EP2644850B1 - A system for analyzing operation of power plant units and a method for analyzing operation of power plant units - Google Patents

Description

• The present invention relates to a system for analysing the operation of power blocks and a method for analysing the operation of power blocks, especially in thermal power plants, such as fossil-fuel power plants.
• Thermal power plants generate electricity as a result of energy transformation. The main element of a thermal power plant is a steam boiler, where fuel is burned, mostly fossil fuel - coal or natural gas, biomass, biogas or waste. The heat from the steam boiler is used for heating, evaporation and superheating of the steam powering a turbine. The turbine, in turn, generates mechanical energy to power the drive shaft of an electric generator. Larger plants can be equipped with several power blocks, in which partially or fully separate energy generation processes can be conducted by means of elements generally independent from one another, such as boilers, turbines, condensers, pumps, heat exchangers, generators and the like.
• Thermal power plants are characterized by a low overall efficiency, usually below 50%, resulting from the irreversibility of the thermal processes and from the shortcomings of the control processes and operational inefficiencies. These losses increase in time, while the typical operational time for a plant is several decades. Therefore, in thermal power plants various monitoring systems are used to observe the operation of the power plant and to generate data that can assist in optimising their operation.
• There are known Distributed Control Systems (DCS), which collect engineering and technical information from different parts of plants in order to automate and control the operation of blocks. To automate the operation of a particular power plant block, separate systems are usually employed, such as boiler management systems, usually based on neural networks, and technical control systems used for observing the thermal cycles of the blocks.
• However, due to the deteriorating quality of measurements over time, as well as due to the deficiencies in measurements, the automation systems based on DCSs and models based on process characteristics obtained during setting up the plant, or after major repairs, are often not accurate enough. In addition, there are no management systems supported by additional sources of data from continuous emissions monitoring systems, carburizing systems or laboratory analysis of fuels.
• A US patent US7840332 presents a system for steam turbine remote monitoring. The document is related to a method for determining efficiency of turbine in a way to continuously monitor mechanical efficiency. The performance of turbine is only observed and not modelled and therefore the approach is fully probabilistic. Another US patent application US2001/034582 presents a method for thermal efficiency diagnostic for a combined cycle power plant block. There is proposed a cycle efficiency analysis for root-cause-analysis of ageing effects.
• Thus, there is a need to develop a system to accurately monitor the operation of individual blocks of the power plant so as to collect the relevant operational data and present it a way which will enable relatively easy analysis of the processes in particular points on the basis of reliable data. This would help in identifying the points where processes are inefficient and which can be optimized, for example by changing parameters or conducting maintenance work in order to increase the efficiency of operation of the plant.
• The invention is defined by appended independent claims 1 and 11.
• The object of the invention is a computer-implemented method for analyzing the operation of power plant blocks, in which, on the basis of collected operational data, the deterministic models of operation of individual blocks are examined and characteristics of operational parameters are created. The selected operational parameters are examined by calculating for them the deviation of heat rate in time on the basis of the deterministic model and the characteristic of the parameter, destructions of exergy in various process points of the block are calculated; for various points of the process and for various power plant blocks, the calculated deviations of heat rate and the destruction of exergy are presented in a graphical form.
• Preferably, the operational data are collected from automatic measurement systems comprising sensors positioned on various elements of the power plant block.
• Preferably, the deterministic model of the block is created according to the first principle of thermodynamics in a form of a set of equations having the following form: $${\mathrm{R}}_{\mathrm{n}}=\mathrm{f}\left({\mathrm{h}}_{\mathrm{i}},{\dot{\mathrm{m}}}_{\mathrm{i}},{\mathrm{u}}_{\mathrm{i}},{\mathrm{\kappa }}_{\mathrm{i}},{\mathrm{\gamma }}_{\mathrm{i}},{\mathrm{x}}_{\mathrm{i}}\right);$$

  

  wherein:
• R_n - resulting function, for example: the power of the turbine, the efficiency of the block, the efficiency of the boiler, heat rate, CO₂ emissions, the rate of fuel consumption per a unit of generated power, destruction of exergy and the like;
• h_i - specific enthalpy of the medium at node i;
• ṁ_i - mass flux, for example of steam, water, condensate, air, gas, or fuel in the node i;
• u_i - fraction of the extraction of steam (on the turbine) in relation to the main flux operating medium for vent 'i';
• κ_i - the fraction of the flux of water injection to steam in relation to the main flux of the operating medium for the injection i;
• γ_i - the fraction of the supplementary water flux in relation to the process at the point i;
• x_i - the concentration of flue gas or fuel in the process used for the balance computations.
• Preferably, the characteristics of the current operational parameters are created on the basis of the current data for predetermined historical time periods preceding their use in the computations.
• Preferably, the characteristics of the operational parameters comprise at least one operational parameter selected from a group comprising the following parameters: temperature of live steam after the shut-off valve; pressure of live steam after the shut-off valve; temperature of secondary steam on the turbine; pressure of secondary steam on the turbine; flux of injection water to live steam; flux of injection water to secondary steam; flux of supplementary water; vacuum of the condenser; temperature of supply water to the boiler; air to fuel ratio; concentration of oxygen in flue gas; concentration of CO₂ in flue gas; amount of unburned coal in the ash.
• Preferably, the method further comprises presenting in a graphical form the comparative plots for characteristics of a given operational parameter made for different power plant blocks.
• Preferably, the method further comprises presenting in a graphical form the comparison of the calculated deviations in heat rate for a given parameter for different power plant blocks.
• Preferably, the method further comprises presenting in a graphical form the comparison of the calculated deviations of the total heat rate for different power plant blocks.
• Preferably, destruction of exergy in a given point of the process is calculated by using the equations: $$\mathrm{I}=\mathrm{\Sigma }{\mathrm{\epsilon }}_{\mathrm{i}}*{\mathrm{m}}_{\mathrm{i}}-\mathrm{\Sigma }{\mathrm{\epsilon }}_{\mathrm{e}}*{\mathrm{m}}_{\mathrm{e}}-\mathrm{w}$$

