Dynamic modeling and optimization of a coal-fired utility boiler to forecast and minimize NOx and CO emissions simultaneously

Accepted Manuscript

Dynamic modeling and optimization of a coal-fired utility boiler to forecast and minimize NOx and CO emissions simultaneously Seyed Mostafa Safdarnejad, Jake F. Tuttle, Kody M. Powell PII: DOI: Reference:

S0098-1354(18)30977-3 https://doi.org/10.1016/j.compchemeng.2019.02.001 CACE 6339

To appear in:

Computers and Chemical Engineering

Received date: Revised date: Accepted date:

18 September 2018 16 January 2019 1 February 2019

Please cite this article as: Seyed Mostafa Safdarnejad, Jake F. Tuttle, Kody M. Powell, Dynamic modeling and optimization of a coal-fired utility boiler to forecast and minimize NOx and CO emissions simultaneously, Computers and Chemical Engineering (2019), doi: https://doi.org/10.1016/j.compchemeng.2019.02.001

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Highlights • Dynamic and steady-state modeling of a coal-fired utility boiler

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• Estimation of NOx and CO with respect to a future power production schedule

• Improved estimation accuracy from training a dynamic model with historical data

• Significant improvement in accuracy of a dynamic forecast compared to a

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static model

• Significant potential in simultaneous reduction of NOx and CO emissions

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with dynamic optimization

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Dynamic modeling and optimization of a coal-fired utility boiler to forecast and minimize NOx and CO emissions simultaneously Seyed Mostafa Safdarnejad, Jake F. Tuttle, Kody M. Powell

Department of Chemical Engineering, 3290 MEB, University of Utah, Salt Lake City, UT 84112, USA

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Abstract

Increasing penetration of renewable energy sources to the power grid has prompted new ramping scenarios to dispatchable thermal power plants to balance the variability caused by intermittent renewable supplies. With many thermal power plants designed to be base-loaded, ramping of the power output results in increased emission of pollutants. This study develops a dynamic data-driven model of a coal-fired

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utility boiler that estimates NOx and CO emissions simultaneously. Given a production schedule of a power plant, estimation of NOx and CO emissions for three hours into the future is performed that can be further utilized in a dynamic optimization

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algorithm to minimize the emissions over a horizon. It is observed that a dynamic model always has a higher prediction accuracy than a static model, when training

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and forecasting of the models are concerned. Application of dynamic and steadystate optimization also results in reduced emissions as compared to historical plant emissions.

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Keywords: Power generation, Dynamic NARX model, Static model,

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Emission forecast, Optimization

1. Introduction Many countries around the world have adopted national targets to increase the

contribution of renewable energy sources into their energy landscape. These targets ∗ Corresponding author. Email: [email protected]

Preprint submitted to Computers & Chemical Engineering

February 6, 2019

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are defined for various purposes such as electricity generation, heating and cooling, transportation, and other general energy consumption purposes. According to the report published by the International Renewable Energy Agency (IRENA), the power

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sector was the main area of focus of 150 countries in order to meet renewable energy targets in 2015 (IRENA [2015]). Among all different renewable sources, wind and solar have had the greatest rates of increasing contribution to the power grid over the

past two decades (Eser et al. [2016], Kubik et al. [2015], Wang et al. [2012], Yan et al. [2017]). For instance, power generation from wind and solar in the US increased

from 6,737 and 543 GW h in 2001 to 254,254 and 52,958 GW h, respectively, in 2017

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(EIA [2018]). While increased contribution of wind and solar power sources can help achieve emissions targets, a major drawback of these technologies is their intermittent nature. To maintain the reliability of the power grid, dispatchable fossilfueled power plants are required to balance the variablity that wind and solar power sources introduce. A recent study demonstrates that future gas and steam turbines are expected to have 70-100% faster ramping rates, 35-60% faster start-up rates, and

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20-80% lower emissions than the current state of the art systems to be able to offer short-time backups to renewables (Gonzalez-Salazar et al. [2018]). This improve-

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ment in the design of gas and steam turbines is imperative to achieve the targets of renewable energy sources. Many fossil-fueled generators in the current power grid are, however, originally designed to be base-loaded. Cycling of these units to accom-

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modate renewable sources results in non-optimized operation of the unit. This is in part due to the air quality control equipment that is negatively impacted, resulting

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in non-optimized air-to-fuel ratios and different staging of the combustion process within the boiler. Consequently, this leads to increased emissions from the power plant (NETL [2012]). NOx is one of the major emissions of thermal power plants

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that is harmful to the environment and human health (Munawer [2018]). Different technologies have been considered to reduce NOx emissions, such as low NOx burners (Lifshits and Londerville [2014]), selective catalytic and non-catalytic reduction (SCR and SNCR) (Nihalani et al. [2018], Shen [2017], Zhang et al. [2018]), less excess air (EPA [1999]), adsorption and absorption (Sloss [1992]), and flue gas recirculation (DiNicolantonio [1992]). One of the common methods used in industry to control 2

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NOx emissions is known as an overfire air system. An overfire air system works to stage combustion within the boiler to reduce overall temperatures, thus, reducing the creation of thermal NOx. This process indirectly adjusts the air flow rate for

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complete combustion of the fuel, resulting in producing the required power with minimum NOx emissions at each time step. The procedure of determining appropriate air distribution throughout the overfire air system is, however, steady-state;

i.e., operation settings are optimized at each time step and they remain fixed until

the next time step. This approach essentially ignores the increase in NOx emissions

between consecutive time steps, caused by the cycling behavior discussed above. It

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is, therefore, critical to minimize the NOx emissions of the power plant from a dy-

namic standpoint; i.e., with consideration of the variations of the power output over a time horizon, instead of a single time step. This paper provides a dynamic modeling approach that is the foundation of dynamic minimization of NOx emissions, which is also demonstrated using an offline optimization approach. Previous research studies have considered developing mathematical models to

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predict NOx based on the individual factors contributing to its formation. These models can be utilized to optimize the combustion process parameters to effec-

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tively minimize NOx emissions. The modeling approaches considered previously are mainly classified into three categories: computational fluid dynamics (CFD) and kinetic modeling (Bris et al. [2007], Chui and Gao [2010], Secco et al. [2015], Tan et al.

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[2017], Zeng et al. [2010]), empirical and statistical relationships (Jung et al. [2001], Kurose et al. [2004]), and artificial neural-networks and fuzzy logic systems (Bekat

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et al. [2012], Li et al. [2004, 2005], Shakil et al. [2009], Smrekar et al. [2009, 2013], Song et al. [2017], Tan et al. [2014], Tüfekci [2014], Tunckaya and Koklukaya [2015], Wei et al. [2013], Zhou et al. [2004, 2010, 2012]). Artificial intelligence has specifi-

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cally gained attention in the past decade for estimation of NOx emissions. This is because the amount of data collected from the industrial units has significantly increased and artificial intelligence helps extract useful information from sensor data. Various methods are used in literature for estimating NOx emissions of power plants including auto-regressive moving-average model with exogenous inputs (ARMAX) (Smrekar et al. [2013]), auto-regressive model with exogenous inputs (ARX) (Smrekar 3

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et al. [2013]), support vector regression (SVR) (Tan et al. [2014], Wei et al. [2013]), neural networks (NN) (Li et al. [2005], Shakil et al. [2009], Smrekar et al. [2013]), advanced extreme learning machine (Tan et al. [2014]), nonlinear ARX (NARX) (Li

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et al. [2004]), auto-regressive integrated moving average (ARIMA) (Tunckaya and Koklukaya [2015]), and globally enhanced general regression neural network (Song et al. [2017]). Many of the previous studies use artificial intelligence to estimate historical NOx emissions without considering the power production schedule (Shakil

et al. [2009], Smrekar et al. [2013]). Noting that the power production schedule of a power plant is typically known from the unit commitment models a few hours

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in advance, a forecast of NOx emissions that corresponds to the power production schedule provides an opportunity to minimize the emissions more effectively. This is because variability of plant operations is taken into account and a dynamic optimization approach can utilize the dynamic forecasts of NOx emissions to minimize over a horizon. This is in contrast to a single time step minimization approach (corresponding to a steady-state optimization process) that only minimizes the emis-

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sions at a given time step. Accordingly, the operation settings remain constant until the next time step, despite the variations that the plant might have experienced be-

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tween the two time steps. The focus of this work is, then, to develop a dynamic model of a boiler that predicts the NOx emissions multiple steps ahead of time with consideration of the projected power production schedule. This study uses the well-

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established NARX modeling approach to develop the dynamic model, while a static neural network is also developed for comparison. Additionally, an estimation of the

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CO emission of this boiler that corresponds to the power production schedule is provided in this work. Estimation of multiple emissions of a boiler, with consideration of a multiple steps ahead power production schedule, is not explored in literature.

