International Conference
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Bled / Slovenia / September 14-17
The Impact of Load Following and Frequency Control on the Determination of Thermal Power in Nuclear Power Plants
Herb Estrada, Ernest Hauser Cameron
Caldon Ultrasonics 1000 McClaren Woods Drive
Coraopolis, PA 15108
herbestrada@comcast.net, ernie.hauser@c-a-m.com ABSTRACT
If a large fraction of the power generated in a network is nuclear, nuclear plants in that network may be required to follow system load and, under some circumstances, to control system frequency. This condition has already been reached abroad, most notably in France and, to a lesser extent, in Taiwan, and Japan. This condition may also apply in countries just developing nuclear power generation. The possibility of some form of carbon tax, along with the simplification of the licensing process, has raised the possibility that, in the coming
generation, a significant fraction of the electrical energy generated in the United States will be from nuclear power plants. These plants too may be subjected to load following and frequency control requirements.
The capability of nuclear plants to follow load requires that the nuclear fuel be capable of sustaining relatively rapid power density changes, and that the plant power be effectively controlled. An additional factor arises with respect to the effectiveness of control. An amendment to Appendix K of Title 10, Part 50 of the code of (US) Federal Regulations[1]
allows licensees to operate at power levels within as little as 0.3% of the power level at which plant safety has been analyzed, on the basis of reduced uncertainty in the instrumentation used for the determination of plant thermal power. These so-called Measurement Uncertainty Recapture (MUR) uprates are also being applied to the new plant designs currently slated for construction. This paper explores the special instrumentation and control issues that arise from the small numerical margin between the licensed power and the power of the safety case in such plants, as well as the regulatory and safety constraints imposed on them.
1 BACKGROUND
The capability of nuclear plants to follow load and perform the other missions typically reserved, in the USA, for coal and gas fired power plants requires that the nuclear fuel be capable of sustaining relatively rapid power density changes, and that the plant power be effectively controlled. France has demonstrated the capability to design nuclear fuel for the power density changes associated with load follow. She has also set forth requirements on their plant controls, which, if fulfilled, ensure effective frequency control.
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In the US, however, an additional factor arises with respect to the effectiveness of control. The amendment to Appendix K of Title 10, Part 50 of the code of (US) Federal Regulations previously referenced allows licensees to operate at power levels within as little as 0.3% of the power level at which plant safety has been analyzed, on the basis of reduced uncertainty in the instrumentation used for the determination of plant thermal power. These so-called Measurement Uncertainty Recapture (MUR) uprates are also being applied to the new plant designs currently slated for construction. The small numerical margin between the licensed power and the power of the safety case in such plants begs the question: Are there special control and instrumentation issues in an uprated plant whose power level changes frequently?
From a regulatory perspective, NRC Inspection and Enforcement (I&E) guidance [2]
has served as a basis for NRC enforcement action with respect to the control of thermal power levels during operation, including operational excursions above the "licensed power level."
Essentially, this guidance allows for excursions above the licensed power level of up to 2%, depending on their duration. Three important conditions are imposed:
a) The plant must not intentionally be controlled above its licensed power level rating.
b) The thermal power averaged over any 8 hour period is not permitted to exceed the licensed power level rating.
c) In no case should 102% power be exceeded.
The different criteria related to power level, including the (up to) 2% allowance in the I&E guidance on power excursion control, are fundamentally independent of the steady state allowance in Appendix K. The Appendix K criterion addresses assumptions related to uncertainties in the instrumentation used to determine thermal power, to establish margin for Emergency Core Cooling System safety analyses. The I&E guidance establishes various criteria, not themselves based on the Appendix K criterion, by which the NRC may consider potential enforcement action for overpower excursions.
From a reactor safety standpoint, there is a solid technical rationale for permitting short term excursions in core thermal power above the licensed rating. The thermal power rating of a reactor is selected to ensure that the integrity of its barriers to fission product release is maintained when it is subjected to a spectrum of anticipated [hypothetical] design basis transients. Generally speaking, these transients limit the design in one of three ways:
a) A design basis transient can lead to a temporary loss of cooling to the fuel pins because of a (temporary) deficiency in coolant—the so-called loss of coolant accidents (LOCAs). Such transients may involve a hypothetical breech of the reactor coolant pressure boundary or, in BWRs, other upsets leading to a deficiency in water inflow versus outflow. Corrective measures for transients of this type must ensure that the temperature of the fuel cladding does not reach a level where its mechanical integrity cannot be assured.
b) A design basis transient can lead to a local fuel pin heat flux that, in combination with the thermal/ hydraulic state of the coolant, does not support stable heat transfer between pin and coolant. Such transients may be produced by reactivity upsets or, in PWRs, by a reduction in coolant flow. Transients of this type must be terminated before the heat transfer becomes unstable, again to ensure the integrity of the clad.
c) A design basis transient can lead to a temporary mismatch in the heat flow into and out of the reactor coolant that in turn can cause a rise in coolant pressure. The pressure rise must be capped to ensure reactor coolant system integrity. Such transients can be produced by a sudden reduction in steam demand, caused by a turbine trip for example.
