- Email: [email protected]
Modeling of a medium speed coal mill
Powder Technology 318 (2017) 214–223
Contents lists available at ScienceDirect
Powder Technology journal homepage: www.elsevier.com/locate/powtec
Modeling of a medium speed coal mill Yaokui Gao a, Deliang Zeng b,⁎, Jizhen Liu b a b
Key Laboratory of Measurement & Control New Technology and System for Industrial Process, North China Electric Power University, Changping District, 102206 Beijing, China State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Changping District, 102206 Beijing, China
a r t i c l e
i n f o
Article history: Received 19 February 2017 Received in revised form 27 April 2017 Accepted 6 May 2017 Available online 11 May 2017 Keywords: Coal mill Coal moisture Mathematical model Genetic algorithm
a b s t r a c t This paper presents a coal mill model that considers the effect of coal moisture on its accuracy. This mathematical model is derived through the analysis of mass flow, heat exchange, and energy transferring balances in which all heat input into or output from the coal mill are calculated quantitatively to reduce the number of unknown parameters that need to be identified. The work presented in this paper focuses on modeling Mill Parter Ship-type coal mills that are widely used in the coal-fired power plants in China. The unknown model parameters are identified using a real-coded genetic algorithm. Simulation results indicate that the model effectively represents the mid-high process of coal mill dynamics and can be used to estimate the key parameters in coal mills, which are difficult to measure or cannot be measured. On this basis, the model can be used for the state monitoring, control optimization, and fault diagnosis of coal mills. © 2017 Published by Elsevier B.V.
1. Introduction China's energy structure (coal resources are rich, while oil and natural gas resources are extremely insufficient) indicates that coal will continue to be its largest energy resource for a long time [1,2]. Therefore, the research works of Chinese scientists on the clean and efficient use of coal are extremely important. This energy structure also indicates that coal-fired power is the main component of China's power generation. Thus, the dynamic characteristics of pulverizing equipment in coal-fired power plants should be studied to realize the clean and efficient utilization of coal in thermal power plants. Coal mills are independent links in pulverizing systems. The sufficient measuring points at the inlet or outlet of a coal mill enables the analysis of the interactions between the control and controlled variables. Consequently, the state estimation signals of key parameters that are difficult to measure or cannot be measured through modeling can be constructed. In recent years, researchers have conducted extensive studies on coal mill models. Tian et al. regarded the milling process as a first-order inertia link with pure delay and established the dynamic fuel model of a pulverizing system; however, it is a single-input, singleoutput model that does not consider the effect of primary air, thereby resulting in low accuracy [3,4]. Shin et al. established a dynamic model with two kinds of coal particles and a differential coal mill pressure; however, the impact of coal moisture on the coal mill outlet temperature is not considered, thereby resulting in poor accuracy [5]. Liu et al. presented a mathematical model of the coal mill outlet temperature;
⁎ Corresponding author. E-mail address: [email protected] (D. Zeng).
http://dx.doi.org/10.1016/j.powtec.2017.05.015 0032-5910/© 2017 Published by Elsevier B.V.
however, the coefficients of the model need to be re-determined according to different units, which makes the versatility of the model weak [6]. Wei et al. established a multi-stage model for coal mills that covers the multiple working conditions of their start and stop processes. Their model has high precision, but requires the identification of numerous parameters, and it does not consider the impact of raw coal moisture on the energy balance of coal mills [7]. On the basis of the above model, Zeng et al. considered the impact of the moisture of raw coal on the energy balance of coal mills and established a nonlinear dynamic model of coal mills; although the model's outputs are consistent with the actual outputs, the problem of having to identify many parameters remains [8]. Coal mills are regarded as lumped-parameter links, and the calculation methods of the static heat balance in coal mills are provided. This balance indicates that the total energy input into the initial section of the coal mill is equal to the total energy output from the terminal section of the coal mill. This method considers all the energy involved in the coal mill; however, no coal mill model has been established based on the heat balance of coal mills [9–11]. Zeng et al. established an equation with an unknown parameter (coal moisture), which is calculated successfully and has high accuracy in steady-state conditions [12]. On the basis of the literature above, a nonlinear dynamic model of a MPS (Mill Parter Ship)-type medium speed coal mill is proposed in this study based on its mass and energy balance. The effect of raw coal moisture on the energy balance of coal mills is considered to improve the accuracy of the model and all heat inputs into or outputs from the coal mill are calculated quantitatively to reduce the number of parameters that need to be identified. This model can be used to estimate the key parameters that are difficult to measure or cannot be measured: 1) coal powder or raw coal contents in coal mills, which can be used
Y. Gao et al. / Powder Technology 318 (2017) 214–223
Nomenclature specific heat capacity of dry-basis coal, kJ/(kg·°C) specific heat capacity of hot air, kJ/(kg·°C) specific heat capacity of water, kJ/(kg·°C) average specific heat capacity of vapor at a constant pressure, kJ/(kg·°C) specific heat capacity of primary air, kJ/(kg·°C) Cin specific heat capacity of cold air, kJ/(kg·°C) CL average specific heat capacity of raw coal, coal powder, Cmix and the metal involved in heat transfer, kJ/(kg·°C) specific heat capacity of wet air at Tout, kJ/(kg·°C) Cout specific heat capacity of coal powder, kJ/(kg·°C) Cpf specific heat capacity of raw coal, kJ/(kg·°C) Crc proportion coefficient between the coal feed flow and Kc the coal feeder speed, rpm conversion coefficient of raw coal to coal powder per Kconv unit time, 1/s model parameters that need to be identified, i = 1, 2, 3 Ki coefficient of heat loss through equipment Kloss coefficient of heat generation in milling process Kmac proportion coefficient of coal powder flow Kpf leakage coefficient of sealed air for medium speed coal Kseal mill raw coal moisture, % Mar raw coal content in coal mill, kg Mc amount of metal involved in the heat exchange, kg Mmetal moisture content in coal powder, % Mpc coal powder content in coal mill, kg Mpf ΔM amount of moisture evaporated in the coal mill, % differential pressure of primary air, mbar ΔPpa physical heat input into the coal mill by the primary air Qair per unit time, kJ/s Qair & seal physical heat output from the coal mill by primary air and sealing air per unit time, kJ/s total heat input into the coal mill per unit time, kJ/s Qin physical heat input into the coal mill by leaking cold air Qle per unit time, kJ/s heat loss through the equipment per unit time, kJ/s Qloss heat produced by the grinding process per unit time, kJ/s Qmac heat consumed for evaporating raw coal moisture per QΔM unit time, kJ/s total heat output from the coal mill per unit time, kJ/s Qout heat consumed for heating fuel per unit time, kJ/s Qpf physical heat input into the coal mill by raw coal per Qrc unit time, kJ/s physical heat input into the coal mill by sealing air per Qseal unit time, kJ/s coal fineness, % R90 inertia time from the air door to the primary air flow, s T1 inertia time from the air door to the primary air temperT2 ature, s valve opening of hot air, % uH valve opening of cold air, % uL primary air flow, kg/s Wair coal feed flow, kg/s Wc max-flow of hot air, kg/s Wmax H max-flow of cold air, kg/s Wmax L amount of coal powder blown out of the coal mill per Wpf unit time, kg/s temperature of hot air, °C θH primary air temperature, kg/s θin temperature of cold air, °C θL coal mill outlet temperature, °C θout temperature of raw coal, °C θrc Cdc CH CH2O C H2 O
215
as the main basis for coal block and break diagnosis; 2) moisture content in coal powder, which can be used to optimize the outlet temperature of coal mills; and 3) coal powder flow at the outlet of the coal mill, which can be used to optimize the control of the pulverizing system's output. This paper is organized as follows: section one opens with a brief introduction of coal mills; section two deduces and establishes the nonlinear differential equations of coal mills; section three presents the identification process of model parameters; section four simulates and verifies the model; and the conclusion is provided in the final section. 2. Brief introduction of a coal mill MPS-type medium speed coal mills are widely used in the thermal power plants in China. They are designed and manufactured by the German company Babcock. This kind of coal mill has the characteristics of low energy consumption and smooth output and has a small effect on abrasive wear and an overhaul period [13,14]. In this study, MPS180HP-II medium speed coal mill is used as the research object. Its maximum output is 44.496 t/h and the fineness of coal powder R90 is 22% [15] (Fig. 1) (R90 refers to the probability that coal powders cannot pass through a sieve with apertures of 90 μm). Raw coals fall into the gap between the grinding roller and the grinding disc via a coal chute. Then, the raw coals are crushed into coal powder under the squeezing pressure of the grinding parts. Subsequently, the primary air that enters the coal mill through the air ring dries and brings the coal powders into the coarse coal separator at the upper part of the grinding area for separation. Qualified coal powders are blown out of the coarse coal separator into the boiler while the others fall on the grinding disc for re-grinding. 3. Modeling of the coal mill In this study, the lumped parameter modeling method is adopted with the following assumptions: 1) the parameters of the medium in the coal mill are uniform; 2) the media in the coal mill are incompressible; 3) the parameters of the medium in the coal mill change along the axial direction only; 4) the change in the flow power in the coal mill is ignored; 5) the coal powder separation process is not considered; 6) only two kinds of coal particles (coal powder and raw coal) exist in the coal mill; 7) the temperatures of the coal powder and the primary air are the same at the outlet of the coal mill.
