A data-driven model for the air-cooling condenser of

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error of 0.68 kPa and a correlation coefficient of 0.9675. It is also ... newly-built power plants are in water-scarce areas in Northwest China. ..... 3.2.2. Data reconciliation. For the 3903 steady-state samples selected, data ..... mean absolute error.
A data-driven model for the air-cooling condenser of large-scale coal-fired power plants based on data reconciliation and support vector regression Xiaoen Lia,b, Ningling Wanga, Ligang Wangb,*, Ivan Kantorb, Jean-Loup Robineaub, Yongping Yanga, François Maréchalb a

National Research Center for Thermal Power Engineering and Technology, North China Electric Power University, Beinong Road 2, Beijing 102206, China

b

Industrial Process and Energy Systems Engineering, École Polytechnique Fédérale de Lausanne, Rue de l’Industrie 17, Sion 1951, Switzerland

Abstract The performance of a direct air-cooling condenser under operation is rather complicated, as it is interactively affected by the operating conditions (e.g., the mode of air fan) and the ambient conditions (e.g., temperature and wind speed). To understand the condenser’s real performance under different situations, it is of great importance to investigate the relationship between the back pressure of the steam turbine and the condenser-related variables. However, direct analytical formulation or numerical simulation techniques both suffer from either inaccuracy or prohibitive computation time. In this paper, support vector regression method is applied to establish a data-driven model to express such a non-explicit relationship from the operating data. During raw-data processing, steady-state operation points are firstly identified by time-window method and properly sized for reasonable computational time. Then the reconciliation method is employed to improve the reliability and accuracy of measured data. The results show that the obtained 1

data-driven model agrees well with the testing operation data under various boundary conditions, with a root mean square error of 0.81 kPa, a mean absolute error of 0.68 kPa and a correlation coefficient of 0.9675. It is also concluded that data reconciliation can increase the accuracy and stability of the data-driven model obtained with a reasonable computation time. Key words: air-cooling condenser; data-driven; data reconciliation; support vector regression; coal-fired power plants 1. Introduction In China, fossil fuels, especially coal, will still be a major energy source for power generation in the next decades. In particular, coal-fired power plants will still account for more than 65% of total power generating capacity in China by 2030 [1, 2]. Condensing Rankine cycle based power plants typically require large volumes of cooling water to establish a reasonably low condensing pressure (e.g., 8 kPa) for deep steam expansion, which imposes a significant restriction to geographical selection. This issue could be addressed by replacing water-cooling with air-cooling at the cost of a certain efficiency penalty due to the low heat transfer coefficient of air. Indeed, the water consumption of an air-cooling system is approximately one fifth of that of a water-cooling system. Air-cooling power plants have already been widely deployed in China as approximately 60% of newly-built power plants are in water-scarce areas in Northwest China. However,

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compared to water-cooling, air-cooling systems are susceptible to the ambient conditions of plant operation, e.g., ambient temperature, wind speed and the fouling on the heat transfer surface of the condenser [3]. A high ambient temperature would generally increase the back pressure and thus result in reduced power generation. High wind speeds reduce the air-cooling condenser (ACC) heat transfer coefficient or cause hot plume recirculation [4], even enclosing with wind wall [5]. Achieving consistently high efficiencies in air-cooling power plants requires different operational strategies of the fan array to maintain the optimal condensing pressure under any ambient conditions. However, the optimal condensing pressure depends not only on the plant operating condition but also on the state of components installed such as the turbine efficiency and condition of heat transfer surface. An important fact is that during operation, the optimal condensing pressure is not known which results in rather rough control of fan frequency in most air-cooling power plants. In communication with many on-site operators, common practice is to utilize all fans continuously and to reach a condensing pressure as low as possible by adapting the fan frequency. Thus, a significant need arises to understand the real performance of air-cooling towers, particularly the relationship between operating variables of the condenser and the condensing pressure established. Generally, there are three approaches to analyze the performance characteristics of air-cooling condensers. The first approach, the analytical approach, uses empirical 3

equations for heat transfer or pressure drop calculations, and ACC design data to describe the performance under off-design conditions [6, 7]. Empirical equations are derived from relevant experimental study. For heat transfer relations, many researchers [8, 9] have built experimental correlations of heat transfer coefficients. Kim and Bullard [10] experimentally investigated heat-transfer and pressure-drop characteristics of fins with 45 different geometries. Kumar et. al. [11] summarized the experimental study on the heat transfer characteristics of ACC for investigating the effect of geometric parameters. O’Donovan [12] discussed the qualitative and quantitative relationship between pressure and fan frequency of the considered modular ACC. However, the performance represented by empirical equations and design data may not be accurate, due to performance degradation [13, 14] after a certain period of operation. More importantly, the performance degradation would most likely be very hard to formulate empirically which has not yet been considered in the literature. The second approach is detailed numerical simulation by computational fluid dynamics to investigate the heat and mass transfer phenomenon under various ambient and operating conditions. Chen and Yang [15] studied the performance of a novel layout of air-cooling condensers. Particularly, multi-scale numerical simulations (from mm-scale fin to 100 m-scale air-cooling towers to km-scale environment) have been developed and employed to investigate the effect of ambient wind [16-20]; however, this approach is generally computational 4

expensive and thus not applicable for real-time identification of optimal operation. Additionally, it is difficult for this method to account for unavoidable performance degradation. The third approach utilizes mathematical algorithms such as data mining [21] or artificial intelligence [22] to consider large historical-operation datasets to identify a reliable relationship between given inputs and desired output. The advantage of this approach, compared with the first two approaches, is that high reliability can mostly be guaranteed for interpolation even without detailed equations for illustrating physical phenomena. The reliable relationships identified could be employed to predict the performance of the considered system under different operating conditions [23]. Additionally, the cheaper computational effort makes the approach suitable for online applications. For the application to power plants, Liu [24] discussed the relational degrees of various environmental factors and operating parameters on the back pressure of a direct air-cooling condenser. Du [25] built a neutral network with 249 operating samples to predict the back pressure of ACC, the predicted value agrees well with the actual back pressures when considering weather conditions and wind direction. Liu [26] applied a modified probabilistic support vector regression (SVR) method for monitoring the state of a nuclear power plant along a period of 406 operating days, which is claimed to be informative for the operators in case of accident. This approach, however, requires

