# 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

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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