# Nuclear Reactor Feedback System

1. Oct 22, 2008

### verybiased

Hello Chaps,

I have been thinking about for a bit and the texts i have are quite vague on the topic. I'd like to know what monitoring devices are used for the control rods. I would have to assume that power output or neutron detection is used for this purpose?

Cheers,
Rhys

2. Oct 22, 2008

### Staff: Mentor

Plants have ex-core and in-core (more recent) neutron detectors which monitor the power, and thermo-couples. The detectors feed into the reactor protection system which contains the logic circuits that will trip the reactor, i.e. drop the control rods (PWR) or insert from below (BWR) control rods. Some plants have fixed in-core probes, while others allow traveling in-core probes for which the axial position can be adjusted. Fixed in-core probes acutally have multiple detectors at different elevations, which enables the operators to monitor the axial power shape during operation. Ex-core detectors at different elevations can also be used to monitor the axial power distribution, but that is very course, and basically they are limited to measuring the average power in the top and bottom of the cores.

In PWRs, the control rods are suspended magnetically and those circuits are switched off (de-energized) when given the appropriate signal. The PWR control assemblies then drop by gravity into the core. During operation, the tips of the control rods sit just below the upper nozzle (head, Kopf, upper tie plate) in the guide tubes.

In BWRs, the control blades (cruciform) reside among four assemblies in a cell. During operation, some control blades are inserted in the core for reactivity control, and they are periodically re-positioned to allow for more uniform burnup accumulation (sequence exchanges or deep-shallow swaps, and pattern adjustments). The in-core detectors reside betweent cells, and are located diagonally away from the control blade corner of the assembly.

3. Oct 22, 2008

### verybiased

Hey, thats exactly what I wanted to know. You are obviously very knowledgeable, thankyou so much!

4. Oct 23, 2008

### gmax137

The following is for PWRs (BWRs are similar but different). The power produced by the reactor is not really controlled by the control rods. The temperature is. The power is determined by the load on the steam generators (and ultimately the turbine-generator). If the load on the turbine goes up, the coolant temperatures in the reactor will go down, and the core power will go up (that's the negative reactivity feedback). In a plant with active rod control, the conrol system would detect the mismatch between the power (measured at the turbine) and the temperatures, and withdraw the rods to increase the reactivity to raise the temperatures. Many plants do not operate this way, preferring to let the operators make the reactivity change (ie, the rod control is not in automatic mode). Since the plants run at full load most of the time it doesn't really matter. The rod control discussed by Astronuc above - tripping the reactor by dropping the rods - that's another thing altogether, and is certainly enabled in automatic.

5. Oct 25, 2008

### vanesch

Staff Emeritus
That's for plants in base load. However, it is also entirely possible (and many people don't know this - there are even ill-informed environmentalists who use this as an argument against nuclear) to use plants in load-following mode, that is, they respond to the needs of the grid.

In France, this is done as follows: the frequency of the grid is used as a measure of the balance of power in to power consumed (if there's less power in than consumed, the frequency, 50 Hz, will reduce slightly), and the steam drawn from the steam generators is regulated as a function of this (using a proportional, or an integrating/proportional regulation scheme). In regulatory mode "G", they use "grey" control rods with special absorption profiles along the rods and different groups of rods, and these are coupled to the coolant exit temperature (maybe also a bit to the actual neutronic nuclear power in feed forward mode but I don't know this). As such, the temperature can be kept constant and nuclear power will follow demanded power by the turbines. The different profiles of absorption are studied in such a way to avoid axial flux fluctuations, which was the problem when trying to regulate power with all black rods.
The power range of an N4 plant is between nominal power 100%, and about 30% of nominal. Below that, manual steering is necessary. The slew rate is about 5% of nominal power per minute, which is sufficient to follow more than 99% of all consumption profiles.

The base load mode, or steering mode "A" is not done with control rods, but with boric acid concentrations, and that is of course a very slow mode of steering with no much flexibility. This was the old power plant mode of steering which gave nuclear plants its name of being unflexible.