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efficient and effective raw-data preprocessing, for example, to remove bad data points. Therefore, in this paper, the relationship between the back pressure and the operating and boundary conditions is investigated by using the third approach with SVR. The novelty of this work is that, in the data preprocessing, the data reconciliation method is employed after steady-state identification to improve the data quality for SVR. This paper is organized as follows: in Section 2, the methodologies of steady-state identification (Section 2.1), data reconciliation (Section 2.2) and SVR (Section 2.3) are introduced. In Section 3, a data-driven model of back pressure is obtained by collecting operating data from a real 660 MW supercritical coal-fired power plant with air-cooling condenser. In Section 4, the model accuracy and the required computational time are discussed to identify the impact of data reconciliation and training data capacity, and to highlight the feasibility for real-time application, respectively. Finally, the conclusions are drawn in Section 5. 2. Methodology In this section, the SVR methodology, the steady-state identification and data reconciliation are introduced in detail. Data reconciliation is employed to correct the measured values by basic energy and mass balances, thus improving the data quality for SVR.

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2.1. Steady-state identification

The input samples for SVR must be steady-state or quasi steady-state, which can be determined by a time-window method (Eq. (1)) [27]: The normalized standard deviation

of the selected state-representative measured parameters

window of N minutes should be less than a given threshold

:

. Note that with a larger threshold value

in a time

(1)

, the number of identified quasi

steady-state samples will be reduced accordingly. Reasonable values of the parameters

and

can be selected from VGB-S-009-S-O-00 [28].

To make the data samples representative for specific operating conditions, an additional time step rule is imposed: starting from the first calculated steady-state sample, the time step between any two neighboring samples from the final selected sample set should be larger than a given value. The selection of proper time step is crucial to reduce the number of samples finally selected at no cost of missing any steady states. Thus, the time step should be generally smaller than the minimum time required for load shifting. With the sample size reduced by such a rule, the computation time can be reduced as well. 2.2. Data reconciliation

The errors of the raw measured values of the selected steady-state samples cannot be avoided, as different types of sensors employed in real-system monitoring have different levels of accuracy. To enhance the reliability of onsite monitoring, 7

measurement redundancy is usually recommended, which can be realized by measuring the same value with several sensors at the same position or at different positions. Data reconciliation takes advantage of this measurement redundancy to remove erroneous measurements and to minimize the measurement errors by imposing the physical constraints of the specific system (e.g., basic mass and energy balances or exergy-related constraints [29]) and thus obtain the most reliable reconciled values. This technique has been successfully applied to performance monitoring [30] and error detection [31] in power plants. Given enough measurement redundancy, a data reconciliation problem can be expressed as follows: for a given number of measured variables

in a system,

the optimization problem is formulated as Eq. (2) and (3) [32]: ,

(2)

,

where the terms The term

and

(3)

are the measured and reconciled values, respectively.

is the standard deviation of the corresponding measured variable,

while the objective function

is the sum of all errors between the reconciled and

measured values. The constraint function

mainly refers to mass and energy

balance equation, and some other physical equations, e.g., exergy. In the constraint function the terms

, the term

is the calculated value of unmeasured variables, while

and

represent the number of measured and unmeasured 8

variables, and the number of constraint equations, respectively. As measurement redundancy is required for data reconciliation, the number of constraint equations should be larger than that of unmeasured variables (

) to solve the

optimization problem in Eq. (2). 2.3. Support vector regression

Support vector regression (SVR) investigates mathematically the best-possible relationship between given inputs vectors

and an output

. For a given input (training)

, the SVR algorithm derives a regression function of

the form shown in Eq. (4) [33]: ,

where

(4)

. The symbols

and

are the weight factor of each support vector and the function bias, respectively. The input vectors x are mapped into a high-dimension space by

. This regression

function can be calculated by minimizing the regularized risk function shown in Eq. (5): (5)

,

where .

A large parameter

(6)

imposes enough penalty to minimize the errors. The term,

, is called the

-insensitive loss function. As expressed in Eq. (6),

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there will not be a penalty if the predicted value is within the error level

. The

Lagrange function of Eq. (5) is shown in Eq. (7) to solve this optimization problem with inequality constraints: ,

(7)

,

where the slack variables

,

(8)

represent the constraint of the output boundary of

the SVR model, as shown in Fig. 1.

Regression function

Fig. 1. Slack variables

and error level

in SVR model (reproduced from [34])

10

A dual form of the optimization problem in Eq. (7) and (8) can be obtained by applying Lagrange multipliers and a standard quadratic programming technique [35]. Finally, the final regression function is derived as Eq. (9): ,

where the symbols product

and

are the calculated Lagrange multipliers. The

is also called kernel function. A most widely used kernel

function, the Gaussian function ( In

(9)

general,

the

input

of

) is applied in this paper. SVR

model

includes

the

and three user-defined parameters and

(in kernel function). The values of

,

and

training ,

vector

(in Eq. (5))

can be determined by

proper derivative-free optimization algorithms such as the grid searching method [36]or evolutionary algorithms [37-42]. In addition, the average root mean square errors (RMSE), mean absolute error (MAE) and the correlation coefficient ensemble error between the output target

are used to describe the and predicted value

when

evaluating the accuracy: ,

(10)

(11)

,

(12)

11

where the symbols

and

covariance between

and

represent the standard deviation and the .

