Estimation of exhaust steam enthalpy and steam

Computers and Chemical Engineering 93 (2016) 25–35

Contents lists available at ScienceDirect

Computers and Chemical Engineering journal homepage: www.elsevier.com/locate/compchemeng

Estimation of exhaust steam enthalpy and steam wetness fraction for steam turbines based on data reconciliation with characteristic constraints Sisi Guo, Pei Liu ∗ , Zheng Li State Key Lab of Power Systems, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China

a r t i c l e

i n f o

Article history: Received 22 December 2015 Received in revised form 30 May 2016 Accepted 30 May 2016 Available online 7 June 2016 Keywords: Steam turbine Data reconciliation Characteristic constraints Uncertainty reduction Wetness fraction

a b s t r a c t Wetness fraction of exhaust steam is important to the economy and safety of steam turbines. Due to lack of commercially available measurement technologies, it is usually obtained from model based calculation via other measurements. However, accuracy of relevant measurement data is usually unsatisfactory due to limits of measuring instruments, and data reconciliation can be applied to improve the accuracy of these measurements. Traditionally, balance constraints of steam turbines are mostly considered in data reconciliation, and results of previous studies illustrate that there is still potential for further improvement. In this work, we present a generalized data reconciliation approach with both balance and characteristic constraints for estimation of wet steam parameters in steam turbines, with case studies on a real-life 1000 MW coal-fired power plant. Results show that uncertainty reduction is enhanced for all measurements. Better estimates of exhaust steam enthalpy and steam wetness fraction can be therefore obtained after data reconciliation. © 2016 Elsevier Ltd. All rights reserved.

1. Introduction Wetness fraction of exhaust steam from low pressure cylinders (LPC) is an important parameter closely related to the economy and safety of steam turbines (Wang et al., 2002), because the occurrence of condensation phenomena in wet steam two-phase flow would reduce the steam turbine efficiency, result in corrosion damage of turbine blades, and threaten the power unit safety (Li et al., 2012). However, on-line measurement of the steam wetness fraction of the LPC has been a difficult task for a long time (Xu and Yuan, 2015), therefore many methods have been investigated to determine the steam wetness fraction, such as numerical simulation (Sun et al., 2015; Du et al., 2013), artificial neural network (Wang and Song, 2012), and steam turbine modeling (Xu and Yuan, 2015; Zhang et al., 2007). Accuracy of measurement data is essential to the effect of these methods and estimates of steam wetness fraction. However, accuracy of on-line measured data is usually unsatisfactory due to measurement errors and uncertainty of measuring instruments (Jiang et al., 2014a). Consequently, data preprocessing techniques aiming at reducing uncertainty of measurements and unmeasured

∗ Corresponding author. E-mail address: liu [email protected] (P. Liu). http://dx.doi.org/10.1016/j.compchemeng.2016.05.019 0098-1354/© 2016 Elsevier Ltd. All rights reserved.

parameters are of great interest to steam turbines. Data reconciliation is a technique explicitly making use of system constraints and redundant measured data to obtain better estimates of system parameters and reduce the effect of random errors (Narasimhan and Jordache, 1999). It adjusts system measurements according to their uncertainties to satisfy the constraint equations of system, and provides better estimates of parameters without measurement. Since 1960s, a number of studies have been conducted on theories and applications of data reconciliation (Kuehn and Davidson, 1961), and up to now this method has become an important data processing technique with wide applications in industry, including chemical reaction process (Prata et al., 2009; Zhang and Chen, 2014; Srinivasan et al., 2015; Zhang and Chen, 2015; Özyurt and Pike, 2004), mineral and metal processing (Vasebi et al., 2012a; Vasebi et al., 2012b; Vasebi et al., 2014), refinery plants (Zhang et al., 2001), absorption refrigeration system (Martínez-Maradiaga et al., 2013), recycle system (Miao et al., 2011), and so on. Besides, data reconciliation has also been applied to power plants, including nuclear power plant (Langenstein, 2006; Valdetaro and Schirru, 2011), gas turbine power plant (Chen and Andersen, 2005; Martini et al., 2013), combined cycle plants (Gülen and Smith, 2009), and steam turbine power plants. Fuchs (2002) studied the data validation method to increase the accuracy of calculated steam turbine exhausting steam enthalpy and heat rate on the basis of acceptance tests and simulation data. Zhou et al.

26

S. Guo et al. / Computers and Chemical Engineering 93 (2016) 25–35

Fig. 1. An illustration of the steam turbine system of a 1000 MW coal-fired power plant.

