Prediction and Control of the Nitrogen Oxides Emission for Environmental Protection Goal Based on Data-Driven Model in the SCR de-NO_x System

Abstract

In order to reduce the nitrogen oxides (NO_x) emission of flue gas, a selective catalytic reduction (SCR) system must be installed. In general, the lag of the inlet NO_x analyzer, the action of the NH₃ injection valve and the feedforward signal are seriously delayed. Therefore, it is necessary to consider the measurement lag of inlet NO_x on the NH₃ injection flowrate control system. In this paper, the data-driven model of inlet NO_x is proposed to improve control system, so as to avoid excessive or insufficient NH₃ injection. First, the measurement lag time of inlet NO_x is estimated by the blowback signal of a CEMS and the change process of the inlet O₂ content. Then, an exponential model is used to predict the inlet NO_x in advance, and recursive LSSVM is proposed to revise the output of the exponential model. Finally, the output of the final model is used as the feedforward signal for improved feedforward (IF) control. Based on IF control and PID control, the IF-PID control strategy for NH₃ injection is proposed. The results show that the outlet NO_x are close to the set value and meet the national environmental regulation. Furthermore, the average value of the NH₃ injection flowrate remains unchanged. It shows that a better control effect and environmental sustainability are achieved without increasing the cost of NH₃ injection.

1. Introduction

Coal-fired power generation is currently the main form of power generation in thermal power plants, and the coal burning in boilers produces large amounts of nitrogen oxides (NO_x), which are absorbed by rain and snow as they fall and are generated in the atmospheric system, resulting in acid rain that can cause building corrosion and crop death, thus affecting the sustainability of natural resources. NO_x also reacts photochemically with other pollutants in the ultraviolet light, creating secondary pollutants known as photochemical smog pollution. If it encounters fine particles in the air, it will form PM2.5, thus endangering the survival of animals and agricultural crops, thus destroying the balance of the ecosystem and causing significant pollution to the environment. So, NO_x emissions from thermal power plants have been under strict supervision. In China, it has been required that NO_x emissions be reduced to below 50 mg/m³. On the one hand, the valve life is easily affected by the frequent action of the NH₃ injection valve. On the other hand, if the NH₃ injection is less frequent, it is easy to cause the outlet NO_x to exceed the national environmental protection standard and allow the NH₃ to escape, causing secondary environmental pollution [1]. Flue gas denitrification technology is used to denitrify the exhaust gas from the coal combustion. A selective catalyst reduction (SCR) system is the current method used by the majority of thermal power units. The common reducers for a SCR system are liquid ammonia, urea and ammonia water. The use of ammonia water as a reducing agent can not only avoid the use of liquid ammonia with high safety risks, but also avoid the use of urea with high operating costs. Due to the large inertia of the SCR system and the response lag of the NO_x analyzer, the control effect of the traditional proportion integration differentiation (PID) control method is poor. So, it is difficult to put the control system into an automatic mode. In addition, the response lag of the NO_x analyzer is up to 1 min, so the SCR system is different from the conventional large inertia control object and has a negative impact on the control effect. So, the existing feedforward control strategy received attention.

The direct reason which affects the fluctuation of the outlet NO_x concentration is the fluctuation of the inlet NO_x concentration, so the control effect of the outlet NO_x concentration will be affected directly when the inlet NO_x concentration has a large fluctuation. In order to improve the control effect of NH₃ injection, it is necessary to consider the response lag of the inlet NO_x analyzer. Although many studies have solved the large inertia of the SCR system by improving the control method, the source of lag is less studied [2,3]. The lag time is mainly caused by the NO_x analyzer in a continuous emission monitoring system (CEMS). The response lag of the inlet NO_x analyzer leads to the NH₃ injection valve action slowly. So, the SCR control system cannot eliminate the lag which undoubtedly increases the difficulty of the NH₃ injection flowrate control and causes the outlet NO_x fluctuation [4,5]. Therefore, by studying the data-driven model of the inlet NO_x concentration, the effect of lag on the SCR system can be compensated to some extent.

