Abstract:
A method is provided for determining and controlling feed water level in a steam generator of a nuclear power plant, whereby the water level sensor is calibrated in terms of the pressure drop across structural components in the feed water path. The water level differential pressure sensor is calibrated so that maximum water level is indicated as the level corresponding to the upper tap level plus the pressure drop across the foregoing structural components at maximum power plant power.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
   This application claims priority under 35 U.S.C. §119(e) to provisional application Ser. No. 60/413,511, filed Sep. 25, 2002. 

   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   This invention relates to a method for determining the feed water measurement in a steam generator such as those used in pressurized water reactors and, more particularly, to a method for using a differential-type transmitter to sense the feed water level in a steam generator in a nuclear power plant. 
   2. Related Art 
   A typical nuclear steam generator comprises a vertically-oriented shell; a plurality of U-shaped tubes disposed in the shell so as to form a tube bundle; a tube sheet for supporting the tubes at the ends opposite the U-like curvature; a dividing plate that cooperates with the tube sheet forming a primary fluid inlet header at one end of the tube bundle and a primary fluid outlet header at the other end of the tube bundle; a primary fluid inlet nozzle in fluid communication with the primary fluid inlet header; and a primary fluid outlet nozzle in fluid communication with the primary fluid outlet header. The steam generator also comprises a wrapper disposed between the tube bundle and the shell to form an annular chamber adjacent the shell, and a feed water ring disposed above the U-line curvature end of the tube bundle. The primary fluid, having been heated by circulation through the nuclear reactor core, enters the steam generator through the primary fluid inlet nozzle. From the primary fluid inlet nozzle, the primary fluid is conducted through the primary fluid inlet header, through the U-tube bundle, out the primary fluid outlet header and through the primary fluid outlet nozzle to the cold leg of the reactor coolant loop. At the same time, feed water is introduced to the steam generator through the feed water ring. The feed water is conducted down the annular chamber adjacent the shell until the tube sheet near the bottom of the annular chamber causes the feed water to reverse direction, passing in heat transfer relationship with the outside of the U-tubes and up through the inside of the wrapper. While the feed water is circulating in heat exchange relationship with the tube bundle, heat is transferred from the primary fluid in the tubes to the feed water surrounding the tubes causing a portion of the feed water to be converted to steam. The steam then rises and is circulated through a series array of moisture separators, which dries out the steam before the steam is conveyed to steam turbine and condensation equipment, which are respectfully employed to drive a generator to produce electricity and to return the condensed fluid back to the steam generator feed water inlet. 
   The current steam generator feed water level measurement system is more fully described in U.S. Pat. No. 5,024,802. The current steam generator feed water level measurement methodology relies on the use of a differential-type transmitter for comparing the steam generator feed water level with a reference leg pressure input. The transmitter responds to a differential of water pressures inputted to it and provides an output representative of the difference between the reference leg pressure and the pressure due to the height of the liquid in the steam generator. This differential is a good correlation to water level when the lower pressure tap, for measuring the water level in the steam generator, is located in a relatively low velocity region of the steam generator, e.g., above the transition section of the steam generator shell. However, if the lower pressure tap is moved to a higher velocity region, e.g., below the transition portion of the shell, an error is introduced due to the effective velocity head of the moving water. In such circumstances, a level measurement penalty must be taken, meaning that the steam generator operating level margin, i.e., a range of permissible water levels, needs to be reduced. However, it is preferable to locate the lower tap in a high velocity region so as to minimize what is known as the shrink/swell phenomenon. 
   The control of feed water level in the secondary loop of a nuclear steam supply system is exemplary of situations where control is difficult because the system behaves with non-minimum phase dynamics. Non-minimum dynamics is a term used to describe a property of the frequency domain transfer function between plant input function and plant output function. Transport lags or pure-time delay between an input signal and its corresponding output is one form of non-minimum phase behavior. Another form of non-minimum phase behavior is an initial negative response of an output signal before changing sign and approaching its positive asymptote. This type of non-minimum phase behavior is what is often called by operators of such nuclear steam supply systems “shrink/swell behavior”. 
