A Hybrid Simulation of DNN-based Gray Box Models

TL;DR

A new hybrid simulation that integrates DNNs into the numerical solvers of simulation engines to fully simulate implicit gray box models of large physical systems is introduced, which improves the accuracy and runtime compared to physics-based simulation and enables reusable DNN models with lower data requirements.

Abstract

Simulation is vital for engineering disciplines, as it enables the prediction and design of physical systems. However, the computational challenges inherent to large-scale simulations often arise from complex device models featuring high degrees of nonlinearities or hidden physical behaviors not captured by first principles. Gray-box models combine deep neural networks (DNNs) with physics-based models to address the computational challenges in modeling physical systems. A well-crafted gray box model capitalizes on the interpretability and accuracy of a physical model while incorporating DNNs to capture hidden physical behaviors and mitigate computational load associated with highly nonlinear components. Previously, gray box models have been constructed by defining an explicit combination of physics-based and DNN models to represent the behavior of sub-systems; however this cannot represent the coupled interactions within physical systems. We explore an implicit gray box model, where both DNNs and physical equations share a common set of state-variables. While this approach captures coupled interactions at the boundary of DNN and physics-based models, simulating the implicit gray box model remains an open-ended problem. In this work, we introduce a new hybrid simulation that integrates DNNs into the numerical solvers of simulation engines to fully simulate implicit gray box models of large physical systems. This is accomplished by backpropagating through the DNN to calculate Jacobian values during each iteration of the numerical method. The hybrid simulation improves the accuracy and runtime compared to physics-based simulation and enables reusable DNN models with lower data requirements. We explore the advantages of this approach as compared to physics-based, black box, and other gray box methods for simulating the steady-state and transient behavior of power systems.

Figures (16)

• Figure 1:
• Figure 2: Simulation of a composite load consisting of a capacitor, resistor and induction motor that is modeled by a static PQ model (whose parameters are learned according to Appendix \ref{['app:pq_dnn']}) and the proposed hybrid simulation. The current response of both models is compared against the ground truth of an electromagnetic transient simulation (EMT).
• Figure 3: The output current, $I$ and sensitivity, $dI/dV$, using different models (EMT model, PQ, hybrid) to represent composite load are recorded at a node-voltage operating point of $V=1.0 pu$ and $V=1.2 pu$. While the PQ and hybrid models accurately predict the current at $V=1.0 pu$, they show different sensitivities, causing the PQ model to inaccurately predict the current at $V=1.2 pu$.
• Figure 4: Loads and renewables in a 14-bus test case are modeled by DNNs.
• Figure 5: A full black box simulation and the hybrid architecture are used to simulate the modified 14-bus network with power set-points of generators and loads deviating from the nominal $1.0pu$ (increasingly outside the training set). The KCL residue resulting from both simulators' output is shown.