Optimization of a 660 MW e Supercritical Power Plant Performance—A Case of Industry 4.0 in the Data-Driven Operational Management Part 1. Thermal E ﬃ ciency

: This paper presents a comprehensive step-wise methodology for implementing industry 4.0 in a functional coal power plant. The overall e ﬃ ciency of a 660 MW e supercritical coal-ﬁred plant using real operational data is considered in the study. Conventional and advanced AI-based techniques are used to present comprehensive data visualization. Monte-Carlo experimentation on artiﬁcial neural network (ANN) and least square support vector machine (LSSVM) process models and interval adjoint signiﬁcance analysis (IASA) identiﬁed at 50%, 75%, and 100% unit load, respectively, without compromising the power plant’s overall thermal e ﬃ ciency. Some authors used IASA to determine the signiﬁcance of the trained network’s input parameters and hidden parameters based on Equation (3) [77]. After selecting insigniﬁcant nodes / parameters, insigniﬁcant nodes can be removed from the network, and bias for the next layer parameters / nodes is updated. Using the IASA method of ﬁnding out the ranking of signiﬁcant nodes deﬁned in [77] of a trained network, we ﬁnd out variables O 2 , N, and P f are the least signiﬁcant and impact on the network’s overall performance is negligible. The signiﬁcance ranking is given in Figure 5c.

the power plant's various operational strategies were conducted using the ANN approach and the Monte Carlo technique.
Two fundamental objectives were considered: (a) the pursuit of minimum potential energies spent (conveniently translatable in various useful measures like the monetary cost of power generation or fuel cost of power generation), and (b) achieving those above while maintaining or enhancing the η thermal of the power plant. The savings in heat input values at 50%, 75%, and 100% unit load relative to the power plant's optimal η thermal were calculated for the power plant's energy-efficient operation control.
Big data analytics, industrial internet of things, and simulation were the three technologies prioritized and incorporated in the study to achieve the power plant's operational excellence by embracing the industry 4.0 digital transformation approach. The process modeling based on process data, process optimization, and data-driven strategy development for the improved process control lead to an increase in the thermal efficiency of the power plant that offers many benefits, i.e., reduced operating cost and optimal fuel consumption. The utilization of advanced and sophisticated technologies dedicated to the implementation of industry 4.0 in the industrial complexes for higher productivity and effective operation control is in line with the objectives of the industry, innovation, and infrastructure program of the united nations sustainable development goals and the Paris agreement to fulfill the nations' commitment for sustainable growth and environment [54,55].