  

  $$\mathrm{\epsilon }=\left(\mathrm{h}-{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">T</figure-callout>}}_{\mathrm{0}}*\mathrm{s}\right)-\left({\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">h</figure-callout>}}_{\mathrm{0}}-{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">T</figure-callout>}}_{\mathrm{0}}*{\mathrm{<figure-callout\; id="0"\; label="s"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">s</figure-callout>}}_{\mathrm{0}}\right)$$

  

  wherein:
• ε - exergy flux,
• h - enthalpy of the process,
• s - entropy of the process,
• To - reference temperature,
• h₀ - enthalpy of the reference state,
• S₀ - entropy of the reference state,
• m - flux of the medium,
• w - work done in the system,
• I - value of destruction of exergy
• Subscript 'I' denotes the input,
• Subscript 'e' denotes the output,
• Preferably, the method further comprises, by using the predetermined characteristics of operational parameters, presenting in a graphical form the simulation of deviations of heat rate and/or changes of fluxes of destruction of exergy for variable values of the parameter of the characteristic.
• Another object of the present invention is a computer-implemented system for analysis of operation of power plant blocks, in which by using data from an operational data warehouse deterministic models of operation of individual blocks are examined and characteristics of operational parameters are created. The system comprises: a module for examining the operational parameters, configured to examine the selected operational parameters by calculating for them the deviation in heat rate in time based on the deterministic model and the characteristic of a given parameter; a module for calculating exergy destruction configured to calculate destruction of exergy in operational process points for the block; and an analysis module configured to present in a graphic form the calculated deviations in heat rate and the destruction of exergy in various points of the process, comparatively for various power plant blocks.
• One advantage of the present invention is that it involves the use of a thermodynamic deterministic model of the block and characteristics of parameters determined on the basis of the current operational data. Therefore, it presents current, reliable information which allows to make decisions leading to more efficient operation of a given power block, so as to adapt its performance to the performance of other blocks, to which its work is compared on the presented comparative graphs. The use of the thermodynamic model allows to comparatively verify different engineering computations. Presentation of both the heat rate and fluxes of destruction of exergy allows to ascertain that the computations are performed correctly and are not burdened with unexpected, unusual errors. This helps to detect analytical errors and sources of inaccuracies by analysing the operation in different points of the operational process of the block.
• The invention is shown by means of exemplary embodiment on a drawing, in which:
• Fig. 1 shows a diagram of a fuel-powered block;
• Fig. 2 shows a graph comparing the computations of the power generated on the turbine with the power output of the generator;
• Fig. 3 shows exemplary comparative characteristics of water injection to steam for two blocks of the plant;
• Fig. 4 shows a graph of the temperature after the shut-off valve versus the supply water flow;
• Fig. 5 shows a graph of the pressure after the shut-off valve versus supply water flux;
• Fig. 6 shows a graph of the linear characteristic of the optimal temperature setting after the shut-off valve on the turbine in relation to the supply water flux;
• Fig. 7 shows a graph of the optimal linear characteristics for the steam pressure after the shut-off valve of block 2;
• Fig. 8 shows an example of the method for calculating the heat rate for parameter t;
• Fig. 9 shows a possible improvement of heat rate vs. temperature;
• Fig. 10 shows a possible improvement of heat rate vs. the pressure of live steam;
• Fig. 11 shows a possible improvement of heat rate for all examined parameters;
• Fig. 12 shows a graph with instantaneous destruction of exergy in the condenser;
• Fig. 13 shows a flux of destruction of exergy for the turbine;
• Fig. 14 shows thermodynamic efficiency according to the second law of thermodynamics;
• Fig. 15 shows a graph of the savings that can be achieved without using water injection to steam;
• Fig. 16 shows an efficiency of the turbine for block 2 after eliminating water injection to steam;
• Fig. 17 shows a graph of the flux of injection water;
• Fig. 18 shows a schematic diagram of the system according to the invention.
Exemplary diagram of a power block
• Fig. 1 shows an exemplary schematic diagram of a coal-fired block (CFB). One plant may have a plurality of blocks of this type - the following example relates to an embodiment with blocks 1, 2 and 3. The principles of operation of the CFB are well known to those skilled in the art. The references to specific energy fluxes in the block are explained below:

1

flux of condensate from the condenser;

2

flux of condensate after the condensate pump and the preliminary heat exchanger;

3

flux of condensate after the first low-pressure heat exchanger;

4

flux of main condensate combined with the flux of condensate from the exchanger (21);