3. Data-driven model of air-cooling condenser It is difficult to predict the back pressure of the ACC, a crucial parameter for power plants, under various ambient conditions. We focus on the establishment of the relationship between the turbine back pressure and variables related of an ACC with its operating data. Five variables, employed to formulate the physical relations in the analytical approach, are selected as input vector: the mass flowrate and enthalpy of exhaust steam, ambient temperature, wind speed and air fan frequency. Among these five variables, the mass flowrate and enthalpy of exhaust steam cannot be measured directly onsite; thus, to have these two variables calculated as reliably as possible, data reconciliation is employed to improve the data quality before training the data-driven model by SVR. 3.1. Plant and measurement description

A 660 MW air-cooling, single-reheat, supercritical pulverized coal-fired power plant located in Northwest China is considered, and is represented schematically in Fig. 2. The ACC is comprised of 56 air-cooling modules with a nominal exhaust mass flowrate of 1255.7 t/h and a nominal back pressure of 15 kPa. Note that the frequencies of all air fans are kept the same during real plant operation.

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Fig. 2. The schematic of the power plant with air-cooling condenser (The red, green and white markers represent measurement points for pressure, temperature and mass flowrate, respectively. The symbols, p, t and , stand for pressure, temperature and mass flowrate, respectively.)

The main steam (stream 1, 24.2 MPa/ 566 ℃) generated in the boiler is expanded in the high-pressure turbine (HPT1-2) and is reheated afterwards. The reheated steam (stream 4, 4.28 MPa/ 566 ℃) then expands through the intermediate-pressure (IPT1-2) and low-pressure turbines (LPT1-4), and is finally condensed in the air-cooling condenser (ACC). For each turbine stage, a certain amount of steam is extracted for heating up feedwater in the feedwater preheater (FWPHi) before entering the boiler. In addition, a de-aerator (DA) is also equipped to remove dissolved gas in the feedwater. As shown in Fig. 2, there are 41 streams in total. As no mixture is involved, the mass flowrate, pressure and enthalpy are enough for each stream to specify its thermodynamic state. Hence, there are 124 variables in this turbine system in total, 13

including the electric generator output (

). Among all stream variables, there are

41 which are measured and recorded in the Supervisory Information System (SIS) in the real system. These measurement points have been described in detail in Table A1 in the appendix, including the design data and measurement accuracy (error standard deviations). Note that some streams with small mass flowrate, such as steam leakage and reheat spray water, are not illustrated in Fig. 2. The corresponding measured variables and constraint equations are also not listed in Table A1 and Table A2. For each of these less important streams, the number of corresponding measured variables plus the number of the corresponding constraint equations should be larger than 3 to specify its mass flow, pressure and enthalpy. Particularly, the mass flowrate and temperature of the reheat spay are measured on site, while the mass flowrate of steam and water leakage, usually proportional to the load according to the manufacturing manual, can be treated as pseudo measurements [31]. 3.2. Data-driven model

Based on the historical operation data, the data-driven model is built in this section for describing the relationship between the five input variables and the back pressure. For data processing before SVR, the transient operation data should be removed first; then, for each of the identified steady-state periods, data reconciliation is employed to improve the quality (reliability) of the training dataset. 14

3.2.1. An overview of the historical operation database Variables

Samples

For data reconciliation

Turbine system (41)

. mex hex

For SVR (6) ffan tair,in Vwind

pback

Used for training the model (3500)

Used for testing the accuracy (403) Time step smaller than 5 minutes (16729)

Unsteady state (20632)

Missing value and outliers (704)

Fig. 3. An overview of data processing for the data-driven model

The overview of how the entire historical operation database was used is illustrated in Fig. 3. The squares in the horizontal direction represent the measured variables for each sample (time) in the vertical direction. How these variables were used will be explained in detail in Section 3.2.2 and 3.2.3. The samples used in this work were gathered every 60 s in September 2015 from the SIS. In total, 43 200 samples

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were recorded in September. Among all samples, 704 were discarded as these samples contained missing values or outliers due to sensor fault or equipment maintenance, thus the remaining 42 496 samples were considered as valid. For the identification of (quasi) steady-state samples by the time window method, we select the mass flowrate of condensed water ( generator output (

) and the gross electric

) as two representative parameters for steady state as

discussed in. Fig. 4 illustrates an example of steady-state sample identification from one-day operating data with a time-window length of 15 minutes and a time step of 5 minutes (see Section 2.1). Note that for clear illustration, in Fig. 4, only the profiles related to

are presented. The blue line is the

from the raw

valid operation data points. The gray line represents the standard deviation

of

calculated by Eq. (1). A commonly-used value (0.015, the yellow line) is specified as the threshold value

. With the application of the time step rule, the

black triangle points with the standard deviation of

and

below 0.015 are

identified as the representative steady-state operating points. Note that some samples between 8:00 to 9:00 in Fig. 4 are not regarded to be steady state due to the variation of the measurement

.

