Integrated Electrical Steady-State Power Flow Simulations on Transmission and Distribution Networks

Research output: ThesisDissertation (TU Delft)

29 Downloads (Pure)


Integrated electrical power flow simulations are concerned with solving the steady-state load flow problem on integrated transmission and distribution electricity networks. We have developed a framework to run these simulations efficiently, whilst keeping in mind the differences between these network types and accommodating the practical considerations of system operators. We need such a framework to analyse the interaction that these systems might have as a result of the energy transition.

To develop a framework to run integrated power flow simulations, we have worked in two stages. Firstly, we have studied how we can model an integrated network. We have found two ways of modelling an integrated network: using a homogeneous configuration in which both networks are modelled using three phases and using a hybrid network configuration in which both networks keep their original configuration but in which the coupling substation takes care of the phase dimension mismatch between the two sides. Next to that, we have found two ways of solving an integrated system: either by coupling them into one system and solving that as a whole (we call this the unified approach) or by keeping two separate systems and iterating between these networks (we call this the Manager‐Fellow Splitting (MFS) method).

We have concluded that the unified methods are generally faster than MFS methods and that a hybrid network configuration leads to faster results, making the interconnected method the most efficient.

In the second stage, we have focused on the efficiency of these simulations. During every Newton‐Raphson iteration in power flow simulations, a linear system is solved. We have therefore studied several Krylov subspace and preconditioning techniques that can solve this linear system efficiently. We have applied Krylov and preconditioning combinations to integrated network simulations to check again the performances of the simulations on large test cases . During this stage, we applied them to networks up to a size of 800,000 buses as we were interested in efficient scaling of the methods that were originally the object of study.

In the second stage, we saw that the MFS methods were performing better than unified methods. Furthermore, preconditioned Krylov subspace methods had a similar performance to direct methods. t is difficult to judge why this happened. A reason could be that the library in which we performed these simulations, PETSc, is optimised for parallel computations in which multiple smaller blocks are solved at the same time whilst we were doing only sequential computations.

Finally, we have striven to incorporate operational convenience for Transmission and Distribution System Operators (TSOs and DSOs) during the development of this integration framework, by considering their computational and privacy concerns. The way that this framework is built, can take away some of their concerns.

To summarise, we have created an open‐source framework to run efficient steady-state power flow simulations on integrated transmission and distribution networks. This framework is tested on simplified test cases but shows potential for large system simulations. Moreover, it takes into account the considerations of system operators and can be utilised in other applications besides integrated analysis.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • Delft University of Technology
  • Vuik, C., Supervisor
  • van Gijzen, M.B., Supervisor
Thesis sponsors
Award date25 Apr 2024
Print ISBNs978-94-6483-990-6
Electronic ISBNs978-94-6483-991-3
Publication statusPublished - 2024


  • Power Flow
  • Numerical analysis
  • Newton-Krylov methods
  • Iterative methods


Dive into the research topics of 'Integrated Electrical Steady-State Power Flow Simulations on Transmission and Distribution Networks'. Together they form a unique fingerprint.

Cite this