Reactor Power Control

During any power increase the temperature, pressure, or void fraction change and the reactivity of the core changes accordingly. It is difficult to change any operating parameter and not affect every other core property. Since it is difficult to separate all these effects (moderator, fuel, void, etc.), the power coefficient is defined. The power coefficient combines the Doppler, moderator temperature, and void coefficients. It is expressed as a change in reactivity per change in percent power, Δρ/Δ% power. The value of the power coefficient is always negative in core life. Still, it is more negative at the end of the cycle primarily due to the decrease in the moderator temperature coefficient.

Let’s assume that the reactor is critical at 75% of rated power and that the plant operator wants to increase power to 100% of rated power. The reactor operator must first bring the reactor supercritical by inserting a positive reactivity (e.g., by control rod withdrawal or boron dilution). As the thermal power increases, moderator temperature and fuel temperature increase, causing a negative reactivity effect (from the power coefficient), and the reactor returns to the critical condition. Positive reactivity must be continuously inserted (via control rods or chemical shim) to keep the power increasing. After each reactivity insertion, the reactor power stabilizes itself proportionately to the reactivity inserted. The total amount of feedback reactivity that must be offset by control rod withdrawal or boron dilution during the power increase (from ~1% – 100%) is known as the power defect.

Let assume:

• the power coefficient:                 Δρ/Δ% = -20pcm/% of rated power
• differential worth of control rods:    Δρ/Δstep = 10pcm/step
• worth of boric acid:                                      -11pcm/ppm
• desired trend of power decrease:              1% per minute

75% → ↑ 20 steps or ↓ 18 ppm of boric acid within 10 minutes → 85% → next ↑ 20 steps or ↓ 18 ppm within 10 minutes → 95% → final ↑ 10 steps or ↓ 9 ppm within 5 minutes → 100%

In general, we have to distinguish between three types of power outputs in power reactors.

• Nuclear Power. Since the thermal power produced by nuclear fissions is proportional to neutron flux level, the most important is a measurement of the neutron flux from the reactor safety point of view. The neutron flux is usually measured by excore neutron detectors, which belong to the so-called excore nuclear instrumentation system (NIS). The excore nuclear instrumentation system monitors the reactor’s power level by detecting neutron leakage from the reactor core. The excore nuclear instrumentation system is considered a safety system because it provides inputs to the reactor protection system during startup and power operation. This system is of the highest importance for reactor protection systems because changes in the neutron flux can be almost promptly recognized only via this system.
• Thermal Power. Although nuclear power provides a prompt response to neutron flux changes and is an irreplaceable system, it must be calibrated. The accurate thermal power of the reactor can be measured only by methods based on the energy balance of the primary circuit or the energy balance of the secondary circuit. These methods provide accurate reactor power, but these methods are insufficient for safety systems. Signal inputs to these calculations are, for example, the hot leg temperature or the flow rate through the feedwater system, and these signals change very slowly with neutron power changes.
• Electrical Power. Electric power is the rate at which electrical energy is generated by the generator. For example, for a typical nuclear reactor with thermal power of 3000 MWth, about ~1000MWe of electrical power is generated in the generator.

See also: Power Distribution

The power distribution significantly changes also with changes in the thermal power of the reactor. During power changes at power operation mode (i.e., from about 1% up to 100% of rated power), the temperature reactivity effects play a very important role. As the neutron population increases, the fuel and the moderator increase their temperature, which results in a decrease in reactivity of the reactor (almost all reactors are designed to have the temperature coefficients negative). The negative reactivity coefficient acts against the initial positive reactivity insertion, and this positive reactivity is offset by negative reactivity from temperature feedbacks.

This effect naturally occurs on a global scale and a local scale.

During thermal power increase, the effectiveness of temperature feedbacks will be greatest where the power is greatest. This process causes the flattening of the flux distribution because the feedback acts stronger on positions where the flux is higher.

It must be noted the effect of change in the thermal power have significant consequences on the axial power distribution (global power distribution).

In reality, when there is a change in the thermal power, and the coolant flow rate remains the same, the difference between inlet and outlet temperatures must increase. It follows from the basic energy equation of reactor coolant, which is below:

P=↓ṁ.c.↑∆t

Power increase. Let’s assume that the reactor is critical at 75% of rated power and that the plant operator wants to increase power to 100% of rated power.

The inlet temperature is determined by the pressure in the steam generators; therefore, the inlet temperature changes minimally during the change of thermal power. It follows the outlet temperature must change significantly as the thermal power changes. When the inlet temperature remains almost the same, and the outlet changes significantly, it stands to reason the average temperature of coolant (moderator) will also change significantly. It follows the temperature of the top half of the core increases more than the temperature of the bottom half of the core. Since the moderator temperature feedback must be negative, the power from the top half will shift to the bottom half. In short, the top half of the core is cooled (moderated) by hotter coolant, and therefore it is worse moderated. Hence the axial flux difference, defined as the difference in normalized flux signals (AFD) between the top and bottom halves of a two-section excore neutron detector, will decrease.

AFD is defined as:

AFD or ΔI = I_top – I_bottom

where I_top and I_bottom are expressed as a fraction of rated thermal power.

Nuclear and Reactor Physics:

1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
6. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
7. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.

Advanced Reactor Physics:

1. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
2. K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
3. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2. 
4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.