Patent Number: 050911392
Section: description

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Referring to FIG. 1, the environment in which this invention resides can be easily understood. A reactor vessel V having a core C generates steam. Steam S passes outwardly on a line L to a main turbine T. As is conventional, turbine T drives a generator G which generator produces electrical power. Discharge of steam occurs to a condenser cooled by coolant (not shown). A system of pumps including a feedpump take the condensate and inject it back into the reactor vessel V where the steam cycle endlessly repeats. (Also not shown) As is common in nuclear reactors, a recirculation pump R is utilized. Typically, the recirculation pump R circulates the water coolant through the core C. As is well known, such circulation is included in peripheral downcomer volumes along the sidewalls of vessel V and reverses flow to pass centrally upward through core C. The coolant has two purposes. First, it acts as a moderator. In acting as a moderator it increases or decreases power. Second, the coolant removes fuel heat and turns itself into steam S which drives turbine T. Having set forth the moderator flow path and the steam cycle in over simplified format, attention can now be directed to the reactor control. Regarding the recirculation of fluid by pump R, a master controller 20 is utilized. Master controller receives a load speed signal from generator G (by conduits not shown). Additionally, it can receive a manual input. Receiving one or both of these inputs, master controller 20 has an output to pump speed controller 22. Pump speed controller 22 acts upon a clutch 26 between a motor 28 and a generator 30. Generator 30 controls a motor 32 driving the recirculation pump R. It will be understood that the particular control used for the variable throughput of pump R can vary, and also that in another configuration multiples of pump R and motor 32 can be located directly within and below the downcomer volumes of vessel V. Likewise, the function of the control rods can be summarized in a simplified format. Typically, a group of control rods 50 are actuated by hydraulic control units (HCU) 52. These control units include precision position monitors for maintaining the rods in given positions of penetration to the core for both the shaping of the core reaction as well as its overall control. The hydraulic control units 52 are in turn activated by a rod control and information system (RCIS) 54. This rod control and information system includes inputs from the operator and outputs to the operator indicating the positions of each of the rods. Referring to FIG. 2, a section of core C is illustrated. Typically, this section includes 16 bundles 60 controlled by four control blades 62. The reader will realize that core C consists of several hundred bundles 60 with many such control rods, there being generally four control rods 62 for each group of 16 bundles. The control rods are raised into the core C and lowered from the core C by the hydraulic control unit 52, these units being below the reactor vessel V. It is this control rod movement which effects reactor operation. Simply stated, when the control rods are inserted, fission reaction is inhibited. When the control rods are withdrawn, fission reaction increases. Each group of 16 fuel bundles is monitored by 16 local power range monitors (LPRMs). Local power range monitors are typically mounted in strings in assemblies extending the vertical length of the core. In FIG. 2, four such strings 63, 64, 65, and 66 are shown. Each string includes four discrete power monitors. These power monitors are shown as A, B, C and D. It will be seen that monitors D are near the top of the core and monitors A are near the bottom of the core. Monitors B and C monitor the medial levels of the core. For the purposes of the application, it will be understood that monitoring occurs against three broad classifications of limits. First, each bundle is examined for its overall power output. It will be understood that the constant "A" which follows in this description is utilized in this function. Second, each individual fuel rod contained in any of the fuel bundles is monitored for its linear power generation. Finally, a planar averaged linear heat generation rate is monitored for each bundle at various fuel planes. For these last two considerations, it will be understood that the constant "B" which follows in this description is utilized. As will hereinafter be more fully developed, it has been found that the ratio of maximum linear heat generation rate in the fuel rods and the ratio of planar average heat generation rate at any one fuel plane of each bundle are analogous. This being the case, the constant "B" as hereinafter described can be used as a generic input to the algorithm protecting against these limits. Brief reference to FIG. 3 can be made. This reference is a schematic which sets forth the processor apparatus of this invention. Simply stated, each of the local power monitors A, B, C, and D passes its signals through a signal