16

700

0.1

600

Selected samples 0.08

Standard deviation of E75 500

Standard deviation = 0.015 0.06

400 300

0.04

200

Standard deviation

Electric generator output (MW)

Gross electric output (E75)

0.02 100 0 20:00

0:00

4:00

8:00

12:00

16:00

0 20:00

Time for one day

Fig. 4. An example of selecting quasi steady-state in one day with a time-window length of 15 minutes and a time step of 5 minutes between any two neighboring selected samples

With the same approach applied to the whole month, 20 632 out of 42 496 samples were discarded as their standard deviations were larger than the threshold value. Eventually, by applying the time step rule, only 3903 representative samples remained to create the data-driven model. Note that 90% of the selected steady-state samples (3500 samples) were used for training the data-driven model with the SVR method, while the remaining 10% (403 samples) were used for testing the accuracy of the trained model. 3.2.2. Data reconciliation

For the 3903 steady-state samples selected, data reconciliation was employed to identify the unmeasured crucial variables and to improve the data quality. In particular, the two crucial variables relevant to back pressure, the enthalpy of exhaust steam (

) and the mass flowrate of exhaust steam (

), are 17

difficult to measure. As the exhaust steam out of LPT4 is within the wet steam region, the corresponding enthalpy or steam dryness cannot be calculated directly by pressure and temperature. However, the enthalpy

could be calculated

indirectly by the energy balance [43]: , where the enthalpy

--

and the mass flowrate

--

(13)

are reconciled with

minimum errors in data reconciliation process. Besides, the mass flowrate of exhaust steam (

) is not measured since the

exhaust flow is with a rather large flowrate and in the wet steam zone, which leads to large exergy destruction if adding a measurement device. The mass flowrate could be calculated indirectly by using the mass flowrates after the condensate and feedwater pumps (

and

), since all mass flowrates are

subjected to mass balance equation after data reconciliation. As described in Section 3.1, there were 124 variables involved in the considered system, among which 41 are measured. The two crucial variables

and

were included in the remaining 83 unmeasured variables. In total, 103 constraints equations were considered as listed in Table A2 in the Appendix. Hence, the condition of having more constraints than unmeasured variables is fulfilled. 19 redundant measurements existed for better reconciled values, as calculated in Eq. (14) and (15):

18

,

(14) .

(15)

Note that the rank of the set of 103 equations is 102, as the flowsheet of power plant has one loop and one of the mass balance equations is redundant. Then, data reconciliation was performed on each of the 3903 samples with the software Ebsilon Professional. 3.2.3. SVR method for ACC

The SVR method was applied to train the model on the relation between the back pressure and the input vector. Fundamentally, all variables involved in the system could be used as the input vector; however, for reasonable computational time and accuracy, the input vector should be selected properly. Usually, the input vector can be determined based on the physical models used in the analytical approach. The analytical formulation for modeling an ACC are usually given as follow: ,

(16)

,

(17) ,

where the terms water;

and

and

(18)

represent the temperature and enthalpy of condensed

stand for the face velocity and frontal area; the terms

and

indicate the density and the specific heat capacity of ambient air at constant

19

pressure; while the symbols total heat transfer area;

and F are the total heat transfer coefficient and the is number of transfer units.

The performance of the ACC represented by Eq. (16) - (18) at the specific design conditions is illustrated in Fig. A1 [44]. However, these equations can hardly be applicable for complicated off-design conditions for the following reasons: (1) Most power plants do not install the instruments for measuring the face velocity

in real-time. Air fan frequency and ambient wind speed would

influence the face velocity in a complex way and is mainly studied through numerical simulation. However, the accuracy of many numerical simulations cannot be ensured. (2) After years of operation, the performance degradation of all components involved naturally occurs, thus the original design characteristics of ACC become invalid. Particularly, due to the fouling on the surface of fin-tube bundles the fin efficiency, fouling coefficient and the heat transfer coefficient become difficult to calculate. (3) The coefficients

and

in

for calculating the heat transfer

coefficient depend highly on the shape and the condition of fin-tube. Based on the related analytical formulations (Eq. (16) - (18)), we simply consider the back pressure

as a function of the five variables: ,

(19)

20

where the input variables,

are fan frequency, ambient

temperature, wind speed, the mass flowrate and enthalpy of the exhaust steam leaving the last turbine stage. The mass flowrate

and enthalpy

the heat rejection in the condenser,

. The parameters

reflect the face velocity,

represent and

. Thus, the selected variables have abundant

information for reflecting the relationship between the back pressure

and

the input variables. 4. Result and discussion In this section, the accuracy of data-driven model, the significance of data reconciliation, the impact of training-data capacity and the required computational time are discussed in detail. 4.1. The data-driven model

Ninety percent of the reconciled steady-state samples were used for training the model and are represented in Fig. 5, where the back pressure is plotted against mass flowrate of the exhausted steam and ambient temperature. As the external interpolation is less reliable for SVR method, the range of each input variable should be investigated, as listed in Fig. 5. The operating condition ranges from 50% load (around 710 t/h) to full load (around 1370 t/h). Around full-load operation, the fan frequency usually reaches its maximum value; thus, the ambient temperature has important influence on the level of back pressure: the back pressure increases obviously with the increase of ambient temperature. However, during part-load 21

operation, the fan frequency is adjusted to keep the back pressure at a low level even at a relatively high ambient temperature. 28 Ambient temperature (C) 30.00

26

27.00 24 24.00

Back pressure (kPa)

22

21.00

Mass flow of exhaust steam : 710.5 t/h - 1371.1 t/h Back pressure : 9.7 kPa - 26.1 kPa Ambient temperature : 9.4 C - 29.7 C Fan frequency : 24.3 Hz - 55 Hz Enthalpy of exhaust steam : 2387 kJ/kg - 2604 kJ/kg

18.00

20

15.00 18 12.00 16

9.000

14

12

10

8 700

800

900

1000

1100

1200

1300

1400

Mass flow of exhaust steam (t/h)

Fig. 5. The reconciled data points for training the SVR model

The prediction for the remaining 10% of the reconciled operation data is illustrated in Fig. 6 and Fig. 7. In particular, the parity plot in Fig. 7 indicates that a good agreement is reached with a RMSE of 0.811 kPa, a MAE of 0.680 kPa, and a of 0.9675.