There's no need in flexible nuclear plants if it is only a minority contribution in the available power generation. As a nuclear plant is capital intensive with cheap fuel, it is economically best to use it in base load if possible. But this is by no means necessary.

6. Oct 25, 2008

### Staff: Mentor

Reactivity control in PWRs is primarily achieved through soluble boric acid (with a LiOH buffer). The control rods reside out of the core. Perhaps that was not clear from my comment, "During operation, the tips of the control rods sit just below the upper nozzle (head, Kopf, upper tie plate) in the guide tubes."

There are a few exceptions in the US in the B&W plants, which used APSRs (Axial Power Shaping Rods - grey rods, which use Inconel absorber), which have been tradiationally inserted for most of the cycle and which have been withdrawn near the end of cycle. The APSR's affect axial power shape in the periphery of the core, and also the radial power distribution in the core. The Westinghouse AP-1000 is being designed with grey rods, so that load following in a possibility, as well as an alternate to soluble boron. PCI will be an issue.

BWRs most certainly use control rods to control reactivity since they cannot use a soluble neutron absorber due to the boiling in core. The control rods are in 4 groups or sequences, and during the operation some control rods are deeply inserted and others are shallow (not so much). The deep and shallow rods are exchanged periodically, and as the cycle progresses, the depth of insertion and number of control rods used decreases. Just before end of cycle (EOC), BWRs go to "all rods out" (ARO).

BWR operators can also use flow control to adjust reactivity and power. Decreasing flow increases the void in the upper part of the core, and that promotes a spectral shift (hardening of the flux, i.e. proportionally more fast flux or lower thermal flux). The greater fast flux produces more Pu-239, Pu-240 in the U-238. Then increasing the flow, the void in the upper part of the core is reduced and the increase in thermal flux burns the fissile Pu.

Both PWRs and BWRs can also use Feedwater Temperature Reduction, but this is usually done near EOC.

Last edited: Oct 25, 2008
7. Nov 1, 2008

### Morbius

vanesch,

You are quite correct. Let me elaborate a little.

In any AC electrical grid - the generators have to turn in unision so that they are all on the same portion
of the 50 Hz {France] or 60 Hz[USA] wave.

Suppose we have a PWR - and PWRs will "load follow" or "follow the turbine". Suppose a big factory
turns on and starts to demand more power from the grid. That will cause an increased current in the
windings of the PWR plant's generator. The increased current flow means that there will be a greater
resistive torque - the turbine will see a generator that is more difficult to turn. This only makes sense;
with more current in the generator windings, and the generator voltage is constant - the increased current
means increased power out of the generator - and that power has to come from the turbine.

If nothing were done - the turbine and generator would slow down since it is harder for the turbine to turn
the generator. If the generator slowed down - it would go out of phase with the rest of the generators on
the grid. Recall I stated above that the generators on the grid turn in unision.

There's a controller or feedback mechanism on the turbine generator that monitors the turbine / generator
speed and corrects for any deviation by opening or closing the turbine throttle valve. In the case above,
the controller will open up the turbine throttle in order to increase the turbine power so that it can turn the
generator at the proper speed under the increased load.

The increased steam flow to the turbine means that more energy is leaving the steam generator; and
hence the primary water leaving the steam generator going back to the reactor will be a little cooler than
it was at equilibrium conditions prior to the factory powering up.

That cooler water will lower the reactor moderator temperature. The reactor responds via the moderator
temperature reactivity coefficient - a cooling moderator gives you an increased reactivity and hence
increased reactor power. The reactor power will increase until the increase in power matches the
increased power being drawn from the steam generator. When the reactor reaches this new power level;
then coolant temperatures will be back at their equilibrium values.

The temperatures will be back at equilibrium - but the reactor is producing more power which is equal to
the increased power being drawn from the steam generator which gives you the increased power of the
turbine which gives you the increased power from the generator - which is what is needed to meet the
demand by the factory that just fired up.

Dr. Gregory Greenman
Physicist

8. Nov 2, 2008

### gmax137

Morbius - You're right on up to the end when you say the reactor temperatures return to their equilibrium temperature. While I agree that the temperature will reach "an" equilibrium, it will be "too low" relative to the desired temperature program (and the steam generator pressure will also be off). The operators (or a reactor regulating system) will have to pull rods a bit or the operators will need to dilute the boron a little to get the temperature back up on the program. And if the load change was big enough, subsequent actions will be required to deal with the xenon transient.

