METHOD OF AND CONTROL SYSTEM FOR MONITORING A PROCESS OF CIRCULATION OF SOLID MATERIAL IN A CIRCULATING FLUIDIZED BED REACTOR

Abstract

A method of monitoring circulation of solid material in a circulating fluidized bed reactor including a reaction chamber, at least one solid material separator, and a return path between the separator and the chamber. The method includes selecting process variables of the process of circulating of solid material in the return path, and selecting performance indicators of the process of circulation of solid material amongst the selected process variables for each performance indicator of the process of circulation of material, creating a multivariate model for each performance indicator, using history data of the process variables and the performance indicators, determining a modelled value of the performance indicators, by applying current measured values of the process variables to the multivariate model, and comparing the modelled value of each performance indicator to a respective measured value and inspecting a presence of an anomaly between the modelled value and the respective measured value.

Claims

1.-21. (canceled)

22. A method of monitoring a process of circulation of solid material in a circulating fluidized bed reactor, the reactor comprising a reaction chamber, at least one solid material separator, a return path between the at least one solid material separator and the reaction chamber and, in which method, the process of circulation of the solid material comprises arranging solid material to be entrained by gas flow in the reaction chamber, and to entrain further from the reaction chamber to the at least one solid material separator and passing solid material from the solid material separator via a return path to the reaction chamber, the method comprising the following steps: (a) selecting process variables of the process of circulation of the solid material in the return path, and selecting performance indicators of the process of circulation of the solid material amongst the selected process variables for each performance indicator of the process of circulation of the solid material; (b) creating a multivariate model for each performance indicator, using history data of the process variables and the performance indicators of the process of circulation of the solid material; (c) determining a modelled value of the performance indicators, by applying current measured values of the process variables to the multivariate model; and (d) comparing the modelled value of each performance indicator to a respective measured value of each performance indicator and inspecting a presence of an anomaly between the modelled value and the respective measured value.

23. A method according to claim 22, wherein the multivariate model is updated after a period of time triggered by a lapse of a constant predetermined time interval, or by a trigger input.

24. A method according to claim 22, wherein, when the reactor comprises at least a first return path between a first solid material separator and the reaction chamber and a second return path between a second solid material separator and the reaction chamber, the method further comprises separately performing the method concerning the process of circulation of the solid material in the first return path and the method concerning the process of circulation of the solid material in the second return path.

25. A method according to claim 22, wherein the multivariate model is a multivariate linear regression having a first number (N) of measured observations of each process variable and a second number (P) of different process variables of the process of circulation of solid material as follows: $y_i=b_0+b_1{x}_{i,1}+b_2{x}_{i,2}+.Math.b_P{x}_{i,P}+{}_i$ where i=1, 2, . . . N, and the method further comprising reading history data of y.sub.i, x.sub.i1, x.sub.i2, . . . , x.sub.ip where y=a performance indicator and x.sub.i,1, x.sub.i,2, . . . , x.sub.i,p are process variables, solving a constant b.sub.0 and factors b.sub.1, b.sub.2, . . . , b.sub.P, and performing a fitting process by minimizing a sum of squares of vertical deviations from each data point to a line that fits best for the history data.

26. A method according to claim 25, wherein the first number of measured observations N is at least ten times the second number (P) of different process variables.

27. A method according to claim 22, wherein a risk index for each performance indicator is calculated using information of a presence of the anomaly.

28. A method according to claim 27, wherein calculating the risk index for each performance indicator uses an anomaly between the modelled value and the respective measured value.

29. A method according to claim 22, wherein the process of circulation of the solid material comprises passing the solid material from the solid material separator directly to the reaction chamber via a loop seal in the return path, and further comprising selecting: (i) a pressure difference of the loop seal in the return path of the circulation of the solid material; and (ii) a temperature in the loop seal in the return path in the circulation of the solid material, as the performance indicators of the process in step (a).

30. A method according to claim 29, wherein: (iii) process variables of the performance indicator of the pressure difference of the loop seal in the return path comprise an aggregate reaction gas flow rate fed into the reactor, temperature of a product gas upstream the loop seal, and bed temperature in the reaction chamber, and (iv) process variables of the performance indicator of temperature in the loop seal in the return path in the circulation of the solid material comprise an aggregate reaction gas flow rate fed into the reactor, a temperature of product gas upstream of the loop seal, and a bed temperature in the reaction chamber.

31. A method according to claim 30, wherein the aggregate reaction gas flow rate is total flow rate of gas flows into the reaction chamber.

32. A method according to claim 30, wherein the bed temperature is an average bed temperature in the reaction chamber, which is calculated from at least two measurement points in the reaction chamber, at least one of which is at a grid level of the reaction chamber.

33. A method according to claim 22, wherein the process of circulation of the solid material comprises passing the solid material from the solid material separator via a fluidized bed heat exchanger to the reaction chamber, and further comprising selecting: (i) a pressure difference of a loop seal in the return path in the circulation of the solid material; (ii) a temperature in the loop seal in the return path in the circulation of the solid material; (iii) a pressure difference of the fluidized bed heat exchanger; and (iv) a temperature of the solid material downstream of a fluidized bed heat exchange unit in the fluidized bed heat exchanger, as the performance indicators of the process in step (a).

34. A method according to claim 33, wherein: (v) process variables of the performance indicator of a pressure difference of the loop seal in the return path comprise an aggregate reaction gas flow rate fed into the reactor, a temperature of a product gas upstream the loop seal, and a bed temperature in the reaction chamber, (vi) process variables of the performance indicator of a temperature in the loop seal in the return path in the circulation of the solid material comprise an aggregate reaction gas flow rate fed into the reactor, a temperature of a product gas upstream of the loop seal, and a bed temperature in the reaction chamber, (vii) process variables of the performance indicator of a pressure difference of the fluidized bed heat exchanger comprise an aggregate reaction gas flow rate fed into the reactor, a temperature in the loop seal in the return path in the circulation of the solid material, a pressure difference of the loop seal, a gas flow rate to the fluidized bed heat exchanger, and a bed temperature in the reaction chamber, and (viii) process variables of the performance indicator of the temperature of the fluidized bed heat exchanger comprise an aggregate reaction gas flow rate fed into the reactor, a temperature in the loop seal in the return path, a pressure difference of the loop seal, a gas flow rate to the fluidized bed heat exchanger, and a bed temperature in the reaction chamber.

35. A method according to claim 34, wherein the aggregate reaction gas flow rate is a total flow rate of gas flows into the reaction chamber.