Some scholars proposed data-driven techniques to build prediction models based on the field data. Shakil et al. [6] established the dynamic neural network (NN) model of the inlet NO_x concentration and inlet O₂ content in the SCR system, and principal component analysis (PCA) is then used to reduce the dimensionality of the input matrix, estimate the lag time by genetic algorithm (GA) algorithm, and finally validate the NN model by field data. Hsieh et al. [7] proposed the data-driven model of the NO_x concentration based on Kalman filtering and the data fusion technique to overcome the lag time of the SCR system, but the method only used a lag time within 200 s. Peng et al. [8] proposed PCA and SVR models to make more accurate and rapid forecasting of the inlet NO_x concentration, respectively. Lv et al. [9] used a model combining an internal LSSVM model with an external linear PLS to predict the outlet NO_x concentrations. Li et al. [10] proposed a modelling approach which combines the moving window partial least squares (MWPLS) and partially weighted regression to predict the outlet NO_x. However, the above method can only predict the inlet NO_x concentration at the current moment. Ahmed et al. [11] used a real-time update strategy based on LSSVM to predict the NO_x, and it enhanced the long-term prediction accuracy. However, the model has some deviation when the boiler is under variable operation conditions. Yang et al. [12] proposed a real-time dynamic prediction model of the inlet NO_x concentration based on LSSVM and considered delay time and prediction error. Xie et al. [13] proposed a sequence-to-sequence dynamic prediction model to predict the future outlet NO_x concentrations. In addition, some scholars analyzed the effect of the inlet NO_x concentration measurement lag on the control effect by predicting the inlet NO_x concentration in advance. Matsumura et al. [14] eliminated the effect of lag time to some extent by predicting the inlet NO_x concentration in advance with LSSVM, which improved the control accuracy and reduced the operation cost. Kříž et al. [15] estimated the time delay by using the Lyapunov exponent and embedding dimension. Kang et al. [16] proposed a bidirectional long- and short-term memory (LSTM) neural network and estimated the lag time of SCR systems by dynamic joint mutual information (MI). Song et al. [17] used an improved MI feature selection algorithm to filter out the input variables of the inlet NO_x concentration model. The input variables are then fed together into the LSTM neural network to build the model. Liu et al. [18] selected 22 key variables of the power plant and built the multiple linear regression (LR) model with three hidden layers. Wu et al. [19] proposed the least absolute shrinkage and selection operator to select input variables and used long short-term memory to establish the model. Yuan et al. [20] combined PCA and SGEM method to build an inlet NO_x concentration model. The MI method was used to select the input variables of the inlet NO_x concentration model. Li et al. [21] built the mechanism models of the SO₂, inlet NO_x concentration and O₂ content, respectively. Then, the improved RBF neural network was then adopted to compensate the prediction error.

Table 1. Different data-driven techniques in the literature.

Literature	Data-Driven Model	Dynamic Model	Model Simplification	Delay Estimation	Prediction Period
Shakil et al. [6]	NN	Yes	Yes	Yes	Current
Hsieh et al. [7]	Kalman filtering	/	/	Yes	Current
Peng et al. [8]	SVR	/	Yes	/	Current
Lv et al. [9]	LSSVM	/	Yes	/	Current
Li et al. [10]	MWPLS	Yes	Yes	/	Current
Ahmed et al. [11]	LSSVM	Yes	/	/	Long-term
Yang et al. [12]	LSSVM	Yes	/	Yes	Long-term
Xie et al. [13]	LSTM	Yes	/	Yes	Long-term
Matsumura et al. [14]	LSSVM	/	/	Yes	Long-term
Kříž et al. [15]	Chaos Theory	/	/	Yes	Long-term
Kang et al. [16]	biLSTM	/	/	Yes	Long-term
Song et al. [17]	LSTM	/	/	/	Long-term
Liu et al. [18]	LR	/	/	/	Long-term
Wu et al. [19]	LSTM	/	Yes	/	Long-term
Yuan et al. [20]	SGEM	/	Yes	/	Long-term
Li et al. [21]	Improved model	/	/	/	Long-term
This paper	Improved model	Yes	Yes	Yes/ quantitative	Long-term

shows the advantages and disadvantages of different data-driven techniques from different aspects in the literature [6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]. The shortcomings of the existing literature are mainly the following two aspects: First, there is a lack of clarity in the analysis of the CEMS measurement lag. Second, there is a lack of quantitative conclusions.

Therefore, in order to improve the control effect of the NH₃ injection flowrate, this paper proposes to improve the existing feedforward control strategy. Firstly, quantitative analysis is adopted to estimate the lag time, and it improves feedforward (IF) control by establishing an improved exponential prediction model for the inlet NO_x concentration and using the output of this model as a feedforward signal. Secondly, in order to further improve the control accuracy of the PID control, an IF-PID control is proposed. Finally, the PID and IF-PID control are compared.