(2012) provided accurate parameter estimates for the spraying water system in a coal-fired power plant by developing a simultaneous data reconciliation and gross error detection method. Jiang et al. (2014d) applied the data reconciliation approach to reduce the uncertainty of primary flow measurements and heat rate of steam turbine, and presented a serial elimination strategy to detect gross errors in measured data (Jiang et al., 2014a). Besides, a mathematical method based on data reconciliation to evaluate the minimum isolable magnitude for a gross error to be isolated from another with a required probability for steam turbine power plants was put forward by Jiang et al. (2014c). Guo et al. (2016a) presented an overall thermal system approach for better results of data reconciliation for steam turbine power plants, and proposed an inequality constrained nonlinear data reconciliation approach to correct the expansion curve of steam turbine and obtain better estimates of isentropic efficiencies (Guo et al., 2016b). In most previous studies, balance constraint equations of steam turbines are usually considered in a data reconciliation problem. Characteristic constraint equations are additionally conditional equations in the so called generalized data reconciliation (Szega, 2009). Introduction of characteristic constraints helps to improve redundancy of the system, thus improving the effect of uncertainty reduction by data reconciliation. In reconciliation of measurements in thermal power unit, these characteristic constraints can include equations of steam flow capacity in turbine and its internal efficiency, the equation of pressure drop in pipelines and heat flow in regenerative heat exchangers (Szega and Nowak, 2013). Jiang et al. (2014b) applied characteristic constraints of pipelines as well as heat exchangers, and proposed a data reconciliation approach for integrated sensor and equipment performance monitoring for steam turbine power plants. Badyda (2014) introduced characteristic constraints of steam turbine and applied data reconciliation to correct the measured steam mass flows, close the mass balance and converge the calculated capacity to the measured generated electric capacity. Szega and Nowak, (2013) used additional equations of conditions in the generalized method of data reconciliation for optimization of measurement placement in redundant measurement system in power units. For the abovementioned studies, applications of characteristic constraints in data reconciliation are carried out with simulation data, while the application and validation in a real-life power plant using on-line operational data are rather insufficient. Besides, applications of the generalized data reconciliation considering characteristic constraints to the estimation of wet steam param-

eters of LPC, such as steam wetness fraction are quite limited to the author’s knowledge. Therefore in this work, we introduce characteristic constraints as well as balance constraints of steam turbines in data reconciliation and apply to the steam turbine system of a real-life 1000 MW ultra-supercritical coal-fired steam turbine power plant by using design data as well as on-line operational measured data. Two case scenarios are constructed respectively (Case A and Case B). In Case A, data reconciliation are carried out with design values at different loads (100%, 70%, 50% and 40%) to theoretically investigate the effect of generalized data reconciliation considering characteristic constraints of steam turbines. In Case B, data reconciliation is carried out with 551 groups of operational measured datasets in steady state in a real-life power plant. Firstly, we describe the steam turbine system and methodology of the generalized data reconciliation method. Secondly, uncertainty reduction results of measurements in two cases are presented and discussed. Finally, we evaluate and analyze the estimates of exhaust steam enthalpy and steam wetness fraction for LPC after data reconciliation. 2. System description 2.1. System configuration An illustration of the steam turbine system of a 1000 MW coalfired ultra-supercritical power plant is shown in Fig. 1. In this study, a steam turbine consists of a high pressure cylinder (HPT1 and HPT2), an intermediate pressure cylinder (IPT1 and IPT2) and two low pressure cylinders (LPT1, LPT2, LPT3, LPT4 and LPT5). Turbine stages are determined by eight extraction steam flows (EP1, EP2, EP3, EP4, EP5, EP6, EP7, and EP8), and extraction steam flows are used to heat feed water. Main steam from the boiler enters the steam turbine through high pressure steam pipes (HPipe) and expands in turbine stages to generate power. Eventually, exhaust steam from the final turbine stage of LPC is condensed in a condenser. 2.2. Measured parameters and measurement uncertainty A list of measured parameters in the system and their corresponding descriptions are shown in Table 1. Pressure, temperature, and flow rates are measured in the system. Since we only focus on the steam turbine system in Fig. 1 in this work, the mass flow rates of eight extraction steam flows are


27

Table 1 Descriptions of the measured parameters. Measurement name

Symbol

Description

High pressure steam pipe (HPipe)

HPipe m out1 HPipe p out1 HPipe T out1

Outlet steam mass flow rate Outlet steam pressure Outlet steam temperature

No.1 High pressure turbine stage (HPT1)

HPT1 p out2 HPT1 T out2

1# Extraction steam pressure 1# Extraction steam temperature

No.2 High pressure turbine stage (HPT2)

HPT2 p out2 HPT2 T out2


Reheat steam pipe (IPipe)

IPipe p out1 IPipe T out1

Hot reheat steam pressure Hot reheat steam temperature

No.1 Intermediate pressure turbine stage (IPT1)

IPT1 p out2 IPT1 T out2


No.2 Intermediate pressure turbine stage (IPT2)

IPT2 p out2 IPT2 T out2


No.1 Low pressure turbine stage (LPT1)

LPT1 p out2 LPT1 T out2













Outlet steam pressure Outlet steam temperature

treated as pseudo measurements, which are calculated by the heat balance of the feed water regenerative heating system. As a result, the number of measurements is thirty-one in total. In order to apply the data reconciliation method, uncertainties of measurements need to be evaluated. In previous studies, standard deviations of measurement errors are determined on the basis of permissible error of measuring instrument (Jiang et al., 2014b), the law of error propagation (Fuchs, 2002) or the guidelines to measurement uncertainty (International Organization for Standardization, 1995). Since the on-line operational measured data may contain gross errors except from random errors, the standard deviation of measurement data is not suitable for uncertainty evaluation. Consequently, we evaluate the standard deviations of measurement errors based on the measuring instrument nominal accuracy, as shown in Eq. (1) (Jiang et al., 2014d): (xi ) =

i

1.96

(1) Ns

where i represents the permissible error of an instrument determined by its accuracy class with a confidence interval of 95%, Ns represents the number of sensors measuring the same parameter. In this work, the accuracy of the pressure transmitters is 0.1 and the permissible error of temperature measurement is 0.4%. The accuracy of the mass flow measurement is determined after corrections of flowmeters. Uncertainties of measurements are listed in the column 8 in Table 2. 2.3. Steady state analysis for operational measured data In this work, measured data only in steady state or quasi-steady state are applied in data reconciliation. The online monitoring system of power plants collects measured data with a time interval of one minute. A sliding window method can be applied to select steady state operational data, as follows (Jiang et al., 2014d): 1 s= x¯

