Normal Operation – Reactor Control

Normal Operation – Reactor Control

reactor power - 75 to 100 of rated power
Power increase. Let 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.

After synchronization of generator, the reactor control system is usually switched to automatic control and the additional power increase is in this mode. After determining that all systems (NSSS and turbine-generator) are functioning properly at the initial load (e.g. 30% of rated power), the plant loading is continued to full power at a limited rate. This rate usually does not exceed 5 percent of rated power per minute. After refueling, the power increase can be further limited in order to minimize fuel cladding strain (e.g. 1 percent of rated power per hour). During this power increase (from 30% to 100% of rated power), additional startup tests can be performed to verify power distribution requirements.

In order to maintain the trend of power increase (from 30% to 100% of rated power), positive reactivity must be continuously inserted (via control rods or boron dilution). After each reactivity insertion, the reactor power stabilize itself on the power level 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 is known as the power defect. The negative reactivity due to xenon and samarium production is counteracted also by dilution of soluble poison from the coolant and by control rods withdrawal.

During reactor operation at nominal power, numerous parameters such as temperature, pressure, power level, and coolant flow are continuously monitored and controlled to ensure safe and stable operation of the reactor. The specific effects of variations in these parameters vary greatly depending upon reactor design, but generally the effects for thermal reactors are as follows.

 
Example: Power increase - from 75% up to 100%
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 property of the core. 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 but is more negative at the end of the cycle primarily due to the decrease in the moderator temperature coefficient.

Let 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 insertion of a positive reactivity (e.g. by control rodwithdrawal 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. In order to keep the power to be increasing, positive reactivity must be continuously inserted (via control rods or chemical shim). After each reactivity insertion, the reactor power stabilize 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%

reactor power - 75 to 100 of rated power
Power increase. Let 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.
Types of Reactor Power
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, from reactor safety point of view, is a measurement of the neutron flux. The neutron flux is usually measured by excore neutron detectors, which belong to so called the excore nuclear instrumentation system (NIS). The excore nuclear instrumentation system monitors the power level of the reactor by detecting neutron leakage from the reactor core. The excore nuclear instrumentation system is considered a safety system, because it provide inputs to the reactor protection system during startup and power operation. This system is of the highest importance for reactor protection system, because changes in the neutron flux can be almost promptly recognized only via this system.
  • Thermal Power. Although the nuclear power provides prompt response on neutron flux changes and it is irreplaceable system, it must be calibrated. The accurate thermal power of the reactor can be measured only by methods based on energy balance of primary circuit or energy balance of 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 a thermal power of 3000 MWth, about ~1000MWe of electrical power is generated in the generator.

Reactor Power Control

WWER-1000 reactor
Description of VVER-1000 reactor.
1) Control Element Drive Mechanism
2) Reactor vessel head
3) Reactor pressure vessel
4) Coolant inlet – outlet nozzles
5) Downcomer for coolant
6) Neutron reflector
7) Fuel assemblies
Source: www.wikipedia.org

In general, the reactor thermal power and the outlet temperature of the coolant from the reactor core are controlled by manipulating several factors which affect the core’s reactivity. In PWRs, these factors are especially:

  • position of control rods,
  • concentration of boric acid in the RCS
  • core inlet temperature

Control Rods

Control rods are rods, plates, or tubes containing a neutron absorbing material (material with high absorption cross-section for thermal neutron) such as boron, hafnium, cadmium, etc., used to control the power of a nuclear reactor. Control rods usually constitute cluster control rod assemblies (PWR) and are inserted into guide thimbles within a nuclear fuel assembly. The absorbing material (e.g. pellets of Boron Carbide) is protected by the cladding usually made of stainless steel. They are grouped into groups (banks) and the movement occurs usually by the groups (banks). Typical total number of clusters is 70. This number is limited especially by number of penetrations of the reactor pressure vessel head.

A control rod is removed from or inserted into the reactor core in order to increase or decrease the reactivity of the reactor (increase or decrease the neutron flux). Control rods (insertion/withdrawal) influences the thermal utilization factor. For example, control rods insertion causes an addition of new absorbing material into the core and this causes a decrease in thermal utilization factor.

In comparison with the chemical shim, which offset positive reactivity excess in entire core, with control rods the unevenness of neutron-flux density in the reactor core may arise, because they act locally.

Concentration of Boric Acid

Boron letdown curve (chemical shim) and boron 10 depletion
Boron letdown curve (chemical shim) and boron 10 depletion during a 12-month fuel cycle.

In pressurized water reactors, chemical shim (boric acid) is used to compensate an excess of reactivity of reactor core along the fuel burnup (long term reactivity control) as well as to compensate the negative reactivity from the power defect and xenon poisoning during power increase to nominal power.

The concentration of boric acid diluted in the primary coolant influences the thermal utilization factor. For example, an increase in the concentration of boric acid (chemical shim) causes an addition of new absorbing material into the core and this causes a decrease in thermal utilization factor.