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Furthermore, the benefits of dynamic modeling of the boiler over a static modeling approach, currently practiced at many coal-fired utility boilers, are highlighted in this paper. Finally, the benefits of dynamic optimization of the combustion process within a plant against a steady-state approach in reducing the overall NOx and CO emissions of the unit are presented by using an offline optimization approach. In both forecasting and optimization of NOx and CO emissions, the algorithm de4

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velopment procedure is described in detail with the goal of making it applicable to similar systems. Simulation results demonstrate that the dynamic model provides a more accurate prediction of both NOx and CO emissions than the static model, both

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when the model is trained with historical data and when the trained model is used to forecast the emissions multiple steps ahead in time. Additionally, dynamic op-

timization of the plant produces less emissions than the steady-state optimization and historical operation of the plant.

The remainder of this paper is divided into five sections. Section 2 provides a description of the system being simulated while a description of the modeling ap-

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proach and assumptions used to develop the static and dynamic models is provided in Section 3.1. Then, Section 3.2 provides the data processing approach that is implemented on the raw data collected from the operation of a utility boiler. The fore-

casting and optimization algorithms are also presented in Sections 3.3 and 3.4, respectively. The simulation results for training of the models and their use in forecasting and minimizing NOx and CO emissions are then discussed in Section 4. A

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2. System Description

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summary of the main findings are provided in Section 5.

A general schematic of a conventional pulverized coal-fired boiler is shown in

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Figure 1. Air and fuel enter the combustion chamber through a number of nozzles either on the walls or in the corners of the boiler (corresponding to wall-fired and tangentially-fired boilers, respectively). These nozzles are often given the des-

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ignations of burner, fuel air, and auxiliary air. Additionally, there are ignitors and warm-up guns located within the boiler near the burners. As these are not included in any models developed in this paper, they will not be discussed further. Short de-

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scriptions of each of these pieces of equipment and their respective functions are provided below (Tomei [2015]). Burners: Pulverized coal enters the boiler through the burners. After being pul-

verized within the coal mills, the pulverized coal is carried from the mills, through coal pipes, and into the boilers by what is known as primary air. Primary air is

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the designation given to the air within the system that is used to carry pulverized coal from the pulverizers to the boiler. Upon entering the boiler, the fuel is combusted. Within the models developed in this study, the coal flow value represents

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the amount of coal fed into the individual pulverizers, which is then moved directly

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to the boiler for combustion.

Figure 1: Conventional Pulverized Coal-Fired Boiler (Tomei [2015]). This figure is used with permission of the publisher (Babcock & Wilcox Company [2018]).

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Fuel Air: This is the air introduced adjacent to the fuel immediately at the outlet of the burners. The primary air alone is not enough to ensure combustion of the coal out of the burners, and it is fuel air which adds the additional air to achieve initial

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combustion conditions. The fuel air value used in the model represents how open this nozzle is, corresponding to the amount of air being introduced.

Auxiliary Air: This is the air introduced in between burners within the boiler. In order to ensure fuel continues to burn as it moves away from the burners, more air

must be introduced to promote this continued combustion. The auxiliary air value

used in the model represents how open this nozzle is, corresponding to the amount

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of air being introduced.

In addition to the variables that could be manipulated by the model, which were mentioned in the system descriptions above, there is also a variable designated as burner tilt which is associated with all of these pieces of equipment. Other variables that could be manipulated by the model include the excess O2 and the windbox differential pressure. These variables are described below:

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Burner Tilt: This is the vertical orientation of the nozzle firing direction. The burners, fuel air dampers, and auxiliary air dampers all share the same burner tilt

the burners.

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angle value; i.e., the fuel air and auxiliary air dampers have the same tilt angle as the

Excess O2 : This is the amount of excess O2 present in the combustion products

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at the exit of the furnace. This is used as an indicator of how much additional air is present during the combustion process.

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Windbox Differential Pressure: This is the pressure difference between the windbox (reservoir of air which the fuel air, auxiliary air, and separated overfire air, as described below, draw from) and the furnace.

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As mentioned previously, one of the methods used in industry to control NOx

emissions is known as an overfire air system, where the combustion process within the boiler is staged to reduce the creation of thermal NOx. The boiler studied in this paper includes such a system, and the ability of the model to control this is described below: Separated Overfire Air (SOFA): This is the air introduced a relatively large dis7

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tance above the burners in the boiler. These dampers provide the remaining air necessary for complete combustion of the fuel. The SOFA value used in the model represents how open this nozzle is, corresponding to the amount of air being intro-

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duced at this point (Steel & Alloy [2018]).

3. Problem Formulation

This section discusses the modeling and optimization approaches used in this study. This discussion includes all the essential components needed to apply to any

similar systems such as training of the data-driven models, data processing, and

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forecasting and optimization algorithms. 3.1. Model Description

The operation of the utility boiler considered in this study is strongly nonlinear. This study considers a nonlinear autoregressive network with exogenous inputs

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to simulate the nonlinear behavior of the boiler. The model of this system corresponds to a recurrent neural network (RNN) that has feedback connections to input the previous values of the output variables to the network, making it dynamic in na-

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ture (Figure 2). The output variables of this study are NOx and CO emissions. The exogenous inputs include the power production schedule as well as 72 variables that operators manipulate to minimize the emissions. The power production schedule

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is an input to the model and is typically available from the unit commitment models while the other input variables are multiple instances of the variables described in

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Section 2 at different locations of the boiler setup. A static model is also developed to compare with the RNN model. The static

model has a similar structure as the RNN model except that the feedback connec-

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tion does not exist. This work assumes one input layer, one hidden layer, and one output layer for both networks. The input layer receives the exogenous inputs and the previous output values, multiplies each by a weighting factor, and add the results together. A bias is also introduced to this weighted sum. The summation of the weighted inputs and the bias value produces the output of the input layer, which

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Figure 2: Schematic of a Recurrent Neural Network

is then passed to the neurons in the hidden layer. A nonlinear activation function (sigmoid function in this study) is applied on the receiving input to the hidden layer. The mathematical representation of this procedure is shown by Equation 1:

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Ã

j =1

w i , j ui + b j

!

