**2. Operational Modes for AC Current Injection**

AC current can be injected to a rechargeable battery on top of DC charging and discharging current. AC current can also be injected solely without DC current. The modes of AC current injection in a battery are expressed by (1).

$$I\_{out}(t) = I\_{bnt}(t) = \begin{cases} I\_{dc} + I\_m \sin(\omega t), & \text{if } \text{Mode 1} \\ 0 + I\_m \sin(\omega t), & \text{if } \text{Mode 2} \\ -I\_{dc} + I\_m \sin(\omega t), & \text{if } \text{Mode 3} \end{cases} \tag{1}$$

where, *t* is the time, *Ibat* is the battery current, *Idc* is the DC offset current, *Im* is the magnitude of AC signal, and *ω* is the angular frequency for AC signal. *Idc* is positive for mode 1 where AC current is injected to the battery while charging. *Idc* is negative for discharging condition. *Idc* is zero for offline AC injection. The waveforms of each mode of AC current injection are shown in Figure 2a. The existing methods available in the literature for AC current injection using power converters can operate in only one mode at a time. All three modes can be operated using proposed controller which is unique in this manuscript.

The voltage vs. current of a battery during different modes of operation shown in Figure 2b. The power converters output is bounded by the rated operating range of the battery (shaded in area in Figure 2b). The rated maximum and minimum operating voltage of a battery is *Vmax* and *Vmin*. The rated currents are *Imax* and *Imin*. The control range for different modes are also shaded and has dashed boundary line. The steady state operating conditions are within the control range and shown as tilted arrow lines. The tilted arrow indicates AC voltage and current for different modes. The magnitude of AC current in Figure 2b is corresponding to the magnitude of of current in Figure 2a. To perform all modes of operation, the power converter should be capable of operating within the right half plane of the power quadrant (two quadrant as in Figure 2b).

**Figure 2.** Modes of operation for AC current injector: (**a**) waveform of converter current and (**b**) operating conditions and control ranges.

#### **3. Topologies and Modulation**

An AC current injector for batteries was implemented using buck, synchronous buck, boost, and resonant power converters [1–4,7–10]. A synchronous buck converter for AC current injection to battery was used in this paper as shown in Figure 3. In addition, a technique is proposed to use H-bridge topology to inject AC current as shown in Figure 4. *Q*1, *Q*2, *Q*3, and *Q*<sup>4</sup> are SiC MOSFETs with anti-parallel diodes. An input network was used to deploy three modes of operation for the versatile control which consists of a DC voltage source *Vin*, a resistor *Rin*, and a capacitor *Cin*. *Iin* is input current which could have three parts *ivin*, *irin*, and *icin*. *S*<sup>1</sup> and *S*<sup>2</sup> are used to control the network as source and/or load which determines online charging/discharging mode or offline mode of operation for AC current injection. The AC injection modes and corresponding possible switch states are in Table 1.



**Figure 3.** AC injector using synchronous buck converter (2 MOSFTETs).

**Figure 4.** AC injector using H-bridge converter (4 MOSFTETs).
