Co-Simulation

Co-simulation integrates specialized solvers—such as an electromagnetic transient (EMT) simulator and a finite element thermal model—into a single unified execution. Each solver operates in its native environment, optimized for its own physics. A dedicated middleware orchestration layer manages the handshake, translating variables like power loss from the electrical domain into heat generation for the thermal domain. This avoids the compromises of monolithic, all-in-one simulators and allows teams to use best-in-class tools for each discipline.

The critical challenge in co-simulation is managing disparate time scales. An EMT model may require microsecond steps, while a thermal model updates in milliseconds or seconds. Co-simulation engines implement sophisticated synchronization schemes:

• Gauss-Seidel (sequential): Solvers run one after another, using the latest available data.
• Jacobi (parallel): Solvers run concurrently, exchanging data at fixed macro-step intervals.
• Variable-step: Adaptive algorithms that dynamically adjust the communication interval to balance accuracy and performance. This ensures causal consistency and numerical stability across the coupled system.

Modern co-simulation frameworks support geographically distributed architectures, where solvers run on different machines, in different locations, and even behind different organizational firewalls. Communication occurs over standard protocols like OPC UA or DDS (Data Distribution Service). This is essential for Hardware-in-the-Loop (HIL) testing, where a physical controller in one lab interacts with a real-time simulated power grid in another, or for collaborative design where an OEM protects its proprietary motor model while sharing interface variables with a system integrator.

The Functional Mock-up Interface (FMI) is the dominant open standard for model exchange and co-simulation. A tool exports its model as a Functional Mock-up Unit (FMU)—a self-contained ZIP file containing the compiled model binary and an XML interface description. The importing co-simulation master algorithm can then instantiate and orchestrate FMUs from dozens of different vendors without needing the original authoring tools. FMI 3.0 adds support for virtual electronic control units (vECUs) and advanced clock synchronization, making it the backbone of modern automotive and energy system co-simulation.

Coupling solvers introduces aliasing errors and potential numerical instability at the interface. Co-simulation frameworks employ advanced techniques to mitigate these:

• Energy-based correction: Ensuring that energy transferred across the interface is conserved, preventing artificial damping or energy injection.
• Extrapolation of inputs: Predicting the coupling variable's value between communication points to reduce the error introduced by discrete data exchange.
• Rollback & re-step: If a solver detects an integration error exceeding a tolerance, the master algorithm can command all coupled solvers to roll back to a previous consistent state and retry with a smaller step size. These methods are critical for stiff systems like power electronics interacting with mechanical loads.

Co-simulation is the execution engine for high-fidelity Digital Twins. It allows a virtual representation to combine a reduced-order electromagnetic model of a transformer, a computational fluid dynamics (CFD) model of its cooling oil, and a data-driven aging model trained on dissolved gas analysis. The co-simulation master orchestrates these heterogeneous sub-models, feeding them live sensor data via stream processing platforms. This enables continuous, cross-domain what-if analysis—such as predicting the thermal impact of a sudden overload on insulation lifespan—that a single-physics model could never achieve.