Fig. 1. Schematic of the MPS medium-speed mill.
216
Y. Gao et al. / Powder Technology 318 (2017) 214–223
3.1. Modeling of inlet primary air of the coal mill On the basis of the energy and mass balances of the primary air at the inlet of the coal mill, the model of the primary air is established in Eqs. (1) and (2) as follows: max T 1 W_air ¼ −W air þ W max L uL þ W H uH ;
T 2 θ_in ¼ −θin þ
max C L W max L uL θL þ C H W H uHθH ; max max C in W L uL þ W H uH
θL −0 C L ¼ 1:011 þ ð1:012−1:011Þ; 25−0
ð1Þ ð2Þ
ð3Þ
3.3.1. Total heat input into the coal mill The total heat input into the coal mill per unit time is calculated as shown in Eq. (13). Q in ¼ Q air þ Q rc þ Q mac þ Q seal þ Q le :
a. Physical heat input into the coal mill by the primary air per unit time Q air ¼ C in θin W air ;
ð14Þ
where θin takes the primary air temperature state after the mixing of hot and cold airs as shown in Eq. (2), and Cin is calculated based on Eq. (5). b. Physical heat input into the coal mill by raw coal per unit time
C H ¼ 1:011 þ
θH −200 ð1:028−1:011Þ; 400−200
ð4Þ
Q rc ¼ C rc W c θrc ;
C in ¼ 1:011 þ
θin −200 ð1:019−1:011Þ: 300−200
ð5Þ
C rc ¼
In Eqs. (3)–(5), CL, CH, and Cin, are functions of θL, θH, and θin, respectively, and are calculated based on the national standard shown in Appendix A, Table 1 [12]. The specific heat capacities of wet air are 1.011 and 1.012 kJ/(kg·°C) when d = 10 g/kg and θL = 0 °C and 25 °C, respectively, while the specific heat capacities of dry air are 1.011, 1.019, and 1.028 kJ/(kg·°C) when θH = 200 °C, 300 °C, and 400 °C, respectively. , Wmax In the above model, Wmax L H , T1, and T2 are the parameters that need to be identified. They can be obtained through the comparison of the actual output and the model output of Wair and θin.
ð13Þ
C H2 O Mar C dc ð100−Mar Þ þ ; 100 100
ð15Þ ð16Þ
where Cdc is determined by the type and temperature of raw coal, θrc is weighted by Cdc (1.884 kJ/(kg·°C)) and CH2O (4.187 kJ/(kg·°C)) as shown in Eq. (16). θrc is the temperature of raw coal, that is, θrc = 20 °C for high-moisture fuel and θrc = 0 °C for the rest. c. Heat produced by the grinding process of the coal mill per unit time Q mac ¼ K mac I;
ð17Þ
where Kmac is taken as 0.6 for a MPS medium speed coal mill according to the national standard. d. Physical heat input into the coal mill by sealing air per unit time
3.2. Modeling of coal quantity in the coal mill On the basis of the mass balance of coal in the coal mill, the model of coal powder and raw coal in the coal mill are established as Eqs. (6) and (7), respectively. M_ c ¼ W c −K conv Mc ;
ð6Þ
M_pf ¼ −W pf þ K conv Mc ;
ð7Þ
W c ¼ K c Nc ;
ð8Þ
where Wpf is the amount of coal powder that is blown out of the coal mill per unit time, which is proportional to Δ Ppa and Mpf [Eq. (9)]. ΔPpa is proportional to θin, and W2air is calculated as shown in Eq. (10). W pf ¼ K pf Mpf ΔP pa ; ΔP pa
22:4 273 þ θin W air 2 ∙ ¼ ; ∙ 273 10 28:8
I ¼ K 1 Mpf þ K 2 M c þ K 3 :
ð9Þ ð10Þ ð11Þ
In the above model, Kconv, Kc, Kpf, K1, K2, and K3 denote the identified parameters, which can be obtained through the comparison of the actual and model outputs of the coal mill's current, as defined in Eq. (11). 3.3. Modeling of outlet temperature of the coal mill On the basis of the energy balance inside the coal mill, the model of the coal mill outlet temperature is established as shown in Eq. (12). _ ¼ Q in −Q out : C mix M c þ Mpf þ Mmetal θout
ð12Þ
The magnitude of Mc and Mpf is 101 while that of Mmetal is 103. Therefore, Cmix takes the specific heat capacity of metal, 0.46 kJ/(kg·°C).
Q seal ¼ C L θL K seal W air :
ð18Þ
The seal air flow is assumed proportional to the primary air flow at the inlet of the coal mill, and Kseal is 0.1. Therefore, KsealWair is the sealing air flow (kg/s), and CL is calculated based on Eq. (3). e. Physical heat input into the coal mill by leaking cold air per unit time Given that the research object in this study is a positive pressure direct-blowing pulverizing system, the air leakage is zero. Thus, the physical heat input into the coal mill by leaking cold air per unit time as follows: Q le ¼ 0:
ð19Þ
3.3.2. Total heat output from the coal mill The total heat output from the coal mill per unit time is calculated as shown in Eq. (20). Q out ¼ Q air&seal þQ ΔM þ Q pf þ Q loss :
ð20Þ
a. Physical heat output from the coal mill by primary air and sealing air per unit time Q air&seal ¼ C out θout ð1 þ K seal ÞW air ;
ð21Þ
where Cout is a function of θout, which is calculated by linear interpolation in Eq. (22), and the specific heat capacity of the wet air is generally 1.012 and 1.015 when the air temperatures are 25 °C and 100 °C, respectively, and the air humidity is 10 g/kg based on the national standard shown in Appendix A, Table 1. C out ¼ 1:012 þ
θout −25 ð1:015−1:012Þ: 100−25
ð22Þ
Y. Gao et al. / Powder Technology 318 (2017) 214–223
217
b. Heat consumed by evaporation of moisture in raw coal per unit time ð23Þ Q ΔM¼ ΔMW c 2500 þ CH2 O θout −4:187θrc ;
Mpf, and θout. The time-varying parameters are θL, θH, θrc, and Mar. , Wmax Wmax L H , T1, T2, Kconv, Kc, Kpf, K1, K2, K3, and Mmetal denote the parameters that need to be identified.
where CH2 O is calculated based on the national standard shown in Table A.1 in Appendix A and is 1.862 kJ/(kg·°C) when the water temperature is 25 °C based on experience. ΔM is calculated in Eq. (24) and Mpc is calculated in Eq. (25), where R90 is 22% according to the design parameters of the coal mill.
