Harmonic electricity is a wave of current or voltage with frequencies that are multiples of the fundamental frequency. In some countries, the regulated fundamental frequency can be 50 Hz or 60 Hz. If the fundamental frequency is 50 Hz, the second harmonic is 100 Hz, and the third harmonic is 150 Hz. Typical harmonic waves are shown in Figure 1 with a fundamental wave. The state of harmonics can be expressed using many methods, but usually through the Total Harmonic Distortion (THD) parameters.

Figure 1: 
Fundamental wave and harmonics

THD is a measure of harmonic distortion in a signal and is defined as the total power ratio of all harmonic components to the power of the fundamental frequency. THD provides information on stability and evaluates the quality of an electrical system.

The THD helps determine the degree of distortion owing to triangular, square, and sawtooth waves mixed in the shape of a desirable sine wave. Harmonics only provide energy sources, and the components produce any frequency. When the THD factor was minimized, the system output exhibited less noise or distortion. Thus, the THD must be maintained as low as possible.

THD(%) was calculated using the following Equation (1) [8]:

V₁, V₂ ~ V_n are the root-mean-square magnitudes of each harmonic from the fundamental wave and n is the harmonic number. V₁ is the magnitude of the fundamental wave.

Undesirable harmonics exist in nonlinear loads, which consist of power conversion devices such as variable frequency drivers (VFD), UPSs, rectifiers, and motor generators, and occur during the energy conversion process.

This paper presents the variation in the magnitude of THD by changing the PWM methods used in vector control modulation. We can consider the effect of the harmonic components on the power current when operating a variable-frequency driver to control a three-phase motor.

In a battery management system, SOC estimation is important for analyzing the internal resistance of the battery. Internal resistance is one of the main causes of aging and affects the battery lifetime. Many methods are used for the estimation, such as the Coulomb counting method (CCM), model-based estimator, and open circuit voltage (OCV) [9]. In the CCM, the SOC is given by the remaining available capacity. However, using the offline OCV method, the exact SOC data obtained consist of the internal resistor in the battery. Therefore, an offline OCV method was used in this study. The OCV of a battery is the electrical disproportion between the positive and negative terminals when the battery is disconnected from any load. This implies that no current flows between the two terminals of the battery. Therefore, the OCV can be analyzed using Randles' primary battery model [10].

The Randles primary battery model is expressed in Figure 2. Figure 3 shows a graph of the battery terminal voltage when the battery performs a charge/discharge current.

Figure 2: 
Equivalent circuit of Randles model and load

R₁: Battery IRR₂: Ionization loss resistanceC: Double-layer capacitance

Figure 3: 
Estimation of battery resistance R₁ and R₂

V_R1= R₁ IV_R2= R₂ I

Ve=R2exp-1R2Ct

(2)

The Randles’ primary battery model is illustrated in Figure 2. A battery is represented by a resistor R₁ (IR) and serially connects to a circuit consisting of capacitor C that is parallel to another resistor R₂.

Figure 3 shows the battery voltage state when the battery is connected to an electronic load and discharged at a constant current, as represented by Equation (2). When the battery was connected to an electronic load, the double-layer capacitance is shorted, resulting in an R₂ of zero.

Therefore, the float voltage of the battery momentarily drops to the V_R2 value, the internal resistance (IR) is calculated by dividing the voltage drop V_R1 by the load current 1A, and the life of the battery is checked by measuring the change in IR after the load experiment [11][12].

Figure 4 shows a typical configuration of the electric vehicle. Through Figure 4, the battery provides power to the inverter to control the three-phase motor. The IR 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 predict the degree of degradation and lifetime.

Figure 4: 
Diagram of electrical propulsion system

A device was used to measure the THD during the discharge process of the EV motor. Thus, the THD can be easily confirmed to compare and check how the harmonics affect the IR and battery lifetimes.

The inverter consists of a microcontroller (MCU), gate driver, and feedback system as current and speed sensors. The three-phase inverter control method is the PMSM Vector Control Technique. Typically, the method utilized is a Voltage Vector Control technology based on PMSM vector control techniques to convert DC into AC [13]. The operating status includes eight switching states for generating voltage space vectors based on the space vector in a three-phase two-level inverter.

The output voltages of the eight switching states of the inverter are presented as a vector diagram, and a regular hexagon is formed, as shown in Figure 5, From the voltage vector V(1) to V(6), the maximum output of the inverter is at the top of the hexagon. Any voltage output V_out in the hexagon can be calculated using three stationary vectors corresponding to the side of the triangle divided by the hexagon and one zero vector. The dwell times for any stationary vector are the duty cycle times of the selected switches during the sampling period T_S. Hence, the duty cycle time of the chosen switches can be determined using Equation (3), (4), and (5).