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Fig. 6. The reconciled data points and the corresponding prediction

23

Fig. 7. Parity plot of the 10% reconciled operation data points and corresponding predicted value

So far, the data-driven model of ACC is obtained based on the historical operating data, which can be used as an off-design model under various boundary conditions. The future work is to establish an off-design model of the steam-turbine subsystem with the operating data in the form of Eq. (20): .

(20)

With a combination of Eq. (19) and (20), the optimum back pressure would be calculated in off-design case as shown in Eq. (21):

24

,

where the parameter

and

(21)

are the gross electric output of generator

and the electric consumption of air fan. 4.2. Comparison of the data-driven model with and without data reconciliation process

To evaluate the effect of data reconciliation in the data-driven model, another SVR model with un-reconciled measurements and no physical constraints was built as follows: .

In this model, instead of using and pressure (

and

, the measured mass flowrate (

(22)

)

) of the main steam is employed to show the advantages of data

reconciliation process. The main steam parameters rather than exhaust steam are used here mainly in these reasons: (1) Without data reconciliation, the value of of

,

,

or

calculated by the mass balance

is slightly different from the one obtained by data

reconciliation, which is more reasonable by using this redundant measurement information. (2) Without data reconciliation, some intermediate parameters may be out of range in several cases, when calculating the enthalpy enthalpy

. For instance, as the

is calculated by Eq. (13) , the dryness of exhaust steam may

reach 1 due to an inaccurate mass flowrate. Besides, the isentropic efficiency of the turbines might be over 1, which can be avoided by employing the auxiliary 25

measuring points (

and

in this case) or by adding an inequality

constrained equation in data reconciliation. Thus, it’s generally not wise to use a group of

and

with wrong intermediate parameters to train the

model. To show the effect of data reconciliation, we use the same 90% data points for training the model and the same 10% data for testing. Fig. 8 shows the accuracy of the model without data reconciliation: The RMSE (1.312 kPa) and MAE (1.042 kPa) of the prediction are much larger with the same points. Note that for the condensing power plant, the variation of the back pressure imposes great influence on the plant efficiency. Thus, the back pressure identified without data reconciliation indeed has been far from the one obtained with data reconciliation. Although the

and

are also related to the exhaust steam, the

prediction accuracy cannot be as high as the one using

and

. The lower

accuracy of the model is mainly due to two reasons: first, the exhaust steam is physically the direct incoming stream of the ACC, changes in which obviously have larger impacts on the ACC performance. Second, data reconciliation increases the reliability of the measured variables, while the measured value of the main steam may have large deviation itself especially after years of operation. It is thus concluded that data reconciliation generally makes the data-driven model more robust and stable.

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Fig. 8. Parity plot of the 10% un-reconciled operation data points vs. corresponding predicted value (the non-homogenous distribution of regression error between low- and high-backpressure data is led to by the interaction of several factors, e.g., the nature of SVR formulation itself, the non-homogenous distribution of inaccuracy and uncertainty of measurement instrument, and the test data) 4.3. Influence of the training data capacity

The above calculation employs 90% operating data to train the model, which may be conservative. Indeed, a smaller capacity of the training data may be already capable of delivering good accuracy, while the computation time can be largely reduced, which is much more preferred for real-time application. Another aspect determining the capacity of the training data is how long the prediction is expected 27

to be. In general, a longer prediction would require a larger capacity of training data with various boundary conditions. Also, the training data must be updated with the latest operating data when the obtained model accuracy is no longer satisfactory, which indicates the training data cannot reflect the current state of the plant any more. In this section, particularly, the optimal capacity of the training data with a fixed prediction period is investigated for the case study. Five training models (Fig. 9) are performed with different capacities of training data (10% to 90% of the total samples) to predict the same period operation (last 3 days of September). The latest samples before the prediction period are selected. For example, for the case with 10% training data capacity, the 10% reconciled samples closest to September 27 are selected. This is because the closer the training samples to the prediction period, the better plant state can be represented. Clearly from Fig. 9, with the increased capacity of training data covering more different boundary conditions, the model accuracy increases with the RMSE dropping from 2.16 kPa (10%) to 0.81 kPa (90%). However, the accuracy increase becomes very small after the capacity of training data reaches around 50% of the total reconciled samples. The identification of the optimal capacity of the training data is of great importance to reduce total computational time for real-time application.

28

6

The period used for testing

Date

Sep. 10

RMSE

4

Sep. 15 Sep. 20

2

RMSE of testing result (kPa)

The period used for training

Sep. 5

Sep. 25 Sep. 30

0 10% 30% 50% 70% 90% The percentage of data used for training in September

Fig. 9 The influence of training data capacity 4.4. Computation time

For real-time application of the data-driven model for state monitoring of the power plant, the computational time is a crucial factor. The most time-consuming part comes from the training of the model and depends largely on the number of samples. The computational time on data reconciliation and the cross validation for training SVR model is shown in Fig. 10. For data reconciliation, the samples were reconciled individually and, for each sample with the same problem size, the time requirement was almost identical (around 1 s), thus the computation time increased linearly with the number of samples. For sample sizes between 500 and 8000, the cross-validation process for training the SVR model was performed five times and the average time is shown in Fig. 10. The time required for cross validation increases exponentially with the number of samples. This was the major reason for