9. Nov 3, 2008

### Morbius

gmax137,

NOPE - in order for the reactor to reacth steady state - i.e. for the reactivity to be zero and the
reactor to be again exactly critical - the temperature has to return to the same equilibrium temperature.

The reactivity is a function of temperature - and when the reactor reaches steady state - the reactivity
has to be exactly zero - and thus the reactor has to return to the equilibrium temperature.

This is an often misundersood property of a reactor.

Dr. Gregory Greenman
Physicist

10. Nov 3, 2008

### gmax137

Are you saying that the temperature returns to the pre-transient value? I don't see how that can be, and I don't think that's what really happens. With no operator action, the final temperature would depend on the relative values of the feedback coefficients for the moderator temperature and fuel temperature. And since these vary with burnup, the final temperature would also vary during the cycle.

11. Nov 3, 2008

### Morbius

gmax137,

Is not the reactivity of the reactor a function of the temperature?

In other words, $$\rho$$ = $$\rho$$(T). where T is the average temperature

Before the change in power; what was the reactivity of the reactor?
Since it was exactly critical - it was steady-state - the reactivity $$\rho$$ = 0 identically.

Now after the transient, when the reactor is back at steady state; what is the criticality of the
reactor. The reactor at steady state is again exactly critical. So what is the reactivity of a
reactor that is exactly critical? The reactivity of an exactly critical reactor is again exactly zero.

So the "average" temperature has to go back to what it was. Now the temperature distribution
is going to be different - the delta T - the difference between input and output temperatures will
be greater - but the average temperature is going to be the same.

How could it be otherwise. Suppose you took an exactly critical reactor and increased the
temperature uniformly by some value. What would happen to the criticality? The criticality
would go down due to lots of effects - moderator temperature coefficient, Doppler broadening...

Since you started with a critical reactor - the increased temperature would drive the reactor
sub-critical.

The final state has to satisfy two conditions. The delta T across the reactor has to increase
because it is at higher power AND the average temperature has to return to equilibrium values
otherwise the reactor is not critical - it's either subcritical or supercritical.

Dr. Gregory Greenman
Physicist

12. Nov 3, 2008

### Homer Simpson

This seems pretty tricky as a way of controlling reactor power. Im a Candu guy, and mod temp is held constant at these plants (and it appears the mod temp coeff is opposite, candu cooler mod means less reactivity)

So in a PWR boiler pressure would have a huge reactivity effect? ie. lower boiler pressure means cooler reactor inlet temps, so more reactivity? I would guess that boiler pressure has to be ramped down with increasing turbine power for reactivty reasons?

I guess that means Candu is way better?

just kidding :)

13. Nov 4, 2008

### Morbius

Homer,

Nope - in terms of moderator coefficient - BOTH US PWR's and CANDU's are the SAME - lower
moderator temperature --> denser moderator --> more reactivity [ not less ].

The difference comes with respect to coolant temperature. Now in a US PWR; the coolant and
moderator are the SAME - so the coolant temperature feedback is as above.

In a CANDU, the reactor is over-moderated; there's enough moderating capability in the heavey water,
D20, moderator that no additional moderation from the light water, H20, coolant is needed. The H2O coolant is
not needed for moderation; but it does absorb neutrons parasitically. [ H2O coolant in a US PWR is a
"mixed bag"; the H2O also absorbs neutrons parasitically, but the US PWR needs the H2O as moderator,
and that effect wins. In the CANDU, the moderating power of the H2O is not needed - so for a CANDU
the H2O coolant is parasitic absorber ].

Because the H2O coolant is a parasitic absorber; when the coolant temperature goes up - the H2O
becomes less dense - hence its macroscopic absorption cross-section goes down - the parasitic
absorption of neutrons by the H2O is less - and hence reactivity INCREASES.