4. Identification of model parameters
ΔM ¼
Mar −Mpc ; 100−Mpc
Mpc ¼ 0:048M ar
ð24Þ R90
θout 0:46
:
ð25Þ
c. Heat consumed for heating fuel per unit time Q pf ¼
100−Mar W c C ðθout −θrc Þ; 100 pf
ð26Þ
The identification of the coal mill model is difficult because θout is affected by numerous factors, such as θL, θH, uL, uH, Wc, and Mar. To reduce identification difficulty, a stepwise identification method is proposed in this paper. This identification method divides the identification process of the model into three steps: identification of the primary air model, of the coal quantity model, and of the mill outlet temperature model. Here, the unknown parameters of the model are identified based on the real-coded genetic algorithm [16–18]. The population size is 50, the maximum number of iterations is 50, the probability of crossing is 0.9, and the probability of mutation is 0.3. The specific identification process is shown in Fig. 2. Fitness functions ffit1, ffit2, and ffit3 are defined as follows: ( N
f fit1 ¼ ∑t¼0 W 1
where Cpf is weighted by CH2O and Cdc is as follows: C pf ¼ C dc þ
4:187M pc : 100−M pc
ð27Þ
d. Heat loss through the equipment per unit time
N
f fit2 ¼ ∑t¼0
N
f fit3 ¼ ∑t¼0 Q loss ¼ K loss Q in ;
ð28Þ
where Kloss is the coefficient of heat loss through the equipment and is 0.02 based on experience. In summary, the model of the coal mill proposed in this paper is as follows: 8 max max _ > > > T 1 W air ¼ −W air þ W L uL þ W H uH > > max max > > > T 2 θ_in ¼ −θin þ C L W L uL θL þ C H W H uHθH > max max > > C in W L uL þ W H uH > > > > > M_ c ¼ W c −K conv Mc > > > > > M_pf ¼ K conv Mc −W pf > > > > > _ ¼ Q in −Q out > C mix M c þ M pf þ M metal θout > > > > > > W pf ¼ K pf ΔP pa M pf > > > > > 22:4 273 þ θin W air 2 > > > ∙ ΔP pa ¼ ∙ > > 273 10 28:8 > > > > > Q ¼ Q þ Q þ Q þ Q > in air rc seal þ Q le mac > > > > > Q air ¼ C in θin W air > > < Q rc ¼ C rc θrc W c ; > > Q mac ¼ K mac I > > > > > > Q seal ¼ C L θL K seal W air > > > > > Q le ¼ 0 > > > > Q out ¼ Q air&seal þQ ΔM þ Q pf þ Q san > > > > > Q air&seal ¼ C out θout ð1 þ K seal ÞW air > > > > > Q ΔM¼ ΔMW c 2500 þ C H2 O θout −C H2 O θrc > > > > M ar −Mpc > > ΔM ¼ > > > 100−M pc > > > > R90 > > > M pc ¼ 0:048Mar > > > θout 0:46 > > > 100−M ar > > > W c C ðθout −θrc Þ Q pf ¼ > > 100 pf > > : Q loss ¼ K loss Q in
) d ∣∣θin ðt Þ−θc ∣∣W air ðt Þ−W in ðt Þ∣∣ air ðt Þ∣∣ þ W2 ; d θc W in ðt Þ air ðt Þ
ð30Þ
∣∣Iðt Þ−^Iðt Þ∣∣ ; ^Iðt Þ
ð31Þ
∣∣θout ðt Þ−θd out ðt Þ∣∣ ; d θout ðt Þ
ð32Þ
where N is the number of measured data points and W1 and W2 are the d c ^ d weight coefficients for θin and Wair; W air ðtÞ, θin ðtÞ, IðtÞ, and θout ðtÞ are the outputs of the model at time t; and Wair(t), θin(t), I(t), and θout(t) are the outputs of the coal mill at time t; During the identification process, the raw coal moisture is calculated online based on the method proposed by Ref. [12], and the model parameters obtained by the identification method are shown in Table 2. Let x1 = Wair, x2 = θin, x3 = Mc, x4 = Mpf, x5 = θout, u1 = uL, u2 = uH, u3 = Wc, y1 = Wair, y2 = θout, y3 = Wpf, w = Mar, θL = 43 °C, θH = 341 °C, and θrc =0 °C.
ð29Þ
where the inputs to the model are uL, uH, and Wc. The outputs of the model are Wair, θout, and Wpf. The states of the model are θin, Wair, Mc,
Fig. 2. Identification process of parameters.
Table 2 Identified model parameters. = 18.83 Wmax L = 55.11 Wmax H
T1 = 10.3004 T2 = 3.6765
Kconv = 0.4522 Kpf = 0.0795
K1 = 0. 1799 K2 = 0. 8496
K3 = 19.7787 Mmetal = 4131.7
218
Y. Gao et al. / Powder Technology 318 (2017) 214–223
The nonlinear state equation of the coal mill is obtained as follows: 8 x_1 ¼ −0:0971x1 þ 0:183u1 þ 0:551u2 −22:2 > > > 7:98u1 þ 192:0u2 > > > x_2 ¼ −0:272x2 −198 þ > > > ð0:183u1 þ 0:551u2 Þ 8x2 10−5 þ 0:995 > > > > _ > x3 ¼ −0:452x3 þ u3 > > > > > x_4 ¼ 0:452x3 −ð0:00285x2 þ 0:778Þx1 2 x4 7:95 10−4 > > > 1 > > > x_ ¼ ð1:1x3 þ 0:233x4 þ 9:42x1 −2:414x1 x5 þ 2:151x1 x2 þ tempA þ tempBÞ > < 5 4171:7 1:1w 2:17u3 ð1:88x5 þ 2499Þ w− 0:45 > > > x5 > > tempA ¼ > > 1:1w > > −100 > > > x5 0:45 > 0 1 > > > > > > B C > 4:62w > > −1:09C tempB ¼ −2:17x5 u3 ð0:01w−1:0ÞB > @ A > 1:1w > 0:45 > −100 x5 : x5 0:45
ð33Þ The output equation is as follows: 8 < y1 ¼ x1 y ¼ x5 : 2 y3 ¼ −ð0:00285x2 þ 0:778Þx1 2 x4 7:95 10−4
:
ð34Þ
5. Simulation and validation 5.1. Verification of model dynamic characteristics To verify the validity of the model, step disturbance is applied to one of the inputs of the model while keeping the others constant, and the inputs and outputs of the model are recorded at the same time (Figs. 3-5).
When a step-increasing signal is applied to uL (Fig. 3(a)), the output of the model changes as follows. The cold air flow increases while the hot air flow remains constant, thus resulting in an increase in the Wair at the inlet of the coal mill (Fig. 4(a)) and a decrease in θout (Fig. 4(b)). The increase in Wair increases the ΔPpa between the outlet and the inlet of the coal mill, resulting in a decrease in Mpf (Fig. 5(b)) and decreasing the current I required for milling (Fig. 5(c)). In addition, the decrease in θout prevents the sufficient drying of coal powders, resulting in an increase in Mpc (Fig. 5(d)). When a step-increasing signal is applied to u H (Fig. 3(b)), the output of the model changes as follows. The hot air flow increases while the cold air flow remains constant, thus resulting in an increase in the Wair at the inlet of the coal mill (Fig. 4(a)) and an increase in θ out (Fig. 4(b)). The decrease in W air decreases the Δ P pa between the outlet and the inlet of the coal mill, resulting in an increase in M pf (Fig. 5(b)) and increasing the current I required for milling (Fig. 5(c)). In addition, the increase in θ out results in the sufficient drying of the coal powders and a decrease in M pc (Fig. 5(d)). When a step-increasing signal is applied to the raw coal moisture Mar (Fig. 3(c)), the output of the model changes as follows. The energy supplied by Wair (Fig. 4(a)) remains constant while the Mar that needs to be evaporated increases. The primary air with same energy level dries the raw coal with a higher moisture content, resulting in a decrease in θout (Fig. 4(b)) and an increase in Mpc (Fig. 5(d)). When a step-increasing signal is applied to coal feed flow Wc (Fig. 3(d)), the output of the model changes as follows. The amount of coal required to be milled increases, resulting in an increase in grinding current I (Fig. 5(c)). The increase in Wc increases the amount of coal that needs to be dried, thereby decreasing the θout (Fig. 4(b)) and increasing the Mpc (Fig. 5(d)).
