Patent Publication Number: US-2023137431-A1

Title: Plant performance management method, plant performance management apparatus, and non-transitory computer readable medium

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     The present application claims priority to Japanese Patent Application No. 2021-178235 filed on Oct. 29, 2021, the entire contents of which are incorporated herein by reference. 
     TECHNICAL FIELD 
     The present disclosure relates to a plant performance management method, a plant performance management apparatus, and a non-transitory computer readable medium. 
     BACKGROUND 
     Methods are known for managing the performance of geothermal plants by monitoring the mutual validity of operating data. For example, see Non-Patent Literature (NPL) 1. 
     CITATION LIST 
     Non-patent Literature 
     NPL 1: Geothermal Energy Handbook Publication Committee (Eds), The Geothermal Research Society of Japan. “Geothermal Energy Handbook”. Ohmsha, Feb. 20, 2014. “Chapter 5: Operation of Geothermal Power Plants”, p. 569 
     SUMMARY 
     A plant performance management method according to an embodiment includes a step of evaluating performance of a plant based on a relationship between at least two items of data from operating data, and a step of analyzing a cause that makes the performance of the plant abnormal based on the operating data in a case in which the performance of the plant is evaluated as abnormal. 
     A plant performance management apparatus according to an embodiment performs the aforementioned plant performance management method. 
     A non-transitory computer readable medium according to an embodiment stores a plant performance management program configured to cause a computer to perform the aforementioned plant performance management method. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In the accompanying drawings: 
         FIG.  1    is a flowchart illustrating a plant performance management method according to a comparative example; 
         FIG.  2    is a block diagram illustrating an example configuration of a plant management system according to an embodiment; 
         FIG.  3    is a flowchart illustrating a plant performance management method according to an embodiment; 
         FIG.  4    is a graph depicting an example of the relationship between two items of data used to evaluate plant performance; 
         FIG.  5    is a graph depicting an example of the relationship among three items of data used to evaluate plant performance; 
         FIG.  6    is a graph depicting an example of a plurality of relationships between two items of data used in a case in which plant performance is analyzed as having declined due to a decline in condenser performance; 
         FIG.  7    is a graph depicting an example of a plurality of relationships between two items of data used in a case in which a pressure gauge that measures condenser pressure is analyzed as being abnormal; 
         FIG.  8    is a graph depicting an example of a plurality of relationships between two items of data used in a case in which plant performance is analyzed as having declined due to a decline in condenser performance and cooling tower performance; 
         FIG.  9    is a graph depicting an example of a plurality of relationships between two items of data used in a case in which plant performance is analyzed as having declined due to a decrease in the amount of water circulating between the condenser and the cooling tower; 
         FIG.  10    is a graph illustrating a case in which operating data for a future period is estimated to be plotted outside the normal range based on change over time in operating data; 
         FIG.  11    is a graph illustrating an example of four data sets including two items of data among a plurality of items of operating data; and 
         FIG.  12    is an example of a table associating plant status with a combination of classification results for each data set. 
     
    
    
     DETAILED DESCRIPTION 
     Demand exists for efficient management of plant performance. 
     A plant performance management method according to an embodiment includes a step of evaluating performance of a plant based on a relationship between at least two items of data from operating data, and a step of analyzing a cause that makes the performance of the plant abnormal based on the operating data in a case in which the performance of the plant is evaluated as abnormal. With this configuration, causes of abnormality are analyzed only when the performance of the plant is evaluated as abnormal. Consequently, the plant performance is efficiently managed. 
     In the step of evaluating the performance of the plant in the plant performance management method according to an embodiment, the performance of the plant may be evaluated based on change over time in at least one item of data from the operating data. With this configuration, signs that the plant performance will become abnormal can be detected. Consequently, the plant performance is efficiently managed. 
     The plant performance management method according to an embodiment may further include a step of evaluating whether at least one item of data from the operating data is abnormal in a case in which the performance of the plant is evaluated as normal. With this configuration, measures are taken for the plant at an early stage in a case in which an abnormality in the operating data is detected. Consequently, the plant performance is efficiently managed. 
     In the step of evaluating the performance of the plant in the plant performance management method according to an embodiment, the performance of the plant may be evaluated based on a relationship among three items of data from the operating data. With this configuration, the correlation between the combination of items for evaluation and the plant performance can be increased. As a result, the accuracy of the evaluation of plant performance increases. 
     In the step of analyzing a cause that makes the performance of the plant abnormal in the plant performance management method according to an embodiment, the operating data may be classified as normal, too high, or too low for each data set among a plurality of data sets including two items of data from the operating data. The cause that makes the performance of the plant abnormal may be analyzed based on a combination of classification results for each data set. With this configuration, the causes of abnormality of the plant can be analyzed in a simplified manner. Consequently, the load for operations to analyze the cause of abnormality can be reduced. The plant performance is also efficiently managed. 
     The plant performance management method according to an embodiment may further include a step of displaying a graph representing a relationship between a combination of at least a portion of items of data from the operating data. With this configuration, the process of evaluating plant performance and analyzing causes of abnormality can be represented visually for the user. Consequently, the user can accept the evaluation and analysis results with piece of mind. 
     The plant performance management method according to an embodiment may further include a step of estimating losses occurring in the plant based on analysis results of the cause that makes the performance of the plant abnormal. With this configuration, it can be easily determined whether to perform maintenance on the plant. Consequently, the plant performance is efficiently managed. 
