SOH is a percentage representation of the remaining lifetime of a battery and is used to estimate the battery lifetime. Based on the new battery, SOH is defined as 100 %, and when the battery capacity reaches 80 % of its initial capacity after continuous use, the battery has reached the end of its lifetime. In general, it is very difficult to accurately measure the level of aging. Equation (1) shows the method of estimating SOH using the amount of electric power [11][12][13].

where N is the number of charging and discharging cycles to end of lifetime (EOL), Q_new is the capacity of the initial battery, and P_b is the amount of power used.

Figure 1 shows Randles' primary battery model. Randles’ model consists of the battery internal resistance R₁, ionization loss resistance R₂ by charge/discharge currents, and double-layer capacitance C. The dynamic response of the battery terminal voltage to the charge/discharge current is shown in Figure 2, V_R1 =R₁I, V_R2 =R₂I, and the response formula is expressed as Vo =R₂ I exp⁡-1R2Ct [6][7].

Figure 1: 
Randles’ model of battery

Figure 2: 
A graph of R1, R2 estimation

When connecting loads, R₁ measures the voltage at the point where the voltage drop occurs for the first time and divides it by the current to obtain a resistance value, which is known to reduce battery lifetime with an increase in the internal resistance [14][15].

A lithium secondary battery can be charged and discharged several times, and its capacity refers to its energy storage capacity, which is defined as the total amount of discharged charges when discharged at a constant current from a fully charged state to a fully discharged state. A fully charged state (SOC 100 % state) is defined as a state in which no more current flows by charging at a constant voltage, and a fully discharged state (SOC 0 % state) is defined as a state in which all dischargeable charges are discharged within the range in which the battery is not damaged [13][16].

THD is an indicator of the degree of distortion of waveforms due to harmonics present in a signal and is defined as the ratio of the fundamental frequency to the sum of all harmonic components. The more harmonic components, the greater the THD value, the farther away the shape of the sinusoidal waveform. This means that there are relatively several harmonics compared to basic waves. If the amplitude of the fundamental wave (quantum of the input) in the output signal is V₁, the amplitudes of the harmonic waves are V₂ and V₃, respectively, and THD (%) is calculated using Equation (2).

Figure 3 shows the system configuration diagram. By measuring the voltage of the battery, the open-circuit voltage (OCV) can be calculated, and the internal resistance value of the battery can be estimated, which not only allows the battery to predict its life-time but also allows the time for replacement. In addition, the THD is measured using the discharge current of the battery, and the degree of battery aging owing to harmonic waves is predicted compared to the internal resistance value estimated from the voltage. The OCV of a battery is its electromotive force when it is not energized. This OCV depends on the SOC, which is the amount of charge. The voltage increases when the SOC increases, and the voltage decreases when the SOC decreases.

Figure 3: 
System configuration

An inverter is a device that produces an alternating current waveform used as an input power source for a ship’s propulsion motor from a direct current power source in the battery. It consists of a microprocessor (MPU), gate driver, and inverter circuit on the control board. In addition, semiconductor switching elements in the inverter must be driven to operate the alternator. These driving signals are produced by the space voltage vector PWM (Pulse width modulation) algorithm of the MPU, which determines the switching frequency and speed of the motor [17].

Consequently, the speed change of the motor changes the harmonic characteristics of the current flowing through the battery and motor, which eventually affects the internal resistance value and lifetime of the battery.

Figure 4 shows the SOH measuring process. After checking the current SOC, charging and discharging are started, and the battery’s voltage and current are measured for each sampling time after charging and discharging. Then, power is calculated from the obtained voltages and currents, which are used to calculate the energy capacity, SOH reduction, and SOH.

Figure 4: 
Flowchart for SOH measurement

Figure 5 shows a photograph of the equipment used in the driving experiment of an electric propulsion motor (TS4632N2050E510 from TAMAGAWA, 26 W 24 V, AC 3 phase PMSM). The control module used for the frequency control of the inverter (SyncWorks Co. SMC75EVM, DC 6.5∼9.0 V) consists of a microprocessor (TMS320F28335 from TI) and a gate driver. The space voltage vector PWM pulse created by the program is amplified by the gate driver to drive six semiconductor devices in each leg (SW_a, SW_b, SW_c) of the inverter. The control module was programmed with Syncworks JTAG, and the battery pack connected four Samsung ICR18650-26J batteries in series to the SMPS. The battery voltage was measured using a microprocessor by distributing the voltage to the resistor [18].

Figure 5: 
Experimental setup

Figure 6 shows the exterior of the lithium-ion battery used in the experiment, and its specifications are listed in Table 1. Prior to the experiment, the internal resistance was measured, the motor was operated for a certain period of time, and the internal resistance was measured again to compare the amount of change before and after the measurement.

Figure 6: 
Lithium-ion battery

Figure 7 shows a waveform measuring the THD for the battery output current when the motor rotates at low (594 rpm), medium (792 rpm), and variable speeds (792±198 rpm) under no-load conditions. Here, the variable speed is the speed with a deviation of ±198 rpm from the average speed of 792 rpm, which is an alternating output of 594 rpm and 990 rpm at regular intervals. As a result of the measurement, the THD values at low and medium speeds were approximately similar at 32.48%, and the THD values at varying speed rotations were measured in the range of 24% to 50% with a deviation of ±13% based on the average of 37%. The average THD value at variable speed operation is higher than that at low and medium speeds because the mechanical friction force generated when the speed is variable appears as a reverse electromotive force, which affects electrical noise.

Figure 7: 
THD waveforms of battery current according to speed change

Table 2 shows the change in SOH [%] and internal resistance [Ω] to the initial value according to the speed change of the motor. The measuring device included an oscilloscope WS3054 and an electronic load (LP900-A). As a result of measuring the SOH from the voltage and current of the battery, the SOH value decreased the most during variable speed operation. In addition, the amount of change in internal resistance was measured using the OCV technique, as shown in Figure 2. The initial internal resistance value was measured before the operation test, and the internal resistance value was measured again after the operation, and the variation was the largest for the variable speed, compared with the low and medium speeds [18].

This phenomenon is analyzed to promote the degradation or aging of the battery connected to the system by electrical noise of the system.