Overview of a Coal Power Plant Operation
Power plants can be classified into sub-critical, critical, supercritical, and ultra-supercritical based on the steam conditions [56]. At critical condition, water is directly converted to steam and no longer exists in separate phases. The critical state of water is defined at 22.1 MPa, and 374 • C. Steam conditions in sub-critical power plants are generally around 16.5 MPa and 538 • C, while the steam parameters in supercritical power plants are generally maintained between 22.1 MPa to 28.9 MPa, and below 600 • C. There is no uniform definition for ultra-super-critical steam conditions. However, steam conditions of 28.9 MPa or higher and 600 • C or higher are generally maintained in ultra-supercritical power plants.
Supercritical power plants have higher thermal efficiency, stable combustion, better fuel economy, reduced emissions, faster load following response than the sub-critical power plants, and are generally employed for electrical power generation systems [57].
The 660 MW e supercritical coal-fired boiler model # HG-2118/25.4-HM16 is manufactured by Harbin Boiler Plant Co., Ltd. at Harbin, China and installed at the Sahiwal Coal Power Plant, as shown in Figure 1. The modern and advanced design features of the boiler include a π-shaped structure, once-through technology (no steam drum), an intermediary reheating system, sliding pressure, balanced draft, wet bottom ash with a single furnace, ultra-sonic leakage detection system, full steel frame, full suspension structure arranged in the open air, and is also equipped with two rotary tri-sector air preheaters (APH). The boiler's sliding pressure ability allows it to continuously provide steam ranging from 330 MW e to 660 MW e unit load.
The boiler furnace consists of diaphragm walls designed to improve the wall water tightness and bear the high structural loads. The lower furnace water walls and hopper adopt spiral coils and have enough cooling capacity under different boiler loads to effectively compensate for the thermal deviation of furnace circumambient. Above the spiral tubes, vertical tubes are used to ensure the heat transfer for fast response characteristics. The intermediary mixing header used for the transition between spiral tubes and vertical tubes also balances the pressure across four sides of water walls.
The furnace and fuel burners' operation is synchronized to ensure the flame burning until burnout, higher combustion efficiency, and minimal NO x formation. The boiler's burning system is equipped with a medium-speed direct-fired pulverizing system with cold and hot primary air. Twenty-four direct-flow fuel burners are arranged, four at the corners in a layer, and a total of six layers for six coal mills. The fuel burner at the bottom of the furnace is provided with a micro oil gun system to save Energies 2020, 13, 5592 5 of 33 fuel during start-up and support the combustion. In addition to that, three layers of big oil guns are provided, consisting of 12 burners. The boiler furnace consists of diaphragm walls designed to improve the wall water tightness and bear the high structural loads. The lower furnace water walls and hopper adopt spiral coils and have enough cooling capacity under different boiler loads to effectively compensate for the thermal deviation of furnace circumambient. Above the spiral tubes, vertical tubes are used to ensure the heat transfer for fast response characteristics. The intermediary mixing header used for the transition between spiral tubes and vertical tubes also balances the pressure across four sides of water walls.
The furnace and fuel burners' operation is synchronized to ensure the flame burning until burnout, higher combustion efficiency, and minimal NOx formation. The boiler's burning system is equipped with a medium-speed direct-fired pulverizing system with cold and hot primary air. Twenty-four direct-flow fuel burners are arranged, four at the corners in a layer, and a total of six layers for six coal mills. The fuel burner at the bottom of the furnace is provided with a micro oil gun system to save fuel during start-up and support the combustion. In addition to that, three layers of big oil guns are provided, consisting of 12 burners.
The efficiently designed tangentially fired fuel burners ensure smooth and gradual pulverized coal combustion in the furnace with the combustion chamber's uniform temperature field. The tangential combustion system ensures uniform heat distribution and stable combustion under varying boiler loads.
The fuel burners adopt a low NOx, horizontal rich, and lean burner. The fuel burner's secondary air is fired in the furnace 5° away from the primary air to form the air-enclosure-coal arrangement The efficiently designed tangentially fired fuel burners ensure smooth and gradual pulverized coal combustion in the furnace with the combustion chamber's uniform temperature field. The tangential combustion system ensures uniform heat distribution and stable combustion under varying boiler loads.
The fuel burners adopt a low NO x, horizontal rich, and lean burner. The fuel burner's secondary air is fired in the furnace 5 • away from the primary air to form the air-enclosure-coal arrangement and oxidation near the water wall zone. Fuel burners are divided into upper and lower groups within a specific distance to reduce the burner zone's thermal load and slagging. Separated over-fire air (SOFA) nozzles are arranged near the furnace's exit and above the burners to supply air for the late combustion and implement efficient combustion to reduce furnace temperature level and to control NO x emissions. The flame detection system is installed with every fuel burner to prevent flameout phenomenon, which detects flame strength both by digital and analog signals. Two sets of temperature sensing thermocouples are installed at a high-temperature position for each fuel burner to prevent the burners melting by high temperature. Moreover, infrared flue gas temperature measuring devices are set on the right and left sides of the furnace outlet to monitor the furnace outlet's flue gas temperature. The boiler Energies 2020, 13, 5592 6 of 33 is also equipped with the ultrasonic leakage detection system, and the flame observation cameras on both sides of the boiler monitor the combustion. It is necessary to mention that the advanced and reliable combustion control systems installed at the power plant ensure the boiler's stable and reliable operation for the power generation. The manufacturer designed the boiler's operating parameters at boiler maximum continuous rating (BMCR), listed in Table 1. The schematic diagram of the coal power plant operation is shown in Figure 2. Coal is supplied by a coal feeder, while primary air is provided by the primary air fan (PAF) to the boiler. Coal and primary air are fed to the coal mill for producing pulverized coal, which is injected into the boiler via coal burners. combustion and implement efficient combustion to reduce furnace temperature level and to control NOx emissions. The flame detection system is installed with every fuel burner to prevent flameout phenomenon, which detects flame strength both by digital and analog signals. Two sets of temperature sensing thermocouples are installed at a high-temperature position for each fuel burner to prevent the burners melting by high temperature. Moreover, infrared flue gas temperature measuring devices are set on the right and left sides of the furnace outlet to monitor the furnace outlet's flue gas temperature. The boiler is also equipped with the ultrasonic leakage detection system, and the flame observation cameras on both sides of the boiler monitor the combustion. It is necessary to mention that the advanced and reliable combustion control systems installed at the power plant ensure the boiler's stable and reliable operation for the power generation. The manufacturer designed the boiler's operating parameters at boiler maximum continuous rating (BMCR), listed in Table 1. The schematic diagram of the coal power plant operation is shown in Figure 2. Coal is supplied by a coal feeder, while primary air is provided by the primary air fan (PAF) to the boiler. Coal and primary air are fed to the coal mill for producing pulverized coal, which is injected into the boiler via coal burners.  The pulverized coal burns in the boiler with the secondary air provided by the forced draft fan (FDF). The hot flue gas produced by the pulverized coal combustion is used for heat transfer to the heating surfaces in the boiler, as shown in Figure 2. An induced draft fan (IDF) is used for the flue gas suction from the boiler, which helps to maintain the desired furnace pressure and discharges flue gas to the ambient environment through the stack. Upon leaving the boiler, flue gas is passed through the APH to heat the primary and secondary air and enter the electrostatic precipitator (ESP) and flue gas desulphurization (FGD) system particulate matter and sulfur oxides removal, respectively. Finally, through strict control of emission parameters, flue gas is discharged to the ambient environment through the stack. Feed-water can be considered the power plant's blood and is converted to superheated steam in the boiler. The condensate pump directs feed-water, now also called condensate water in the condenser, to the low-pressure heaters (LPH) for the feed-water heating. After passing through the LPH, feed-water is passed through a deaerator where deoxygenation is applied to the feed-water. The feed-water pump builds up the feed-water pressure and forces it to the series of high-pressure heaters (HPH) for further feed-water heating. The steam extractions heat feed-water in the HPH and LPH from high-pressure (HP) and intermediate-pressure (IP) turbines. After passing through the HPH, feed-water passes through a series of heating surfaces like the economizer (ECO), low-temperature superheater (LTSH), division platen superheater (DPSH), and the final superheater (FSH), etc. for producing superheated main steam by the heat transfer from the flue gas. The superheated main steam is expanded in the HP turbine, where its temperature and pressure are dropped during expansion. After leaving the HP turbine, steam is directed to the low-temperature re-heater (LT REHEATER) and final re-heater (FRH) for reheating the steam. Attemperation water flow is used to control the temperature of the main steam and reheat steam. The reheat steam is expanded in the IP turbine and is directed to lowpressure (LP) turbines A and B for further expansion. The steam, after expanding in LPA and LPB turbines, is condensed to condensate water in the condenser, and the cycle continues. The expansion of superheated and reheated steam in HP, IP, and LP turbines is used for the rotor rotation, coupled with the generator (G) for electricity generation.
The Sahiwal coal power plant was commissioned in 2017 and has been operational and integrated with the national grid since then. It is equipped with state-of-the-art measuring sensors as well as an SIS data storage system. All the sensors measuring the control variables involved in this study are hard sensors measuring the power plant's different operating parameters. The data generated constitute a large number of variables, with each variable having randomly distributed values. It has been extensively reported in the literature that mining causal relationships out of such data is beyond the capability of any type of multi-variate regression technique. AI-based data analytic techniques perform significantly better for modeling such scenarios [39,58]. The sensors' location for measuring the power plant's different operating parameters is shown with numbers in Figure 2. The sensors make and model numbers are mentioned in Table 2.

AI-Based Data Visualization and Process Modeling
AI-based process models are developed to learn the complex, non-linear, and interacting relationship between the system's input and output variables [59][60][61]. ANN and LSSVM are considered the most efficient approximation tools of AI and can generalize the relationship between input and output variables. These AI tools also have the proven ability to mine the hidden details in the training data, thereby ensure their reliable applications in real-world problems [40,62,63].