     The plant performance management method according to an embodiment may further include a step of generating a maintenance plan for the plant based on a result of estimating the losses. With this configuration, the amount of generated power is maximized. Consequently, the plant performance is efficiently managed. 
     A plant performance management apparatus according to an embodiment performs the aforementioned plant performance management method. With this configuration, causes of abnormality are analyzed only when the performance of the plant is evaluated as abnormal. Consequently, the plant performance is efficiently managed. 
     A non-transitory computer readable medium according to an embodiment stores a plant performance management program configured to cause a computer to perform the aforementioned plant performance management method. With this configuration, causes of abnormality are analyzed only when the performance of the plant is evaluated as abnormal. Consequently, the plant performance is efficiently managed. 
     According to the present disclosure, a plant performance management method, a plant performance management apparatus, and a non-transitory computer readable medium that can efficiently manage plant performance can be provided. 
     A plant performance management system  100  according to an embodiment of the present disclosure (see  FIG.  2   ) manages the performance of a plant  10  (see  FIG.  2   ), such as a geothermal power plant. An embodiment of the plant performance management system  100  for managing the performance of the plant  10  is described below in comparison with a system according to a comparative example. 
     COMPARATIVE EXAMPLE 
     The system according to a comparative example manages the performance of the plant  10  by performing a plant performance management method including the example procedures illustrated in  FIG.  1   . The system according to the comparative example acquires operating data from the plant  10  (step S 91 ). The operating data includes the atmospheric wet bulb temperature, the cooling water temperature of a condenser  50 , the vacuum level of the condenser  50 , and the power output by the generator  40 . The system according to the comparative example evaluates the performance of the cooling tower  60  based on the relationship between the atmospheric wet bulb temperature and the cooling water temperature of the condenser  50  (step S 92 ). The system according to the comparative example evaluates the performance of the condenser  50  based on the relationship between the cooling water temperature of the condenser  50  and the vacuum level of the condenser  50  (step S 93 ). The system according to the comparative example evaluates the performance of a turbine  30  and the generator  40  based on the relationship between the vacuum level of the condenser  50  and the change in power output (step S 94 ). The system according to the comparative example analyzes the cause that makes the performance of the plant  10  abnormal based on the evaluation results of the performance of the plant  10  acquired by steps S 92  through S 94  (step S 95 ). 
     As described above, the system according to the comparative example evaluates the performance of the plant  10  based on a plurality of combinations of each item of the operating data and analyzes the cause that makes the performance of the plant  10  abnormal based on the evaluation results. Here, in the case of evaluating the performance of the plant  10  based on a plurality of combinations, many procedures are necessary. Consequently, the load for evaluation can be high. In other words, the efficiency of the work to manage the performance of the plant  10  can decrease. 
     In the present disclosure, a plant performance management system  100  that can efficiently manage the performance of the plant  10  is described. 
     EMBODIMENT OF THE PRESENT DISCLOSURE 
     As illustrated in  FIG.  2   , a plant performance management system  100  according to an embodiment of the present disclosure includes a plant  10  and a management apparatus  110 . The management apparatus  110  is also referred to as a plant performance management apparatus. 
     In the present embodiment, the plant  10  is assumed to be configured as a geothermal power plant that generates electricity using steam supplied from a geothermal reservoir  200  via a steam/water separator  20 . The plant  10  includes the steam/water separator  20 , a turbine  30 , a generator  40 , a condenser  50 , a cooling tower  60 , and a wet bulb thermometer  70 . The plant  10  is not limited to being a geothermal power plant and may be configured as other facilities such as a geothermal binary power plant or thermal power plant. 
     The management apparatus  110  includes a detector  112  and an output interface  114 . The detector  112  acquires operating data of the plant  10 . The operating data of the plant  10  includes, for example, the output of the generator  40 , the temperature of the cooling water at the inlet of the condenser  50 , the vacuum level of the condenser  50 , the atmospheric wet bulb temperature measured by the wet bulb thermometer  70 , or the like. The operating data of the plant  10  is not limited to these examples and may include various data such as the temperature of the cooling water at the outlet of the cooling tower  60  or the amount of cooling water circulating between the condenser  50  and the cooling tower  60 . The management apparatus  110  may further include a communication module configured to communicate with the plant  10 . The communication module may be capable of communicating with the plant  10  in a wired or wireless manner. 
     The detector  112  evaluates the performance of the plant  10  based on the operating data of the plant  10  and analyzes the cause that makes the performance of the plant  10  abnormal. The detector  112  may output the evaluation results of the performance or the analysis results of the causes of abnormality via the output interface  114 . 
     The detector  112  may, for example, be configured by a processor such as a central processing unit (CPU). The detector  112  may implement predetermined functions by having the processor execute a predetermined program. The detector  112  may include a memory. The memory may store various information used for operations of the detector  112 , programs for implementing the functions of the detector  112 , and the like. The memory may function as a working memory of the detector  112 . The memory may, for example, be a semiconductor memory. The memory may be included in the detector  112  or may be configured as a separate entity from the detector  112 . 
