Statistical modeling of an integrated boiler for coal fired thermal power plant.

The coal fired thermal power plants plays major role in the power production in the world as they are available in abundance. Many of the existing power plants are based on the subcritical technology which can produce power with the efficiency of around 33%. But the newer plants are built on either supercritical or ultra-supercritical technology whose efficiency can be up to 50%. Main objective of the work is to enhance the efficiency of the existing subcritical power plants to compensate for the increasing demand. For achieving the objective, the statistical modeling of the boiler units such as economizer, drum and the superheater are initially carried out. The effectiveness of the developed models is tested using analysis methods like R2 analysis and ANOVA (Analysis of Variance). The dependability of the process variable (temperature) on different manipulated variables is analyzed in the paper. Validations of the model are provided with their error analysis. Response surface methodology (RSM) supported by DOE (design of experiments) are implemented to optimize the operating parameters. Individual models along with the integrated model are used to study and design the predictive control of the coal-fired thermal power plant.

Introduction

Electricity is the most essential thing in the day-to-day life of everyone in this active world. Without electricity this contemporary world cannot last even for a moment. The difference between energy source and demand is always present and it requires foremost consideration. To overcome the scenario of the difference between the supply and demand, the efficiency of the existing power plants need to be taken care and also the newer power plants need to be established with the supercritical technology. Nearly 41% of power is obtained through coal-fired thermal power plants. Efficiency of the subcritical plants can be improved in the following ways: a) to improve the quality of coal; b) proper air fuel ratio for the combustion; c) to avoid pressure drop between the oiler units etc. To achieve this, proficient simulations of individual units need to be built to examine the reliability of the variables of interest on a set of independent variables. Boiler of the subcritical power plant consists of combustion chamber, economizer, drum, superheater and reheater. All these units are interrelated to each other such that changes in one unit affect the performance of the another unit. Statistical analysis of the units of power plant is not well established and this motivated to build the regression model for the individual boiler unit (economizer, drum and superheater) and the integrated unit. Data driven models based on real time data can be helpful in analyzing performance of the existing plant. This type of model is based on computational intelligence for investigating the state variables of system without the awareness of their physical behavior.

Modeling of the boiler drum of the coal-fired thermal power plant through the mass balance and energy balance was initiated by Astrom and Bell [1] and Astrom and Eklund [2]. The different control configurations for the developed model was studied and compared by them.

Richard [3] proposed for the improvement of the components of the prevailing plant to increase the efficiency of the coal-fired power plant instead of swapping it with the new skills. Flynn [4] discussed the types of thermal power plant and their individual component. The modeling and the computer simulation with different control structures for the power plant model are analyzed by the author. The overview of the modeling of individual units and the integrated units of coal-fired and gas-fired thermal power plant and several simulation methods have been presented by Lu [5]. The derivation of pressure equation and the temperature equations of boiler units using physical laws are presented in [6] and [7]. Data driven model based on artificial neural network (ANN) has been proposed by Smrekar et al. [8] and [9] for the estimation of power output and main steam properties of the power plant. It was proved that the proposed model can provide better results with minimal number of parameter compared to the physical model.

Another type of modeling based on plant data is the statistical modeling technique. It helps to develop relation between the independent variables and dependent variables. Douglas [10], Scott and Jeremy [11] discussed on the regression model and their usage on the process industry to predict the product outcome of the plant. It also contains the types of regression equations applicable for the linear process, nonlinear process and multivariable process. The regression models are developed keeping in mind that the residual between the plant and the model are normally distributed. Different type of statistical model called MAID-M was proposed by Martin and Maynard [12] to predict the model of the plant. Algorithm for the iterative predictive modeling for the interrelated response and the study of its performance is proposed by Tom et al. [13]. This method uses the partial least square method and the logistic regression to find the parameters of the model. Richard and William [14] collected data from the plant and assumed linear model for it. The parameters of the model were identified using Maximum Likelihood Estimator (MLE) method. The comparison between the identified model and the plant output were analyzed using R2 analysis, which gives the degree of fit of the model.