Variables Selection for AI Process Modeling
In this paper, thirteen control variables were initially selected to model the 660 MW e supercritical coal power plant's η thermal in Sahiwal, Pakistan. The variables were selected based upon the recommendation of experienced plant managers of the power plant and a comprehensive literature review [33,[64][65][66][67][68]. Some control variables were controllable by the operator, e.g., the main steam temperature (MST), reheat steam temperature (RST), and oxygen content in flue gas at the boiler outlet (O 2 ). On the other hand, some control variables were uncontrollable during the power plant operation, e.g., turbine speed (N). The coal properties measured under the air-dried basis are listed in Table 3.  Figure 3. The data points were taken at intervals of one minute during the power plant's controlled continuous operation. It is important to note here that the power plant's load varied from 50% to 100% rated load of the unit as per the requirement and stability of the national grid of Pakistan to which the power plant is connected to by a 500 kV transmission line. The statistics of training data of the initially selected control variables for the development of AI process models are shown in Table 4. The operation parameters that were essential for the stability and effective control of combustion include the coal flow rate (M c ), the air flow rate (M a ), furnace pressure (P f ), the APH air outlet temperature (T a ), % O 2 in flue gas at the boiler outlet (O 2 ), the APH outlet flue gas temperature (T fg ), feed water temperature (FWT), main steam pressure (MSP), main steam temperature (MST), reheat steam temperature (RST), condenser vacuum (P vac ), attemperation water flow rate (AWF), and turbine speed (N). It is evident from Table 4 that control variables possess wide operating ranges of the power plant control parameters, which contain not only all possible operating modes of the power plant but also possess the detailed and comprehensive information of the plant operation required for the development of a generalized AI process model.
The histograms of the control variables are shown in Figure 3a-m. M c values in the operating range, as mentioned in Table 4, correspond to the various unit load generation from the power complex and are shown in Figure 3a. Figure 3b represents air consumption in the boiler during different load generation. Figure 3c shows a nearly normal distribution of P f , while Figure 3d illustrates the distribution of T a . T a was selected as the training parameter to better account for the heat recovery from the flue gas after its exhaust from the boiler and the subsequent benefit for improving the power plant's η thermal . Figure 3e represents the % O 2 in the flue gas exhaust from the boiler. T fg was a very critically controlled and sensitive parameter for the boiler operation as it was one of the critical parameters of the boiler operation for ensuring its effective operation control. The variation in T fg is shown in Figure 3f. The increase in T fg indicated that heat transfer from flue gas to the heating surfaces decreased, which might be caused due to soot accumulation on the heating surfaces, high flame center, or large access air coefficient of combustion re-burning of un-burnt carbon in the tail of the boiler.     A regeneration system was installed at the power plant. Three HPH and four LPH utilized the steam extractions from the HP and IP turbines for heating the feed-water. The distribution of FWT achieved by regenerative heating is shown in Figure 3g. Figure 3h represents the operating range of the MSP. The MSP was a critical parameter for the unit load generation. Similarly, the MST controllable range was critically controlled as it affected the thermal efficiency, safety, and stable power plant operation. The distribution of the MST is depicted in Figure 3i. As mentioned in Table 4, the MST working range was a good operating range for evaluating its effect on the η thermal of the power plant. The reheat system positively influenced the η thermal of the power plant. The distribution of RST is shown in Figure 3j. Figure 3k represents the variation in vacuum maintained in the condenser, while Figure 3l shows the distribution of AWF data in the input space used to control the MST and RHT. Lastly, Figure 3m represents the variation in N during power plant operation. It is evident from Figure 3a-m that the distribution of control variables data points across their operating ranges was wide and meaningful and thus can be confidently used to develop AI process models of the η thermal of the power plant.

Elimination of Insignificant Control Variables
Each selected control variable's significance on the output variable ought to be investigated to train effective AI models. For physical system modeling through equations representing a process, many input variables are required to describe an output variable accurately. In contrast, AI process models have an excellent, proven ability to model such a system with fewer significant variables. The selection of significant variables for AI process models development is crucially important, and therefore, sensitivity analysis was performed to eliminate insignificant control variables that had a minimal or negligible effect on the output variable [64].

Monte Carlo Experimentation for Significance Analysis
Monte Carlo experimentation was used to determine each variable's effect on the output variables considering the uncertainties in the control variables' data set. Monte Carlo experiments operate by generating the random values between the control variables [69,70]. The detailed description of the working of Monte Carlo experimentation for the variable elimination purpose is described below.

2.
Each input vector containing all control variables x i can estimate output variable y o where, o = 1,2,3, . . . .,m, where m is equal to the number of input vectors in the training data set.

3.
The Monte Carlo experimentation can be illustrated by considering a control variable x i and all other control variables as x j, were (i j). As an example, let x i = x 1 and x j = x 2 , . . . .. , x 13 , where (i j).

5.
Generate M random values for each division k (k = 1,2, 3, . . . , n) by keeping x ik , at a constant value. All other input control variables for these M replications are generated so that the probability (P) of any value (u) between x jmin and x jmax is equal. The Mth input vector will be [x 1kM , x 2u , x 3u , x 4u . . . , x 13u ], and the corresponding output will be y okM .

6.
The output value y okM is obtained by ANN and LSSVM prediction for the Mth input vector Compute a mean value (µ) for each y okM having M replications, which will give y ok for each x ik. 7.
Repeat step number iii to step number vi for all remaining control variables 8.
Compute ∆y i where ∆y i = y okmax − y okmin for all control variables x i and compute the summation value Y for all ∆y i

9.
Compute the percentage significance (r i ) of each x i by dividing ∆y i with Y and multiplying it by 100 The least insignificant variables obtained from Monte Carlo experimentation performed on ANN and LSSVM are shown later in the paper. The elimination of insignificant control variables is essential to develop a useful process model based on ANN and LSSVM. This elimination of insignificant control variables is usually obtained by coupling an algorithm (in our case, Monte Carlo experimentation) to ANN and LSSVM. Therefore, the significance of control variables obtained by Monte Carlo experimentation is confirmed with the Interval Adjoint Significance Analysis (IASA) method.