A deficiency in feedwater flow can also lead to a reduction in the heat flow from the coolant.
Of the factors affecting the peak clad temperature reached in type (a) transients only the power generated by the radioactive decay of fission products is affected by the core thermal power. However, decay power is not particularly sensitive to the power immediately
preceding the LOCA transient but rather is determined by the long term power history—
approximately, the power averaged over many hours preceding the transient. Hence, type (a) transients require that the long term average of the core thermal power be maintained at or below the licensed power rating of the reactor. This technical requirement on the long term average justifies the I&E guidance that the power, averaged over any 8 hour period, not exceed the licensed rating.
In type (b) transients, the integrity of the reactor core is maintained by the Reactor Protection System, which scrams (trips) the reactor (i.e. reduces thermal power by rapidly inserting the control rods). Transients of this kind may involve an overpower condition (usually the result of a hypothetical inadvertent reactivity insertion) or in PWRs an
interruption to the electric or mechanical power supplied to reactor coolant pumps. Protection for such transients is supplied in part by nuclear instrumentation. For some transients in this class, the neutron flux, as measured by the power range nuclear instruments (in BWRs, neutron monitors), is a key protection variable; in others, it is the ratio of neutron flux to core flow. Appropriate nuclear instrument response in these transients requires that they be
calibrated to the thermal power, within their design basis allowance, before the transient occurs. Carrying out this calibration usually involves a comparison of the output of the
nuclear instruments against the plant calorimetric power over a period long enough to average out transient variations in either. The calibration function therefore imposes no direct
requirement on transient power control.
Given calibrated nuclear instruments, the nature of the plant dynamics is such that the margin between the core heat flux calculated for type (b) transients and the critical heat flux is not particularly sensitive to the power level prevailing just before the transient starts. Should a type (b) upset occur during a slow power transient in which the power is slightly above its nominal rating, the scram set point may be reached sooner but the margin of core safety will not be materially altered. Because of this insensitivity, type (b) transients do not, in
themselves, impose a limiting requirement on the control of thermal power.
Likewise, the peak pressure reached in type (c) transients—transients involving a
mismatch between the thermal power delivered to the coolant by the core and that removed by the steam plant—is not particularly sensitive to initial power level. The peak pressure reached in such transients is determined primarily by the setpoint of the over pressure reactor trip, which is backed up by overpressure relief devices such as electromagnetically controlled valves and safety valves.
The discussions above provide technical support the transient allowances of up to 2%
(relative to the pre MUR rating) provided in the existing I&E guidance for thermal power control. The imposition of the 2% overall transient limit in this guidance can be considered as a prudent means to ensure that plant systems other than the reactor core and reactor coolant system boundary are operated within their design basis.
In current US practice, nuclear plants are base loaded, so that the compliance with the I&E guidance imposes no great burden on plant operators: The plant is normally in a nominal
steady state at or near full power, so that it can readily be demonstrated that the thermal power, as determined from a steam plant calorimetric and averaged over 8 hours, is at or below the licensed rating. The invariance of power level also facilitates small adjustments to it, so that the licensed rating can be closely approached, without violating the requirements of the license. Finally, the absence of significant power transients facilitates the calibration of power range nuclear instrumentation. Because the plant operates in an essentially steady state, the neutron flux seen by the nuclear instruments changes only very gradually. The
concentrations of neutron absorbing fission products like Xenon and Samarium reach
equilibrium, and only the very gradual depletion of fissile material and fixed burnable poisons produce changes in the neutron flux seen by the instruments. Consequently, the current US practice of confirming the calibration of the nuclear instruments once per shift or once per day ensures their effective accuracy for transients of type (b) above.
If nuclear plants are used to follow system load or to control system frequency, however, maintaining nuclear instrument accuracy for transients of type (b) becomes more challenging. The large power changes, sometimes in the 50% range, associated with following load will produce large changes in fission product inventory. The periods of constant power during load follow, say 8 to 12 hours, will be such that equilibrium fission product
concentrations, if attained at all, will be attained only briefly. Since changes in fission product inventory can change the spatial distribution of neutron flux, the maintenance of an accurate calibration of nuclear instruments could become a continuing and burdensome task.