1 N (x − x¯ )2 < 0.001 N − 1 i=1 i

(2)

where s represents the relative standard deviation of the steady state criteria parameter, xi and x¯ represents the measured value at time point i and the average value of the steady state criteria parameter respectively, N represents the length of a time window. Electric generator output is one typical steady state criteria parameter, and Ref. (Fuchs, 2002) points out the condensed water mass flow is another major parameter due to the power controlling strategy. Since the steam temperature shows only minor fluctuation and the steam pressure is consistent to the electrical power output, steam parameters are not needed (Fuchs, 2002). Therefore, electric generator output and condensed water mass flow are used for steady state analysis and the time window length is set to be 15 min. As a result, 551 groups of datasets at nominal load are selected as steady state operational data. One set of steady state operational data at nominal load is shown in Table 2, together with the design values of measured parameters at 100%, 70%, 50% and 40% loads.

2.4. Constraint equations Balance constraint equations are usually applied in a steam turbine data reconciliation problem, which include mass balance, energy balance, and pressure drop calculation. In this work, characteristic constraints of steam turbine stages are also introduced for more redundancy in the data reconciliation problem, including Ellipse Law and Isentropic Efficiency Equation. Constraint equations are listed in Table 3. All thermodynamic properties of steam and water are calculated according to the IAPWS-IF97 standard.

2.4.1. Ellipse law The Law of the Ellipse, or Stodola’s Cone Law provides a method for calculating the highly nonlinear dependence of extraction pressure with a flow for multistage turbine with high backpressure (Cooke, 1985). Ellipse Law was found empirically by Stodola and

28


Table 2 Values and uncertainties of measurements. Measurements

Unit

Design data (100% load)




Operational data (100% load)

Error standard deviations

‘HPipe m out1’ ‘HPipe p out1’ ‘HPipe T out1’ ‘HPT1 m out2’ ‘HPT1 p out2’ ‘HPT1 T out2’ ‘HPT2 m out2’ ‘HPT2 p out2’ ‘HPT2 T out2’ ‘IPipe p out1’ ‘IPipe T out1’ ‘IPT1 m out2’ ‘IPT1 p out2’ ‘IPT1 T out2’ ‘IPT2 m out2’ ‘IPT2 p out2’ ‘IPT2 T out2’ ‘LPT1 m out2’ ‘LPT1 p out2’ ‘LPT1 T out2’ ‘LPT2 m out2’ ‘LPT2 p out2’ ‘LPT2 T out2’ ‘LPT3 m out2’ ‘LPT3 p out2’ ‘LPT3 T out2’ ‘LPT4 m out2’ ‘LPT4 p out2’ ‘LPT4 T out2’ ‘LPT5 p out1’ ‘LPT5 T out1’

kg/s bar ◦ C kg/s bar ◦ C kg/s bar ◦ C bar ◦ C kg/s bar ◦ C kg/s bar ◦ C kg/s bar ◦ C kg/s bar ◦ C kg/s bar ◦ C kg/s bar ◦ C bar ◦ C

759.29 250.00 600.00 67.03 81.90 423.00 62.59 47.30 344.80 42.50 600.00 29.89 22.80 499.40 56.92 11.10 393.10 21.90 6.24 316.20 23.18 3.40 243.40 21.52 1.59 163.20 41.49 0.69 89.55 0.06 35.23

509.34 191.00 600.00 36.68 55.90 421.90 36.50 32.70 346.90 29.50 600.00 18.58 15.80 497.80 34.86 7.83 391.10 13.83 4.41 313.30 14.96 2.41 239.80 13.81 1.13 159.00 24.36 0.50 84.99 0.06 35.23

358.29 136.00 600.00 22.16 39.80 426.90 22.73 23.50 353.10 21.10 600.00 12.22 11.40 497.10 23.05 5.67 390.20 9.18 3.20 312.00 10.06 1.76 238.20 9.24 0.83 157.10 14.33 0.37 83.99 0.06 35.23

289.11 111.00 600.00 16.53 32.30 429.40 17.06 19.00 355.20 17.10 600.00 9.67 9.21 483.50 15.21 4.66 380.60 7.17 2.64 303.60 7.90 1.45 230.90 7.26 0.68 151.00 10.04 0.31 79.67 0.06 35.23

813.59 257.82 592.28 81.70 87.79 428.17 64.27 47.97 342.01 44.74 603.59 34.34 23.73 507.61 65.29 11.48 393.40 24.17 6.35 344.31 24.75 3.75 262.35 28.96 1.44 203.52 37.20 1.00 129.16 0.08 42.56

