CN109615084A - Positive-pressure type medium-speed pulverizer fuel pulverizing plant fineness of pulverized coal real-time monitoring system - Google Patents

Positive-pressure type medium-speed pulverizer fuel pulverizing plant fineness of pulverized coal real-time monitoring system Download PDF

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CN109615084A
CN109615084A CN201710916832.1A CN201710916832A CN109615084A CN 109615084 A CN109615084 A CN 109615084A CN 201710916832 A CN201710916832 A CN 201710916832A CN 109615084 A CN109615084 A CN 109615084A
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王亚顺
梁绍华
陈小强
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China Electric Huachuang Electric Power Technology Research Institute Co Ltd
Nanjing Institute of Technology
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Nanjing Institute of Technology
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Abstract

The present invention relates to a kind of positive-pressure type medium-speed pulverizer fuel pulverizing plant fineness of pulverized coal real-time monitoring systems, monitoring system includes that coal pulverizer inlet apparatus for measuring air quantity, coal pulverizer inlet wind-warm syndrome measuring device, coal pulverizer go out one's intention as revealed in what one says powder temperature measuring device, dynamic separator rotation-speed measuring device, coal-supplying amount measuring device, grinding roller load force measuring device and processor, processor is for executing following program: obtaining the measurement result of each measuring device in real time, the operating condition operating parameter for calculating fuel pulverizing plant obtains fineness of pulverized coal according to trained supporting vector machine model.Compared with prior art, the present invention can run for the optimization of boiler powder combustion system and provide foundation, improve unit safety, economy and environmental benefit.

Description

Positive-pressure type medium-speed pulverizer fuel pulverizing plant fineness of pulverized coal real-time monitoring system
Technical field
The present invention relates to a kind of coal pulverizer fuel pulverizing plant fineness of pulverized coal to monitor system, more particularly, to a kind of positive-pressure type middling speed Coal pulverizer fuel pulverizing plant fineness of pulverized coal real-time monitoring system.
Background technique
Fineness of pulverized coal is the important factor in order of Combustion Efficiency for Pulverized Fired Boiler, and the fineness of pulverized coal coal dust after-flame bigger than normal that will lead to is stranded Difficulty, boiler combustion efficiency are low;And fineness of pulverized coal is less than normal, and coal pulverizer power consumption is caused to rise, grinding roller rate of depreciation is accelerated.In addition coal Powder fineness to burner hearth NOx generate concentration, burner region fire intensity etc. have larger impact, therefore exist for different types of coal The fineness of pulverized coal of an optimization so as to reach economy under the precondition of safe and environment-friendly operation best for boiler.
Medium-speed pulverizer generally uses pressurized direct pulverizing coal system, and fineness of pulverized coal is generally obtained by test method, In the case where coal quality is changed with load change, the fineness of pulverized coal needs of operation are adjusted accordingly, if coal quality volatile matter increases Should be thicker to prevent from burning nozzle by fineness of pulverized coal tune, it then should be thin by fineness of pulverized coal tune when unit is run under depth peak regulation situation It is some to prevent underload from putting out a fire.However Present Thermal Power factory operation coal quality and load is regular fluctuates widely, it can not application test Means obtain current fineness of pulverized coal as combustion adjustment foundation at any time.
Currently, also there is more research for fineness of pulverized coal real time monitoring, the experience for there are some fineness of pulverized coal to calculate Formula, but due to coal varitation, the variation of load variations and coal pulverizer operation conditions, these calculated results are difficult to effectively be applicable in In various operation conditions.
Summary of the invention
It is an object of the present invention to overcome the above-mentioned drawbacks of the prior art and provide one kind can be monitored in real time The positive-pressure type medium-speed pulverizer fuel pulverizing plant fineness of pulverized coal real-time monitoring system of fineness of pulverized coal.
