Unlike synchronous generators whose physics are well understood and documented, inverter-based resources (IBR) contain proprietary controls that manufacturers do not disclose and that look like black boxes to system operators and plant developers. Neural network-based surrogate models offer a way to learn the dynamic input-output behavior of an IBR directly from its terminal measurements, requiring no or little knowledge of its internal control structure. In the grid that increasingly depends on IBRs this may enable operators to build accurate device-specific models from observable data.

In this paper we study recently proposed neural network methods for learning input-output behavior from field or simulation inverter data. These methods were typically demonstrated on simple inverter control structures. We implemented some of these methods and used them to train surrogate models with data obtained from electromagnetic transient simulations of an inverter model that contains a larger number of states and nonlinear elements. Thus, one of the objectives of the paper is to evaluate the methods on these more complicated control structures.

The focus is on the two methods that produce continuous-time state-space models which can seamlessly be used in existing stability simulation tools. The first method is Neural Ordinary Differential Equations (NODE). This foundational continuous-time framework learns the controller state derivative function directly and integrates it numerically. A Multi-Layer Perceptron (MLP) architecture is well-suited for this because it is a universal function approximator. The second method is Neural Kalman Filter (NKF). It separates the state space from the output space by adding an encoder network that estimates virtual state variables from measurements and uses two MLPs — for state transition and for output. The Kalman filter inspiration means it explicitly handles measurement and process noise in the training loss function.

The control structures studied in this paper enable both grid-following (GFL) and grid-forming (GFM) inverter controls. A GFL inverter measures the grid voltage, uses a PLL to synchronize, and injects a current. A GFM inverter effectively regulates its internal voltage phasor, but sometimes also includes current controllers. Additionally, when terminal voltage magnitude falls below a certain threshold, many controller states are frozen. This all means the state space is high-dimensional and the dynamics are nonlinear near faults.

In our evaluation we recognize how the basic NODE method requirement of state variables matching the black-box outputs limits its expressiveness for high-order inverter dynamics. On the other hand, although NKF architecture is more expressive, for a straightforward GFL inverter where the dynamics are not extremely high-order, the NKF three-network architecture may be more than is necessary. Our analysis shows that NKF method produces considerably more complex models than the NODE method, as it results in 20-30 times larger number of model parameters.

For the voltage ride-through training, we observe the needed variation in voltage fault depths, duration and distance. We compare the training computational requirements in two methods and discuss our experience related to the number of required datasets to train the models for voltage fault scenarios. Finally, we analyze how the selection of the training accuracy metric impacts the predictions of inverter stability during faults.