±18.293 ±0.289 ±0.953 ±0.880 ±0.167 ±1.500 ±0.696 ±0.100 ±1.000 ±0.067 ±1.650 ±0.409 ±0.067 ±1.500 ±0.347 ±0.033 ±1.125 ±0.306 ±0.033 ±1.000 ±0.374 ±0.033 ±0.875 ±0.435 ±0.017 ±0.750 ±0.462 ±0.017 ±0.750 ±0.017 ±0.250

was later proven theoretically by Fluegul (Traupel, 2013). In this work, we consider the simplified Ellipse Law, as shown in Eq. (3): cf =

˙f m pf 2 −pd 2 Tf +273.15K

=

˙ f,0 m

(3)

pf,0 2 −pd,0 2 Tf,0 +273.15K

˙ f,0 represent design and off-design flow rates ˙ f and m where m respectively, pf and Tf are design pressure and temperature at the stage group intake, pd and pd,0 are design and off-design outlet pressure respectively, pf,0 and Tf,0 are off-design inlet pressure and temperature. Characteristic coefficient of the steam flow capacity of a turbine stage is Cf , which has a relationship with the equivalent mass flow √ m T +273.15K . This relationship can be obtained using rate G = 0 0 p 0 the dominant factor modeling on the basis of operational measurements at various loads (Szega and Nowak, 2013). 2.4.2. Isentropic efficiency equation Isentropic efficiency describes how efficiently a steady-flow process approximates a corresponding isentropic process (Cengel et al., 2002). Isentropic efficiency of turbines is calculated as follows: s =

hin − hout hin − hs

(4)

where hin represents the enthalpy at the entrance state, hout represents the enthalpy at the exit state for the actual process, hs represents the enthalpy at the exit state for the isentropic process. Characteristic coefficient of the adiabatic internal efficiency of groups of stage iss , which proves to has a relationship with the p equivalent mass flow rate G and pressure ratiopr = pd . This relaf

tionship can also be obtained by operational measurement data of the power unit.

Furthermore, values and uncertainties of these coefficients are calculated on the basis of operational measurement data. Empirical coefficients in these two kinds of characteristic equations are treated as pseudo-measurements (Szega and Nowak, 2013), and used in data reconciliation.

3. Methodology 3.1. Data reconciliation formulation The nonlinear steady state data reconciliation problem is generally formulated as follows (Narasimhan and Jordache, 1999): min(y − x)T −1 (y − x) =

n (yi − xi )2

x,u

i=1

i 2

(5)

Subject to: f (x, u) = 0

(6)

g (x, u) ≤ 0

(7)

wherey and x represent vector of measured values and reconciled values of measured variables respectively, represents uncertainty of measured variables, n is the number of measured variables, represents the n ∗ n variance-covariance matrix, u is vector of calculated values of unmeasured variables, f and g represent equality and inequality constraints respectively. In this work, there are 44 constraint equations and 57 variables in total, including 31 measured variables and 26 unmeasured variables. The number of redundancy is obtained by the difference between the number of equations and unknowns. As a result, the redundancy of this system is 18.

S. Guo et al. / Computers and Chemical Engineering 93 (2016) 25–35 Table 3 Constraint equations in the data reconciliation problem. Equipment

Constraint equations

Equation type

HPIPE

m in1-m out1 + m in LKG-m out LKG = 0

Mass balance

HPT1

m in1-m out1-m out2 + m in LKG-m out LKG = 0 m in1, 0 m in1 =

Mass balance

p in1 −p out1 2

2

T in1+273.15K

p in1,0 −p out1,0 2

hin1,0 − hout1,0 hin1 − hout1 = hin1 − hs hin1,0 − hs,0 p out2-p out1 = 0 T out2-T out1 = 0 HPT2

Isentropic efficiency calculation Pressure balance Energy balance


p in1 −p out1 2

2

T in1+273.15K

p in1,0 −p out1,0 2

2

2

T in1+273.15K


p in1,0 −p out1,0 2

2

2

T in1+273.15K


p in1,0 −p out1,0 2

2

2

T in1+273.15K


p in1,0 −p out1,0 2

2

2

T in1+273.15K


p in1,0 −p out1,0 2

2

2

T in1+273.15K


p in1,0 −p out1,0 2

2

2

T in1+273.15K


p in1,0 −p out1,0 2

2

2

T in1+273.15K

Ellipse Law

2


m in1-m out1 + m in LKG-m out LKG = 0 m in1, 0 m in1 =

p in1 −p out1

Mass balance

T in1,0+273.15K

hin1,0 − hout1,0 hin1 − hout1 = hin1 − hs hin1,0 − hs,0 p out2-p out1 = 0 T out2-T out1 = 0 LPT5

Ellipse Law

2


p in1 −p out1

Mass balance

T in1,0+273.15K


Ellipse Law

T in1,0+273.15K


p in1 −p out1

Mass balance

2


Ellipse Law

2


p in1 −p out1

Mass balance

T in1,0+273.15K


Ellipse Law

2


p in1 −p out1

Mass balance

T in1,0+273.15K


Ellipse Law

2


p in1 −p out1

Mass balance

T in1,0+273.15K

hin1,0 − hout1,0 hin1 − hout1 = hin1 − hs hin1,0 − hs,0 p out2-p out1 = 0 T out2-T out1 = 0 IPT2

Ellipse Law

2


p in1 −p out1

Mass balance

T in1,0+273.15K

hin1,0 − hout1,0 hin1 − hout1 = hin1 − hs hin1,0 − hs,0 p out2-p out1 = 0 T out2-T out1 = 0 IPT1

Ellipse Law

2

T in1,0+273.15K

p in1,0 −p out1,0 2

Mass balance Ellipse Law

2

T in1,0+273.15K

hin1,0 − hout1,0 hin1 − hout1 = hin1 − hs hin1,0 − hs,0

Note: In Ellipse Law and Isentropic Efficiency Equation, 0 represents parameters before data reconciliation.