2. The Lag Time of the Inlet NO_x Concentration

In this paper, a quantitative estimation of the lag time of the inlet NO_x concentration is required before building a data-driven model. Firstly, the reasons for the lag time are analyzed in this section; then, the analysis method for estimating the lag time is proposed.

2.1. The Reason for the Lag Time

A CEMS comprises a gaseous pollutant monitoring subsystem, a data acquisition and communication subsystem, a flue gas parameter monitoring subsystem and a particulate matter monitoring subsystem. Here, we analyze the gaseous pollutant monitoring subsystem involving NO_x and SO₂ monitoring, whereby the CEMS extracts flue gas directly from the flue through the long pipe. Flue gas is directed to the pre-treatment system for dust removal, dehumidification and corrosive gas treatment, and finally reaches the flue gas analyzer. Measurement data from the flue gas analyzer are transmitted to the industrial control computer for processing, thus realizing the real-time monitoring of NO_x and SO₂.

The schematic diagram of SCR de-NO_x system is shown in Figure 1. The flue gas channel at the exit of the economizer is divided into two paths, each path of flue gas corresponds to an SCR reactor, and the flue gas enters the catalyst layer after passing through the flow equalizer. At the same time, before the flue gas enters the catalyst layer, the mixed gas of NH₃ and air enters the ammonia injection grid, and then reaches the SCR reactor, where it reacts with NO_x in the flue gas under the action of the reaction temperature (280~400 °C) and the activity of the catalyst. The flue gas after the reaction is discharged into the chimney through equipment such as an air preheater, electrostatic precipitator and induced-draft fan.

Because the measurement of the NO_x concentration requires a long pipe to reach the NO_x analyzer and the analysis of NO_x also takes some time, this is the reason why the CEMS measurements have a long lag time.

2.2. The Analysis of Lag Time

Because the blowback signal of the CEMS is usually accessed in the distributed control system (DCS) of thermal power plant, the NO_x concentration fluctuates drastically during the blowback, so it is easy to obtain abnormal values of the NO_x concentration, which cannot be used for analysis. In fact, the NO_x concentration is usually correlated with O₂ content, the reason being that the measured NO_x concentration is corrected by the standard O₂ content. In addition, most significant factors affect the inlet NO_x concentration in the literature [5], and the O₂ content has the greatest influence on the inlet NO_x concentration. Based on the above factors, this paper proposes estimating the lag time by using the purge signal of the CEMS and the variation of inlet O₂ content, and then the lag of the inlet NO_x concentration is obtained.

Figure 2 shows that the inlet NO_x concentration during the blowback fluctuates drastically because air is used during the blowback. So, the maximum O₂ content is 21%, and the change time for the inlet NO_x concentration and inlet O₂ content are the same as the blowback time, i.e., 3 min. So, it shows that it is more convenient and accurate to use the inlet O₂ content to estimate the lag time of the NO_x analyzer.

Figure 3 shows that when the blowback signal is 1, the blowback starts, and the lag time can be judged by the rise time of inlet O₂ content at the moment of the blowback. Similarly, when the blowback signal is 0, the blowback has ended, and the CEMS will re-pump the flue gas, and the lag time can also be estimated by the fall time of the inlet O₂ content. In addition, Figure 3 shows that the rise time and fall time of inlet O₂ content are basically the same, and the lag time can be determined at 60 s.

3. Data-Driven Model of the Inlet NO_x Concentration

To implement the data-driven model of the inlet NO_x concentration, it is necessary to first analyze the main influencing factors of the inlet NO_x concentration and determine the input variables of the inlet NO_x concentration prediction model. In addition, data pre-processing should be carried out, which includes dynamic correction of abnormal data points, online filtering and pre-processing of the blowback process.

3.1. Input Variables

The inlet NO_x concentration is mainly related to the boiler combustion process, and the main factors of the process are obtained by analyzing the relevant factors of the boiler combustion process. According to the analysis of thermal NO_x and fuel-based NO_x generation process, NO_x generation is mainly influenced by the following factors. In addition, the combustion zone temperature and O₂ content are both related to NO_x generation.

(1) When the power plant is put into automatic gain control (AGC), the load will fluctuate continuously, which will directly affect the total coal feed rate and total air volume. Since the total coal feed rate and total air volume changes are not synchronized, the air–coal ratio changes, thus affecting the variation of O₂ content and leading to the fluctuation of the inlet NO_x concentration.

(2) When the opening of combustion air baffle changes, it will also lead to unbalanced air combustion classification, and it will cause changes for the temperature field and O₂ content distribution in the combustion area, which in turn leads to the variations of the inlet NO_x concentration.