When compared with burnable absorbers (long term reactivity control) or with control rods (rapid reactivity control) the boric acid avoids the unevenness of neutron-flux density in the reactor core, because it is dissolved homogeneously in the coolant in entire reactor core. On the other hand high concentrations of boric acid may lead to positive moderator temperature coefficient and that is undesirable. In this case more burnable absorbers must be used.

Moreover this method is slow in controlling reactivity. Normally, it takes several minutes to change the concentration (dilute or borate) of the boric acid in the primary loop. For rapid changes of reactivity control rods must be used.

 
Thermal Power and Power Distribution
See also: Power Distribution
axial-temperature-profile
It follows the temperature of top half of the core increases more than the temperature of bottom half of the core. Since the moderator temperature feedback must be negative, the power from top half will shift to bottom half.

The power distribution significantly changes also with changes of 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 very important role. As the neutron population increases, the fuel and the moderator increase its temperature, which results in 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 also on 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 feedbacks 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 basic energy equation of reactor coolant, which is below:

P=↓ṁ.c.↑∆t

Power increase. Let 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 minimallyduring the change of thermal power. It follows the outlet temperaturemust 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 change also significantly. It follows the temperature of top half of the core increases more than the temperature of bottom half of the core. Since the moderator temperature feedback must be negative, the power from top half will shift to 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 = Itop – Ibottom

where Itop and Ibottom are expressed as a fraction of rated thermal power.

Nuclear Power Plant Control – Electric Power Control

Steam generator - counterflow heat exchanger
Temperature gradients in typical PWR steam generator.

As was written, after synchronization of generator, the reactor control system is usually switched to automatic control and the additional power increase is in this mode. The power plant is then controlled by plant control system, that coordinates the NSSS and the turbine control system. The interfacing variable is in this case the core inlet temperature, which is fully determined by steam pressure inside steam generators. Note that, the core inlet temperature and the steam pressure are interconnected, since heat (or power) transferred across a steam generator is:

q = h . ΔT

 where:

  • q is amount of heat transferred (heat flux), W/m2 i.e., thermal power per unit area
  • h is heat transfer coefficient, W/(m2.K)
  • ΔT is the difference in temperature across the steam generator (in this case, the difference between the average temperature of the reactor coolant – Tavg and the saturation temperature determined by system pressure.

For all practical purposes, the heat transfer coefficient (h) is constant, since the heat transfer coefficient is a function of the materials used in the construction of the steam generator and the U-tubes are completely covered with water.

See also: Steam Turbine

When a reactor is in the automatic control, it follows the core inlet temperature – Tin (or the core average temperature – Tavg). Note that Tavg = (Tout + Tin) / 2. When there is a difference between actual Tin, actual and the temperature Tin, set, which is set in the system, the reactor control system initiate control rods movement. For example, when Tin, actual > Tin, set, the reactor control system automatically inserts control rods in order to decrease Tin, actual. The reactor thermal power remains constant, because the rods movement only offsets the reactivity from the difference (Tin, actual – Tin, set) x MTC = moderator defect.

On the other hand, if the energy demand in the external system increases, more energy is removed from reactor system causing the temperature of the reactor coolant (Tin) to decrease. As the reactor coolant temperature decreases, positive reactivity is added and a corresponding increase in reactor power level results. This reactor power increase occurs without any change in control rods position and without any change in boron concentration. The same inherent stability can be observed as the energy demand on the system is decreased.

Steam turbine of typical 3000MWth PWR
Schema of a steam turbine of a typical 3000MWth PWR.

It must be added, in case of disconnected automatic control, the turbine controls the steam pressure and the reactor control system is in manual regime. In this case a control rods insertion causes a decrease in reactor thermal power since the steam pressure remains constant. The turbine load decreases as the reactor thermal power decreases.

 
Self-regulating properties of nuclear reactor
Operating with a negative MTC is favorable operational characteristics also during power changes. At normal operation there is an exact energy balance between the primary circuit and secondary circuit. Therefore when the operator decreases the load on the turbine (e.g. due to a grid requirement), the steam demand decreases (see the initial electrical output decrease at the picture). At this moment, the reactor will produce more heat than the steam turbine can consume. This disbalance causes the steam pressure, the saturation temperature in the steam generators to increase (see II. pressure at the picture). As a result of increasing saturation temperature in the steam generators the moderator temperature will simply increase (see inlet temperature). Increasing the temperature of the moderator adds negative reactivity, which reduces reactor power (without any operator intervention). As can be seen, to a certain extent the reactor is self-regulating and the reactor power may be controlled  via the steam turbine and via grid requirements. This feature is limited, because also the range of allowable inlet temperatures is limited. It is power plant specific, but in general, power changes of the order of units of % are common.