Isentropic efficiency calculation

29

30


Fig. 2. Measured and reconciled uncertainties of mass flow rates at different loads.

Fig. 3. Measured and reconciled uncertainties of pressure measurements at different loads.

3.2. Solution and validation of data reconciliation Data reconciliation can be mathematically expressed as a constrained weighted least-squares optimization problem (Narasimhan and Jordache, 1999). There are several solution techniques for the nonlinear data reconciliation problem, for instance,

Lagrange multipliers or successive linearization. In this work, we apply MATLAB to solve this nonlinear data reconciliation problem (Narasimhan and Jordache, 1999). In this study, data reconciliation results will be validated only if no gross error is detected. The global test is carried out after data reconciliation to detect gross errors in the operational measured


31

data. The test statistic in the global test is formulated as in Ref. (Narasimhan and Jordache, 1999). The test criterion is the critical value of distribution at a chosen significance level. If the test statistic is less than the test criterion after data reconciliation, no gross error exists.

system under various working loads by using design data. Further study will be carried out in the next section in Case B using on-line operational measured data.

4. Results and discussion

In Case B, data reconciliation are carried out with 551 groups of operational measured datasets in steady state at nominal load in a real-life power plant. It is noted that we consider characteristic constraints as well as mass balance constraints for LPT5 in this data reconciliation problem since the outlet steam from LPT4 is still superheated, thus the redundancy in the system is 18. Results are validated after gross error detection and shown as follows.

On the basis of former sections, the data reconciliation problem is formulated and solved. Results and discussions are shown in this section. 4.1. Case A: uncertainty reduction of measurements using design data In the design data, steam from the outlet of LPT4 has already entered the wet steam region. Characteristic equations of LPT5 in Table 3 are no longer applicable in this case, so only mass balance constraints of LPT5 are considered in data reconciliation. Since the variables remain the same as before, the system redundancy is 16 in Case A. After data reconciliation, reconciled values and uncertainties of measured parameters are obtained. Results are validated since no gross error is detected. Comparison of uncertainties before and after data reconciliation is discussed into three categories: mass flow rate, pressure and temperature. Fig. 2 shows uncertainties of mass flow rates at different loads (100%, 70%, 50% and 40%) before and after data reconciliation. From Fig. 2, we can see that uncertainties of most mass flow rates are reduced, including mass flow rates of extraction steam from high pressure and intermediate pressure turbine stages. Especially for primary mass flow (HPipe m out1), the uncertainty of reconciled data is reduced by 95% compared with measured uncertainty. Since mass flow rate of extraction steam from LPT4 (LPT4 m out2) has no corresponding redundant parameter, its uncertainty remain the same after data reconciliation. Besides, uncertainty of reconciled data at different loads are reduced differently, and reconciled data at 40% load achieves the maximum uncertainty reduction. Uncertainties of measured and reconciled values for pressure measurements are shown in Fig. 3. It can be seen that uncertainties of reconciled values of pressure measurements are reduced compared with measured uncertainties, especially for extraction steam pressure of LPT2 (LPT2 p out2), extraction steam pressure of LPT3 (LPT3 p out2), extraction steam pressure of LPT1 (LPT1 p out2), extraction steam pressure of IPT1 (IPT1 p out2) and extraction steam pressure of HPT1 (HPT1 p out2).Their uncertainties are reduced by 74.2%, 58.9%, 58.7%, 52.6% and 34.8%, respectively. As stated previously, uncertainty of outlet pressure of LPT5 (LPT5 p out1) are not reduced due to no redundancy. Furthermore, uncertainties of measured and reconciled data for temperature measurements at different loads are shown in Fig. 4. Since the outlet steam from LPT4 and LPT5 has entered the wet steam region, the steam temperature is not independent to pressure, so the percentage of uncertainty reduction is consistent with pressure. We can see that the uncertainties of reconciled values are much smaller than those of measured values for all temperature measurements, especially for extraction steam temperature of IPT1 (IPT1 T out2), outlet temperature of reheat pipe (IPipe T out1), extraction steam temperature of HPT1 (HPT1 T out2), extraction steam temperature of IPT2 (IPT2 T out2) and LPT1 (LPT1 T out2), with a percentage of uncertainty reduction of 60.5%, 59.6%, 57.3%, 55.0% and 54.9%, respectively. In a word, the results indicate that data reconciliation can effectively improve the accuracy of measurements in a steam turbine