(3) The start and stop of the coal mill also affect the boiler combustion process, and causes the air–coal ratio to change, thus causing the O₂ content in the boiler to change, which in turn causes the inlet NO_x concentration to fluctuate.

According to the field data, the input variable data for the inlet NO_x concentration data-driven model were determined as shown in

Table 2. Input variable data of inlet NO_x concentration data-driven model.

Main influencing Factor	Related Parameters	Parameter Range
Boiler load	Boiler load	677 MW~896 MW
Burning coal	Wind–coal ratio	0.876~1.0793
Combustion condition	Outlet O2 content	2.76~4.25%
	Total air volume	2787 t/h~3601 t/h
Excess air coefficient	Average opening of secondary air damper	42.16~48.75%

. Since the data from the boiler are obtained earlier than the data from the SCR system, the model can be built by the variable data from the boiler side to predict the inlet NO_x concentration in advance.

3.2. Data Pre-Processing of Blowback Process

This paper adopts the method of linear interpolation to preprocess the inlet NO_x concentration signal for the CEMS blowback process, because the signal of the CEMS blowdown has periodicity. According to the analysis of field data, the CEMS will execute a continuous 3 min blowback at about 4 h intervals. Because there are still some abnormal data points after the end of blowback process, the data preprocessing needs to increase the data of the blowback time. In this paper, the data of the inlet NO_x concentration is measured for a period of 1 s. For example, data preprocessing uses 280 data every 14,300 data by Equation (1).

$${\widehat{x}}_t=x_1+\frac{x_m-x_1}{m}\left(t-1\right), 1<t\le m$$

(1)

Here, ${\widehat{x}}_t$ is the inlet NO_x concentration at time t after preprocessing, m is the number of purge data processing points, $x_1$ is the inlet NO_x concentration at the start of blowback process, and $x_m$ is the inlet NO_x concentration at the end of blowback process. The pre-processed results of the inlet NO_x concentration during the CEMS blowback process are shown in Figure 4. It can be seen from Figure 4 that all abnormal data points during the blowback process are eliminated.

3.3. Data-Driven Model of the Inlet NO_x Concentration

The data-driven model of the inlet NO_x concentration in many studies [1,2,3,4,5,6,7,8,9,10] is mainly one which only predicts the inlet NO_x concentration in advance for the current time and uses times series data to validate the model. There are two main drawbacks. One is that the predicted values are affected by the mean and standard deviation of the training set. So, it is impossible to track the curve changes in time when the inlet NO_x concentration fluctuates drastically. The other one is that the model parameter search is generally computationally time consuming. So, it is impossible to predict the inlet NO_x concentration in multiple steps in advance, which is contradictory to the purpose of the inlet NO_x concentration for a feedforward signal.

The exponential prediction can predict the inlet NO_x concentration, which can predict the true value in advance for a longer period of time [22]. In order to compensate for the output bias of the exponential prediction model, this paper proposes an improved exponential prediction model. The schematic diagram is shown in Figure 5.

First, the predicted inlet NO_x concentration at time t is obtained based on the exponential prediction model at time t-L, and then, the deviation between the predicted value and the measured inlet NO_x concentration at time t is obtained. The deviation prediction model is established by RLSSVM. The model predicts the future L-step deviations between the values of the exponential prediction model output and the real values of the inlet NO_x concentration, as shown in Equation (2). The output value of the RLSSVM model adds the output value of the exponential prediction model to achieve the purpose of correcting the exponential prediction model output.

$$\Delta \widehat{y}\left(t+L\right)=F\left(x\left|t\right.\right)=f\left(\Delta \widehat{y}\left(t\right),u\left(t\right),u\left(t-1\right)\right)$$

(2)

Here, u represents the input variable of the exponential prediction model. $\Delta \widehat{y}\left(t\right)$ represents the deviation between the real value of the inlet NO_x concentration at step t and the predicted inlet NO_x concentration by the exponential prediction model.

3.3.1. Exponential Prediction Model

According to Table 1, the input variables of improved exponential model were determined. A numerical model established the exponential prediction model of the inlet NO_x concentration. The equation is as follows.

$$y_{\mathrm{NO}}=A\times [{(\frac{B}{W_1})}^a-C]\times [\ln {(W_2)}^{\beta }][D-{(W_3)}^{\gamma }]\times [{(W_4)}^{\delta }-E]\times [{(\frac{W_5}{F})}^{\epsilon }-G]$$

(3)

Here, W₁ is the total air volume, W₂ is the average opening of secondary air register, W₃ is the boiler load, W₄ is the air–coal ratio, and W₅ is the O₂ content of flue gas in the boiler outlet. Each of the above parameters is determined by non-linear fitting experiments, and the parameters are adjusted according to the operational condition of the boiler and the SCR system.