The power changes associated with frequency control, while smaller, are more frequent and abrupt; in France steps of ± 7% power about power levels as high as 92% are specified for this purpose. Because such steps may occur in rapid succession, ensuring that thermal
equilibrium has been reached, so as to establish thermal power and at least a temporary calibration of nuclear instruments, could be difficult.
This study examines, on a quantitative basis, the implications of load following and frequency control on the calorimetric measurement of thermal power. It also investigates measures whereby an operator can ensure the calibration of his nuclear instruments in plants dedicated to this service.
2 SUMMARY
Virtually all nuclear plants rely on a secondary calorimetric calculation—feedwater mass flow times the enthalpy rise across the steam supply— to establish the core thermal power on an absolute basis. The study concludes that inherent variations in feedwater mass flow due to turbulence and limit cycling of the feedwater regulating valves impose a
minimum averaging requirement of about 1 minute on any secondary calorimetric calculation.
For step disturbances in steam demand, a secondary calorimetric with 1 minute
averaging equilibrates with the core power in about 4 minutes; the duration, while affected by averaging time, is primarily the result of plant and control system dynamics.
A calorimetric calculation based on a rolling average of feedwater flow for a specified averaging period (as opposed to a first order filter with a time constant of the same averaging period) provides superior dynamic performance. That is, the rolling average calorimetric equilibrates with core power more rapidly than does a calorimetric using a first order filter.
A means that facilitates a comparison, by the operator, between nuclear instruments and the secondary calorimetric, for purposes of detecting nuclear instrument calibration errors, is proposed. The means is effective both during and following transients representative of both load following and frequency control.
Some plants use a primary calorimetric (reactor coolant enthalpy rise times mass flow) as a short term power indicator, in lieu of, or in addition to nuclear instruments. The primary
calorimetric, like the nuclear instrumentation, is subject to calibration errors that arise in both the short and long term. A means for the rapid detection of such errors is described. The means, which compares the primary calorimetric with the secondary calorimetric, is similar to that proposed for the nuclear instrumentation.
3 THE PLANT MODEL
For the analysis, a four loop PWR is modeled. Fuel loadings, the liquid masses of reactor coolant and the secondary side of the steam generators, heat transfer coefficients and areas, coolant temperatures and steam conditions are representative of a contemporary 3400 MWt unit. The model has been adapted from one used for a study of the sensitivities, to a range of upsets, of PWRs with once-through and recirculating steam generators [3]. Models of each PWR design were verified by comparisons of model predictions with actual plant data.
The results of the study were submitted to the USNRC and accepted in an NRC Safety Evaluation Report.
The model is described in some detail in the Appendix to this paper.
4 RESULTS AND CONCLUSIONS
Most US nuclear plants establish the calibration of their nuclear instruments by
comparing their indication with a secondary calorimetric calculation averaged over a period of 5 to 20 minutes. As noted above, this process imposes no great operational burden because the plants are base-loaded. The resulting calibration is extremely precise because of the large amount of data employed in the comparison. But, as noted in an earlier section, the calibration demands of load following and frequency control may not permit calibration processes lasting as long as 20 minutes. One question this study seeks to address is: How brief can the
calibration process be?
For a nuclear instrument calibration based on a secondary calorimetric calculation to be valid, the feedwater flow, on which the calorimetric is based, must, on average, equal the steam flow for the period of comparison. Compliance with this requirement leads to
considerations of the dynamic response of the steam generator (or reactor) water level control, which response will be examined presently. But there are additional requirements: The period of comparison must also be long enough—the feedwater data sample must be large enough—
to reduce to an acceptable level the random contributions to the flow measurement of turbulence and of feedwater regulating valve limit cycling (if present).
Feedwater flow measurements, whether from ultrasonic or differential pressure
instruments, are subject to the fluctuations produced by turbulence. If the flow measurement is averaged over a period of finite duration, the residue of these fluctuations amounts to an
“observational uncertainty” in the determination of power level. In typical feedwater flow instrument locations the fluctuations will form a normal distribution, having two standard deviations of about 2.5%.1 Occasionally, the variations may be smaller, but not less than 2%.
They can also be greater, if the measurement location is downstream of a hydraulic feature that increases turbulence such as a compound bend. In any case, if a plant has been uprated on the basis of enhanced feedwater instrumentation, feedwater data must be averaged over a period long enough to reduce this observational uncertainty to a level such that, when it is combined with the other uncertainties of the calorimetric power determination, the resultant accuracy is consistent with the commitments of the uprate license amendment.
1 The turbulent variations seen in the output of transit time ultrasonic instruments and differential pressure feedwater instruments having a typical time constant of about 1 second are similar in magnitude. Local turbulent variations are higher—often above 10%.
For example, suppose an ultrasonic system samples the feedwater flow with a frequency of 50 Hz. Data collected for a period of 1 minute will produce 50 × 60 = 3000 flow samples.