Fig. 3. Step disturbance on model inputs.
Y. Gao et al. / Powder Technology 318 (2017) 214–223
Fig. 4. Curves for model outputs (I).
Fig. 5. Curves for model outputs (II).
219
220
Y. Gao et al. / Powder Technology 318 (2017) 214–223
Fig. 6. Curves for input data.
The result of the verification and analysis of model dynamics above indicates that the model proposed in this paper is inherently accurate. 5.2. Verification of the model output To verify the versatility and accuracy of the coal mill model further, two sets of historical data are used to simulate and validate the model. The specific verification process is as follows:
(1) To verify the versatility of the model under multiple operating conditions, five days of actual operational data are collected as the first validation data set, during which the load rate of the coal mill is from 59.88%–97.59% (Figs. 6 and 7). The output of the model is compared with the actual output of the coal mill as shown in Figs. 8 and 9, which show that the model outputs are coincident with the online measurements. The correlation coefficient and the relative root-mean-square deviation between
Fig. 7. Curves for time-varying parameters.
Y. Gao et al. / Powder Technology 318 (2017) 214–223
221
Fig. 8. Comparison of actual outputs and model outputs (I).
Fig. 9. Comparison of actual outputs and model outputs (II).
the model and actual outputs are shown in Table 3. The table shows that three of the parameters have correlation coefficients greater than 0.7 with a lower error value for Wair, and the relative root-mean-square deviations of θin, I, and θout are lower than 3% with a slightly higher error for Wair. This phenomenon is due to the fact that the measurement of Wair is inherently inaccurate in actual operations of the coal mill. The online estimation of
Table 3 Correlation coefficient and Root-mean-square deviation between model output and actual output. Outputs of the object
Wair
θin
I
θout
Correlation coefficient Relative root-mean-square deviation (%)
0.5219 8.14
0.9762 2.54
0.8705 2.37
0.7132 1.41
coal content in the coal mill is shown in Fig. 10, which can be used as the main basis for the diagnosis of coal block and break. (2) To quantify the delay time of the milling process, 9 h of actual operational data are collected as the second set of validation data, and the sampling time is 2 s. Fig. 11 shows that the trend of change in Wpf is to the same as that of Wc, and the former is delayed at approximately 20 s relative to the latter, which verifies that the estimated coal powder flow at the outlet of the coal mill is accurate.
6. Conclusions On the basis of the comprehensive consideration of the key state parameters, such as the coal content in the coal mill, the moisture content
222
Y. Gao et al. / Powder Technology 318 (2017) 214–223
Fig. 10. Estimation of coal content in the coal mill.
in coal powder, and the coal powder flow at the outlet of the coal mill, a nonlinear dynamic model of the medium speed coal mill based on mass and energy balance is proposed. In the model, the effect of coal moisture on the energy balance of coal mill is considered to improve the accuracy of the model, and all heat input into or output from the coal mill are
quantitatively calculated to reduce the number of unknown parameters that need to be identified. After the simulation and verification, the model is proven effective in reflecting the dynamics of a coal mill and has good precision. This nonlinear dynamic model can be used for the state monitoring, control optimization, and fault diagnosis of coal mills.
Fig. 11. Comparison of Wc and Wpf.
Y. Gao et al. / Powder Technology 318 (2017) 214–223
Appendix A
Table 1 Specific heat capacity of common gases (kJ/(kg·°C)). Humid air t/°C
d = 10 g/kg
d = 20 g/kg
H2O
Dry air
O2
N2
CO2
0 25 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400
1.011 1.012 1.015 1.020 1.028 1.037 1.048 1.058 1.070 1.081 1.091 1.101 1.110 1.119 1.127 1.135
1.020 1.022 1.023 1.028 1.037 1.046 1.057 1.068 1.079 1.091 1.101 1.111 1.120 1.130 1.138 1.147
1.859 1.862 1.872 1.894 1.919 1.947 1.977 2.009 2.041 2.075 2.109 2.143 2.197 2.210 2.242 2.274
0.914 0.915 0.922 0.934 0.949 0.964 0.978 0.992 1.004 1.015 1.025 1.034 1.042 1.050 1.057 1.064
1.030 1.031 1.032 1.034 1.040 1.047 1.056 1.066 1.077 1.088 1.098 1.107 1.117 1.125 1.134 1.142
0.809 0.831 0.860 0.904 0.942 0.976 1.006 1.032 1.056 1.078 1.097 1.115 1.131 1.145 1.158 1.170
1.003 1.005 1.006 1.011 1.019 1.028 1.039 1.049 1.060 1.071 1.081 1.090 1.099 1.108 1.116 1.124
References [1] J. Bugge, S. Kjær, R. Blum, High-efficiency coal-fired power plants development and perspectives[J], Energy 31 (10) (2006) 1437–1445. [2] C. Xu, Y. Yuan, Analysis of present operating situation of large size coal-fired utility boilers[J], Electr. Power 1 (2003) 000. [3] L. Tian, D. Zeng, X. Liu, et al., A simplified non-linear dynamic model of 500 MW unit[J], Power Eng. 4 (2004) 015.
223
[4] L. Tian, D. Zeng, J. Liu, et al., A simplified non-linear dynamic model of 330 MW unit[J], Proc. Chin. Soc. Electr. Eng. 24 (8) (2004) 180–184. [5] H.B. Shin, X.L. Li, Modeling and parameter identification of coal mill[J], J. Power Electron. 9 (5) (2009) 700–705. [6] C. Liu, W. Yao, Y. Qu, C. Zhen, An improved genetic algorithm and its application in thermal process control, Process. Autom. Instrum. 23 (9) (2002) 13e6 (in Chinese). [7] J.L. Wei, J. Wang, Q.H. Wu, Development of a multisegment coal mill model using an evolutionary computation technique[J], IEEE Trans. Energy Convers. 22 (3) (2007) 718–727. [8] D. Zeng, Y. Hu, S. Gao, et al., Modelling and control of pulverizing system considering coal moisture[J], Energy 80 (2015) 55–63. [9] J.K. Feng, Y.T. Shen, R.C. Yang, The Principle and Calculation of Boiler[J], 1997. [10] V. Ganapathy, Industrial Boilers and Heat Recovery Steam Generators: Design, Applications, and Calculations[M], CRC Press, 2002. [11] N.M. Magdalinović, Calculation of energy required for grinding in a ball mill[J], Int. J. Miner. Process. 25 (1) (1989) 41–46. [12] D. Zeng, Y. Hu, J. Liu, et al., Soft sensing of coal moisture[J], Measurement 60 (2015) 231–239. [13] J.F. Yue, J.F. Yue, L. Huang, et al., Experimental investigation of the operating characteristics of a MPS coal mill[J], Reneng Dongli Gongcheng (J. Eng. Therm. Energy Power), 20 (1) (2005) 65–68. [14] X. Zhu, Z. Zhao, Q. Zhang, Research on mill rejects characteristics for medium speed mill [J], Proc. CSEE 23 (2010) 013. [15] H.F. Yuan, Changchun generating equipment group [EB/OL], http://www.chinacge. com 2016-08-16/2016-10-04. [16] V. Rashtchi, E. Rahimpour, S. Fazli, Genetic algorithm application to detect broken rotor bar in three phase squirrel cage induction motors[J], Int. Rev. Electr. Eng. 6 (5) (2011) 2286–2292. [17] O. Mohamed, J. Wang, S. Guo, et al., Modelling Study of Supercritical Power Plant and Parameter Identification Using Genetic Algorithms[C]//Proceedings of the World Congress on Engineering, Newswood Ltd., London, United Kingdom, 2010 973–978. [18] D. Simon, Kalman filtering with state constraints: a survey of linear and nonlinear algorithms[J], IEEE Trans. Ind. Electron. 57 (12) (2010) 4178–4187.
