Practical Implementation of a Transmission–Distribution Co-Simulation Framework Using FMU and OpenDSS

Introduction

The increasing integration of distributed energy resources (DERs) into electrical grids has significantly altered the operational characteristics of modern power systems. Understanding the dynamic interactions between different parts of these systems has therefore become increasingly important. In particular, transmission systems (TS) and distribution systems (DS), which have traditionally been studied separately, are now more tightly coupled due to high levels of DERs, power-electronic interfaces, and advanced control strategies. Analyzing these interactions requires simulation approaches capable of representing heterogeneous subsystems while preserving the specific modeling assumptions and numerical methods best suited for each domain.

Co-simulation has emerged as a practical approach to address this need. In a co-simulation framework, different subsystems are simulated using separate tools or models that exchange information during runtime. This allows each subsystem to be modeled using specialized software while still enabling the study of system-level interactions. Such an approach is particularly useful when combining models with different time scales, levels of detail, or physical domains.

However, co-simulation of electrical systems presents significant challenges. Electrical networks often involve tightly coupled variables such as voltages and currents that must satisfy instantaneous physical constraints. When a network is partitioned into subsystems simulated by different tools, the boundary between subsystems must be placed at a specific physical location. At such interfaces, quantities like voltage and current must remain consistent across the coupled simulations. As a result, the variables computed in one simulator depend directly on those produced by the other, creating algebraic loops across subsystem boundaries. Resolving these loops typically requires iterative coordination between simulators at each time step, which can significantly increase computational complexity and reduce robustness.

One possible approach to overcome this difficulty is to separate the subsystems by introducing a transmission line between them. In this case, the subsystem boundaries no longer coincide at the same physical point; instead, the two simulators are connected through the transmission line, which introduces a propagation delay. This delay breaks the instantaneous dependency between voltages and currents at the interface, allowing each simulator to advance independently while exchanging delayed signals. The transmission line may represent a real physical element present in the system, or it may be introduced artificially to facilitate numerical coupling.

The work referenced in [1] proposes such an approach by introducing a fictitious Bergeron transmission line between the transmission and distribution models. The artificial delay created by the transmission line removes the algebraic loop between the subsystems while maintaining a physically meaningful representation of power exchange. However, an important question is under what conditions such artificial delays remain acceptable and how they influence the accuracy and stability of the resulting co-simulation.

Motivated by these considerations, this paper evaluates the proposed transmission–distribution co-simulation approach in [1] and demonstrates its practical implementation. The framework interfaces a dynamic transmission-system Functional Mock-up Unit (FMU) with a quasi-static distribution solver using a fictitious Bergeron transmission line. Our goal is to reproduce the method in [1], investigate practical implementation aspects, and assess how the approach can be used for studying interconnected electrical networks such as those found in ship power systems or other complex grid architectures. In addition to validating the original concept, we present a reproducible implementation, a GUI-based parameter exploration tool, and a discussion of modeling assumptions that influence the behavior of the co-simulation. The implementation is openly available at https://github.com/Novia-RDI-Seafaring/fmu_dss_cosim/.

Acknowledgements

This work was conducted within the scope of the Virtual Sea Trial project and was supported by Business Finland. The author acknowledges Novia for providing the research environment and infrastructure, and thanks all project partners for their collaboration and insights.

Texten har granskats och godkänts av Novias redaktionsråd 26.3.2026.