   Changes in reactor power, steam flow, feed water temperature and feed water flow all affect the measured level of secondary loop feed water contained in the steam generator. The feed water level controller&#39;s basic task is, therefore, to maintain the secondary side steam generator water level on target and within limits by changing feed water flow to compensate for changes in level produced by the other factors. The main consequence of the long lags and shrink and swell effects is that a controller must anticipate the affects of changes in plant state or control actions on steam generator level, and make compensatory responses before the ultimate affect of the event on steam generator level is manifested in measured level. Accordingly, it is very desirable to minimize the shrink/swell phenomenon by locating the lower pressure tap in a region such that the velocity head will be about 6 in. to 8 in. 
   U.S. Pat. No. 5,024,802 teaches a method for compensating for the velocity head effects experienced by the lower tap in high velocity regions by adding compensation during calibration so as to reduce the margin added to the high level trip set point to account for uncertainty in water level. This invention recognizes the need to further compensate the differential-type pressure transmitter signal for the pressure-altering effects of the feed water level caused by certain structural restrictions that impact the feed water pressure experienced at the lower tap, such as the middle deck plate pressure delta. 
   SUMMARY OF THE INVENTION 
   It is an object of this invention to provide, in a steam generator used in a pressurized water reactor nuclear power system, an improved method of measuring the feed water level in the steam generator taking into account process variations which impact the calibration accuracy of the level measurements. The water level differential pressure sensor is calibrated so as to account for process variations in addition to or instead of velocity head variations, such as middle deck plate delta-pressure variation. These process variations are functions of power and level. If these variations are not compensated for in the water level measurements and are accounted for in the uncertainty calculations, they will be entered as bias terms and will reduce the operating margins, i.e., the range of water levels within which operation is controlled. In accordance with this object, calibration of the differential pressure transmitter includes adding a first bias factor from the differential pressure at maximum water level, the first bias factor being equal to the middle deck plate delta-pressure at 100% power level, or another determined fraction of the maximum middle deck plate delta-pressure, to adjust the transmitter reading at any water level to account for the middle deck plate delta-pressure. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     A further understanding of the invention can be gained from the following description of the preferred embodiments when read in conjunction with the accompanying drawings in which: 
       FIG. 1  is an overall block diagram showing the environment of a steam generator for which the method of this invention is used; 
       FIG. 2  is a partial cross-sectional view, in elevation, of a typical steam generator; 
       FIG. 3  is a partial cross-sectional view, in elevation, of the upper portion of the steam generator of  FIG. 2 ; 
       FIG. 4  is a schematic representation indicating measurements taken in carrying out the method of this invention; 
       FIG. 5  is a graphical representation of the middle deck plate delta-pressure variation versus percent power; 
       FIG. 6  is a graphical representation of the bias in calibration versus percent level span; and 
       FIG. 7  is a graphical representation of velocity head v. percent power. 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENT 
     FIG. 1  shows a rudimentary block diagram of a typical pressurized water reactor system. The reactor  30  generates hot water which is coupled through suitable piping  31 , commonly referred to as the hot leg of the primary coolant loop, to a steam generator  34 . The water coolant from the reactor is circulated through heat transfer tubes illustrated at  36 , where it imparts its heat to feed water introduced as shown at  37 , and then is returned to the reactor. The rising steam generated from heating the feed water is passed through moisture separation apparatus illustrated at  38 . As is well known, there is a minimum level of feed water that must be maintained in the steam generator, to draw heat from the primary loop of the reactor so that the reactor does not overheat. There is also a maximum level of feed water that should be maintained within the steam generator which, if exceeded, would prevent the moisture separators from properly separating moisture from the steam. 