5

combined flux of condensate after the second low-pressure heat exchanger;

6

flux of condensate including the supplementary water flux (37);

7

supply water after the open heat exchanger (degasifier);

8

supply water after the main assembly of the supply pumps;

9

supply water after the first high-pressure exchanger;

10

supply water after the second high-pressure exchanger;

11

supply water for the boiler;

12

flux of water injected to the live steam after the boiler;

13

live steam after the boiler;

14

steam after injection of water;

15ab

separated fluxes of steam before the shut-off valve;

15cd

fluxes of steam after the shut-off valve;

16

flux of steam from vent 1 (ul) on the high-pressure exchanger 2;

17a

fraction of the steam flux from vent II to the open exchanger II, and to the collector 17k;

17b

fraction of the steam flux from vent II(uII) to the high-pressure exchanger 1;

18

steam flux from vent III (uIII) to the open exchanger and to the steam collector 18k;

19

steam flux from vent IV (uIV) to the low-pressure exchanger 2;

20

steam flux from vent V (UV) to the cogeneration exchanger and to the the low pressure heat exchanger 1;

20

fraction of the flux 20 to the cogeneration exchanger;

20b

fraction of the flux to the low-pressure exchanger 1;

21

condensate after the cogeneration exchanger added to the main flux of condensate;

22

heating water (input flux) to the cogeneration exchanger;

23

heating water from the cogeneration exchanger;

24

cooling water to the condenser - inlet, flux 1;

25

cooling water from the condenser - outlet, flux 1;

26

cooling water to the condenser - inlet, flux 2;

27

cooling water from the condenser - outlet, flux 2;

28

condensate after the high-pressure exchanger 2;

29

condensate after the high-pressure exchanger 1;

30

condensate after the low-pressure exchanger 2;

31

condensate after the low-pressure exchanger 1;

33

condensate after the supplementary heat exchanger;

34

vapour from various outlets to the supplementary heat exchanger;

37

supplementary water flux;

38

steam from the last, low-pressure turbine stage;

39

steam for soot blowers;

40

potential loss of water on injections;

41

potential loss of water on thermal boosters.

A Deterministic Model
• For the power block presented in Fig. 1, a deterministic model describing its current process scheme can be developed in accordance with the first law of thermodynamics. This model is defined with a set of equations having the following general form: $${\mathrm{R}}_{\mathrm{n}}=\mathrm{f}\left({\mathrm{h}}_{\mathrm{i}},{\dot{\mathrm{m}}}_{\mathrm{i}},{\mathrm{u}}_{\mathrm{i}},{\mathrm{\kappa }}_{\mathrm{i}},{\mathrm{\gamma }}_{\mathrm{i}},{\mathrm{x}}_{\mathrm{i}}\right);$$

  

  wherein:
• R_n - resulting function, for example: the power of the turbine, the efficiency of the block, the efficiency of the boiler, heat rate, CO₂ emissions, the rate of fuel consumption per a unit of generated power, destruction of exergy and the like;
• h_i - specific enthalpy of the medium at node i;
• ṁ_i - mass flux, for example of steam, water, condensate, air, gas, or fuel in the node i;
• u_i - fraction of the extraction of steam (on the turbine) in relation to the main flux operating medium for vent 'i';
• K_i - the fraction of the flux of water injection to steam in relation to the main flux of the operating medium for the injection i;
• γ_i - the fraction of the supplementary water flux in relation to the process at the point i;
• x_i - the concentration of flue gas or fuel in the process used for the balance computations.
• It is obvious that for various technical implementations the resulting model equations will be different. What is important in this case is to test the correctness of the model. The easiest way to check the quality of the model is to compare the result of the computation of the power generated on the turbine with the power measured on the generator.
• The following equation for the flux of the complete heat input to the process follows from the thermal balance of the boiler: $$\mathit{Qin}=m*\left(h15-\mathrm{<figure-callout\; id="11"\; label="h"\; filenames="imgf0003.png,imgf0004.png"\; state="\{\{state\}\}">h</figure-callout>}11\right)$$

  
• The thermal balance of the condenser provides the following resulting equations:
• from the cooling water thermal balance: $$\mathit{Qoutk}=f24*\left(h25-h24\right)+f26*\left(h27-h26\right)$$
  
• from the condensate flux balance $$\mathit{Qout}=f38*\left(h38-\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">h</figure-callout>}1\right)$$
  
• from the heat exchange flux of the condenser: $$\mathit{Qoutw}=K*A*\mathrm{\Delta }\mathit{tm}$$
  
• Apart from the convection heat losses through the condenser jacket, the following relation must take place: $$\mathit{Qoutk}=\mathit{Qoutw}=\mathit{Qout}$$

  
• Equation (5) is used to verify the measurements of parameters on the condenser. This verification allows to draw conclusions regarding possible errors in measurement of particular parameters.
• The thermal balance of the turbine leads to the following relation: $$\begin{array}{l}\mathit{wt}=\left(h15-h16\right)+\left(1-\mathit{uI}\right)*\left(h17-h16\right)+\left(1-\mathit{uI}-\mathit{uII}\right)*h17-h18)+\\ \left(1-\mathit{uI}-\mathit{uII}-\mathit{uIII}\right)*\left(h18-h19\right)+\left(1-\mathit{uI}-\mathit{uII}-\mathit{uIII}-\mathit{uIV}\right)*\left(h19-\mathrm{<figure-callout\; id="20"\; label="h"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">h</figure-callout>}20\right)+\\ \left(1-\mathit{uI}-\mathit{uII}-\mathit{uIII}-\mathit{uIV}-\mathit{uV}\right)*\left(\mathrm{<figure-callout\; id="20"\; label="h"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">h</figure-callout>}20-h38\right)\end{array}$$