     The output interface  114  outputs information acquired from the detector  112 . The output interface  114  may notify a user of information by outputting visual information, such as characters, graphics, or images, directly or via an external apparatus or the like. The output interface  114  may include a display device and may be connected to the display device in a wired or wireless manner. The display device may include various types of displays, such as a liquid crystal display. The output interface  114  may notify the user of information by outputting audio information, such as sound, directly or via an external apparatus or the like. The output interface  114  may include an audio output device, such as a speaker, and may be connected to the audio output device in a wired or wireless manner. The output interface  114  may notify the user of information not only with visual information or audio information but also by outputting, directly or via an external apparatus or the like, information that the user is capable of perceiving with a different sense. 
     EXAMPLE FLOWCHART OF PLANT PERFORMANCE MANAGEMENT METHOD 
     The detector  112  of the management apparatus  110  may perform a plant performance management method that includes the steps of the flowchart illustrated in  FIG.  3   . The plant performance management method may be implemented as a plant performance management program executed by the processor of the detector  112  or the like. The plant performance management program may be stored on a non-transitory computer readable medium. The plant performance management program may cause the computer executing the plant performance management program to function as the management apparatus  110 . 
     The detector  112  acquires the operating data (step S 1 ). 
     The detector  112  evaluates the performance of the plant  10  based on the relationship between at least two items of data from the operating data (step S 2 ). 
     The detector  112  may evaluate whether the performance of the plant  10  is normal or abnormal based on the relationship between the atmospheric wet bulb temperature (WBT) and the specific steam consumption (SSC), as illustrated by the two-dimensional graph in  FIG.  4   , for example. In the graph in  FIG.  4   , the vertical axis corresponds to 
     SSC. The horizontal axis corresponds to WBT. 
     In the graph in  FIG.  4   , the WBT and SSC data obtained at the plant  10  at a certain point in time is plotted. A boundary A_ 2 D of the two-dimensional region where the data is plotted in a case in which the performance of the plant  10  is normal is indicated by a dashed dotted line. The region where data is plotted in a case in which the performance of the plant  10  is normal is also referred to as the normal region. In a case in which a plotted point of data is located within the normal region, as indicated by the white circle, the performance of the plant  10  is evaluated as being normal. In a case in which a plotted point of data is located outside the normal region, as indicated by the white triangle, the performance of the plant  10  is evaluated as being abnormal. 
     The detector  112  may evaluate whether the performance of the plant  10  is normal or abnormal based on the relationship among steam flow rate, WBT, and power output, as illustrated by the three-dimensional graph in  FIG.  5   , for example. In other words, the detector  112  may evaluate the performance of the plant  10  based on the relationship among three items of data from the operating data. In the graph of  FIG.  5   , the axis in the height direction of the three-dimensional graph corresponds to the power output. The two axes corresponding to the plane of the three-dimensional graph respectively correspond to the steam flow rate and the atmospheric wet bulb temperature. 
     In the graph in  FIG.  5   , the data for the steam flow rate, atmospheric wet bulb temperature, and power output obtained at the plant  10  at a certain point in time are plotted. A boundary A_ 3 D of the three-dimensional region where the data is plotted in a case in which the performance of the plant  10  is normal is indicated by a dashed dotted line. In a case in which a plotted point of data is located within the normal region, as indicated by the white circle, the performance of the plant  10  is evaluated as being normal. In a case in which a plotted point of data is located outside the normal region, as indicated by the white triangle, the performance of the plant  10  is evaluated as being abnormal. 
     The detector  112  may evaluate whether the performance of the plant  10  is normal or abnormal based on the relationship among the condenser vacuum level, the steam flow rate, and the power output. 
     The correlation between the combination of items for evaluation and the performance of the plant  10  can be increased by increasing the number of items of operating data used to evaluate the performance of the plant  10 . As a result, the accuracy of the evaluation of performance of the plant  10  can increase. 
     Returning to the flowchart in  FIG.  3   , the detector  112  determines whether the performance of the plant  10  is abnormal (step S 3 ). In a case in which the performance of the plant  10  is abnormal (step S 3 : YES), the detector  112  analyzes the cause of the abnormality based on a plurality of graphs representing the relationship between the two items (step S 4 ). For example, the detector  112  may analyze the cause of the abnormality based on the relationship between the WBT and the SSC, the relationship between the WBT and the temperature of the cooling water entering the condenser  50 , the relationship between the condenser pressure and the temperature of the cooling water entering the condenser  50 , and the relationship between the condenser pressure and the power output. 
     The detector  112  may analyze the cause of the abnormality using graphs representing the respective relationships, as illustrated in  FIG.  6   . The upper-left graph in  FIG.  6    represents the relationship between WBT (horizontal axis) and SSC (vertical axis). The lower-left graph in  FIG.  6    represents the relationship between WBT (horizontal axis) and cooling water temperature (vertical axis). The lower-right graph in  FIG.  6    represents the relationship between condenser pressure (horizontal axis) and cooling water temperature (vertical axis). The upper-right graph in  FIG.  6    represents the relationship between condenser pressure (horizontal axis) and power output (vertical axis). 
     The solid curves depicted in each graph in  FIG.  6    represent the curves that approximate the region where data is plotted in a case in which the performance of the plant  10  is normal. In other words, in  FIG.  6   , the normal region is represented by a curve as an approximation, but the normal region is not actually limited to being linear. A method of analyzing causes of abnormality is described below assuming that, in a case in which two items of data from the operating data acquired from a plant  10  with normal performance are plotted on a graph, the plotted points lie on an approximate curve of the normal region. 
