09.05.2018

Graph theory contributes to stable power supply under the large and complex electric power systems

A joint research team from Tokyo Institute of Technology (Tokyo Tech) and North Carolina State University has clarified the fundamental principles for achieving the synchronization of power generator groups[1] in power networks, which is essential for the stable supply of electric power. Based on this principle, the team developed a method for constructing an aggregated model of a power network that can efficiently analyze and control the behavior of generator groups (including rotor phase angles and connection point voltages) with complex connection to a power grid.

A power network consisting of four generators and six buses (connection points). Generators 1 and 2 and Buses 1 and 2 to which these are connected become a symmetrical network for Bus 5. Similarly, Generators 3 and 4 and Buses 3 and 4 become symmetrical for Bus 6. The two sets of symmetrical generator groups and buses are shown as Clusters 1 and 2.

Credit: Proceedings of the IEEE

**Background**

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

... more about:

»algebraic »electric power »power grid »power plants »power supply »synchronization »thermal power plants

»algebraic »electric power »power grid »power plants »power supply »synchronization »thermal power plants

In addition, energy problems caused by global warming and the depletion of fossil fuels have become more serious on a global scale. Therefore, from the viewpoint of reducing carbon dioxide and systematic use of energy, high expectations have been placed on renewable energy such as typified by photovoltaic (PV) generation. When large-scale PV generation equipment and power storage equipment are introduced, in addition to power generation such as thermal power, hydraulic power, and nuclear power that are commonly used today, it is necessary to consider power charge and discharge by PV generated output and storage batteries in order to maintain equilibrium between supply and demand. However, the amount of power from PV generation fluctuates since there is uncertainty related to changes in weather and changes in solar radiation volume according to the time zone. This makes it more difficult to maintain the synchronization of generator groups. The need to analyze synchronization is greater than ever.

With conventional analysis, a major approach is based on numerical simulation. There are no studies that theoretically clarify the basic principles for how to properly synchronize generator groups according to the network structure of power transmission. There is an urgent need to build a power supply and demand framework that efficiently utilizes power storage equipment to allow for the uncertainty of PV generation and demand predictions.

Overview of Research Achievement

Assistant Professor Takayuki Ishizaki, Professor Jun-ichi Imura of Tokyo Tech, and Associate Professor Aranya Chakrabortty of the NSF ERC FREEDM System Center at North Carolina State University worked on multiple studies including power network modeling, stability analysis, and stabilization control from the perspective of graph theory[2]. They have clarified that the symmetry of the network in graph theory is the fundamental principle for realizing the synchronization of generator groups at thermal power plants integrated with power grids (connected to a network).

The behavior of generators connected through a network in a power grid is represented by complex equations (differential algebraic equations) that combine differential equations and algebraic equations. The differential equations express "behavior of generators" derived from Newton's second law of motion, and the algebraic equations express "power balance at power grid connection points" derived from Ohm's law and Kirchhoff's law[3]. 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 problems were that with the existing approach, since the algebraic equation representing the power grid is eliminated by deleting the redundant variable representing the connection point voltage, it was not very suitable for analyzing the relationship between the network structure of the power grid and the behavior of the generator.

To resolve this issue, they analyzed the network structure of the power grid contained in the algebraic equations from the viewpoint of symmetry based on an understanding of graph theory. Specifically, by analyzing the behavior of the generator without eliminating the algebraic equations, they discovered that the symmetry of the power grid (Figure 1) is the basic principle for realizing synchronization of generator groups. In addition, based on a new idea of simultaneously integrating generator groups that show synchronous behavior and the power grid that couples these, it became possible to mathematically and physically construct a feasible aggregated model (Figure 2).

It is expected that this achievement will result in a basis for developing analysis and control methods for realizing stable power supply to large and complex electric power systems. In the future, Professor Imura says that it aims to develop more complex electric power systems including converters, and to establish a theory to approximate the synchronization of generator groups.

This research result was published in *Proceedings of the IEEE* on April 25, 2018.