Contents lists available at ScienceDirect
Powder Technology journal homepage: www.elsevier.com/locate/powtec
Modeling of a medium speed coal mill Yaokui Gao a, Deliang Zeng b,⁎, Jizhen Liu b a b
Key Laboratory of Measurement & Control New Technology and System for Industrial Process, North China Electric Power University, Changping District, 102206 Beijing, China State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Changping District, 102206 Beijing, China
a r t i c l e
i n f o
Article history: Received 19 February 2017 Received in revised form 27 April 2017 Accepted 6 May 2017 Available online 11 May 2017 Keywords: Coal mill Coal moisture Mathematical model Genetic algorithm
a b s t r a c t This paper presents a coal mill model that considers the effect of coal moisture on its accuracy. This mathematical model is derived through the analysis of mass flow, heat exchange, and energy transferring balances in which all heat input into or output from the coal mill are calculated quantitatively to reduce the number of unknown parameters that need to be identified. The work presented in this paper focuses on modeling Mill Parter Ship-type coal mills that are widely used in the coal-fired power plants in China. The unknown model parameters are identified using a real-coded genetic algorithm. Simulation results indicate that the model effectively represents the mid-high process of coal mill dynamics and can be used to estimate the key parameters in coal mills, which are difficult to measure or cannot be measured. On this basis, the model can be used for the state monitoring, control optimization, and fault diagnosis of coal mills. © 2017 Published by Elsevier B.V.
1. Introduction China's energy structure (coal resources are rich, while oil and natural gas resources are extremely insufficient) indicates that coal will continue to be its largest energy resource for a long time [1,2]. Therefore, the research works of Chinese scientists on the clean and efficient use of coal are extremely important. This energy structure also indicates that coal-fired power is the main component of China's power generation. Thus, the dynamic characteristics of pulverizing equipment in coal-fired power plants should be studied to realize the clean and efficient utilization of coal in thermal power plants. Coal mills are independent links in pulverizing systems. The sufficient measuring points at the inlet or outlet of a coal mill enables the analysis of the interactions between the control and controlled variables. Consequently, the state estimation signals of key parameters that are difficult to measure or cannot be measured through modeling can be constructed. In recent years, researchers have conducted extensive studies on coal mill models. Tian et al. regarded the milling process as a first-order inertia link with pure delay and established the dynamic fuel model of a pulverizing system; however, it is a single-input, singleoutput model that does not consider the effect of primary air, thereby resulting in low accuracy [3,4]. Shin et al. established a dynamic model with two kinds of coal particles and a differential coal mill pressure; however, the impact of coal moisture on the coal mill outlet temperature is not considered, thereby resulting in poor accuracy [5]. Liu et al. presented a mathematical model of the coal mill outlet temperature;
⁎ Corresponding author. E-mail address: [email protected] (D. Zeng).
http://dx.doi.org/10.1016/j.powtec.2017.05.015 0032-5910/© 2017 Published by Elsevier B.V.
however, the coefficients of the model need to be re-determined according to different units, which makes the versatility of the model weak [6]. Wei et al. established a multi-stage model for coal mills that covers the multiple working conditions of their start and stop processes. Their model has high precision, but requires the identification of numerous parameters, and it does not consider the impact of raw coal moisture on the energy balance of coal mills [7]. On the basis of the above model, Zeng et al. considered the impact of the moisture of raw coal on the energy balance of coal mills and established a nonlinear dynamic model of coal mills; although the model's outputs are consistent with the actual outputs, the problem of having to identify many parameters remains [8]. Coal mills are regarded as lumped-parameter links, and the calculation methods of the static heat balance in coal mills are provided. This balance indicates that the total energy input into the initial section of the coal mill is equal to the total energy output from the terminal section of the coal mill. This method considers all the energy involved in the coal mill; however, no coal mill model has been established based on the heat balance of coal mills [9–11]. Zeng et al. established an equation with an unknown parameter (coal moisture), which is calculated successfully and has high accuracy in steady-state conditions [12]. On the basis of the literature above, a nonlinear dynamic model of a MPS (Mill Parter Ship)-type medium speed coal mill is proposed in this study based on its mass and energy balance. The effect of raw coal moisture on the energy balance of coal mills is considered to improve the accuracy of the model and all heat inputs into or outputs from the coal mill are calculated quantitatively to reduce the number of parameters that need to be identified. This model can be used to estimate the key parameters that are difficult to measure or cannot be measured: 1) coal powder or raw coal contents in coal mills, which can be used
Y. Gao et al. / Powder Technology 318 (2017) 214–223
Nomenclature specific heat capacity of dry-basis coal, kJ/(kg·°C) specific heat capacity of hot air, kJ/(kg·°C) specific heat capacity of water, kJ/(kg·°C) average specific heat capacity of vapor at a constant pressure, kJ/(kg·°C) specific heat capacity of primary air, kJ/(kg·°C) Cin specific heat capacity of cold air, kJ/(kg·°C) CL average specific heat capacity of raw coal, coal powder, Cmix and the metal involved in heat transfer, kJ/(kg·°C) specific heat capacity of wet air at Tout, kJ/(kg·°C) Cout specific heat capacity of coal powder, kJ/(kg·°C) Cpf specific heat capacity of raw coal, kJ/(kg·°C) Crc proportion coefficient between the coal feed flow and Kc the coal feeder speed, rpm conversion coefficient of raw coal to coal powder per Kconv unit time, 1/s model parameters that need to be identified, i = 1, 2, 3 Ki coefficient of heat loss through equipment Kloss coefficient of heat generation in milling process Kmac proportion coefficient of coal powder flow Kpf leakage coefficient of sealed air for medium speed coal Kseal mill raw coal moisture, % Mar raw coal content in coal mill, kg Mc amount of metal involved in the heat exchange, kg Mmetal moisture content in coal powder, % Mpc coal powder content in coal mill, kg Mpf ΔM amount of moisture evaporated in the coal mill, % differential pressure of primary air, mbar ΔPpa physical heat input into the coal mill by the primary air Qair per unit time, kJ/s Qair & seal physical heat output from the coal mill by primary air and sealing air per unit time, kJ/s total heat input into the coal mill per unit time, kJ/s Qin physical heat input into the coal mill by leaking cold air Qle per unit time, kJ/s heat loss through the equipment per unit time, kJ/s Qloss heat produced by the grinding process per unit time, kJ/s Qmac heat consumed for evaporating raw coal moisture per QΔM unit time, kJ/s total heat output from the coal mill per unit time, kJ/s Qout heat consumed for heating fuel per unit time, kJ/s Qpf physical heat input into the coal mill by raw coal per Qrc unit time, kJ/s physical heat input into the coal mill by sealing air per Qseal unit time, kJ/s coal fineness, % R90 inertia time from the air door to the primary air flow, s T1 inertia time from the air door to the primary air temperT2 ature, s valve opening of hot air, % uH valve opening of cold air, % uL primary air flow, kg/s Wair coal feed flow, kg/s Wc max-flow of hot air, kg/s Wmax H max-flow of cold air, kg/s Wmax L amount of coal powder blown out of the coal mill per Wpf unit time, kg/s temperature of hot air, °C θH primary air temperature, kg/s θin temperature of cold air, °C θL coal mill outlet temperature, °C θout temperature of raw coal, °C θrc Cdc CH CH2O C H2 O
215
as the main basis for coal block and break diagnosis; 2) moisture content in coal powder, which can be used to optimize the outlet temperature of coal mills; and 3) coal powder flow at the outlet of the coal mill, which can be used to optimize the control of the pulverizing system's output. This paper is organized as follows: section one opens with a brief introduction of coal mills; section two deduces and establishes the nonlinear differential equations of coal mills; section three presents the identification process of model parameters; section four simulates and verifies the model; and the conclusion is provided in the final section. 2. Brief introduction of a coal mill MPS-type medium speed coal mills are widely used in the thermal power plants in China. They are designed and manufactured by the German company Babcock. This kind of coal mill has the characteristics of low energy consumption and smooth output and has a small effect on abrasive wear and an overhaul period [13,14]. In this study, MPS180HP-II medium speed coal mill is used as the research object. Its maximum output is 44.496 t/h and the fineness of coal powder R90 is 22% [15] (Fig. 1) (R90 refers to the probability that coal powders cannot pass through a sieve with apertures of 90 μm). Raw coals fall into the gap between the grinding roller and the grinding disc via a coal chute. Then, the raw coals are crushed into coal powder under the squeezing pressure of the grinding parts. Subsequently, the primary air that enters the coal mill through the air ring dries and brings the coal powders into the coarse coal separator at the upper part of the grinding area for separation. Qualified coal powders are blown out of the coarse coal separator into the boiler while the others fall on the grinding disc for re-grinding. 3. Modeling of the coal mill In this study, the lumped parameter modeling method is adopted with the following assumptions: 1) the parameters of the medium in the coal mill are uniform; 2) the media in the coal mill are incompressible; 3) the parameters of the medium in the coal mill change along the axial direction only; 4) the change in the flow power in the coal mill is ignored; 5) the coal powder separation process is not considered; 6) only two kinds of coal particles (coal powder and raw coal) exist in the coal mill; 7) the temperatures of the coal powder and the primary air are the same at the outlet of the coal mill.
