Simplification algorithms for large-scale power system transmission grids

Abstract

The simulation of large-scale power system models including transmission grid representations is limited by available computation power and time. Therefore, the reduction of transmission grid models is of paramount importance. This report proposes and tests a new method of reducing power grids. This method allows to reduce an existing transmission grid model to any desired size, however, at the cost of accepting increasing levels of inaccuracy. An algorithm is developed that reforms the total number of nodes in the full grid representation into a smaller number of clusters, which are then connected by equivalent power lines. The algorithm is designed in such way that those power lines remain in the transmission grid that are likely to form a bottleneck, thus restraining power flows. The accuracy of this method is measured by comparing the power flows in the reduced power grid to the flows from the original grid. The power flows of the full and reduced model are calculated by applying linear approaches based on PTDF matrices. PTDF matrices are commonly used in transmission grid analysis, linking node injections to power flows. The power flows are calculated based on a pre-defined set of injections, which represent cases of realistic power plant dispatches. The PTDF matrix for the reduced matrix is derived with the method proposed by Shi et al. The reduced matrix is operating point dependent, based on a set of reference injections. The results show that every country can be reduced up to 37.5% of its original size, when maintaining an allowable error of 20% of the available transfer capacity of a power line. Most countries can even be reduced further before they exceed the set accuracy benchmark. In addition to this, the report researches whether guidelines can be identified to which extend power grids can be reduced within preset limits of accuracy. Power grids in countries have different properties like topologies and grid characteristics, possibly leading to differing error behavior. The results show that no clear relation can be identified between the properties of a country s power grid and its error behavior, but is dependent on case specific situations in which node injections play a particularly decisive role. As the node capacity and node generation are random though, so are the occurring errors. Finally, the relation between accuracy and gained computation time in optimization simulations is identified. The relation between the number of variables in an optimization model and required computation time is exponential. This relation shows that without exceeding the preset boundaries of accuracy significant gains in computation time can be acquired. A grid reduced to 22.5% of its original sizes does not exceed the error limit in power lines, while the computation time reduces by a factor of 261.