the physical device versus the model. Figure 7(b) presents the comparison under two step changes in the dq-axis voltages: 10% or 20%. The physical device and the model have very similar step responses. Another admittance model identification technology is to use time-domain step responses. Converting the step responses into s-domain expressions and assembling lead directly to an s-domain dq admittance model. In real-world applications, step response data are polluted with noise. The resulting model may not be accurate in the high-frequency range or when the measurement data have small values. Remark: Frequency scans and frequency-domain data fitting are two mature technologies and can be employed for IBR's dq admittance model identification. The admittance model identified is a linear model associated with an operating condition. An IBR may have a variety of operating conditions. Thus, one challenge is how to find any admittance model associated with a random operating condition. A straightforward solution is to build a nonlinear model that can reflect the operating condition. This approach is the gray-box modeling approach: building the model structure 20 40 -40 -20 100 200 -200 100 20 40 -40 -20 100 200 -200 100 Frequency (Hz) (a) figure 7. (a) Frequency-domain data-fitting results. Solid blue line: model; black crosses: measurements. Operating condition: Case 3 where P = 0 MW, Q = 500 kVar. (Continued) 72 ieee power & energy magazine may/june 2022 102 102 200 -200 100 Frequency (Hz) 102 Yqd 102 20 40 -40 -20 100 102 Yqq 102 200 -200 100 102 based on the first principles and prior knowledge while estimating the model parameters using measurement data. On the other hand, IBR gray-box model identification is a more challenging problem from both the IBR dynamic modelbuilding perspective and mathematic optimization problemsolving perspective. Challenges in Gray-Box Model Identification Using the 2.3-MVA inverter as an example, we will further demonstrate how to use dq admittance measurement data to speculate the inverter control structure and parameters. As the first step, the control structure needs to be specified. In this case, two types of popular control structures are examined. Figure 8 presents the converter control structures and a comparison of the frequency responses of the two models versus the measurements. In both models, the converter controls have the same goal of following the real power and reactive power orders. Both employ a cascaded control structure: outer controls to track real and reactive power orders and inner controls to track current orders. The two models differ in the inner Ydd 20 40 -40 -20 100 102 Ydq Phase (Degrees) Mag (dB) Phase (Degrees) Mag (dB) Phase (Degrees) Mag (dB) Phase (Degrees) Mag (dB)