See also: Reactor Stability

self-regulating reactor-min

Back to the automatic control, in which reactor control system controls the floating Tin, actual and is actuated when Tin, actual  – Tin, actual is greater than the preset deadband. From this point of view (Tin or Tavg control), usually three regimes are defined:
  • Constant Pressure Regime (sliding Tavg). Constant pressure (psteam) regime means that the reactor control system maintains the steam pressure inside steam generators (or at the turbine inlet) constant as turbine load changes. Also in this case, the automatic system follows  Tavg, set, but Tavg, set is a function of turbine load. For example, increasing turbine load causes steam pressure to decrease. The reactor control system would sense this decrease in steam pressure and withdraw control rods to increase the reactor coolant temperature. This type of reactor control produces ideal steam conditions at the main turbine inlet for all loads from initial load (e.g. 30%) to 100% load. The temperature difference (ΔT) between primary side and secondary side is increased by raising Tavg or proportionally by raising Tin.  The disadvantage of this type of control scheme is that just minimal changes in turbine load requires (negative MTC) an intervention of the reactor control system. Moreover there are problems with in a high reactor outlet temperature (Tout), which approaches saturation values. Therefore it is not widely used in PWRs especially for U-tube steam generators.
  • Constant Tavg Regime (sliding psteam). Constant Tavg regime means that the reactor control system maintains the average core temperature of the reactor coolant constant as turbine load changes. The automatic system follows  Tavg, set, which is constant. For example, increasing turbine load causes steam pressure to decrease. This, in turn, causes Tavg to decrease, because the turbine uses more energy than that produced by the reactor. The reactor control system would sense this decrease in Tavg and withdraw control rods to increase the reactor coolant temperature. This regime causes minimal changes in reactivity of the core, due to minimal changes in the average coolant temperature. Since the coolant temperature remains constant the coolant volume does not change and therefore the pressurizer level is remains constant for all load conditions. The disadvantage of this type of control scheme is that steam conditions (steam pressure) significantly changes from hot zero power to full load, which is unacceptable.
  • Reactor Control - Turbine Control
    Sliding Tavg and Sliding psteam Regime. The automatic system follows Tavg, set, but Tavg, set is a function of turbine load and it is programmed for best performance of the entire system.

    Sliding Tavg and Sliding psteam Regime. This regime combines the previous regimes. The automatic system follows  Tavg, set, but Tavg, set is a function of turbine load and it is programmed for best performance of the entire system. Sometimes, there are many programmed functions of Tavg, set, which are for different purposes (e.g. for initial power increase, for load-follow, for coast down). The control scheme most often selected to control the reactor is the sliding Tavg and sliding psteam regime. This regime is a compromise between the other two regimes of control and contains some of the advantages and disadvantages of each.

Pressure Control

Nuclear reactor - WWER 1200
Nuclear reactor and primary coolant system of WWER-1200.
Source: gidropress.podolsk.ru
used with permission of АО ОКБ “ГИДРОПРЕСС”

Pressurized water reactors use a reactor pressure vessel (RPV) to contain the nuclear fuel, moderator, control rods and coolant. They are cooled and moderated by high-pressure liquid water (e.g. 16MPa). At this pressure water boils at approximately 350°C (662°F).  This high pressure is maintained by pressurizer, a separate vessel that is connected to the primary circuit (hot leg) and partially filled with water which is heated to the saturation temperature (boiling point) for the desired pressure by submerged electrical heaters.

Extensive vs. intensive thermodynamic properties
Extensive and intensive properties of medium in the pressurizer.

On the other hand there are spray lines to decrease pressure inside the pressurizer, which in turn causes decrease in pressure in reactor coolant system. These spray lines sprays reactor coolant from the cold leg of a loop into the steam space and condenses a portion of the steam. The quenching action reduces pressure and limits the pressure increases.

Temperature in the pressurizer can be maintained at 350 °C (662 °F), which gives a subcooling margin (the difference between the pressurizer temperature and the highest temperature in the reactor core) of 30 °C. Subcooling margin is very important safety parameter of PWRs, since the boiling in the reactor core must be excluded. The basic design of the pressurized water reactor includes such requirement that the coolant (water) in the reactor coolant system must not boil. To achieve this, the coolant in the reactor coolant system is maintained at a pressure sufficiently high that boiling does not occur at the coolant temperatures experienced while the plant is operating or in an analyzed transient.

The pressure applied to the reactor system can also affect reactor operation by causing changes in reactivity. The reactivity changes result from changes in the density of the moderator in response to the pressure changes. Although water is considered to be incompressible, in reality, it is slightly compressible (especially at 325°C (617°F)). It is obvious, the effect of pressure in the primary circuit have similar consequences as the moderator temperature. In comparison with effects of moderator temperature changes, changes in pressure have of lower order impact on reactivity and the causes are only in the density of moderator, not in the change of microscopic cross-sections.

For example, as the system pressure rises, the moderator density increases and results in greater moderation, less neutron leakage, and therefore the insertion of positive reactivity. A reduction in system pressure results in the addition of negative reactivity. In two-phase systems such as boiling water reactors (BWR), however, the effects of pressure changes are more noticeable because there is a greater change in moderator density for a given change in system pressure.

