# A Novel Energy Optimization Control Strategy for Electric Drive System Based on Current Angle
## 3 Efficiency Optimization Control Based on Current Angle Look-Up Table
### Study on the Effect of Current Angle on EDS Efficiency  
According to Section 2, the inverter and PMSM modules have been modeled. On this basis, this paper established an optimization model with \(\beta\) as the control parameter based on the traditional field-oriented control (FOC) block diagram [35; 36] in MATLAB/Simulink, as illustrated in Figure 6. When the motor load torque and speed are given, by changing \(\beta\) (the red input in Figure 6), the motor speed loop PI controller will automatically adjust the stator current \(i_{s}\), and generate \(i_{d}\) and \(i_{q}\) through the two current loop PI controllers, so as to make the motor reach the given working condition. It should be noted that when using this optimization method for efficiency optimization, \(i_{s}\) can be limited within the current limit circle directly by the limiting module after speed loop PI controller, and the voltage can also be limited within the voltage limit circle by the limiting module after the current loop PI controller [37]. Therefore, no additional calculation formula is needed during optimization. To study and verify the effectiveness of \(\beta\) on EDS efficiency optimization, five groups of EDS target working conditions were selected in this paper, namely 1000 rpm/50 Nm, 2000 rpm/50 Nm, 3000 rpm/50 Nm, 4000 rpm/50 Nm, and 5000 rpm/50 Nm, respectively. Then, by changing the value of input \(\beta\) from 0.25\(\pi\) to 0.5\(\pi\) gradually, PMSM controller will automatically control the EDS to reach the target working conditions. Subsequently, the EDS steady-state efficiency, stator current \(i_{s}\), and various losses under different \(\beta\) were obtained, as shown in Figure 7.  
Figure 6: Schematic diagram of current angle \(\beta\) optimization model proposed in this paper. The left side of Figure 7 shows the EDS efficiency and \(i_{s}\) change in different \(\beta\). The left Y-axis represents the EDS efficiency, and the right Y-axis represents the stator current \(i_{s}\). From the efficiency  
Figure 7: Efficiency, \(i_{s}\), and various losses of EDS under different \(\beta\) at 1000 rpm/50 Nm (**a**); efficiency, \(i_{s}\), and various losses of EDS under different \(\beta\) at 2000 rpm/50 Nm (**b**); efficiency, \(i_{s}\), and various losses of EDS under different \(\beta\) at 3000 rpm/50 Nm (**c**); efficiency, \(i_{s}\), and various losses of EDS under different \(\beta\) at 4000 rpm/50 Nm (**d**); efficiency, \(i_{s}\), and various losses of EDS under different \(\beta\) at 5000 rpm/50 Nm (**e**). curve, it can be seen from the efficiency curve that the increase of \(i_{s}\) will not always reduce the EDS efficiency. This is because with the decrease of \(\beta\) and the increase of \(i_{s}\), copper loss, iron loss, and inverter loss change nonlinearly. There is a trough in the sum of the three losses, which means that there will be a certain set of \(\beta\) and \(i_{s}\) to minimize the total loss of EDS. In other words, EDS has the highest efficiency at a certain set of \(\beta\) and \(i_{s}\). This can be found in the right side of Figure 7a-e. As Figure 7a-e shows, as the working point of the motor moved from the region before the base speed to the region of flux weakening region continuously, the arc top of the efficiency curve was moved to the left continuously, and the optimal value of \(\beta\) decreased continuously. It should be mentioned that in the region before the base speed, the change of \(\beta\) had a great influence on the EDS efficiency. For example, in Figure 7a, the efficiency was 66.81% when \(\beta=0.25\pi\) while the highest efficiency was 80.03% when \(\beta=0.47\pi\), between which the difference was 13.22%. When the working point exceeded the base speed, with the increase of EDS speed, the effect of \(\beta\) on EDS efficiency became smaller, while there was still some optimization room. As shown in Figure 7, the efficiency was 89.64% when \(\beta=0.25\pi\) while the efficiency was 92.26% when \(\beta=0.36\pi\), between which the difference was 2.62%.