(1)

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ϕ = t anh

N X

where ϕ and u i represent the output from the hidden layer and exogenous input data to the input layer, respectively, while w i , j and b i are the weight factor and bias

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applied in the input layer. The number of input data variables is also represented by N . The outcomes of all neurons in the hidden layer are weighted by a different set of factors and they are added together while a new bias is also introduced to this

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weighted sum. This produces the network output, as shown by Equation 2:

ψ=

H X

j =1

Wj ϕj + B

(2)

where ψ, W j , and B represent the network output, weighting factors, and bias applied on the outputs of the hidden layer. The number of neurons in the hidden layer is also represented by H . To predict the output variables correctly, the neural network model should be 9

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trained; i.e., the weighting and bias factors should be updated to minimize the deviation between the model prediction and target values. This study uses the LevenbergMarquardt backpropagation algorithm (Hagan and Menhaj [1994]), provided by the

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Neural Network ToolboxTM of Matlab (Mathwork [2017]), to find the optimum weight and bias values. This toolbox initializes the weight and bias factors randomly and

then updates them according to the Levenberg-Marquardt backpropagation algorithm until a reasonable agreement is realized between the model prediction and

measurements. This study assumes the minimization of the mean of squared er-

rors between the measurement and model prediction for NOx and CO. For a given

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number of neurons, a validation procedure is also implemented in Matlab toolbox

(built-in function of the toolbox) to avoid overfitting of the problem; i.e., overfitting means that the model can predict the input/output relationships very well for the training data set but the prediction accuracy for unseen data set is poor. One cause of overfitting is when the model is trained too extensively to the training data and it begins to predict relationships that do not actually exist, either due to sensor noise

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in the training set or other phenomenon. This causes the model to perform poorly when attempting to predict the results of unseen data. The number of neurons in

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the hidden layer is a tuning parameter that should be decided based on the level of complexity needed to represent the relationships between the variables without overfitting the model. Generally, more neurons can better represent the nonlinear

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relationships between the variables. However, increasing the number of neurons might result in overfitting of the problem. Increasing the number of neurons also

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adds to the computational complexity of the problem. It is, therefore, critical to find the optimum number of neurons in the hidden layer that balances between model complexity and prediction accuracy. A sensitivity analysis is implemented in this

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study to obtain the optimal number of neurons that can represent the nonlinear relationships between the inputs and output variables. 3.2. Data Processing The time-series data associated with the variables described in Section 2 is collected from a 480 MW coal-fired power generation unit in the United States. This 10

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data is for the period between September 21, 2017 and March 5, 2018 with a 5minute sampling time. However, there are instances when the raw data includes out-of-range data for the input and output variables. The data used to train the neu-

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ral network is cleaned from all out-of-range or bad quality data for all variables in a post-processing approach. Additionally, the data acquisition system of this utility boiler is setup such that it checks for out-of-range values of NOx. Thus, if an out-

of-range value of NOx is observed, it skips writing that record. Additionally, there is a flag within the system which indicates if calibration or maintenance is being per-

formed on any of the sensors. The data acquisition system does not record the data

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if these flags are active. The quality of the CO emission data is not currently verified in the industrial unit that the data was collected from, except for the calibration or maintenance signal described above. Although it might be helpful, no data smooth-

ing or noise reduction effort is currently practiced in the industrial unit. Thus, the data is not further processed for these effects.

Additionally, the variables used in this study vary significantly in magnitude.

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Scaling the raw data can significantly increase the robustness of the trained neural network as well as the multiple steps ahead prediction accuracy of the model.

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The input and output variables as well as the power production from the plant are

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all scaled according to Equation 3:

v isc al ed =

v i − v i ,mi n

v i ,max − v i ,mi n

(3)

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where v iscal ed represents the scaled form of the variable while v i , v i ,mi n , and v i ,max are the raw data and its minimum and maximum values, respectively, observed over the entire time horizon that the data was collected. The NOx and CO production

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shown on the graphs of Section 4 are also based on scaling according to Equation 3. In contrast, the power output data, shown in Figures 5 and 8, is based on scaling the actual power with its maximum (over the entire time horizon that the data was available). This is solely for better visualization of the power output variations over the training and forecasting periods, as described below, and the power data given to the static and dynamic models follows the same scaling rule as shown by Equation 11

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3. The data set that was collected from this utility boiler is divided into training and forecasting segments. The training data set incorporates 75% of the data for

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the period between September 21, 2017 to January 30, 2018, which is used to train the static and dynamic neural network models. The Neural Network ToolboxTM of

Matlab also has built-in cross-validation algorithms that divide the training data set further to ensure that the model generalizes well for independent data sets. The pe-

riod between January 31, 2018 to March 5, 2018 is also used to forecast and minimize the NOx and CO emissions multiple time steps in advance. While a longer forecast-

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ing horizon could be used, this study considers a 3-hour ahead prediction of NOx

and CO. This is because a time frame of 2-3 hours is required in actual operation of the plant to complete a ramping event.

The prediction accuracy of the model, for training and forecasting cases, is obtained by comparing its predictions with historical data of NOx and CO emissions. Two criteria are used to assess the model accuracy; the first assessment factor is the

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coefficient of correlation (R) while the root mean squared error (RMSE) between the model prediction and measured data is the second criterion.

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3.3. Forecasting Algorithm

Once the models are trained, they are used to forecast emissions into the fu-

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ture. To achieve this objective, the trained recurrent neural network model is used recursively for prediction of the emissions into the future; a trained RNN model can provide a one-step ahead prediction of NOx and CO by using their previous mea-

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sured or predicted values. The other inputs to the one-step ahead prediction of NOx and CO are the power demand and decision variables of the overfire air and com-

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bustion systems. Utilizing the predictions of each time step recursively, forecasts of emissions into the future can be made. Figure 3 provides a schematic representation of this algorithm for the RNN model. For simplicity, a case with only three steps-ahead prediction is shown in this figure, but this procedure can be applied to generate predictions of emissions for essentially any desired horizon into the future, provided that the corresponding power production schedule is available. In con12

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trast, the static model does not utilize the previous measurements or predictions of NOx and CO; i.e., it predicts NOx and CO based only on the power production schedule of each time step. A schematic representation of the static algorithm is

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also shown in Figure 3. In the dynamic model, the actual plant measurements for NOx and CO are used at the beginning of each forecasting horizon. Utilizing the available measurements in the dynamic model enables more accurate predictions of NOx and CO. This is because the measurements provide a reference for the model

to correct its predictions. The static model, however, does not benefit from the avail-

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able measurements of the plant due to its steady-state nature.

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(a) Dynamic model

(b) Static model Figure 3: Schematic representation of the dynamic and static forecasting algorithms

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3.4. Optimization Algorithm As mentioned previously, a dynamic model is the foundation of dynamically minimizing the emissions of the plant effectively in presence of power output vari-

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ations. This section goes over the optimization algorithm developed for total emissions minimization of the utility boiler while the primary difference between a dynamic and a steady-state optimization algorithm is discussed.

This study considers a particle swarm optimization (PSO) algorithm (Kennedy

and Eberhart [1995]) to minimize the emissions of this plant. A PSO algorithm is selected because it can obtain the global minimum of the problem at each state of the

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utility plant while still being easy to develop and implement in an actual plant. The

primary difference between a dynamic and a steady-state optimization approach is in the structure of the neural network model of the plant used to evaluate the objective function (i.e., the overall emissions of the plant over a horizon). The dynamic particle swarm optimizer (DPSO) uses the trained dynamic model (RNN) of the plant while a steady-state PSO utilizes the trained static model to estimate NOx

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and CO. Accordingly, the previous predictions of NOx and CO are utilized recursively in the DPSO algorithm to obtain the emissions over the whole horizon, thus en-

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abling the algorithm to capture the dynamics of the plant. In contrast, the steadystate PSO estimates the emissions only based on the projected power output of each time step of the horizon; i.e., NOx and CO are estimated independent of their previ-

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ous predictions, thus the dynamics of the plant between subsequent time steps are ignored. For more detail about the algorithmic difference between the dynamic and

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static forecasting models, reference should be made to Section 3.3 and Figure 3). The objective function considered for both dynamic and steady-state optimiza-

tion of the plant is the sum of NOx and CO emissions over a horizon of plant op-

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eration while both variables are scaled according to Equation 3. The optimization algorithms manipulate the decision variables of the overfire air system at each time step of the horizon to achieve the minimum overall objective function over this horizon. The PSO algorithm works by initializing potential sets (particles) of the decision variables for the whole horizon. These potential sets are generated using a random number generator that provides random decision variables between their upper and 14

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lower bounds, thus allowing to probe the search space. The projected power output as well as the potential sets of the decision variables are then scaled according to Equation 3. The scaled variables and power output are then fed to the trained neural

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network models of the plant to obtain an estimation of the NOx and CO emissions for each time step of the horizon. In both steady-state and dynamic optimization algorithms, the sum of estimated NOx and CO over the whole horizon constructs the objective function associated with each potential set of decision variables. The

value of the objective function for each set of decision variables as well as the minimum objective value among all potential sets are also recorded. These provide the

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basis of variation of the decision variables for the next iteration of each algorithm, as described below.