     FIG. 2  shows a more detailed view of the steam generator  34  shown in  FIG. 1  and referred to generally by reference character  110  in  FIG. 2 . The steam generator  110  comprises a lower shell  112  connected to a frustoconical transition shell  114  which connects lower shell  112  to an upper shell  116 . A dished head  118  having a steam nozzle  120  disposed thereon encloses upper shell  116  while a substantially semispherical head  122  having inlet nozzle  124  and outlet nozzle  126  disposed thereon encloses lower shell  112 . A dividing plate  128  centrally disposed in the semispherical head  122  divides the semispherical head  122  into an inlet compartment  130  and an outlet compartment  132 . The inlet compartment  130  is in fluid communication with inlet nozzle  124  while outlet compartment  132  is in fluid communication with outlet nozzle  126 . A tube sheet  134  having tube holes  136  therein is attached to the lower shell  112  and the semispherical head  122  so as to isolate the portion of the steam generator  110  above the tube sheet  134  from the portion below the tube sheet  134  in a fluid-tight manner. The tubes  138 , which are heat transfer tubes shaped with a U-like curvature, have their ends disposed in tube holes  136 . The tubes  138 , which may number about 7000, form a tube bundle  140 . Dividing plate  128  is attached to the tube sheet  134  so that the inlet compartment  130  is physically separated from the outlet compartment  132 . Each tube  138  extends from the tube sheet  134  where one end of each tube  138  is in fluid communication with the inlet compartment  130 , up into transition shell  114  where each tube  138  is formed in a U-like configuration, and back down to the tube sheet  134  where the other end of each tube  138  is in fluid communication with the outlet compartment  132 . In operation, the reactor coolant having been heated from circulation through the reactor core, enters steam generator  110  through inlet nozzle  124  and flows into inlet compartment  130 . From the inlet compartment  130 , the reactor coolant flows through tubes  138  in tube sheet  134 , up through the U-shaped curvature of tubes  138 , down through tubes  138  into outlet compartment  132 . From outlet compartment  132 , the reactor coolant is circulated through the remainder of the reactor coolant system in a manner well known in the art. 
   Tube bundle  140  is encircled by a wrapper  42  which extends from near the tube sheet  134  into the region of the transition shell  114 . The wrapper  142  together with the lower shell  112  form an annular chamber  144 . A secondary fluid or feed water inlet nozzle  146  is disposed on upper shell  116  above the tube bundle  140 . A feed water header  148  comprises three loops forming a generally cloverleaf shaped ring, is attached to feed water inlet nozzle  146 . Feed water header  148  has therein a plurality of discharge ports  150  arranged in varying arrays so that a greater number of discharge ports  150  are directed toward annular chamber  144 , then are directed otherwise. 
   During operation, feed water enters steam generator  110  through feed water inlet  146 , flows through feed water header  148  and out of feed water header  148  through discharge ports  150 . The greater portion of the feed water exiting discharge ports  150  flows down annular chamber  144  until the feed water contacts tube sheet  134 . Once reaching the bottom of annular chamber  144 , near tube sheet  134 , the feed water is directed inward around tubes  138  of tube bundle  140  where the feed water passes in heat transfer relationship with the tubes  138 . The hot reactor coolant within the tubes  138  transfers heat through the tubes  138  to the feed water, thereby heating the feed water. The heated feed water then rises by natural circulation up through the tube bundle  140 . In its travel around the tube bundle  140 , the feed water continues to be heated until steam is produced in a manner well known in the art. 
   The wrapper  142  has an upper cover or wrapper head  152  disposed thereon above the tube bundle  140 . The wrapper head  152  is sometimes referred to as the middle deck plate. Disposed on the middle deck plate  152  are sleeves or risers  154 , which are in fluid communication with the steam produced near the tube bundle  140  and have centrifugal swirl vanes  156  disposed therein. Disposed above the sleeves  154  is a moisture separator  158 , which may be a chevron moisture separator. The steam that is produced near the tube bundle  140  rises through the sleeves  154 , where centrifugal swirl vanes  156  cause some of the moisture in the steam to be removed. From the sleeves  154 , the steam continues to rise through moisture separator  158  where more moisture is removed. Eventually, the steam rises through steam nozzle  120  from where it is conducted through usual machinery to produce electricity all in a manner well known in the art. 
   As can be appreciated from  FIG. 3 , which is a partial cross-sectional view in elevation, of the upper portion of the steam generator of  FIG. 2 , steam generated within the wrapper or tube bundle enclosure  214 , which corresponds to the wrapper  142  shown in  FIG. 2 , along with entrained water, flows upwardly through a plurality of primary vapor separators or risers  248  extending vertically from a lower deck plate  222 , which serves as the wrapper cover  152  noted in  FIG. 2 , and in vapor flow communication with the wrapper interior. The upper ends of the separators  248  pass through and are supported by an upper plate member, or mid-deck plate  250  and discharge the steam into the upper chamber  252  in the shell  212 . The separators  248  are further supported by an intermediate horizontal plate or intermediate deck plate  254 . 