     In the graph representing the relationship between WBT and SSC in the upper left of  FIG.  6   , data is plotted by a white circle at a position outside the approximate curve. In addition, a dashed perpendicular line is drawn from the white circle to each axis. Specifically, the value of SSC at the point plotted by the white circle is greater than the value of SSC corresponding to the value of the same WBT for the case in which the performance of the plant  10  is normal (the value at the point where the solid curve and the dashed line intersect). The detector  112  evaluates that the performance of the plant  10  has declined based on the upper-left graph. 
     In the upper-left graph, a dashed dotted perpendicular line is drawn to the vertical axis from the point where the approximate curve and the perpendicular dashed line intersect. The value of SSC represented by the intersection of the dashed dotted line and the vertical axis corresponds to the value of SSC in the normal state. The actual value of SSC represented by the perpendicular line (horizontal dashed line) drawn to the vertical axis from the point where the white circle is plotted is greater than the value of SSC in the normal state. 
     The detector  112  evaluates the performance of the plant  10  based on the upper-left graph as the procedure in step S 3  of  FIG.  3   . The detector  112  performs the procedure corresponding to the analysis of the causes of the abnormality in step S 4  of  FIG.  3    below. 
     In the graph representing the relationship between WBT and the cooling water temperature in the lower left of  FIG.  6   , data is plotted by a white circle on the approximate curve. In addition, a dashed perpendicular line is drawn from the white circle to each axis. The detector  112  evaluates that the cooling water temperature is normal based on the relationship between WBT and the cooling water temperature. 
     In the graph representing the relationship between the condenser pressure and the cooling water temperature in the lower right of  FIG.  6   , data is plotted by a white circle at a position outside the approximate curve. In addition, a dashed perpendicular line is drawn from the white circle to each axis. Specifically, the value of the condenser pressure at the point plotted by the white circle is greater than the value of the condenser pressure corresponding to the value of the same cooling water temperature for the case in which the performance of the plant  10  is normal (the value at the point where the approximate curve and the horizontal dashed line intersect). The detector  112  evaluates that the condenser pressure is abnormal based on the lower-right graph. 
     In the graph representing the relationship between the condenser pressure and the power output in the upper right of  FIG.  6   , data is plotted by a white circle on the approximate curve. In addition, a dashed perpendicular line is drawn from the white circle to each axis. The detector  112  evaluates that the turbine performance is normal based on the relationship between condenser pressure and power output. 
     The lower-right graph and the upper-right graph in  FIG.  6    have a common horizontal axis representing the condenser pressure. In the lower-right graph, the value of the condenser pressure at the point of intersection between the approximate curve and the horizontal dashed line corresponds to the value of the condenser pressure in the normal state. The value of the condenser pressure in the normal state, which is common to the lower-right graph and the upper-right graph, is represented as the intersection between the perpendicular dashed dotted line and the horizontal axis representing the condenser pressure. In the upper-right graph, the value of the power output at the point of intersection between the approximate curve and the perpendicular dashed dotted line corresponds to the value of the power output in the normal state. In the upper-right graph of  FIG.  6   , the value of the actual power output is smaller than the value of the power output in the normal state. 
     As described above, the detector  112  can analyze the cause behind the performance of the plant  10  becoming abnormal based on the relationship between the two items of data in the procedure of step S 4 . After executing the procedure of step S 4 , the detector  112  ends execution of the procedures of the flowchart in  FIG.  3   . 
     Returning to the flowchart in  FIG.  3   , in a case in which the performance of the plant  10  is not abnormal (step S 3 : NO), that is, in a case in which the performance of the plant  10  is normal, the detector  112  evaluates each item of the operating data (step S 5 ). In other words, the detector  112  evaluates whether at least one item of data from the operating data is abnormal. For example, the detector  112  may evaluate whether the measured value is normal in the measurement apparatus or sensor that measures each item of the operating data. With this configuration, measures can be taken for the plant  10  before the performance of the plant  10  becomes abnormal in a case in which an abnormality in the operating data is detected at an early stage. Consequently, the plant performance is efficiently managed. After executing the procedure of step S 5 , the detector  112  ends execution of the procedures of the flowchart in  FIG.  3   . 
     As described above, in the plant performance management system  100  according to the present embodiment, the detector  112  of the management apparatus  110  evaluates whether the performance of the plant  10  is normal or abnormal based on the relationship of a combination of at least two items of data from the operating data. The detector  112  analyzes the cause of abnormality based on the evaluation results. By the evaluation being based on the relationship of one combination of data, the performance of the plant  10  can easily be evaluated. Also, by analysis of the cause of abnormality in a case in which the performance of the plant  10  is evaluated as being abnormal, the load of the process to analyze the cause of abnormality can be reduced compared to a case in which the causes of abnormality are analyzed each time the operating data is evaluated. Consequently, the performance of the plant  10  can be efficiently managed. 
     OTHER EMBODIMENTS 
     Example of Analysis of Cause of Abnormality 
     Other examples of the analysis of the cause of abnormality in the procedure of step S 4  in  FIG.  3    are described with reference to  FIGS.  7 ,  8 , and  9   . 