The PSO algorithm relies on exchange of information between potential sets of decision variables; i.e. each set of decisions variables adjusts its trajectory based on its best previous objective value, as well as the best objective value among all sets

j +1

j

j

j

j

j

j

j

= W Vi +C 1 r i ,1 (X g − X i ) +C 2 r i ,2 (X i ,B − X i )

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Vi

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(the swarm) of decision variables, as shown by Equations 4 and 5.

j +1

j

= X i + Vi

j +1

(5)

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Xi

(4)

where V represents the velocity vector that is used to update the decision variables,

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represented by vector X . In Equation 4, W is the inertia weight, C 1 and C 2 are cognitive and social parameters, and r i ,1 and r i ,2 are uniformly distributed random vari-

ables with i being the index of each set of decision variables. In addition, j is an

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index for the iteration number, g represents the candidate set of decision variables with the minimum objective value among all possible sets (global minimum), and B is used to represent the best previous values of the decision variables that result in the minimum objective function of that set. Using Equations 4 and 5, the decision variables of each potential set are updated for all time steps of the horizon. In every update of the decision variables, it is also ensured that they stay within their applica15

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ble bounds. The updated decision variables are then used to estimate the new values of NOx and CO emissions, thus the new value of the overall objective function associated with each set of decision variables. Starting with an initial value for W , this

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study assumes that its value is decreased according to Equation 6 in each iteration of both optimization algorithms with α representing the rate of decrease in W . This procedure is continued until the maximum number of iterations is reached. Equiv-

alently, the incremental decrease in the objective value against a selected threshold

could be selected as the stopping criteria for the algorithm. A summary of the main

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steps of both optimization algorithms is shown in Figure 4.

W j +1 = W j (1 − α)

(6)

The values of α, initial W , C 1 , and C 2 are tuning parameters for each opimization algorithm, although this study adopts the proposed parameters by (Clerc and Kennedy [2002]). The number of potential sets of decsion variables that the opti-

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mization algorithm should try in each iteration is also user-defined. This study assumes 80 candidate sets of decision variables should be evaluated in each iteration

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of the algorithm. For more details about the PSO algorithm, reference should be made to Kennedy and Eberhart [1995].

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4. Simulation Results

This section provides a summary of the main simulation results. First, the simu-

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lation results of training the dynamic and static models are provided in Section 4.1. Then, the 3-hour in advance forecast of NOx and CO emissions is provided in Sec-

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tion 4.2. Finally, the simulation results for an offline optimization of the plant are presented. 4.1. Model Training A summary of the simulation results for the training data set is first presented in

this section. As mentioned previously, power production is an input to the model

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Figure 4: Main steps of the steady-state and dynamic optimization algorithms

that significantly influences the dynamics of boiler operation. Figure 5a presents the scaled power production data for the entire training period while Figure 5b provides a one-week segment of the training period. It is evident from Figure 5b that the power production from this coal-fired unit undergoes significant fluctuations

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throughout the week. One possible reason for fluctuations of the power output is the increased contribution of renewable power sources to the power grid that introduces new ramping scenarios to fossil-fueled power plants such as those considered

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in this study. This behavior also emphasizes the need for dynamic simulation of the boiler that can better capture its transient operation. 1

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Figure 5: Scaled power production of the training period

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As stated previously, the dynamic NARX model uses the past values of the out-

put variables to predict the next time step values of NOx and CO emissions. The

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number of past output variables used in the model defines its order. For instance, a model order of two uses two past values of NOx and CO to predict the next time step values. A sensitivity analysis is implemented to find the model order that best balances between complexity and prediction accuracy. For each case, the training of the model is also repeated multiple times to ensure that random initialization of the weight and bias factors in the Levenberg-Marquardt backpropagation algorithm

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result in the best observed R- and RMSE values. This study investigates a model order of one to four with various numbers of neurons. It is observed that a model order of one to four, with different numbers

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of neurons, always results in an R-value greater than 91% and 83% for estimation of NOx and CO, respectively. The RMSE observed for NOx estimation is also less

than 0.046 for model orders two to four and less than 0.110 for model order one, while the RMSE of CO estimation is less than 0.032 for all model orders (all observed

when considering various numbers of neurons). Additionally, it is observed that increasing the model order, while maintaining the same number of neurons, generally

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results in a marginal increase in the R-value and a marginal decrease in the RMSE observed for both NOx and CO. For instance, the R-values observed for NOx predic-

tion with 45 neurons in the hidden layer are 0.929, 0.936, 0.936, and 0.939 for the model orders one to four, respectively, while they are 0.856, 0.863, 0.863, and 0.864 when CO is estimated. The RMSE values observed for the NOx estimation for model orders two to four are 0.041, while it is 0.043 for model order one. The RMSE values

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of CO estimation are also 0.030, 0.030, 0.029, and 0.029 for orders one through four, respectively. These results are also summarized in Table 1. The difference in the R-

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and RMSE values of the model orders one to four is less than 1% with 45 neurons. Although a model order of one could also be chosen, a second order model is selected for the remainder of this study to balance between the complexity and prediction

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accuracy of the model. The results presented in the remainder of this section are also for a case with 45 neurons, as this configuration displays the best accuracy for

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the training data set. For comparison, a static model, which is equivalent to a zeroorder NARX model, with 45 neurons is also developed with the associated training results reported in Table 1. As observed in Table 1, a static model has the lowest

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R-value among all models while the RMSE is also the highest for both NOx and CO. This confirms that a dynamic model provides a more accurate prediction of the NOx and CO emissions over the training period. The scaled estimations of the NOx and CO emissions, corresponding to the train-

ing period with a scaled power production of Figure 5a, are shown in Figures 6 and 7 for the static and second order models, respectively. Although the overall trends 19

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Table 1: Summary of the training results with 45 neurons in the hidden layer

R-value (NOx)

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0.798

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Model order

0.030 0.029 0.029

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of both models match relatively well with the historical data of NOx and CO, one

obvious observation is that the static model has more out-of-range predictions than the second order dynamic model. It is observed that the second order model predicts a value above one or below zero, on a scaled basis, for NOx with a maximum occurrence of 7 times over 27,305 training data points while this occurs 28 times with the static model. The out-of-range predictions of CO for the static and second

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order dynamic models occur 980 and 670 times, respectively, over 27,305 training data points. Although an out-of-range prediction is unacceptable for both models, it demonstrates that the second order dynamic model produces less erroneous pre-

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dictions of NOx and CO than the static model.

