1. Introduction

2. Materials and Methods

2.1. Equivalent Circuit Model Background

The most widespread battery cell modeling technique that ensures a good trade-off between accuracy and computational complexity is the ECM [5,6]. This combination is a key element for reproducibility within effective BMS, in which high accuracy and minimum possible computational time must be ensured. ECM technique allows the representation of the complex internal electrochemical phenomena of the battery cell through an equivalent circuit of electrical components, namely a voltage source, a single resistor, and -n- parallel resistor-capacitor subcircuits, connected in series. The ECM order number -n- can vary to achieve the desired characteristics of each application, but in general, the second-order (n=2) ensures an effective balance between complexity and accuracy. The topology of a second-order equivalent electric circuit is presented in Figure 5.

Figure 1. Schematic representation of the topology of a second-order Equivalent Circuit Model.

Figure 1. Schematic representation of the topology of a second-order Equivalent Circuit Model.

The voltage source of the circuit is denoted as V_OC in the figure circuit and is named open-circuit voltage, whereas the voltage drop V₀ across the series resistance, which is denoted as R₀ in the circuit, represents the instantaneous voltage drop due to an applied current profile and the transient voltage drop V₁+V₂ across the 2 RC branches, which are denoted as R₁-C₁ and R₂-C₂ in the circuit, is captured by the 2 corresponding time constants introduced and is connected with diffusion effects. I_L is the current supplied by (positive) or injected to (negative) the battery cell through its terminals.

Characterization tests may include i) the capacity test, ii) the pulse discharge test, and iii) the hybrid pulse power characterization (HPPC) test. Voltage response is monitored, and the measurements are utilized for parameter fitting. A detailed description of the implementation of the parameter extraction process through experimental measurements has been given in [13]. Tran et al. [14] have recently published the parameter datasets extracted from measurements of four different lithium-ion battery chemistry types. These chemistry types classified by the positive electrode material, are lithium iron phosphate (LFP), lithium manganese oxide (LMO), lithium nickel cobalt aluminum oxide (NCA), and lithium nickel manganese cobalt oxide (NMC). The authors have also proceeded to the validation of the battery model for each chemistry type through 2 different applied current profiles. The extracted OCV-SOC curves and the parameter lookup tables for each lithium-ion battery chemistry are retrieved from this source and are reproduced in the current study. An important aspect is that these cells refer to 4 chemistry types of battery cells that are commonly used in EV battery applications. This is an important aspect for the reproduction of the model developed in this research work for a wide range of applications with different operating requirements (e.g. high-power or high-energy battery cells could be selected depending on the application).

The specifications of the four cells are listed in Table 3.

Table 3. Cell specifications for each chemistry type [14].

Table 3. Cell specifications for each chemistry type [14].

Chemistry	Manufacturer	Cell name	Nominal capacity (mAh)	Nominal voltage (V)	Voltage range (V)
LMO	EFEST	IMR18650V1	2600	3.70	2.50–4.20
LFP	K2 Energy Solutions, Inc.	LFP26650P	2600	3.20	2.00–3.65
NMC	Samsung SDI	INR18650-20S	2000	3.60	2.50–4.20
NCA	Panasonic	NCR18650B	3200	3.60	2.50–4.20

The equation set of the second-order ECM is as follows:

$$\mathrm{SoC}=\mathrm{SoC}\left(0\right)-\frac{{\int }_0^{\mathrm{t}}{\mathrm{I}}_{\mathrm{L}}\mathrm{dt}}{{\mathrm{C}}_{\mathrm{available}}},$$

(1)

$${\mathrm{V}}_{\mathrm{s}}={\mathrm{I}}_{\mathrm{L}}\text{⋅}{\mathrm{R}}_{\mathrm{s}},$$

(2)

$${\mathrm{I}}_{{\mathrm{C}}_1}={\mathrm{C}}_1\text{⋅}\frac{{\mathrm{dV}}_1}{\mathrm{dt}},$$

(3)

$${\mathrm{I}}_{{\mathrm{C}}_2}={\mathrm{C}}_2\text{⋅}\frac{{\mathrm{dV}}_2}{\mathrm{dt}},$$

(4)

$${\mathrm{V}}_{\mathrm{OC}}=\mathrm{f}\left(\mathrm{SoC},\mathrm{T}\right),$$

(5)

$${\mathrm{R}}_{\mathrm{s}}=\mathrm{f}\left(\mathrm{SoC},\mathrm{T}\right),$$

(6)

$${\mathrm{R}}_1=\mathrm{f}\left(\mathrm{SoC},\mathrm{T}\right),$$

(7)

$${\mathrm{C}}_1=\mathrm{f}\left(\mathrm{SoC},\mathrm{T}\right),$$

(8)

$${\mathrm{R}}_2=\mathrm{f}\left(\mathrm{SoC},\mathrm{T}\right),$$

(9)

$${\mathrm{C}}_2=\mathrm{f}\left(\mathrm{SoC},\mathrm{T}\right),$$

(10)

$${\mathrm{V}}_{\mathrm{t}}={\mathrm{V}}_{\mathrm{OC}}-{\mathrm{V}}_{\mathrm{s}}-{\mathrm{V}}_1-{\mathrm{V}}_2,$$

(11)

3. Results

5. Conclusions

References

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