  

  $$\mathit{wn}=\mathit{wt}-\mathit{<figure-callout\; id="1"\; label="wp"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">wp</figure-callout>}1-\mathit{<figure-callout\; id="2"\; label="wp"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">wp</figure-callout>}2$$

  
• The balances of the heat exchangers allow computation of the values of extraction of steam from the turbine - as mass fractions of the fluxes of steam on the vents in relation to the main flux of the steam: $$\mathit{uI}=\frac{\mathrm{<figure-callout\; id="10"\; label="h"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">h</figure-callout>}10-h9}{h16-h28};$$

  

  $$\mathit{uII}=\left(m29+2*m17k\right)/m;$$

  

  $$\mathit{uIII}=\left(m-m5-m37-m17k+m18k\right)/m;$$

  

  $$\mathit{uIV}=\left(\frac{m5}{m}\right)*\frac{\mathrm{<figure-callout\; id="5"\; label="h"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">h</figure-callout>}5-h4}{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">h</figure-callout>}1-\mathrm{<figure-callout\; id="30"\; label="h"\; filenames="imgf0002.png,imgf0007.png"\; state="\{\{state\}\}">h</figure-callout>}30};$$

  

  $$\mathit{uV}=1/m*\left(\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">m</figure-callout>}2*\frac{\mathrm{<figure-callout\; id="3"\; label="h"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">h</figure-callout>}3-h2}{\mathrm{<figure-callout\; id="20"\; label="h"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">h</figure-callout>}20-\mathrm{<figure-callout\; id="31"\; label="h"\; filenames="imgf0006.png"\; state="\{\{state\}\}">h</figure-callout>}31}+m22*\frac{h23-h22}{\mathrm{<figure-callout\; id="20"\; label="h"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">h</figure-callout>}20-h21}\right);$$

  

  wherein the enthalpies, extraction coefficients and fluxes relate to the points marked on the diagram of Fig. 1
• The comparison of the computations of the power generated on the turbine with the power output from the generator (for actual data) is shown in Fig. 2. The computations of power generated on the turbine have been made on the basis of equation (6). The specific enthalpies and fractions of the extractions have been made with the use of process data measured for the shown block. The thermal values (enthalpies, specific heat) for water and steam have been calculated on the basis of the thermodynamic properties of water and steam of 2007, based on " Revised Release on the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam", The International Association for the Properties of Water and Steam, Lucerne, Switzerland, 2007. All the thermodynamic computations for the thermal cycle have been made on the basis of the data of this publication.
• As follows from Fig. 2, statistically, the calculated power correlates well with the measured power. Therefore, it can be assumed that both the deterministic model and the data used in the computation of the resulting function are good enough to convey a comparative analysis and calculate the other values. Such a test should be applied when conducting comparative analyses and calculating heat rate deviations, efficiency and destruction of exergy.
Characteristics of operating parameters.
• The number of characteristics of operating parameters which should be developed, depends on the specific technological solution. It will be higher for blocks with multistage turbines than for small installations with single-stage turbines.
• The characteristics are built from actual data for predetermined historical periods preceding the use of the characteristics in the model computations. Monthly periods can be used, which correlate well with monthly cycles of fuel consumption and emission settlements, and therefore allow using balance data from other sources.
• The functions of operating parameters are presented in relation to an independent variable - the flux of the working medium (steam or supply water).
• For example, the characteristics of the parameters may relate to the following factors: temperature of live steam after the shut-off valve; pressure of live steam after the shut-off valve; temperature of secondary steam on the turbine; pressure of secondary steam on the turbine; flux of injection water to live steam; flux of injection water to secondary steam; flux of supplementary water; vacuum of the condenser; temperature of supply water to the boiler; air to fuel ratio; concentration of oxygen in flue gas; concentration of CO₂ in flue gas; amount of unburned coal in the ash.
• Fig. 3 shows exemplary comparative characteristics for injection of water to steam, made for two blocks of the plant.
• The characteristics convey a substantial amount of information for analysis of the current operation of blocks and allow building idealized reference functions, which allow calculating the deviations from the ideal states and the possible savings that can be achieved by reducing the heat rate.
Comparative analysis of operating parameters
• One of the stages of comparing the operation of blocks in the system according to the invention, should be a comparative analysis of operating parameters for different blocks. Such an analysis allows detecting possible different influences on the operation of the block or measurement of parameters. It is possible that for two similar blocks there is a significant discrepancy in the settings of operating parameters. Such dependencies have been presented for two blocks of the power plant in Fig. 4 - the temperature after the shut-off valve on the turbine in relation to the flux of supply water; and in Fig. 5 - the pressure after the shut-off valve in relation to the flux of supply water.
• As can be seen in the plots, there are substantial differences between the blocks in keeping the parameters. This analysis, covering all the essential parameters, is aimed at pointing out the sources of discrepancies from optimal plots and their factors: human (the work of the operators), technical (the different operating conditions of the equipment), exploitation (the lack of possibility to keep the values of parameters due to exploitation problems or the problems with the quality of measurements). All these influences must be taken into consideration by the technical and engineering crew.
Building reference curves
• The reference curves are described by equations employing a linear regression method for the maximal and minimal areas limiting the choice of parameters. Fig. 6 shows a line of linear characteristics of the optimal setting of the temperature after the shut-off valve on the turbine in relation to the flux of supply water, for an exemplary set of measurement data for this parameter in block 2.
• All characteristics of the examined parameters are built in manner similar to that shown in Fig. 6. As a result, the following functions are obtained: $${\mathrm{p}}_{\mathrm{j}}=\mathrm{f}\left(\mathrm{m},\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d},\dots \right)$$