Fig. 1. Schematic of the MPS medium-speed mill.
216
Y. Gao et al. / Powder Technology 318 (2017) 214–223
3.1. Modeling of inlet primary air of the coal mill On the basis of the energy and mass balances of the primary air at the inlet of the coal mill, the model of the primary air is established in Eqs. (1) and (2) as follows: max T 1 W_air ¼ −W air þ W max L uL þ W H uH ;
T 2 θ_in ¼ −θin þ
max C L W max L uL θL þ C H W H uHθH ; max max C in W L uL þ W H uH
θL −0 C L ¼ 1:011 þ ð1:012−1:011Þ; 25−0
ð1Þ ð2Þ
ð3Þ
3.3.1. Total heat input into the coal mill The total heat input into the coal mill per unit time is calculated as shown in Eq. (13). Q in ¼ Q air þ Q rc þ Q mac þ Q seal þ Q le :
a. Physical heat input into the coal mill by the primary air per unit time Q air ¼ C in θin W air ;
ð14Þ
where θin takes the primary air temperature state after the mixing of hot and cold airs as shown in Eq. (2), and Cin is calculated based on Eq. (5). b. Physical heat input into the coal mill by raw coal per unit time
C H ¼ 1:011 þ
θH −200 ð1:028−1:011Þ; 400−200
ð4Þ
Q rc ¼ C rc W c θrc ;
C in ¼ 1:011 þ
θin −200 ð1:019−1:011Þ: 300−200
ð5Þ
C rc ¼
In Eqs. (3)–(5), CL, CH, and Cin, are functions of θL, θH, and θin, respectively, and are calculated based on the national standard shown in Appendix A, Table 1 [12]. The specific heat capacities of wet air are 1.011 and 1.012 kJ/(kg·°C) when d = 10 g/kg and θL = 0 °C and 25 °C, respectively, while the specific heat capacities of dry air are 1.011, 1.019, and 1.028 kJ/(kg·°C) when θH = 200 °C, 300 °C, and 400 °C, respectively. , Wmax In the above model, Wmax L H , T1, and T2 are the parameters that need to be identified. They can be obtained through the comparison of the actual output and the model output of Wair and θin.
ð13Þ
C H2 O Mar C dc ð100−Mar Þ þ ; 100 100
ð15Þ ð16Þ
where Cdc is determined by the type and temperature of raw coal, θrc is weighted by Cdc (1.884 kJ/(kg·°C)) and CH2O (4.187 kJ/(kg·°C)) as shown in Eq. (16). θrc is the temperature of raw coal, that is, θrc = 20 °C for high-moisture fuel and θrc = 0 °C for the rest. c. Heat produced by the grinding process of the coal mill per unit time Q mac ¼ K mac I;
ð17Þ
where Kmac is taken as 0.6 for a MPS medium speed coal mill according to the national standard. d. Physical heat input into the coal mill by sealing air per unit time
3.2. Modeling of coal quantity in the coal mill On the basis of the mass balance of coal in the coal mill, the model of coal powder and raw coal in the coal mill are established as Eqs. (6) and (7), respectively. M_ c ¼ W c −K conv Mc ;
ð6Þ
M_pf ¼ −W pf þ K conv Mc ;
ð7Þ
W c ¼ K c Nc ;
ð8Þ
where Wpf is the amount of coal powder that is blown out of the coal mill per unit time, which is proportional to Δ Ppa and Mpf [Eq. (9)]. ΔPpa is proportional to θin, and W2air is calculated as shown in Eq. (10). W pf ¼ K pf Mpf ΔP pa ; ΔP pa
22:4 273 þ θin W air 2 ∙ ¼ ; ∙ 273 10 28:8
I ¼ K 1 Mpf þ K 2 M c þ K 3 :
ð9Þ ð10Þ ð11Þ
In the above model, Kconv, Kc, Kpf, K1, K2, and K3 denote the identified parameters, which can be obtained through the comparison of the actual and model outputs of the coal mill's current, as defined in Eq. (11). 3.3. Modeling of outlet temperature of the coal mill On the basis of the energy balance inside the coal mill, the model of the coal mill outlet temperature is established as shown in Eq. (12). _ ¼ Q in −Q out : C mix M c þ Mpf þ Mmetal θout
ð12Þ
The magnitude of Mc and Mpf is 101 while that of Mmetal is 103. Therefore, Cmix takes the specific heat capacity of metal, 0.46 kJ/(kg·°C).
Q seal ¼ C L θL K seal W air :
ð18Þ
The seal air flow is assumed proportional to the primary air flow at the inlet of the coal mill, and Kseal is 0.1. Therefore, KsealWair is the sealing air flow (kg/s), and CL is calculated based on Eq. (3). e. Physical heat input into the coal mill by leaking cold air per unit time Given that the research object in this study is a positive pressure direct-blowing pulverizing system, the air leakage is zero. Thus, the physical heat input into the coal mill by leaking cold air per unit time as follows: Q le ¼ 0:
ð19Þ
3.3.2. Total heat output from the coal mill The total heat output from the coal mill per unit time is calculated as shown in Eq. (20). Q out ¼ Q air&seal þQ ΔM þ Q pf þ Q loss :
ð20Þ
a. Physical heat output from the coal mill by primary air and sealing air per unit time Q air&seal ¼ C out θout ð1 þ K seal ÞW air ;
ð21Þ
where Cout is a function of θout, which is calculated by linear interpolation in Eq. (22), and the specific heat capacity of the wet air is generally 1.012 and 1.015 when the air temperatures are 25 °C and 100 °C, respectively, and the air humidity is 10 g/kg based on the national standard shown in Appendix A, Table 1. C out ¼ 1:012 þ
θout −25 ð1:015−1:012Þ: 100−25
ð22Þ
Y. Gao et al. / Powder Technology 318 (2017) 214–223
217
b. Heat consumed by evaporation of moisture in raw coal per unit time ð23Þ Q ΔM¼ ΔMW c 2500 þ CH2 O θout −4:187θrc ;
Mpf, and θout. The time-varying parameters are θL, θH, θrc, and Mar. , Wmax Wmax L H , T1, T2, Kconv, Kc, Kpf, K1, K2, K3, and Mmetal denote the parameters that need to be identified.
where CH2 O is calculated based on the national standard shown in Table A.1 in Appendix A and is 1.862 kJ/(kg·°C) when the water temperature is 25 °C based on experience. ΔM is calculated in Eq. (24) and Mpc is calculated in Eq. (25), where R90 is 22% according to the design parameters of the coal mill.