Interval Adjoint Significance Analysis (IASA)
The sensitivity-based method is advantageous in finding out the significance of control variables in a given sample [71,72]. The deviation in output ∆y caused by the deviations in the input is defined as sensitivity [71]. By finding out the sensitivities of given control variables, we can find out their significance. In this sub-section, intervals are represented by uppercase letters (e.g., A, B, C, . . .) and scalars are represented by lower case letters (e.g., a, b, c, . . .). The interval is defined as X = x l , x u , where l and u represent the lower and upper limit of the interval, respectively.
Interval arithmetic (IA) [73] is used to evaluate a function f [X] in a given range over a domain and it gives us a guaranteed enclosure To illustrate the basic working of the interval adjoint method, here is an example of significance analysis on a very simple interval function f (X) = log(X 0 · X 1 )/10 + X 1 /100. Let 36,000]. The computational graph for function f is given in Figure 4a, and a possible code list of f is listed in Table 5.
After the reverse mode, AD significance values are generated based on Equation (3) (see the computational graph given in Figure 4b). Note the significance value of the intermediate node V 1 is equal to 2.098, which is way below the significance values of the other nodes. This node and the preceding nodes connecting to V 1 are removed and replaced with the mean value of interval V 1 as shown in Figure 4c.  After the reverse mode, AD significance values are generated based on Equation (3) (see the computational graph given in Figure 4b). Note the significance value of the intermediate node is equal to 2.098, which is way below the significance values of the other nodes. This node and the preceding nodes connecting to are removed and replaced with the mean value of interval as shown in Figure 4c.  Some authors used IASA to determine the significance of the trained network's input parameters and hidden parameters based on Equation (3) [77]. After selecting insignificant nodes/parameters, insignificant nodes can be removed from the network, and bias for the next layer parameters/nodes is updated. Using the IASA method of finding out the ranking of significant nodes defined in [77] of a trained network, we find out variables O 2 , N, and P f are the least significant and impact on the network's overall performance is negligible. The significance ranking is given in Figure 5c. Some authors used IASA to determine the significance of the trained network's input parameters and hidden parameters based on Equation (3) [77]. After selecting insignificant nodes/parameters, insignificant nodes can be removed from the network, and bias for the next layer parameters/nodes is updated. Using the IASA method of finding out the ranking of significant nodes defined in [77] of a trained network, we find out variables O2, N, and Pf are the least significant and impact on the network's overall performance is negligible. The significance ranking is given in Figure 5c. The results of both Monte Carlo experimentation for variables elimination and IASA indicated that the control variables O2, N, and Pf were relatively insignificant variables and could be eliminated from the data set of control variables for the sake of decreasing the computational time, eliminating the redundant control variables, and achieving accurate results [69]. Therefore, ten control variables out of thirteen initially selected control variables highlighted in blue in Figure 5a-c were finalized for training the AI process modeling of the power plant's ηthermal.

Self-Organizing Feature Map
A self-organizing feature map, also known as the Kohonen feature map, is primarily used in data visualization techniques. An unsupervised learning machine maps the underlying possible statistical features in training data on to the nodes in the two-dimensional lattice. Owing to its excellent ability to distribute the control variables data on the nodes in the form of homogenous groups, SOFM is used in many real-life applications [78][79][80]. In this work, a two-dimensional output layer carrying 10 × 10 nodes was created, and the distribution of control variables data points are shown in Figure 6. The z-axis represents the frequency of occurrence of data points on a node. It is evident from Figure 6, that control variables data points were well-distributed on the 10 × 10 nodes on the output layer and confidently directed the construction of the AI process models for the ηthermal of the power plant. The results of both Monte Carlo experimentation for variables elimination and IASA indicated that the control variables O 2 , N, and P f were relatively insignificant variables and could be eliminated from the data set of control variables for the sake of decreasing the computational time, eliminating the redundant control variables, and achieving accurate results [69]. Therefore, ten control variables out of thirteen initially selected control variables highlighted in blue in Figure 5a-c were finalized for training the AI process modeling of the power plant's η thermal .

Self-Organizing Feature Map
A self-organizing feature map, also known as the Kohonen feature map, is primarily used in data visualization techniques. An unsupervised learning machine maps the underlying possible statistical features in training data on to the nodes in the two-dimensional lattice. Owing to its excellent ability to distribute the control variables data on the nodes in the form of homogenous groups, SOFM is used in many real-life applications [78][79][80]. In this work, a two-dimensional output layer carrying 10 × 10 nodes was created, and the distribution of control variables data points are shown in Figure 6. The z-axis represents the frequency of occurrence of data points on a node. It is evident from Figure 6, that control variables data points were well-distributed on the 10 × 10 nodes on the output layer and confidently directed the construction of the AI process models for the η thermal of the power plant.

Development of ANN Process Model
The multilayer perceptron (MLP) consisted of three layers. The first input layer consisted of neurons, which number corresponded to the number of control variables. The MLP may consist of one or more hidden layers, depending on its architecture, and the optimum one is determined by hit and trial methods [58]. It was proved that one hidden layer was enough to approximate the nonlinearity present in the data provided enough number of neurons were present in the hidden layer [81]. The neurons' number in the output layer was equal to the number of outputs. The optimal ANN, thus trained, had ten neurons in the input layer, 17 neurons in the hidden layer, and one neuron in the output layer. The MLP architecture is represented as [10-17-1] and shown in Figure 7.

Development of ANN Process Model
The multilayer perceptron (MLP) consisted of three layers. The first input layer consisted of neurons, which number corresponded to the number of control variables. The MLP may consist of one or more hidden layers, depending on its architecture, and the optimum one is determined by hit and trial methods [58]. It was proved that one hidden layer was enough to approximate the nonlinearity present in the data provided enough number of neurons were present in the hidden layer [81]. The neurons' number in the output layer was equal to the number of outputs. The optimal ANN, thus trained, had ten neurons in the input layer, 17 neurons in the hidden layer, and one neuron in the output layer. The MLP architecture is represented as [10-17-1] and shown in Figure 7.
The feed-forward backpropagation network algorithm was used to develop a process model for the power plant's η thermal . It has a well-established ability to dig and learn the complex nonlinearities and interactions out of high dimensional and complex input space data [82][83][84]. Gradient descent with momentum was employed as a training function, and tangent hyperbolic was used as a transfer function between the layers of MLP for the neural network model development [64,85].
The ANN training was carried out until one of the two stopping criteria was met, i.e., either a 0.0000001 change in convergence error or a maximum number of epochs was reached. The best MLP architecture is represented as [10-17-1] and shown in Figure 7. The trained ANN achieved a good correlation coefficient (R) value, i.e., 0.917 for training, 0.911 for validation, and 0.92 for testing purposes during ANN development.

Development of LSSVM Process Model
The support vector machine is a powerful machine learning tool and is utilized for non-linear classification, function approximation, and density estimation [86][87][88]. LSSVM can be trained more effectively for modeling a system based on the structural risk minimization (SRM) principle. The Gaussian kernel function is generally used for mapping the complicated non-linear relationship between the input and output variables onto the feature space [40]. It is essential to mention here that the training data set should be standardized for developing a useful LSSVM model. Bayesian optimizer and expected improvement per second plus acquisition function was used to optimize the regularized Energies 2020, 13, 5592 17 of 33 constant (C) and epsilon (ε) parameters for LSSVM [89][90][91][92]. Thus, the optimal value for C and ε for the developed LSSVM model was 305.30 and 0.0057, respectively. The R-value for the developed LSSVM model was equal to 0.922. The feed-forward backpropagation network algorithm was used to develop a process model for the power plant's ηthermal. It has a well-established ability to dig and learn the complex nonlinearities and interactions out of high dimensional and complex input space data [82][83][84]. Gradient descent with momentum was employed as a training function, and tangent hyperbolic was used as a transfer function between the layers of MLP for the neural network model development [64,85].
The ANN training was carried out until one of the two stopping criteria was met, i.e., either a 0.0000001 change in convergence error or a maximum number of epochs was reached. The best MLP architecture is represented as [10-17-1] and shown in Figure 7. The trained ANN achieved a good correlation coefficient (R) value, i.e., 0.917 for training, 0.911 for validation, and 0.92 for testing purposes during ANN development.