36. A method according to claim 34, wherein the bed temperature is an average bed temperature in the reaction chamber, which is calculated from at least two measurement points in the reaction chamber, at least one of which is at a grid level of the reaction chamber.

37. A method according to claim 22, wherein creating the multivariate model comprises: measuring values of predetermined process variables, storing the measured values of the predetermined process variables with a time stamp, thus, forming the history data of the process variables; measuring values of the performance indicator and storing the measured values of the performance indicator with a time stamp, thus, forming the history data of performance indicators; and selecting valid history data using predetermined data filters.

38. A method according to claim 37, wherein the data filters are configured to approve data that is not older than two months.

39. A method according to claim 37, wherein the data filters are configured to filter out from history data at least any data from shut down situations and from any abnormal operation, based on predefined limits for input variables or external information of abnormal operation.

40. A method according to claim 37, wherein the data filters are configured to approve data that is older than a pre-set quarantine time.

41. A method according to claim 40, wherein the data filters are configured to approve data that is older than two weeks.

42. A control system for monitoring a process of circulation of solid material in a circulating fluidized bed reactor between a reaction chamber and at least one solid material separator, and to the reaction chamber via a return path comprising a loop seal, the control system comprising: a performance modelling unit comprising: (a) access to source history data of performance indicators of the process of circulation of the solid material in the return path and process variables for each performance indicator; (b) a multivariate model for each performance indicator; and (c) executable instructions which, when executed in the control system, update the multivariate model for each performance indicator, using history data of predetermined process variables and the performance indicators of the process of circulation of the solid material, resulting in a calibrated multivariate model; and a performance diagnostic module comprising: (a) inputs for receiving measurement data of process variables and performance indicators of the process of circulation of the solid material; and (b) executable instructions which, when executed in the control system, (i) determine a modelled value of the performance indicators, by applying current measured values of the process variables to the calibrated multivariate model; and (ii) compare the modelled value of each performance indicator to a measured respective value of the performance indicator and inspecting a presence of an anomaly between the modelled value and the measured respective value.

43. A control system according to claim 42, further comprising measurement sensors for at least the following process variables: pressure sensors for measuring a pressure drop in the loop seal; a product gas temperature sensor downstream of the solid material separator; and sensors for determining an aggregate gas flow rate to the reactor and bed temperature in the reaction chamber of the reactor.

44. A control system according to claim 42, further comprising: a fluidized bed heat exchanger in the return path; measurement sensors for at least following process variables: pressure sensors for measuring a pressure drop in the loop seal; a temperature sensor in the loop seal; a product gas temperature sensor downstream of the solid material separator; pressure sensors for measuring a pressure drop in the fluidized bed heat exchanger; temperature sensors for measuring temperature of solid material downstream of a heat exchange unit in the fluidized bed heat exchanger; and sensors for determining an aggregate gas flow rate to the reactor and bed temperature in the reaction chamber of the reactor.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0160] In the following, the invention will be described with reference to the accompanying exemplary, schematic drawings, in which:

[0161] FIG. 1 illustrates a circulating fluidized bed reactor according to an embodiment of the invention;

[0162] FIG. 2 illustrates a control system according to an embodiment of the invention,

[0163] FIG. 3 illustrates a circulating fluidized bed reactor according to another embodiment of the invention;

[0164] FIG. 4 illustrates results obtained with method according to the invention; and

[0165] FIG. 5 illustrates a circulating fluidized bed reactor according to another embodiment of the invention.

DETAILED DESCRIPTION OF THE INVENTION

[0166] In the following, the description of the figures generally relates to examples of method of air combustion of fuel in a CFB reactor. Even if some minor structural changes may be needed, the CFB reactor and its embodiments described in the figures are as well applicable for producing syngas by practicing a gasification process in the reactor. Correspondingly the described CFB reactor and its embodiments may be utilized for practicing a so called oxy-combustion process, meaning combustion with oxygen enriched gas, which may contain air and/or recycled product gas.

[0167] FIG. 1 schematically depicts a circulating fluidized bed reactor 10, being specifically, a circulating fluidized bed boiler 10, which is configured to produce superheated steam in a manner known per se. The circulating fluidized bed boiler will be referred to as a CFB boiler for the sake of conciseness. The CFB boiler 10 comprises a combustion chamber 12, at least one solid material separator 14 and a solid material return channel 16. Generally, the route of separated solid material from the separator back to the combustion chamber is called a return path 15. The combustion chamber 12 comprises tube walls, so-called finned tube walls, wherein fins are welded between tubes. The wall tubes are connected to a water-steam circuit of a boiler system (not shown). The solid material separator 14 is preferably cooled, also comprising tube walls similarly to the combustion chamber 12. The combustion chamber 12 comprises a wind box 18, which is configured to feed fluidization gas, typically air, through nozzles of a grid 20 at the bottom of the combustion chamber 12. The air introduced through the grid acts as fluidization gas and is the primary combustion air. Secondary air may be fed into the combustion chamber 12 at a higher level via one or more air inlets 21. As discussed earlier, the fluidizing gas and the combustion gases are usually air, but they can also comprise circulated product gas and/or oxygen or a mixture thereof. It should be understood that, generally, the term product gas may be understood that the gas exiting the separator 14 is a product gas of the reactions in the reaction chamber. For example, in the case the method comprises gasification of fuel material, the product gas is combustible gasso called syngas, and, in the case the method comprises combustion of fuel in the reaction chamber and producing steam with released heat, the product gas may be referred to as flue gas. In some practical applications, such as so-called oxygen combustion, part of the flue gas can be recycled back to the reaction chamber as fluidization gas, and may therefore be referred to as recycling gas.

[0168] The wind box 18, and also other air inlets, are in connection with a source of air 24. This is an example of an air operated CFB boiler. There is at least one inlet 22 for fuel in connection with the combustion chamber 12. Operation of the CFB boiler involves a process of circulation of solid material, which, in this connection may also be referred to as bed material, as well. Bed material may comprise sand, limestone, and/or clay, that in particular may comprise kaolin, and also unburned fuel. Due to the bed material inside the boiler, CFB boilers have high heat transfer coefficients and a substantially uniform temperature distribution and have a considerably low stable combustion temperature. Combustion of fuel in the circulating fluidized bed results in heating, evaporating the water in the water-steam circuit, and superheating the steam, which can be used in a manner known as such, for example, production of electric power in a steam turbine generator. The steam cycle is not described here in more detailed.