     Case of Normal Performance of Plant  10  and One Abnormal Item 
     In the graph representing the relationship between WBT and SSC in the upper left of  FIG.  7   , data is plotted by a white circle at a position on the approximate curve. In addition, a dashed perpendicular line is drawn from the white circle to each axis. In this case, the detector  112  evaluates that the performance of the plant  10  is normal based on the upper-left graph. The detector  112  evaluates the performance of the plant  10  based on the upper-left graph as the procedure in step S 3  of  FIG.  3   . In a case in which the performance of the plant  10  is evaluated as normal, the detector  112  performs the procedure below corresponding to the evaluation of each item of the operating data in step S 5  of  FIG.  3   . 
     In the graph representing the relationship between WBT and the cooling water temperature in the lower left of  FIG.  7   , data is plotted by a white circle on the approximate curve. In addition, a dashed perpendicular line is drawn from the white circle to each axis. In this case, the detector  112  evaluates that the cooling water temperature is normal based on the relationship between WBT and the cooling water temperature. 
     In the graph representing the relationship between the condenser pressure and the cooling water temperature in the lower right of  FIG.  7   , data is plotted by a white circle at a position outside the approximate curve. In addition, a dashed perpendicular line is drawn from the white circle to each axis. Specifically, the value of the condenser pressure at the point plotted by the white circle is greater than the value of the condenser pressure corresponding to the value of the same cooling water temperature for the case in which the performance of the plant  10  is normal (the value at the point where the approximate curve and the horizontal dashed line intersect). In this case, the condenser pressure might be abnormal. 
     In the graph representing the relationship between the condenser pressure and the power output in the upper right of  FIG.  7   , data is plotted by a white circle at a position outside the approximate curve. In addition, a dashed perpendicular line is drawn from the white circle to each axis. In this case, the turbine performance might be abnormal. 
     Here, the lower-right graph and the upper-right graph in  FIG.  7    have a common horizontal axis representing the condenser pressure. In the lower-right graph, the value of the condenser pressure at the point of intersection between the approximate curve and the horizontal dashed line corresponds to the value of the condenser pressure in the normal state. The value of the condenser pressure in the normal state, which is common to the lower-right graph and the upper-right graph, is represented as the intersection between the perpendicular dashed dotted line and the horizontal axis representing the condenser pressure. In the upper-right graph, the value of the power output at the point of intersection between the approximate curve and the perpendicular dashed dotted line corresponds to the value of the power output in the normal state. In the upper-right graph of  FIG.  7   , the value of the actual power output matches the value of the power output in the normal state. In this case, it is likely that only the value of the condenser pressure is measured at a value greater than the normal value. Therefore, the detector  112  evaluates the measured value of the pressure of the condenser  50  as abnormal. 
     Case of Plurality of Abnormal Items 
     In the graph representing the relationship between WBT and SSC in the upper left of  FIG.  8   , data is plotted by a white circle at a position outside the approximate curve. In addition, a dashed perpendicular line is drawn from the white circle to each axis. In this case, the detector  112  evaluates that the performance of the plant  10  is abnormal based on the upper-left graph. The detector  112  evaluates the performance of the plant  10  based on the upper-left graph as the procedure in step S 3  of  FIG.  3   . In a case in which the performance of the plant  10  is evaluated as abnormal, the detector  112  performs the procedure corresponding to the analysis of the causes of the abnormality in step S 4  of  FIG.  3    below. 
     In the upper-left graph, a dashed dotted perpendicular line is drawn to the vertical axis from the point where the approximate curve and the perpendicular dashed line intersect. The value of SSC represented by the intersection of the dashed dotted line and the vertical axis corresponds to the value of SSC in the normal state. The actual value of SSC represented by the perpendicular line (horizontal dashed line) drawn to the vertical axis from the point where the white circle is plotted is greater than the value of SSC in the normal state. 
     In the graph representing the relationship between WBT and the cooling water temperature in the lower left of  FIG.  8   , data is plotted by a white circle at a position outside the approximate curve. In addition, a dashed perpendicular line is drawn from the white circle to each axis. Specifically, the value of the cooling water temperature at the point plotted by the white circle is greater than the value of the cooling water temperature corresponding to the value of the same WBT for the case in which the performance of the plant  10  is normal (the value at the point where the approximate curve and the perpendicular dashed line intersect). In this case, the cooling water temperature might be abnormal. In other words, the cooling tower performance might be abnormal. 
     In the graph representing the relationship between the condenser pressure and the cooling water temperature in the lower right of  FIG.  8   , data is plotted by a white circle at a position outside the approximate curve. In addition, a dashed perpendicular line is drawn from the white circle to each axis. Specifically, the value of the condenser pressure at the point plotted by the white circle is greater than the value of the condenser pressure corresponding to the value of the same cooling water temperature for the case in which the performance of the plant  10  is normal (the value at the point where the approximate curve and the horizontal dashed line intersect). In this case, the condenser pressure might be abnormal. 
     In the graph representing the relationship between the condenser pressure and the power output in the upper right of  FIG.  8   , data is plotted by a white circle on the approximate curve. In addition, a dashed perpendicular line is drawn from the white circle to each axis. In this case, the detector  112  evaluates that the turbine performance is normal based on the relationship between the condenser pressure and the power output. 