4. Identification of model parameters
ΔM ¼
Mar −Mpc ; 100−Mpc
Mpc ¼ 0:048M ar
ð24Þ R90
θout 0:46
:
ð25Þ
c. Heat consumed for heating fuel per unit time Q pf ¼
100−Mar W c C ðθout −θrc Þ; 100 pf
ð26Þ
The identification of the coal mill model is difficult because θout is affected by numerous factors, such as θL, θH, uL, uH, Wc, and Mar. To reduce identification difficulty, a stepwise identification method is proposed in this paper. This identification method divides the identification process of the model into three steps: identification of the primary air model, of the coal quantity model, and of the mill outlet temperature model. Here, the unknown parameters of the model are identified based on the real-coded genetic algorithm [16–18]. The population size is 50, the maximum number of iterations is 50, the probability of crossing is 0.9, and the probability of mutation is 0.3. The specific identification process is shown in Fig. 2. Fitness functions ffit1, ffit2, and ffit3 are defined as follows: ( N
f fit1 ¼ ∑t¼0 W 1
where Cpf is weighted by CH2O and Cdc is as follows: C pf ¼ C dc þ
4:187M pc : 100−M pc
ð27Þ
d. Heat loss through the equipment per unit time
N
f fit2 ¼ ∑t¼0
N
f fit3 ¼ ∑t¼0 Q loss ¼ K loss Q in ;
ð28Þ
where Kloss is the coefficient of heat loss through the equipment and is 0.02 based on experience. In summary, the model of the coal mill proposed in this paper is as follows: 8 max max _ > > > T 1 W air ¼ −W air þ W L uL þ W H uH > > max max > > > T 2 θ_in ¼ −θin þ C L W L uL θL þ C H W H uHθH > max max > > C in W L uL þ W H uH > > > > > M_ c ¼ W c −K conv Mc > > > > > M_pf ¼ K conv Mc −W pf > > > > > _ ¼ Q in −Q out > C mix M c þ M pf þ M metal θout > > > > > > W pf ¼ K pf ΔP pa M pf > > > > > 22:4 273 þ θin W air 2 > > > ∙ ΔP pa ¼ ∙ > > 273 10 28:8 > > > > > Q ¼ Q þ Q þ Q þ Q > in air rc seal þ Q le mac > > > > > Q air ¼ C in θin W air > > < Q rc ¼ C rc θrc W c ; > > Q mac ¼ K mac I > > > > > > Q seal ¼ C L θL K seal W air > > > > > Q le ¼ 0 > > > > Q out ¼ Q air&seal þQ ΔM þ Q pf þ Q san > > > > > Q air&seal ¼ C out θout ð1 þ K seal ÞW air > > > > > Q ΔM¼ ΔMW c 2500 þ C H2 O θout −C H2 O θrc > > > > M ar −Mpc > > ΔM ¼ > > > 100−M pc > > > > R90 > > > M pc ¼ 0:048Mar > > > θout 0:46 > > > 100−M ar > > > W c C ðθout −θrc Þ Q pf ¼ > > 100 pf > > : Q loss ¼ K loss Q in
) d ∣∣θin ðt Þ−θc ∣∣W air ðt Þ−W in ðt Þ∣∣ air ðt Þ∣∣ þ W2 ; d θc W in ðt Þ air ðt Þ
ð30Þ
∣∣Iðt Þ−^Iðt Þ∣∣ ; ^Iðt Þ
ð31Þ
∣∣θout ðt Þ−θd out ðt Þ∣∣ ; d θout ðt Þ
ð32Þ
where N is the number of measured data points and W1 and W2 are the d c ^ d weight coefficients for θin and Wair; W air ðtÞ, θin ðtÞ, IðtÞ, and θout ðtÞ are the outputs of the model at time t; and Wair(t), θin(t), I(t), and θout(t) are the outputs of the coal mill at time t; During the identification process, the raw coal moisture is calculated online based on the method proposed by Ref. [12], and the model parameters obtained by the identification method are shown in Table 2. Let x1 = Wair, x2 = θin, x3 = Mc, x4 = Mpf, x5 = θout, u1 = uL, u2 = uH, u3 = Wc, y1 = Wair, y2 = θout, y3 = Wpf, w = Mar, θL = 43 °C, θH = 341 °C, and θrc =0 °C.
ð29Þ
where the inputs to the model are uL, uH, and Wc. The outputs of the model are Wair, θout, and Wpf. The states of the model are θin, Wair, Mc,
Fig. 2. Identification process of parameters.
Table 2 Identified model parameters. = 18.83 Wmax L = 55.11 Wmax H
T1 = 10.3004 T2 = 3.6765
Kconv = 0.4522 Kpf = 0.0795
K1 = 0. 1799 K2 = 0. 8496
K3 = 19.7787 Mmetal = 4131.7
218
Y. Gao et al. / Powder Technology 318 (2017) 214–223
The nonlinear state equation of the coal mill is obtained as follows: 8 x_1 ¼ −0:0971x1 þ 0:183u1 þ 0:551u2 −22:2 > > > 7:98u1 þ 192:0u2 > > > x_2 ¼ −0:272x2 −198 þ > > > ð0:183u1 þ 0:551u2 Þ 8x2 10−5 þ 0:995 > > > > _ > x3 ¼ −0:452x3 þ u3 > > > > > x_4 ¼ 0:452x3 −ð0:00285x2 þ 0:778Þx1 2 x4 7:95 10−4 > > > 1 > > > x_ ¼ ð1:1x3 þ 0:233x4 þ 9:42x1 −2:414x1 x5 þ 2:151x1 x2 þ tempA þ tempBÞ > < 5 4171:7 1:1w 2:17u3 ð1:88x5 þ 2499Þ w− 0:45 > > > x5 > > tempA ¼ > > 1:1w > > −100 > > > x5 0:45 > 0 1 > > > > > > B C > 4:62w > > −1:09C tempB ¼ −2:17x5 u3 ð0:01w−1:0ÞB > @ A > 1:1w > 0:45 > −100 x5 : x5 0:45
ð33Þ The output equation is as follows: 8 < y1 ¼ x1 y ¼ x5 : 2 y3 ¼ −ð0:00285x2 þ 0:778Þx1 2 x4 7:95 10−4
:
ð34Þ
5. Simulation and validation 5.1. Verification of model dynamic characteristics To verify the validity of the model, step disturbance is applied to one of the inputs of the model while keeping the others constant, and the inputs and outputs of the model are recorded at the same time (Figs. 3-5).
When a step-increasing signal is applied to uL (Fig. 3(a)), the output of the model changes as follows. The cold air flow increases while the hot air flow remains constant, thus resulting in an increase in the Wair at the inlet of the coal mill (Fig. 4(a)) and a decrease in θout (Fig. 4(b)). The increase in Wair increases the ΔPpa between the outlet and the inlet of the coal mill, resulting in a decrease in Mpf (Fig. 5(b)) and decreasing the current I required for milling (Fig. 5(c)). In addition, the decrease in θout prevents the sufficient drying of coal powders, resulting in an increase in Mpc (Fig. 5(d)). When a step-increasing signal is applied to u H (Fig. 3(b)), the output of the model changes as follows. The hot air flow increases while the cold air flow remains constant, thus resulting in an increase in the Wair at the inlet of the coal mill (Fig. 4(a)) and an increase in θ out (Fig. 4(b)). The decrease in W air decreases the Δ P pa between the outlet and the inlet of the coal mill, resulting in an increase in M pf (Fig. 5(b)) and increasing the current I required for milling (Fig. 5(c)). In addition, the increase in θ out results in the sufficient drying of the coal powders and a decrease in M pc (Fig. 5(d)). When a step-increasing signal is applied to the raw coal moisture Mar (Fig. 3(c)), the output of the model changes as follows. The energy supplied by Wair (Fig. 4(a)) remains constant while the Mar that needs to be evaporated increases. The primary air with same energy level dries the raw coal with a higher moisture content, resulting in a decrease in θout (Fig. 4(b)) and an increase in Mpc (Fig. 5(d)). When a step-increasing signal is applied to coal feed flow Wc (Fig. 3(d)), the output of the model changes as follows. The amount of coal required to be milled increases, resulting in an increase in grinding current I (Fig. 5(c)). The increase in Wc increases the amount of coal that needs to be dried, thereby decreasing the θout (Fig. 4(b)) and increasing the Mpc (Fig. 5(d)).