[0169] It is a characteristic of the CFB boiler that, during its operation, a process of circulation of solid material is maintained via a route formed by the combustion chamber, a separator, and a solids return path. Combustion of fuel in the CFB results in high-efficiency combustion of various solid fuels with low emissions, even when burning fuels with completely different calorific values at the same time. Due to fluidization, there is an internal movement of solid material inside the combustion chamber 12, generally, upwards at the mid-section of the chamber and downwards flow of solids near the walls, as is depicted by the arrows in FIG. 1. Product gases and solid material are sent from the combustion chamber 12 to the solid material separator 14 inlet, of which is connected to the combustion chamber by a connector duct 26. The solid material separator 14, which is preferably a cooled cyclone separator, comprises a first outlet 28 for product gas, and a second outlet 30 for separated solid material 32. The first outlet 28 of the separator is, in practice, connected to a back pass 40. The back pass 40 comprises a number of heat exchanges, which may include an air preheater 46, an economizer 44, and superheaters and reheaters 42. The actual amount of different heat transfer surfaces in each of these components, for example, may be selected for each CFB boiler differently according to actual needs.

[0170] The solid material, which is transported by the product gases to the separator 14 is separated from the gas as, is depicted by the arrow in the figure. The second outlet 30, which may also be referred to as a particle outlet, is connected to a lower part of the combustion chamber 12 by the return path 15 for returning separated solid material back to the combustion chamber 12. The return path 15 is provided with a so called loop seal 32 that prevents back-flow from the combustion chamber 12 to the particle outlet and makes it possible to feed separated solid material controllably back to the combustion chamber 12. The loop seal may also be referred to as a gas seal. Operation of the loop seal is controlled by fluidization air, which can be controllably supplied through an air inlet 23. Thus, the circulation of the solid material comprises the flow of solid material from the combustion chamber 12 to the solid material separator 14 and from the solid material separator 14 via the return path 15 and the loop seal 32, back to the combustion chamber 12. The process of circulation of the solid material is maintained and controlled while the CFB boiler is operating. The general direction of movement of the solid material may be used for referring to positions in the CFB boiler, which direction becomes clear in the description above.

[0171] In CFB boilers, the solid material circulation may be divided in two categories: internal circulating material flow that means solids material circulating inside the combustion chamber (12), which are depicted schematically with upside-down U-shaped arrows in FIG. 1 and, as discussed above, and external circulating material flows that means solid material circulating outside the combustion chamber, i.e., in the particle separator and the loop seal and return path 15 (in FIG. 1). The external circulating material flows may also involve processing of solid material in a fluidized bed heat exchanger, as is shown in FIG. 3. Advantageously, according to an aspect of the invention, the solid material in the return path may, in other terms, be referred to as solid material in the external circulation of the CFB boiler.

[0172] In order to monitor the process of circulation of the solid material, the CFB boiler 10 comprises a plurality of sensors for obtaining online data of performance indicators and process variables. The online data becomes history data when stored after the time moment of measurement. There are at least following sensorsand point of measurementsarranged to the CFB boiler for practicing the method according to the invention: [0173] (i) a first pressure sensor 101 arranged upstream of the loop seal 32, but downstream of the solid material separator, i.e., between the loop seal and the solid material separator 14; [0174] (ii) a second pressure sensor 102 arranged downstream of the loop seal 32, between the loop seal 32 and the combustion chamber 12, the purpose of the first pressure sensor and the second pressure sensor being to determine pressure difference provided by the loop seal 32; [0175] (iii) a first temperature sensor 100 arranged in the loop seal 32; [0176] (iv) a second temperature sensor 103 arranged upstream of the loop seal 32 it being shown in FIG. 1 that the second temperature sensor 103 is arranged at the first outlet 28 of the solid separator 14, which also represents the temperature of the solid material upstream of the loop seal 32 in the sense of in FIG. 1; [0177] (v) a first air flow rate sensor 105 for measuring the primary air flow rate through the grid 20 of the CFB boiler 10; [0178] (vii) a second air flow rate sensors 106 for measuring the secondary air flow rate, the purpose of the first and the second air flow rate sensors being to determine an aggregate air flow rate fed into the CFB boiler; and [0179] (viii) a number of third temperature sensors 104 in connection with the combustion chamber 12 arranged to determine bed temperature in the combustion chamber 12.

[0180] Additionally, there may be an air flow rate sensor 109 for measuring the air flow rate to the loop seal, which may optionally the included in the aggregate air flow rate, as is depicted in FIG. 1. The temperature sensors downstream of the second outlet 30 of the separator 14 provide measurement values that represent temperature of the solid material.

[0181] The CFB boiler further comprises a control system 48 for handing numerical operations relating to control of the CFB boiler and, particularly, to monitor the process of circulation of solid material in the CFB boiler. It should be understood that FIG. 1 is an exemplary description of a process of circulation of solid material via a certain type of return path and a description of a process of circulation of solid material via one return path. Should the CFB boiler comprise more than one return path, which would often be the case in practice, the invention is applicable to each one of the return paths separately. Advantageously, the CFB boiler may be provided with the solid material separators 14 and corresponding return paths 15 on opposite sides of the combustion chamber 12 (not shown in the figures).

[0182] FIG. 2 is a general illustration of the method and the control system 48 in the control system by means of which the process of circulation of solid material in a CFB reactor 10 can be monitored, such that an indication of a condition relating to the circulation of solid material that could lead to shutting down the reactor is observed early enough to take corrective actions and the shut down of the reactor may be avoided.

[0183] The control system 48 participates in practicing a method of monitoring a process of circulation of solid material in the circulating fluidized bed boiler 10. The control system 48 comprises one or more computers and executable instructions, i.e., computer programs which, when executed in the control system 48 perform the method in the circulating fluidized bed boiler 10. The method comprises: [0184] (a.) selecting performance indicators of the process of circulation of solid material and process variables for each performance indicator of the process of circulation of solid material; [0185] (b.) calibrating a multivariate model for each performance indicator, using history data of the process variables and the performance indicators of the process of circulation of solid material; [0186] (c.) determining a modelled value of the performance indicators, by applying current measured values of the process variables to the multivariate model; and [0187] (d.) comparing the modelled value of each performance indicator to a respective measured value of each performance indicator and inspecting presence of an anomaly between the modelled value and the measured value.

[0188] The control system comprises a performance modelling unit 400. The modelling unit 400 comprises executable instructions which, when executed in the control system 48, calibrate the multivariate model for each performance indicator, using history data of predetermined process variables and the performance indicators of the process of circulation of solid material, resulting in a calibrated multivariate model.