The purpose of the present invention can be achieved through the following technical solutions:
As the first scheme, a kind of positive-pressure type medium-speed pulverizer fuel pulverizing plant fineness of pulverized coal real-time monitoring system is described Fuel pulverizing plant include positive-pressure type medium-speed pulverizer and feeder, the feeder passes through dynamic separator and positive-pressure type middling speed Coal pulverizer connects, and grinding roller is equipped in the positive-pressure type medium-speed pulverizer, the monitoring system includes coal pulverizer inlet air quantity Measuring device, coal pulverizer inlet wind-warm syndrome measuring device, coal pulverizer go out one's intention as revealed in what one says powder temperature measuring device, dynamic separator tachometric survey Device, coal-supplying amount measuring device, grinding roller load force measuring device and processor, the processor is for executing following journey Sequence: obtaining the measurement result of each measuring device in real time, calculates the operating condition operating parameter of fuel pulverizing plant, according to it is trained support to Amount machine model obtains fineness of pulverized coal, the input quantity of the support vector machines be coal pulverizer inlet air quantity, coal pulverizer inlet wind-warm syndrome, Raw coal moisture in dynamic separator revolving speed, coal-supplying amount, grinding roller loading force and feeder, the raw coal moisture in the feeder are logical Cross fuel pulverizing plant heat balance principle, using coal pulverizer inlet air quantity, coal pulverizer inlet wind-warm syndrome, coal pulverizer go out one's intention as revealed in what one says powder temperature and to Coal weighing obtains.
Preferably, the training method of the support vector machines includes: that change coal pulverizer inlet air quantity, coal pulverizer enter respectively Raw coal moisture in one's intention as revealed in what one says temperature, dynamic separator revolving speed, coal-supplying amount, grinding roller loading force and feeder carries out multi-state test, will Various operating condition operating parameters and corresponding fineness of pulverized coal are input in the supporting vector machine model of fineness of pulverized coal prediction as sample, into Row model training and machine learning.
Alternatively, a kind of positive-pressure type medium-speed pulverizer fuel pulverizing plant fineness of pulverized coal real-time monitoring system, it is described Fuel pulverizing plant include positive-pressure type medium-speed pulverizer and feeder, the feeder passes through static separation device and positive-pressure type middling speed Coal pulverizer connects, and grinding roller is equipped in the positive-pressure type medium-speed pulverizer, the monitoring system includes coal pulverizer inlet air quantity Measuring device, coal pulverizer inlet wind-warm syndrome measuring device, coal pulverizer go out one's intention as revealed in what one says powder temperature measuring device, static separation device deflector baffle Openness measuring device, coal-supplying amount measuring device, grinding roller load force measuring device and processor, the processor is for executing such as Under program: obtain each measuring device measurement result in real time, the operating condition operating parameter of fuel pulverizing plant calculated, according to trained branch It holds vector machine model and obtains fineness of pulverized coal, the input quantity of the support vector machines is coal pulverizer inlet air quantity, coal pulverizer inlet Raw coal moisture in wind-warm syndrome, static separation device deflector baffle aperture, coal-supplying amount, grinding roller loading force and feeder, the feeder In raw coal moisture by fuel pulverizing plant heat balance principle, go out using coal pulverizer inlet air quantity, coal pulverizer inlet wind-warm syndrome, coal pulverizer One's intention as revealed in what one says powder temperature and coal-supplying amount are calculated.
Preferably, the processor is connected with data display equipment.
Preferably, the monitoring system further includes seal fan, and the seal fan entrance enters with coal pulverizer temperature wind Mouth connection, outlet are connected to feeder and grinding roller.
Preferably, the processor passes through fault-tolerant processing to the measurement result of each measuring device, then carries out operating condition operation Parameter calculates.
Preferably, the training method of the support vector machines includes: that change coal pulverizer inlet air quantity, coal pulverizer enter respectively Raw coal moisture in one's intention as revealed in what one says temperature, static separation device deflector baffle aperture, coal-supplying amount, grinding roller loading force and feeder carries out multi-state Test is input to the support vector machines mould of fineness of pulverized coal prediction using various operating condition operating parameters and corresponding fineness of pulverized coal as sample In type, model training and machine learning are carried out.
Preferably, it is temperature sensing that coal pulverizer inlet wind-warm syndrome measuring device and coal pulverizer, which go out one's intention as revealed in what one says powder temperature measuring device, Device.
Preferably, grinding roller load force measuring device is pressure sensor.
Preferably, the coal-supplying amount measuring device is the electronic belt with weighing sensor and tread speed sensor Scale.
Compared with prior art, the present invention reaches real-time monitoring fineness of pulverized coal by establishing fineness of pulverized coal prediction model Purpose can run for the optimization of boiler powder combustion system and provide foundation, improve unit safety, economy and environmental benefit; Operating parameter is easy to get, and belongs to hard measurement device, and abrasion, the corrosion that there is no hardware devices in coal dust, accuracy is high, transports Row is easy to maintain.
