## 4 Calibration of Electrical Inertia Simulation Accuracy
### Calibration of Standard Inertia  
In the electrical inertia simulation test, the main factors affecting the accuracy of the test results are the accuracy of the inertia simulation and the system response time [39]. In this paper, a set of calibrated high-precision standard inertia boxes are used to calibrate the electric inertia. Suppose that the inertia of one stage in the flywheel box and driving components to be calibrated is \(J_{s}\) and \(J_{hu}\), respectively. Then, the inertia to be simulated by the motor is \(J_{a}\). To achieve \(J_{hu}\pm J_{a}=J_{s}\), the inertia box and the tested motor are driven with the same torque to obtain the speed-up curve. By comparing the experimental results of the two groups, the calibration of the electric inertia simulation is completed. The mechanical structure of the standard inertia (flywheel box) test is shown in Figure 14. According to Formula (44), when the input torque is constant, the speed of the system should rise uniformly in a constant angular acceleration \(\alpha\). Therefore, the standard inertia of the system can be calculated by the input torque and the measured velocity curve. In practical experiments, the formula is modified to \(T_{t}-T_{d}=J\alpha\) because of the resistance of the system, which is mainly related to the rotation speed [25; 28]. When the rotation speed of the system is at a proper level, the resistance of the system is basically stable. Therefore, the angular acceleration can be measured by changing different driving torques, and the standard inertia of the system can be obtained by two sets of equations. As shown in Figure 15, the driving torque values \(T_{t1}\) and \(T_{t2}\) are set separately at different stages of the same test, and the acceleration values \(\alpha_{1}\) and \(\alpha_{2}\) corresponding to the stage of higher speed curve steady speed rise \((r_{1}\sim r_{2})rpm\) are selected. Because the acceleration at the same speed is collected at different stages, it is considered that the resistance \(T_{di}\) of each stage is equal. The inertia value \(J_{s}\) of the standard inertia disc can be calculated by taking the difference between \(T_{t1}\) and \(T_{t2}\). The accuracy of the standard inertia simulation is thus verified. \[T_{t1}-T_{d1}=J_{s}\alpha_{1} \tag{45}\]  
\[T_{t2}-T_{d2}=J_{s}\alpha_{2} \tag{46}\]  
\[J_{s}\approx\frac{T_{t1}-T_{t2}}{\alpha_{1}-\alpha_{2}} \tag{47}\]  
Figure 14: Structure of a standard inertia calibration test. Figure 15: Test flow. The actual structure of the standard inertia box is a flywheel set with large inertia, and its inertia simulation range is (50-1000) kg\(\cdot\)m\({}^{2}\). In order to improve the upper limit of inertia simulation and provide more reference data for electric inertia simulation calibration, a gearbox equipped with speed ratios of 1:2.36 and 1:6.48 is equipped to improve the equivalent inertia of the equipment being marked. The maximum equivalent inertia of the original 1000 kg\(\cdot\)m\({}^{2}\) is 42,006.60 kg\(\cdot\)m\({}^{2}\) after considering the gear box deceleration ratio. That is to say, the inertia ranging from 255-42,000 kg\(\cdot\)m\({}^{2}\) can be simulated by different combinations of inertia plates in the flywheel box. In this simulation method, although it is a simulation, through data processing, it can completely reflect the data curve within 250-41,000, to meet the requirements of comparison. In this way, the inertia calibration test of 400 kg\(\cdot\)m\({}^{2}\) inertia box with a 1:2.36 transmission ratio is carried out. The test results are shown in Figure 16.  
Figure 16a is the overall data of the test while Figure 16b is the calibration section. In the test, the equivalent inertia of the flywheel is 2227.84 kg\(\cdot\)m\({}^{2}\). The average acceleration of the system is 1.3 rad/s\({}^{2}\) under the condition of average torque \(T_{t1}=3140.09\)Nm, and 1.54 rad/s\({}^{2}\) under the condition of \(T_{t2}=3674.7\) Nm. Therefore, the inertia of the system is 2229.94 kg\(\cdot\)m\({}^{2}\) and the measurement deviation is 0.19%.