  

  wherein:
• m - flux of supply water;
• p_j - the parameter;
• a, b, c, d, ... - constants of the linear equation for the parametric curve.
• The optimal characteristic for the temperature of the steam after the shut-off valve for the presented block is linear and its equation for the analyzed exemplary block 2 shown in Fig. 6 is the following: $${\mathrm{<figure-callout\; id="2"\; label="p\; t"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">p</figure-callout>}}_{\mathrm{t}}=\mathrm{0},\mathrm{093366}*\mathrm{m}+\mathrm{510},\mathrm{48};$$

  
• For block 3 the equation has the following form: $${\mathrm{<figure-callout\; id="3"\; label="p\; t"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">p</figure-callout>}}_{\mathrm{t}}=\mathrm{0},\mathrm{138995}*\mathrm{m}+\mathrm{492},\mathrm{26};$$

  
• Fig. 7 shows the line of the optimal characteristics for the pressure of steam after the shut-off valve for block 2, for which the equation has the following form: $${\mathrm{<figure-callout\; id="2"\; label="p\; p"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">p</figure-callout>}}_{\mathrm{p}}=\mathrm{0},\mathrm{02918}*\mathrm{m}+\mathrm{3},\mathrm{814};$$

  
• In turn, for block 3 the equation has the following form: $${\mathrm{<figure-callout\; id="3"\; label="p\; p"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">p</figure-callout>}}_{\mathrm{p}}=\mathrm{0},\mathrm{0294}*\mathrm{m}+3,\mathrm{418};$$

  
• The other characteristics are created in a similar manner.
Computation of deviations of heat Rate (HR) with use of the deterministic model
• A deterministic algorithm may be used for calculating the deviations of heat Rate (HR) by using the created characteristics of the process parameters of the block. All the computations can be made in real time. $$\mathrm{Since\; hr}=\mathrm{Qin}/\mathrm{wn},$$

  

  wherein:
• hr - heat rate [MJ/MWh];
• Qin (hi,mi) - input flux of heat [MJ/h] from equation (1)
• Wn (hj,mj,uj,κj,γj) - output power [MW] from equation (7);
• h - enthalpy of the medium
• m - fluxes of the flow of the medium;
• u - extraction factor on the turbine;
• κ - fraction of flux of injection of water;
• γ - fraction of flux of supplementary water;
• i,j - subscripts related to the measurement points of the technological diagram for a given parameter
• The deviation of the heat rate for the examined parameter is calculated in the following manner: $$\mathrm{\Delta hrt}=\mathrm{hr}-\mathrm{hrt}$$

  

  wherein:
• Δhrt - deviation of heat rate for parameter t [MJ/MWh];
• hr - heat rate for the currently measured parameters [MJ/MWh];
• hrt - heat rate for parameter t, whose value is calculated from the characteristic function set for this parameter.
• Fig. 8 shows an example of the method for calculating the heat rate 'hrt' wherein the parameter 't' is calculated from the optimal characteristics curve, created as shown in the previous paragraph. In step 101 the enthalpy is calculated at a point of the process where control of the parameter is desired, for example the temperature of steam after the shut-off valve from the optimal characteristics for the measured flux of steam 'm'. Next, in step 102, the power output 'wnt' is calculated for the calculated enthalpy, and, if necessary, the input flux of heat 'Qin_t'. Next, in step 103, the power output 'wn' and the input flux of heat 'Qin' are calculated for the current operational parameters. Then, in step 104, the heat rate for parameter t - 'hrt' and the heat rate for the parameters currently being measured 'hr', as well as the deviation of the heat rate for parameter t - 'Δhrt', are calculated. These computations can be made for each characteristic.
• The deviations of heat rate can be presented as a function of 'Δhrt' (time), or in form of histograms for limited time periods, such as hours, days etc.
Simulation of possible improvement of process efficiency
• Taking into account the previously defined rules of simulation of calculation of heat rate deviations, the following plots of Figs. 9, 10 and 11 show graphically the possible improvements in the heat rate for selected parameters: temperature and pressure of the live steam, as well as for all examined parameters.
• The computations from the simulations optimal plots show that the adjustment of procedures for the operation of the power block to the model indications can, for the analyzed power blocks, result in reduction of fuel consumption by about 100 t/day and corresponding reduction of CO₂ by about 140 t/day.
• Fig. 8 shows the result of the computation of deviations of heat rate for a case of use of the temperature characteristic for the live steam input to the turbine. The computations were made comparatively for two blocks. As can be seen, a better control of steam temperature indicated by the characteristic may result in some improvement of heat rate. The computations for the other parameters may be carried out in similar manner.
• The computations can be also made by using all the process characteristics simultaneously. A histogram of the total heat rate deviation, taking into account all the optimal characteristics for the other parameters, is presented in Fig 11. The analysis of values of these deviations indicates that the greatest value impact is present for the heat rate deviation resulting from injection of water to steam.
Computations of destruction of exergy
• In order to confirm the computation of heat rate deviations and additional analyzes of the irreversibility of the processes, it is helpful to calculate the destruction of exergy in different points of the process. It is particularly essential in the analysis of the operation of condensers and in the analysis of injection of water to steam, because balance computations according to the first principle of thermodynamics do not indicate unambiguously the losses caused by irreversibility in these points.
• Using the equations:
• The equation for the exergy flux: $$\mathrm{\epsilon }=\left(\mathrm{h}-{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">T</figure-callout>}}_{\mathrm{0}}*\mathrm{s}\right)-\left({\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">h</figure-callout>}}_{\mathrm{0}}-{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">T</figure-callout>}}_{\mathrm{0}}*{\mathrm{<figure-callout\; id="0"\; label="s"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">s</figure-callout>}}_{\mathrm{0}}\right)$$
  