If two standard deviations of the turbulence distribution are 2.5%, the observational
uncertainty associated with the average of all samples is 2.5% / (3000)1/2 or ±0.046%. If the mass flow accuracy commitment of the license amendment is, say, ±0.30%, an observational uncertainty of ±0.046%, when randomly combined with it, will increase the overall
uncertainty applicable to a calorimetric calibration of 1 minute duration to (0.302 + 0.0462)1/2 or ±0.304%. Thus a 1 minute average of the feedwater data does not significantly degrade the measurement uncertainty. But an averaging period shorter by a factor of two, a sample rate lower by a factor of two, or turbulent variations increased by a factor of two will increase the mass flow uncertainty to more than ±0.31%, possibly a small infringement on the margin incorporated in the uprate license amendment.
Accordingly, a 1 minute average of the feedwater flow data appears to be a prudent lower limit to the averaging time for a secondary calorimetric, based on the uncertainty produced by turbulence.
Non linearities in the actuating mechanisms of feedwater regulating valves can cause them to limit-cycle. The force balance on the valve stem is non-linear such that the valve is unable to reach an equilibrium position which produces exactly the flow demanded by the steam generator (or reactor) water level control. Consequently the valve oscillates about an equilibrium position. The resultant flow oscillations are small—usually no larger than ±½%
and the period irregular—typically in the range of one or two seconds per cycle. Assuming the longer period, a 1 minute average reduces the operational uncertainty of a ±½% limit cycle to
½ / (30)1/2 = 0.09%. In this case, the postulated ±0.30% mass flow uncertainty of the
hypothetical uprated plant would be increased to ±0.31%—again a small infringement on the margin incorporated in the license. Both turbulence and limit cycling set an approximate lower limit for the averaging time of a secondary calorimetric of about 1 minute.
A steam generator (or reactor) water level control system can take longer than 1 minute to reach a steady state following a disturbance. Figures 1A and 1B illustrate water level control responses to a relatively severe transient, a step decrease in steam demand of 20%
(which nevertheless is a transient classified as “normal” in some plants). In Figure 1A, the water level control set point is programmed linearly with steam flow, so that the set point decreases, from 100% to 0 steam demand, so as to match, approximately, the natural “shrink”
of the generator. In Figure 1B a fixed level set point is employed. In both controls the
feedwater demand is the sum of the then-prevailing stream flow and a level error term. In both cases, the sensitivity of the level error term is set such that, if level beneath set point by an amount equal to the full natural “shrink” and steam flow is zero, a demand for full feedwater flow will be generated. (And vice versa: if the level is above set point by the full “swell” and steam flow is rated, a zero feedwater flow demand will be generated.) As can be seen from the figures, this setting provides a well damped response in both variable and fixed set point controls. The control with the varying set point requires, surprisingly, somewhat more time to reach an approximate steady state following the step change—about 3 minutes versus 2 minutes for the fixed set point system.
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Figure 1A: Steam Generator Water Level Control Response to a 20% Down Step in Steam Demand, Varying Water Level Set Point
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Figure 1B: Steam Generator Water Level Control Response to a 20% Down Step in Steam Demand, Fixed Water Level Set Point The differences in the water level control responses to the same change in steam demand lead to different calorimetric power responses, as shown in Figures 2A and 2B.
Because of the shape of the feedwater response in the varying set point system, the computed calorimetric power reaches an approximate equilibrium with the core power about 1 minute sooner (despite the fact that this system takes longer to reach a true steady state). Note that approximate equilibrium between the secondary calorimetric, filtered with a first order filter having a 1 minute time constant, and the neutron flux is reached in about 3 minutes in Figure 2A, the variable set point case, while nearly 4 minutes are required in the fixed set point case (Figure 2B) to reach equilibrium. Because the fixed set point control appears more demanding with respect to calorimetric averaging time, that control arrangement was used for the
remaining analyses.
As noted above, Figure 2B shows that the secondary calorimetric filtered with a 1 minute first order filter requires a time approaching 4 minutes to equilibrate with the core thermal power following a 20% down step in steam demand. As has also been noted, the reduction of turbulent and other flow variations to acceptable levels makes a 1 minute averaging time an approximate lower bound for the calorimetric calculation. The question arises: Will another filtering configuration achieve the same improvement in flow statistics but provide a more rapid equilibrium between the core power and the secondary calorimetric?
