Case 4: real power at 1 MW (0 dB) and reactive power at 0 Mvar. At each operating condition, about 40 sinusoidal injection experiments are conducted. For each sinusoidal injection experiment, injection in the d-axis voltage is first conducted, and the resulting dq-axis current measurements are collected. A Fourier transform is then applied to the steady-state timedomain data to find the phasors. From there, the first column admittance components Ydd(f) and Yqd(f) are found. Next, injection in the q-axis voltage is conducted, and the second column admittance components Ydq(f) and Yqq(f) are found. From the 20 40 -40 -20 10-1 100 101 Frequency (Hz) (a) 200 -200 10-1 100 101 Frequency (Hz) (c) 20 40 -40 -20 10-1 100 101 Frequency (Hz) (e) 200 -200 10-1 100 101 Frequency (Hz) (g) 102 103 200 -200 10-1 100 101 Frequency (Hz) (h) figure 6. dq admittance of a 2.3-MVA inverter under four operating conditions: black: case 1; blue: case 2; green: case 3; red: case 4. Case 1: real power at 0 MW and reactive power at 0 Mvar. Case 2: real power at 500 kW or 0.5 p.u. (-6 dB), reactive power at 0 Mvar. Case 3: real power at 0 MW and reactive power at 500 kVar or 0.5 p.u. (-6 dB). Case 4: real power at 1 MW (0 dB) and reactive power at 0 Mvar. (a) Ydd's magnitude. (b) Ydq's magnitude. (c) Ydd's angle. (d) Ydq's angle. (e) Yqd's magnitude. (f) Yqq's magnitude. (g) Yqd's angle. (h) Yqq's angle. may/june 2022 ieee power & energy magazine 71 102 103 102 103 Yqd -8 20 40 -40 -20 10-1 100 101 Frequency (Hz) (f) 102 103 Yqq 102 103 200 -200 10-1 100 101 Frequency (Hz) (d) 102 103 102 103 frequency-domain measurement, we may apply frequencydomain data-fitting methods and obtain a black-box model. This step is necessary if we aim to have an s-domain admittance for eigenvalue analysis, which can lead to an overall picture of the system modes. The data in Figure 6 have been fitted using a frequencydomain data-fitting package. A comparison of the frequency responses of the model versus the measurements are shown in Figure 7(a). The figure shows that data fitting leads to a high matching degree in the studied frequency spectrum. One more comparison can be made: the step responses of Ydd 20 40 -40 -20 10-1 100 101 Frequency (Hz) (b) 102 103 Ydq -6.28 Phase (Degrees) Mag (dB) Phase (Degrees) Mag (dB) Phase (Degrees) Mag (dB) Phase (Degrees) Mag (dB)