Development of LSSVM Process Model
The support vector machine is a powerful machine learning tool and is utilized for non-linear classification, function approximation, and density estimation [86][87][88]. LSSVM can be trained more effectively for modeling a system based on the structural risk minimization (SRM) principle. The Gaussian kernel function is generally used for mapping the complicated non-linear relationship between the input and output variables onto the feature space [40]. It is essential to mention here that the training data set should be standardized for developing a useful LSSVM model. Bayesian optimizer and expected improvement per second plus acquisition function was used to optimize the regularized constant (C) and epsilon (ε) parameters for LSSVM [89][90][91][92]. Thus, the optimal value for C and ε for the developed LSSVM model was 305.30 and 0.0057, respectively. The R-value for the developed LSSVM model was equal to 0.922.

Evaluation Criteria
The performance of the developed AI process models can be assessed based upon the prediction error against the validation data set that was unseen to the networks during their development phase. Root-mean-square error (RMSE), normalized RMSE (NRMSE), and mean absolute percentage errors (MAPE) were calculated on the models predicted values to evaluate their robustness and effectiveness for modeling the η thermal of the power plant. The definitions of the error criteria are given below: where n is the sample size,ŷ i and y i are the predicted and actual values, y max and y min are the maximum and minimum value of y i , respectively.

External Validation Case of Trained AI Process Models
After training the ANN and LSSVM process models using the control variables dataset consisting of 27,267 observations, the developed models were externally validated using a new operating data of the power plant that was "unseen" to ANN and LSSVM models during their development. An additional 28,460 observations of the control variables that serve as a characteristics data set for external validation cases were taken from the SIS to compare the ANN and LSSVM models' predictions with the power plant's actual ηthermal. The ANN and LSSVM predicted response for actual vs. predicted η thermal , and the corresponding residuals are shown in Figure 8a,b. Comparing the ANN and LSSVM models' responses, as shown in Figure 8a,b, the ANN model had more effectively predicted the external validation data set than the LSSVM model. The spread of residuals for the ANN model was comparatively smaller than the one for the LSSVM model. The performance comparison of ANN and LSSVM models for predicting the power plant's η thermal , in terms of the evaluation criteria, is presented in Table 6.    It is clear from Table 6 that various error estimations, i.e., RMSE, NRMSE, and MAPE for the ANN predicted response was 0.5051%, 8.2159%, and 1.016% respectively, which was lower than the ones for LSSVM model predictions, i.e., 0.7164%, 11.6538%, and 1.2819%, respectively. It confirmed that the ANN process model had effectively modeled the power plant's η thermal concerning the control variables compared to LSSVM. The ANN presented a good generalization ability to model the complex power plant operation with better network robustness, confirming its superior efficacy for data analysis and decision making.

Results and Discussion
Generally, power generation from a power plant is either 50%, 75%, or 100% of unit load capacity, as determined by the national grid's demand. The control variables' operating regimes are different under the different power generating capacity of the power plant. The minimum, average, and maximum control variables at 50%, 75%, and 100% unit load are listed in Table 7. It was crucial to evaluate the effect of selected control parameters on the output variable by keeping remaining control variables at the select value (generally the mean values) corresponding to the specific unit load to simulate the power plant operation's actual operating scenario. The individual or combined effect of the essential control variables on the η thermal was evaluated.
The detailed procedure for creating the experiments is discussed below: 1. Let x i be the control variable(s) where i = 1,2,3 . . . .,10, whose effect is to be studied, and x j (i j) represents the remaining control variables.

2.
Let yo represent the output value corresponding to x i where o = 1.
Keep the remaining control variables xj constant at the selected value at every step size d. The input vector with x i say, i = 1, step size d and remaining input control variables x j is represented as [x 1d , x 2d , x 3d , x 4d , x 5d , x 6d , x 7d , x 8d , x 9d , x 10d ]. Create "m" replications for the input vector for every step size d.

5.
Generate "m" Gaussian noise values (g) from the 1% range value of control variables x i and x j . Add g with the input vector for all step size d.
Energies 2020, 13, 5592 20 of 33 6. Predict the developed ANN process model from an input vector and compute mean (µ) and standard deviation (σ) of the predicted values y od against x id input vector, which is represented as µ yod and σ yod relative to x id input vector, respectively. 7.

Effect of MST and RST on η thermal of Power Plant
MST and RST are critically and simultaneously controlled power plant operating parameters. The power production was generally maintained at either 50%, 75%, or 100% unit load, which depends on the connected national grid's demand and stability. MST and RST parameters under such an operation scenario should be effectively controlled within the operating control limits to ensure economical, safe, and fuel-efficient power production from the power plant.
To evaluate the effect of MST and RST on the power plant's η thermal at 50%, 75%, and 100% unit load, MST and RST were varied from 550 to 570 • C. The remaining control parameters were set at the corresponding average values at 50%, 75%, and 100% unit load, as mentioned in Table 7. Thus, the experiments were used to evaluate the combined effect of MST and RST on the power plant's η thermal .
The operating range of MST (x 1 ) and RST (x 2 ) was divided into ten equal divisions (d) in order to conduct experiments according to the procedure described in Section 4. MST and RST remained constant in each division, while the other control variables (x j = 3,4, 5,6,7,8,9,10) were set at their average values, as mentioned in Table 7. A total of 100 replications (m) of the control variables were created and added with the Gaussian noise values (g). The constructed experiment was simulated using the ANN process model of η thermal of the power plant and mean (µ yod ), and the standard deviation (σ yod ) of the predicted values of η thermal (y o ) was calculated. The procedure was repeated for remaining division values (d), and mean UCL and LCL trend lines against MST and RST were plotted for 50%, 75%, and 100% unit load and represented in Figure 9a-c. Figure 9a-c relates to the effect of the MST and RST on the power plant's η thermal . A general increasing trend of the power plant's η thermal was observed when MST and RST increased from 550 • C to 570 • C. The power plant's η thermal at 50%, 75%, and 100% unit load had, on average, a relative increase of 1.50%, 1.50%, and 1.32%, respectively, with every 10 • C rise in MST and RST. The upper control limits of the temperatures were restricted by material properties [93]. Figure 9d compares the effect of the MST and RST on the power plant's η thermal at 50%, 75%, and 100% unit load. It was apparent from Figure 9d that the η thermal of the power plant at 100% unit load was higher than 50% and 75% unit load efficiencies. It was because the heart rate of the power plant was improved at 100% unit load. Moreover, the power plant operating mode was also supercritical under which the boiler operation was fuel-efficient, stable, and economical [56,93]. The heat inputs to produce 50%, 75%, and 100% unit load at 550 • C, 560 • C, and 570 • C MST and RST are mentioned as MW values on each trend in Figure 9d. The heat inputs required to sustain the highest η thermal , i.e., 39.78%, 41.05%, and 41.59% at 50%, 75%, and 100% unit load at higher temperature limit (570 • C) of MST and RST were 905 MW, 1206 MW, 1587 MW respectively. Meanwhile, at a lower temperature limit (550 • C) of MST and RST, the overall thermal efficiencies achieved were 38.62%, 39.85%, and 40.51% at 50%, 75%, and 100% unit load. The corresponding energies spent to keep the plant operational were 932 MW, 1242 MW, 1629 MW, respectively, which were comparatively higher heat inputs for the same power production. Therefore, it was advantageous to maintain the MST and RST at a higher temperature limit to ensure the fuel-efficient and optimum power plant operation for sustainable power production. average values, as mentioned in Table 7. A total of 100 replications (m) of the control variables were created and added with the Gaussian noise values (g). The constructed experiment was simulated using the ANN process model of ηthermal of the power plant and mean (μyod), and the standard deviation (σyod) of the predicted values of ηthermal (yo) was calculated. The procedure was repeated for remaining division values (d), and mean UCL and LCL trend lines against MST and RST were plotted for 50%, 75%, and 100% unit load and represented in Figure 9a-c.  A general increasing trend of the power plant's ηthermal was observed when MST and RST increased from 550 °C to 570 °C. The power plant's ηthermal at 50%, 75%, and 100% unit load had, on average, a relative increase of 1.50%, 1.50%, and 1.32%, respectively, with every 10 °C rise in MST and RST. The upper control limits of the temperatures were restricted by material properties [93].