conditioner 70 and thereafter to a bank of optical-isolators 72. The optical-isolators input to an input/output bus 73 which bus communicates signal to the local power range monitor processing bus. Utilizing this bus, all inputs throughout the reactor in the order of 200 are scanned by the processor unit. This scanning occurs in the processing unit denominated at block 74. Thereafter, and as appropriate for each monitor block of 16 bundles, the sum and averages of the local power range monitors are computed at block 75. Once this has occurred, two microprocessor outputs are utilized. A first output at 76 goes to an algorithm microprocessor, which microprocessor processes for the so-called operating limits setpoints. A second output 78 goes to an algorithm microprocessor unit which unit is not shown and is identical to that illustrated connected at 76. This microprocessor process for so-called "safety limits" and furnishes the degree of redundancy and backup protection that this disclosure enables. Having set forth the overall architectural schematic, the specific inputs can be set forth. At 81, into a self-test unit are placed the plant parameters. Additionally, at 82 a set point result from an optional identical redundant channel is put through for cross channel comparison check. The algorithm unit receives through 84 a reference APRM which represents the reactor power level, at 85 a core simulator thermal limit output, at 86 a rod position indication. Input 87 includes applicable core flow data from recirculation pump R (see FIG. 1). The algorithm unit computes a set point. This set point is compared at comparator 93 to actual instantaneous local power range monitors based signals 92. When the reading from the actual power range monitors exceeds the set point, trip unit 94 issues a trip order. The trip order then proceeds from the automated thermal limit monitor along two conduits 96, 98. Referring back to FIG. 1, conduit 96 blocks all further rod insertions. Additionally, and as seen further in FIG. 1, conduit 98 blocks any further attempts to change core flow. As has been emphasized, it is known to have core simulator. This core simulator receives input from a neutron monitoring system 100 and constructs in a large, fast computer 102 a model of the overall reactor operation. This model of the overall reactor operation can be predicted on a time basis approaching once every two minutes by modern high speed computation equipment. This calculation result of core thermal limits is downloaded into a memory in the automated thermal limit monitor system 120. Based on these core thermal limits, the algorithm unit computes and outputs setpoints. This computation occurs to the unit in real time, in a very short calculation cycle on the order of 0.1 to 0.2 seconds. Having generalized this system, a detailed discussion of the algorithms herein utilized can now be set forth. Component Arrangement The ATLM system signal processing and logic diagram as shown in FIG. 3 can be conceptually summarized. The ATLM takes all LPRM detector readings as inputs. All LPRM signals are fed into two redundant channels of the ATLM by first passing through an analog to digital converter and sets of optical communication links. For each channel, after the LPRMs pass through the scan/process unit, they then pass through a summing and averaging circuit unit. Except for the peripheral region of the core, every square block of 16 fuel bundles are monitored by the four LPRM strings at the four corners of this block. For minimum critical power ratio (MCPR) limit monitoring, the sum of the average of each level of B, C, D, of the four LPRM strings is used to monitor the MCPR among these 16 bundles. For peripheral bundles where only three or two LPRM strings are available, specific but similar assignment methods are used. Thus, the readings of each LPRM string are used four times to provide the sum and average outputs for the four different but neighboring block regions of fuels for each of the two ATLM channels. The initial regional MCPRs of every block of 16 bundles calculated by the process computer core simulator/monitor are selected and downloaded in the algorithm unit memory in matrix form for comparison. For the power density limit (KW/FT) algorithm, the average reading of each of the four levels is used separately for monitoring local power densities in the four vertical sections of the 16 bundle block. These four vertical section correspond to the four LPRM levels, (see FIG. 2) The processed LPRM readings that cover each and every region of the core are read to both the comparator unit and the algorithm unit in matrix form. The algorithm unit takes as inputs the reference APRM value (as reactor power), the selected rod identification and its position from the RCIS, the core flow, and the regional thermal limit data from the core monitor. The algorithm unit then performs setpoint calculations for every region, separately for operating thermal limit and safety thermal limit setpoints in different sub-units. The calculated setpoint data then pass to the comparator unit