Detailed description of the invention
Fig. 1 is the positive-pressure type medium-speed pulverizer fuel pulverizing plant and its real-time monitoring system structural schematic diagram of the present embodiment 1.
Appended drawing reference:
1 is positive-pressure type medium-speed pulverizer;2 be coal pulverizer inlet apparatus for measuring air quantity;3 go out the survey of one's intention as revealed in what one says powder temperature for coal pulverizer Measure device;4 be coal-supplying amount measuring device;5 be fineness measurement device for pulverized coal;6 be seal fan;7 be coal pulverizer inlet temperature wind;8 For feeder;9 load force measuring device for grinding roller;10 be coal pulverizer inlet wind-warm syndrome measuring device;11 be dynamic separator revolving speed Measuring device;12 be dynamic separator;13 be coal pipe.
Specific embodiment
The present invention is described in detail with specific embodiment below in conjunction with the accompanying drawings.The present embodiment is with technical solution of the present invention Premised on implemented, the detailed implementation method and specific operation process are given, but protection scope of the present invention is not limited to Following embodiments.
Embodiment
As shown in Figure 1, a kind of positive-pressure type medium-speed pulverizer fuel pulverizing plant fineness of pulverized coal real-time monitoring system, fuel pulverizing plant packet Positive-pressure type medium-speed pulverizer 1 and feeder 8 are included, feeder 8 is connect by dynamic separator with positive-pressure type medium-speed pulverizer 1, just Grinding roller is equipped in pressure type medium-speed pulverizer 1, monitoring system includes coal pulverizer inlet apparatus for measuring air quantity 2, coal pulverizer inlet wind-warm syndrome Measuring device 10, coal pulverizer go out one's intention as revealed in what one says powder temperature measuring device 3, dynamic separator rotation-speed measuring device 11, coal-supplying amount measurement dress 4, grinding roller load force measuring device 9 and processor are set, processor is for executing following program: obtaining each measuring device in real time Measurement result calculates the operating condition operating parameter of fuel pulverizing plant, obtains fineness of pulverized coal, branch according to trained supporting vector machine model The input quantity of vector machine is held to add for coal pulverizer inlet air quantity, coal pulverizer inlet wind-warm syndrome, dynamic separator revolving speed, coal-supplying amount, grinding roller The raw coal moisture in power and feeder is carried, the raw coal moisture in feeder is by fuel pulverizing plant heat balance principle, using coal pulverizer Entrance air quantity, coal pulverizer inlet wind-warm syndrome, coal pulverizer go out one's intention as revealed in what one says powder temperature and coal-supplying amount is calculated, and by taking coal pulverizer 1 as an example, calculates Method specifically comprises the following steps:
(1) the dry dosage Q of online acquisition coal pulverizer operation datav, coal-supplying amount Bm, import wind-warm syndrome t1, go out one's intention as revealed in what one says powder temperature t2, 1 coal amount B of coal pulverizerm1
(2) coal pulverizer inputs heat Calculation;
(3) assume 1 raw coal moisture M of coal pulverizer1j=10%, below M in calculation formulajWith M1jSubstitution is calculated;
(4) dry agent flux is calculated:
(5) desiccant physical thermal: q is calculatedag1=cag1×t1×g1
(6) sealing air physical thermal is calculated:
(7) it gives coal pulverizer to mill heat: qmac=12;
(8) coal pulverizer total heat input is calculated;qin=qag1+qs+qmac
(9) 1 quantity of heat given up of coal pulverizer calculates:
(10) heat of evaporation water consumption: q is calculatedev=Δ M × (2500+c "H2O×t2-4.187×trc);
(11) it calculates lack of gas desiccant and takes heat out of:
(12) equipment cooling loss: q is calculated5=0.02 × qin
(13) it calculates coal pulverizer and exports total amount of heat: qout=qev+qag2+qf+q5
(14) heat of heating fuel consumption: q is calculatedf=qout-(qev+qag2+q5)=qin-(qev+qag2+q5);
(15) heat of heating fuel consumption is calculated:
(16) raw coal moisture M can be solved by formula (14) and formula (15)jIf | Mj-M1j| > 1%, then by MjAs new Assumed value, i.e. M1j=Mj, return to (3) stepping row iteration and calculate;Until | Mj-M1j| < 1%, obtain coal pulverizer raw coal moisture M1j =Mj
Related property parameter value:
Serial number Physical quantity Code name Unit Value
1 Seal air quantity Qs t/h 3.8
2 Import desiccant specific heat cag1 kJ/(kg·℃) 1.028