Over-pressure Relief System

Part of the pressurizer system is an over-pressure relief system. In the event that pressurizer pressure exceeds a certain maximum, there is a relief valve called the pilot-operated relief valve (PORV) on top of the pressurizer which opens to allow steam from the steam bubble to leave the pressurizer in order to reduce the pressure in the pressurizer, thus leads to reduction of pressure in the whole system. This steam is routed to a large relief tank  in the reactor containment building where it is cooled and condensed back into liquid and stored for later disposition. There is a finite volume to these tanks and if events deteriorate to the point where the tanks fill up, a secondary pressure relief device on the tank(s), often a rupture disc, allows the condensed reactor coolant to spill out onto the floor of the reactor containment building where it pools in sumps for later disposition.

The pressurizer is equipped also with safety valves system (“safety system”), which are also routed to the relief tank. The safety valves system is used to emergency pressure reduction during emergency conditions.

Typical Pressures in Nuclear Engineering

  • Typically most of nuclear power plants operates multi-stage condensing steam turbines. These turbines exhaust steam at a pressure well below atmospheric (e.g. at 0.08 bar or 8 kPa or 1.16 psia) and in a partially condensed state. In relative units it is a negative gauge pressure of about – 0.92 bar, – 92 kPa, or – 13.54 psig.
  • A high-pressure stage of condensing steam turbine at nuclear power plant operates at steady state with inlet conditions of  6 MPa (60 bar, or 870 psig), t = 275.6°C, x = 1
  • A boiling water reactor is cooled and moderated by water like a PWR, but at a lower pressure (e.g. 7MPa, 70 bar, or 1015 psig), which allows the water to boil inside the pressure vessel producing the steam that runs the turbines.
  • Pressurized water reactors are cooled and moderated by high-pressure liquid water (e.g. 16MPa, 160 bar, or 2320 psig). At this pressure water boils at approximately 350°C (662°F), which provides subcooling margin of about 25°C.
  • The supercritical water reactor (SCWR) is operated at supercritical pressure. The term supercritical in this context refers to the thermodynamic critical point of water (TCR = 374 °C;  pCR = 22.1 MPa)

Temperature Control

Steam generator - counterflow heat exchanger
Temperature gradients in typical PWR steam generator.

As was written, the interfacing variable is in pressurized water reactors the core inlet temperature, which is fully determined by steam pressure inside steam generators. Note that, the core inlet temperature and the steam pressure are interconnected, since heat (or power) transferred across a steam generator is:

q = h . ΔT

where:

  • q is amount of heat transferred (heat flux), W/m2 i.e., thermal power per unit area
  • h is heat transfer coefficient, W/(m2.K)
  • ΔT is the difference in temperature across the steam generator (in this case, the difference between the average temperature of the reactor coolant – Tavg and the saturation temperature determined by system pressure.

For all practical purposes, the heat transfer coefficient (h) is constant, since the heat transfer coefficient is a function of the materials used in the construction of the steam generator and the U-tubes are completely covered with water.

Core inlet temperature is directly given by system parameters in steam generators. When steam generators are operated at approximately 6.0MPa, it means the saturation temperature is equal to 275.6 °C. Since there must be always ΔT (~15°C) between the primary circuit and the secondary circuit, the reactor coolant (in the cold leg) have about 290.6°C (at HFP) at the inlet of the core. As the system pressure increases, the core inlet temperature must also increase. This increase causes slight increase in fuel temperature.

See also: Power Plant Control

The most significant effect of a variation in temperature upon reactor operation is the addition of positive or negative reactivity. As previously discussed, reactors are generally designed with negative temperature coefficients of reactivity (moderator and fuel temperature coefficients) as a self-limiting safety feature. A rise in reactor temperature results in the addition of negative reactivity. If the rise in temperature is caused by an increase in reactor power, the negative reactivity addition slows, and eventually turns the increase in reactor power. This is a highly desirable effect because it provides a negative feedback in the event of an undesired power excursion.

 
Self-regulating properties of nuclear reactor
Operating with a negative MTC is favorable operational characteristics also during power changes. At normal operation there is an exact energy balance between the primary circuit and secondary circuit. Therefore when the operator decreases the load on the turbine (e.g. due to a grid requirement), the steam demand decreases (see the initial electrical output decrease at the picture). At this moment, the reactor will produce more heat than the steam turbine can consume. This disbalance causes the steam pressure, the saturation temperature in the steam generators to increase (see II. pressure at the picture). As a result of increasing saturation temperature in the steam generators the moderator temperature will simply increase (see inlet temperature). Increasing the temperature of the moderator adds negative reactivity, which reduces reactor power (without any operator intervention). As can be seen, to a certain extent the reactor is self-regulating and the reactor power may be controlled  via the steam turbine and via grid requirements. This feature is limited, because also the range of allowable inlet temperatures is limited. It is power plant specific, but in general, power changes of the order of units of % are common.