[0189] The performance modelling unit 400 has, or is provided with an access, such as a data transfer communication with a source of history data 401 of (a) performance indicators of the process of circulation of solid material obtained from the CFB boiler, and (b) process variables for each performance indicator. The history data is stored in a data media, which is used as the source of history data 401, is obtained by measuring the values of predetermined process variables 101, 102, 103, . . . , and 109 (see FIG. 1) over a period of time, and storing the measured values with a time stamp, thus forming the history data of process variables. Acquiring the history data involves respectively measuring the values of the performance indicator, storing the measured values with a time stamp, thus forming the history data of performance indicators. The control system 48 comprises a data filter unit 406, which is configured to filter out invalid process data and, thus, the history data comprises data that has been subjected to filtering process of using predetermined data filters. The history data is, therefore, data that describes normal operation conditions of the CFB boiler 10.

[0190] Advantageously, the filtering process 406 may comprise the following conditions or rules. Firstly, a quarantine time for measured data is set so that only the data that is older than a pre-set quarantine time is approved. The quarantine time depends on the case. In some practical applications, the quarantine time may be even as short as three to seven days. However, preferably, the quarantine time is seven to fourteen days, even more preferably, at least two weeks. Additionally, it is preferred to filter out data that may be obsolete due to being too old and, therefore, the predetermined data filter is configured to approve data, which is not older than a predetermined time, advantageously, not older than two months. Also, the filter unit is configured to filter out from history data any data from shut down situations and/or data originating from any abnormal operation condition, e.g., based on predefined limits for input variables or an external information setting the data to be unusable or data of abnormal operation.

[0191] This way, the model is based on history data that represents normal operation conditions. The history data relating to the CFB boiler shown for example in FIG. 1 comprises data of process variables and the performance indicators: [0192] pressure values (sensor 101) upstream of the loop seal 32, but downstream of the solid material separator, i.e., between the loop seal and the solid material separator 14; pressure values (sensor 102) downstream of the loop seal 32, between the loop seal 32 and the combustion chamber 12; [0193] or, alternatively, pressure difference over the loop seal 32 (combined sensors 101, 102); a temperature (sensor 103) upstream of the loop seal 32; [0194] aggregate air flow rate sensors 105,106 fed into the CFB boiler; and [0195] aggregate bed temperature sensors 104 in the combustion chamber 12.

[0196] The performance indicators represent factors that describe the state of the process of circulation of solid material. In that case of the embodiment shown in FIG. 1 the performance indicators are advantageously: [0197] (i.) a pressure difference of a loop seal in the return path; and [0198] (ii.) a temperature in the loop seal in the return path in the circulation of the solid material.

[0199] The data in the source of history data 401 is used as an input for the modelling unit 400, which is configured to prepare and/or to calibrate a multivariate model assigned separately for each performance indicator, in this case, for two performance indicators. The performance modelling unit 400 thus provides the multivariate model for each performance indicator. The calibration may be repeated at predefined intervals, or periodically. This helps to keep the model actual, reflecting the possible changes caused by normal use of the CFB boiler, but also, to changes in fuel quality, the environmental conditions (temperature, ambient humidity, ambient pressure changes), which may lead to operation parameters changing over time. The calibration may be prevented upon detecting an anomaly in the process. In this manner, it may be ensured that a problem in bed material circulation that is just developing will not contaminate the calibration and the model.

[0200] The model can be constructed by the modelling unit 400 using a multivariate linear regression. In principle, past input values of the model (i.e., history data of measurements) are used for estimating the coefficients of the model. The model is then used to estimate the prevailing situation by making use of current online data and the estimated coefficients.

[0201] For example, in linear regression, the response variable is expected to be a linear combination of process variables. Multiple linear regression can be used to model the relationship between multiple process variables and a performance indicator by fitting a linear equation to history data.

[0202] In a case of the embodiment shown in FIG. 1, a multivariate model for a loop seal temperature with N observations is defined as follows:

[00003]$y_i=b_0+b_1{x}_{i,1}+b_2{x}_{i,2}+b_3{x}_{i,3}+{}_i,$ [0203] where: [0204] y denotes the value of a performance indicator as the loop seal temperature; [0205] x.sub.i,1 is the ith value of temperature upstream the loop seal 32 (sensor 103); [0206] x.sub.i,2 is the ith value of aggregate air flow rate (sensors 105,106) fed into the CFB boiler; and [0207] x.sub.i,3 is the ith value of bed temperature (sensors 104) in the combustion chamber 12; [0208] b.sub.0 is a constant, b.sub.1 . . . b.sub.3 are the unknown, KPI-specific coefficients to be estimated; and [0209] .sub.i comprises experimental errors of the model.

[0210] In the case of the embodiment shown in FIG. 1 a multivariate model for ua loop seal pressure difference with N observations is defined as follows:

[00004]$y_i=b_0+b_1{x}_{i,1}+b_2{x}_{i,2}+b_3{x}_{i,3}+{}_i,$ [0211] where: [0212] y denotes the value of a performance indicator; [0213] x.sub.i,1 is the ith value of temperature upstream the loop seal 32 (sensor 103); [0214] x.sub.i,2 is the ith value of aggregate air flow rate sensors 105,106 fed into the CFB boiler; and [0215] x.sub.i,3 is the ith value of bed temperature sensors 104 in the combustion chamber 12; and [0216] b.sub.0 is a constant, b.sub.1 . . . b.sub.3 are the unknown, KPI-specific coefficients to be estimated; and [0217] .sub.i comprises experimental errors of the model.

[0218] The fitting is performed by minimizing the sum of the squares of the vertical deviations from each data point to the line that fits best for the observed data, that is the optimal coefficient values by minimizing the sum of squared errors.

[0219] The modelling unit 400 provides required coefficients of the model that are based on viable history data, to be used for modelling the performance indicators by applying online data of process variable to the model. While the control system 48 and the CFB boiler 10 are in operation, the history data comprising data of process variables and the performance indicators is continuously read and stored to the source of history data 401. The modelling unit 400 is configured to update or to calibrate the model, i.e., the coefficients of the model in order to learn the model the latest conditions of normal operation of the process of circulation of solid material.