So as the coolant temperature increases - reactivity goes up - and reactor power goes up; which is
the exact OPPOSITE of what you want it to do. The CANDU has a positive coolant temperature
reactivity coefficient.

That's why a CANDU can not be licensed in the USA. The CANDU does not meet one of the US
Nuclear Regulatory Commission's safety requirements - that the reactor have a negative reactivity
coefficient for coolant temperature.

NOPE - the reactor pressure is kept constant - and the temperature feedback that I described above
means the reactor naturally "load follows". You keep the reactor pressure constant - and the reactor
will automatically match its power to the power demad of the turbine.

The CANDU doesn't "load follow" - in fact - it runs the other way. Without external reactivity controls;
the CANDU would tend to ramp power down in response to increased demand; and would ramp power
up in response to reduced demand.

Dr. Gregory Greenman
Physicist

14. Nov 4, 2008

### Morbius

For example, suppose before the big factory fires up the intlet temperature to the PWR is 550 F
and the outlet temp is 650 F - for an "average" of 600 F. The differential is 100 F.

Suppose the power needs to be increased by 10% and the coolant flow rate remains constant.
That means we now need a temperature differential of 110 F.

Suppose the new inlet temperature was the same as the old 550 F; so with the new differential,
the outlet temp would be 660 F. Would you not agree under these circumstances that every
bit of coolant in the reactor was hotter than before? Near the inlet the difference would be small;
and near the outlet - the increase is 10 F.

Now since coolant at all levels in the core is warmer than before - the coolant temperature coefficient
would dictate that the reactivity would be less than the before condition. However, at the before
condition, the reactor was exactly critical - reactivity = 0; so the fact that the temperature feedback
due to the above conditions would imply that the reactivity was less than 0; i.e. the core was sub-critical.

Therefore, inlet of 550 F and outlet of 660 F is NOT an equilibrium solution - it has the reactor subcritical.

However, if the inlet temperature were 545 F and the outlet temperature was 655 F - then the average
temperature would be 600 F as before. The constraint is that the temperature distribution has to be
such that the reactor is back to exactly critical in order for there to be a new steady state - and that
new steady state looks a lot like the old steady state.

Suppose however that the coolant flow rate in the reactor were increased by 10% with the reactor
at an increased power of 10% more. In that case, the temperature differential across the core would
again be 100 F; and the equilibrium temperatures would be EXACTLY as before; inlet temperature
of 550 F and outlet temperature of 650 F.

Dr. Gregory Greenman
Physicist

Last edited: Nov 4, 2008
15. Nov 4, 2008

### gmax137

I'm sorry but I'm going to drag this out just a little longer - Morbius's explanation above seems to neglect the fact that the fuel temperature will change in addition to the moderator/coolant temperature change. In the increased load scanario, we end up with higher reactor power, and assuming that the coolant flow rate is unchanged, the temperature difference between the fuel and the coolant must also increase (this is required to transfer the increased power (heat) from the fuel to the coolant). This occurs through (1) an increase in the fuel temperature and (2) a decrease in the coolant temperature. The increased fuel temperature adds a negative component to the reactivity (since the fuel temperature feedback is negative). To reach the final equilibrium condition (reactivity exactly zero, as Morbius states), the coolant temperature must decrease (since the moderator reactivity feedback is also taken here to be negative). The negative reactivity due to the fuel temperature increase must be balanced by the positive reactivity due to the coolant temperature decrease. The relative magnitudes of the temperature changes is determined by the relative magnitudes of the reactivity feedback coefficients.

16. Nov 4, 2008

### Morbius

gmax,

EXACTLY - and when you plug in the numbers - you find that the difference between the bulk average
coolant temperature before vs. after is quite small.

The coolant temperature coefficient is the LARGEST feedback in a PWR; and hence you don't have
much of a temperature difference at all.

As you stated, if any thing; the coolant temperature is a little less.

Most of the time people think that the coolant temperature is going to be greater due to the
higher power.

Dr. Gregory Greenman
Physicist

17. Nov 4, 2008

### Homer Simpson

This should be fun...