See also: Reactor Stability

self-regulating reactor-min

Power Distribution Limits

Nuclear reactors produce enormous amount of heat (energy) in a small volume. The density of the energy generation is very large and this puts demands on its heat transfer system (reactor coolant system). For a reactor to operate in a steady state, all of the heat released in the system must be removed as fast as it is produced. This is accomplished by passing a liquid or gaseous coolant through the core and through other regions where heat is generated. The heat transfer must be equal to or greater than the heat generation rate or overheating and possible damage to the fuel may occur.

The temperature in an operating reactor varies from point to point within the system. As a consequence, there is always one fuel rod and one local volume, that are hotter than all the rest. In order to limit these hot places the peak power limits must be introduced. The peak power limits are associated with such phenomena as the departure from nucleate boiling and with the conditions which could cause fuel pellet melt.

Therefore power distribution within the core must be properly limited. These limitations are usually divided into two basic categories:

  • Limitation of global power distribution
    • Axial flux difference
    • Power tilt
  • Limitation of local power distribution
    • Local Heat Flux
    • Enthalpy Rise in Hot Channel

See also: Factors that affect the power distribution

Axial Flux Difference – Axial Offset

AFD - Axial Flux Difference - Axial Offset ControlAt power operation (i.e. above 1% of rated power) the reactivity feedbacks causes the flattening of the flux distribution, because the feedbacks acts stronger on positions, where the flux is higher. It follows there must be differences also in an axial direction.

For example, let assume the inlet temperature (Tin), which is determined by the pressure in the steam generators, therefore the inlet temperature changes minimally as the thermal power changes. It follows the outlet temperature must change significantly as the thermal power increases. When the inlet temperature remains almost the same and the outlet changes significantly, it stands to reason, the average temperature of coolant (moderator) will change also significantly. It follows the temperature of top half of the core increases (in case of power increase) more than the temperature of bottom half of the core. Since the moderator temperature feedback must be negative, the power from top half will shift to bottom half. 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 = Itop – Ibottom

where Itop and Ibottom are expressed as a fraction of rated thermal power. As an example, assume the core is operating at 100% power. When the Itop = 49% and Ibottom = 51% the resulting ΔI = -2%. When the delta flux target is -5%. The core would then be able to operate with a delta flux of -10% to 0%. The + 5% and -5% flux difference around the target allows for a small amount of movement of the control rods.

During power operation, the AFD is maintained within the specified limits. Compliance with the AFD limits prevents a highly top- or bottom skewed axial power distribution. By limiting the amount of power distribution skewing, core peaking factors are consistent with the assumptions used in the safety analyses. Limiting power distribution skewing over time also minimizes the xenon distribution skewing, which is a significant factor in axial power distribution control.

The operating scheme used to control the axial power distribution involves maintaining the AFD within a tolerance band around a burnup dependent target, known as the target flux difference, to minimize the variation of the axial peaking factor and axial xenon distribution during unit maneuvers.

For plants operating with so called “constant axial offset control – CAOC”, the AFD limit involves a target band. This target band is, for example, +5% and -5% around the target value. Since the xenon concentration and distribution is flux and time dependent, the longer the core operates outside its target band, the greater the probability of initiating a xenon transient.

The target flux difference (ΔItarget) and its burnup dependent value is determined at equilibrium xenon conditions. The AFD is sensitive to many core related parameters such as control bank positions, core power level, axial burnup, axial xenon distribution and, to a lesser extent, reactor coolant temperature and boron concentrations.

Constant Axial Offset Control (CAOC) is a strategy, which is used to control axial power distribution in normal operation. CAOC requires that the AFD must be controlled within a narrow tolerance band around a burnup dependent target to minimize the probability of initiation xenon oscillations during power maneuvers. It also minimizes the variation of axial peaking factors.

Axial offset is defined as:

A/O = (Itop – Ibottom)/(Itop + Ibottom)

where Itop and Ibottom are expressed as a fraction of rated thermal power.

AFD and Safety Analyses

In summary, the AFD and the QPTR are direct and continuous measures of the core’s global power distribution. AFD measures global axial power distribution, whereas QPTR measures global azimuthal power distribution. Staying within their limits and proper operation of the control rods should maintain acceptable peaking factors (FQ(z) and FΔH) on a continuous basis. The AFD and QPTR limits ensure that peaking factors (FQ(z) and FΔH) remain below their limiting values by preventing an undetected change in the gross axial and radial power distribution.

Together, the LCO limits on the AFD, the QPTR, the rod insertion limits and the power distribution (i.e. the Heat Flux Hot Channel Factor (FQ(z)), the Nuclear Enthalpy Rise Hot Channel Factor (FNΔH)) are established to preclude core power distributions that exceed the safety analyses limits.