3.3.2. Recursive LSSVM (RLSSVM) Model

(1)

LSSVM Model

Suykens et al. [23] proposes LSSVM by improving the quadratic optimization problem of SVM. LSSVM uses the least squares method to transform the SVM learning into solving the problem of linear equation. So LSSVM reduces the computational complexity and has a better prediction accuracy.

Let the training set $W=\{\left(x_i,y_i\right)\left|x_i\in R^n,i=1,2,\cdots ,n\}\right.$, $x_i$ is the input sample point, and $y_i$ is the output sample point corresponding to $x_i$, then the SVM problem is represented by a simple transformation as

$$\mathit{min}J\left(\mathit{\omega },e\right)=\frac{1}{2}{\mathit{\omega }}^T\mathit{\omega }+\frac{C}{2}{\displaystyle \sum }_{i=1}^l{e}_i{}^2$$

(4)

$$s.t.y_i={\mathit{\omega }}^T\mathit{\varphi }\left(x_i\right)+b+e_i, i=1,2,\cdots ,n$$

(5)

A Lagrangian function is established to turn the constrained optimization formula into an unconstrained optimization formula.

$$L\left(\mathit{\omega },b,e;a\right)=\frac{1}{2}{\mathit{\omega }}^T\mathit{\omega }+\frac{C}{2}{\displaystyle \sum }_{i=1}^l{e}_i{}^2+{\displaystyle \sum }_{i=1}^n{a}_i\left(y_i-{\mathit{\omega }}^T\mathit{\varphi }\left(x_i\right)-b-e_i\right)$$

(6)

The KKT condition, then, is

$$\left\{\begin{array}{l}\frac{\partial L}{\partial \mathit{\omega }}=0\to \mathit{\omega }={\displaystyle {\displaystyle \sum }_{i=1}^n}{\alpha }_i\mathit{\varphi }\left(x_i\right)\\ \frac{\partial L}{\partial b}=0\to {\displaystyle {\displaystyle \sum }_{i=1}^n}{a}_i=0\\ \frac{\partial L}{\partial e_i}=0\to a_i=C{e}_i\\ \frac{\partial L}{\partial \alpha }=0\to {\mathit{\omega }}^T\mathit{\varphi }\left(x_i\right)+b+e_i-y_i=0\end{array}\right.$$

(7)

After eliminating $e_i$ and $\omega$, Equation (7) can be rewritten as

$$\left[\begin{array}{cc}0& I^T\\ I& K\end{array}\right]\left[\begin{array}{c}b\\ \alpha \end{array}\right]=\left[\begin{array}{c}0\\ y\end{array}\right]$$

(8)

Here,

$$\mathit{I}=\left[1_1,1_2,\cdots ,1_n{]}^T, \mathit{\alpha }=\right[{\alpha }_1,\cdots ,{\alpha }_n{]}^T, \mathit{y}={[y_1,\cdots ,y_n]}^T$$

(9)

$${\delta }_{ij}=\left\{\begin{array}{l}1, i=j\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}i, j=1,2,\cdots ,n\\ 0, i\ne j\end{array}\right.$$

(10)

According to Equation (10), it can be seen that the training problem of LSSVM boils down to a solution problem of linear equations, so the training speed of LSSVM is faster than the training speed of SVM. The solution for $\alpha$ and b are as follows.

$$b=\frac{I^T{K}^{-1}y}{I^T{K}^{-1}I}$$

(11)

$$\alpha ={{\rm K}}^{-1}\left(y-\frac{I{I}^T{K}^{-1}y}{I^T{K}^{-1}I}\right)$$

(12)

The LSSVM model is obtained as Equation (13). The kernel function uses the radial basis function.

$$\widehat{y}\left(x\right)={\displaystyle {\displaystyle \sum }_{i=1}^n}{\alpha }_{i}k\left(x,x_i\right)+b$$

(13)

(2)

RLSSVM Model

Assume the kernel matrix at time t is as follows [24].

$$\mathit{Q}\left(t\right)=\left[\begin{array}{ccc}k\left(x_1,x_1\right)& \cdots & k\left(x_t,x_1\right)\\ ⋮& ⋮& ⋮\\ k\left(x_1,x_t\right)& \cdots & k\left(x_t,x_t\right)\end{array}\right]$$