• The equation for the destruction of exergy in the analyzed process: $$\mathrm{\Sigma }{\mathrm{\epsilon }}_{\mathrm{i}}*{\mathrm{m}}_{\mathrm{i}}-\mathrm{\Sigma }{\mathrm{\epsilon }}_{\mathrm{e}}*{\mathrm{m}}_{\mathrm{e}}-\mathrm{w}=\mathrm{l}$$
  
  wherein:
  • ε - exergy flux,
  • h - enthalpy of the process,
  • s - entropy of the process,
  • T₀ - reference temperature,
  • h₀ - enthalpy of the reference state,
  • S₀ - entropy of the reference state,
  • m - flux of the medium,
  • w - work done in the system,
  • I - value of destruction of exergy
  • Subscript 'I' denotes the input,
  • Subscript 'e' denotes the output,
the value of destruction of exergy can be calculated at different points in the process, which facilitates analysis of heat rate deviations.
• For example, the computations for destruction of exergy in the condenser may be carried out as follows:
• According to equation (13), the fluxes of output exergy for the condenser (designation of fluxes as in scheme 1) are the following: $${\mathrm{\epsilon }}_{\mathrm{24}}=\left(\mathrm{h}\mathrm{24}-\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">T</figure-callout>}\mathrm{0}*\mathrm{s}\mathrm{24}\right)-\mathrm{<figure-callout\; id="0"\; label="Ex"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">Ex</figure-callout>}\mathrm{0};$$
  
• Ex0 is the exergy flux of the reference state, in this case the minimum temperature of the cooling water recorded in all measurements. However, this is irrelevant as this element is cancelled in the further equations. $${\mathrm{\epsilon }}_{\mathrm{25}}=\left(\mathrm{h}\mathrm{25}-\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">T</figure-callout>}\mathrm{0}*\mathrm{s}\mathrm{25}\right)-\mathrm{<figure-callout\; id="0"\; label="Ex"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">Ex</figure-callout>}\mathrm{0};$$

  

  $${\mathrm{\epsilon }}_{\mathrm{26}}=\left(\mathrm{h}\mathrm{26}-\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">T</figure-callout>}\mathrm{0}*\mathrm{s}\mathrm{26}\right)-\mathrm{<figure-callout\; id="0"\; label="Ex"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">Ex</figure-callout>}\mathrm{0};$$

  

  $${\mathrm{\epsilon }}_{\mathrm{27}}=\left(\mathrm{h}\mathrm{27}-\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">T</figure-callout>}\mathrm{0}*\mathrm{s}\mathrm{27}\right)-\mathrm{<figure-callout\; id="0"\; label="Ex"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">Ex</figure-callout>}\mathrm{0};$$

  
• Exe = m24*( ε₂₅ - ε₂₄) + m26*( ε₂₇ - ε₂₆); is a total change in flux of exergy at the output of the condenser (at the side of the cooling water)
  ε₁ = (h1 - T0*s1) - Ex0; is the flux of the exergy of the condensate
  ε₃₈ = (h38 - T0*s38) -Ex0; is the flux of the input exergy
• Exi = m1*( ε₃₈ - ε₁); is the total change of exergy on the condenser input (on the condensate side)
  I_k = Exi - Exe; is the destruction of exergy flux on the condenser
• The last equation has served to calculate the instantaneous destruction of exergy in the condenser for power blocks 2 and 3. The results of these computations are shown on the graph of fig. 12. From this graph it clearly follows that the operation on the condenser of power block 3 was significantly better - it shows less irreversibility than for power block 2.
• The analysis for each destruction of exergy for every process in the thermal cycle can be performed in a similar manner.
• The analysis of destruction of exergy in real time, as shown on the exemplary graph of Fig. 12, can provide information which may lead to improvement of the power block operation, reduction of the value of the irreversibility of the process, and thus improve the efficiency of the process.
• The equations for exergy destructions for a turbine, taking into account injection of water to steam, are the following:
• Exit = (m*(ε15 - ε11) + m12*(ε15 - ε11) + m37*(ε5 - ε37)); is the input flux of exergy on the turbine; $$\mathrm{\epsilon }15=\left(\mathrm{h}\mathrm{15}-\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">T</figure-callout>}\mathrm{0}*\mathrm{s}\mathrm{15}\right)-\mathrm{<figure-callout\; id="0"\; label="Ex"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">Ex</figure-callout>}\mathrm{0};$$
  