29

using a time step of 5 minutes to choose steady-state operation data points (Section 3.2.1), as this reduced the number of data points from 20 000 to 4 000, leading to a much faster training. 180 Time consumed by data reconciliation

Computation time / min

150

Average time for training SVR model 120 90 60 30 0

0

2000

4000 The number of samples

6000

8000

Fig. 10. Computation time consumed by data reconciliation and the average cross-validation time for training the SVR model (Intel Xeon CPU E5-2400 2.1GHz, RAM 12GB)

5. Conclusions In this paper, the SVR method was applied to derive a data driven model for the back pressure of the steam turbine from historical operating data to express the characteristics of ACC under real operation. Based on the analytical formulations, the fan frequency, ambient temperature, wind speed, the mass flowrate and enthalpy of exhaust steam were chosen as the input vector. Data reconciliation and the time-window method were employed to identify a set of steady-state operation samples with higher accuracy and reliability. The support vector regression method was then employed to derive the best model. Such a data-driven model is useful to

30

guide the optimal operation of the air fan under different operating and climatic conditions to maintain the optimal vacuum for the steam turbine. The main conclusions of the paper include: 

At full-load operation, the ambient temperature was the dominating factor affecting the back pressure of the steam turbine, while in partial load operation, fan frequency imposed greater influence.



The trained data-driven model agreed well with the actual operating data under various ambient and operating conditions. The employment of data reconciliation to correct the raw measured data improved the model accuracy and reliability (the correlation coefficient of the predicted data with the reconciled operational data increased by 5.3%).



The computation time to derive such a data-driven model was mainly due to cross-validation to identify the best kernel function and data reconciliation. For the case study handling one month of operating data, the total computation time was 1.5 hours, indicating that the approach can be promising for online application.

Moreover, to complete this approach and make it usable in power plants it would be necessary to understand how large the training database should be and when should the model to be updated due to the changing of ambient condition or fouling of the ACC.

31

Acknowledgement The research work is supported by the National Basic Research Program (973 Program) (2015CB251505),

National Key Technology Support Program

(2014BAA06B02), Fundamental Research Funds for the Central Universities (2015MS43, 2015XS81, 2014XS19, 2014XS13). The author, Xiaoen Li, also thanks the China Scholarship Council (CSC) for supporting his research in Industrial Process and Energy Systems Engineering at École Polytechnique Fédérale de Lausanne. Nomenclature ACC

air-cooling condenser

DA

deaerator

FWPH

feed-water preheater

G

generator

HPT

high pressure turbine

IPT

intermedia pressure turbine

LPT

low pressure turbine

MAE

mean absolute error

RMSE

root mean square error

SIS

supervisory information system

SVR

support vector regression

32

correlation coefficient pressure, MPa temperature, ℃ mass flow, t/h enthalpy, kJ/kg Reynolds number Nusselt number the number of samples the number of measured variables the number of unmeasured variables the number of constraint equations reconciled values of th measured variables calculated value of unmeasured variables x

input vectors weight of the support vectors

b

bias of the support vectors penalty parameter in SVR total heat transfer coefficient, W/(m2·K) total heat transfer area, m2 face velocity, m/s

33

frontal area, m2 specific heat capacity, kJ/(kg·K) number of transfer units frequency of air fan, r/min wind speed, m/s

Greek letters slack variables in SVR error level in SVR parameter in kernel function of SVR objective function in data reconciliation standard deviation of the measured variables density, kg/m3

Subscripts and superscripts ex

exhaust steam

main

main steam

in

inlet

out

outlet

gross

gross electric power

34

c

condensed water

T

matrix transposition

35

Appendix Table A1.

Description of measured variables

Symbol

Description

Unit

THA

660.0

Error standard deviations 0.5

1

E75

Electric generator output

MW

2

p1

Main steam pressure

MPa

3 4

t1 p11

Main steam temperature 1# Extracted-steam pressure

5

t11

6 7 8

Symbol

Description

Unit

THA

Inlet mass flowrate of the main steam

t/h

1956.6

Error standard deviations 20

22

24.2

0.03

23

Outlet mass flowrate of the condenser pump Inlet mass flowrate of Da Outlet mass flowrate of feedwater pump

t/h

1427.7

10

℃ MPa

566 7.277

1 0.02

24 25

t/h t/h

1472.7 1956.6

10 12

1# Extracted-steam temperature



381.8

1

26

t20

Outlet temperature of condenser pump



55.1

0.8

p12

2# Extracted-steam pressure

MPa

4.765

0.02

t12 p4

2# Extracted-steam temperature Reheat steam pressure

℃ MPa

323.8 4.288

1 0.02

27

t21

Outlet temperature of FWPH7



100.5

0.8

28 29

t22 t23

Outlet temperature of FWPH6 Outlet temperature of FWPH5

℃ ℃

122 142.4

0.8 0.8

9

t4

Reheat steam temperature



566

10

p13

3# Extracted-steam pressure

MPa

2.359

1

30

t25

Inlet temperature of feed water pump



192.4

1

0.02

31

t26

Inlet temperature of FWPH3



218.2

1

11 12

t13 p14

3# Extracted-steam temperature 4# Extracted-steam pressure

℃ MPa

473.6 1.221

1 0.02

32 33

t27 p28

Inlet temperature of FWPH2 Outlet pressure of FWPH1

℃ MPa

259.1 28

1 0.03

13 14

t14 p6

15

p15

4# Extracted-steam temperature Inlet pressure of low pressure turbine 5# Extracted-steam pressure