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Figure 6: Scaled NOx estimation of the static and second order dynamic models for the training period

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Figure 7: Scaled CO estimation of the static and second order dynamic models for the training period

4.2. Three Hour In Advance Forecast

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After training the static and recurrent neural networks, they are used to fore-

cast the NOx and CO emissions for 36 time steps in advance, corresponding to three hours, and with respect to a given power production schedule. It is important to emphasize that the data set used to investigate the model forecasting capability is different from that used to train the models. Different time periods, all with a duration of three hours, could be chosen from the forecasting period between January 22

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31, 2018 to March 5, 2018. This study considers a time horizon during which the variation of power production throughout a day is among the highest. Additionally, a second time horizon during which power production initially experiences a

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moderate rate of change followed by small variations at the end of the horizon is considered. The first time horizon considered in this section corresponds to the operation of the plant on February 11, 2018 and the power production of the first three

hours of this day is selected. The second horizon is in the afternoon of February 21,

2018. The scaled power production profiles of these time periods are presented in

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Figure 8: Scaled power production of the forecasting period

The forecasts of NOx and CO emissions, corresponding to the power produc-

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tion profiles of Figure 8, are shown in Figures 9 and 10, respectively. As observed, the predictions from the second order dynamic model are closer to the overall trend of target data for both NOx and CO emissions over each 3-hour horizon than the static model. A comparison between the R- and RMSE values confirms this finding; i.e., the R-values of NOx estimation for the dynamic and static models are 0.794

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and 0.401, respectively, for the horizon on February 11 and 0.716 (dynamic model) and 0.598 (static model) for that of February 21. The R- values of CO estimation for February 11 are 0.788 and 0.701 for the dynamic and static predictions, respectively,

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while they are 0.661 (dynamic model) and 0.349 (static model) for February 21. The RMSE values for NOx estimation are 0.035 and 0.053 for the dynamic and static models, respectively, for February 11 and 0.042 (dynamic model) and 0.048 (static model) for February 21. Additionally, the RMSE of CO estimation are 0.025 (dynamic model)

and 0.028 (static model) for February 11 and 0.033 (dynamic model) 0.041 (static model) for February 21. It is evident from the R - and RMSE values that the predic-

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tions of the second order dynamic model are more accurate than the static model.

These results are summarized in Table 2. One possible reason for the lower R- values of both models for the forecasting case, as opposed to the training case, is that the data used for this study is only cleaned from out-of-range values; i.e., there is no attempt in the industrial unit to clean the data from possible noise issues associated with the data collection system. Although different settings, including the number

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of neurons, are attempted to avoid overfitting of the training data set, it is still possible that both models suffer from this issue to some extent; i.e., for the training data

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set, better estimations of NOx and CO are observed because the models attempt to mimic the many data points that are available (that may include noisy data). For the forecasting data set, it is possible that the model prediction is affected more with the

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smaller target data set that may also include noisy data, leading to a lower R-value for the forecasting case. The focus of this paper is, however, on demonstrating the

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increased prediction accuracy of dynamically simulating the boiler, as opposed to a static modeling approach. It is, therefore, anticipated that the raw data obtained from the utility boiler, after it is cleaned from out-of-range values, is satisfactory for

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the purpose of this paper. Further cleaning of the data from noise issues is the focus of future work. Close inspection of the NOx and CO forecasts, when they are scaled back to their

original orders of magnitude, are also intuitive. In this case, Equation 3 is used to back-calculate the unscaled forecasts of NOx and CO as well as the relative error between the model and actual unscaled data from the plant. Table 3 provides a sum25

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0.6 Target data Static Model Second Order Model

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Figure 9: NOx estimation for the forecast period

mary of the average relative error of the predictions from the static and dynamic

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models with respect to unscaled NOx and CO data from the plant. The average relative errors are also obtained over the same 3-hours horizons of Figures 9 and 10. It is apparent from this table that the relative prediction errors of NOx and CO are always smaller in the dynamic model than the static model. This is in agreement with the observations mentioned above for the better performance of the dynamic

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Figure 10: CO estimation for the forecast period

model in comparison to the static model from the R- and RMSE values standpoints.

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The trends of error between target data and model estimation, on an unscaled basis, are also shown in Figures 9 and 10 for the entire horizons of this study. The error shown in the far right plots of these figures is the mathematical difference between the unscaled target and estimated data, that can be positive or negative. From an operational standpoint, a deviation of ±0.06 l b/M M BT U for NOx and ±100 ppm

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Table 2: Summary of the results for typical 3-hour horizons with high and moderate degrees of variation in power production

Model

R-value (NOx) R-value (CO) RMSE (NOx) RMSE (CO)

February 11 Zero (Static)

0.401

0.701

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0.794

0.788

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0.598

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0.716

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Date

Table 3: Summary of the average relative errors and number of unacceptable estimations for typical 3-

Date

Model

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hour horizons with high and moderate degrees of variation in power production

Average error Average error No. of unacceptable No. of unacceptable (CO)

predictions (NOx)

predictions (CO)

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(NOx)

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for CO between the model estimates and the actual plant data is considered a bad prediction of the emission. Table 3 provides the number of times (over the entire

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36-time points of the prediction horizon) that the static and dynamic models estimate values outside the assumed acceptable deadbands. Accordingly, it is observed that the number of unacceptable predictions of NOx and CO in the static model is

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significantly higher than the dynamic model. This is more evident for the case on February 11 when the utility boiler undergoes more severe transients in the power

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output, as observed in Figure 8a. Additionally, it is observed in Table 3 that CO estimation has larger average rel-

ative errors than NOx in both dynamic and static models. This is attributed to the general sporadic behavior observed in the plant CO data, which is caused by the sensitive relationship between CO and excess oxygen in the unit (Yokogawa [2019]); i.e., the unit tends to oscillate on its excess oxygen readings due to changes in the fireball

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caused by mixing of constituents, changes in combustion from moment to moment, and feedback control systems trying to respond to these many changes. Because of the sensitive relationship between excess oxygen and CO, any minor changes in ex-

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cess oxygen lead to changes in CO in the plant data, which in turn results in less precise estimation of CO in comparison to NOx. It is, however, noticeable that the average error of CO estimation in the dynamic model is still less than 29%, with up to two

unacceptable predictions, as opposed to 88.26% error with up to 15 unacceptable estimates observed with the static model for the two cases considered here. In contrast, the average error of NOx estimation from the dynamic model reaches values

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as high as 15.55% with only 2 unacceptable estimates for the horizons considered in this study, compared to 30.3% error for the static model with up to 24 unacceptable

estimates. Noting that the deadbands assumed for the unacceptable predictions of NOx and CO are the same for the dynamic and static models, the abovementioned metrics (number of unacceptable estimates and average relative error) that are calculated based on unscaled data also demonstrate that the dynamic model is more

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accurate than the static model in forecasting NOx and CO.

As mentioned previously, the selection of the 3-hour period for the forecasting

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case is based on two days that display large and modereate magnitudes of variation of the power output throughout the day. The power output, however, varies significantly from day-to-day operation of the boiler, as observed in Figures 5 and 8.