  $$\mathrm{\epsilon }11=\left(\mathrm{<figure-callout\; id="11"\; label="h"\; filenames="imgf0003.png,imgf0004.png"\; state="\{\{state\}\}">h</figure-callout>}\mathrm{11}-\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">T</figure-callout>}\mathrm{0}*\mathrm{s}\mathrm{11}\right)-\mathrm{<figure-callout\; id="0"\; label="Ex"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">Ex</figure-callout>}\mathrm{0};$$
  
  $$\mathrm{\epsilon }15=\left(\mathrm{h}\mathrm{15}-\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">T</figure-callout>}\mathrm{0}*\mathrm{s}\mathrm{15}\right)-\mathrm{<figure-callout\; id="0"\; label="Ex"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">Ex</figure-callout>}\mathrm{0};$$
  
  $$\mathrm{\epsilon }5=\left(\mathrm{<figure-callout\; id="5"\; label="h"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">h</figure-callout>}\mathrm{5}-\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">T</figure-callout>}\mathrm{0}*\mathrm{s}\mathrm{5}\right)-\mathrm{<figure-callout\; id="0"\; label="Ex"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">Ex</figure-callout>}\mathrm{0};$$
  
  $$\mathrm{\epsilon }37=\left(\mathrm{h}\mathrm{37}-\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">T</figure-callout>}\mathrm{0}*\mathrm{s}\mathrm{37}\right)-\mathrm{<figure-callout\; id="0"\; label="Ex"\; filenames="imgf0007.png,imgf0008.png"\; state="\{\{state\}\}">Ex</figure-callout>}\mathrm{0};$$
  
• I_t= Exit - Exe - wn; is the destruction of exergy on the turbine;
• Ψ = wn/Exit; is the turbine efficiency according to the second principle of thermodynamics.
• For example, the graph in Fig. 13 shows a comparison of the flux of exergy destruction for the turbines of power blocks 2 and 3. The results presented in the graph of Fig. 13 relate to the flow of the flux of exergy destruction for one selected day. The highest influence on the observed differences follows from injection of water to steam.
• The graph of Fig. 14 shows the thermodynamic efficiency Ψ according to the second principle of thermodynamics. As expected, block 3 has a higher efficiency - a lower irreversibility of the process and lower destruction of exergy.
Calculating destruction of exergy for simulated operation of blocks in comparison with database data
• In a similar manner as for the deviations of heat rate, the change of the fluxes of destruction of exergy during simulated operation can be calculated for a chosen parameter, for example, for optimal working conditions.
• The graph of Fig. 15 shows the savings that can be obtained by not using injection of water to steam. For block 2 as much as 8MW can be saved and for block 3 as much as 5MW. It results from the fact that for block 2 significantly higher fluxes were used than for block 2, which can be seen in the graph of Fig. 17 - data for the same measurement period. Fig. 16 shows the efficiency of the turbine for block 2 after eliminating injection of water to steam.
Analysis of causes of deviation of heat rate and fluxes of destruction of exergy
• The analysis of the causes of deviation of heat rate and the value of changes in destruction of exergy should be made on a current basis by the engineering crew of the plant. Some causes can be attributed to the specific technical conditions, such as the technical condition of the equipment, others to exploitation factors (for example, the cleanness of the condenser), and some to the actions of the operators of the blocks (for example, excessive use of injection water to control the parameters of the steam).
• The presented manner of analyzing the operation of the blocks significantly helps in formulating appropriate conclusions on how to improve the working procedures to achieve better results, i.e. the efficiency of the blocks, and consequently to decrease the amount of fuel consumption per a unit of generated energy and to decrease the emission of CO2.
A system for analysis of operation of a power plant block
• Fig. 18 shows a schematic of a system according to the invention. The system contains an operational data warehouse 201, for collecting and integrating data from system sources (automatic measurement systems comprising sensors placed on different elements of the block) and non-system sources (external files and data entered manually). The data warehouse can be in the form of a centralized or a distributed database, serviced by an appropriate computer system. On the basis of the data gather in this way, according to the method described above, the deterministic models are created in module 202, and the characteristics of operational parameters are created in module 203. The system comprises a module for examining the operational parameters 211, configured to examine the selected parameters by calculating the deviation of heat rate in time on the basis of the deterministic model and the characteristic of a given parameter. Moreover, the system contains a module for calculating the destruction of exergy 212, configured to calculate the destruction of exergy in points of the process to confirm computation of the deviations of heat rate, as in the above-described method. The analysis module 213 is configured to show in a graphical form the calculated deviations of heat rate to allow further analysis, for example, as shown in the graphs of Figs. 9-17. The individual modules are technical means in form of computers connected with each other via a network, running appropriate software providing the functionality of particular modules.

