The integration of renewable energies in the electrical network leads to an increasing presence of power electronic components, which makes phenomena involving electromagnetic transients (EMT), faster than electromechanical transients, more frequent than until recently.
This evolution of the network must be accompanied by an evolution of the simulation methods. This thesis focuses on the development of numerical methods for EMT-TS co-simulation, taking advantage of the detailed but time-consuming EMT simulation and the computationally efficient TS simulation, which captures only smooth oscillations, to simulate different parts of the network. Several numerical difficulties appear in such a coupling to solve systems of differential algebraic equations (DAE): the partitioning can have an impact on the contraction of the error operator of the numerical method, the difference in solver time step between EMT-TS simulations requires an interaction protocol to avoid any delay in data exchange, the difference in mathematical modeling requires a specific translation of the data to be exchanged.
We develop a restrictive additive Schwarz domain decomposition method to simulate linear RLC circuits or their linearization around each time step if there are non-linear components. Convergence or divergence studies in the EMT-EMT or TS-TS homogeneous modeling cases show that they depend on the partitioning, the time step size, the values of the components circuits. Nevertheless, we take advantage of their purely linear behavior in order to apply the Aitken convergence acceleration technique and thus obtain simulation results in a limited number of iterations even in the case of a divergent method. The constraint imposed on the fractionation to have a convergent method is then no longer relevant. Heterogeneous EMT-TS splitting requires that the RAS take into account the difference in time step between the two simulations. We develop translation operators, as accurate as possible, not too expensive, without additional constraints on the time steps used, and finally linear in order to keep the linear convergence/divergence and thus the advantage of being able to use the Aitken convergence acceleration technique. Then, we show that our domain decomposition method applied to the DAE system is a special case of a general method called dynamic iteration. We then show that dynamic iteration with the domain decomposition method can be accelerated using Aitken’s convergence acceleration technique and in particular that several time steps can be accelerated at the same time even if they have variable sizes programmed in advance, and in the presence of nonlinear components in the circuit.
Finally, we study the advantages and disadvantages of Modelica-based tools such as OpenModelica to implement our domain decomposition. These tools allow us to produce the DAE system from the mathematical description of the network components. The result is the development of a platform using a master/slave implementation of our domain decomposition method, through the MPI (Message Passing Interface) library. This platform is intended to be as general as possible, using either models (part of the network) in the form of a functional mockup unit (FMU) from industrial modeling tools, or a DAE system coded in
Director of thesis: Damien TROMEUR-DERVOUT