3 Sealing air specific heat cs 1.014
4 Mill machinery heat qmac kJ/kg 12
5 Coal dust moisture Mpc % 1.5
6 Water vapour avergae specific heat C″H2O 1.866
7 Water specific heat cH2O 4.187
8 Export lack of gas specific heat cag2 1.106
9 Into system raw coal temperature trc 0
10 Coal pulverizer radiation loss q5 0.02*qin
11 Seal air temperature ts Take environment temperature
The training method of support vector machines includes: to change coal pulverizer inlet air quantity, coal pulverizer inlet wind-warm syndrome, dynamic point respectively Multi-state test is carried out from the raw coal moisture in device revolving speed, coal-supplying amount, grinding roller loading force and feeder, various operating conditions are run and are joined Several and corresponding fineness of pulverized coal is input in the supporting vector machine model of fineness of pulverized coal prediction as sample, carries out model training and machine Device study.
Processor is connected with data display equipment, for showing the real-time calculated value of fineness of pulverized coal.
Monitoring system further includes seal fan 6, and 6 entrance of seal fan is connect with coal pulverizer temperature wind entrance, and outlet is connected to Feeder 8 and grinding roller.
Processor passes through fault-tolerant processing to the measurement result of each measuring device, then carries out operating condition operating parameter calculating.
It is temperature sensor, mill that coal pulverizer inlet wind-warm syndrome measuring device 10 and coal pulverizer, which go out one's intention as revealed in what one says powder temperature measuring device 3, It is pressure sensor that roller, which loads force measuring device 9, and coal-supplying amount measuring device 4 is with weighing sensor and tread speed sensor Belted electronic balance.
The working principle of the system:
(1) medium-speed pulverizer wind powder flow path: coal pulverizer inlet temperature wind 7 enters positive-pressure type medium-speed pulverizer 1 by bellows In, the raw coal combination drying being sent into herein with feeder 8, the raw coal after drying is after grinding roller is milled into the powder of certain fineness in wind Carrying under after dynamic separator 12, pulverized coal distributor 14 enter coal pipe 13 in.In addition, a small amount of coal pulverizer inlet temperature wind 7 Sealed blower 6 enters in feeder 8 and Roller of Coal Grinder after being pressurized to be sealed, and prevents coal dust from entering feeder and coal pulverizer In grinding roller.
(2) by successively changing coal pulverizer inlet air quantity, coal pulverizer inlet wind-warm syndrome, dynamic separator revolving speed, coal-supplying amount, mill The parameter values such as coal elemental composition (can be identified with raw coal moisture) carry out multi-state test, Mei Gegong in roller loading force and feeder Condition carries out coal dust on coal pipe 13 and samples and analyzes the corresponding fineness of pulverized coal of acquisition, by the operating parameter and coal dust of these operating conditions Fineness, which is input in the supporting vector machine model of fineness of pulverized coal prediction as sample, carries out model training and machine learning.
(3) coal pulverizer inlet apparatus for measuring air quantity 2, coal pulverizer inlet wind-warm syndrome measuring device 10, Dynamic Separation are acquired in real time The parameter value of device rotation-speed measuring device 11, coal-supplying amount measuring device 4 and grinding roller load force measuring device 9, and calculate feeder 8 These parameter values are inputted medium-speed pulverizer fineness of pulverized coal real-time monitoring software, pass through real-time operation by Central Plains moisture content of coal value Export fineness of pulverized coal monitor value.
For active service coal dust generating set, most units use positive-pressure type medium-speed pulverizer pulverized coal preparation system, normal to transport Fineness of pulverized coal can not be known when row, therefore can not correctly carry out optimizing and revising for powder combustion system processed, lead to boiler efficiency Deviate optimal value with NOx concentration, while there is also combustions when burning nozzle or low volatile coal when boiler uses high volatile coal Burn the risk of unstable even fire extinguishing.Therefore, by the real-time monitoring of fineness of pulverized coal, be conducive to operations staff and carry out boiler optimization tune It is whole, it increases economic efficiency, safety benefit and environmental benefit, has practical significance.