Claims (11)

1. A computer-implemented method for analyzing the operation of power plant blocks, in which, on the basis of collected operational data (201), the deterministic models (202) of operation of individual blocks are examined and characteristics of operational parameters (203) are created, characterized in that

   - the selected operational parameters are examined by calculating for them the deviation of heat rate in time on the basis of the deterministic model (202) and the characteristic of the parameter (203),

   - destructions of exergy in various process points of the block are calculated;

   - for various points of the process and for various power plant blocks, the calculated deviations of heat rate and the destruction of exergy are presented in a graphical form.
2. The method according to claim 1, wherein the operational data (201) are collected from automatic measurement systems comprising sensors positioned on various elements of each of the power plant blocks.
3. The method according to any of the previous claims, characterized in that the deterministic model (202) of the block is created according to the first principle of thermodynamics in a form of a set of equations having the following form: $${\mathrm{R}}_{\mathrm{n}}=\mathrm{f}\left({\mathrm{h}}_{\mathrm{i}},{\dot{\mathrm{m}}}_{\mathrm{i}},{\mathrm{u}}_{\mathrm{i}},{\mathrm{\kappa }}_{\mathrm{i}},{\mathrm{\gamma }}_{\mathrm{i}},{\mathrm{x}}_{\mathrm{i}}\right);$$

   

   wherein:

   R_n - resulting function, for example: the power of the turbine, the efficiency of the block, the efficiency of the boiler, heat rate, CO₂ emissions, the rate of fuel consumption per a unit of generated power, destruction of exergy and the like;

   h_i - specific enthalpy of the medium at node i;

   ṁ_i - mass flux, for example of steam, water, condensate, air, gas, or fuel in the node i;

   u_i - fraction of the extraction of steam (on the turbine) in relation to the main flux operating medium for vent 'i';

   κ_i - the fraction of the flux of water injection to steam in relation to the main flux of the operating medium for the injection i;

   γ_i - the fraction of the supplementary water flux in relation to the process at the point i;

   x_i - the concentration of flue gas or fuel in the process used for the balance computations.
4. The method according to any of previous claims, characterized in that the characteristics of the current operational parameters (203) are created on the basis of the current data for predetermined historical time periods preceding their use in the computations.
5. The method according to any of previous claims, characterized in that the characteristics of the operational parameters (203) comprise at least one operational parameter selected from a group comprising the following parameters: temperature of live steam after the shut-off valve; pressure of live steam after the shut-off valve; temperature of secondary steam on the turbine; pressure of secondary steam on the turbine; flux of injection water to live steam; flux of injection water to secondary steam; flux of supplementary water; vacuum of the condenser; temperature of supply water to the boiler; air to fuel ratio; concentration of oxygen in flue gas; concentration of CO₂ in flue gas; amount of unburned coal in the ash.
6. The method according to any of previous claims, characterized by presenting in a graphical form the comparative plots for characteristics of a given operational parameter made for different power plant blocks.
7. The method according to any of previous claims, characterized by presenting in a graphical form the comparison of the calculated deviations in heat rate for a given parameter for different power plant blocks.
8. The method according to any of previous claims, characterized by presenting in a graphical form the comparison of the calculated deviations of the total heat rate for different power plant blocks.
9. The method according to any of previous claims, characterized in that the destruction of exergy in a given point of the process is calculated by using the equations: $$\mathrm{I}=\mathrm{\Sigma }{\mathrm{\epsilon }}_{\mathrm{i}}*{\mathrm{m}}_{\mathrm{i}}-\mathrm{\Sigma }{\mathrm{\epsilon }}_{\mathrm{e}}*{\mathrm{m}}_{\mathrm{e}}-\mathrm{w}$$

   

   $$\mathrm{\epsilon }=\left(\mathrm{h}-{\mathrm{T}}_{\mathrm{0}}*\mathrm{s}\right)-\left({\mathrm{h}}_{\mathrm{0}}-{\mathrm{T}}_{\mathrm{0}}*{\mathrm{s}}_{\mathrm{0}}\right)$$

   

   wherein:

   ε - exergy flux,

   h - enthalpy of the process,

   s - entropy of the process,

   T₀ - reference temperature,

   h₀ - enthalpy of the reference state,

   s₀ - entropy of the reference state,

   m - flux of the medium,

   w - work done in the system,

   I - value of destruction of exergy

   Subscript 'I' denotes the input,

   Subscript 'e' denotes the output,
10. The method according to any of previous claims, characterized in that by using the predetermined characteristics of operational parameters (203), presenting in a graphical form the simulation of deviations of heat rate and/or changes of fluxes of destruction of exergy for variable values of the parameter of the characteristic.
11. A computer-implemented system for analysis of operation of power plant blocks, in which by using data from an operational data warehouse (201) deterministic models (202) of operation of individual blocks are examined and characteristics of operational parameters (203) are created, characterized in that the system comprises:

    - a module for examining the operational parameters (211), configured to examine the selected operational parameters by calculating for them the deviation in heat rate in time based on the deterministic model and the characteristic of a given parameter;

    - a module for calculating exergy destruction (212) configured to calculate destruction of exergy in operational process points for the block;

    - an analysis module (213) configured to present in a graphic form the calculated deviations in heat rate and the destruction of exergy in various points of the process, comparatively for various power plant blocks.

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