RapidPF

Rapid prototyping for distributed power flow problems

The power flow problem is the cornerstone problem in power systems analysis: find all (complex) quantities in an AC electrical network in steady state. Mathematically, the power flow problem is a system of nonlinear equations

$$g(x) = 0$$

that can be solved by the Newton method, for instance. However, the power flow problem can also be solved in a distributed fashion,

$$ \begin{align} g_{i}(x_i) &= 0, \\ \sum_{i = 1}^{n} A_i x_i &= 0, \end{align} $$ where $i \in \{ 1, \dots, n\}$ corresponds to the $i$-th subproblem. In plain words, the distributed power flow problem means

to solve a power flow problem within each region $i$ whilst ensuring that the neighboring power flows satisfy the overall power flow equations.

There are several advantages of distributed approaches:

• distribute computational effort,
• preserves privacy,
• increases reliability,
• and adds flexibility.

What to expect

The code allows to formulate distributed power flow problems easily. Specifically, the features of the code include:

• Starting from several individual case files, generate a merged case file for given connections.
• Formulate distributed power flow problems in terms of function handles.
• Solve distributed power flow problems using the Aladin toolbox.
• Fully compliant with matpower case files, hence allowing to use all of the built-in matpower functions.
• Insightful post-processing features.

What not to expect

• An introduction to the power flow problem as such. There are excellent references for this, for example this one
• Optimal power flow problems.
• A collection of numerical routines to solve distributed power flow problems.
• A visualizer of matpower case files; use STAC for this.

Installation

See here.

Use of matpower

The code relies heavily on Matpower, especially on the idea of a matpower case file (or mpc). This bulky name is nothing but a standardized Matlab struct, with the advantage that it has become a de facto standard for Matlab-based power systems research. Also, mpc can be converted within matpower to/from IEEE CDF or PSS/E RAW, see the Matpower docs for details.

Citing

If you find the code useful for your own academic research, please cite it.

@ARTICLE{2020arXiv201110322M,
       author = {{M{\"u}hlpfordt}, Tillmann and {Dai}, Xinliang and {Engelmann}, Alexander and {Hagenmeyer}, Veit},
        title = "{Distributed Power Flow and Distributed Optimization -- Formulation, Solution, and Open Source Implementation}",
      journal = {arXiv e-prints},
     keywords = {Mathematics - Optimization and Control, Electrical Engineering and Systems Science - Systems and Control},
         year = 2020,
        month = nov,
          eid = {arXiv:2011.10322},
        pages = {arXiv:2011.10322},
archivePrefix = {arXiv},
       eprint = {2011.10322},
 primaryClass = {math.OC},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2020arXiv201110322M},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}