Effect of T fg on the η thermal of Power Plant
T fg is a critically controlled operating parameter of the boiler operation. It indicates the efficiency of fuel combustion and heat transfer to the heating surfaces inside the boiler, thereby directly influencing the power plant's η thermal . The increase in this temperature beyond its normal controllable operating range, as mentioned in Table 7, indicates that heat transfer from the flue gas to the heating surfaces is decreasing, which might be caused by soot accumulation on the heating surfaces, high flame center, large access air coefficient of combustion and burning of unburned carbon in the tail of boiler. This is an indicator of poor control of boiler operation resulting in the power plant's reduced η thermal .
The effect of T fg on the power plant's η thermal at 50%, 75%, and 100% unit load is given in Figure 10a-c. The η thermal of the power plant decreased with the increase in T fg . With every 5 • C rise in the T fg , the relative decrease in the power plant's η thermal was an average of 0.65%, 0.25%, and 0.28% at 50%, 75%, and 100% unit load respectively. Figure 10d compares the effect of T fg on the power plant's η thermal at 50%, 75%, and 100% unit load. At 100% unit load, the power plant's η thermal was relatively higher than 75% and 50% unit load due to the improved heat transfer conditions. At 50% unit load, there was a sharp decreasing trend of the power plant's η thermal with increased flue gas temperature after APH. Thus, the temperature should be effectively controlled mainly at 50% unit load as it had a relatively more significant adverse impact on the power plant's η thermal . This was explained by the fact that the increase in T fg indicated the decreased heat transfer from flue gas to the heating surfaces, which was responsible for the decrease Energies 2020, 13, 5592 22 of 33 in the η thermal of the power plant. The temperature was critically controlled by the significant soot blowing on various heating surfaces in the boiler, improved fuel combustion, lower irreversibility losses in the boiler, and significant operational control. The lower limit of the temperature was strictly controlled as it may cause corrosion to the downstream equipment due to the condensation of flue gas containing various acidic gases [93][94][95].
fuel combustion and heat transfer to the heating surfaces inside the boiler, thereby directly influencing the power plant's ηthermal. The increase in this temperature beyond its normal controllable operating range, as mentioned in Table 7, indicates that heat transfer from the flue gas to the heating surfaces is decreasing, which might be caused by soot accumulation on the heating surfaces, high flame center, large access air coefficient of combustion and burning of unburned carbon in the tail of boiler. This is an indicator of poor control of boiler operation resulting in the power plant's reduced ηthermal.
The effect of Tfg on the power plant's ηthermal at 50%, 75%, and 100% unit load is given in Figure  10a-c. The ηthermal of the power plant decreased with the increase in Tfg. With every 5 °C rise in the Tfg, the relative decrease in the power plant's ηthermal was an average of 0.65%, 0.25%, and 0.28% at 50%, 75%, and 100% unit load respectively.  Figure 10d compares the effect of Tfg on the power plant's ηthermal at 50%, 75%, and 100% unit load. At 100% unit load, the power plant's ηthermal was relatively higher than 75% and 50% unit load due to the improved heat transfer conditions. At 50% unit load, there was a sharp decreasing trend of the power plant's ηthermal with increased flue gas temperature after APH. Thus, the temperature should be effectively controlled mainly at 50% unit load as it had a relatively more significant adverse impact on the power plant's ηthermal. This was explained by the fact that the increase in Tfg indicated the decreased heat transfer from flue gas to the heating surfaces, which was responsible for the decrease in the ηthermal of the power plant. The temperature was critically controlled by the significant soot blowing on various heating surfaces in the boiler, improved fuel combustion, lower irreversibility losses in the boiler, and significant operational control. The lower limit of the temperature was strictly controlled as it may cause corrosion to the downstream equipment due to the condensation of flue gas containing various acidic gases [93][94][95].
The heat inputs required to achieve the power plant's overall thermal efficiencies at 50%, 75%, and 100% unit load are shown in Figure 10d. At the highest ηthermal of the power plant, i.e., 39.97%, 40.96%, and 42.23% at 50%, 75%, and 100% unit load, the corresponding heat inputs were 901 MW, 1208 MW, and 1563 MW, respectively. The possible lowest overall thermal efficiencies, i.e., 39.18%, 40.66%, and 41.87% at 50%, 75%, and 100% unit load, were 919 MW, 1218 MW, and 1576 MW, respectively. Resultantly, heat input values at lower thermal efficiencies caused by the increased temperature of flue gas after APH were comparatively higher for the same unit load generation. It accounted for the effective control of the flue gas temperature after APH near the lower controllable limits, as mentioned The heat inputs required to achieve the power plant's overall thermal efficiencies at 50%, 75%, and 100% unit load are shown in Figure 10d. At the highest η thermal of the power plant, i.e., 39.97%, 40.96%, and 42.23% at 50%, 75%, and 100% unit load, the corresponding heat inputs were 901 MW, 1208 MW, and 1563 MW, respectively. The possible lowest overall thermal efficiencies, i.e., 39.18%, 40.66%, and 41.87% at 50%, 75%, and 100% unit load, were 919 MW, 1218 MW, and 1576 MW, respectively. Resultantly, heat input values at lower thermal efficiencies caused by the increased temperature of flue gas after APH were comparatively higher for the same unit load generation. It accounted for the effective control of the flue gas temperature after APH near the lower controllable limits, as mentioned in Table 7, to achieve optimal η thermal under various power plant operating modes.