Multiple linear regression analysis of the geothermal power plant model was developed to estimate the performance of the power plant by Murat et al. [15]. Later Ulrik et al. [16] developed four multiple regression model for the prediction of the efficiency of the organic Rankin cycle of the thermal power plant. The regression model developed by them showed better result compared to the models available in the literature. The model for the production rate of the thermal power plant was developed by Yasin and Koklukaya [17] using three different methods namely Artificial Neural Network (ANN), Autoregression integrated moving Average model (ARIMA) and Multiple Linear Regression (MLR). The comparison of methods is analyzed using R2 analysis and root mean square error. In conclusion, ANN showed better result.

Statistical model for the desalination of sea water was proposed by Sobana and Panda [18]. The regression analysis and ANOVA was performed for the developed statistical model. In the same way, Krishna et al. [19] correlated the variables using statistical models for predicting output in degradation of pollutants and analyzed the models. Valsalam et al. [20] developed mathematical model for the 210 MW coal-fired boiler for which MPC controller was designed to control the steam from superheater. A general investigation on modeling, identification and control of the coal fired thermal power plants are provided by Sreepradha et al. [21]. Subsequently, authors recommended for the improvement in efficiency of overall power plant by performing proper studies on the material balance and energy balance of the each unit. The role of excess air in the combustion of coal and in the efficiency of the boiler is analyzed by Pattanayak using energy and exergy analysis [22]. The statistical modeling for the optimization of ammonia production to improve the efficiency of the electrostatic precipitator in the coal fired thermal power plant was proposed by Sahu et al. [23] and Mahalik et al. [24].

A detailed literature analysis shows that there is no much study on the economizer unit and superheater unit as the study for drum section. Moreover, statistical modeling for the individual boiler units and the integrated units were missing. Most of the research papers on the thermal power plant and the boiler, the data driven models were based on the artificial intelligent technology. These limitations in the literature had concluded that there is a need for better modeling for the existing plants. In this proposed work, the temperature of all the interactive units are correlated with respective inputs and are analyzed using multiple regression equations. The significance level of the independent variables and the interactions are discussed to know the dependability of the temperature of the individual unit on the flow rate, enthalpy, specific heat capacity, etc. Another objective of the study is to find optimal values of the inputs based on regression analysis for the integrated pressure and temperature model. The integrated model of temperature and pressure seems to have good performance and improved efficiency when compared to the individual units.

The paper is organized as follows: Section 2 briefs about the basic functioning of the coal-fired thermal power plant and also gives the details of data collected from the plant for the validation of derived model. Section 3 is about the approaches of statistical analysis and execution of the same for the boiler units. The results and description of Table and figures found through statistical analysis are present in Section 4. The optimal working conditions obtained for the integrated boiler system through the RSM studies have been emphasized here. A comparison between the results of united performances of separate units with that of integrated unit has also been presented here. Conclusion of the proposed work is drawn at the end of the paper.

Materials and methods

In this work, data were collected from a typical coal-fired thermal power plant with 210 MW capacity over a period of 2–3 h in two different schedules. Then the analysis has been carried out using ‘Origin-Pro’ and ‘Matlab’ v.12.2 softwares.

Process description

The thermal power plant produces power by converting thermal energy to mechanical energy and from mechanical energy to electrical energy. Thermal energy is generated in the boiler section which consists of furnace, economizer, drum, superheater and reheater. Correct proportion of the coal and air are given to the furnace for the complete combustion of the coal to produce flue gas. The obtained hot flue gas from this unit transfers heat to all the other units of boiler as shown in Fig. 1. Meanwhile, feedwater enters the economizer unit for the preheating purpose. The preheated liquid enters drum unit for the conversion of liquid to steam. Drum unit in turn comprises of downcomer, riser and a drum. Downcomer transfers hot water from economizer and riser, where the conversion of water to unsaturated steam takes place. The steam and the droplets of water from the unsaturated steam are separated in the upper and lower part of the drum unit respectively. The steam is later transferred to superheater and the water is circulated in the drum for the conversion. The unsaturated steam is converted to saturated steam in the superheater unit. There are three stages in the superheater, between which attemporator is placed for the temperature regulation.

