# Battery-SOC Estimation for Hybrid-Power UAVs Using Fast-OCV Curve with Unscented Kalman Filters

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## Abstract

**:**

## 1. Introduction

## 2. Model Selection, Testing Method, and Parameter Identification

#### 2.1. Equivalent Circuit Models

#### 2.2. Open-Circuit Voltage and Testing Method

#### 2.3. Parameter Identification

## 3. AUKF for SOC Estimation

#### 3.1. State Equation and Observation Equation for Thevenin Battery Model

#### 3.2. Adaptive Unscented Kalman Filter

- (1)
- State value and covariance initialization:

- (2)
- Sigma-point generation:

- (3)
- Coefficient calculation:

- (4)
- Process update for sigma points and covariance:

- (5)
- Kalman-gain calculation:

- (6)
- State and covariance update:

- (7)
- Adaptive noise estimation:

## 4. Experiments, Results, and Discussion

## 5. Conclusions

- (1)
- The “batch-mode” proposed was able to make good use of all the data sampled, with a much higher frequency than the parameter-updating task, and it demonstrated a good de-noising effect in the battery-parameter estimation. Combined with the limited-memory recursive least-square algorithm, successful parameter estimation was achieved.
- (2)
- The fast-OCV curve based on the Rint model was applied effectively for battery-SOC estimation. Compared with the traditionally obtained OCV curve, it even proved to offer much better accuracy in SOC estimation. Combined with an adaptive UKF, good accuracy in SOC estimation was achieved.
- (3)
- Compared with the traditional approach to OCV curve identification, the fast-OCV method is much more time-efficient, with a completely fluctuating charging-and-discharging process. As hybrid power for UAVs should be configured with low capacity (light batteries), the fast-OCV method is highly suitable for these situations.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**The key facilities used for signal sensing, testing-system control, and data sampling: (

**a**) current transducer LA 55-P/SP1 used for current sensing; (

**b**) STM32 Nucleo-144 boards F429ZI (MB1137) used for voltage sensing, data sampling, and system control.

**Figure 5.**The method for sensing current reported in this paper: (

**a**) operating principle of current transducer LA 55-P/SP1; (

**b**) the method of current measurement with shift current in this paper.

**Figure 6.**OCV obtained through direct measurement and dynamic current experiments (fast OCV) described in this paper.

**Figure 7.**Explanation of ${\mathrm{X}}_{\mathrm{t},\mathrm{i}}$ ${\mathrm{Y}}_{\mathrm{t},\mathrm{i}}$; sample time h and refresh time T.

**Figure 9.**Estimated parameters ${\mathrm{R}}_{0}$, ${\mathrm{R}}_{1}$, and ${\mathrm{C}}_{1}$ with Thevenin model.

**Figure 12.**Comparison of SOC estimation: fast OCV versus traditional OCV under continuous-discharge condition.

**Figure 13.**Comparison of SOC estimations: fast OCV versus traditional OCV under step-discharge conditions.

$\mathbf{Primary}\text{}\mathbf{Nominal}\text{}\mathbf{RMS}\text{}\mathbf{Current}\text{}\mathbf{(}{\mathbf{I}}_{\mathbf{p},\mathbf{N}}$) | $\mathbf{Primary}\text{}\mathbf{Current}\text{}$ $\mathbf{Measuring}\text{}\mathbf{Range}\text{}\mathbf{(}{\mathbf{I}}_{\mathbf{p},\mathbf{M}}$) | $\mathbf{Turns}\text{}\mathbf{Ratio}\text{}$ $\mathbf{(}{\mathbf{N}}_{\mathbf{p}}/{\mathbf{N}}_{\mathbf{s}}$) | $\mathbf{Supply}\text{}\mathbf{Voltage}\text{}$ $\mathbf{(}\pm 5\%\mathbf{)}\text{}\mathbf{(}{\mathbf{U}}_{\mathbf{C}}$) |
---|---|---|---|

50 A | 0~±100 A | 1:2000 | ±12~15 V |

$\mathbf{Measuring}\text{}\mathbf{Resistance}\text{}({\mathit{R}}_{\mathit{M}}$) | ||||
---|---|---|---|---|