Effect of T a and T fg on the η thermal of Power Plant
T a and T fg is an essential pair of power plant control parameters for the effective boiler operation and improved η thermal under various power plant operating modes. Flue gas leaving the boiler had some thermal energy depending upon the boiler thermal efficiency, which would otherwise be lost if Energies 2020, 13, 5592 23 of 33 not recovered and decrease the power plant's η thermal . A part of this energy was recovered by the air passing through the APH. Thus, the pre-heated air improved the power plant's η thermal and helped coal combustion at high air temperature for producing high-quality steam. The combined effect of rising T a and falling T fg represented the flue gas's waste heat recovery system.
The operating ranges of two temperatures were divided into ten equal divisions to evaluate the combined effect of T a and T fg . T a was varied systematically in the ascending order, while T fg was decreasing systematically. The remaining operating parameters were kept at the average values corresponding to the 50%, 75%, and 100% unit load, as mentioned in Table 7. The further treatment for constructing the experiment's design for evaluating the effect of T a and T fg on the power plant's η thermal was executed as per the procedure described in Section 4.
The combined effect of T a and T fg at 50%, 75%, and 100% unit load on the power plant's η thermal is represented in Figure 11a-c. As expected, an increasing trend in the power plant's η thermal was observed at 50%, 75%, and 100% unit load with the increase in T a and fall in T fg . The relative increase in the η thermal of the power plant on an average was 0.43%, 0.44%, and 0.42% at 50%, 75%, and 100% unit load respectively against every 5 • C rise in T a and 5 • C fall in T fg . It is essential to mention here that the extent of waste heat recovery was limited to the dew point temperature of flue gas and the APH material metallurgy [96,97].
Energies 2020, 13, x FOR PEER REVIEW 24 of 35 corresponding to the 50%, 75%, and 100% unit load, as mentioned in Table 7. The further treatment for constructing the experiment's design for evaluating the effect of Ta and Tfg on the power plant's ηthermal was executed as per the procedure described in Section 4. The combined effect of Ta and Tfg at 50%, 75%, and 100% unit load on the power plant's ηthermal is represented in Figure 11a-c. As expected, an increasing trend in the power plant's ηthermal was observed at 50%, 75%, and 100% unit load with the increase in Ta and fall in Tfg. The relative increase in the ηthermal of the power plant on an average was 0.43%, 0.44%, and 0.42% at 50%, 75%, and 100% unit load respectively against every 5 °C rise in Ta and 5 °C fall in Tfg. It is essential to mention here that the extent of waste heat recovery was limited to the dew point temperature of flue gas and the APH material metallurgy [96,97]. Figure 11d compares the combined effect of Ta and Tfg on the power plant's ηthermal at 50%, 75%, and 100% unit power generation capacity. At 100% unit power generation capacity, the power plant's ηthermal was relatively higher than 50% and 75% unit power generation capacity because of its improved heat rate. Trend lines in Figure 11d show the heat inputs to achieve the power plant's thermal efficiency at 50%, 75%, and 100% unit load. At the highest ηthermal of the power plant, i.e., 39.77%, 41.08%, and 42.29% at 50%, 75%, and 100% unit load, the corresponding heat inputs were 905 MW, 1205 MW, and 1561 MW, respectively. The possible lowest overall thermal efficiencies at 50%, 75%, and 100% unit load would be 917 MW, 1221 MW, and 1580 MW, respectively. The lowest heat inputs corresponding  Figure 11d compares the combined effect of T a and T fg on the power plant's η thermal at 50%, 75%, and 100% unit power generation capacity. At 100% unit power generation capacity, the power plant's η thermal was relatively higher than 50% and 75% unit power generation capacity because of its improved heat rate.
Trend lines in Figure 11d show the heat inputs to achieve the power plant's thermal efficiency at 50%, 75%, and 100% unit load. At the highest η thermal of the power plant, i.e., 39.77%, 41.08%, and 42.29% at 50%, 75%, and 100% unit load, the corresponding heat inputs were 905 MW, 1205 MW, and 1561 MW, respectively. The possible lowest overall thermal efficiencies at 50%, 75%, and 100% unit load would be 917 MW, 1221 MW, and 1580 MW, respectively. The lowest heat inputs corresponding to the power plant's highest η thermal at 50%, 75%, and 100% unit load was possible due to improved heat recovery from the flue gas leaving the boiler. The effective operation control of T a and T fg promised the boiler's efficient operation and the improved η thermal of the power plant.