℃ MPa

376.8 1.197

1 0.02

34 35

t28 t29

Outlet temperature of FWPH1 Drain-water temperature of FWPH1

℃ ℃

288 264.7

1 1

MPa

0.44

0.01

36

t30

Drain-water temperature of FWPH2



232.8

1

16 17

t15 p16

5# Extracted-steam temperature 6# Extracted-steam pressure

℃ MPa

225.4 0.243

1 0.01

37 38

t31 t32

Drain-water temperature of FWPH3 Drain-water temperature of FWPH5

℃ ℃

198 127.6

1 0.8

18 19

t16

6# Extracted-steam temperature



191.3

1

39

t33

Drain-water temperature of FWPH6



106.1

0.8

p17

7# Extracted-steam pressure

MPa

0.12

0.01

40

t34

Drain-water temperature of FWPH7



60.7

0.8

20 21

t17 p10

7# Extracted-steam temperature Back pressure

℃ kPa

123.5 15

0.8 0.05

41

p38

Inlet pressure of DA

MPa

1.18

0.02

1 20

23 25

36

Table A2.

The constraint equations of turbine system of data reconciliation

problem Equipment

Equation

Equation number

Boiler

2

HPT1-LPT3

3*7

LPT4

1

G

1

ACC

3

FWPH1-3 and

7*6

FWPH5-7

DA

5

CWP, FWP

2*2

Pipe

3*7

Mix

3

37

103

59 54 49

Back pressure / kPa

44 39

t=4℃

Ambient pressure: 86.75 kPa

t=7℃ t = 10 ℃

100% mass flow of exhaust steam: 1236.6 t/h

t = 15 ℃

Fan speed: 67.6 r/min

t = 20 ℃ t = 25 ℃ t = 30 ℃

t = 35 ℃ 34

t = 40 ℃

29 24 19 14 9 80%

85%

90% 95% 100% 105% 110% Mass flow percentage of exhaust steam

115%

120%

Fig. A1. Performance characteristics of ACC based on empirical equation and designed data in summer condition

38

References [1] P. Fu, N. Wang, L. Wang, T. Morosuk, Y. Yang, G. Tsatsaronis, Performance degradation diagnosis of thermal power plants: A method based on advanced exergy analysis, Energy Conversion and Management, 130 (2016) 219-229. [2] L. Wang, P. Fu, N. Wang, T. Morosuk, Y. Yang, G. Tsatsaronis, Malfunction diagnosis of thermal power plants based on advanced exergy analysis: The case with multiple malfunctions occurring simultaneously, Energy Conversion and Management, 148 (2017) 1453-1467. [3] D.G. Kröger, Air-cooled heat exchangers and cooling towers, Stellenbosch Stellenbosch University, 6 (2004) 96. [4] J.G. Bustamante, A.S. Rattner, S. Garimella, Achieving near-water-cooled power plant performance with air-cooled condensers, Applied Thermal Engineering, 105 (2016) 362-371. [5] L. Yang, X. Du, Y. Yang, Improvement of thermal performance for air-cooled condensers by using flow guiding device, Journal of Enhanced Heat Transfer, 19 (2012) 63-74. [6] J. Liu, Y. Hu, D. Zeng, W. Wang, Optimization of an air-cooling system and its application to grid stability, Applied Thermal Engineering, 61 (2013) 206-212. [7] W.F. He, Y.P. Dai, J.F. Wang, M.Q. Li, Q.Z. Ma, Performance prediction of an air-cooled steam condenser using UDF method, Applied Thermal Engineering, 50 (2013) 1339-1350. [8] J. Yang, H. Zhang, Experimental Research on Heat Transfer Performance for Finned-tubes of Direct Air-cooled Condensers, Proceedings of the Csee, 32 (2012) 74-79. [9] H. Chen, J.R. Lai, Study of heat-transfer characteristics on the fin of two-row plate finned-tube heat exchangers, International Journal of Heat & Mass Transfer, 55 (2012) 4088-4095. [10] M.H. Kim, C.W. Bullard, Air-side thermal hydraulic performance of multi-louvered fin aluminum heat exchangers, International Journal of Refrigeration, 25 (2002) 390-400. [11] A. Kumar, J.B. Joshi, A.K. Nayak, P.K. Vijayan, A review on the thermal hydraulic characteristics of the air-cooled heat exchangers in forced convection, Sadhana, 40 (2015) 673-755. [12] A. O’Donovan, R. Grimes, J. Moore, The Influence of the Steam-side Characteristics of a Modular Aircooled Condenser on CSP Plant Performance, Energy Procedia, 49 (2014) 1450-1459. [13] L. Wang, Y. Yang, T. Morosuk, G. Tsatsaronis, Advanced Thermodynamic Analysis and Evaluation of a Supercritical Power Plant, Energies, 5(6) (2012) 1850-1863. [14] L. Wang, Y. Yang, C. Dong, Z. Yang, G. Xu, L. Wu, Exergoeconomic Evaluation of a Modern Ultra-Supercritical Power Plant, Energies, 5 (2012) 3381-3397. [15] L. Chen, L. Yang, X. Du, Y. Yang, A novel layout of air-cooled condensers to improve thermo-flow performances, Applied Energy, 165 (2016) 244-259. [16] L. Yang, X. Du, Y. Yang, Influences of wind-break wall configurations upon flow and heat transfer characteristics of air-cooled condensers in a power plant, International Journal of Thermal Sciences, 50 (2011) 2050-2061. [17] C. Butler, R. Grimes, The effect of wind on the optimal design and performance of a modular air-cooled condenser for a concentrated solar power plant, Energy, 68 (2014) 886-895. [18] K. Duvenhage, D.G. Kröger, The influence of wind on the performance of forced draught air-cooled heat exchangers, Journal of Wind Engineering & Industrial Aerodynamics, 62 (1996) 259-277. [19] M. Owen, D.G. Kröger, Contributors to increased fan inlet temperature at an air-cooled steam condenser, Applied Thermal Engineering, 50 (2013) 1149-1156. [20] J.R. Bredell, D.G. Kröger, G.D. Thiart, Numerical investigation of fan performance in a forced draft air-cooled steam condenser, Applied Thermal Engineering, 26 (2006) 846-852. [21] N. Wang, P. Fu, D. Chen, Z. Yang, Y. Yang, Application of Big Data Analytics in Plant-level Load Dispatching of Power Plant, Proceedings of the Csee, 35 (2015) 68-73. [22] F. Rossi, D. Velázquez, I. Monedero, F. Biscarri, Artificial neural networks and physical modeling for determination of baseline consumption of CHP plants, Expert Systems with Applications, 41 (2014) 4658-4669.