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The varying day-to-day operation of the plant also results in varying performance of both static and dynamic forecasts. For instance, it is evident from Figures 9a and

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10a that both static and dynamic forecasts of NOx and CO emissions for February 11 tend to be underpredicted. In contrast, Figures 9b and 10b for February 21 show a mixed performance; i.e., the static and dynamic forecasts include both overpredic-

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tion and underprediction of the emissions over the horizon, although the dynamic model still predicts the overall trend of the historical data more accurately. While the issues mentioned previously (i.e., the models suffering from some level of overfitting and industrial data not being cleaned from noise) are still applicable here and contribute to the deviations observed between the model estimates and actual data, another possibility for such performance could be that the NARX modeling 29

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approach might suffer from a short memory. This means that further down the prediction horizon, it forgets about the measured NOx and CO data that were used at the beginning of the horizon as a self-correcting reference for the model. One possi-

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ble solution could be to break the horizon into pieces and introduce measurements at the beginning of each new subset of horizons. This solution is practiced for the horizon on February 21 by breaking the 36-steps horizon into three 12-steps horizons (corresponding to three 1-hour horizons) and comparing the predictions met-

rics for both cases. The R-value of NOx estimation for the dynamic model for this case is 0.825, up from 0.716 when no horizon breakdown is implemented. Similarly,

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the R-value of CO estimation for the dynamic model with three 12-steps horizon is 0.747, up from 0.661 with one 36-steps horizon. Similar results are observed for the RMSE values of NOx and CO estimation. It should also be noted that no difference is expected with the static model because it does not utilize the measurements or previous predictions of NOx and CO, as discussed in Section 3.3. Application of shorter time resolutions for forecasting of unknown variables is particularly appli-

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cable in real-plant operations when such soft sensors are utilized for optimization of the plant in closed-loop. Despite the better performance of shorter horizons, a 36-

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steps horizon is still preferable for the remainder of this analysis because a shorter horizon might not be sufficiently long to have a ramping event completed, as mentioned before. Instead, to generalize the better performance of the dynamic model

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with more certainty, another approach is utilized as the basis of comparison. This procedure is further explained below.

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This procedure is based on dividing the forecasting horizon into periods with steady-state and dynamic behavior and running the models over these periods. To achieve this goal, the standard deviation of the scaled power output for consequent

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3-hour horizons in the forecasting period is obtained and used as a measure of steady-state detection. For the forecasting period of January 31, 2018 to March 5, 2018, there are 9,032 periods with a duration of three hours. A plot of the standard deviation of power output over the 9,032 periods is presented in Figure 11. The minimum and maximum standard deviation of power output observed in this figure are 2.512 x 10−4 and 0.371, respectively. This study assumes that any 3-hour period that 30

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has a standard deviation of less than 0.005 for the power output has a steady-state behavior while a standard deviation of greater than 0.27 is representative of a horizon with significant dynamic behavior. The selection of thresholds for steady-state

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or significant dynamic behavior is arbitrary but the thresholds selected in this analysis result in a similar number of periods that would qualify for steady-state and dynamic behavior; thus, this selection of the thresholds makes the performance com-

parison of the static and second order dynamic models more meaningful. With this

assumption, there are 387 periods that have a standard deviation of less than 0.005 while 391 periods have a standard deviation of greater than 0.27. The static and

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second order models are both run over these periods, all of which have a 3-hour

duration. Then, the R- and RMSE values of all simulations as well as an average of these metrics are obtained for both models. The average R- and RMSE values of NOx and CO estimation for periods with steady-state and significant dynamic behavior are summarized in Tables 4 and 5, respectively. It is evident from these tables that the average R-value of the second order dynamic model for the estimation of

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NOx and CO is greater than that of the static model for periods with steady-state and dynamic behavior. Additionally, the average RMSE observed for prediction of

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NOx and CO from the second order dynamic model is smaller than the static model for periods with steady-state and dynamic behavior. Therefore, both metrics imply that the second order dynamic model outperforms the static model in prediction of

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NOx and CO during periods with steady-state and dynamic behavior. This conclusion is in agreement with the previous observations from a single 3-hour horizon

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forecast. It should, however, be emphasized that real-time decision making with assistance from such data-driven models should still be based on the model prediction for each individual prediction horizon, rather than its average performance, in

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industrial units. 4.3. Offline Optimization of the Plant This section provides a preliminary analysis of dynamic optimization of the util-

ity boiler while using the trained models of Section 4.1. This optimization is applied in an offline mode to the overfire air system to find the optimal settings that 31

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Table 4: Summary of the results for 3-hour horizons with steady-state behavior (forecasting data set)

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Table 5: Summary of the results for 3-hour horizons with dynamic behavior (forecasting data set)

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Second order

R-value (NOx)

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would result in minimum total emissions over a horizon. The NOx and CO emissions from the dynamic optimization case are then compared with the emissions associated with historical operation of the plant as well as steady-state optimization

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of the plant over the same horizon. While an offline optimization approach is still suitable to demonstrate the potential reduction in overall emissions of the plant, as is the case here, it is critical to emphasize that a closed-loop optimization of the plant is required to fully investigate the feasibility and effectiveness of this approach; i.e., the proposed dynamic optimization algorithm should be applied to a real-time

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or a physics-based simulated plant to investigate the impact of the optimized decisions when implemented on the plant. A closed-loop optimization of the utility boiler is the focus of future research.

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The optimization case considered here uses the same 3-hour horizon as Section 4.2 with a projected power production similar to Figure 8a. This enables to demon-

strate that optimizing the operation strategy of the plant (i.e., changing the decision variables of the overfire air system optimally) would result in reduced emissions

when compared to historical plant operation. Figure 12 shows the trend of NOx

generation from the optimization scenarios against the historical emissions from

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the plant. As observed in this figure, NOx generation from the optimized scenarios

is always lower than historical NOx generated by the plant, regardless of the type of optimization algorithm utilized. This demonstrates that by optimizing the operational strategy of the plant, it is possible to lower the emissions of an actual plant. In other words, by utilizing all degrees of freedom in the system and manipulating them within a safe range, lower emissions are achievable without the need to

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change any major infrastructure in the plant. It is also noticeable that close to hour one of the horizon, the scaled NOx generation from the dynamic optimization case

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is negative. This is because the actual unscaled NOx value that the dynamic optimizer outputs is lower than the minimum NOx value used in Equation 3 for scaling purposes. The actual unscaled NOx generation from the dynamic optimizer is fur-

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ther investigated and it is confirmed that a positive NOx value within the reasonable range is generated by the optimizer. Occurrence of such negative scaled values is in-

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structive and highlights the importance of close inspection of the results generated from a data-driven approach. One possible scenario for such negative estimated values could be the intrinsic prediction inaccuracy of the data-driven models when

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input values are outside the range of their training data set. When such cases are observed frequently, one possible solution could be to retrain the neural network models with the most recent plant data. For the scenarios considered in this analysis, the range that the optimizer can manipulate the decision variables is actually tighter than the training data set, also confirming that the negative scaled NOx values around hour one are not due to decision variables being outside of their training 33

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data set. Additionally, a tighter range of decision variables ensures that the operational changes recommended by the optimizer would stay within the safe operating range of the plant despite the stochastic nature of the PSO optimization algorithms

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used here. To avoid the impact of negative values observed in NOx emissions from the dynamic optimizer, the comparison with historical data is made on an unscaled basis. Accordingly, it is observed that the overall NOx emissions over the three hour

horizon of this analysis for cases with steady-state and dynamic optimization are 49.2% and 51.3% less than historical data, respectively.

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Figure 12: Optimization result for NOx for the forecast period on February 11, 2018

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Optimized results for CO emissions also provide additional insights. When steadystate optimization is utilized, it produces 25.3% higher CO than the historical data over the three hour horizon of this analysis. In contrast, 19.5% lower CO emissions

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are observed with dynamic optimization when compared with historical plant data. Both of these comparisons are made based on unscaled data for CO emissions. It is apparent that the dynamic optimization of the plant performs better than the steady-state optimization and historical operation of the plant when CO generation is concerned. In summary, findings from the optimization scenarios considered here demon34

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0.3 Target data Static Model Second Order Model

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Figure 13: Optimization result for CO for the forecast period on February 11, 2018

strate a significant potential for simultaneous NOx and CO reduction from this util-

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ity boiler, as well as similar systems in power or other energy generation sectors, when a dynamic optimization approach is utilized. It should also be noted that

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while the steady-state optimization results of this study demonstrate a potential for NOx reduction in comparison to the historical data, this method is not recommended. This is because of the less accurate predictions of the static model, as was

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observed in Table 3, that are then used in the steady-state optimization algorithm, which makes the static optimization results less reliable. This is the main finding of

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this paper; it is critical to implement dynamic modeling and optimization in the current highly variable power grids to be able to more effectively and reliably minimize the emissions from the fossil-fueled power plants. Additional investigations should

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be conducted in future work to ensure that the operation of the plant in closed-loop optimization scenario is smooth.