[0220] There is also a performance diagnostic module 404 provided in the control system 48. The performance diagnostic module is configured to receive current online data by a source of current data 402 from the CFB boiler of the performance indicators, and the process variables and a newly calibrated model of the performance indicators from the modelling unit 400. The performance diagnostic module 404 comprises instructions to determine a modelled value of the performance indicators by applying current measured values of the process variables to the calibrated multivariate model. Additionally, the performance diagnostic module 404 is configured to compare the modelled value of each performance indicator to a measured respective value of performance indicator and inspecting a presence of an anomaly between the modelled value and the measured value. Based on the outcome of the comparison, a predetermined measure or measures can be taken and generated as a diagnostic output 408.

[0221] The presence of an anomaly and the need for remedial actions can be realized by estimating a risk index of each KPI. The performance diagnostic module 404 may comprise instructions to practice a method estimating the risk index for a performance indicator, which performs the following acts: [0222] current data of performance indicators (KPI) of circulation of solid material is measured; based on the current data of the boiler, at least one of the following: [0223] (i) an average of the performance indicators is computed; [0224] (ii) a standard deviation of measured performance indicators is computed; [0225] (iii) a difference between a maximum measured performance indicator value and a minimum measured performance indicator is computed; and [0226] (iv) a difference between an average performance indicator KPI and a measured performance indicators is computed; [0227] using the computation results from (i), (ii), (iii) and/or (iv), preparing a risk index for the performance indicator KPI. The computation results from (i), (ii), (iii) and/or (iv) are compared with corresponding predefined limits so as to get risk indexes for average, a standard deviation, a difference between a maximum and a minimum KPI, and a difference between an average KPI and measured KPIs. In computation of deviation of a KPI.sub.k from an average KPI, the average includes all KPI measurements, except the measurement of KPI.sub.k.

[0228] Preferably, in the method also, or alternatively, [0229] (v) modelled values of KPI.sub.k; k=1, . . . , K are computed, and residuals between the measured values of the performance indicators and the modelled values of the performance indicators are computed. The results from step (v) are advantageously also used in the preparing of the risk index, preferably, such that residuals are compared with a corresponding predefined limit so as to get a sintering risk index for KPI residuals.

[0230] The final risk index may then be the maximum of the above risk indexes, for example. In this manner, the predictive accuracy of bed sintering index can be still improved.

[0231] The present inventors have observed that, in this manner, the resulting risk index provides an indication of a condition in the process of circulation of solid material in a circulating fluidized bed boiler, that could lead to shutting down the boiler unless treated, early enough to take corrective actions, such that the need to shut down the boiler may be avoided.

[0232] Optionally, the control system comprises a storage of history coefficients of the model 410, where each calibrated model is stored. The performance diagnostic module 404 may comprise a model evaluation function, which checks the newly created model and in case a newly created model is found to be imperfect, a model from the storage of history coefficients of the model 410 is used until an intact fresh model can be provided.

[0233] FIG. 3 schematically depicts a circulating fluidized bed boiler 10 that has at one of its return paths 15 (only one shown for clarity reasons) provided with a fluidized bed heat exchanger 50. It should be understood that the return path 15 shown in FIG. 3 may be conceived to be in the same CFB boiler disclosed in FIG. 1, which means that the CFB boiler may be provided with several return paths 15, where more than one of the return paths 15 is preferably provided with a fluidized bed heat exchanger 50. FIG. 3 also refers to a practical application where the CFB boiler comprises several return paths 15, all of which are provided with a fluidized bed heat exchanger 50. The method according to the invention practiced in connection with all of the return paths 15 separately.

[0234] The fluidized bed heat exchanger 50 is arranged to the return path 15 downstream of the loop seal 32 in the return channel 16. Solid material flows through the loop seal 32 into the fluidized bed heat exchanger 50 where a bubbling bed of solid material is formed by introducing fluidization air into the fluidized bed heat exchanger 50 through a grid 52 at the bottom thereof. The fluidized bed heat exchanger 50 is provided with a lifting chamber 54 with a respective inlet 54 of transport air. The lifting chamber transfers the solid material from the fluidized bed heat exchanger 50 back to the combustion chamber 12 via a return duct 55.

[0235] The fluidized bed heat exchanger 50 is provided with one or more heat exchange units 58, which are preferably connected to, for example, the steam cycle. The heat exchange units may be evaporators, steam superheaters and/or steam reheaters. The heat exchange units comprise a heat transfer surface, such as one or more tube bundles inside the bubbling bed of solid material forming the fluidized bed heat exchanger 50.

[0236] In the CFB boiler, the solid material which is transported by the product gases to the separator 14, is separated from the gas as is depicted by the arrow in the figure. The second outlet 30, which may also be referred to as a particle outlet of the separator 14, is connected to a lower part of the combustion chamber 12 by the return path 15 for returning separated solid material back to the combustion chamber 12. The return path 15 is provided with a so called loop seal 32, which prevents back-flow from the combustion chamber 12 to the particle outlet and makes it possible to feed separated solid material controllably forward in the return path 15. Operation of the loop seal is controlled by fluidization air, which can be controllably supplied through an air inlet 23. Thus, the circulation of solid material comprises the flow of solid material from the combustion chamber 12 to the solid material separator 14 and from the solid material separator 14 via the return channel 16 to the fluidized bed heat exchanger 50, and from the fluidized bed heat exchanger 50 back to the combustion chamber 12. While the fluidized bed heat exchanger 50 is operated, heat is transferred from the solid material to the steam flowing in the heat exchange unit 58, this cooling the solid material prior to its introduction back to the combustion chamber 12.

[0237] In order to monitor the process of circulation of solid material, the CFB boiler 10, according to the embodiment of FIG. 3, comprises a plurality of sensors for obtaining online data of performance indicators and process variables. The online data becomes history data when it is stored after the time moment of measurement. There are at least following sensorsand point of measurementsarranged to the CFB boiler for practicing the method according to the invention: [0238] (i) a first pressure sensor 101 arranged upstream of the loop seal 32, but downstream the solid material separator, i.e., between the loop seal and the solid material separator 14; [0239] (ii) a second pressure sensor 102 arranged downstream of the loop seal 32, between the loop seal 32 and the fluidized bed heat exchanger 50, the purpose of the first and the second pressure sensors being to determine pressure difference provided by the loop seal 32; [0240] (iii) a first temperature sensor 100 arranged in the loop seal 32; [0241] (iv) a second temperature sensor 103 arranged upstream of the loop seal 32, it is shown in FIG. 2 that the second temperature sensor 103 is arranged at the first outlet 28 of the solid separator 14, which also represents the temperature of the solid material upstream to the loop seal 32 in FIG. 2; [0242] (v) a first air flow rate sensor 105 for measuring the primary air flow rate through the grid 20 of the CFB boiler; [0243] (vi) a second air flow rate sensors 106 for measuring the secondary air flow rate, the purpose of the first and the second air flow rate sensors being to determine an aggregate air flow rate fed into the CFB boiler, a number of third temperature sensors 104 in connection with the combustion chamber 12 arranged to determine a bed temperature in the combustion chamber 12; [0244] (viii) a third air flow rate sensor 108 for measuring the air flow rate fed to the fluidized bed heat exchanger 50; [0245] a third pressure sensor 110 arranged upstream of the heat exchange unit 58 in the fluidized bed heat exchanger 50; [0246] (ix) a fourth pressure sensor 112 arranged downstream of the heat exchange unit 58 in the fluidized bed heat exchanger 50; and [0247] (x) a third temperature sensor 114 arranged downstream of the heat exchange unit 58 in the fluidized bed heat exchanger 50.

