A Nuclear Reactor: a Dynamic System to Control

In April 2006, twenty years after the Chernobyl accident, the public in general and the scientific community in particular were strongly reminded about the dynamic character of that type of nuclear reactors.

The neutron kinetics equations primarily determine the transient behavior of nuclear reactors. These are an inherently unstable set of equations. Their application will be presented in a MATLAB code to explain the Chernobyl power surge.

However, commonly used nuclear reactors also have stabilizing internal capabilities. These come from the nuclear fuel and the moderator. They are called the fuel temperature coefficient and the moderator temperature coefficient respectively. External control is accomplished with control rods. Inserting or withdrawing them will result in a power decrease or increase. This is illustrated with MATLAB calculations and verification, with results from a reactor in Ringhals.

At the beginning of the Swedish nuclear era in the 1960s different type of reactors were studied. Extensive simulations with an analogue computer were performed to study the inherent safety character of the planned heavy water reactor. There too the cooling medium’s coefficient plays a decisive role. The chart illustrating the stable and unstable areas with the variety of the fuel temperature coefficient and the cooling medium’s reactivity coefficient will be discussed.

An analytical study with z-transform illustrating the importance of choosing the right control systems completes the seminar.

Nuclear Reactor Control

Frigyes Reisch
Automatic Control, Electrical Engineering,
KTH Royal Institute of Technology
Stockholm, Sweden
Seminar 2007 February 22

To encourage students to study the automatic control of nuclear reactors, it is useful to let them make their own computer codes instead of only using huge detailed programmes with “invisible” contents. It also proves how straightforward direct analyses without using sophisticated codes can give valuable results.

Lately I was asked by the New Scientist whether I was surprised that an accident with a Chernobyl type of reactor could have happened. I answered that I was not surprised at all. Now, twenty years later, it was easy to demonstrate it, as it is shown in the 2006 summer addition of Nuclear News. The simple equations were verified in that year’s autumn edition.

However, the story started long ago, in the mid 1960s.

As part of my Ph. D. work I analyzed the dynamic behavior of a boiling heavy water reactor. As the parameters were uncertain at the design stage I had to make parameter studies and indeed, with certain parameters, a small perturbation could cause an oscillatory increase of power or a straight forward avalanche increase of the neutron flux.

The other part of my PhD work was to study a suitable control system for a multi channel reactor. The obvious method was to choose a sampled data control system. Here too, the importance of selecting the correct control parameters to avoid instability was soon apparent.

With such a background it was easy to imagine in April 1986 what could have happened with a multi-channel boiling water reactor with a positive void coefficient.

References

New Scientist, Careers Guide 2007 (pages 10 and 11)
www.exacteditions.com/exact/browse/324/337/1979/3/12

ENS News 2006 (autumn edition)
Reactor Kinetics Equations applied to the start-up phase of a Ringhals PWR
www.euronuclear.org/e-news/e-news-14/pwr.htm

ENS News 2006 (summer edition)
Neutron Kinetics of the Chernobyl Accident
www.euronuclear.org/e-news/e-news-13/neutron-kinetics.htm

Nucl. Appl., 3: 590-8(Oct. 1967).
ANALYTICAL STUDY OF THE DYNAMIC BEHAVIOR OF THE SELF-CONTROLLED MARVIKEN BOILING HEAVY-WATER REACTOR (1.8MB)

Nucl. Sci. Eng., 26: 378-84(Nov. 1966).
STABILITY ANALYSIS OF A SAMPLED-DATA CONTROLLED NUCLEAR REACTOR SYSTEM. (2.6MB)