The electrical method deals with current and voltage. The chemical method deals with the change of constituent materials.

The electrochemical method, thus, can effectively explain simple phenomena via the relation of voltage, current, and chemistry.

Unfortunately, the electrochemical method cannot obtain enough information about a simple voltage–current relationship when it is applied to a battery that uses a complicated reaction. The complementary method needed is EIS. This method measures the voltage–current in response to frequency and analyzes the impedance [4][6][7].

2.2.1 EIS theory

When a small AC voltage signal (V) is injected into a battery, an AC current (I) is generated according to the battery’s internal impedance, which causes a phase difference in the AC current. This phase difference is called a “phase shift.” [8]

Impedance is represented by a complex number (R + jX). R represents the resistance component, and X represents the reactance component. Impedance, Z, is expressed as follows:

△Z=△V△I, R=sin⁡θ, X=cos⁡θ

(2)

The relationship between the sinusoidal voltage and the response current is shown in Figure 2[6].

Figure 2: 
Battery voltage and current waveforms

2.2.2 EIS graph

Figure 3 shows the internal impedance circuit of the battery and the EIS graph. R_s is the internal resistance of the battery. At high frequencies, C_p is shorted, and only R_s measured. As the aging process progresses, the value of R_s rises. This is used as a criterion for determining battery life. R_p is the ionization loss resistance caused by the current. C_p is a capacitor function created by the electric double layer between the electrode and the electrolyte. Because the voltage accumulates after a certain frequency, current can flow in R_p, and a value can be measured. The R_p value, according to the frequency, can be continually measured to observe the reaction rate according to the ionization loss. R_p and C_p are thus used to determine the SOC of the battery [4][8].

Figure 3: 
Impedance circuit and graph

Figure 4 shows the proposed AC-voltage injection circuit and offset-adjustment circuit for EIS. The AC voltage injection circuit injects AC voltage into the battery and measures the current. The shape of the push-pull circuit is modified. A PNP transistor uses three separately doped regions with two junctions: one N region sandwiched between two P regions. An NPN has one P region sandwiched between two N regions. A bipolar junction transmitter circuit is designed connecting a shunt resistor to one PNP and one NPN to measure the current.

Figure 4: 
AC injection and offset adjusting circuits for EIS

The existing push-pull circuit operates by injecting a single input signal that creates crossover distortion in the output AC voltage. A circuit is needed to offset this distortion. The circuit in the dotted rectangle of Fig. 3 is the proposed offset circuit. The frequency injected is input as micro AC signal, Amp_AC, superimposed on the BJT1_E terminal, which is the turn-on reference of Q1. Offset1 is added, so that BJT1_B is higher than BJT1_E from the turn-on voltage. Additionally, if Amp_AC is superimposed on the BJT2_E terminal, the turn-on reference of Q2 and BJT2_B is injected to the push-pull circuit by subtracting Offset2 from BJT2_E from the turn-on voltage. An AC voltage waveform without distortion is thus created.

The separated waveform is then input into the push-pull circuit to produce a distortion-free AC voltage waveform. Conventional crossover distortion phenomenon is proposed using a diode. However, for this paper, a sinusoidal AC voltage that does not become distorted waveform is output through the offset circuit.

Figure 5 presents an algorithm that measures the impedance of the battery running on the microcontroller unit (MCU). First, we check the battery voltage. If above 3.0 V, we stop charging and inject the first frequency of current into the battery from the MCU. When the frequency is injected, the voltage and current are measured after a slight delay.

Figure 5: 
Impedance Measurement Algorithm

The resistance component, R, and the reactance component, X, are obtained by measuring a change value of a current, a change value of a voltage, and a phase angle between the voltage and current. This angle is obtained by multiplying the applied frequency by the time difference between the points where the voltage and the current become zero, respectively.

If the initial X value of the reactance value is zero, it is calculated as R_s. If the resultant X value is 0, it is calculated as R_s + R_p. We repeat the above steps while decreasing the frequency one-by-one to continuously measure impedance. It is possible to analyze the battery life and state by expressing the value measured sequentially by the user in the frequency band specified by the impedance graph.

Figure 6 shows the experimental device, where the lithium polymer battery is charged by a direct-current power supply. An electronic load is used for discharging at a constant current. The battery model and specifications are shown in Figure 7 and Table 1, respectively.

Figure 6: 
Experimental device

Figure 7: 
Lithium Polymer battery

To measure R_s, the battery was charged by the MCU when the voltage reached 3.0 V and discharged when the voltage reached 4.2 V. After 100 charge/discharge cycles, the battery was measured using the EIS module. The charge amount of the battery was adjusted according to the SOC by the controller to examine the change of the value with respect to the charging state.

The circuits in Figure 4 were used to measure the AC voltage signal injected into the battery. Thus, the sinusoidal AC voltage signal without distortion is equal to that shown in Figure 8 (b). Distortion occurred in the range of + 0.04 V to -0.04 V, and the peak-to-peak deviation from the distorted waveform and the improved sinusoidal waveform was 0.08 V.

Figure 8: 
Waveform of injected AC Voltage (Ch 2: offset voltage, 3.5 V)

Figure 9 and Figure 10 show the changes in impedance when the frequency is changed from 5 kHz to 50 mHz to confirm the impedance characteristic theory mentioned in Section 2. [8] The left graph in Figure 9 displays the new battery, and the right side displays the battery after 500 rapid charge/discharge cycles.

Figure 9: 
Impedance change according to lifetime

Figure 10: 
Impedance change according to SOC

The R_s value is measured largely on the battery used for longer than the new battery. From this result, it can be seen that the value of R₁ gradually increases as the battery is used.

Figure 10 shows that R_p was measured to be larger at SOC 20% than at 100%. These results show that the value of R_p increased in accordance with the decrease of SOC. Therefore, as the value of R_p increases, the capacity decreases.