[0248] The control system 48 described in FIG. 2 is applicable to the CFB boiler 10 described in FIG. 3 with the necessary modifications relating to data of performance indicators and process variables. The actual, accurate location of the sensors can be determined case by case. For example, the third temperature sensor may, in some cases, be arranged between the lifting chamber 54 and the combustion chamber 12, because temperature in the particular location represents the temperature of the solid material downstream of the heat exchange unit 58. Similarly, the temperature sensor 103 at the outlet 28 of the separator 14 may be positioned differently, as long as it represents the temperature of the solid material upstream position to the loop seal 32.

[0249] When applied to the CFB boiler according to FIG. 3, the control system 48 participates in practicing a method of monitoring a process of circulation of solid material in the circulating fluidized bed boiler 10. The control system comprises one or more computers and executable instructions, i.e., computer programs which, when executed in the control system 48, perform the method in the circulating fluidized bed boiler 10. The method comprises: [0250] (a.) selecting performance indicators of the process of circulation of solid material and process variables for each performance indicator of the process of circulation of solid material; [0251] (b.) calibrating a multivariate model for each performance indicator, using history data of the process variables and the performance indicators of the process of circulation of solid material; [0252] (c.) determining a modelled value of the performance indicators, by applying current measured values of the process variables to the multivariate model; and [0253] (d.) comparing the modelled value of each performance indicator to a respective measured value of each performance indicator and inspecting a presence of an anomaly between the modelled value and the measured value.

[0254] The control system comprises a performance modelling unit 400. The modelling unit 400 comprises executable instructions which, when executed in the control system 48, calibrate the multivariate model for each performance indicator, using history data of predetermined process variables and the performance indicators of the process of circulation of solid material, resulting in a calibrated multivariate model.

[0255] The performance modelling unit 400 has, or is provided with an access, such as a data transfer communication with a source of history data 401 of (a) performance indicators of the process of circulation of solid material obtained from the CFB boiler, and (b) process variables for each performance indicator. The history data is stored in a data media, which is used as the source of history data 401, is obtained by measuring the values of predetermined process variables 101, 102, 103, . . . , and 114 (see FIG. 3) over a period of time, and storing the measured values with a time stamp, thus forming the history data of process variables. Acquiring the history data involves respectively measuring the values of the performance indicator, storing the measured values with a time stamp, thus forming the history data of performance indicators. The control system 48 comprises a data filter unit 406 that is configured to filter out invalid process data and thus the history data comprises data which has been subjected to filtering process of using predetermined data filters. The history data is, therefore, data that describes normal operation conditions of the CFB boiler 10. The filter unit is described in more detailed in connection with the description of FIG. 2.

[0256] The history data relating to the CFB boiler shown in FIG. 3 comprises data of process variables and the performance indicators: [0257] (i) pressure values (sensor 101) upstream of the loop seal 32, but downstream of the solid material separator, i.e., between the loop seal and the solid material separator 14; [0258] (ii) pressure values (sensor 102) downstream of the loop seal 32, between the loop seal 32 and the fluidized bed heat exchanger 50; [0259] (iii) or, alternatively, a pressure difference over the loop seal 32 (combined sensors 101,102); temperature sensor 100 in the loop seal 32; [0260] (iv) temperature sensor 103 upstream of the loop seal 32; [0261] (v) pressure values (sensor 110) upstream of the heat exchange unit 58 in the fluidized bed heat exchanger 50; [0262] (vi) pressure values (sensor 110) downstream of the heat exchange unit 58 in the fluidized bed heat exchanger 50; [0263] (vii) temperature sensor 114 downstream of the heat exchange unit 58 in the fluidized bed heat exchanger 50; [0264] (viii) aggregate air flow rate sensor 108 fed into the fluidized bed heat exchanger 50; [0265] (ix) aggregate air flow rate sensors 105,106 fed into the CFB boiler; and [0266] (x) bed temperature (sensors 104) in the combustion chamber 12.

[0267] The performance indicators represent factors that describe the state of the process of circulation of solid material and the fluidized bed heat exchanger. In case of the embodiment shown in FIG. 3, the performance indicators are advantageously: [0268] (i.) a pressure difference of a loop seal in the return path, [0269] (ii.) a temperature in the loop seal in the circulation of solid material; [0270] (iii.) a pressure difference of the fluidized bed heat exchanger; and [0271] (iv.) a temperature of solid material downstream the fluidized bed heat exchange unit.

[0272] The data in the source of history data 401 is used as an input for the modelling unit 400, which is configured to prepare and/or to calibrate a multivariate model assigned separately for each performance indicator, in this case, for two performance indicators. The performance modelling unit 400 thus provides the multivariate model for each performance indicator. The calibration may be repeated at predefined intervals, or periodically. This helps to keep the model actual, reflecting the possible changes caused by normal use of the CFB boiler, but also, to changes in fuel quality, the environmental conditions (temperature, ambient humidity, ambient pressure changes), which may lead to operation parameters changing over time. The calibration may be prevented upon detecting an anomaly in the process. In this manner, it may be ensured that a problem in bed material circulation that is just developing will not contaminate the calibration and the model.

[0273] The model can be constructed by the modelling unit 400 using a multivariate linear regression. In principle, past input values of the model (i.e., history data of measurements) are used for estimating the coefficients of the model. The model is then used to estimate the prevailing situation by making use of current online data and the estimated coefficients.

[0274] For example, in linear regression, the response variable is expected to be a linear combination of process variables. Multiple linear regression can be used to model the relationship between multiple process variables and performance indicator by fitting a linear equation to history data.