Such a configuration would permit a more timely determination of the actual plant thermal power and a quicker check of the nuclear instrument calibration
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Figure 2A: Indicated Thermal Power Response to a 20% Step Down in Steam Demand, Varying Level Set Point
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Figure 2B: Indicated Thermal Power Response to a 20% Step Down in Steam Demand, Fixed Level Set Point
Figure 3A shows that a 1 minute rolling average responds more rapidly to the 20%
down step in steam demand than does the 1 minute first order filter. A rolling average is usually as effective as a first order filter in reducing the observational uncertainty due to flow statistics. The difference however is not dramatic. But if flow statistics require a 3 minute averaging time and this is implemented using a first order filter, Figure 3B shows that over 12
minutes are required for the secondary calorimetric calculation to equilibrate with the neutron flux. In this case, if a 3 minute rolling average is employed the equilibration time is reduced to about 6 minutes. Because its greater dynamic effectiveness, the rolling average will be used for the remainder of the analyses.
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Figure 3A: Indicated Power Reponses to a 20% Step Down in Steam Demand, Rolling Average vs. First Order Filter on Secondary Calorimetric Calculation,
1 Minute Averaging Time
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Secondary calorimetric 3 minute rolling verage
Figure 3B: Indicated Power Reponses to a 20% Step Down in Steam Demand, Rolling Average vs. First Order Filter on Secondary Calorimetric Calculation,
3 Minute Averaging Time
Load changes of up to 50% of rated power may be expected if a nuclear plant is used in load follow service. Such changes may take place at rates as rapid as 5% per minute, a typical rate limit for a large nuclear plant. Figure 4A shows that a secondary calorimetric calculation based on a 1 minute rolling average differs from the instantaneous core power (i.e. that set by the neutron flux) by about 4% for most of the 10 minutes over which a 50% power reduction is effected. The differential is about the same for the subsequent 50% power increase in the same figure. Power changes of this magnitude will bring about substantial changes in fission
product inventory thereby necessitating an effective means for checking the calibration of the nuclear instruments in the aftermath of the power change.
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Reactor Coolant calorimetric Th - Tc
Figure 4A: Thermal Power Response to 50% Load Ramps at 5% per Minute Figure 4B shows a method for facilitating the comparison of nuclear instruments with the calorimetric calculation during and following the load transient. This figure shows the transient response of “Delta Q”, the difference between a time-conditioned neutron flux signal and the 1 minute rolling average calorimetric calculation. The time conditioning of the
neutron flux includes:
(a) A first order filter, with a time constant of 20 seconds (to simulate the aggregate of the thermal capacities of the reactor fuel and coolant) and
(b) A 1 minute rolling average to duplicate the signal processing of the calorimetric calculation itself.
It will be seen that Delta Q remains within ± 0.6% throughout both down and up transients, providing the operator with assurance that, despite the transient, his nuclear
instruments are within acceptable calibration bounds. (A typical nuclear instrument calibration allowance is ± 2%— not to be confused with the allowance for the uncertainty of the
calculation of thermal power itself in the original 10CFR50 Appendix K.) Delta Q also reaches equilibrium less than 4 minutes after the final power level is reached. It thus becomes immediately useful in detecting a degradation of nuclear instrument calibration owing to the fission product transient that follows the power change.
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conditioned neutron flux - secondary calorimetric Secondary calorimetric
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Th - Tc
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Figure 4B: Thermal Power Response to 50% Load Ramps at 5% per Minute With Conditioned Flux-Secondary Difference Indication
Figures 2, 3 and 4 also show the responses of a calorimetric calculation based on the temperature increase of the reactor coolant—the hot leg (Th) minus cold leg (Tc) temperature rise times the average specific heat of the coolant times the total coolant mass flow. This calculation is of course only a relative power indicator for PWRs—there is no traceable measurement of reactor coolant mass flow with an accuracy acceptable for calorimetry in any pressurized water reactor. It is also subject to substantial errors owing to uncertainties in the temperature measurements. The temperature increase at full power in a pressurized water reactor is in the range 50° to 60°F (28° to 33°C). The uncertainty in the temperature difference due to the aggregate of the uncertainties in calibration, self heating, and lead resistance
changes of the resistance thermometers used for the temperature measurements can easily aggregate to ±1.5°F (±0.83°C) —2.5 to 3% of the temperature difference, therefore 2.5 to 3%
of the reactor power. Furthermore the temperature difference is subject to errors similar in character to the errors affecting the neutron flux. “Temperature streaming” in the hot leg can lead to local temperature gradients in the coolant hot leg of as much as 20°F (11°C). Efforts to extract a continuous sample representative of the average hot leg temperature have met with mixed success. And the hot leg gradients are a function of the core power distribution which is in turn affected by the same fission product transients that affect the neutron flux.
Consequently, for those plants that use a primary coolant calorimetric as a short term power indication, a comparison between a conditioned primary calorimetric signal and the secondary calorimetric is appropriate—to ensure the short term accuracy of the primary calorimetric signal.