I can assure you that Candu has a positive mod temp co-eff, hotter mod, more reactivity. It's due in part to what you said, the reactor is overmoderated. So, hotter mod, less dense, less moderation: less overmoderated, less parsitic absorbtion... so more reactivity. The other reason, which is actually more dominant, is the increase in reproduction factor 'n' since the warmer mod hardens the spectrum of the thermalized neutrons, upshifting the energy nearer to the 0.3 eV peak for Pu-239 absorbtion/fission. Since Candu equilibreum fuel has significant Pu-239, this effect is relatively large.

It is true for Candu, as you did mention, that as COOLANT gets hotter, reactivity goes up, mainly due to spectrum hardening as touched on above.

All the Candu's Im familiar with use D2O pressurized coolant loop. There is a light water version yet to to be built I believe. As for power coefficiant, the Candu actually has a negative one. As power goes up, core reactivity goes down. (light water liquid zones drop to maintain critical) the neg power coeff is due to the dominant overall factor of negative fuel power coefficiant. As the fuel heats, the doppler broadening effect causes increased resonance capture in U238, wasted neutrons, lower reactivity.

I believe the main reason the States bock at the Candu is due to the positive void co-efficiant.

I was talking about the secondary side boiler pressure. If as you say, the average temp of the reactor is held constant as power increases, then this must mean that inlet temps are lower and outlet higher. So if inlet temps are lower, this must mean that the secondary side boiler is running cooler, so at a lower pressure? This would also be supported by the fact that you need more heat transfer to the secondary side boiler water, so if the the reactor side water is the same average temp, then the boiler water must be lower average temp in order to achieve higher heat transfer according to Q=U A dT

Last edited: Nov 4, 2008
18. Nov 5, 2008

### vanesch

Staff Emeritus
Although it is true that a "free-running" PWR naturally works in load following, nevertheless, people prefer to use active control mechanisms to do so, simply because this limits the temperature excursions (and hence the thermal load) on all of the vessel and piping and materials. I know that the french load-following reactors are equipped with active feedback loops which try essentially to keep the temperature of the primary water constant within a few degrees.

But it is true that any "passively safe" reactor will in principle work in load following. I guess one of the most dramatic examples are the pebble bed reactors.

19. Nov 5, 2008

### Staff: Mentor

PWR's operate with a narrow range of temperature 285-291°C (545-556°F) inlet, and the outlet being something like 325-330°C (617-626°F). At HZP, the outlet temperature is the same as inlet. Flowrate is generally constant regardless of power, except it can vary with number of pumps, e.g. 3 or 4 in a 4 loop plant.

The average coolant and exit temperatures will vary with power, but at most the variation of the average would be 20°C.

The inlet temperature can be lowered by lower the inlet (lower) temperature of the feedwater to the steam generator.

The fuel temperature is largely dependent on the linear heat generation rate (power density) and fuel thermal conductivity which decreases with burnup, and it affects the resonance absorption (Doppler feedback).

Some advanced reactor designs like the AP-1000 and EPR are designed to use grey rods, which use an inconel absorber, as opposed to Ag-In-Cd, B4C, Hf or dysprosia/dysprosium titanate.

BWR load follow with flow (and pressure) control primarily. The coolant temperature is mostly at saturation, with the lower single phase (and with nucleate boiling) portion of the core having to rise from inlet temperature (~ 278°C (533°F)) increasing to saturation 286°C (547°F).

20. Nov 5, 2008

### Morbius

GEESH - a positive moderator temperature coefficient too?? The CANDU is LESS SAFE in terms
of feedback than I had envisioned. I knew that it was overmoderated to the degree that the coolant
temperature coefficient was negative; but I didn't think the moderator coefficient was also positive.
I keep getting this one confused; whether the coolant is light or heavy water; I flipped this one because
I usually remember this wrong - and I flipped it one too many times. As I recall, there was one built
that was a "one-off" - it had the opposite of what the others had. Also wasn't one CANDU built
rotated 90 degrees. A graduate school colleague of mine that is Canadian always called that the
"CANDU on its side" - and I called it the "only CANDU that is right side up"
Yes - but I believe that I'm correct that you can NOT license a CANDU in the USA.

Dr. Gregory Greenman
Physicist