     Here, the lower-left graph and the lower-right graph in  FIG.  8    have a common vertical axis representing the cooling water temperature. In the lower-left graph, the value of the cooling water temperature at the point of intersection between the approximate curve and the perpendicular dashed line corresponds to the value of the cooling water temperature in the normal state. The value of the cooling water temperature in the normal state, which is common to the lower-left graph and the lower-right graph, is represented as the intersection between the horizontal dashed dotted line and the horizontal axis representing the cooling water temperature. In the lower-right graph, the value of the condenser pressure at the point of intersection between the approximate curve and the horizontal dashed dotted line corresponds to the value of the condenser pressure in the normal state. In the lower-right graph of  FIG.  8   , the actual value of the condenser pressure is greater than the value of the condenser pressure value in the normal state. 
     Furthermore, the lower-right graph and the upper-right graph in  FIG.  8    have a common horizontal axis representing the condenser pressure. The value of the condenser pressure in the normal state, which is common to the lower-right graph and the upper-right graph, is represented as the intersection between the perpendicular dashed dotted line and the horizontal axis representing the condenser pressure. In the upper-right graph, the value of the power output at the point of intersection between the approximate curve and the perpendicular dashed dotted line corresponds to the value of the power output in the normal state. In the upper-right graph of  FIG.  8   , the value of the actual power output is smaller than the value of the power output in the normal state. 
     Given that the power output is actually reduced in the case illustrated in  FIG.  8   , it is likely that both the cooling water temperature and the condenser pressure are abnormal. In other words, both the performance of the cooling tower  60  and the performance of the condenser  50  are likely to have declined. Therefore, the detector  112  evaluates the cooling tower  60  and the condenser  50  as abnormal. 
     Another example of causes of abnormality in a case in which a plurality of items are found to be abnormal is described with reference to  FIG.  9   . 
     In the graph representing the relationship between WBT and SSC in the upper left of  FIG.  9   , data is plotted by a white circle at a position outside the approximate curve. In addition, a dashed perpendicular line is drawn from the white circle to each axis. In this case, the detector  112  evaluates that the performance of the plant  10  is abnormal based on the upper-left graph. The detector  112  evaluates the performance of the plant  10  based on the upper-left graph as the procedure in step S 3  of  FIG.  3   . In a case in which the performance of the plant  10  is evaluated as abnormal, the detector  112  performs the procedure corresponding to the analysis of the causes of the abnormality in step S 4  of  FIG.  3    below. 
     In the upper-left graph, a dashed dotted perpendicular line is drawn to the vertical axis from the point where the approximate curve and the perpendicular dashed line intersect. The value of SSC represented by the intersection of the dashed dotted line and the vertical axis corresponds to the value of SSC in the normal state. The actual value of SSC represented by the perpendicular line (horizontal dashed line) drawn to the vertical axis from the point where the white circle is plotted is greater than the value of SSC in the normal state. 
     In the graph representing the relationship between WBT and the cooling water temperature in the lower left of  FIG.  9   , data is plotted by a white circle at a position outside the approximate curve. In addition, a dashed perpendicular line is drawn from the white circle to each axis. Specifically, the value of the cooling water temperature at the point plotted by the white circle is less than the value of the cooling water temperature corresponding to the value of the same WBT for the case in which the performance of the plant  10  is normal (the value at the point where the approximate curve and the perpendicular dashed line intersect). In this case, the cooling water temperature is instead lower than the temperature in the normal state. Therefore, the performance of the cooling tower  60  might be improved. 
     In the graph representing the relationship between the condenser pressure and the cooling water temperature in the lower right of  FIG.  9   , data is plotted by a white circle at a position outside the approximate curve. In addition, a dashed perpendicular line is drawn from the white circle to each axis. Specifically, the value of the condenser pressure at the point plotted by the white circle is greater than the value of the condenser pressure corresponding to the value of the same cooling water temperature for the case in which the performance of the plant  10  is normal (the value at the point where the approximate curve and the horizontal dashed line intersect). In this case, the condenser pressure might be abnormal. In other words, the performance of the condenser  50  may have declined. 
     In the graph representing the relationship between the condenser pressure and the power output in the upper right of  FIG.  9   , data is plotted by a white circle on the approximate curve. In addition, a dashed perpendicular line is drawn from the white circle to each axis. In this case, the detector  112  evaluates that the turbine performance is normal based on the relationship between the condenser pressure and the power output. 
     Here, the lower-left graph and the lower-right graph in  FIG.  9    have a common vertical axis representing the cooling water temperature. In the lower-left graph, the value of the cooling water temperature at the point of intersection between the approximate curve and the perpendicular dashed line corresponds to the value of the cooling water temperature in the normal state. The value of the cooling water temperature in the normal state, which is common to the lower-left graph and the lower-right graph, is represented as the intersection between the horizontal dashed dotted line and the horizontal axis representing the cooling water temperature. In the lower-right graph, the value of the condenser pressure at the point of intersection between the approximate curve and the horizontal dashed dotted line corresponds to the value of the condenser pressure in the normal state. In the lower-right graph of  FIG.  9   , the actual value of the condenser pressure is greater than the value of the condenser pressure value in the normal state. 
     Furthermore, the lower-right graph and the upper-right graph in  FIG.  9    have a common horizontal axis representing the condenser pressure. The value of the condenser pressure in the normal state, which is common to the lower-right graph and the upper-right graph, is represented as the intersection between the perpendicular dashed dotted line and the horizontal axis representing the condenser pressure. In the upper-right graph, the value of the power output at the point of intersection between the approximate curve and the perpendicular dashed dotted line corresponds to the value of the power output in the normal state. In the upper-right graph of  FIG.  9   , the value of the actual power output is smaller than the value of the power output in the normal state. 