Figure 4C shows the response of a primary-secondary comparison signal to the load ramps of Figures 4A and 4B. A simple 1 minute rolling average of the Th minus Tc signal is compared with the 1 minute rolling average secondary calorimetric. The “Delta Q” indicator in this case remains within about ± 1%, again providing the operator with assurance both during the transient and in the following steady state that the accuracy of his short term power indicator is within acceptable bounds.
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Delta Q Primary -Secondary Neutron flux
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Figure 4C: Thermal Power Response to 50% Load Ramps at 5% per Minute With Conditioned Coolant Calorimetric-Secondary Calorimetric Difference Indication
Plants assigned to the control of network frequency are subjected to power demand transients substantially smaller but more rapid than those of Figure 4. A bounding
specification of steam demand steps of ±7% of rated power is representative of the
requirements of such service. Obviously the power level about which such steps are imposed must be such that the demand after the step does not exceed the plant rating. Most turbine governors are equipped with limiters to ensure that a network frequency transient does not call for a steam demand greater than rating.
Figure 5A shows the responses of thermal power indications to a step increase in demand from 92% to 99% of rated power. The 1 minute rolling average secondary calorimetric reaches equilibrium in less than 4 minutes. The “Delta Q” signal based on
conditioned neutron flux (as in Figure 4B) remains within +0.15%/-0.65% bounds throughout the transient, again providing the operator with rapid assurance that his nuclear instrument calibration is (or is not) within acceptable bounds.
Note that the actual neutron flux (and hence power generated in the fuel) exceeds 100%
for a brief period in this transient. This response meets the spirit and letter of the NRC
Inspection and Enforcement guidance previously cited. The overshoot results from the proper operation of the automatic reactor control. An energy flow above rating is necessary to restore the energy “borrowed” from reactor coolant and from fluid on the secondary side of the steam generators by the instantaneous increase in steam demand. As the figure shows core power does not and cannot respond instantaneously.2
2 It should be noted that the neutron response of Figure 6A might not meet the requirements of draft regulations, which, as of this writing, are under consideration as a replacement for the I&E guidance previously referenced.
The replacement regulations prohibit any operation above rated power if the reactor is being manually controlled.
But a brief period during which the reactor power exceeds rating must occur if the average reactor coolant temperature is to be restored to its design value in a transient such as that of Figure 5A. This restoration of stored energy must occur whether the reactor is controlled manually or automatically. It is assumed that eventually the regulations will reflect this reality.
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Primary calorimetric Th - Tc
Secondary calorimetric 1 minute rolling average
Delta Q
Conditioned neutron flux -secondary calorimetric
Figure 5A: Frequency Control: Thermal Power Response to a Step Increase in Steam Demand from 92% to 99%
Figure 5B shows the responses of thermal power indications to an instantaneous step down in steam demand, from 99% to 92%, again a representative upper bound for a frequency control transient. Again equilibrium for the 1 minute secondary calorimetric is reached in less than 4 minutes. Again the “Delta Q” indicator provides the operator with assurance that his nuclear instrument calibration is satisfactory, remaining within +0.65%/-0.15% of zero, exactly symmetrical with its response to the demand increase.
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Conditioned neutron flux -
Figure 5B: Frequency Control: Thermal Power Response to a Step Increase in Steam Demand from 99% to 92%
REFERENCES
[1] Title 10, (US) Code of Federal Regulations, Part 50, Appendix K, as revised June 2000 [2] NRC Inspection Manual, Inspection Procedure 61706, "Core Thermal Power Evaluation,"
Section 03.01d.
[3] “A Comparative Study of the Sensitivity of B&W Reactor Plants”, January 1987, MPR- 948, submitted to NRC by the B&W Owners Group.
APPENDIX
Further Description of the Analytical Model
Figures A-1A and A-1B are block diagrams of the plant model as adapted for the analyses of this paper. The nomenclature used in the figures is given in Table A-1, at the end of this appendix. The two figures show differences in the control system models used for the analyses. In the “Turbine lead” mode (Figure A-1A), the unit is at the disposal of the load dispatcher for the control of system frequency, and the steam demand is set by the dispatcher (or by the reactor operator under the direction of the dispatcher) and the turbine governor (which adjusts turbine speed and load to maintain the desired system frequency). In the turbine lead mode the rod control system maintains steam pressure at a preset value.3 Short term feedback for the reactor control is provided by comparing neutron flux to steam demand, as measured by turbine first stage bowl pressure or main steam flow.
In the “Reactor lead” mode (Figure 1B), the plant power is set by the reactor operator, who adjusts control rod position to maintain power at a desired target or to transit from one power level to another at a pre set rate. In this mode, steam pressure is maintained by the turbine governor valves. In so doing the governor control ensures that the turbine absorbs the power generated by the reactor. The reactor lead mode might be used by plants dedicated to load following, but not for system frequency control.