39

[23] N. Wang, P. Fu, H. Xu, D. Wu, Z. Yang, Y. Yang, Heat transfer characteristics and energy-consumption benchmark state with varying operation boundaries for coal-fired power units: An exergy analytics approach, Applied Thermal Engineering, 88 (2015) 433-443. [24] L. Liu, X. Du, X. Xi, L. Yang, Y. Yang, Experimental analysis of parameter influences on the performances of direct air cooled power generating unit, Energy, 56 (2013) 117-123. [25] X. Du, L. Liu, X. Xi, L. Yang, Y. Yang, Z. Liu, X. Zhang, C. Yu, J. Du, Back pressure prediction of the direct air cooled power generating unit using the artificial neural network model, Applied Thermal Engineering, 31 (2011) 3009-3014. [26] J. Liu, R. Seraoui, V. Vitelli, E. Zio, Nuclear power plant components condition monitoring by probabilistic support vector machine, Annals of Nuclear Energy, 56 (2013) 23-33. [27] S. Guo, P. Liu, Z. Li, Data reconciliation for the overall thermal system of a steam turbine power plant, Applied Energy, 165 (2016) 1037-1051. [28] V. PowerTech, VGB standard: application of measurement data validation according to VDI 2048, in, VGB-S-009-SO-00. Essen, Germany, 2012. [29] S. Guo, P. Liu, Z. Li, Inequality constrained nonlinear data reconciliation of a steam turbine power plant for enhanced parameter estimation, Energy, 103 (2016) 215-230. [30] M.S. Syed, K.M. Dooley, F. Madron, F.C. Knopf, Enhanced turbine monitoring using emissions measurements and data reconciliation, Applied Energy, 173 (2016) 355-365. [31] X. Jiang, P. Liu, Z. Li, Data reconciliation and gross error detection for operational data in power plants, Energy, 75 (2014) 14-23. [32] C. Jordache, C. Jordache, Data reconciliation & gross error detection: an intelligent use of process data, Gulf Publishing Co., 123 (17) (1999) 1121-1128. [33] V. Kecman, Learning and Soft Computing: Support Vector Machines, Neural Networks, and Fuzzy Logic Models, 47 (2002) 305-307. [34] K.H. Yoo, J.H. Back, M.G. Na, J.H. Kim, S. Hur, C.H. Kim, Prediction of golden time using SVR for recovering SIS under severe accidents, Annals of Nuclear Energy, 94 (2016) 102-108. [35] D.P. Bertsekas, Constrained optimization and Lagrange multiplier methods, (1982) 383-392. [36] C.-C. Chang, C.-J. Lin, LIBSVM: a library for support vector machines, ACM Transactions on Intelligent Systems and Technology (TIST), 2 (2011) 27. [37] L. Wang, Thermo-economic evaluation, optimization and synthesis of large-scale coal-fired power plants, in, Ph. D. thesis Technical University of Berlin, 2016. [38] L. Wang, Y. Yang, C. Dong, T. Morosuk, G. Tsatsaronis, Parametric optimization of supercritical coal-fired power plants by MINLP and differential evolution, Energy Convers. Manage., 85 (2014) 828-838. [39] L. Wang, P. Voll, M. Lampe, Y. Yang, A.e. Bardow, Superstructure-free synthesis and optimization of thermal power plants, Energy, 91 (2015) 700-711. [40] L. Wang, Y. Yang, C. Dong, T. Morosuk, G. Tsatsaronis, Multi-objective optimization of coal-fired power plants using differential evolution, Appllied Energy, 115 (2014) 254-264. [41] L. Wang, M. Lampe, P. Voll, Y. Yang, A. Bardow, Multi-objective superstructure-free synthesis and optimization of thermal power plants, Energy, 116 (2016) 1104-1116. [42] E. Yao, H. Wang, L. Wang, G. Xi, F. Maréchal, Multi-objective optimization and exergoeconomic analysis of a combined cooling, heating and power based compressed air energy storage system, Energy Conversion and Management, 138 (2017) 199-209. [43] L. Xu, J. Yuan, Online application oriented calculation of the exhaust steam wetness fraction of the low pressure cylinder in thermal power plant, Applied Thermal Engineering, 76 (2015) 357-366. [44] X. Li, N. Wang, P. Fu, Y. Yang, Characteristic Study on Optimal Vacuum of a Direct Air-cooling System Under Summer Conditions, Journal of Chinese Society of Power Engineering, 11 (2016) 927-933.

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Highlights 1. A data-driven model of the air-cooling condenser by support vector regression 2. Data reconciliation for quality improvement of identified steady-state operating data 3. The derived model performs well under various ambient and operating conditions

41