     Given that the power output is actually reduced in the case illustrated in  FIG.  9   , some kind of abnormality may have occurred in the plant  10 . Here, the detector  112  can estimate that the performance of the cooling tower  60  has improved. On the other hand, the detector  112  can estimate that the performance of the condenser  50  has declined. Based on these two events, the detector  112  can evaluate that the amount of water circulating between the condenser  50  and the cooling tower  60  has likely decreased. 
     Summary 
     As described above, the management apparatus  110  according to the present embodiment can generate combinations of at least two items of operating data and analyze various causes of abnormality based on a plurality of combinations. 
     Performance Evaluation Based on Change Over Time in Operating Data 
     The detector  112  may evaluate the performance of the plant  10  based further on the change over time in at least one item of data from the operating data. For example, as illustrated in  FIG.  10   , in the graph representing the relationship between WBT and SSC, multiple operating data of the plant  10  obtained during a first period are plotted as white circles labeled first data P_T 1 . The plotted first data P_T 1  is classified into a group surrounded by a solid oval represented as T 1 . Furthermore, multiple operating data of the plant  10  obtained in a second period after the first period are plotted as white rectangles labeled second data P_T 2 . The plotted second data P_T 2  is classified into a group surrounded by a solid oval represented as T 2 . 
     In the graph in  FIG.  10   , the vertical axis represents SSC, and the horizontal axis represents WBT. The graph in  FIG.  10    illustrates the change over time in SSC and WBT in the operating data when the period progresses from the first period to the second period. The operating data of the plant  10  obtained in the first and second periods is located within the normal region surrounded by the boundary A_ 2 D. Therefore, the detector  112  evaluates the performance of the plant  10  as normal. 
     Based on the change in the positions where the operating data is plotted when progressing from the first period to the second period, the detector  112  estimates the position where the operating data of the plant  10 , to be obtained in a third period after the second period, will be plotted. In the graph in  FIG.  10   , the data estimated as the operating data of the plant  10  to be obtained in the third period is plotted as third data P_T 3 . The plotted third data P_T 3  is classified into a group surrounded by a dashed oval represented as T 3 . 
     In a case in which the operating data of the plant  10  estimated to be obtained in the third period is located outside the normal region surrounded by the boundary A_ 2 D, the detector  112  can predict that the performance of the plant  10  will become abnormal when the period progresses to the future third period. Before the period progresses to the future third period, the detector  112  may output the prediction result that the performance of the plant  10  will become abnormal. 
     The detector  112  may set the period for checking the change over time in the operating data in units of days, weeks, months, or years, for example, or in units of seconds, minutes, or hours. 
     As described above, even in a case in which the plot of operating data obtained from the plant  10  at a present or past period is located within the normal range, the management apparatus  110  can estimate that the plot of operating data at a future time or period will be out of the normal range based on the trend of the change over time in the operating data. In other words, the management apparatus  110  can detect signs that the performance of the plant  10  will become abnormal. Detection of signs that the performance of the plant  10  will become abnormal allows action to be taken for the plant  10  at an early stage. Consequently, the plant performance is efficiently managed. 
     Performance Evaluation Based on Classification of Plot Position 
     The detector  112  may generate a data set that includes two items of data from the plurality of items in the operating data. The detector  112  may generate a plurality of data sets. The detector  112  may generate a graph for each of the plurality of data sets, as illustrated in  FIG.  11   , and may set a range in the graph that includes positions such that the performance of the plant  10  can be evaluated as normal when the operating data is plotted at those positions. The upper-left graph in  FIG.  11    represents the relationship between WBT (horizontal axis) and SSC (vertical axis). The lower-left graph in  FIG.  11    represents the relationship between WBT (horizontal axis) and cooling water temperature (vertical axis). The lower-right graph in  FIG.  11    represents the relationship between condenser pressure (horizontal axis) and cooling water temperature (vertical axis). The upper-right graph in  FIG.  11    represents the relationship between condenser pressure (horizontal axis) and power output (vertical axis). 
     The approximate curve depicted in each graph in  FIG.  11    represents a range that includes positions at which the performance of the plant  10  can be evaluated as normal when the operating data is plotted at those positions. In other words, when two items of data from the operating data acquired from the plant  10  are plotted on the graphs in  FIG.  11    and the points are located on the approximate curves, the performance of the plant  10  can be evaluated as normal. The region above the solid line depicted in each graph in  FIG.  11    is represented by A. The region below the approximate curve is represented by B. The region represented by A corresponds to the region where the operating data is above normal. The region represented by B corresponds to the region where the operating data is below normal. 
     When operating data is plotted on each graph, the detector  112  evaluates whether the data is classified as normal, A, or B. In other words, the detector  112  classifies the operating data as normal, above normal, or below normal for each data set. The detector  112  analyzes the cause that makes the performance of the plant  10  abnormal based on combinations of the classification result for each data set. Specifically, as illustrated in  FIG.  12   , the detector  112  sets combinations in which each of the four data sets (four graphs) is classified as normal, A, or B. Classifying each of the four data sets into three types yields 81 possible combinations of classification results (i.e., 3×3×3×3). The detector  112  associates the performance of the plant  10  with each of the combinations of classification results. 