 
Axial Offset Anomaly
As was written, the axial offset – A/O (or AFD) and the QPTR are direct and continuous measures of the core’s global power distribution. A/O measures global axial power distribution, whereas QPTR measures global azimuthal power distribution. Staying within their limits and proper operation of the control rods should maintain acceptable peaking factors (FQ(z) and FΔH) on a continuous basis. The AFD and QPTR limits ensure that peaking factors (FQ(z) and FΔH) remain below their limiting values by preventing an undetected change in the gross axial and radial power distribution.

In past, some PWR-type nuclear power plants (with LiOH water chemistry) have experienced small radial and especially axial offset anomalies (AOA). That means, some PWRs have experienced a unexpected and gradual shift in the target flux difference (ΔItarget) towards more negative values – shift of power from top half to bottom half.

After extensive research, it was found that AOA can be caused by crud buildup on high-power fuel assemblies, in which an increased subcooled nucleate boiling can occur. Since this subcooled nucleate boiling occurs in the upper part of the assembly, crud accumulation causes an accumulation of boron on the surface of the upper part of the assembly. Lithium borate is absorbed and concentrated in the crud layer, reducing the fission rate in the upper portion of the core. It must be noted, not all reactor cores have experianced the AOA, it is now known that AOA is caused by a combination of high crud level in the coolant, high boiling intensity in the core and is strongly dependent on reactor water chemistry. Note that, some reactor design use LiOH to control pH of the reactor coolant and some use KOH.

In result, during fuel cycle the neutron flux shifts from top half to bottom half and causes an increase in local peaking factors. Crud accumulation may also cause a reduction in available SDM (3-4 pcm/day).  Near the end of cycle, excess burnup in the bottom of the core and reduced boron and lithium concentrations in the reactor coolant system cause the power distribution to shift back toward the upper portion of the core, partially restoring the burnup distribution.

Special Reference: Information Notice No. 97-85: Effects of Crud Buildup and Boron Deposition on Power Distribution and Shutdown Margin, US NRC, 12/1997.

Power Tilt – Flux Tilt – Quadrant – Sextant Symmetry

A power tilt, or flux tilt, is a specific type of core power distribution problem. It is a non-symmetrical variation of core power in one quadrant (PWRs) or in one sextant (WWERs) of the core relative to the others. The power in one quadrant (or sextant) might be suppressed by over-insertion of control rods in that quadrant of the core, which, for a constant overall power level, results in a relatively higher flux in the remainder of the core. This situation can also lead to spatial xenon oscillations (azimuthal oscillations).

Therefore, plant operators define a parameter known as quadrant power tilt (QPT) or quadrant power tilt ratio (QPTR) in the Technical Specifications.

Special link: NRC – Standard Technical Specifications

QPTR is defined as:

The ratio of the maximum upper excore detector calibrated output to the average of the upper excore detector calibrated outputs, or the ratio of the maximum lower excore detector calibrated output to the average of the lower excore detector calibrated outputs, whichever is greater.

QPTR is usually provided by four or six tandem (upper and lower) excore power range neutron detectors, which belong to so called the excore nuclear instrumentation system (NIS). During normal operation, this parameter must be continuously verified. The limit (Limiting Condition for Operation – LCO) for QPRT and SPTR is usually QPTR < 1.02. Operation beyond these limits could invalidate core power distribution assumptions used in the accident analysis.

QPTR and Safety Analyses

In summary, the AFD and the QPTR are direct and continuous measures of the core’s global power distribution. AFD measures global axial power distribution, whereas QPTR measures global azimuthal power distribution. Staying within their limits and proper operation of the control rods should maintain acceptable peaking factors (FQ(z) and FΔH) on a continuous basis. The AFD and QPTR limits ensure that peaking factors (FQ(z) and FΔH) remain below their limiting values by preventing an undetected change in the gross axial and radial power distribution.

Together, the LCO limits on the AFD, the QPTR, the rod insertion limits and the power distribution (i.e. the Heat Flux Hot Channel Factor (FQ(z)), the Nuclear Enthalpy Rise Hot Channel Factor (FNΔH)) are established to preclude core power distributions that exceed the safety analyses limits.

Hot Channel (Peaking) Factors

Heat Flux Hot Channel Factor – FQ(z)

The Heat Flux Hot Channel Factor – FQ(z) is defined as:

  1. The ratio of the maximum local linear power density, where there is a minimal margin to limiting fuel temperature (during AOOs), to the average local linear power density in the core.
  2. The maximum local linear power density [kW/ft] in the core divided by the core average fuel rod linear power density [kW/ft].