4.2. Case B

4.2.1. Uncertainty reduction of measured parameters In this section, we compare uncertainties of measured parameters before and after data reconciliation, as shown in Fig. 5-7. The average uncertainties of 551 groups of steady state datasets are plotted in these figures. Fig. 5 shows uncertainties of measured and reconciled values for mass flows rates. It can be seen that uncertainty of primary mass flow rate (HPipe m out1) is reduced greatly by 95.6% after data reconciliation. Uncertainties of other reconciled values are also reduced in varying degrees. Different from previous results in Case A, uncertainty of mass flow rate of extraction steam from LPT4 (LPT4 m out2) is reduced because it is redundant to other parameters by characteristic constraints of LPT5 in Case B. Besides, Fig. 6 shows uncertainties of measured and reconciled values for pressure measurements. We can see that uncertainties of reconciled values are much smaller than those of measured values for all pressure measurements, especially for outlet pressure of LPT5 (LPT5 p out1), extraction steam pressure of LPT4 (LPT4 p out2), extraction steam pressure of LPT3 (LPT3 p out2), extraction steam pressure of LPT2 (LPT2 p out2) and extraction steam pressure of LPT1 (LPT1 p out2). Their uncertainties are reduced by 93.4%, 85.5%, 81.9%, 81.8% and 73.2% respectively. Furthermore, comparison of uncertainties of measured and reconciled values for temperature measurements is shown in Fig. 7. Uncertainties of reconciled values for temperature measurements are reduced by 30% ∼ 50% compared with measured ones. Since the outlet steam of LPT5 has enter the wetness steam region and the adjustment for reconciled temperature is limited, thus the uncertainty of saturated temperature (LPT5 T out1) are not reduced significantly. In short, the data reconciliation approach used in this work proves to be effective to reduce uncertainties of measurements in operational measured data for a real-life steam turbine. 4.2.2. Estimation of exhaust steam enthalpy As mentioned before, the outlet steam from LPT5 (exhaust steam) has entered the wetness region. The enthalpy of superheated steam can be calculated directly with measured pressure and temperature, while enthalpy of wet steam cannot be determined by pressure and temperature. In this work, exhaust steam enthalpy is determined by turbine energy balance, as shown in Eq. (8) (ASME, 2000). ˙ 1 (hHPIPE − hHTP1 ) + m ˙ 2 (hHTP1 − hHTP2 ) + m ˙ 3 (hIPIPE − hITP1 ) m ˙ 8 (hLTP3 − hLTP4 ) ˙ 5 (hITP2 − hLTP1 ) + · · · + m ˙ 4 (hITP1 − hITP2 ) + m +m ˙ 9 (hLTP4 − hLTP5 ) = +m

w e

(8)

32


Fig. 4. Measured and reconciled uncertainties of temperature measurements at different loads.

Fig. 5. Uncertainties of measured and reconciled values for mass flows rates.

˙ represents mass flow of each turbine stage; h represents where m outlet steam enthalpy, W represents generated electricity power, e represents steam turbine power generation efficiency, and hLTP5 represents exhaust steam enthalpy.

Then we can calculate the estimates of exhaust steam enthalpy based on measured data and reconciled data. Estimates of exhaust steam enthalpy calculated by measured data and reconciled data are shown in Fig. 8.


33

Fig. 6. Uncertainties of measured and reconciled values for pressure measurements.

Fig. 7. Uncertainties of measured and reconciled values for temperature measurement.

For parameters with no measurement, there is no direct way to obtain their uncertainties since their true values are unknown. Therefore, the uncertainty of exhaust steam enthalpy is not comparable based on measured data and reconciled data directly. Since exhaust steam enthalpy is calculated by measured data based on turbine energy balance, and the uncertainties of measured parameters are reduced by data reconciliation, the uncertainty of exhaust steam enthalpy calculated by reconciled data should be theoretically smaller than that calculated by measured data based on the law of error propagation (Fuchs, 2002). 4.2.3. Estimation of steam wetness fraction As mentioned before, online measurement of the exhaust steam wetness fraction of the low pressure cylinder has been a difficult

task for a long time (Xu and Yuan, 2015), so the wetness fraction of steam is usually calculated by other approaches. Therefore, the true value of wetness fraction is also unknown. Based on the values of exhaust steam enthalpy, wetness fraction of steam can be evaluated as follows: y=

h − hl hg − hl

(9)

where y represents wetness fraction of steam, h represents enthalpy of exhaust steam, hg represents saturated vapor enthalpy, and hl represents saturated liquid enthalpy. After data reconciliation, reconciled data of parameters are obtained and thus exhaust steam enthalpy can be calculated. Then the estimates of steam wetness fraction can be obtained by mea-

34


Fig. 8. Estimates of exhaust steam enthalpy based on measured data and reconciled data.

Fig. 9. Estimates of steam wetness fraction based on measured data and reconciled data.

sured data as well as reconciled data according to Eq. (9), as shown in Fig. 9. In industrial practice, the exhaust steam wetness fraction must be less than 14% for safety concern according to Ref. (Huang et al., 2002). Estimates of steam wetness fraction in Fig. 9 are less than 14%, which are reasonable in a sense. Uncertainty of steam wetness fraction is also unknown since the true values of steam wetness fraction is unavailable. Consequently, further information and research are needed for uncertainty evaluation of unmeasured parameters such as exhaust steam enthalpy and steam wetness fraction. 5. Conclusions In this work, we apply the generalized data reconciliation method to the steam turbine system of a real-life 1000 MW ultrasupercritical coal-fired power plant considering both characteristic