     For example, the row labeled “Analysis-1” in the leftmost cell corresponds to the classification result of the operating data illustrated in  FIG.  6   . As described above, in a case in which the operating data illustrated in  FIG.  6    is obtained from the plant  10 , the cause of the abnormality in the plant  10  is estimated to be a decrease in the pressure of the condenser  50 . Therefore, the detector  112  associates the row labeled “Analysis-1” with a decrease in condenser pressure as the performance of the plant  10 . 
     The row labeled “Analysis-2” in the leftmost cell corresponds to the classification result of the operating data illustrated in  FIG.  7   . As described above, in a case in which the operating data illustrated in  FIG.  7    is obtained from the plant  10 , the cause of the abnormality in the plant  10  is estimated to be an abnormal measured value for the pressure of the condenser  50 . Therefore, the detector  112  associates the row labeled “Analysis-2” with an abnormal condenser pressure gauge as the performance of the plant  10 . 
     The row labeled “Analysis-3” in the leftmost cell corresponds to the classification result of the operating data illustrated in  FIG.  8   . As described above, in a case in which the operating data illustrated in  FIG.  8    is obtained from the plant  10 , the cause of the abnormality in the plant  10  is estimated to be a decrease in the performance of the cooling tower  60  and the condenser  50 . Therefore, the detector  112  associates the row labeled “Analysis-3” with a decrease in the performance of the cooling tower  60  and the condenser  50  as the performance of the plant  10 . 
     The row labeled “Analysis-4” in the leftmost cell corresponds to the classification result of the operating data illustrated in  FIG.  9   . As described above, in a case in which the operating data illustrated in  FIG.  9    is obtained from the plant  10 , the cause of the abnormality in the plant  10  is estimated to be an abnormal amount of water circulating between the condenser  50  and the cooling tower  60 . Therefore, the detector  112  associates the row labeled “Analysis-4” with a decrease in the amount of water circulating between the condenser  50  and the cooling tower  60  as the performance of the plant  10 . 
     As described above, the detector  112  classifies the operating data for each data set and analyzes the cause that makes the performance of the plant  10  abnormal based on combinations of the classification result for each data set. By advance preparation of a table in which the causes of abnormality of the plant  10  are associated with combinations of classification results, the causes of abnormality of the plant  10  can be analyzed in a simplified manner. Consequently, the load for operations to analyze the cause of abnormality can be reduced. The performance of the plant  10  can also be efficiently managed. 
     Graphical Display of Operating Data 
     The detector  112  of the management apparatus  110  evaluates the performance of the plant  10  based on each item of the operating data, as described above, and analyzes the cause of abnormality. The detector  112  may display a graph, on the output interface  114 , representing the relationship between a combination of at least a portion of items of data among the operating data used to evaluate the performance of the plant  10 . With this configuration, the content of the evaluation and analysis processes executed by the detector  112  can be represented visually for the user. Consequently, the user can accept the evaluation and analysis results with piece of mind. 
     Maintenance Plan for Plant  10   
     The detector  112  of the management apparatus  110  may generate a maintenance plan for the plant  10  based on the result of evaluating the performance of the plant  10 . The maintenance of the plant  10  is performed at a predetermined timing, such as once a year. Based on the result of evaluating the performance of the plant  10 , the detector  112  may determine whether it is necessary to perform maintenance on the plant  10  on an ad hoc basis before the predetermined timing is reached. In a case in which ad hoc maintenance of the plant  10  is determined to be necessary, the detector  112  may generate a maintenance plan for the plant  10 . 
     The detector  112  may estimate losses occurring in the plant  10  based on the result of evaluating the performance of the plant  10 . The losses in the plant  10  result from a decrease in the performance of the plant  10 , such as a decrease in the output of the plant  10 . In a case in which the plant  10  is a geothermal power plant, the losses in the plant  10  result from a decrease in power generation (decrease in power output). The detector  112  may determine that maintenance of the plant  10  on an ad hoc basis is necessary in a case in which the losses caused by the decrease in the output of the plant  10  during the period until the next maintenance are greater than predetermined losses. 
     The losses at the plant  10  include the opportunity loss caused by shutting down the plant  10  in the case of performing maintenance on an ad hoc basis. The losses in the plant  10  also include the cost of work hours, parts, and the like incurred to perform maintenance on the plant  10 . In other words, the losses in the plant  10  include losses resulting from ad hoc maintenance of the plant  10 . The detector  112  determines that ad hoc maintenance of the plant  10  is necessary in a case in which the losses that would be caused by not maintaining the plant  10  until the next scheduled maintenance are greater than the losses that would result from ad hoc maintenance of the plant  10 . In other words, the detector  112  may generate a maintenance plan for the plant  10  based on the result of estimating losses. 
     By estimation of the losses in the plant  10 , it can be easily determined whether to perform maintenance on the plant  10 . Also, by generation of a maintenance plan for the plant  10  based on the result of estimating the losses in the plant  10 , excessive costs or workload for maintenance of the plant  10  can be reduced. Consequently, the performance of the plant  10  is efficiently managed. 
     Although embodiments of the present disclosure have been described through drawings and examples, it is to be noted that various changes and modifications can be made by those skilled in the art on the basis of the present disclosure. Therefore, such changes and modifications are to be understood as included within the scope of the present disclosure. For example, the functions or the like included in the various components or steps may be reordered in any logically consistent way. Furthermore, components or steps may be combined into one or divided.