Embodiment 2
Unlike the first embodiment, feeder 8 is connect by static separation device with positive-pressure type medium-speed pulverizer 1, will dynamic Separator rotation-speed measuring device replaces with static separation device deflector baffle openness measuring device, and dynamic separator revolving speed is replaced with Static separation device deflector baffle aperture, equally may be implemented the function of embodiment 1, other are same as Example 1.

Claims (10)

1. a kind of positive-pressure type medium-speed pulverizer fuel pulverizing plant fineness of pulverized coal real-time monitoring system, the fuel pulverizing plant includes positive pressure Formula medium-speed pulverizer (1) and feeder (8), the feeder (8) pass through dynamic separator and positive-pressure type medium-speed pulverizer (1) It connects, grinding roller is equipped in the positive-pressure type medium-speed pulverizer (1),
It is characterized in that, the monitoring system includes coal pulverizer inlet apparatus for measuring air quantity (2), the measurement of coal pulverizer inlet wind-warm syndrome Device (10), coal pulverizer go out one's intention as revealed in what one says powder temperature measuring device (3), dynamic separator rotation-speed measuring device (11), coal-supplying amount measurement Device (4), grinding roller load force measuring device (9) and processor, the processor is for executing following program: obtaining in real time The measurement result of each measuring device calculates the operating condition operating parameter of fuel pulverizing plant, is obtained according to trained supporting vector machine model Fineness of pulverized coal is taken, the input quantity of the support vector machines is coal pulverizer inlet air quantity, coal pulverizer inlet wind-warm syndrome, dynamic separator Raw coal moisture in revolving speed, coal-supplying amount, grinding roller loading force and feeder, the raw coal moisture in the feeder pass through fuel pulverizing plant Heat balance principle goes out one's intention as revealed in what one says powder temperature using coal pulverizer inlet air quantity, coal pulverizer inlet wind-warm syndrome, coal pulverizer and coal-supplying amount calculates It arrives.
2. a kind of positive-pressure type medium-speed pulverizer fuel pulverizing plant fineness of pulverized coal real-time monitoring system, the fuel pulverizing plant includes positive pressure Formula medium-speed pulverizer (1) and feeder (8), the feeder (8) pass through static separation device and positive-pressure type medium-speed pulverizer (1) It connects, grinding roller is equipped in the positive-pressure type medium-speed pulverizer (1),
It is characterized in that, the monitoring system includes coal pulverizer inlet apparatus for measuring air quantity (2), the measurement of coal pulverizer inlet wind-warm syndrome Device (10), coal pulverizer go out one's intention as revealed in what one says powder temperature measuring device (3), static separation device deflector baffle openness measuring device, coal-supplying amount Measuring device (4), grinding roller load force measuring device (9) and processor, the processor is for executing following program: in real time Each measuring device measurement result is obtained, the operating condition operating parameter of fuel pulverizing plant is calculated, according to trained supporting vector machine model Fineness of pulverized coal is obtained, the input quantity of the support vector machines is coal pulverizer inlet air quantity, coal pulverizer inlet wind-warm syndrome, static separation Raw coal moisture in device deflector baffle aperture, coal-supplying amount, grinding roller loading force and feeder, the raw coal moisture in the feeder are logical Cross fuel pulverizing plant heat balance principle, using coal pulverizer inlet air quantity, coal pulverizer inlet wind-warm syndrome, coal pulverizer go out one's intention as revealed in what one says powder temperature and to Coal weighing obtains.
3. a kind of positive-pressure type medium-speed pulverizer fuel pulverizing plant fineness of pulverized coal real-time monitoring system according to claim 1 or 2, It is characterized in that, the processor is connected with data display equipment.
4. a kind of positive-pressure type medium-speed pulverizer fuel pulverizing plant fineness of pulverized coal real-time monitoring system according to claim 1 or 2, It is characterized in that, the monitoring system further includes seal fan (6), the seal fan (6) entrance and coal pulverizer temperature wind Entrance connection, outlet are connected to feeder (8) and grinding roller.
