# Online Reliable Peak Charge/Discharge Power Estimation of Series-Connected Lithium-Ion Battery Packs

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## Abstract

**:**

## 1. Introduction

## 2. Power Estimation for One Single Battery Cell

#### 2.1. Lumped Parameter Battery Model

_{OC}represents the open circuit voltage (OCV) which relates with SOC directly. R

_{O}is the ohmic resistance, and R

_{TH}and C

_{TH}are the impedance parameters normally corresponding to charge transfer and double layer capacitor effects. U

_{B}and U

_{TH}are the terminal voltage and the voltage on C

_{TH}respectively, I

_{B}is the working current. All parameters (R

_{O}, R

_{TH}and C

_{TH}) change with different temperatures, SOC and SOH of the battery.

#### 2.2. Online Model Parameter Identification

#### 2.3. Power Estimation

_{max}and U

_{min}are the allowed maximum and minimum voltages of the battery, I

_{min}is the maximum charge current and I

_{max}is the maximum discharge current, k is the sampling point, and Δt is the sampling period.

_{min,batt}and I

_{max,batt}are the permitted maximum charge and discharge currents suggested by the battery suppliers. Then, the peak power estimation of the battery can be obtained by:

## 3. Power Prediction of Series-Connected Battery Packs

#### 3.1. Improved Parameter Identification for Series Connected Battery Systems

_{O}

_{1}, R

_{HT}

_{1}, C

_{TH}

_{1}, and R

_{O}

_{2}, R

_{TH}

_{2}, C

_{TH}

_{2}. A battery cell, called “mean cell”, with the mean characteristics of the two individual cells is constructed; the impedance parameters of the mean cell are R

_{Om}, R

_{THm}, C

_{THm}. With the fabricated mean cell, the battery pack can be considered to be composed of two same mean cells, and the system is shown in Figure 3.

_{O}

_{1}and U

_{O}

_{2}are the voltages of R

_{O}

_{1}and R

_{O}

_{2}under current I (shown in Figure 1). Then, theoretically, vector A can be determined with:

_{O}

_{1}, U

_{O}

_{2}and U

_{Om}online because they cannot be directly measured, thus it is difficult to get the value of A with Equation (14). However, according to the model shown in Figure 1, we can find that, if the current changes suddenly, R

_{O}will cause a sudden voltage change. Based on this analysis, we can determine A with the sudden voltage changes of each individual cell and the mean cell, as shown in Equation (15), where ΔU

_{s}

_{1}, ΔU

_{s}

_{2}and ΔU

_{sm}are the sudden voltage changes of the cells respectively.

_{O}for the cells in this case are shown in Figure 4b. We can find, from Figure 4, that the sudden voltage change ratio of the cells is very close to the R

_{O}ratio of the cells (in this case, the ratio is close to 1.05), which proves that Equation (15) can be used to determine vector A.

_{TH}C

_{TH}network is much larger than the sampling period (generally several or tens of mini seconds), thus:

_{d}is the dynamic voltage response caused by the impedance, and can be calculated by Equation (2).

_{m}, we can get τ

_{1}and τ

_{2}with Equation (22), then with Equations (25) and (26), we can finally determine vector C, as shown in Figure 5.

_{A}is an adjustment gain for vector A.

_{B}and g

_{C}are the adjustment gains for vectors B and C respectively.

#### 3.2. Power Estimation Considering Cell Difference

## 4. Case Study

#### 4.1. Experimental Setups

#### 4.2. Results and Discussions

_{max}and U

_{min}. Generally, the difference between the OCV and U

_{min}is much larger than the difference between the OCV and U

_{max}, especially when the battery works in a middle SOC range, which makes the charging power capability smaller than the discharging power capability.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

U_{B} | Battery terminal voltage |

U_{OC} | Battery open circuit voltage |

I_{B} | Battery working current |

R_{O} | Ohmic resistance of the battery |

U_{TH} | Voltage on network describing the charge transfer effect |

R_{TH} | Resistance of charge transfer |

C_{TH} | Double layer capacitor |

U_{d} | Dynamic voltage on the impedance under current excitation |

Δt | Sampling period |

k | Sampling point |

θ | Parameter vector of the battery model |

U_{max} | Allowed maximum voltage of the battery |

U_{min} | Allowed minimum voltage of the battery |

I_{max,batt} | Allowed maximum discharge current of the battery suggested by the battery suppliers |

I_{min,batt} | Allowed maximum charge current of the battery suggested by the battery suppliers |

I_{max,volt} | Allowed maximum discharge current of the battery limited by voltage |

I_{min,volt} | Allowed maximum charge current of the battery limited by voltage |

R_{Om} | Ohmic resistance of the mean battery cell |

R_{THm} | Charge transfer resistance of the mean battery cell |

C_{THm} | Equivalent capacitor of charge transfer effect of the mean battery cell |

U_{O} | Voltage on the ohmic resistance under current excitation |

ΔU_{sm} | Sudden voltage change during current pulse of the mean battery cell |

ΔU_{s} | Sudden voltage change during current pulse of the battery |

A | Vector reflecting the difference of ohmic resistance |

B | Vector reflecting the difference of time constant of charge transfer effect |