where they are compared against the instantaneous LPRM data from the sum/average unit for each monitoring region. Rod block signal is issued if the instantaneous LPRM output from any one region exceeds the setpoint output of that region. A separate set of units that issues flow block signal is also included in both channels. Flow block signal will be issued if MCPR limit or KW/FT limit is approached during flow change. A separate self-test unit is included in each channel to issue test command and to perform processor calculation verification and monitor calculation verification. System Algorithm Algorithm to Prevent MCPR Limit Violation During Control Rod Withdrawal The equations that govern the relationships between the thermal limits and the processed LPRM sum outputs are as follows, for each monitoring region: ##EQU1## where: RBS.sub.o : Operating limit rod block setpoint RBS.sub.s : Safety limit rod block setpoint PA0 LPRM.sub.i : Initial sum of average of four LPRMs from B,C,D levels of the four LPRM strings that surround each 16-bundle region, (or of available LPRMs for corresponding peripheral region.) PA0 A.sub.o : Margin factor for operating limit rod block, a known function of rod pull distance. PA0 A.sub.s : Margin factor for safety limit rod block, a known function of rod pull distance. PA0 RMCPR.sub.i : Regional initial minimum CPR, i.e., the minimum CPR of the 16 bundles in the region spanned by the four LPRM strings, (less than 16 bundles for peripheral regions.) Known inputs from core simulator/monitor. PA0 OLMCPR: Operating limit MCPR in current cycles, a known function of power and flow. PA0 SLMCPR: Safety limit MCPR in current cycle, a known bounding value for all power and flow conditions. PA0 RBS.sub.s : Safety limit rod block (flow block) setpoint PA0 LPRM.sub.i : Initial sum of average of four corner LPRMs from B,C,D levels. (See System Algorithm) PA0 A.sub.o : Margin factor for operating limit rod block due to rod withdrawal, a known function of rod pull distance. Same A.sub.o as in System Algorithm. PA0 A.sub.s : Margin factor for safety limit rod block due to rod withdrawal, a known function of rod pull distance. Same A.sub.s as in System Algorithm. PA0 RMCPR.sub.i : Regional initial MCPR. See System Algorithm. PA0 OLMCPR: Same as in System Algorithm. PA0 SLMCPR: Same as in System Algorithm. PA0 A.sub.f : Margin factor for rod block due to core flow change, a known function of initial core flow and final core flow. EQU A.sub.f =1+f(W.sub.i, W.sub.f), A.sub.f =1 if W.sub.i =W.sub.f PA0 A.sub.total,o : Total margin factor that considers both rod pull and flow change for operating limit block PA0 A.sub.total,s : Total margin factor that considers both rod pull and flow change for safety limit block PA0 LPRM.sub.i (X): Initial average of the four LPRMs (level X) at the four corners of each 16 bundle fuel region. The region monitored by the X level LPRMs is the region covered up to 1.5 ft above the LPRM and 1.5 ft below the LPRM. (For peripheral region, there may be less than 4 LPRMs which cover a region with fewer bundles.) PA0 B.sub.m (X): Margin factor for MAPLHGR operating limit rod block for X level LPRMs. This factor is a function of power and rod position. PA0 M.sub.p : Off-rated power factor to consider overpower condition during worst transient at off-rated condition. This is a known function of power. PA0 MAPRAT.sub.i (X): Regional initial maximum MAPRAT for level X. i.e., the maximum MAPRAT of the 16 bundles with the 3 feet section covered by the X level LPRMs. (Less than 16 bundles for peripheral regions.) MAPRAT.sub.i is known input from the core monitor model. PA0 LPRM.sub.i (X)=Initial average of the four LPRMs (Level X) at the four corners of each 16 bundle fuel region. The region monitored by the X level LPRMs is the region covered up to 1.5 ft. above the LPRM and 1.5 ft. below the LPRM. (For peripheral region, there may be less than 4 LPRMs which cover a region with fewer bundles.) PA0 B.sub.M (X): Margin factor for MLHGR operating limit rod block for X level LPRMs. This factor is a function of power and rod position. PA0 M.sub.P : Off-rated power factor to consider over power condition during worst transient at off-rated condition. This is a known function of power. If 13.4 KW/FT is used as the operating limit for all power condition, then M.sub.P =1. PA0 KW/FT.sub.i (X): Regional initial maximum KW/FT for level X, i.e., the maximum KW/FT of the 16 bundles within the 3 feet section covered by the X level LPRMs, (less than 16 bundles for peripheral regions.) KW/FT.sub.i (X) is known input from the core monitor. The above algorithm is derived assuming no flow change. Basis of Algorithm The critical power ratio (CPR) is related to the critical quality (X.sub.c), bundle power (P) and channel flow (W) as follows: ##EQU2## For two different power conditions, ##EQU3## Assume the flow change caused by control rod withdrawal is very small. Also, if there is no adjacent rod withdrawal, assume X.sub.c change is negligible, ##EQU4## If there is axial power peaking shift caused by adjacent rod motion, then ##EQU5## where K.sub.a is the coefficient to account for axial power peaking shift. ##EQU6## (The above equation assumes no flow change.) Determination of A-factor The A-factor correlates bundle MCPR ratio to integrated LPRM ratio through combined relationships between MCPR to bundle power and bundle power to LPRM value. The construction of bundle power from LPRM readings is a major calculation task in the plant process computer model, where large amount of coefficients and data are used in lengthy calculations. In order to establish a simple relationship between measured LPRMs and "absolute" bundle power and corresponding MCPR that involves very few input data and calculations, as required by quick on-line monitoring and control purpose, an approximation method is used. This method is to construct an A-factor curve dependent only on a very few parameters, that is based on statistical interpretation of semi-empirical results from exact core physics calculations at various conditions. In order to obtain A-factor curves from rod withdrawal cases at various operating conditions, a family of operating power and flow conditions with corresponding typical rod patterns are developed in advance. These families of operating power and flow conditions are selected from spaced apart operating flow and power levels contained within the bound of the total universe of power and flow condition. This universe of power and flow conditions is illustrated in FIG. 4A. Six selected positions of power and flow specifically analyzed are shown. These are shown for core flows of 43% FIG. 4B and 70% FIG. 4C. Rod withdrawal cases with rods of higher worth are developed based on these initial conditions. Based on the highest rod worth and largest size of rod gang for rod withdrawal a family of A-factor curves are developed for various power and flow conditions and at different core cycle conditions. With the above data base, a proposed statistical A-factor curve for operating limit rod block algorithm for a typical 1100 MW reactor is shown at 200 in FIG. 4C. This is the curve of one-sided A-factor values at 95% probability at 50% confidence (best estimate) using the current data base of various A-factor data and assuming a normal distribution of the data, and with the following assumptions: a) Highest worth gang rod withdrawal cases (i.e., highest worth rods which has a gang size of eight rods) based on typical rod pattern at various power and flow conditions. b) Data included both initial core and equilibrium cycle conditions. c) Equilibrium Xenon initially and constant Xe during rod withdrawal. d) An average 15% random LPRM failure rate is included in developing the 95/50 bounding value. Based on the similar method, another set of A-factor curves is developed for any rod which is at least half way withdrawn from the core since the last core monitor update. By implementing this additional set of A-factor curves in the algorithm, the conservatism in A-factor for rods more than half withdrawn can be reduced significantly. Bounding A Factor for SLMCPR Protection The limiting rod pattern method is used to generate the A factor curve for SLMCPR protection. The highest worth rod or gang of rods is chosen as the error rod (rods) in the Rod Withdrawal Error event with a corresponding limiting rod pattern developed which would give the worst thermal limit change upon continuous rod withdrawal. This worst condition result is then used to define the rod block setpoint based on the concept that no rod withdrawal case will give a worse result; this setpoint thus prevents any SLMCPR violation under all circumstances. This same method is used here in determining the bounding A factor for SLMCPR protection. If one develops an A factor which represents the worst thermal limit change condition, then by using this A factor in MCPR protection setpoint algorithm, it will prevent any SLMCPR violation under all circumstances. (A factor is a multiplier to the setpoint itself.) The A factor curve for SLMCPR protection is calculated for a typical 1100 MW reactor and shown at 201 in FIG. 4C. Referring to FIG. 4B, typical curves relating to rod withdrawal at a selected location within the core are shown. These plots are for various power levels, at 43% core flow. Referring to FIG. 4C, a group of such curves is shown for an alternate rod location and core flow. MCPR Protection Algorithm During Core Flow Change Algorithm ##EQU7## Where: RBS.sub.o : Operating limit rod block (flow block) setpoint where EQU f(W.sub.i, W.sub.f)=1.953.times.10.sup.-2 (W.sub.f -W.sub.i)-1.722.times.10.sup.-4 (W.sub.f.sup.2 -W.sub.i.sup.2)+0.534.times.10.sup.