   A pair of vertically-stacked chevron moisture separators  256  and  258  are supported within the chamber  252  in a series flow relationship with the primary vapor separator outlet nozzles  260 , such that the steam within chamber  252  must pass through the separators prior to being discharged from the generator through the outlet port  262 , which corresponds to the steam nozzle  120  shown in  FIG. 2 . The entrained water, which is separated from the vapor by the chevron separators  256  and  258 , is collected and drains through a central vertical drain pipe  264 , which extends to a point near the lower deck plate  222 . 
   Vapor separating swirl vanes  266  are disposed within each primary vapor separator  248  adjacent to the discharge nozzle and orifice  260  to initially separate the entrained water from the vapor passing therethrough. Due to the contour of the swirl vanes, the mixture velocity and mixture density differences, the separated water is centrifuged in an outward fashion toward the primary separator enclosures where it flows through annular water downcomers  268 , which discharge the water onto the upper surface of the intermediate support or deck plate  254 . This intermediate support plate has a plurality of openings  70  for gravity draining of the separated water. 
   Thus, it can be seen that all water condensed or separated from the vapor discharged from the wrapper  214  is eventually collected and directed back to the lower deck plate  222 . The transition portion  212 B and lower portion  212 C of the shell  212  form an upwardly open chamber which receives the recirculating water and feed water mixture, which forms a pool having a top level  271 , as shown in  FIG. 3 . 
   Referring now to  FIG. 4 , there is shown a schematic diagram illustrating the measurements taken in practicing the method of this invention. A steam generator is illustrated at  34  and the nominal water level is illustrated at  41 . The top of the riser, through which the steam comes, is illustrated at  42 . The operating premise is that the water level should not rise above the top of the riser. The annular channel between the shell and the wrapper, through which recirculated water is passed, is illustrated at  43 . The upper tap for the differential pressure sensor employed to measure feed water level is illustrated at  45 ; steam is condensed in condensate pot  46 , which fills the reference leg between  46  and  48 . This provides a reference pressure, which is inputted to a first input of a differential pressure transmitter  48 , e.g., about 262 in. (6.655 meters) of water at 80° F. (26.67° C.). Thus, the first input to the differential transmitter  48  is a pressure representing a reference leg. The lower tap  49  provides a second water pressure signal which is inputted to the differential pressure transmitter  48 , the transmitter generating a signal which is representative of the difference of the steam generator water level and the reference leg. The lower tap  49  is located in the high velocity region for the reasons mentioned above. Thus, when the feed water is at its maximum level, the transmitter output is at its minimum; when the feed water is at its lowest level, the transmitter output is at its maximum. In practice, the output of transmitter  48  is connected to a feed water controller  50 , which controls the steam generator water level by controlling feed water input at  37 . 
   In accordance with the original method of operation, the differential pressure seen by the transmitter  48  is calibrated to be the difference between the reference leg pressure and the pressure due to the column of water or process liquid at the 100% level, i.e., at the upper tap. The method described in U.S. Pat. No. 5,024,802 proposed a correction factor to the static pressure measurement at 100% level, to account for the velocity head generated at the lower tap. This invention further reduces the operating margin penalty imposed to compensate for other process variations, such as the middle deck plate,  50 , delta-pressure, that are functions of power and feed water level. The middle deck plate delta-pressure variation, i.e., the pressure drop across the middle deck plate introduces a positive error, i.e., the indicated feed water level is higher than the actual level. Part or all of the middle deck plate error can be accounted for during calibration and hence, reduce the uncertainties used in the analysis to determine reactor trips/safeguards actuation setpoints. 