Fig. 1

The boiler in coal fired thermal power plant.

The data necessary for the validation of the developed model are collected from 210 MW coal fired thermal power plant. The data collected from the thermal power plant are: feedwater flow rate; pressure at the exit of economizer unit, drum unit and superheater unit; temperature at the exit of the same three units; main steam flow rate; attemperator flow rate, turbine unit pressure, and the power. The data were collected for the duration of 120 min with the sampling interval of three minutes.

Model

A statistical model is capable of explaining the correlations between input and output variables. Boiler unit of the subcritical thermal power plant involves several interacting loops. The objective of the statistical modeling technique is to understand the interactions in the unit and between the units. Also, this modeling strategy can overcome the difference between the model and the plant as the model is built from the plant data. Regression analysis is the basic form of statistical analysis and is classified as linear regression, nonlinear regression and multivariate regression. Linear regression is used if the system output depends on one independent variable; nonlinear regression is used if the system is nonlinear and also used in the lack of pre-defined input-output correlation; multivariate regression is used if the system depends on two or more independent variables. The coefficients of the regression equation need to be improved to find ideal response. There are many optimization techniques for SISO (single input single output) systems that are affected by only one variable. When output is affected by many variables, output can be optimized using RSM.

Statistical optimizations using design of experiments (DOE) finds the main factors of the multi-dimensional systems to evaluate optimal operating conditions of the integrated units. There is not much literature on the usage of RSM in optimization of thermal power plants.

The proposal of applying multi-factorial design for finding variables and its optimal value of the integrated unit of the coal-fired boiler process have been reported for the first time. Collected data from the plant are used in the response surface methodology (RSM) program written in MATLAB (2012a) to find the optimum input variables of the regression equation of integrated pressure output and temperature output.

The multiple linear regression equation involving two or more input variables can be expressed as,

In the above equation, Y is the dependent variable; X1, X2, ..., Xn are the input variables; α0 to αm are the parameters to be identified. Alternative form of interactive multiple regression equation is expressed in Eq. (2), where the output Y depends on X1, X2, X1X2, X12 and X22. This interactive multiple regression equation is used in this work for deriving the prediction equation of the economizer unit, drum unit and superheater unit.

Economizer unit

In economizer unit, model of the temperature of the preheated water at the exit of the economizer is formulated. For the formulation, the plant data collected from this unit are feed water flow rate (w, t/h), pressure of exit steam of drum unit (P, bar), temperature of the preheated water at the exit of economizer unit (T, °c), the specific heat flow from the combustion chamber (Q, kJ/s) and the enthalpy of feed water (h, kJ/kg).

Temperature loop of the economizer has one dependent variable and four independent variables. Hence in the concept of the multivariate regression equation there are eighteen parameters to be evaluated from the analysis of the regression Eq. (3).

Drum

Similar to the economizer unit, the regression equation for the temperature of the drum unit is given as in the Eq. (4). The data collected from the power plant for the model are temperature of steam in drum (T, °C), feedwater flowrate W, pressure of the preheated water from the economizer, P, and the specific heat transfer rate from the flue gas to the drum unit, Q. Hence the drum equation has one dependent variable and three independent variables.

Superheater

Similar to other units, plant data are collected from the superheater unit of the plant. Flow rate of supersaturated steam is a function of its pressure. Regression model of the temperature has one dependent variable and three independent variables. The regression equation of the main steam temperature from the superheater unit is written as,

From the above equation, Qsh is the specific heat transfer rate from the flue gas to the superheater unit and Watm is the water (droplets) flow rate from the attemporator unit.

The regression equation of the pressure and temperature of the main steam of the integrated model are also developed and analyzed in the next section. Once the regression equations for the individual units are developed, the coefficients (α0, α1, α2,...) of the regression equations need to be identified. This identification is done with the help of OriginPro software. The fitness of the model is found using the value obtained by coefficient of determination. At the same time, analysis of variance (ANOVA) is also carried out to analyze the effectiveness of the model.