-6 (W.sub.f.sup.3 -W.sub.i.sup.3) This algorithm shows that A.sub.f caused by flow change is uniform throughout the whole core. Overall total A factor with combination of rod pull and flow change can be obtained by multiplying the A factor due to rod pull to the A factor due to flow change. Basis of Algorithm Since core flow change is in general uniform throughout the whole core, the uniform bundle flow change will cause uniform bundle power change. The ratio of MCPR change is also uniform under specific power and flow conditions. This gives a constant A.sub.f for all core regions at specific power and flow conditions. A.sub.f value at specific power and flow conditions is proportional to the ratio of the critical power change only. This relationship is shown as follows, by definition of A.sub.f : ##EQU8## where LPRM represents the sum of the B, C, D LPRM ##EQU9## where CP represents the bundle critical power under specific flow condition (and power condition). ##EQU10## This shows that A.sub.f equals approximately the ratio between the final critical power after flow change and the initial critical power before flow change. If taking the most conservative A.sub.f value from various power conditions at a constant core flow, an A.sub.f curve as a function of core flow only can be established, which will follow the same trend as the change ratio of the bundle critical power. Since the critical power increases as flow increases. A.sub.f is always greater than 1. At lower flow A.sub.f is larger since critical power change ratio is larger: at higher flow A.sub.f is smaller since critical power change ratio is smaller. A.sub.f can be established as EQU A.sub.f =a+f(W.sub.f,W.sub.i); A.sub.f =1 if W.sub.f =W.sub.i where W.sub.f and W.sub.i are the final and initial core flow. A.sub.f due to core flow change is an independent factor that is not changed during rod withdrawal operation. A total A factor that represents a combined operation of both rod withdrawal and flow change can be obtained by multiplying the A.sub.f due to flow change by the A factor due to rod withdrawal. Determination of A.sub.f Function The exact A.sub.f value is determined based on a 10% core flow change operation (with no rod pull) performed at each typical operating point. The A.sub.f values for 10% flow change are shown in FIG. 5A, as a function of initial core flow. Based on the A.sub.f results, it shows that at any fixed core flow A.sub.f at lower power is always lower. Since lower A.sub.f represents more conservative A.sub.f (i.e., rod block setpoint is lower), the average A.sub.f values with a margin at these lowest power conditions are taken to construct an A.sub.f function which depends only on core flow. The margin used is the 95% probability and 50% confidence. This curve is shown in FIG. 5A. It is also stated as follows: ##EQU11## By integrating the above equation, one obtains EQU A.sub.f -1=1.953.times.10.sup.-2 (W.sub.f -W.sub.i)-1.772.times.10.sup.-4 (W.sub.f.sup.2 -W.sub.i.sup.2)+0.534.times.10.sup.-6 (W.sub.f.sup.3 -W.sub.i.sup.3) This relationship is included in the rod block algorithm due to core flow change to determine A.sub.f as a function of initial and final core flow. It is plotted in FIG. 5B with initial flow being 40%, 50%, and 60%. Those having skill in the art will realize that these resultant equations are capable of rapid solution in a programmed microprocessor. Algorithm to Prevent Fuel Mechanical Thermal Limit Violation During Rod Withdrawal There are two operating limits related to fuel mechanical thermal limit. One is the maximum fuel rod power density, or maximum linear heat generation rate (MLHGR), which mainly monitors the limit for prevention of cladding rupture due to pellet expansion stress. The other one is the maximum average planar linear heat generation rate, or MAPLHGR, which has to be maintained to limit cladding temperature during a loss of coolant accident (LOCA). It has been demonstrated during this study that the LPRM response to the regional maximum average planar linear heat generation rate change due to rod withdrawal is almost identical to the LPRM response to the regional MLHGR change. The MAPLHGR limit is derived from fuel rod heat flux limit with fuel rod local peaking factors taken into consideration. The MAPLHGR limit and the MLHGR limit are closely related, and are in general differed by a few percent. Due to the almost identical LPRM responses to changes of the two limits, either limit can be used in the ATLM rod block logic for fuel mechanical limit protection. With bounding conservative margins added to the B values, as to be explained later, the algorithm based on MAPLHGR or MLHGR will adequately cover both MAPLHGR and MLHGR fuel mechanical limits protection. In the core monitor model, the average planar LHGR is calculated by the model and the MAPLHGR limit is an input value being a function of fuel type and bundle exposure. The ratio of the two, called MAPRAT. is also calculated by the model and is readily obtainable through output editing. This MAPRAT value is to be used by the algorithm for rod block setpoint calculation. Also, since the overpower condition during worst transient at off-rated condition can be more severe than rated condition, a power and flow dependent multiplier factor has to be included in the MAPLHGR or MLHGR limit for off-rated condition applications. MAPLHGR Algorithm Equation The equation that governs the relationship between the MAPLHGR limit and the processed LPRM outputs are described as follows for each fuel monitoring region: ##EQU12## Where: RBS.sub.m (X): MAPLHGR operating limit rod block setpoint at LPRM level X Basis of Algorithm The average planar LHGR (APLHGR) is a calculated bundle average fuel pellet power density, expressed in term of kw/ft. The maximum APLHGR in the region monitored by the LPRM can be assumed to be proportional to the LPRM output that represents neutron flux level, or, EQU LPRM.varies.RAPLHGR where RAPLHGR is the regional maximum APLHGR. For two different power levels: ##EQU13## When a rod is being withdrawn next to a LPRM string, the true fuel power density of the fuel section around this rod next to the LPRM string are under measured. For two power conditions with one being the limiting condition, one has ##EQU14## Where B is the under-measure factor. If representing the right-hand side values in MAPRAT, i.e., dividing the RAPLHGR by MAPLHGR, one has ##EQU15## Since MAPLHGR is power and flow dependent based on over-power conditions during worst transient at off-rated conditions, an off-rated power multiplier factor for MAPLHGR (M.sub.p) has to be included in the above equation for off-rated condition setpoint calculations. Or ##EQU16## B has to be determined to cover all power and flow conditions and for all four LPRM level applications. B-Value Determination The strategy of determining the B-value is similar to the method of determining A-factor in the MCPR setpoint algorithm. For any power and flow condition, the relationship between the LPRM output and the local regional maximum APLHGR depends mainly on the withdrawal position of the adjacent control rod in this region. B-values are different for different power and flow conditions. To obtain the dependence relationship of B-values on core power, flow, and control rod position, typical power and flow conditions from the same family of operating conditions used in MCPR algorithm are selected and used. These typical cases are rod withdrawal cases with higher worth gang of rods being pulled from typical operating conditions which cover the entire power/flow operating region. Based on the above cases, a family of B-value curves are developed as a function of rod withdrawal position for the various operating conditions, for each of the four regions monitored by LPRM level A, B, C and D. The exemplary results are shown in FIGS. 6A and 6B. The results show that in general B-values vary depending on the distance between the rod position to the elevation of the concerned LPRM. For an initially deep rod. B-value tends to be close to one until the control rod is withdrawn to the vicinity of the LPRM elevation, where B-value starts to decrease. For example, for LPRM C level, the B-value drops to as low as 0.84. After the control rod is withdrawn to a position very close to the LPRM elevation, the B-value starts to increase back to near one, where the control rod is away from the LPRM. This is due to the control rod density effect described earlier. However, if the control rod initial position is very close to the LPRM or at the LPRM elevation, then the B-value no longer decreases with further rod pull. Instead, it stays close to one until the rod is completely withdrawn. Also, the results show that for higher core power conditions, the B-values stay at higher values even at rod position close to LPRM. This makes it possible to select two different set of bounding B-values for two different power ranges. Based on the bounding case results, a set of very conservative bounding margin factor B-value curves are derived for each LPRM level application. This is shown in solid line and in dashed line in FIGS. 6A and 6B. Solid line is to be applied in low power range (below 65% power); dashed line is to be applied to high power range (above 65% power). It has been demonstrated that these set of B-value margins can appropriately accommodate a random 15% probability failure of LPRMs sensors. MLHGR Algorithm Equation The equation that governs the relationship between the MLHGR limit and the processed LPRM outputs is similar to MAPLHGR algorithm equation and is described as follows for each fuel monitoring region: ##EQU17## Where: RBS.sub.M (X)=LHGR operating limit rod block setpoint at LPRM Level X Basis of Algorithm The basis of MLHGR algorithm is similar to that of the MAPLHGR algorithm. The maximum LHGR in the region monitored by the LPRM can be assumed to be proportional to the LPRM output that represents neutron flux level, or, EQU LPRM.varies.M. KW/FT Where M. KW/FT is the regional maximum KW/FT. For two different power levels: ##EQU18## When a rod is being withdrawn next to a LPRM string, the true fuel power density of the fuel section around this rod next to the LPRM string is under measured. For two power conditions with one being the limiting condition, one has ##EQU19## If an off-rated power multiplier factor for MLHGR (M.sub.P) is included, then ##EQU20## B has to be determined to cover all power and flow conditions and for all four LPRM level applications. B-Value Determination The Method of determining B value for MAPLHGR algorithm is followed to determine B value for MLHGR algorithm. Same typical