(14)

$\mathit{K}\left(t\right)={\mathit{Q}}_t\left(i,j\right)+\frac{{\delta }_{ij}}{C}=\mathit{\varphi }{({\mathit{x}}_i)}^T\mathit{\varphi }\left({\mathit{x}}_j\right)+\frac{{\delta }_{ij}}{C}$, so

$$\mathit{K}\left(t\right)=\left[\begin{array}{ccc}k\left(x_1,x_1\right)+\frac{1}{C}& \cdots & k\left(x_t,x_1\right)\\ ⋮& ⋮& ⋮\\ k\left(x_1,x_t\right)& \cdots & k\left(x_t,x_t\right)+\frac{1}{C}\end{array}\right]$$

(15)

At time t + 1, a new sample $\left(x_{t+1},y_{t+1}\right)$ is obtained. Similarly

$$\mathit{K}\left(t+1\right)=\left[\begin{array}{cccc}k\left(x_1,x_1\right)+\frac{1}{C}& \cdots & k\left(x_t,x_1\right)& k\left(x_{t+1},x_1\right)\\ ⋮& ⋮& ⋮& ⋮\\ k\left(x_1,x_t\right)& \cdots & k\left(x_t,x_t\right)+\frac{1}{C}& k\left(x_t,x_t\right)\\ k\left(x_1,x_{t+1}\right)& \cdots & k\left(x_t,x_{t+1}\right)& k\left(x_t,x_{t+1}\right)+\frac{1}{C}\end{array}\right]$$

(16)

At time t + 1, $\mathit{K}\left(t+1\right)$ can be written as a block matrix as follows

$$\mathit{K}\left(t+1\right)=\left[\begin{array}{l}\mathit{K}\left(t\right) \mathit{V}\left(t+1\right)\\ \mathit{V}{(t+1)}^T v\left(t+1\right)\end{array}\right]$$

(17)

Here, $\mathit{V}\left(t+1\right)={[k\left(x_1,x_{t+1}\right),\cdots ,k\left(x_t,x_{t+1}\right)]}^T, v\left(t+1\right)=k\left(x_{t+1},x_{t+1}\right)+\frac{1}{C}$.

Equations (11) and (12) involve the inverse of kernel matrix, so

$$\mathit{K}{(t+1)}^{-1}={\left[\begin{array}{cc}\mathit{K}\left(t\right)\hfill & \hfill \mathit{V}\left(t+1\right)\\ \mathit{V}{(t+1)}^{\mathrm{T}}\hfill & \hfill V\left(t+1\right)\end{array}\right]}^{-1}=\left[\begin{array}{cc}\mathit{K}\left(t\right){]}^{-1}\hfill & \hfill 0\\ 0\hfill & \hfill 0\end{array}\right]+r\left(t+1\right)r{(t+1)}^{\mathrm{T}}z\left(t+1\right)$$

(18)

Here, $r\left(t+1\right)={(V{(t+1)}^{\mathrm{T}}\mathit{K}{(t)}^{-1},-1)}^{\mathrm{T}},z\left(t+1\right)=\frac{1}{v\left(t+1\right)-V{(t+1)}^{\mathrm{T}}K{(t)}^{-1}V\left(t+1\right)}$.

Equation (18) shows that the $\mathit{K}\left(t+1\right)$ can be obtained recursively from the $\mathit{K}\left(t\right)$ at the previous moment and the newly added sample $v\left(t+1\right)$.

3.4. Simulation Experiment

The prediction model of the inlet NO_x concentration is developed. The simulation data come from field data from an operation condition near 800 MW. The parameters of the exponential prediction model were finally determined by optimization algorithm, as showed in

Table 3. Parameters of inlet NO_x concentration exponential prediction model.

A/(mg/m3)	B	C	D	E	F	G	α	β	γ	δ
1	25	0.8	0.01	0.5	2	0.5	0.15	5	0.05	0.8

. For the exponential prediction model, the comparison of the predicted values and real values are shown in Figure 6.