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5. Conclusion The introduction of intermittent renewable supplies to the current power grid has increased the variability of the grid. Noting that many fossil fuel-fired units are

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traditionally designed to be base-loaded, dynamic modeling of these plants plays an important role in minimizing the emission of pollutants when the plant cycles. This

study is focused on developing a dynamic model of a coal-fired utility boiler, using a nonlinear autoregressive neural network with external inputs (NARX). Additionally, a static model is developed that serves as a comparison basis for the dynamic

model. Both models are set up to provide simultaneous estimations of the NOx and

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CO emissions.

These models are first trained with historical data from the boiler that includes 72 inputs that the operators manipulate and a given power production profile. The outputs from the model are estimations of the NOx and CO emissions, which are compared with the historical plant data. The simulation results from a sensitivity

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analysis implemented in this study reveal that a second order dynamic model is sufficient to represent the time-series input/output data of this boiler. When predictions of a second order dynamic and static models are compared with historical

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NOx and CO data, it is observed that the dynamic model provides a higher coefficient of correlation (R) and a lower root mean square error (RMSE). Additionally, the

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number of out-of-range predictions of NOx and CO over the training period is less with a dynamic model.

After the dynamic and static models are trained with historical data, they are

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used to forecast NOx and CO multiple steps ahead in time, given a future power production schedule for the power plant. A 3-hour forecasting horizon is considered in this study to allow a transient event such as a ramp up/down in power output

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to complete. It is observed that the estimations of NOx and CO from the dynamic model are closer to the trend of historical data, when compared with estimations from the static model. The R- values of NOx estimation are 0.794 and 0.401 for the dynamic and static models, respectively, while they are 0.788 and 0.701 when CO is estimated. The RMSE values of NOx estimation are also 0.035 and 0.053 for the

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dynamic and static models, respectively, while they are 0.025 and 0.028 for CO estimation. These values are obtained for a 3-hour period during which the power production profile has a high degree of variability. Additionally, when unscaled esti-

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mates of NOx and CO are examined, it is observed that the dynamic model produces estimates with lower average relative error and number of unacceptable predictions

for both NOx and CO. When the dynamic and static models are run for several periods that show significantly dynamic and static behavior, on the basis of power production schedule, it is still observed that the average R- and RMSE values of NOx and

CO estimation for a dynamic model are higher and lower, respectively. It is, there-

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fore, concluded that the dynamic model outperforms the static model in accurately

predicting the NOx and CO emissions over periods with steady-state and dynamic behavior.

A preliminary analysis to optimize the plant operation, on an offline basis over a three-hour horizon, is also investigated in this study. The simulation results demonstrate that applying steady-state and dynamic optimization algorithms to trained

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static and dynamic models of the plant results in 49.2% and 51.3% reduction in NOx generation when compared with plant historical data. Additionally, a dynamic op-

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timization algorithm is capable of reducing CO emissions by 19.5% as compared to plant historical data while a steady-state optimizer actually results in 25.3% increase in CO emissions. It should, however, be noted that the steady-state optimization

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results, unlike the dynamic approach, are less reliable due to the lower prediction accuracy associated with the static forecasting algorithm. Dynamic simulation and

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optimization are, therefore, recommended in the current highly variable power grids to be able to minimize the emissions more effectively. The future direction of this work includes additional cleaning of the historical

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data from noise issues. Additionally, dimension reduction of the problem using methods such as principal component analysis can simplify the realization of the plant behavior. Developing a closed-loop optimization of the plant and comparing the performance of steady-state and dynamic optimization algorithms in minimizing the plant emissions over a future horizon and in response to a given power production schedule is an additional direction for this research. 37

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Acknowledgments The authors acknowledge the Sustainable Transportation and Electricity Plan

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Program of Pacificorp for their financial and technical supports.

References

Babcock & Wilcox Company. http://www.babcock.com, (accessed July 2018).

EPA [1999], Nitrogen Oxides (NOx), Why and How They Are Controlled. https:

AN US

//www3.epa.gov/ttncatc1/dir1/fnoxdoc.pdf, (accessed May 2018).

EIA [2018], Electricity Data Browser. https://www.eia.gov/electricity/data/

browser/. (accessed May 2018).

http://www.irena.org/

IRENA [2015], Renewable Energy Target Setting.

documentdownloads/publications/irena_re_target_setting_2015.pdf,

M

(accessed May 2018).

Mathwork [2017], MATLAB programming language. https://www.mathworks.

ED

com/,(accessed May 2018).

NETL [2012], Impact of Load Following on Power Plant Cost and Performance:

Literature Review and Industry Interviews.

https://www.netl.

PT

doe.gov/File%20Library/Research/Energy%20Analysis/Publications/ NETL-DOE-2013-1592-Rev1_20121010.pdf, (accessed May 2018).

CE

Steel & Alloy [2018], Low NOx Burner System.

http://steelalloy.com/

power-generation/burners/,(accessed May 2018).

AC

Yokogawa [2019],

CO measurement in coal fired plants.

https://

www.yokogawa.com/us/library/resources/application-notes/ co-measurement-in-coal-fired-plants/,(accessed January 2019).

Tugce Bekat, Muharrem Erdogan, Fikret Inal, and Ayten Genc. Prediction of the bottom ash formed in a coal-fired power plant using artificial neural networks. Energy, 45(1):882 – 887, 2012. doi: 10.1016/j.energy.2012.06.075. 38

ACCEPTED MANUSCRIPT

Thomas Le Bris, Francisco Cadavid, Sebastien Caillat, Stanislas Pietrzyk, Jacques Blondin, and Bernard Baudoin. Coal combustion modelling of large power plant, for NOx abatement. Fuel, 86(14):2213 – 2220, 2007. doi: 10.1016/j.fuel.2007.05.

CR IP T

054. Eddy H. Chui and Haining Gao. Estimation of NOx emissions from coal-fired utility boilers. Fuel, 89(10):2977 – 2984, 2010. doi: 10.1016/j.fuel.2010.05.008.

M. Clerc and J. Kennedy. The particle swarm - explosion, stability, and convergence

in a multidimensional complex space. IEEE Transactions on Evolutionary Com-

AN US

putation, 6(1):58–73, Feb 2002. ISSN 1089-778X. doi: 10.1109/4235.985692.

Arthur R. DiNicolantonio. Flue gas recirculation for NOx reduction in premix burne, 1992. US Patent 5092761A.

Patrick Eser, Antriksh Singh, Ndaona Chokani, and Reza S. Abhari. Effect of increased renewables generation on operation of thermal power plants. Appl. En-

M

ergy, 164:723 – 732, 2016. doi: 10.1016/j.apenergy.2015.12.017.

Miguel Angel Gonzalez-Salazar, Trevor Kirsten, and Lubos Prchlik. Review of the

ED

operational flexibility and emissions of gas- and coal-fired power plants in a future with growing renewables. Renew. Sust. Energy Rev., 82:1497 – 1513, 2018. doi:

PT

10.1016/j.rser.2017.05.278.

Martin T. Hagan and Mohammad B. Menhaj. Training feed-forward networks with the marquardt algorithm. IEEE Trans. Neural Networks, 5(6):989 – 993, 1994. doi:

CE

10.1109/72.329697.

AC

Kyung Sook Jung, Tim C Keener, and Soon-Jai Khang. Compositional factors affecting NOx emissions from Ohio coals. Fuel Process. Tech., 74(1):49 – 61, 2001. doi: 10.1016/S0378-3820(01)00223-5.