constraints as well as balance constraints of steam turbines. We construct two case scenarios namely Case A and Case B using design data and on-line measured operational data respectively to validate the effect of the proposed data reconciliation method. Firstly, we apply the data reconciliation approach with design data at different loads (100%, 70%, 50% and 40%). Results indicate that uncertainties of all kinds of measurements including mass flow rate, pressure and temperature are reduced obviously after data reconciliation. The introduction of characteristic constraints for steam turbines improve the redundancy in the system, thus better effect of accuracy improvement by data reconciliation is achieved. Secondly, we carry out data reconciliation to the steam turbine system using 551 groups of steady state operational measured datasets at nominal load in a real-life power plant. Results show that uncertainties of all measurements are also reduced significantly compared with measured uncertainties. Application to operational measured data further indicates the effect of uncer-


tainty reduction for measurements via the generalized data reconciliation approach. Finally, we evaluate the estimates of unmeasured parameters, namely exhaust steam enthalpy and steam wetness fraction after data reconciliation. Since the true values of these unmeasured parameters are unavailable, the uncertainty is not comparable directly based on measured data and reconciled data. However, according to the law of error propagation, the uncertainty of exhaust steam enthalpy and wetness fraction after data reconciliation should be theoretically reduced if the uncertainty of measured data is reduced. Therefore, better estimates of exhaust steam enthalpy and steam wetness fraction are obtained in this work, which is beneficial to the performance monitoring of steam turbine in power plants. We have mainly considered the equality constraint equations in this work. Further research can be carried out to consider inequality constraints as well for better effect via data reconciliation. Acknowledgments The authors gratefully acknowledge the support by Tsinghua University Initiative Scientific Research Program, the Coal-based Key Scientific and Technological Project of Shanxi Province, and the Phase III Collaboration between BP and Tsinghua University. References ASME, 2000. ASME PTC 6A-2000: Steam Turbines Performance Test Codes. American Society of Mechanical Engineers. Badyda, K., 2014. Mathematical model for digital simulation of steam turbine set dynamics and on-line turbine load distribution. Trans. Inst. Fluid-Flow Mach. Cengel, Y.A., Boles, M.A., Kano˘glu, M., 2002. Thermodynamics: an Engineering Approach. McGraw-Hill, New York. Chen, P.-C., Andersen, H., 2005. The implementation of the data validation process in a gas turbine performance monitoring system. In: ASME Turbo Expo 2005: Power for Land, Sea, and Air. American Society of Mechanical Engineers, pp. 609–616. Cooke, D.H., 1985. On prediction of off-design multistage turbine pressures by Stodola’s ellipse. J. Eng. Gas Turbines Power 107, 596–606. Du, L.-P., Tian, R.-F., Liu, X.-Y., Sun, Z.-N., 2013. Numerical simulation and experimental investigation of structural optimization of capacitance sensors for measuring steam wetness with different coaxial cylinders. Nucl. Eng. Des. 262, 88–97. Fuchs, F., 2002. Development and Testing of an Operational Data Validation Method for Thermal Cycles. University of Stuttgart, Stuttgart, Germany. Gülen, S.C., Smith, R.W., 2009. A simple mathematical approach to data reconciliation in a single-shaft combined cycle system. J. Eng. Gas Turbines Power 131, 021601. Guo, S., Liu, P., Li, Z., 2016a. Data reconciliation for the overall thermal system of a steam turbine power plant. Appl. Energ. 165, 1037–1051. Guo, S., Liu, P., Li, Z., 2016b. Inequality constrained nonlinear data reconciliation of a steam turbine power plant for enhanced parameter estimation. Energy 103, 215–230. Huang, B., Bai, Y., Niu, W., 2002. The Principle and Structure of Steam Turbine. China Power Press, Beijing (in Chinese). International Organization for Standardization, 1995. Guide to the Expression of Uncertainty in Measurement. International Organization for Standardization. Jiang, X., Liu, P., Li, Z., 2014a. Data reconciliation and gross error detection for operational data in power plants. Energy 75, 14–23. Jiang, X., Liu, P., Li, Z., 2014b. A data reconciliation based framework for integrated sensor and equipment performance monitoring in power plants. Appl. Energ. 134, 270–282. Jiang, X., Liu, P., Li, Z., 2014c. Gross error isolability for operational data in power plants. Energy 74, 918–927. Jiang, X., Liu, P., Li, Z., 2014d. Data reconciliation for steam turbine on-line performance monitoring. Appl. Therm. Eng. 70, 122–130.