cases of rod withdrawal cases are used. Based on the above cases, a family of B-value curves is developed as a function of rod withdrawal position for the various operating conditions, for each of the four regions monitored by LPRM level A, B, C, and D. The results are found to be almost identical to the results of MAPLHGR B values. MLHGR and MAPLHGR Algorithm due to Core Flow Change The B-Value to monitor KW/FT change during core flow change is evaluated. From theoretical point of view, it is concluded that the B-value during flow change is always one, for the following reasons: a) Flow change is a core-wide uniform change, the resultant power change is uniform and proportional to initial power core-wide. b) The bundle power change, or KW/FT change is uniform and proportional to the initial bundle power, independent in general of bundle location. c) The LPRM change, which monitors regional power change is proportional to the power (or KW/FT) change. This gives a B-value of one. The above conclusion is confirmed and verified by 3 dimensional core monitor model analysis. It is determined that the B-value of MLHGR algorithm due to flow change is one, regardless of power/flow conditions. Algorithm of Self Test Unit In addition to the built-in self test feature of the hardware, the self test unit has four test functions in both channels: a) Calculated versus Measured Plant Parameters Receive inputs of measured data of reactor pressure, feedwater flow, feedwater temperature, core flow, reactor power (APRM), and selected LPRMs. Compare these data with calculated data at the time when the monitor results are downloaded (including the above parameters). Issue rod block and warning if the two sets of data are different by a preset uncertainty factor. b) ATLM Algorithm Test For either channel, receive setpoint calculation result from the other channel. Compare this result with the result of own channel. Issue rod block and warning if the two do not agree by a preset error margin. c) Overall Functional Test (Manual) Upon initiation of test demand by the operator, a simulated high LPRM ratio signal is transmitted to the algorithm/comparator units to generate a trip signal. d) Setpoint Calculation Test (Manual) Upon initiating test demand, a display of a standard calculation data is available for setpoint calculation check as an ATLM functional test. System Logic a) Data Input Regional (16 bundle block or less) thermal limit data calculated by on-line monitor are downloaded to the ATLM processor memory automatically when no active rod movement is in progress. Operating limit table (a function of power and flow), safety limit MCPR value, and A-factor curves as a function of relative rod pull distance are manually entered at the beginning of cycle before startup. APRM (reference), core flow, LPRM readings, rod positions are scanned continuously and input to ATLM processor memory, MCPR, processed LPRM reading, rod position are two-dimensional matrices, (power density in KW/FT, processed LPRM reading for KW/FT monitoring are three-dimensional matrices.) B-factors tables are manually entered at the beginning of cycle before startup. Regional maximum KW/FT data or MAPRAT data (three dimensional) calculated by the on-line monitor are downloaded to the processor memory. b) Initialization Upon new monitor calculation and data download, all A-factors are initialized to one, all relative rod pull distances initialized to zero, and all rod positions are renamed as initial positions. Upon rod selection, selected rod(s) I.D., its position, and associated region(s) are identified and recorded. At beginning of first rod pull after a monitor data download, all input thermal limit and LPRM data are renamed as initial values, e.g., LPRM.sub.i, RMCPR.sub.i. The LPRM.sub.i and RMCPR.sub.i values are kept unchanged until the next monitor data update and download. A-factor is only dependent upon rod position difference between current position and initial position of the same rod(s) since the last monitor data update. All B-factor values are initialized to their designated values as a function of the initial rod position upon new monitor calculation and data download. All input KW/FT or MAPRAT data are renamed as initial values. Algorithm Calculation Time Cycle The algorithm will use the most recently scanned values of rod position and OLMCPR for calculation. The calculation will be on the order of 100 ms to 200 ms. The actual calculation (i.e., CPU) time will be much less than 100 ms, due to the simplicity of the algorithm and the current micro-processor capability. Algorithm calculation is initiated at the beginning of first rod pull and terminated a few minutes after rod motion stops. (Proposed time is 5 minutes.) With no active rod movement in progress, the algorithm calculation will still be performed periodically with a larger time cycle to monitor margin to OLMCPR and/or power density limit, caused by flow change and/or xenon variation. d) Table Look Up A-factor and OLMCPR are determined through on-line table lookup, with the former as a function of relative rod