Figure 6 shows that from point 500 to point 1300, the boiler is in steady-state operation condition. So, the predicted values from the exponential prediction model are relatively well fitted with the real values, and the root mean square error (RMSE) value is 6.8990 mg/m³. However, from point 200 to 300, the inlet NO_x concentration increases as increased total air volume, and the lag time of the NO_x analyzer can be estimated at 100 s or so based on the time difference between the rising curves of the predicted and real values. From point 1300, the predicted values and real values of the inlet NO_x concentration show a large deviation due to the increase in load from 800 MW to 900 MW. The predicted value is higher than the real value, and the RMSE value is 26.7963 mg/m³. In all, the exponential prediction model can track the curve change when the inlet NO_x concentration changes significantly, but the disadvantage is that the predicted values from the exponential prediction model have some deviation from the real values when the boiler is exposed to variable operational working conditions. If the prediction value of the exponential prediction model under variable operating conditions is higher than the real value, it is easy to cause the SCR system to over-regulate the amount of NH₃ injection and cause NH₃ slip, so the amount of feedforward control usually adopts the speed limit and amplitude limit measures. On the one hand, the time delay of the model can be set at 60 s. On the other hand, the RLSSVM is used to predict the output deviation of the exponential prediction model and correct the output deviation. Taking the 600th to 1800th points of the inlet NO_x concentration as an example, the prediction curves of output deviation of exponential prediction model are shown in Figure 7.

According to Figure 7, the exponential prediction model output deviation can be predicted 60 s in advance with a high prediction accuracy by using the improved exponential prediction model, which indicates that the deviation value is corrected in real time by using the RLSSVM model, and the trend change in the deviation prediction curve is basically consistent with the real value. Then, the relative errors and the comparative results between the improved exponential prediction model and exponential prediction model are shown in Figure 8.

Figure 8 shows that the relative errors of two models are small before the 1300th point, when the boiler is under steady-state conditions. From the 1300th point, the relative errors of the two prediction models increase, but the relative errors of the improved exponential prediction model are smaller compared with the exponential prediction model. The experiment results show that the improved exponential prediction model can make the predicted values of the inlet NO_x concentration under variable working conditions closer to the real values of the inlet NO_x concentration, thus effectively avoiding the problem of high predicted value when using an exponential prediction model and, to a certain extent, avoiding the phenomenon of excessive NH₃ injection when using the exponential prediction model output as the feedforward signal.

4. Improved Feedforward Control Based on the Data-Driven Model of the Inlet NO_x Concentration

For a NH₃ injection control system, the inlet NO_x content is obtained by multiplying the inlet flue gas flow and the inlet NO_x concentration, and it is often introduced in the control logic as a feedforward signal to achieve feedforward control [25]. In order to quickly respond to the condition changes on the perturbation of the inlet NO_x concentration under different operation conditions, the lag time of the SCR reaction and flue gas analysis can be compensated to a certain extent. However, the feedforward control method is not ideal because of the response lag of the NO_x analyzer in the SCR system. So, this section achieves the goal of improving the feedforward control by predicting the inlet NO_x concentration in advance and using it as a feedforward signal.

4.1. Control System Structure

To further improve the PID control effect, the improved exponential prediction model output of the inlet NO_x concentration is used as a feedforward signal to improve feedforward control. The block diagram of an NH₃ injection composite control system based on an improved feedforward control and PID control is detailed in Figure 9.

In Figure 9, the real-time predicted value of the improved exponential prediction model output is used as the feedforward signal, and the NH₃ injection valve opening variation $\Delta n_{N{H}_3}$ is used as the feedforward control parameter. $\Delta n_{N{H}_3}$ is converted from the improved exponential prediction model output by the following equation.

$$\Delta y_{N{H}_3}=\frac{\Delta C_{N{O}_x}\times Q\times M_{N{H}_3}\times {\eta }_{N{O}_x}}{M_{N{O}_x}}\times {10}^{-6}$$

(19)

$$\Delta n_{N{H}_3}=\frac{\Delta y_{N{H}_3}}{k}$$

(20)

Here, $\Delta C_{N{O}_x}$ is the change in the inlet NO_x concentration after improving feedforward control, mg/m³. That is the difference between the improved exponential prediction model output and the measured inlet NO_x concentration at the current moment t. $Q$ is the inlet flue gas flow rate, m³/h. $M_{N{H}_3}$ and $M_{N{O}_x}$ are the molar masses of NH₃ and NO_x. ${\eta }_{N{O}_x}$ is the SCR de-NO_x efficiency, %. $\Delta y_{N{H}_3}$ is the variation of NH₃ injection flow after adding feedforward control, kg/h. k is the linear coefficient between the variation of NH₃ injection flow and the variation of NH₃ injection valve opening. In general, NH₃ supply pressure remains unchanged, so the intermediate distance between the NH₃ injection valve opening and closing is a linear relationship. In this paper, according to the samples of the NH₃ injection flow and NH₃ injection valve opening, k = 3.82744.