[0275] In the case of the embodiment shown in FIG. 3, a multivariate model for the temperature of solid material downstream fluidized bed heat exchange unit (FBHX in the following) with N observations is defined as follows:

[00005]$y_i=b_0+b_1{x}_{i,1}+b_2{x}_{i,2}+b_3{x}_{i,3}+b_4{x}_{i,4}+b_5{x}_{i,5}+{}_i,$ [0276] where: [0277] y denotes the value of a performance indicator; [0278] x.sub.i,1 is the ith value of pressure difference over the loop seal 32 (sensors 110,112); [0279] x.sub.i,2 is the ith value of temperature in the loop seal 32 (sensor 100); [0280] x.sub.i,3 is the ith value of aggregate air flow rate (sensors 105,106) fed into the CFB boiler; [0281] x.sub.i,4 is the ith value of bed temperature (sensors 104) in the combustion chamber 12; and [0282] x.sub.i,5 is the ith value of air flow rate (sensor 108) fed to the chamber of the fluidized bed heat exchanger 50; and [0283] b.sub.0 is a constant, b.sub.1 . . . b.sub.5 are the unknown, KPI-specific coefficients to be estimated; and [0284] comprises experimental errors of the model.

[0285] In the case of the embodiment shown in FIG. 3, a multivariate model for the pressure difference over the fluidized bed heat exchanger with N observations is defined as follows:

[00006]$y_i=b_0+b_1{x}_{i,1}+b_2{x}_{i,2}+b_3{x}_{i,3}+b_4{x}_{i,4}+b_5{x}_{i,5}+{}_i,$ [0286] where: [0287] y denotes the value of a performance indicator; [0288] x.sub.i,1 is the ith value of pressure difference over the loop seal 32 (sensors 110,112); [0289] x.sub.i,2 is the ith value of temperature in the loop seal 32 (sensor 100); [0290] x.sub.i,3 is the ith value of aggregate air flow rate (sensors 105,106) fed into the CFB boiler; [0291] x.sub.i,4 is the ith value of bed temperature (sensors 104) in the combustion chamber 12; and [0292] x.sub.i,5 is the ith value of air flow rate (sensor 108) fed to the chamber of the fluidized bed heat exchanger 50; and [0293] b.sub.0 is a constant, b.sub.1 . . . b.sub.5 are the unknown, KPI-specific coefficients to be estimated; and [0294] comprises experimental errors of the model.

[0295] The fitting is performed by minimizing the sum of the squares of the vertical deviations from each data point to the line that fits best for the observed data, that is the optimal coefficient values by minimizing the sum of squared errors.

[0296] The modelling unit 400 provides required coefficients of the model that are based on viable history data to be used for modelling the performance indicators by applying online data of process variable to the model. While the control system 48 and the CFB boiler 10 are in operation, the history data comprising data of process variables and the performance indicators is continuously read and stored to the source of history data 401. The modelling unit 400 is configured to update or to calibrate the model, i.e., the coefficients of the model, in order to learn the model the latest conditions of normal operation of the process of circulation of the solid material.

[0297] There is also a performance diagnostic module 404 provided in the control system 48 that is applicable to the CFB boiler also provided with one or more fluidized bed heat exchangers. The description or the performance diagnostic module in connection with FIG. 2 is, therefore, applicable to the embodiment of FIG. 3 as well.

[0298] FIG. 4 describes results obtained with a method of monitoring a process of circulation of solid material in a circulating fluidized bed boiler according to FIG. 3. FIG. 4 discloses online measurement results provided by the third temperature sensor 114. The third temperature sensor is located in the fluidized bed heat exchanger below the heat exchange unit 58, near the grid of the chamber, and, thus, the curve M114 shows the temperature of the performance indicator (iv.)temperature of solid material downstream the fluidized bed heat exchange unit. The other curve P114 shown in FIG. 4 depicts modelled values of the performance indicator when current measured values of the process variables are applied to the multivariate model of the KPI. The horizontal axis shows time where the zero-moment is the actual time of shut down of the boiler. As can be seen in the chart, the modelled value of the model shows a deviation from the measured value several hours before the process will be too disturbed to recover, and no remedy action would prevent the shut down. As it becomes clear from the example the model will indicate the coming problem more than thirty hours before the shut down it will be irreversible. Unfavorable conditions can be observed early enough within a time window (hatched area) that is suitably long and sufficiently much in advance before occurrence of the actual problem.

[0299] FIG. 5 schematically depicts a circulating fluidized bed boiler 10 that has at one of its return paths 15 (only one shown for clarity reasons) provided with a fluidized bed heat exchanger 50 and with a by-pass path 56, which connects the solid material return path 15 at a location between the loop seal 32 and the fluidized bed heat exchanger 50 to the combustion chamber 12. Thus, the by-pass path 56 is arranged for controllably passing 0 to 100% of the solid material flow in the return path 15 directly to the combustion chamber, while passing the possible remining portion to the fluidized bed heat exchanger 50. This way, the process of circulation of solid material comprises two modes: the first one (the by-pass mode) in which the method is applied to the circulation of solid material directly form the loop seal 32 to the combustion chamber 12 of the CFB boiler (when there is a flow of solid material through the by-pass path), and the second one, in which the method is applied to the circulation of solid material form the loop seal 32 to the combustion chamber 12 of the CFB boiler via the fluidized bed heat exchanger 50 (when there is a flow of solid material through the fluidized bed heat exchanger 50). Hence, the embodiment shown in FIG. 5 can be understood to be a combination of the embodiments shown in FIGS. 1 and 3 in a single solid material return path 15, in terms of applying the method according to the invention.

[0300] It is to also to be understood that the return path 15 shown in FIG. 5 may be conceived to be in the same CFB boiler disclosed in FIG. 1 or FIG. 3, which means that the CFB boiler may be provided with several return paths 15 with a different setup, where more than one of the return paths 15 is preferably provided with a fluidized bed heat exchanger 50. FIG. 5 refers also to a practical application where the CFB boiler comprises several return paths 15, all or some of which are provided with a fluidized bed heat exchanger 50 with a by-pass path 55. The method according to the invention is practiced in connection with all of the return paths 15 separately.

[0301] In addition, or alternatively to having the by-pass path 56, in FIG. 5, there is disclosed a solid material discharge path 56 connected to the solid material return path 15 at a location between the loop seal 32 and the fluidized bed heat exchanger 50. Location of the discharge path 56, or its point of extraction of material, may be other than shown here if so desired. By means of the solid material discharge path 56, it possible to remove 0 to 100% of the solid material flow from the process of circulation of solid material. The portion of removed material may be later returned back to the reactor 10, as such, or after a desired processing performed to the solid material.

