## 4 Separated Phase-Current Control Using IBDGs  
The most common faults in a typical distribution system are unsymmetrical faults [24]. To maintain recloser-fuse coordination and regulate \(V_{dc}\) and the grid voltage during the occurrence of these unsymmetrical faults, separated phase-current control using IBDGs is proposed. Under separated phase-current controls, the current reference of the nonfaulty phase is not reliant on Equation (6) because the protective device in the nonfaulty phase is hardly affected by unsymmetrical faults. The current reference of each nonfaulty phase is mainly determined depending on \(V_{dc}\) and the voltage deviation in that phase. This action is to avoid excessive \(V_{dc}\) and regulate the grid voltage of each nonfaulty phase. Hence, to realize the separated phase-current control, the three-phase currents are controlled independently. The separated phase-current control is applied with four-leg IBDGs. The topology of the four-leg inverter is shown in Figure 2.  
The control diagram of the separated phase-current control for phase \(a\) is illustrated in Figure 3. Similarly, the separated phase-current controls for phases \(b\) and \(c\) are implemented in the same fashion. The separated phase-current control for phase \(a\) consists of the current reference generator, current controller, and fault detection (FD) module. The current reference generator includes three strategies, namely voltage control (VC), fault impact mitigation (FIM), and islanding strategies. The VC and FIM strategies are switched depending on the FIM signal resulting from the logical multiplication of the fault signal (FLT) and the SDG connection signal (CON). The FD module detects the fault by considering the transient monitoring function (TMF) [25]. If the \(d\)-axis voltage (\(V_{d}\)), which is computed by the terminal voltage, is below 0.9 per unit (pu), the current feedback is sent to the FD module. It is used for computing the TMF in the FD module. When the calculated TMF exceeds the predefined threshold, the fault is detected. Then, the FD module sends the fault signal to the current reference generator. Otherwise, the connection status of the SDG is recognized by considering the tripping signal sent by the SDG breaker \((\textit{trip}_{SDG})\). The tripping signal passes through the NOT gate before it reaches the current reference generator. While the SDG is connected to the grid, the NOT gate does not receive any tripping signal. Thus, there is a high signal produced by the NOT gate. This high signal is named the SDG connection signal. Figure 2: Four-leg inverter topology. When the AND gate of the current reference generator obtains both the fault signal and SDG connection signal, it generates the FIM signal. Then, the VC strategy is switched to the FIM strategy: On the other hand, the VC and FIM strategies are changed to the islanding strategy when the current reference generator receives the tripping signal sent from the recloser (\(\textit{trip}_{Re}\)). Teleprotection is applied for sending the tripping signal of the SDG breaker and recloser. Due to the smart grid communication, utilizing the teleprotection is feasible. For the nonfaulty phase, the FIM signal is not generated due to no fault signal being sent from the FD module. The VC strategy, therefore, is enabled. The VC strategy consists of the \(V_{dc}\) control, voltage regulator, current limiters, power factor (PF) limiter, voltage selector, and phase-locked-loop (PLL) control. The active current reference (\(I^{\prime}_{d-ref}\)) is provided by the \(V_{dc}\) control. To regulate \(V_{dc}\), a PI controller is simply adopted to compensate for the error between the DC-link voltage reference (\(V^{*}_{dc}\)) and the feedback [20]. The voltage regulation feature is performed by the voltage regulator. The voltage regulator gives the reactive current reference (\(I^{\prime}_{q-ref}\)) for regulating the grid voltage [26].