• V_ref : Reference voltage
• V_d : DC voltage
• T_s : Sampling period

Figure 5: 
Block diagram of space vector

With the calculated dwell time and space vectors selected, the table of the switching times for V_ref was presented as Table 1 and Table 2.

Table 1 lists the switching times for V_ref with three-phase symmetrical modulation. Table 2 lists the switching times for V_ref with three-phase asymmetrical modulation. The switching sequence for V_ref with the three-phase symmetrical modulation of sector 1 is illustrated in Figure 6 (a). The switching sequence for V_ref with the three-phase asymmetrical modulation of Sector 1 is shown in Figure 6(b) [14].

Figure 6: 
Pulse width of Sector 1 in (a) symmetrical modulation and (b) asymmetrical modulation

The experimental device includes a 4-pack li-ion battery, microcontroller, switching gate drive, three-phase inverter circuit with a permanent magnet synchronous motor (PMSM), current sensors, and voltage sensors, as shown in Figure 7. The three-phase inverter consists of six IGBTs and takes on the role of converting the DC voltage of the 4-pack li-ion battery into AC output voltage to supply electric power for the PMSM. Switching the IGBTs PWM pulses to the output of the microcontroller was amplified through isolated gate drivers. The PWM pulses were generated using the two types of space vector algorithms proposed in Section 3.1.

Figure 7: 
Experimental devices

The module was controlled by interfacing it with a computer through the Sync works JTAG emulator (XDS 300S). The Li-ion battery pack consisted of four batteries connected in series, and the battery voltage and current were measured using an oscilloscope. The harmonic level was analyzed by collecting the parameter data of the output current using MATLAB Simulink. The lithium-ion battery pack characteristics are listed in Table 3.

To perform the discharging operation test for the battery, a 14.8 V, 2,600 mAh module composed of four batteries was utilized. The battery pack was discharged continuously for 360 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 PMSM connected to a three-phase inverter was rotated under no-load conditions. The three–phase inverter was set to operate commonly with 4.85 to 4.9 watts in all the proposed methods.

Figure 8 shows the phase current measured at the motor terminal. Figure 8 (a) shows the measured phase current of the motor when operated with symmetrical modulation. Figure 8 (b) shows the measured phase current of the motor in the asymmetrical modulation. The phase current of the motor created by the asymmetrical modulation was distorted and included sharper noise current peaks than the phase current of the motor when operating with symmetrical modulation.

Figure 8: 
Output AC current of inverter with (a) symmetrical modulation and (b) asymmetrical modulation

When the motor was driven with symmetrical modulation, the measured total value of the harmonic flowing through the motor was 11.99% as shown in Figure 9 (a). However, when the motor was driven with asymmetrical modulation, the measured total values of the harmonic increased highly in the range of 15.77%, as shown in Figure 9 (b). It was found that the current harmonics varied depending on the PWM method. Generally, The asymmetric method is known to have a relatively large number of low-order harmonics due to the reduced switching frequency, as the phase voltage waveform has a square wave shape compared to the symmetric method.

Figure 9: 
Output AC current THD% of inverter with (a) symmetrical modulation and (b) asymmetrical modulation

Figures 10 (a) and (b) show the output DC of the battery at the front end of the inverter. Figure 10 (a) shows the symmetric modulation, Figure 10 (b) shows the asymmetric modulation, and the harmonic modulation is larger in asymmetric modulation. The switching noise at the inverter power end affected the input side, thereby affecting the internal resistance of the battery.

Figure 10: 
DC current in the inverter input with (a) symmetrical modulation and (b) asymmetrical modulation

Figure 11 shows a graph measuring the changes in the internal resistance of the battery before and after operation and performing symmetric and asymmetric modulation switching control of the inverter.

Figure 11: 
IR fluctuation of the battery according to symmetrical and asymmetrical modulation

The driving time was 360 min, and seven operations were performed. The graph shows that in comparison with the symmetric modulation method, the asymmetric switching control increases the change in the internal resistance of the battery.

The average value of the internal resistance change during symmetric modulation is 0.00937 ohms, and 0.00651 ohms for asymmetric modulation; the difference between the two values is 0.00286 ohms. This phenomenon is considered to have degraded the integrity of the battery owing to the harmonic distortion of the inverter input.