C | Vector reflecting the difference of charge transfer resistance |

$\Delta {U}_{s}^{pre}$ | Predicted sudden voltage change during current pulse |

N | Number of the battery cells connected in series |

g_{A} | Adjustment gain for vector A |

g_{B} | Adjustment gain for vector B |

g_{C} | Adjustment gain for vector C |

P_{sysmin} | Maximum charge power of the battery system |

P_{sysmax} | Maximum discharge power of the battery system |

${K}_{\mathsf{\tau},k}^{pre}$ | Predicted ratio of the charge transfer voltages at sampling point k |

${K}_{\mathsf{\tau}}$ | Ratio of charge transfer voltages |

${K}_{RTH}$ | Ratio of the charge transfer resistance |

${K}_{RTH,k}^{pre}$ | Predicted ratio of the charge transfer resistance at sampling point |

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**Figure 2.**Peak power estimation of a single battery cell. SOC: state of charge; and OCV: open circuit voltage.

**Figure 4.**Voltage and ohmic resistance of the two cells: (

**a**) voltage of the two cells; and (

**b**) ohmic resistance of the two cells.

**Figure 6.**Power estimation of the battery pack consisting of series-connect battery cells considering cell difference.

**Figure 7.**Current profiles of the tests: (

**a**) current profile of the J1015 cycle test; (

**b**) current profile of the New European Driving Cycle (NEDC) cycle test; and (

**c**) current profile of the Federal Test Procedure-75 (FTP-75) cycle test.

**Figure 9.**Identified parameters under the NEDC cycle test: (

**a**) R

_{O}identified by the repetitive recursive least squares (RLS); (

**b**) R

_{O}identified by the proposed new method; (

**c**) R

_{TH}identified by the repetitive RLS; (

**d**) R

_{TH}identified by the proposed new method; (

**e**) C

_{TH}identified by the repetitive RLS; and (

**f**) C

_{TH}identified by the proposed new method.

**Figure 10.**Identified parameters under the J1015 cycle test: (

**a**) R

_{O}identified by the repetitive RLS; (

**b**) R

_{O}identified by the proposed new method; (

**c**) R

_{TH}identified by the repetitive RLS; (

**d**) R

_{TH}identified by the proposed new method; (

**e**) C

_{TH}identified by the repetitive RLS; and (

**f**) C

_{TH}identified by the proposed new method.

**Figure 11.**Identified parameters under the FTP-75 cycle test: (

**a**) R

_{O}identified by the repetitive RLS; (

**b**) R

_{O}identified by the proposed new method; (

**c**) R

_{TH}identified by the repetitive RLS; (

**d**) R

_{TH}identified by the proposed new method; (

**e**) C

_{TH}identified by the repetitive RLS; and (

**f**) C

_{TH}identified by the proposed new method.

**Figure 12.**Power estimation results under the NEDC cycle test: (

**a**) 1 s discharge power estimation result; (

**b**) 1 s charge power estimation result; (

**c**) 10 s discharge power estimation result; (

**d**) 10 s charge power estimation result; (

**e**) 30 s discharge power estimation result; and (

**f**) 30 s charge power estimation result.

**Figure 13.**Power estimation results under the FTP75 cycle test: (

**a**) 1 s discharge power estimation result; (

**b**) 1 s charge power estimation result; (

**c**) 10 s discharge power estimation result; (

**d**) 10 s charge power estimation result; (

**e**) 30 s discharge power estimation result; and (

**f**) 30 s charge power estimation result.

No. | Parameter | Value |
---|---|---|

1 | Nominal capacity (Ah) | 80 |

2 | Nominal voltage (V) | 3.7 |

3 | Discharge cut-off voltage (V) | 2.8 |

4 | Charge cut-off voltage (V) | 4.2 |

5 | Allowed maximum 30 s pulse discharge current (15%–85% SOC) (A) | 480 |

6 | Allowed maximum 30 s pulse charge current (15%–85% SOC) (A) | 240 |

Test Cycles | Computation time of the RLS (s) | Computation Time of the New Method (s) | Time Reduced (%) |
---|---|---|---|

J1015 | 1.46 | 0.67 | 54.1 |

NEDC | 2.74 | 1.28 | 53.2 |

FTP75 | 5.71 | 2.66 | 53.4 |

© 2017 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**

Jiang, B.; Dai, H.; Wei, X.; Zhu, L.; Sun, Z. Online Reliable Peak Charge/Discharge Power Estimation of Series-Connected Lithium-Ion Battery Packs. *Energies* **2017**, *10*, 390.
https://doi.org/10.3390/en10030390

**AMA Style**

Jiang B, Dai H, Wei X, Zhu L, Sun Z. Online Reliable Peak Charge/Discharge Power Estimation of Series-Connected Lithium-Ion Battery Packs. *Energies*. 2017; 10(3):390.
https://doi.org/10.3390/en10030390

**Chicago/Turabian Style**

Jiang, Bo, Haifeng Dai, Xuezhe Wei, Letao Zhu, and Zechang Sun. 2017. "Online Reliable Peak Charge/Discharge Power Estimation of Series-Connected Lithium-Ion Battery Packs" *Energies* 10, no. 3: 390.
https://doi.org/10.3390/en10030390