Operation within the Heat Flux Hot Channel Factor – FQ(z) limits prevents power peaks that exceed the loss of coolant accident (LOCA) limits derived from the analysis of the Emergency Core Cooling Systems (ECCS). In this analysis, fuel cladding failure during a postulated LOCA is limited by restricting the maximum linear heat rate (LHR) so that the peak cladding temperature does not exceed the acceptance criterion (e.g. 2200°F or 1204°C). Cladding temperatures below this criterion exclude severe cladding failure by oxidation due to a cladding-steam reaction. The Heat Flux Hot Channel Factor – FQ(z) is an assumption in these and other analyses as well as it is an assumption for Safety Limits (SLs) calculations. Operation beyond the Heat Flux Hot Channel Factor – FQ(z) could invalidate core power distribution assumptions used in these analyses (Safety Analyses and Safety Limits derivation).

Now, consider a case where power distribution is limited only by the FQ(z). But FQ(z) can be limiting at each elevation of the core (axially flat distribution). The maximum heat flux at several core elevations can occur in the same channel. In this case the coolant enthalpy rise would be very high, most probably over-limit. In this case, DNB is more likely to occur, because the critical heat flux is significantly lower when coolant enthalpy is higher. Therefore, the FQ(z) itself cannot be used to prevent DNB occurrence and the enthalpy rise hot channel factor must be introduced.

Nuclear Enthalpy Rise Hot Channel Factor – FNΔH

The Nuclear Enthalpy Rise Hot Channel Factor – FNΔH is defined as:

  1. The ratio of the integral of linear power along the fuel rod on which minimum departure from nucleate boiling ratio occurs (during AOOs) , to the average fuel rod power in the core.
  2. The ratio of the integral of linear power along the fuel rod with the highest integrated power [kW/rod] to the average rod power [kW/rod].

Operation within the Nuclear Enthalpy Rise Hot Channel Factor – FNΔH limits prevents departure from nucleate boiling (DNB) during accidents, that are limiting from DNB point of view. For example, a loss of forced reactor coolant flow accident, a loss of normal feedwater flow or an inadvertent opening of a pressurizer relief valve. The Nuclear Enthalpy Rise Hot Channel Factor FNΔH is an assumption in these and other analyses as well as it is an assumption for Safety Limits (SLs) calculations. Its merit is that FNΔH provides with an information about power distribution as well as about the coolant temperature (enthalpy). Both are crucial for DNB occurrence. Operation beyond the Nuclear Enthalpy Rise Hot Channel Factor – FNΔH could invalidate core power distribution assumptions used in these analyses (Safety Analyses and Safety Limits derivation).

DNB occurs when a fuel rod cladding surface is overheated, which causes the formation of a local vapor layer, causing a dramatic reduction in heat transfer capability. Proximity to the DNB condition is expressed by the departure from nucleate boiling ratio (DNBR), defined as the ratio of the cladding surface heat flux (known as the critical heat flux) required to cause DNB to the actual cladding surface heat flux. The minimum DNBR value during both normal operation and anticipated transients is limited to the DNBR correlation limit for the particular fuel design in use, and is accepted as an appropriate margin to DNB. The DNB acceptance criterion for an anticipated operational occurrence (AOO) is met when there is a 95 percent probability at a 95 percent confidence level (the 95/95 DNB criterion) that DNB will not occur, and the fuel centerline temperature stays below the melting temperature.

Base load vs Load Follow

Base Load - Load Follow - Peak Load
Base Load vs Peak Load Power Plants

Nuclear power plants may take many hours, if not days, to startup or to change their power output. Modern power plants can and do operate as load following power plants and alter their output to meet varying demands. But base load operation is the most economical and technically simple mode of operation. It is primarily due to the fact, they require a long period of time to heat up the nuclear steam supply system and the turbine-generator to operating temperature. From this point of view power plant generally are divided into two basic categories:

  • Base Load Power Plant
  • Load Following Power Plant

Base Load Power Plant

Electricity Generation by SourceIn general, nuclear power plants (NPPs) have been considered as base load sources of electricity as they rely on a technology with low variable costs and high fixed costs. This is the most economical and technically simple mode of operation. In this mode, power changes are limited to frequency regulation for grid stability purposes and shutdowns for safety purposes. Different plants and technologies may have differing capacities to power changes on demand.  Base load power plants are generally run at close to maximum output (100% of rated power) continuously (apart from maintenance, refueling outages). During refueling, every 12 to 18 months, some of the fuel – usually one third or one quarter of the core – is replaced by a fresh fuel assemblies. After refueling the reactor is usually started up and operated again at nominal power.

Although most of nuclear power plants were designed as base load power plants, today, the utilities have had to implement or to improve the manoeuvrability capabilities of their NPPs in order to be able to adapt electricity supply to daily, seasonal or other variations in power demand. It is due to the share of nuclear power in the national electricity mix of some countries has become large, and due to the significant increase renewable energy sources.

Load Following Power Plant

As was written, nuclear power plants (NPPs) have been considered as base load sources of electricity as they rely on a technology with low variable costs and high fixed costs. However that situation is changing in several countries. Today, the main motivation for load following with nuclear power plants comes from the large-scale deployment of intermittent electricity sources (like wind and solar power). An intermittent energy source is any source of energy or electrical power that is not continuously available due to some factor outside direct control. For example, in the absence of an energy storage system, solar does not produce power at night or in bad weather and varies between summer and winter.