Power Voltage | @TA = 70 °C | @TA = 85 °C | ||

${\mathit{R}}_{\mathit{M}}$ Min | ${\mathit{R}}_{\mathit{M}}$ Max | ${\mathit{R}}_{\mathit{M}}$ Min | ${\mathit{R}}_{\mathit{M}}$ Max | |

with ±12 V | 0 Ω | 215 Ω | 0 Ω | 210 Ω |

0 Ω | 35 Ω | 0 Ω | 30 Ω | |

with ±15 V | 0 Ω | 335 Ω | 30 Ω | 330 Ω |

0 Ω | 95 Ω | 30 Ω | 90 Ω |

$\mathbf{Error}\text{}@{\mathbf{I}}_{\mathbf{p}},{\mathit{T}}_{\mathit{A}}=25\text{}\xb0\mathrm{C}$ | Linearity Error | $\mathbf{Offset}\text{}\mathbf{Current}\text{}@{\mathbf{I}}_{\mathbf{p}}=0,{\mathit{T}}_{\mathit{A}}=25\text{}\xb0\mathrm{C}$ | $\mathbf{Delay}\text{}\mathbf{Time}\text{}@10\mathbf{\%}\text{}\mathbf{o}\mathbf{f}\text{}{\mathit{I}}_{\mathit{p},\mathit{N}}$ | $\mathbf{Delay}\text{}\mathbf{Time}\text{}\mathbf{to}\text{}90\%\text{}\mathbf{of}\text{}{\mathit{I}}_{\mathit{p},\mathit{N}}$^{(1)} | |
---|---|---|---|---|---|

@±15 V (±5%) | @±12~15 V (±5%) | <0.15% | within ±0.10 mA | <500 ns | <1 μs |

±0.65% | ±0.90% |

**Table 4.**Battery information and coefficients of ${\mathrm{R}}_{0}$ and $\mathrm{O}\mathrm{C}\mathrm{V}$ polynomials.

Coefficient | Value | Coefficient | Value | Coefficient | Value |
---|---|---|---|---|---|

${\mathrm{a}}_{0}$ | 0.18178 | ${\mathrm{a}}_{1}$ | −0.92811 | ${\mathrm{a}}_{2}$ | 3.6568 |

${\mathrm{a}}_{3}$ | −6.8357 | ${\mathrm{a}}_{4}$ | 5.9269 | ${\mathrm{a}}_{5}$ | −1.7057 |

${\mathrm{a}}_{6}$ | −0.22173 | ${\mathrm{b}}_{0}$ | 13.951 | ${\mathrm{b}}_{1}$ | 8.3961 |

${\mathrm{b}}_{2}$ | −18.459 | ${\mathrm{b}}_{3}$ | −4.6272 | ${\mathrm{b}}_{4}$ | 69.866 |

${\mathrm{b}}_{5}$ | −82.283 | ${\mathrm{b}}_{6}$ | 29.877 | ||

Battery information: Lipo, 4S1P, 14.8V,45C |

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## Share and Cite

**MDPI and ACS Style**

He, Z.; Martín Gómez, D.; de la Escalera Hueso, A.; Flores Peña, P.; Lu, X.; Armingol Moreno, J.M.
Battery-SOC Estimation for Hybrid-Power UAVs Using Fast-OCV Curve with Unscented Kalman Filters. *Sensors* **2023**, *23*, 6429.
https://doi.org/10.3390/s23146429

**AMA Style**

He Z, Martín Gómez D, de la Escalera Hueso A, Flores Peña P, Lu X, Armingol Moreno JM.
Battery-SOC Estimation for Hybrid-Power UAVs Using Fast-OCV Curve with Unscented Kalman Filters. *Sensors*. 2023; 23(14):6429.
https://doi.org/10.3390/s23146429

**Chicago/Turabian Style**

He, Zhuoyao, David Martín Gómez, Arturo de la Escalera Hueso, Pablo Flores Peña, Xingcai Lu, and José María Armingol Moreno.
2023. "Battery-SOC Estimation for Hybrid-Power UAVs Using Fast-OCV Curve with Unscented Kalman Filters" *Sensors* 23, no. 14: 6429.
https://doi.org/10.3390/s23146429