35

Kuehn, D., Davidson, H., 1961. Computer control II. mathematics of control. Chem. Eng. Prog. 57, 44–47. Langenstein, M., 2006. Power recapture and power uprate in NPPS with process data reconciliation in accordance with VDI 2048. 14th International Conference on Nuclear Engineering: American Society of Mechanical Engineers, 7–14. Li, M., Cai, X.-S., Tian, C., Li, J.-F., Qin, S.-X., Ning, D.-L., 2012. Research on the measurement of wet steam in a test steam turbine. Therm. Turbine 2, 004. Martínez-Maradiaga, D., Bruno, J.C., Coronas, A., 2013. Steady-state data reconciliation for absorption refrigeration systems. Appl. Therm. Eng. 51, 1170–1180. Martini, A., Sorce, A., Traverso, A., Massardo, A., 2013. Data reconciliation for power systems monitoring: application to a microturbine-based test rig. Appl. Energ. 111, 1152–1161. Miao, Y., Su, H.-Y., Wang, W., Chu, J., 2011. Simultaneous data reconciliation and joint bias and leak estimation based on support vector regression. Comp. Chem. Eng. 35, 2141–2151. Narasimhan, S., Jordache, C., 1999. Data Reconciliation and Gross Error Detection: An Intelligent Use of Process Data. Gulf Professional Publishing. Özyurt, D.B., Pike, R.W., 2004. Theory and practice of simultaneous data reconciliation and gross error detection for chemical processes. Comp. Chem. Eng. 28, 381–402. Prata, D.M., Schwaab, M., Lima, E.L., Pinto, J.C., 2009. Nonlinear dynamic data reconciliation and parameter estimation through particle swarm optimization: application for an industrial polypropylene reactor. Chem. Eng. Sci. 64, 3953–3967. Srinivasan, S., Billeter, J., Narasimhan, S., Bonvin, D., 2015. Data reconciliation in reaction systems using the concept of extents. In: Krist, V., Gernaey, J.K.H., Rafiqul, G. (Eds.), Computer Aided Chemical Engineering. , pp. 419–424. Sun, W., Chen, S., Niu, L., Hou, Y., 2015. Wetness loss prediction for a wet-type cryogenic turbo-expander based on 3-D numerical simulation. Appl. Therm. Eng. 91, 1032–1039. Szega, M., Nowak, G.T., 2013. Identification of unmeasured variables in the set of model constraints of the data reconciliation in a power unit. Arch. Thermodyn. 34, 235–245. Szega, M., 2009. Advantages of an application of the generalized method of data reconciliation in thermal technology. Arch. Thermodyn. 30, 219–232. Traupel, W., 2013. Thermische Turbomaschinen Band 2: Geänderte Betriebsbedingungen, Regelung, Mechanische Probleme, Temperaturprobleme. Springer-Verlag. Valdetaro, E.D., Schirru, R., 2011. Simultaneous model selection, robust data reconciliation and outlier detection with swarm intelligence in a thermal reactor power calculation. Ann. Nuclear Energy 38, 1820–1832. Vasebi, A., Poulin, É., Hodouin, D., 2012a. Dynamic data reconciliation in mineral and metallurgical plants. Ann. Rev. Control. 36, 235–243. Vasebi, A., Poulin, É., Hodouin, D., 2012b. Dynamic data reconciliation based on node imbalance autocovariance functions. Comp. Chem. Eng. 43, 81–90. Vasebi, A., Poulin, É., Hodouin, D., 2014. Selecting proper uncertainty model for steady-state data reconciliation −Application to mineral and metal processing industries. Miner. Eng. 65, 130–144. Wang, S.-L., Song, T.-H., 2012. The application on the forecast of steam turbine exhaust wetness fraction with GA BP neural network. World Automation Congress (WAC), 2012: IEEE, 1–4. Wang, J., Yang, S., Xu, Z., Song, B., 2002. A Review of the Measurement Technique on the Wetness Fraction of Turbine Exhaust Steam. Intelligent Control and Automation, 2002. Proceedings of the 4th World Congress On: IEEE, 2154–2158. Xu, L., Yuan, J., 2015. Online application oriented calculation of the exhaust steam wetness fraction of the low pressure cylinder in thermal power plant. Appl. Therm. Eng. 76, 357–366. Zhang, Z., Chen, J., 2014. Simultaneous data reconciliation and gross error detection for dynamic systems using particle filter and measurement test. Comp. Chem. Eng. 69, 66–74. Zhang, Z., Chen, J., 2015. Correntropy based data reconciliation and gross error detection and identification for nonlinear dynamic processes. Comp. Chem. Eng. 75, 120–134. Zhang, P., Rong, G., Wang, Y., 2001. A new method of redundancy analysis in data reconciliation and its application. Comp. Chem. Eng. 25, 941–949. Zhang, C.-F., Zhao, N., Wang, H.-J., Chen, Y.-M., Yan, Y.-R., 2007. An on-Line monitoring method of the exhaust steam dryness in steam turbine. Machine Learning and Cybernetics, 2007. International Conference On: IEEE, 437–442. Zhou, W., Qiao, Z., Zhou, J., Si, F., Xu, Z., 2012. A simultaneous data reconciliation and gross error detection method for thermodynamic systems. Zhongguo Dianji Gongcheng Xuebao (Proceedings of the Chinese Society of Electrical Engineering): Chinese Society for Electrical Engineering, 115–121.

Estimation of exhaust steam enthalpy and steam

Estimation of exhaust steam enthalpy and steam

Suggest Documents

steam

Firm's partnership builds up STEAM - STEAM Studio

Firm's partnership builds up STEAM - STEAM Studio

Steam Energy, Steam Lab, Boiler System ...

STEAM CLEANER WITH STEAM GENERATOR IRON

steam trap selection guide - Steam Supply

STEAM CLEANER WITH STEAM GENERATOR IRON

Precise Steam Iron steam/spray shot - pdfstream.manualsonline.com

Maintenance and Overhaul of Steam Turbines - Steam & Power

Steam Tracing

Manual - Steam

Steam Tables

Steam Boilers

STEAM AND CONDENSATE

steam and smoke

manual - Steam

manual - Steam

Steam Tracing

manual - Steam

Steam and VR

Saturated Steam and Water

Estimation of water level and steam temperature using ensemble ...

Professionalism and Management of Steam

Design of Steam Turbines