Coefficient of determination (R) is the essential test for the regression analysis. It determines the degree of which the model output replicated the plant data. It is found as the proportion of variance in the dependent variable that can be estimated from the independent variable. The R value lies from 0 to 1. The value near to zero indicates that the developed model cannot be used for representing the plant data and on the other side; the value near to 1 says that the developed model can represent the plant output very efficiently.

The regression analysis also provides the significant test results along with the coefficient of determination. It is the test which analyzes the degree of reliability of output variable on the input variables. The significance value (p-value) of 0.01 or 0.05 is often chosen for this purpose. The p-value of the regression analysis determines whether the coefficients of the framed model significantly have some effect on the dependent variable or not. If p-value is less than the chosen significance value, then there exists statistical significance between that particular independent variable on the dependent variable.

ANOVA is another analysis to study on the variance of the data collected from the plant. For this purpose, it primarily determines the variability of the collected data between the groups and the variability within the groups. ANOVA test provides informative of degree of freedom (between the data set and within the data), sum of squares of the data, mean square of the data (ratio of sum of squares to degree of freedom), F-value (mean square of the model to the mean square of the error) and lastly the significance value. If F value is far away from the value ‘1' then the purpose of test (replicating model and the plant data) is true. Also if p-value is less than 0.05, then it is evident that mean of all the independent variable is different, proving the null hypothesis.

Thus, the independent variables for the control of the temperature of the preheated water from the economizer unit are specific heat transfer from the flue gas to the unit, feedwater flow rate and the pressure of steam from the drum. The independent variables for the temperature control of the drum unit are the specific heat transfer rate from the flue gas to the walls of drum unit, feed water flow rate and the pressure of the preheated water from the economizer unit. Similarly the independent variable for the temperature control of the main steam from the superheater are specific heat transfer rate from the flue gas to the unit walls, flowrate of the attemporator and the pressure of the outlet steam from the drum. Since the manipulation of pressure of the any unit is not possible, using Clausius-Clapeyron equation, the pressure can be changed to temperature and therefore the temperature of the boiler unit can be varied.

Results and discussion

Inputs and outputs from boiler units are collected and the analysis of regression equation is performed. The analysis gives the predicted values for the coefficients of the model along with the standard error values of each variable, the t-value and the p-value to analyze the significance of the manipulated variable on the respective process variable.

The results of the ANOVA test for the individual units are tabulated in Table 1, Table 2 and Table 3. ANOVA Table gives F-value and the p-value for the experimental observations. Findings and the conclusion drawn from the analysis are discussed in this section.

Table 1

ANOVA of the prediction model of the temperature at the exit of economizer unit.

	DOF	Sum of Squares	Mean Square	F-Value	P-value
Model	18	1.1E + 06	63138.67	618675.4	0
Error	23	2.347	0.102
Total	41	1.1E + 06

Table 2

ANOVA of the prediction model of the temperature at the exit of drum unit.

	DOF	Sum of Squares	Mean Square	F-Value	P-Value
Model	9	6.1E + 06	686945.4	1.06E + 11	0
Error	32	2.0E-04	6.46E-06
Total	41	6.1E + 06

Table 3

ANOVA of the prediction model of the temperature at the exit of drum unit.

	DOF	Sum of Squares	Mean Square	F-Value	P-Value
Model	9	1.18E + 07	1.31E + 06	5.63e + 12	0
Error	32	7.4E-06	2.3E-07
Total	41	1.18E + 07

Temperature of economizer unit

As discussed in the previous section, there are four manipulated/input variables considered for the control of economizer temperature namely are Q (X), w (X2), he (X) and P (X). Flowrate of liquid from economizer unit is stated in terms of differential pressure. The equation with the predicted coefficients obtained from the regression analysis is given in the Eq. (6). The value of the coefficient of the regression, R2, for this model is 1 which indicates the perfect fit of the model and the real time data. By analyzing the p-value of the regression analysis, the variable , and will affect the temperature. Model significance is also proved in ANOVA table. The deviation of the model response from the plant output is very less which is evident from Fig. 2.