Two steam generator water level control configurations were investigated: one in which the level set point is fixed, and a second in which the level set point is increased with
increasing steam demand. The latter arrangement maintains the total mass of liquid in the steam generator approximately constant over the full power range. However, this arrangement may not be possible for some steam generator designs, where the volume of the steam drum is limited.
The model does not include a pressurizer; it is assumed that the pressurizer and its auxiliary systems (spray and heaters) have been designed to maintain coolant pressure within acceptable bounds during the “normal” transients imposed in this analysis.4
Thermal power is computed at three model locations: (1) the thermal power generated in the fuel by fissions, as determined by the neutron flux, (2) the thermal power delivered by the reactor coolant to the steam generators as determined by the difference in the hot leg and cold leg coolant temperatures (the coolant mass flow being assumed invariant), and (3) the thermal power as computed by a heat balance around the secondary side of the steam generators. The secondary heat balance computation used in virtually all power plants assumes the feedwater flow into the steam generators is in equilibrium with the steam flow out of the steam
generators. The model makes the same assumption and determines the enthalpy rise across the steam generator secondary from the difference in the enthalpy of steam, saturated at the steam pressure delivered by the steam generators, and the enthalpy of the feedwater as determined from its temperature, which for the transients analyzed was held constant at its initial value.
In the time frame of the “normal” transients analyzed in this study, the core power—that produced by fissions in the fuel—responds essentially instantaneously to the neutron flux. The reactor coolant calorimetric power—that based on the hot leg-cold leg temperature
difference—lags the power produced by the fuel because of the energy storage capacities of the fuel and the reactor coolant. It is also subject to the time response of the resistance thermometers which measure the coolant temperatures. For this analysis, the thermometer
3 Many PWRs operate on a program wherein the temperature of the reactor coolant at the steam generator outlet is maintained constant over the full power range. The constant steam pressure program used in this study results in similar dynamic responses, but leads to a slightly greater change in coolant inventory from zero to full power.
4 The analytical model of reference (3) included a pressurizer because it was used to study plant responses to transients beyond those classified as “normal” (e.g., full load rejection with and without scram).
response is characterized by a first order differential equation response with a 5 second time constant. The secondary calorimetric, as implemented in most plants, is of course only valid as an indicator of core thermal power over the longer term, when the feedwater flow must, on average, equal the steam flow. In the short term, the feedwater responds to steam generator water level as well as steam flow. Accordingly a first order differential equation was used to simulate the “smoothing” of the secondary calorimetric calculation, employed in most nuclear plants to ensure a representative thermal power indication. The smoothing time constant was varied parametrically in the study. Additionally, a different approach to “smoothing”,
specifically a rolling average for a specified period, was also investigated.
Neutron flux is calculated from “point kinetics” equations, which assume that the reactor is only slightly sub- or super-critical in the transients analyzed. The point kinetics equations relate the neutron flux to the concentration of delayed neutron precursors, the fraction of neutrons that are delayed, and the net reactivity –the difference between the neutron multiplication and 1. The rate of change of the concentration of delayed neutrons is made equal to the difference between those that are produced by the then prevailing flux and those that are removed by the decay of the precursors. A mean effective decay constant is used for the delayed neutron precursors (which are treated as a single group). Two inherent reactivity feedback mechanisms are included:
a) The Doppler coefficient of reactivity, which accounts for the resonant capture of prompt neutrons by U238. The Doppler feedback is negative and is proportional to the departure of the average fuel temperature from its zero power value.
b) The moderator coefficient of reactivity, which accounts for the change in neutron concentration with changes in moderator density (hence its temperature). This feedback is also negative and is made proportional to the difference between the then-prevailing average coolant temperature and the average coolant temperature at zero power. Two moderator coefficients were investigated: one representative of that prevailing at the beginning of a fuel cycle, when the presence of high concentrations of boric acid in the coolant reduces the net reactivity change with temperature, and one representative of that prevailing at the end of the fuel cycle, when the absence of boric acid in the coolant makes the coefficient more strongly negative.
Long term reactivity effects from fission product buildup and burn out are not modeled.
For fixed mass systems such as the reactor fuel and the reactor coolant, dynamic heat balances (or, more precisely, power balances) are of the following form:
M cP dT/dt = q IN - qOUT (A-1)
Where:
M is the mass of energy storing material in the heat balance and cP is its specific heat, T is the average temperature of the energy storing material, and
q IN and qOUT are the energy flows into and out of the system.
