current control implementation frames. The dq-frame control has its inner current control implemented in a dq-frame; that is, the phase current measurements are first converted to a dq-frame. This dq-frame has the rotating speed of the nominal frequency at steady state. When projected to the dq-frame, periodic signals with the nominal frequency be - come dc signals. The proportional-integral control units are known for their capability of tracking dc signals. They can enforce the dq-axis current measurements to follow the current orders generated by the outer controls. The stationary-frame control has its inner current control implemented in a stationary frame. In this frame, currents are still periodic. To track a current order, proportional-resonant control units Measurement 1 0.5 -0.5 -1 -0.5 -1 -1.5 -2 0.02 0.04 0.06 Time (s) Event 2: vq Step Up 2 1 -1 -2 2 1 -1 -2 0.02 0.04 0.06 Time (s) (b) figure 7. (Continued) (b) Comparison of the step response of the identified black-box model versus the time-domain measurements. may/june 2022 ieee power & energy magazine 73 0.08 iq (2) 0.02 0.04 0.06 0.08 id (2) 2 1 -1 -2 0.1 0 2 1 -1 -2 0.1 0 0.02 0.04 0.06 Time (s) 0.08 0.1 iq (2) 0.02 0.04 0.06 0.08 0.1 id (2) 0.08 iq (1) 0.02 0.04 0.06 0.08 0.1 id (1) Event 1: vd Step Down 1 10% Step Change 20% Step Change id 0.5 -0.5 -1 -0.5 -1 -1.5 -2 0.1 0 0.02 0.04 0.06 Time (s) 0.08 0.1 iq (1) 0.02 0.04 0.06 0.08 0.1 (1) are employed to ensure the error between the measurement and the order achieving zero at the nominal frequency. A comparison of the dq admittance of the 2.3-MW inverter versus the two models shows that the second model results in better matching for the diagonal components Ydd and Yqq. Specifically, for the dd component, a large mismatch is observed in the range of 1-100 Hz if the dq-frame control is assumed. On the other hand, the 2.3-MW inverter and the model match well in the range of 0.1-100 Hz if the stationary-frame control is assumed. Refining the model structure and parameter tuning are the next steps. Specifically, parameter tuning can be achieved using an automatic procedure instead of manual tuning. To achieve automatic tuning, optimization problem formulation Model 10% Step Change 20% Step Change