Analysis of battery lifetime based on the inverter driving pulse

2.1 Total harmonic distortion (THD)

THD is expressed as the sum of all harmonic components and the ratio of the fundamental frequency. THD represents the degree of distortion owing to harmonics mixed in the waveform; the more the harmonic components, the more distorted the shape of the sine wave.

THD (%) may be expressed as the following Equation (1).

• V₁, V₂ ~ V_n : Amplitudes of each harmonic from the fundamental wave

Harmonics appear in nonlinear loads, which are power conversion devices, such as inverters, and rectifiers, and occur during the energy conversion process.

This study controlled the magnitude of the harmonic wave by changing the dead time, as it has a nonlinear effect on the power current when operating an inverter that controls the induction motor.

2.2 Battery deterioration

Charging and discharging must be repeated to use the battery. As the battery is charged and discharged, it is degraded by internal chemical reactions, and its lifetime is reduced. The state of health (SOH) and state of charge (SOC) were identified to determine the degree of battery degradation.

SOH refers to the health state of the battery and is a value indicating the degree of degradation as the battery is frequently used.

It is feasible to determine the degree of degradation as the battery is used, and it is difficult to accurately measure the SOH; however, there is a method of estimation using several parameters. The deterioration state of the SOH can be estimated as shown in Equation (2) using the consumed amount of power [2][3][4].

• N : Number of charge/discharge cycles
• Q_new : Initial battery capacity
• P_b : Amount of power

SOC is a value that indicates the capacity of the remaining battery to be among the total capacities. SOC 100% means fully charged, and SOC 0% means that no battery remains. Accurate figures were obtained using a battery management system (BMS) to estimate the remaining SOC.

2.3 Impedance estimation using OCV

Figure 1 shows Randles' primary battery model, and Figure 2 shows the response of the battery terminal voltage to the charge/discharge current [5].

Figure 1:

Equivalent circuit of Randles' model

• R₁ : Battery IR
• R₂ : Ionization loss resistance.
• C : Double layer capacitance

Figure 2:

Estimation of battery resistance R1 and R2

• V_R1 = R₁ I
• V_R2 = R₂ I
• $$ V_e=R_{2}exp\left(-\frac{1}{R_2 C}t\right)$$

As illustrated in Figure 2, when the battery is connected to the load, the load current is divided by the voltage drop V_R1 owing to an instantaneous short circuit to calculate the IR R₁ of the battery, thereby confirming the battery lifetime [6][7].

The IR of a battery can be measured using a voltage difference in a state in which a DC load is instantaneously connected to a charged battery and a voltage in an open state, or using an electrochemical impedance spectroscopy (EIS) method. In general, the lifetime of a battery is predicted using this IR value, and it is known that, as the state of the battery degrades, the IR increases [8].

3.1 System configuration

A configuration diagram of the EV is shown in Figure 3. First, the IR value of the battery is estimated using the OCV technique. This value can be used to determine the change in the IR of the battery and to predict the degree of degradation and lifetime.

Figure 3:

Diagram of EV system

The THD is measured from the discharge current of the EV motor and compared with the estimated IR value of the battery. It checks the way the harmonic affects the battery lifetime.

The inverter includes a microprocessor (MCU), a gate driver, and an inverter circuit. The inverter control method is controlled by the spatial voltage vector, and the three-phase motor operates using a control algorithm. Space vector pulse width modulation (SVPWM) is a modulation technology that converts DC into AC and uses eight switching states in a three-phase two-level inverter to generate voltage space vectors on the space vector.

The case where the upper and lower semiconductors are operated according to the effective voltage vector U_eff is expressed as 1 and 0, respectively, depending on the eight switching states, as shown in Table 1. Depending on the phase, the three-phase a, b, and c operations show a sine wave graph with a difference of 120°and output voltage.

Table 1:

Ueff according to IGBT switching

The block diagram of space vector is illustrated in Figure 4 and if T_s is applied within one period through the command voltage U_out between the effective voltage vectors U₀ and U₆₀, U_out can be output, as shown in Equation (3) [9].

• U_out: Command voltage
• T_s: Time at which effective voltage vector U_eff is applied.