The energy flow into the fuel is instantaneously related to the neutron flux; the energy flow out is related to the difference between the average fuel temperature and the average coolant temperature. The energy flow out of the fuel becomes the energy flow into the coolant. The energy flow out of the coolant is related to the difference between the average coolant temperature and the temperature of saturated liquid at the steam pressure prevailing in the secondary side of the steam generators.
Recirculating steam generators without preheaters are modeled. Each of the four steam generators is assumed to share the total steam demand equally, and the water level of all steam generators is assumed to respond identically to steam and feedwater flow disturbances so that one dynamic energy balance and one dynamic mass balance about a single steam generator produces energy and mass results representative of all four steam generators.
Because the mass of fluid on the secondary side of the steam generators can vary in time, the dynamic heat balance differs in form from that for fixed mass systems:
d(M h)/dt = h dM/dt + Mdh/dt = q IN - qOUT (A-2) Here:
M is the total mass of fluid on the secondary side of the steam generator, which for the analysis is taken as the liquid mass (the mass of steam is in the order of 1/100 of the liquid mass),
h is the mean enthalpy of the fluid on the secondary side of the steam generator, which is assumed to be that of saturated liquid. This approximation assumes that the energy stored in the steam is approximately offset by that stored in the subcooled liquid in the steam generator downcomer.
The rate of change of mass in the steam generator, dM/dt is given by:
dM/dt = WFW - WS SG (A-3)
Here:
WS SG is the steam flow from one steam generator, ¼ of the total steam demand.
The feedwater flow, WFW, is controlled by the steam generator water level control. This control generates a flow demand equal to the then prevailing steam generator steam flow plus a term proportional to the difference between a level set point and the then prevailing level of liquid in the drum portion of the steam generator. The flow itself is made to follow the flow demand according to a first order differential equation having a time constant of 10 seconds, to simulate the action of the flow control loop and the regulating valve positioner.
The effective liquid level signal is computed on the basis of the volume of liquid in the drum-downcomer region of the steam generator. The distribution of the liquid mass in the steam generator between the boiling region around the tube bundle and riser, on the one hand, and in the drum and downcomer, on the other, is computed using approximate mass and momentum balances. A subsidiary heat balance around the downcomer-drum is also part of this computation, for the calculation of the enthalpy entering the boiling region (in turn required for the computation of the mass residing in this region).
Table A-1: Nomenclature
∂kRODS The net reactivity contribution of the control rods, relative to their contribution at zero power
∂kRODS/dt|set
The maximum rate-of-change of reactivity produced by the control rods for control during normal transient operation
n The thermal neutron flux
n0 The thermal neutron flux at rated power
TF The average temperature of the fuel
TAV The average temperature of the reactor coolant
pSAT The pressure of the steam produced by the steam generators
pset
The set point to which steam pressure is
controlled, either by control of reactor power or control of steam demand
WS The steam demand—the mass flow rate of steam from all steam generators
l Steam generator water level—the level of liquid in the drum/downcomer region of the steam generator
WFW The feedwater flow mass rate to each steam generator
Rod Control
Neutron Kinetics
Dynamic Heat Balance
Rx Fuel
Dynamic Heat Balance
Rx Coolant
Dynamic Heat Balance
Steam Generator
Steam Demand
Doppler Coefficient
Moderator Coefficient
Dynamic Mass and Momentum
Balance Steam Generator
Dynamic Heat Balance
Downcomer
Steam Generator Water Level
Control
n TF TAV
WS
WFW
l
∂kRODS
Rod Control
Y = WS/ WS0 – n/n0 + K (pset – pSAT) If Abs(Y) > 0.005
∂kRODS/dt = ∂kRODS/dt|set × Y/Abs(Y) Else
∂kRODS/dt = 0.0 pSAT
Steam Demand
Set by
Load Dispatcher Turbine Governor (frequency control only)
Turbine Lead
Figure A-1A: Plant Dynamic Model, Turbine Lead
Rod Control
Neutron Kinetics
Dynamic Heat Balance
Rx Fuel
Dynamic Heat Balance
Rx Coolant
Dynamic Heat Balance
Steam Generator
Steam Demand
Doppler Coefficient
Moderator Coefficient
Dynamic Mass and Momentum
Balance Steam Generator
Dynamic Heat Balance
Downcomer
Steam Generator Water Level
Control
n
TF TAV
WS
WFW
l
∂kRODS
Reactor Lead
Rod Control
If n/n0 < n/n0|SET – Tol
∂kRODS/dt = +∂kRODS/dt|SET
If n/n0 > n/n0|SET + Tol
∂kRODS/dt = - ∂kRODS/dt|SET
If n/n0 = n/n0|SET ± Tol
∂kRODS/dt = 0
Steam Demand WS = K (pset – pSAT)
pSAT
Figure A-1B: Plant Dynamic Model, Reactor Lead