## 3 Proposed Current Detection Schemes with Reduced Sensors
### Sensors-Based Current Detection Scheme for EMSRM  
Based on the phase grouping principle, the lower dc bus of the AHBC is split into \(N_{\rm p}/2+1\) buses including a demagnetization bus for all phases, as well as \(N_{\rm p}/2\) buses for excitation and freewheeling, each of which is shared by a phase group. At any time, the demagnetization current of any phase can only flow through the demagnetization bus, and only one phase current in excitation mode or freewheeling mode II will flow through the excitation and freewheeling bus. Therefore, the current through each excitation and freewheeling bus and thus the current of each phase in the corresponding group can be detected by a single current sensor. Take the four-phase SRM for example again, the modified converter is shown in Figure 4, where phases A and C share the excitation and freewheeling bus I while phases B and D share the excitation and freewheeling bus II. The converter for phases A and C is independent of that for phases B and D. In the expected conduction region (ECR) of phase C, power switches S\({}_{1}\) and S\({}_{2}\) for phase A are both turned off. Whether the turn-off is advanced enough to force the phase A current to zero before the region, the bus I is occupied by phase C exclusively in the region, and thus the phase C current can be detected by the sensor HS\({}_{1}\) with the lower switch S\({}_{6}\) on. Possible current paths through the bus I in the ECR of phase C are shown in Figure 5, from which we can see that the possible residual current of phase A will not flow through the bus I and affect the phase C current sampling. Thus, currents of phases A and C can be completely detected by a single sensor. Similarly, currents of phases B and D can be measured by HS\({}_{2}\). The measured currents can be expressed as  
\[ \begin{cases}i_{\rm{HS1}}=DS_{2}\cdot i_{\rm{A}}&\theta\in R_{\rm{con,A}}^{*}\\ i_{\rm{HS1}}=DS_{6}\cdot i_{\rm{C}}&\theta\in R_{\rm{con,C}}^{*}\\ i_{\rm{HS2}}=DS_{4}\cdot i_{\rm{B}}&\theta\in R_{\rm{con,B}}^{*}\\ i_{\rm{HS2}}=DS_{8}\cdot i_{\rm{D}}&\theta\in R_{\rm{con,D}}^{*}\end{cases}  \tag{7}\]  
where \(R_{\rm{con,A}}^{*}\), \(R_{\rm{con,B}}^{*}\), \(R_{\rm{con,C}}^{*}\) and \(R_{\rm{con,D}}^{*}\) denote the ECRs of phases A, B, C, and D, respectively, \(DS_{1}\), \(DS_{2}\), \(DS_{3}\), and \(DS_{4}\) denote the drive signals of the power switches S\({}_{1}\), S\({}_{2}\), S\({}_{3}\), and S\({}_{4}\), respectively, and the signal values of 1 and 0 indicate the on and off states of  
Figure 4: Modified AHBC with two current sensors for the four-phase SRM. Figure 5: Possible current paths through bus I in the expected conduction region of phase C. (**a**) Phase C in excitation mode. (**b**) Phase C in freewheeling mode I.  
the corresponding switch, respectively. The phase currents at sampling points can be obtained by  
\[ \begin{cases}i_{\text{AS}}[k]=&i_{\text{HS1}}\quad\theta\in R_{\text{con,A}}^{*} \\ i_{\text{BS}}[k]=&i_{\text{HS2}}\quad\theta\in R_{\text{con,B}}^{*}\\ i_{\text{CS}}[k]=&i_{\text{HS1}}\quad\theta\in R_{\text{con,C}}^{*}\\ i_{\text{DS}}[k]=&i_{\text{HS2}}\quad\theta\in R_{\text{con,D}}^{*}\end{cases}  \tag{8}\]  
if the samplings are conducted with the corresponding switches turned on. In (8), \(k\) denotes the number of the sampling step. Considering that the current through the bus I or II always flows towards the ground of the power supply, the bus currents could also be detected by using shunt resistors with non-isolated single-supply non-inverting amplifiers as shown in Figure 6. The current detection with shunt resistors is much more cost-effective than that with the hall effect sensors. The actual conduction region (ACR) of each phase includes the ECR and the demagnetization region after the ECR. One may note that if the ACR can be guaranteed to be smaller than \(\tau_{\text{r}}/2\), the phase currents in the four operation modes can all be detected by directly passing the phase conductor through the hall effect sensor without splitting the lower dc bus.