.; Wang, Y. A composite estimation method for state of charge of batteries in a power station engineering. In Proceedings of the 2017 IEEE Conference on Energy Internet & Energy System, Beijing, China, 26–28 November 2017; pp. 1–6. [Google Scholar]
- Chen, Y.; Yang, Z.; Wang, Y.; Guo, L.; Huang, X. State of charge estimation of lead-carbon batteries in actual engineering. In Proceedings of the 2017 20th International Conference on Electrical Machines & Systems, Sydney, Australia, 11–14 August 2017; pp. 1–6. [Google Scholar]
- Boubchir, L.; Boashash, B. Wavelet denoising based on the MAP estimation using the BKF with application to images and EEG signals. IEEE Trans. Signal Process.
**2013**, 61, 1880–1894. [Google Scholar] [CrossRef] - Hu, X.S.; Li, S.B.; Li, H.; Peng, F.C. Robustness analysis of State-of-Charge estimation methods for two types of Li-ion batteries. J. Power Sources
**2012**, 217, 209–219. [Google Scholar] [CrossRef] - Farahani, M.A.; Wylie, M.T.V.; Guerra, E.C.; Colpitts, B.G. Reduction in the number of averages required in BOTDA sensors using wavelet denoising techniques. J. Lightw. Technol.
**2012**, 30, 1134–1142. [Google Scholar] [CrossRef] - Ismail, B.; Khan, A. Image De-noising with a New Threshold Value Using Wavelets. J. Data Sci.
**2012**, 10, 259–270. [Google Scholar] - Zafar, S.; Zhang, Y.Q.; Jabbari, B. Multiscale video representation using multiresolution motion compensation and wavelet decomposition. IEEE J. Sel. Areas Commun.
**2002**, 11, 24–35. [Google Scholar] [CrossRef] - Dong, W.; Ding, H. Full Frequency De-noising Method Based on Wavelet Decomposition and Noise-type Detection. Neurocomputing
**2016**, 214, 902–909. [Google Scholar] [CrossRef] - Baykal-Gursoy, M. Forecasting: State-Space Models and Kalman Filter Estimation; ResearchGate: Berlin, Germany, 2011. [Google Scholar]
- Sun, F.; Xiong, R. A novel dual-scale cell state-of-charge estimation approach for series-connected battery pack used in electric vehicles. J. Power Sources
**2015**, 274, 582–594. [Google Scholar] [CrossRef] - Paschero, M.; Storti, G.L.; Rizzi, A.; Mascioli, F.M.F.; Rizzoni, G. A Novel Mechanical Analogy-Based Battery Model for SoC Estimation Using a Multicell EKF. IEEE Trans. Sustain. Energy
**2016**, 7, 1695–1702. [Google Scholar] [CrossRef] [Green Version] - He, Z.; Gao, M.; Xu, J. EKF-Ah Based State of Charge Online Estimation for Lithium-ion Power Battery. In Proceedings of the 2009 International Conference on Computational Intelligence and Security, Beijing, China, 11–14 December 2009; Volume 1, pp. 142–145. [Google Scholar]
- Kim, J.; Cho, B.H. State-of-Charge Estimation and State-of-Health Prediction of a Li-Ion Degraded Battery Based on an EKF Combined with a Per-Unit System. IEEE Trans. Veh. Technol.
**2011**, 60, 4249–4260. [Google Scholar] [CrossRef]

Parameters | Values |
---|---|

Nominal capacity | 500 Ah |

Nominal voltage | 2 V |

End of discharge voltage | 1.8 V |

High voltage protection | 2.4 V |

Maximum charge current | 300 A (0.6 C) |

Maximum discharge current | 300 A (0.6 C) |

Parameters | Value 1 | Value 2 | Value 3 | Value 4 | Value 5 | Value 6 |
---|---|---|---|---|---|---|

Current rate (A) | 0.1 C | 0.2 C | 0.3 C | 0.4 C | 0.5 C | 0.6 C |

Charge efficiency (%) | 99.31 | 94.26 | 89.05 | 82.93 | 77.54 | 72.24 |

Discharge efficiency (%) | 98.02 | 92.52 | 87.23 | 81.47 | 75.75 | 70.96 |

Average efficiency (%) | 98.67 | 93.39 | 88.14 | 82.20 | 76.65 | 71.45 |

SOC (%) | R_{0} (mΩ) | R_{1} (mΩ) | C_{1} (F) | R_{2} (mΩ) | C_{2} (F) |
---|---|---|---|---|---|

92% | 0.77 | 0.001 | 24,234 | 0.029 | 56,345 |

83% | 0.69 | 0.003 | 24,453 | 0.027 | 56,342 |

74% | 0.65 | 0.005 | 24,534 | 0.025 | 56,837 |

65% | 0.61 | 0.008 | 24,636 | 0.022 | 56,839 |

56% | 0.6 | 0.012 | 24,355 | 0.019 | 56,946 |

47% | 0.59 | 0.017 | 24,627 | 0.02 | 56,932 |

38% | 0.6 | 0.024 | 24,743 | 0.025 | 56,156 |

29% | 0.61 | 0.03 | 24,864 | 0.035 | 56,926 |

20% | 0.64 | 0.035 | 24,652 | 0.045 | 56,426 |

11% | 0.7 | 0.04 | 24,865 | 0.055 | 56,826 |

1% | 0.81 | 0.045 | 24,764 | 0.065 | 56,832 |

Parameters | Total Values |
---|---|

PV | 2 MWp |

Lead-acid batteries (2 V 500 Ah for single) | 500 KWh |

Lead carbon batteries (2 V 500 Ah for single) | 500 KWh |

Max output power of the ESS | 1.2 MW |

Local load | 3 MW |

SVG | 500 KVA |

Parameters | Level 1 | Level 2 | Level 3 | Level 4 |
---|---|---|---|---|

voltage | 0.002 | 0.003 | 0.005 | 0.009 |

current | 4.224 | 3.765 | 6.333 | 6.917 |

Parameters | Total Values |
---|---|

PV | 102.3 KWp |

Lead carbon battery (2 V 500 Ah for single) | 210 KWh |

Max output power | 100 KW |

Local load | 103 KW |

Parameters | Level 1 | Level 2 | Level 3 | Level 4 |
---|---|---|---|---|

voltage | 0.0118 | 0.0161 | 0.0045 | 0.0118 |

current | 3.8457 | 4.2906 | 2.3466 | 3.8457 |

Parameters | Level 1 | Level 2 | Level 3 | Level 4 |
---|---|---|---|---|

voltage | 0.003 | 0.002 | 0.003 | 0.003 |

current | 0.763 | 1.166 | 1.508 | 0.763 |

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**MDPI and ACS Style**

Chen, Y.; Yang, Z.; Wang, Y.
SOC Estimation of Lead Carbon Batteries Based on the Operating Conditions of an Energy Storage System in a Microgrid System. *Energies* **2020**, *13*, 33.
https://doi.org/10.3390/en13010033

**AMA Style**

Chen Y, Yang Z, Wang Y.
SOC Estimation of Lead Carbon Batteries Based on the Operating Conditions of an Energy Storage System in a Microgrid System. *Energies*. 2020; 13(1):33.
https://doi.org/10.3390/en13010033

**Chicago/Turabian Style**

Chen, Yuanyuan, Zilong Yang, and Yibo Wang.
2020. "SOC Estimation of Lead Carbon Batteries Based on the Operating Conditions of an Energy Storage System in a Microgrid System" *Energies* 13, no. 1: 33.
https://doi.org/10.3390/en13010033