pull distance and the latter as a function of reactor power (APRM) and core flow. A-factor is applied to the algorithm based on relative rod pull distance since the last monitor update, for all control rods being pulled and for all corresponding fuel regions being affected. B-factor values and M.sub.p values are determined through on-line table lookup, with the former as a function of rod position and power, and the latter as a function of reactor power (APRM) and core flow. e) 3D Monitor Result Download Monitor calculation result is downloaded automatically upon completion of the calculation when there is no active rod movement and after completion of successful self test. The monitor calculation and download is always carried out at the end of a set of rod withdrawal motion. This will avoid any error introduced due to continuous rod motion during monitor calculation. For operating limit MCPR and KW/FT (or MAPRAT) setpoint calculation, the monitor result is automatically transferred into the algorithm input data entry memory after self test completion. For safety limit MCPR setpoint calculation, operator acknowledgement of the correctness of the monitor thermal limit data is required before this data is transferred into the algorithm input data entry memory. The SLMCPR setpoint thermal limit input update is required if the SLMCPR setpoint exceeds the operating limit MCPR setpoint. f) Rod Block If any single setpoint is exceeded by the instantaneously scanned and processed LPRM values, a rod block signal is generated by the comparator unit and sent to the RCIS for action. However, this rod block signal can be reset and cleared if a new setpoint calculation shows the setpoint is no longer exceeded. Other rod(s) then can be selected and withdrawn, either automatically through programmed rod withdrawal sequence or manually. If the number of failed LPRM detectors exceeds an allowed limit (defined in next section), a rod block signal will be issued (by RCIS). g) Rod Block Reset For rod block on SLMCPR, it cannot be reset either automatically or manually. Under this condition, operation must be transferred to manual if it is in auto. It cannot go back to auto until the OLMCPR rod block function is operational. The operator can then manually reset the block only if further setpoint calculation shows the instantaneous ATLM signal no longer exceeds this SLMCPR setpoint. For rod block on OLMCPR, it can be reset only if further setpoint calculation shows the instantaneous ATLM signal no longer exceeds the setpoint. For rod block on OLMCPR, the reset clearance can be done automatically or manually. For auto reset, the blocked rod is first to be inserted slightly (1% stroke). This logic can be programmed into the auto rod motion logic. h) Flow Block & Reset If the setpoint calculated by the flow block algorithm is exceeded by the LPRM values, a flow block signal is sent to the recirculation flow control system. It can be cleared by the operator action if subsequent ATLM readings do not exceed the setpoint. i) Self Test There are four functions in the self test unit: test of calculated versus measured plant parameters, test of ATLM algorithm performance, manual functional test, and test display check. If any one of the first two tests fails, rod block signal and warning are issued. The functional tests will always issue rod block and warning. j) 3D Monitor Calculation Frequency During constant power operation, the monitor calculation frequency can be set at every 1 to 2 hours. During power change operation, the frequency can be set at once for every 10% power change or once every 20 minutes, whichever is sooner. Monitor calculation also can be demanded by the plant's power generation and control system automatically when all rod withdrawals are temporarily inhibited by the ATLM logic due to conservatism in A-factors. A new monitor update will clear all rod blocks under this condition. It can also be demanded anytime by operator request. LPRM Failures Failure of LPRM chambers will affect the processed LPRM readings of the ATLM which in turn will affect proper rod block setpoint. Allowable failure rate thus must be established for the designed LPRM monitoring assignment. The final bounding A/B factors include a margin that cover an average 15% random LPRM failure rate. The following logic is implemented that specifies allowable failure rate for any 4 LPRM strings surrounding a 16 bundle block, if the failure number of LPRM exceeds 50% out of the designed sensor number for monitoring from these 4 strings then this region output will issue rod block. However, such rod block can be cleared with this region bypassed. During any ganged rod withdrawal operation which covers either four or eight fuel regions, up to three regions can be bypassed and still allow active rod pull in these regions with the ATLM operational. This has taken gang rod operation into consideration. Specifically, for KW/FT monitoring this means at least 2 out of 4 LPRM sensors on each level should be operational, otherwise, up to three regions can be bypassed during gang rod operation.