Figure 4 :

Block diagram of space vector

3.2 Experiment

Figure 5 shows an experimental device for vector control of an electric motor. The experimental device consisted of a battery, a microprocessor, a gate drive, and an inverter circuit. An inverter is a device that converts the DC output voltage supplied from a battery into AC output voltage and is amplified by a gate drive to input PWM pulses to the semiconductor devices up and down of the inverter to drive an electric motor. PWM pulses are applied to SW_a and $$ \overline{{SW}_a}$$ in Figure 3, where a section in which two pulses are not simultaneously applied is called dead time.

Figure 5 :

Experimental setup

Table 2:

Specifications of test equipment

The module is driven by inputting a source to the JTAG emulator (XDS 100S) of SyncWorks. The battery (PWS4S1P-2.6A) configuration involves four batteries connected in series, and the battery voltage is measured using an oscilloscope. The specifications of the lithium-ion battery are presented in Table 3.

Table 3:

Lithium-ion battery specifications

For the battery discharge operation test, a 14.8 V, 2,600 mAh module composed of four batteries was used, with a discharge time per time of 330 min, and an electron load was applied after discharge to measure the IR of the battery through the instantaneous discharge of 1 A constant current. For the discharge operation test, the electric motor connected to the inverter was subjected to a no-load operation of 0.2 A at 792 rpm, and the battery discharge capacity was 0.077 C-rate. The C-rate is represented as the charge/discharge current (A) for the rated capacity (Ah); a higher C-rate indicates that a higher current is consumed.

As a result of measuring IR, as shown in Figure 6, it can be observed that IR itself gradually increases. It can be observed that 0.0064 Ω increased as a result of charging and discharging six times compared to the first 0.1768 Ω. It was confirmed that the IR of the battery gradually increased because of internal degradation caused by charging and discharging the battery.

Figure 6 :

IR of battery after charging and discharging

As described in Section 2.1, after charging the battery, the IR of the battery is measured under no load, and the current harmonic characteristics are verified by operating an electric motor while changing the dead time to 0.5 μs and 3.5 μs, respectively.

To relatively compare the harmonic and internal resistance values according to the dead time, a value of 0.5 μs with the small dead time and a value of 3.5 μs with the large dead time were selected.

When the dead time is operated at 0.5 μs and 3.5 μs, the average values of the harmonics flowing through the motor are 13.5 ~ 18.9 %f and 19.5 ~ 28.9 %f, respectively, and it is found that the larger the dead time, the more the current harmonics are affected.

Figure 7 shows the IR fluctuation values measured while the dead time was operated at 0.5 μs and 3.5 μs, respectively. For the operation, the fluctuation value of the IR was measured after operating for 330 minutes every time over 7 times. The reason for comparing the data values with the fluctuation in IR is that the C-rate is too low to see the change in the IR itself, hence to obtain comparable data in a short time, the change in IR is measured immediately after charging and discharging the battery.

Figure 7:

IR fluctuation of battery according to dead time

In the case of 0.5 μs, it gradually increased from 0.008 Ω to 0.0112 Ω, and the average value was 0.0075 Ω. In addition, when it was 3.5 μs, it gradually decreased from 0.0152 Ω to 0.0136 Ω, and the average value was 0.0118 Ω.

Comparing the graph values when the dead time is 0.5 μs and 3.5 μs, it can be found that the larger the dead time, the greater the variation in the IR.

The fluctuation value of IR is very small. Comparing the cases of 0.5 μs and 3.5 μs, it can be observed that the overall trend of increase and decrease is similar, although there is a slight difference in values.

As the increase in the IR of the battery is a parameter that promotes the aging of the battery, it is predicted that the harmonic wave increases as the dead time increases and the battery ages more.

Author Contributions

Conceptualization, H. S. Kim and S. G. Lee; Methodology, H. S. Kim; Software, H. S. Kim; ; Formal Analysis, H. S. Kim; Investigation, S. G, Lee; Data Curation, H. S. Kim; Writing—Original Draft Preparation, H. S. Kim; Writing—Review & Editing, S. G. Lee; Visualization, H. S. Kim; Supervision, S. G. Lee; Project Administration, S. G. Lee; Funding Acquisition, S. G. Lee.