[0302] The control system 48 described in the FIG. 2 is applicable to the CFB boiler 10 described in FIG. 5 with the necessary modifications relating to data of performance indicators and process variables.

[0303] An exemplary embodiment of calculation of residual-based KPIs and the risk index for a case wherein a circulating fluidized bed boiler 10 has at one of its return paths 15 provided with a fluidized bed heat exchanger 50. The following steps are taken: [0304] creating the KPI models based on pressure difference and temperature in loop seal and pressure difference and temperature in the fluidized bed heat exchange chamber; [0305] comparing the modelled values of the KPI's to measured values at the current point of time (t), for example, KPI for a modelled loop seal temperature can be computed as follows:

[00007]${\mathrm{KPI}}_{\mathrm{loop}\mathrm{seal}\mathrm{temp},\mathrm{modelled}}\left(t\right):=y_t=b_0+b_1{x}_{t,1}+b_2{x}_{t,2}+b_3{x}_{t,3}+{}_t$ [0306] where b.sub.0 is a KPI-specific constant (as solved earlier), and b.sub.0 . . . b.sub.3 are known (as solved earlier) KPI-specific coefficients, and [0307] x.sub.t,1 is the tth value of temperature upstream the loop seal 32 (sensor 103); [0308] x.sub.t,2 is the tth value of aggregate air flow rate (sensors 105,106) fed into the CFB boiler; and [0309] x.sub.t,3 is the tth value of bed temperature (sensors 104) in the combustion chamber 12. [0310] a comparison being made of computing deviations between the model outputs and the measured values so as to obtain residuals (KPI.sub.k,res(t) where k=1 to K (K=number of KPIs) (e.g. modelled temperaturemeasured temperature in the loop seal that is

[00008]${\mathrm{KPI}}_{\mathrm{loop}\mathrm{seal}\mathrm{termp},\mathrm{res}}\left(t\right)={\mathrm{KPI}}_{\mathrm{loop}\mathrm{seal}\mathrm{temp},\mathrm{modelled}}\left(t\right)-{\mathrm{KPI}}_{\mathrm{loop}\mathrm{seal}\mathrm{temp},\mathrm{meas}}\left(t\right))$

[0311] The residual limits for each KPI type are shown schematically in below table:

TABLE-US-00001 lower limit upper limit KPI (l.sub.lo, k) (l.sub.up, k) Residuals of pressure difference (loop A.sub.lo A.sub.up seal) Residuals of temperature (loop seal) B.sub.lo B.sub.up Residuals of temperature (fluidized bed C.sub.lo C.sub.up heat exchange chamber bottom down- stream each heat exchange unit) Residuals of pressure difference (in the D.sub.lo D.sub.up fluidized bed heat exchange chamber) [0312] wherein A, B, C, and D depict predefined limit values. [0313] Calculating the risk index for each KPIs as follows:

[00009]$r_k=100\left(.Math.{\mathrm{KPI}}_{k,\mathrm{res}}\left(t\right)-\left(l_{\mathrm{up},k}+l_{\mathrm{lo},k}\right)/2.Math.\right)/\left(\left(l_{\mathrm{up},k}-l_{\mathrm{lo},k}\right)/2\right)$ [0314] where |.Math.| is an absolute value, k=1 to K (K=number of KPIs) [0315] Calculating the overall risk index RI as follows:

[00010]$\mathrm{RI}=\max \left(r_k\right),$ [0316] where r.sub.k=single risks and where k=1 to K (K=number of KPIs).

[0317] As an example, let us assume that a residual for temperature in the loop seal is KPI.sub.loop seal temp,res(t)=KPI.sub.loop seal temp,modelled(t)KPI.sub.loop seal temp,meas (t)=B.sub.up. Then, using the above formula, we get for the loop seal temperature risk index:

[00011]$r_{\mathrm{loop}\mathrm{seal}\mathrm{temp}}=100\left(.Math.B_{\mathrm{up}}-\left(B_{\mathrm{up}}+B_{\mathrm{lo}}\right)/2.Math.\right)/\left(\left(B_{\mathrm{up}}-B_{\mathrm{lo}}\right)/2\right).$

In the case B.sub.up=B and B.sub.lo=B, then r.sub.loop seal temp=100 and, thus, calculation of the overall risk index with above formula results in RI=max(r.sub.k)=100.

[0318] The case without the fluidized bed heat exchange chamber goes similarly than the above example, but omitting the values (KPIs) related to the fluidized bed heat exchange chamber.

[0319] According to an aspect of the invention, the overall risk index may be calculated using at least one of the following formulas: as maximum RI=max(r.sub.k), average RI=mean(r.sub.k), weighted average RI=Wmean(r.sub.k) or median RI=median(r.sub.k).

[0320] According to a preferable aspect of the invention, a risk index for each of the KPIs is limited to have a maximum value of one hundred and a lowest value of zero, i.e., r.sub.k=[0, . . . , 100]. So, if an absolute value of KPI.sub.k is greater than an absolute value of a lower limit (l.sub.lo,k) or upper limit (l.sub.up,k), then r.sub.k=100. Generally, if KPI.sub.k does not belong to the interval [l.sub.lo,k, l.sub.up,k], then r.sub.k=100. It is also possible to have a condition written as if 100(|KPI.sub.k(t)(l.sub.up,k+l.sub.lo,k)/2|)/((l.sub.up,kl.sub.lo,k)/2)>100, then r.sub.k=100 and else r.sub.k=100(KPI.sub.k(t)(l.sub.up,k+l.sub.lo,k)/2|)/((l.sub.up,kl.sub.lo,k)/2).

[0321] In the above example, the table indicates that absolute limit values may be equal. It is possible, however, that upper limits and lower limits may be defined differently, so that the absolute values of the upper and lower limits differ for the corresponding KPI. It should be noted, however, that l.sub.lo,k<l.sub.up,k.

[0322] The above-described example is made for clarifying purposes only and not meant to limit the scope of the claimed invention. Furthermore, instead of residuals, other mathematical comparisons are possible, for example, computing a ratio between corresponding values.

[0323] While the invention has been described herein by way of examples in connection with what are, at present, considered to be the most preferred embodiments, it is obvious to the skilled person that, along with the technical progress, the basic idea of the invention can be implemented in many ways. The details mentioned in connection with any embodiment above may be used in connection with another embodiment when such a combination is technically feasible.