James Kennedy and Russell Eberhart. Particle swarm optimization. In Proceedings of the IEEE Int. Conf. Neural Networks, pages 1942–1948, Piscataway, NJ, 1995.

39

ACCEPTED MANUSCRIPT

Marek L. Kubik, Phil J. Coker, and Janet F. Barlow. Increasing thermal plant flexibility in a high renewables power system. Appl. Energy, 154:102 – 111, 2015. doi: 10. 1016/j.apenergy.2015.04.063.

CR IP T

Ryoichi Kurose, Michitaka Ikeda, Hisao Makino, Masayoshi Kimoto, and Tetsuo Miyazaki. Pulverized coal combustion characteristics of high-fuel-ratio coals. Fuel, 83(13):1777 – 1785, 2004. doi: 10.1016/j.fuel.2004.02.021.

K. Li, J. Peng, G.W. Irwin, L. Piroddi, and W. Spinelli. Estimation of NOx emissions in thermal power plants using eng-genes neural networks. IFAC Proceedings Vol-

AN US

umes, 38(1):115 – 120, 2005. doi: 10.3182/20050703-6-CZ-1902.01748. 16th IFAC World Congress.

Kang Li, Steve Thompson, and Jianxun Peng. Modelling and prediction of NOx emission in a coal-fired power generation plant. Control Eng. Prac., 12(6):707 – 723, 2004. doi: 10.1016/S0967-0661(03)00171-0.

M

Vladimir Lifshits and Stephen B. Londerville. Low NOx burner, 2014. US Patent 8794960B2.

ED

Muhammad E. Munawer. Human health and environmental impacts of coal combustion and post–combustion wastes. J. Sustain. Min., 17(2):87 – 96, 2018. doi: 10.1016/j.jsm.2017.12.007.

PT

S A Nihalani, Y Mishra, and J Juremalani. Emission control technologies for thermal power plants. IOP Conference Series: Materials Science and Engineering, 330(1):

CE

012122, 2018.

Sandro Dal Secco, Olivier Juan, Myriam Louis-Louisy, Jean-Yves Lucas, Pierre Plion,

AC

and Lynda Porcheron. Using a genetic algorithm and CFD to identify low NOx configurations in an industrial boiler. Fuel, 158:672 – 683, 2015. doi: 10.1016/j. fuel.2015.06.021.

Muhammad Shakil, Moustafa Elshafei, Mohamed A. Habib, and Farzaneh Maleki. Soft sensor for NOx and O2 using dynamic neural networks. Comput Electr Eng, 35(4):578 – 586, 2009. doi: 10.1016/j.compeleceng.2008.08.007. 40

ACCEPTED MANUSCRIPT

Ze Shen. Simulation of NOx reduction in power plant flue gas. Master’s thesis, Lehigh University, 2017.

CR IP T

Lesley Sloss. Nitrogen Oxides Control Technology Fact Book. Elsevier, 1992. Jure Smrekar, Mohsen Assadi, Magnus Fast, Igor Kuštrin, and Sudipta De. Devel-

opment of artificial neural network model for a coal-fired boiler using real plant data. Energy, 34(2):144 – 152, 2009. doi: 10.1016/j.energy.2008.10.010.

Jure Smrekar, Primož Potoˇcnik, and Andrej Senegaˇcnik. Multi-step-ahead prediction

10.1016/j.apenergy.2012.10.056.

AN US

of NOx emissions for a coal-based boiler. Appl. Energy, 106:89 – 99, 2013. doi:

Jingge Song, Carlos E. Romero, Zheng Yao, and Boshu He. A globally enhanced general regression neural network for on-line multiple emissions prediction of utility boiler. Know.-Based Syst., 118:4 – 14, 2017. doi: 10.1016/j.knosys.2016.11.003. Peng Tan, Ji Xia, Cheng Zhang, Qingyan Fang, and Gang Chen. Modeling and op-

M

timization of NOx emission in a coal-fired power plant using advanced machine learning methods. Energy Procedia, 61:377 – 380, 2014. doi: 10.1016/j.egypro.

ED

2014.11.1129. International Conference on Applied Energy, ICAE2014. Peng Tan, Dengfeng Tian, Qingyan Fang, Lun Ma, Cheng Zhang, Gang Chen, Li-

PT

jin Zhong, and Honggang Zhang. Effects of burner tilt angle on the combustion and NOx emission characteristics of a 700 MWe deep-air-staged tangentially pulverized-coal-fired boiler. Fuel, 196:314 – 324, 2017. doi: 10.1016/j.fuel.2017.02.

CE

009.

AC

Gregory L. Tomei. Steam/its Generation and Use. The Babcock & Wilcox Company, 2015.

PÄ´snar Tüfekci. Prediction of full load electrical power output of a base load operated combined cycle power plant using machine learning methods. Int. J. Electr. Power Energy Syst., 60:126 – 140, 2014. doi: 10.1016/j.ijepes.2014.02.027.

41

ACCEPTED MANUSCRIPT

Yasin Tunckaya and Etem Koklukaya. Comparative prediction analysis of 600 MWe coal-fired power plant production rate using statistical and neural-based models. J. Energy Inst., 88(1):11 – 18, 2015. doi: 10.1016/j.joei.2014.06.007.

CR IP T

Jianhui Wang, Antonio J. Conejo, Chengshan Wang, and Jinyue Yan. Smart grids, renewable energy integration, and climate change mitigation - future electric energy systems. Appl. Energy, 96:1 – 3, 2012. doi: 10.1016/j.apenergy.2012.03.014.

Zhongbao Wei, Xiaolu Li, Lijun Xu, and Yanting Cheng. Comparative study of computational intelligence approaches for NOx reduction of coal-fired boiler. Energy,

AN US

55:683 – 692, 2013. doi: 10.1016/j.energy.2013.04.007.

Jinyue Yan, Yongping Zhai, Priyantha Wijayatunga, Abdul Matheen Mohamed, and Pietro Elia Campana. Renewable energy integration with mini/micro-grids. Appl. Energy, 201:241 – 244, 2017. doi: 10.1016/j.apenergy.2017.05.160.

Lingyan Zeng, Zhengqi Li, Guangbo Zhao, Shanping Shen, and Fucheng Zhang. Nu-

M

merical simulation of combustion characteristics and NOx emissions in a 300 MWe utility boiler with different outer secondary-air vane angles. Energy Fuels,

ED

24(10):5349–5358, 2010. doi: 10.1021/ef100682s. Kangkang Zhang, Jun Zhao, and Yucai Zhu. MPC case study on a selective catalytic reduction in a power plant. Journal of Process Control, 62:1 – 10, 2018. doi: 10.

PT

1016/j.jprocont.2017.11.010.

Hao Zhou, Kefa Cen, and Jianren Fan. Modeling and optimization of the NOx emis-

CE

sion characteristics of a tangentially fired boiler with artificial neural networks. Energy, 29(1):167 – 183, 2004. doi: 10.1016/j.energy.2003.08.004.

AC

Hao Zhou, Ligang Zheng, and Kefa Cen. Computational intelligence approach for NOx emissions minimization in a coal-fired utility boiler. Energ. Convers. Manage., 51(3):580 – 586, 2010. doi: 10.1016/j.enconman.2009.11.002.

Hao Zhou, Jia Pei Zhao, Li Gang Zheng, Chun Lin Wang, and Ke Fa Cen. Modeling NOx emissions from coal-fired utility boilers using support vector regression with

42

ACCEPTED MANUSCRIPT

ant colony optimization. Eng. Appl. Artif. Intel., 25(1):147 – 158, 2012. doi: 10.

AC

CE

PT

ED

M

AN US

CR IP T

1016/j.engappai.2011.08.005.

43