###

[1] Synchronization of Generator Groups: The phase angles of the rotors such as the turbines of multiple generators must be the same or reasonably close. Each rotor rotates according to the standard of a specific frequency (50 Hz or 60 Hz in Japan) in order to maintain its frequency. A difference in the frequency of each generator creates a difference in phase angle.

[2] Graph Theory: This is a mathematical theory related to graphs (network structure) composed of sets of vertices (nodes) and sets of edges. 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.

[3] Ohm's Law, Kirchhoff's Law: These are physical laws that express the relationship between physical quantities such as voltage and current in an electric circuit. Ohm's law indicates that the voltage difference between two points in a circuit is proportional to the current flowing between them. Kirchhoff's law indicates that at the branch point in the circuit, the sum of the currents flowing to that point is equal to the sum of the currents flowing from that point.

Emiko Kawaguchi | EurekAlert!

**Further reports about:**
> algebraic
> electric power
> power grid
> power plants
> power supply
> synchronization
> thermal power plants

Nano-scale process may speed arrival of cheaper hi-tech products

09.11.2018 | University of Edinburgh

Nuclear fusion: wrestling with burning questions on the control of 'burning plasmas'

25.10.2018 | Lehigh University

Researchers at the University of New Hampshire have captured a difficult-to-view singular event involving "magnetic reconnection"--the process by which sparse particles and energy around Earth collide producing a quick but mighty explosion--in the Earth's magnetotail, the magnetic environment that trails behind the planet.

Magnetic reconnection has remained a bit of a mystery to scientists. They know it exists and have documented the effects that the energy explosions can...

Biochips have been developed at TU Wien (Vienna), on which tissue can be produced and examined. This allows supplying the tissue with different substances in a very controlled way.

Cultivating human cells in the Petri dish is not a big challenge today. Producing artificial tissue, however, permeated by fine blood vessels, is a much more...

Faster and secure data communication: This is the goal of a new joint project involving physicists from the University of Würzburg. The German Federal Ministry of Education and Research funds the project with 14.8 million euro.

In our digital world data security and secure communication are becoming more and more important. Quantum communication is a promising approach to achieve...

On Saturday, 10 November 2018, the research icebreaker Polarstern will leave its homeport of Bremerhaven, bound for Cape Town, South Africa.

When choosing materials to make something, trade-offs need to be made between a host of properties, such as thickness, stiffness and weight. Depending on the application in question, finding just the right balance is the difference between success and failure

Now, a team of Penn Engineers has demonstrated a new material they call "nanocardboard," an ultrathin equivalent of corrugated paper cardboard. A square...

Anzeige

Anzeige

Event News

“3rd Conference on Laser Polishing – LaP 2018” Attracts International Experts and Users

09.11.2018 | Event News

On the brain’s ability to find the right direction

06.11.2018 | Event News

European Space Talks: Weltraumschrott – eine Gefahr für die Gesellschaft?

23.10.2018 | Event News

Latest News

Purdue cancer identity technology makes it easier to find a tumor's 'address'

16.11.2018 | Health and Medicine

Good preparation is half the digestion

16.11.2018 | Life Sciences

Microscope measures muscle weakness

16.11.2018 | Life Sciences

VideoLinks

Science & Research

Science & Research

NASA | A Year in the Life of Earth's CO2

NASA Computer Model Provides a New Portrait of Carbon Dioxide

Black Holes Come to the Big Screen

The new movie "Interstellar" explores a longstanding fascination, but UA astrophysicists are using cutting-edge technology to go one better.

NASA's Swift Mission Observes Mega Flares from a Mini Star

NASA's Swift satellite detected the strongest, hottest, and longest-lasting sequence of stellar flares ever seen from a nearby red dwarf star.

NASA | Global Hawks Soar into Storms

NASA's airborne Hurricane and Severe Storm Sentinel or HS3 mission, will revisit the Atlantic Ocean for the third year in a row.

Baffin Island - Disappearing ice caps

Giff Miller, geologist and paleoclima-tologist, is walking the margins of melting glaciers on Baffin Island, Nunavut, Canada.

The Infrasound Network and how it works

The CTBTO uses infrasound stations to monitor the Earth mainly for atmospheric explosions.