  # Symmetry helps hybrid power network stability

Technology News |
By Nick Flaherty

The team from the Tokyo Institute of Technology (Tokyo Tech) and North Carolina State University have developed a method for constructing an aggregated model of a power network that can efficiently analyze and control the behaviour of generator groups including rotor phase angles and connection point voltages that have complex connections to a power grid. The phase angles of the rotors such as the turbines of multiple generators must be the same or reasonably close to maintain its frequency. A difference in the frequency of each generator creates a difference in phase angle.

The synchronization of generator groups such as at multiple thermal power plants is closely related to the stable supply of electric power, and if a generator becomes out of synchronization, that generator and its surrounding generators will not be able to operate stably, and in worst cases, power outages can occur.

When large-scale solar energy farms and storage batteries are added to the network alongside thermal, hydraulic and nuclear power, it is vital to consider power charge and discharge by the solar cells and batteries in order to maintain equilibrium between supply and demand. The variation in the solar output makes it more difficult to maintain the synchronization of generator groups, and the need to analyse synchronisation is greater than ever. This is one reason why there is a lot of focus on flow batteries to allow more control of the electrical output of solar farms.

Assistant Professor Takayuki Ishizaki, Professor Jun-ichi Imura of Tokyo Tech, and Associate Professor Aranya Chakrabortty of the FREEDM System Centre at North Carolina State University worked on multiple studies including power network modeling, stability analysis, and stabilisation control using graph theory rather than traditional numerical analysis.

Next: Graph theory

This showed that the symmetry of the network in graph theory is the fundamental principle for achieving effective synchronisation of generator groups. Graph theory is composed of sets of vertices (nodes) and sets of edges and used in machine learning and social network analysis. The power grid network is interpreted as a graph in which the connection point is the vertex and the transmission line linking the connection points is the edge.

The behaviour of generators connected through a network in a power grid is represented by differential algebraic equations where the differential equations express “behaviour of generators” derived from Newton’s second law of motion, and the algebraic equations express the “power balance at power grid connection points” derived from Ohm’s law and Kirchhoff’s law. Analysis of these differential algebraic equations was generally performed by transformation into a mathematically equivalent differential equation through a simplification method called the Kron reduction. However, the existing approach is not suitable for analysing the relationship between the network structure of the power grid and the behaviour of the generator.

Instead the researchers analysed the network structure of the power grid contained in the algebraic equations from the viewpoint of symmetry based on an understanding of graph theory. By analysing the behaviour of the generator without eliminating the algebraic equations, they showed that the symmetry of the power grid (above) is key to the synchronisation of generator groups. They developed a new approach of simultaneously integrating generator groups that show synchronous behaviour and the power grid, allowing a mathematically and physically model.

This model can be used to develop new analysis and control methods for stable power supply to large and complex electric power systems. The team is working on more complex electric power systems including converters, and on a theory to approximate the synchronisation of the generator groups for faster analysis and modelling.

This research result was published in Proceedings of the IEEE.

www.titech.ac.jp/english/index.html

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