5. a kind of positive-pressure type medium-speed pulverizer fuel pulverizing plant fineness of pulverized coal real-time monitoring system according to claim 1 or 2, It is characterized in that, the processor passes through fault-tolerant processing to the measurement result of each measuring device, then carry out operating condition operating parameter It calculates.
6. a kind of positive-pressure type medium-speed pulverizer fuel pulverizing plant fineness of pulverized coal real-time monitoring system according to claim 1, It is characterized in that, the training method of the support vector machines includes: to change coal pulverizer inlet air quantity, coal pulverizer inlet wind respectively Raw coal moisture in temperature, dynamic separator revolving speed, coal-supplying amount, grinding roller loading force and feeder carries out multi-state test, will be various Operating condition operating parameter and corresponding fineness of pulverized coal are input in the supporting vector machine model of fineness of pulverized coal prediction as sample, carry out mould Type training and machine learning.
7. a kind of positive-pressure type medium-speed pulverizer fuel pulverizing plant fineness of pulverized coal real-time monitoring system according to claim 2, It is characterized in that, the training method of the support vector machines includes: to change coal pulverizer inlet air quantity, coal pulverizer inlet wind respectively Raw coal moisture in temperature, static separation device deflector baffle aperture, coal-supplying amount, grinding roller loading force and feeder carries out multi-state examination It tests, the supporting vector machine model of fineness of pulverized coal prediction is input to using various operating condition operating parameters and corresponding fineness of pulverized coal as sample In, carry out model training and machine learning.
8. a kind of positive-pressure type medium-speed pulverizer fuel pulverizing plant fineness of pulverized coal real-time monitoring system according to claim 1 or 2, It is characterized in that, coal pulverizer inlet wind-warm syndrome measuring device (10) and coal pulverizer go out one's intention as revealed in what one says powder temperature measuring device (3) for temperature biography Sensor.
9. a kind of positive-pressure type medium-speed pulverizer fuel pulverizing plant fineness of pulverized coal real-time monitoring system according to claim 1 or 2, It is characterized in that, grinding roller load force measuring device (9) is pressure sensor.
10. a kind of positive-pressure type medium-speed pulverizer fuel pulverizing plant fineness of pulverized coal real-time monitoring system according to claim 1 or 2 System, which is characterized in that the coal-supplying amount measuring device (4) is the electronic belt with weighing sensor and tread speed sensor Scale.
CN201710916832.1A 2017-09-30 2017-09-30 Positive-pressure type medium-speed pulverizer fuel pulverizing plant fineness of pulverized coal real-time monitoring system Pending CN109615084A (en)

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CN111612211A (en) * 2020-04-10 2020-09-01 杭州电子科技大学 Predictive modeling method for coal powder fineness of coal mill
CN111612210A (en) * 2020-04-10 2020-09-01 杭州电子科技大学 Online optimization method for coal powder fineness of coal mill
CN112163350A (en) * 2020-11-02 2021-01-01 国能黄金埠发电有限公司 Double-model real-time online soft measurement system and method for coal powder fineness of powder making system
CN112871429A (en) * 2021-02-02 2021-06-01 浙江浙能技术研究院有限公司 Rare earth motor control method of coal mill
CN112934452A (en) * 2021-02-02 2021-06-11 浙江浙能技术研究院有限公司 Method for adjusting and real-time controlling pulverized coal fineness of medium-speed coal mill based on rare earth motor variable speed
CN113102088A (en) * 2021-04-10 2021-07-13 南京工程学院 Full-automatic autonomous centralized control device and method for large-scale blast furnace pulverizing system
CN113457831A (en) * 2021-06-30 2021-10-01 苏州西热节能环保技术有限公司 Coal mill outlet temperature control method
CN113532894A (en) * 2021-06-09 2021-10-22 苏州西热节能环保技术有限公司 Thermal balance monitoring method for coal-fired power plant
CN113743672A (en) * 2021-09-09 2021-12-03 西安热工研究院有限公司 Coal mill economic coal powder fineness on-line analysis and operation optimization guidance method
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CN113743672B (en) * 2021-09-09 2024-04-05 西安热工研究院有限公司 Online analysis and operation optimization guiding method for economic coal fines fineness of coal mill
CN117803946A (en) * 2024-02-29 2024-04-02 山西漳电科学技术研究院(有限公司) Safety control system and method for low-calorific-value coal burning boiler

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