Fig. 2

Response of predicted temperature model and the plant temperature output of economizer unit.

Temperature of steam from drum

The variables influencing the drum temperature are Q (X1), W (X2) and P (X3). The temperature model of the drum with the predicted parameters is shown in Eq. (7). Fig. 3 shows the perfect fit of the predicted and actual temperature of drum with R2 value of 1.

Fig. 3

Response of predicted temperature model and the plant temperature output of drum unit.

Temperature of supersaturated steam from superheater

The manipulated variables of the temperature model of the steam of the superheater are Q (X1), W (X2) and P (X3). The regression equation of the temperature of the superheater obtained from the regression analysis is in Eq. (8).

Fig. 4 shows the fit of predicted temperature model of superheater and the plant output. The manipulated variables considered for the integrated unit are Q, W and h and the outputs are P and T. the regression equation obtained through the regression analysis is in Eq. (9) and (10).

Fig. 4

Response of predicted temperature model and the plant temperature output of superheater unit.

The approachability of the model is provided by the analysis of variance. The F-values of Anova Table suggests that the prediction equation are in good agreement with the plant data. The value of the coefficient of determination suggests that the model is suitable to analyse the importance of individual inputs, cumulative inputs, and interactive effects of selected inputs on the main steam of the integrated unit.

The proposed method is compared with the main steam temperature model by Valsalam [18]. The MSE value for the proposed method is 1.8595e-08 and the MSE value for the Valsalam model is 7.2531. This proves that the proposed model is better when compared to the previous model. The comparison of the temperature output from the plant, predictive model and the Valsalam model are given in Fig. 5.

Fig. 5

Comparison of the superheater temperature of the proposed model and the Valsalam model.

Design of experiment (DOE) on the plant data generated optimal values of the inputs, Q, W and h, as 842.94 kJ/s, 625.22 t/h and 6891.06 kJ/kg. RSM analysis on the data were carried out to generate the optimal value of the manipulated variables.

RMS errors between experimental and predicted values of the temperature for economizer, drum, super heater units and integrated unit are 0.3194, 0.0025, 5.69E-04 and 2.9205 respectively. This leads to calculate the error values at the end of the units by propagating the individual errors till the end of unit as 4.5435E-07 for temperature. The values suggest having individual regression models for efficient calculation of performance.

Conclusion

Statistical methods for the analysis of the subcritical coal fired boiler is presented in this paper. Three units of the boiler considered for the present work are economizer, drum and super-heater whose inputs and outputs are highly interactive in nature. The temperature output of each unit is considered for the analysis. The temperature models (regression model) for the economizer unit, drum unit and the superheater unit are formulated to analyze the significance of each manipulated variable through regression analysis; fitness of the regression equations (validation) through the value of coefficient of determination and ANOVA. The R values for all the models obtained from the analysis confirm the best fit with the value around 1. Significance of model is found from the ANOVA Table with p value (prob) nearly equal to zero. Complete analysis shows that the statistical regression model fits well for the real time plant data. These equations can be used for designing the strategies for the safe operation and also for the control of boiler unit. The manipulated inputs considered for the integrated model are specific heat transfer rate of flue gas (x1), flow rate of feed water (x2) and enthalpy of the feedwater(x3) and the process variables are temperature and pressure at the exit of superheater. The integrated model is better in analyzing management and audit of energy and performance. The optimum values of the input variables are found to be 842.94 KJ/Sec, 625.22 T/h and 6891.06 KJ/Kg through RSM studies. Thus the developed regression equations can be used for prediction of properties of steam during scaling up or scaling down of the plant specification.

Declarations

Author contribution statement

Sreepradha Chandrasekharan: Performed the experiments; Contributed reagents, materials, analysis tools or data; Wrote the paper.

Rames C. Panda: Conceived and designed the experiments; Performed the experiments; Analyzed and interpreted the data.

Bhuvaneswari N. Swaminathan: Conceived and designed the experiments.

Funding statement

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Competing interest statement

The authors declare no conflict of interest.

Additional information

No additional information is available for this paper.