The feedforward signal of the inlet NO_x concentration can be predicted 60 s in advance and then through the feedforward control, so the PID controller can realize the early action of NH₃ injection valve to control the amount of NH₃ injection and adapt to the change in operation conditions.

4.2. Simulation Experiment

Before studying the control strategy for NH₃ injection, this section analyzes the effect of the inlet NO_x concentration measurement lag on the control system and the analysis of the control effect with the improved feedforward control.

First, the lag of the inlet NO_x analyzer on the control system is analyzed, and then the absolute error between the measured values and the real values of inlet NO_x are analyzed based on the lag time determined in Section 2.2, as shown in Figure 10.

Figure 10 shows that there are deviations between the measured and real inlet NO_x to the influence of lag. The deviations are much bigger when the inlet NO_x concentration fluctuates drastically. The absolute error reaches up to 73 mg/m³. Therefore, in order to ensure the effect of the NH₃ injection control, the lag influence of the inlet NO_x analyzer on the control system must be considered.

The control effect of the composite control based on the improved feedforward (IF) control and PID control (IF-PID), and the PID control is compared with: the IF-PID control on the outlet NO_x concentration, as shown in Figure 11; the NH₃ injection flow rate, as shown in Figure 12; and the optimization index, as shown in

Table 4. Optimization index of IF-PID control and PID control.

Index	IF-PID	PID
Average de-NOx efficiency/(%)	80.0918	80.0001
Average NH3 slip/(ppm)	1.7517	1.7358
Average NH3 injection flowrate/(kg/h)	69.8445	69.6047
Average outlet NOx concentration/(mg/m3)	37.2295	37.1478
Standard deviation of outlet NOx concentration/(mg/m3)	5.8491	4.6684

.

According to Figure 11, the measured values of the inlet NO_x concentration deviate significantly from the real values of the inlet NO_x concentration. It can be seen that the improved feedforward control can make the NH₃ injection valve operate earlier at the peaks and troughs of the outlet NO_x curve. Compared with the feedforward control, the outlet NO_x concentration converges to the set value of 37 mg/m³. It indicates that the HP-PID control can reduce the excessive NH₃ injection and the NH₃ slip to a certain extent. On the one hand, the cost of NH₃ injection is reduced, and sustainable development of the enterprise is achieved; on the other hand, NH₃ slip is reduced, so air pollution is avoided, and environmental sustainability is achieved.

According to the optimization index results in Table 4, the average outlet NO_x concentration is slightly reduced, the standard deviation of the outlet NO_x concentration decreases 20% (most outlet NO_x concentration points meet the national environmental protection regulation), the average de-NO_x efficiency remains the same, and the average NH₃ injection flowrate and average NH₃ slip are slightly reduced. It indicates that the inlet NO_x data-driven model based on the exponential prediction model and the RLSSVM can accurately predict the inlet NO_x concentration in advance, and the NH₃ injection control effect can be improved by improving the feedforward control.

Figure 12 shows that the IF-PID control further increases the NH₃ injection flow rate from point 1300 to point 1500 compared with the PID control, which reduces the outlet NO_x concentration but exceeds the maximum value of the NH₃ injection flow rate when the PID control is used. According to the analysis of the field data, the NH₃ injection valve opening reaches 50% at the 1300th to 1500th points using PID control, indicating that the actuator of the NH₃ injection valve has reached saturation at this time when an automatic control is used. Therefore, the outlet NO_x concentration is too high through the IF-PID control. The amount of NH₃ injection appears to overshoot. In field, if the actuator saturates during automatic control, the control effect will be adversely affected.

In addition, the feedforward control can make the NH₃ injection valve act in advance according to the change in the inlet NO_x concentration data-driven model. However, to some extent, the response lag of the PID control is due to the lag in the feedback signal of the outlet NO_x concentration. Because the CEMS is installed at the outlet of the SCR reactor, the measurement lag of outlet NO_x should not be neglected.

5. Conclusions

The output of the inlet NO_x concentration data-driven model is used as a feedforward signal, which can improve the feedforward control. The IF-PID control has a compensating effect when the boiler is under variable operation conditions, and the adaptability of the SCR system to variable operation conditions is improved. By improving the feedforward control, the NH₃ injection valve can be operated earlier, which enhances the timeliness of the system in variable operation conditions. The validity of the model is verified in this paper. Furthermore, the better effect of NH₃ injection control and environmental sustainability are achieved without increasing the cost of NH₃ injection.

In future research, in order to further improve the control effect, model predictive control can be considered instead of PID control to achieve rapid feedback of the outlet NO_x concentration signal.