On the other hand, electrical energy must be generated at the same rate at which it is consumed. A sophisticated control system is required to ensure that the power generation very closely matches the demand. If the demand for power exceeds supply, the imbalance can cause power plants and transmission equipment to automatically disconnect and/or shut down to prevent damage. In the worst case, this may lead to a cascading series of shut downs and a major regional blackout. The challenge is not only technical. Due to the sudden influx of large amounts of wind power, German, Dutch, Czech and Austrian power markets have experienced several hours of negative electricity prices in recent years and many more hours with prices that were lower than the variable costs of nuclear power plants, which have the lowest variable costs among the large-scale established power sources. Moreover the load follow operation is economically very inefficient as nuclear power generation is composed almost entirely of fixed and sunk costs. Therefore, lowering the power output doesn’t significantly reduce generating costs and the plant.

To manage this problem, the utilities have had to implement or to improve the manoeuvrability capabilities of their NPPs in order to be able to adapt electricity supply to daily, seasonal or other variations in power demand. The power plant with this improved manoeuvrability is known as load follow power plant. In general, load following power plant is a power plant that adjusts its power output as demand for electricity fluctuates throughout the day. Load following plants are typically in-between base load and peaking power plants.

For example, according to the current version of the European Utilities Requirements (EUR) the nuclear power plant must be capable of daily load cycling operation between 50% and 100 % of its rated power, with a rate of change of electric output of 3-5% of rated power per minute.

From the reactor operation viewpoint, in the case of pressurised water reactors (PWRs), the reactor thermal power and the global power distribution (especially the AFD) are controlled by manipulating several factors which affect the core’s reactivity. In PWRs, these factors are especially:

  • position of control rods,
  • concentration of boric acid in the RCS
  • core inlet temperature

A control rod is removed from or inserted into the reactor core in order to increase or decrease the reactivity of the reactor (increase or decrease the thermal power). For example, control rods insertion causes an addition of new absorbing material into the core and this causes a decrease in thermal power.

Boric acid is used to compensate an excess of reactivity of reactor core along the fuel burnup (long term reactivity control) as well as to compensate the negative reactivity from the power defect and xenon poisoning during power increase to nominal power.

AFD - Axial Flux Difference - Axial Offset ControlSpecial attention requires the axial flux difference control. The axial flux difference, is defined as the difference in normalized flux signals (AFD) between the top and bottom halves of a two section excore neutron detector:

AFD or ΔI = Itop – Ibottom

The AFD is sensitive to many core related parameters such as control bank positions, core power level, axial burnup, axial xenon distribution and, to a lesser extent, reactor coolant temperature and boron concentrations.

During power maneuvers, the operating scheme used to control the axial power distribution involves maintaining the AFD within a tolerance band around a burnup dependent target, known as the target flux difference, to minimize the variation of the axial peaking factor and axial xenon distribution.

For plants operating with so called “constant axial offset control – CAOC”, the AFD limit involves a target band. This target band is, for example, +5% and -5% around the target value. Since the xenon concentration and distribution is flux and time dependent, the longer the core operates outside its target band, the greater the probability of initiating a xenon transient.

Load Follow without Boron Adjustment

reactor power - 100 to 75 of rated powerSmaller load changes does not require boron adjustment. For a power decrease, without using boron addition to overcome the positive reactivity added by the power defect, the control rods must be inserted to maintain Tavg. From this point on with a continuing decrease in power, pressure inside the steam generator will increase adding negative reactivity.

Load Follow with Boron Adjustment

More extensive maneuvers usually require boron adjustment to compensate for xenon reactivity changes, thereby keeping the control rods within its axial flux distribution (AFD) target band.  Boron concentration changes during plant operation are required whenever axial flux difference (AFD) would extend outside the allowable target band. As was written, this target band is, for example, +5% and -5% around the target value. Following the power level change made by the control rods, the plant operator or the control system makes boron concentration adjustments whenever the AFD approach the limits of the target band.

Grey control rods

Some nuclear power plants use so called “grey control rods” for load following. These plants have the capability to make power maneuvering between 30% and 100% of rated power, with a slope up to 5% of rated power per minute. They can respond very quickly to the grid requirements. In order to fulfill these requirements without introducing a large perturbation of the power distribution, special control rods have to be used. These control rods are called “grey” control rods. Grey control rods use a grey neutron absorber, which absorbs less neutrons than a “black” absorber.  Consequently, they cause smaller depressions in the neutron flux and power in the vicinity of the rod. The rod control system automatically modulates the insertion of the axial offset (grey) control bank, which controls the axial power distribution.

In the case of the boiling water reactors (BWRs), the power regulation is performed by changing the coolant flow rate (using the recirculation pumps) and/or the control rods. No boron regulation is used in BWRs.

 
References:
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.

See above:

Reactor Operation