Fig. 3. Step disturbance on model inputs.
Y. Gao et al. / Powder Technology 318 (2017) 214–223
Fig. 4. Curves for model outputs (I).
Fig. 5. Curves for model outputs (II).
219
220
Y. Gao et al. / Powder Technology 318 (2017) 214–223
Fig. 6. Curves for input data.
The result of the verification and analysis of model dynamics above indicates that the model proposed in this paper is inherently accurate. 5.2. Verification of the model output To verify the versatility and accuracy of the coal mill model further, two sets of historical data are used to simulate and validate the model. The specific verification process is as follows:
(1) To verify the versatility of the model under multiple operating conditions, five days of actual operational data are collected as the first validation data set, during which the load rate of the coal mill is from 59.88%–97.59% (Figs. 6 and 7). The output of the model is compared with the actual output of the coal mill as shown in Figs. 8 and 9, which show that the model outputs are coincident with the online measurements. The correlation coefficient and the relative root-mean-square deviation between
Fig. 7. Curves for time-varying parameters.
Y. Gao et al. / Powder Technology 318 (2017) 214–223
221
Fig. 8. Comparison of actual outputs and model outputs (I).
Fig. 9. Comparison of actual outputs and model outputs (II).
the model and actual outputs are shown in Table 3. The table shows that three of the parameters have correlation coefficients greater than 0.7 with a lower error value for Wair, and the relative root-mean-square deviations of θin, I, and θout are lower than 3% with a slightly higher error for Wair. This phenomenon is due to the fact that the measurement of Wair is inherently inaccurate in actual operations of the coal mill. The online estimation of
Table 3 Correlation coefficient and Root-mean-square deviation between model output and actual output. Outputs of the object
Wair
θin
I
θout
Correlation coefficient Relative root-mean-square deviation (%)
0.5219 8.14
0.9762 2.54
0.8705 2.37
0.7132 1.41
coal content in the coal mill is shown in Fig. 10, which can be used as the main basis for the diagnosis of coal block and break. (2) To quantify the delay time of the milling process, 9 h of actual operational data are collected as the second set of validation data, and the sampling time is 2 s. Fig. 11 shows that the trend of change in Wpf is to the same as that of Wc, and the former is delayed at approximately 20 s relative to the latter, which verifies that the estimated coal powder flow at the outlet of the coal mill is accurate.
6. Conclusions On the basis of the comprehensive consideration of the key state parameters, such as the coal content in the coal mill, the moisture content
222
Y. Gao et al. / Powder Technology 318 (2017) 214–223
Fig. 10. Estimation of coal content in the coal mill.
in coal powder, and the coal powder flow at the outlet of the coal mill, a nonlinear dynamic model of the medium speed coal mill based on mass and energy balance is proposed. In the model, the effect of coal moisture on the energy balance of coal mill is considered to improve the accuracy of the model, and all heat input into or output from the coal mill are
quantitatively calculated to reduce the number of unknown parameters that need to be identified. After the simulation and verification, the model is proven effective in reflecting the dynamics of a coal mill and has good precision. This nonlinear dynamic model can be used for the state monitoring, control optimization, and fault diagnosis of coal mills.
Fig. 11. Comparison of Wc and Wpf.
Y. Gao et al. / Powder Technology 318 (2017) 214–223
Appendix A
Table 1 Specific heat capacity of common gases (kJ/(kg·°C)). Humid air t/°C
d = 10 g/kg
d = 20 g/kg
H2O
Dry air
O2
N2
CO2
0 25 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400
1.011 1.012 1.015 1.020 1.028 1.037 1.048 1.058 1.070 1.081 1.091 1.101 1.110 1.119 1.127 1.135
1.020 1.022 1.023 1.028 1.037 1.046 1.057 1.068 1.079 1.091 1.101 1.111 1.120 1.130 1.138 1.147
1.859 1.862 1.872 1.894 1.919 1.947 1.977 2.009 2.041 2.075 2.109 2.143 2.197 2.210 2.242 2.274
0.914 0.915 0.922 0.934 0.949 0.964 0.978 0.992 1.004 1.015 1.025 1.034 1.042 1.050 1.057 1.064
1.030 1.031 1.032 1.034 1.040 1.047 1.056 1.066 1.077 1.088 1.098 1.107 1.117 1.125 1.134 1.142
0.809 0.831 0.860 0.904 0.942 0.976 1.006 1.032 1.056 1.078 1.097 1.115 1.131 1.145 1.158 1.170
1.003 1.005 1.006 1.011 1.019 1.028 1.039 1.049 1.060 1.071 1.081 1.090 1.099 1.108 1.116 1.124
References [1] J. Bugge, S. Kjær, R. Blum, High-efficiency coal-fired power plants development and perspectives[J], Energy 31 (10) (2006) 1437–1445. [2] C. Xu, Y. Yuan, Analysis of present operating situation of large size coal-fired utility boilers[J], Electr. Power 1 (2003) 000. [3] L. Tian, D. Zeng, X. Liu, et al., A simplified non-linear dynamic model of 500 MW unit[J], Power Eng. 4 (2004) 015.
223
[4] L. Tian, D. Zeng, J. Liu, et al., A simplified non-linear dynamic model of 330 MW unit[J], Proc. Chin. Soc. Electr. Eng. 24 (8) (2004) 180–184. [5] H.B. Shin, X.L. Li, Modeling and parameter identification of coal mill[J], J. Power Electron. 9 (5) (2009) 700–705. [6] C. Liu, W. Yao, Y. Qu, C. Zhen, An improved genetic algorithm and its application in thermal process control, Process. Autom. Instrum. 23 (9) (2002) 13e6 (in Chinese). [7] J.L. Wei, J. Wang, Q.H. Wu, Development of a multisegment coal mill model using an evolutionary computation technique[J], IEEE Trans. Energy Convers. 22 (3) (2007) 718–727. [8] D. Zeng, Y. Hu, S. Gao, et al., Modelling and control of pulverizing system considering coal moisture[J], Energy 80 (2015) 55–63. [9] J.K. Feng, Y.T. Shen, R.C. Yang, The Principle and Calculation of Boiler[J], 1997. [10] V. Ganapathy, Industrial Boilers and Heat Recovery Steam Generators: Design, Applications, and Calculations[M], CRC Press, 2002. [11] N.M. Magdalinović, Calculation of energy required for grinding in a ball mill[J], Int. J. Miner. Process. 25 (1) (1989) 41–46. [12] D. Zeng, Y. Hu, J. Liu, et al., Soft sensing of coal moisture[J], Measurement 60 (2015) 231–239. [13] J.F. Yue, J.F. Yue, L. Huang, et al., Experimental investigation of the operating characteristics of a MPS coal mill[J], Reneng Dongli Gongcheng (J. Eng. Therm. Energy Power), 20 (1) (2005) 65–68. [14] X. Zhu, Z. Zhao, Q. Zhang, Research on mill rejects characteristics for medium speed mill [J], Proc. CSEE 23 (2010) 013. [15] H.F. Yuan, Changchun generating equipment group [EB/OL], http://www.chinacge. com 2016-08-16/2016-10-04. [16] V. Rashtchi, E. Rahimpour, S. Fazli, Genetic algorithm application to detect broken rotor bar in three phase squirrel cage induction motors[J], Int. Rev. Electr. Eng. 6 (5) (2011) 2286–2292. [17] O. Mohamed, J. Wang, S. Guo, et al., Modelling Study of Supercritical Power Plant and Parameter Identification Using Genetic Algorithms[C]//Proceedings of the World Congress on Engineering, Newswood Ltd., London, United Kingdom, 2010 973–978. [18] D. Simon, Kalman filtering with state constraints: a survey of linear and nonlinear algorithms[J], IEEE Trans. Ind. Electron. 57 (12) (2010) 4178–4187.