Effect of Change in All Control Variables on the η thermal of Power Plant
In this sub-section, first, the power plant's possible worst operating scenario during which overall thermal efficiencies of the power plant may drop to the lowest value at 50%, 75%, and 100% unit load was constructed. Further, in the Monte Carlo experiments, certain adjustments in operating parameters were simulated to recover the power plant's η thermal . This strategy of adjusting operating parameters can be practically implemented to achieve the maximum overall thermal efficiencies at various power plant operation modes.
AWF controls the temperature of the MST and RST. Low adjustment of AWF, i.e., the exceptionally high flow rate, may significantly drop the MST and RST. However, the MSP may have a little increase depending upon the AWF and unit load. Moreover, MST and RST drop may also be linked with lower heat transfer to the boiler's heating surfaces, indicated by higher T fg . In such an operating scenario, FWT would also drop, and the P vac would be slightly increased. Meanwhile, the M c , M a , and AWF were adjusted to recover the plant operation to the stable operating conditions at any unit load. The operational ranges of all the control variables within which the corresponding variables' values were systematically changed at 50%, 75%, and 100% unit load are s mentioned in Table 7.
To conduct the experiments for optimizing the η thermal of the power plant at 50%, 75%, and 100% unit load, M c , M a , T fg , T a , MSP, P vac , and AWF were varied from maximum to average values as mentioned in Table 7. FWT was varied from minimum to average, while MST and RST were changed between the minimum and the maximum operating limits. The operating ranges of all variables were divided into ten equal divisions. To evaluate the response of the power plant's ηthermal under such an operating scenario, we applied the procedure as described in Section 4.
The effect of changes in control variables (MST and RST are conveniently represented along the lower and upper x-axes while the operating range of remaining control variables is mentioned in the description of Figure 12) on the power plant's η thermal at 50%, 75%, and 100% unit load is shown in Figure 12a-c. At 50% unit load, the power plant's η thermal was initially stagnant (~550 • C~555 • C MST), and then it started increasing. On the other hand, at 75% and 100% unit load, an increasing trend of the power plant's η thermal was observed. For 550 • C to 560 • C and 560 • C to 570 • C of MST and RST with the corresponding changes in remaining control parameters at 50%, 75%, and 100% unit load, the relative increase in the η thermal of the power plant on an average was equal to 3.36%, 3.21%, and 4.29% respectively. Figure 12a-c. At 50% unit load, the power plant's ηthermal was initially stagnant (~550 °C ~555 °C MST), and then it started increasing. On the other hand, at 75% and 100% unit load, an increasing trend of the power plant's ηthermal was observed. For 550 °C to 560 °C and 560 °C to 570 °C of MST and RST with the corresponding changes in remaining control parameters at 50%, 75%, and 100% unit load, the relative increase in the ηthermal of the power plant on an average was equal to 3.36%, 3.21%, and 4.29% respectively. Figure 12d compares power plant thermal efficiencies against the changes in all control variables at 50%, 75%, and 100% unit load. At 100% unit load, the power plant's thermal efficiency was higher than 75% and 50% unit load. It explained that the heat rate was generally improved at the power plant's supercritical operating mode.
The heat input values for achieving the thermal efficiencies against the changes in control variables at 50%, 75%, and 100% unit load are mentioned as MW values in Figure 12d. It is observed from Figure  12d that at a specific unit load, heat input values at higher operating limits of the control variables were significantly reduced as compared to lower operating limits of the control parameters. The heat input values corresponding to the power plant's maximum thermal efficiencies, i.e., 40.48%, 41.35%, and 42.20% at 50%, 75%, and 100% unit load, were 889 MW, 1197 MW, and 1564 MW, respectively. On the other hand, the possible lowest thermal efficiencies, i.e., 37.9%, 38.8%, and 38.8% at 50%, 75%, and 100% unit load, were 958 MW, 1285 MW, and 1711 MW. The difference in heat input values at a specific unit load reflects the savings in heat input energy ensured under the power plant's optimal operating conditions. Such savings can be safely interpreted as the total energies spent to produce output electricity and, therefore, be directly related to savings in the cost of power plant operation. Table 8 compares the percentage savings or losses in the heat input values for power plant operation concerning the operating ranges of control parameters at 50%, 75%, and 100% unit load.  Figure 12d compares power plant thermal efficiencies against the changes in all control variables at 50%, 75%, and 100% unit load. At 100% unit load, the power plant's thermal efficiency was higher than 75% and 50% unit load. It explained that the heat rate was generally improved at the power plant's supercritical operating mode.
The heat input values for achieving the thermal efficiencies against the changes in control variables at 50%, 75%, and 100% unit load are mentioned as MW values in Figure 12d. It is observed from Figure 12d that at a specific unit load, heat input values at higher operating limits of the control variables were significantly reduced as compared to lower operating limits of the control parameters. The heat input values corresponding to the power plant's maximum thermal efficiencies, i.e., 40.48%, 41.35%, and 42.20% at 50%, 75%, and 100% unit load, were 889 MW, 1197 MW, and 1564 MW, respectively. On the other hand, the possible lowest thermal efficiencies, i.e., 37.9%, 38.8%, and 38.8% at 50%, 75%, and 100% unit load, were 958 MW, 1285 MW, and 1711 MW. The difference in heat input values at a specific unit load reflects the savings in heat input energy ensured under the power plant's optimal operating conditions. Such savings can be safely interpreted as the total energies spent to produce output electricity and, therefore, be directly related to savings in the cost of power plant operation. Table 8 compares the percentage savings or losses in the heat input values for power plant operation concerning the operating ranges of control parameters at 50%, 75%, and 100% unit load.
The energy savings were achievable by the effective operational control of the combustion that ultimately influenced power plant operation. The energy savings or energy losses were expressed in % of heat input values and were mentioned against the operating parameters, i.e., MST and RST, T fg , T a and T fg, and all control variables, as discussed in Sections 4.1-4.4, respectively. The energy savings or energy losses for any control variable at a specific unit load were calculated from the heat input values corresponding to the control variable's operating range, as mentioned in Figures 9d, 10d, 11d and 12d. (+) the sign indicates the % energy savings while the (−) sign indicates the % energy losses in heat input values against the control variable in its operating range. At 50%, 75%, and 100% unit load, MST and RST indicated energy savings in heat input values of 2.94%, 2.92%, and 2.59%. T a and T fg noted energy savings of 1.27%, 1.31%, and 1.25%, respectively. All control variables showed significant energy savings of 7.20%, 6.85%, and 8.60%, respectively, whereas, T fg expressed energy losses of 1.99%, 0.70%, and 0.35% in heat input values for the operation of the power plant.

Conclusions
In this work, industrial operation data, advanced data analytic tools, and AI algorithms are incorporated to formulate the step-wise methodology in the spirit of industry 4.0-data analytics to optimize the power plant's η thermal for sustainable power generation from a power complex.
The quality of operation data is ensured by employing data visualization techniques like histograms and SOFM. Monte-Carlo experiments on ANN and LSSVM process models and IASA were performed to eliminate insignificant variables from the list of initially selected control variables.
For every 5 • C rise in T a and 5 • C fall in T fg , the relative increase in the η thermal of the power plant on average was 0.43%, 0.44%, and 0.42%, respectively, under 50%, 75%, and 100% unit load.
From 550 • C to 560 • C and 560 • C to 570 • C MST and RST with the corresponding changes in remaining control variables, the relative increase in the η thermal of the power plant on an average was 3.36%, 3.21%, and 4.29% respectively at 50%, 75%, and 100% unit load.
The true implementation of industry 4.0 built by the modern data analytics tools for power plant operation ensured the increase in the power plant's thermal efficiency and, therefore, the techno-economic benefits that offer reduced operation cost, optimal fuel consumption, and effective operational control.
Big data analytics, industrial internet of things, and simulation were the three technologies prioritized and incorporated in the study to achieve the power plant's operational excellence by embracing the industry 4.0 digital transformation approach.
The process modeling based on process data, process optimization, and data-driven strategy development for improved process control using sophisticated technologies dedicated to the implementation of industry 4.0 in the industrial complexes for higher productivity and effective operation control is in line with the objectives of the industry, innovation, and infrastructure program of the united nations for sustainable development and the Paris agreement allowing to fulfill the nations' commitment to sustainable growth and the environment.
The effect of auxiliaries' system operation, separately or combined, on the power plant's η thermal needs to be evaluated in the future.