   Originally, the differential pressure transmitter in the feed water level measurement system was calibrated at minimum and maximum water levels, assuming static conditions. Thus, for a minimum water level corresponding to the lower tap  49 , the pressure differential is greatest, and the differential pressure transmitter is calibrated to its maximum output. For example, for a span between the lower and upper taps of 262 in. (6.655 meters), the differential pressure calculates to 220 in. (5.588 meters), corresponding to a differential pressure transmitter output of 20 milliamps. For 100% water level, where the differential pressure transmitter output should be minimum, calibration is performed by inputting a calculated differential pressure corresponding to the 100% level and adjusting the meter to provide a minimum output. Thus, calibration is made without any consideration of the effect of the velocity head or the pressure drop experienced across some of the structural elements in the feed water flow path, e.g., the middle deck plate. For example, a water level at the upper tap results in a calculated 60 in. (1.524 meters) differential pressure and a differential pressure transmitter reading of 4 milliamps. 
   The pressure drop across the middle deck plate is a function of steam flow and the maximum occurs at 100% steam flow, as shown in  FIG. 5 . 
   The maximum velocity occurs between 50–60% power as seen in  FIG. 7 . The maximum velocity head error is defined as the penalty due to the velocity head. 
   The maximum pressure drop across the middle deck plate occurs at 100% power as seen in  FIG. 5 . The maximum deck plate delta-pressure variation is defined as a penalty due to the pressure drop across the middle deck plate. Unlike the velocity head penalty, the middle deck plate pressure drop introduces a positive error, indicating a feed water level higher than the actual level. 
   In the invention of this application, calibration is adjusted by introducing a bias at the 100% feed water level indication. A negative bias to account for the penalty due to the velocity head, if appropriate, and a positive bias for the penalty due to the pressure drop across the middle deck plate. A bias correction for the velocity head may not always be appropriate, for example, where the lower tap is placed in a stagnant region of the feed water pool, e.g., above the shell transition  12 B shown in  FIG. 3 . Additionally, while the middle deck plate pressure drop is used as an example in the preferred embodiment, it should be appreciated that the invention covers the pressure drop across any of the structural elements in the feed water path between the upper and lower taps such as intermediate deck plate, feed ring, etc. Thus for maximum water level, corresponding to the minimum differential pressure transmitter output, the differential pressure is in part the difference between the reference leg pressure and the pressure due to the column of the process liquid further adjusted in the negative direction by a bias “B” illustrated at  FIG. 7  and further adjusted by a bias “E” in the positive direction as illustrated in  FIG. 5 . Bias “B−E” may be selected as the velocity head at 100% power level minus mid-deck plate delta-pressure at 100% power, or alternatively, may be any other fraction of the difference. 
   In addition, for maximum water level, corresponding to the minimum differential transmitter output, the differential pressure is the difference between the reference leg pressure and the pressure due to the column of the process liquid adjusted by a bias “B” as described above, further adjusted by a bias “E” illustrated at  FIG. 5 . Bias “E” may be selected as the pressure drop across the middle deck plate at 100% power level, or alternately, may be any other fraction of the maximum middle deck plate delta-pressure. The bias to compensate for the middle deck plate pressure drop should be taken at the same power level as that of the velocity head bias is calculated at if the velocity head correction factor is appropriate. The middle deck plate pressure drop “E” is determined by the vendor. Thus in the practice of this invention, the maximum water level calibration is performed by calculating the pressure due to the water and subtracting from that calculation, a bias “B” calculated as set forth above (if the velocity head is a factor) and adding a bias “E” calculated as set forth immediately above. The calculated equivalent differential water pressure is inputted to the differential transmitter, and the transmitter is calibrated to its minimum value. By way of example, for a “B” value of 30 in. (0.762 meters) and for a “E” of 10 in. (0.254 meters), the net calculated differential pressure at full water level is calculated to be 80 in. (2.032 meters) (30−10+60, where 60 in. (1.524 meters) is the pressure difference due to the reference leg and steam generator (process) side pressure difference), which would correspond to a minimum transmitter reading of 4 milliamperes. The low water level differential pressure would again typically be 220 in. (5.588 meters) of water corresponding to a maximum or full meter reading of 20 milliamperes. 
   While specific embodiments of the invention have been described in detail, it will be appreciated by those skilled in the art that various modifications and alternatives to those details could be developed in light of the overall teachings of the disclosure. Accordingly, the particular embodiments disclosed are meant to be illustrative only and not limiting as to the scope of the invention which is to be given the full breadth of the appended claims and any and all equivalents thereof.