Flue gas baffle self-adaptive adjustment control method and system giving consideration to main steam temperature adjustment
The adaptive flue gas damper control method optimizes main steam temperature regulation by dynamically adjusting damper openings using PID controllers, addressing the limitations of traditional methods and reducing flue throttling losses in thermal power units.
Patent Information
- Application Number
- CN202410907774.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-07-08
- Publication Date
- 2024-12-27
- Estimated Expiration
- 2044-07-08
AI Technical Summary
Traditional flue gas damper control methods in thermal power units lack flexibility in adjusting reheat steam temperature, leading to poor rapidity and increased flue throttling losses, especially under conditions of under- or over-temperature, as they fix the sum of reheat and superheat side damper openings, limiting the ability to simultaneously control main steam temperature.
A method and system for adaptively adjusting flue gas dampers based on real-time and set steam temperatures, using PID controllers and preprocessing to determine damper instructions, allowing for flexible and rapid adjustment of damper openings to optimize main steam temperature control and reduce flue throttling losses.
Improves the flexibility and rapidity of reheat steam temperature control, reduces flue throttling losses, and enhances the operational flexibility of thermal power units by allowing independent adjustment of damper openings based on real-time conditions.
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Figure CN119200692A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of thermal control of thermal power plants, and in particular to a method and system for adaptively adjusting and controlling a flue gas damper taking main steam temperature regulation into consideration. Background Art
[0002] At present, the reheat steam temperature of thermal power units is mainly based on convection heat exchange, and the regulation method usually adopts the adjustment of the reheater flue gas damper to control it, and the emergency water spray cooling is used as an auxiliary regulation method. However, the water spray cooling regulation method has a greater impact on the unit's economy, and this regulation method is only used as an emergency water spray for over-temperature accidents; the traditional flue gas damper regulation method usually fixes the sum of the reheat side and superheat side damper openings and the dampers on both sides are reversely linked, that is, when the superheat side flue gas damper is closed, the reheat side flue gas damper will be opened to control the reheat steam temperature by changing the flue gas flow through the reheater flue.
[0003] However, for the operating conditions where the reheated steam temperature is within a reasonable range and the main steam temperature is seriously under-temperatured, under the traditional reheated steam temperature control method, the reheated flue gas damper opening remains unchanged, and the sum of the reheated side and superheated side damper openings is fixed. Therefore, the superheated side flue gas damper cannot adjust the main steam temperature, causing the flue to be throttled by the flue gas damper in real time, and the induced draft fan unit consumption is high; for the operating conditions where the reheated steam temperature is seriously over-temperature or under-temperatured, the superheated flue gas damper can only be opened and closed or opened and closed as the reheated damper opening is closed under the constraint of a fixed sum of openings. The opening and closing amplitude is limited by the fixed sum of the openings of the two, resulting in poor rapidity of reheated steam temperature control. Therefore, although this flue gas damper control method that fixes the sum of the reheated side and superheated side damper openings has a simple structure and convenient operation, it has poor flexibility in adjusting the reheated steam temperature, and cannot simultaneously take into account flue throttling losses and main steam temperature control. Therefore, it is necessary to introduce a new flue gas damper control method to improve the regulation performance of the main and reheat steam temperatures, thereby fundamentally improving the flexibility of the transient process of the coal-fired unit. Summary of the invention
[0004] The purpose of this section is to summarize some aspects of embodiments of the present invention and briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section and the specification abstract and the invention title of this application to avoid blurring the purpose of this section, the specification abstract and the invention title, and such simplifications or omissions cannot be used to limit the scope of the present invention.
[0005] In view of the above existing problems, the present invention is proposed.
[0006] Therefore, the present invention provides a flue gas damper adaptive adjustment control method and system taking into account main steam temperature regulation, which can solve the problems mentioned in the background technology.
[0007] In order to solve the above technical problems, the present invention provides the following technical solutions:
[0008] In a first aspect, the present invention provides a flue gas damper adaptive adjustment control method taking into account main steam temperature regulation, comprising:
[0009] Obtaining a real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler, a real-time value of the main steam temperature at the outlet of the coal-fired unit boiler, a set value of the reheat steam temperature of the coal-fired unit, and a set value of the main steam temperature of the coal-fired unit, and obtaining a first deviation value according to the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler and the set value of the reheat steam temperature of the coal-fired unit;
[0010] Performing a first preprocessing on the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler and the set value of the reheat steam temperature of the coal-fired unit to obtain a reheat flue gas damper instruction;
[0011] Performing a second preprocessing on the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler, the real-time value of the main steam temperature at the outlet of the coal-fired unit boiler, the set value of the reheat steam temperature of the coal-fired unit, the set value of the main steam temperature of the coal-fired unit, and the first deviation value to obtain a sum adaptive adjustment value of the flue gas damper opening;
[0012] The superheated smoke damper instruction is obtained according to the reheated smoke damper instruction and the sum of the smoke damper openings adaptively adjusted value, combined with the sum of the preset minimum smoke damper openings.
[0013] As a preferred scheme of the flue gas damper adaptive adjustment control method taking into account the main steam temperature regulation described in the present invention, the first deviation value includes: the difference between the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler and the set value of the reheat steam temperature of the coal-fired unit.
[0014] As a preferred solution of the flue gas damper adaptive adjustment control method taking into account main steam temperature regulation described in the present invention, the first preprocessing includes:
[0015] Converting the load command of the coal-fired unit into a feedforward control signal of a reheat flue gas damper command of the coal-fired unit through a first preset function;
[0016] According to the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler and the set value of the reheat steam temperature of the coal-fired unit, in combination with the first PID controller, an output adjustment value of the real-time reheat steam temperature is obtained;
[0017] The sum of the feedforward control signal of the reheat flue gas damper instruction of the coal-fired unit and the output adjustment value of the real-time reheat steam temperature is obtained, and the reheat flue gas damper instruction is obtained according to the first preset limit value.
[0018] As a preferred solution of the flue gas damper adaptive adjustment control method taking into account main steam temperature regulation according to the present invention, the second preprocessing includes:
[0019] According to the real-time value of the main steam temperature at the outlet of the coal-fired unit boiler and the set value of the main steam temperature of the coal-fired unit, in combination with the second PID controller, the sum of the openings of the first flue gas damper is obtained;
[0020] According to the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler and the set value of the reheat steam temperature of the coal-fired unit, in combination with the third PID controller, the sum of the opening degrees of the second flue gas damper is obtained.
[0021] Whether the first deviation value is reasonable is judged by the first preset deviation threshold, and an adaptive adjustment value of the sum of the corresponding smoke damper openings is output according to the judgment result.
[0022] As a preferred solution of the flue gas damper adaptive adjustment control method taking into account main steam temperature regulation according to the present invention, the second preprocessing further includes:
[0023] Determining whether the first deviation value is reasonable by using a first preset deviation threshold;
[0024] If it is reasonable, the sum of the first smoke damper openings and the adaptive adjustment value are limited by the second preset limit value, and the sum of the first smoke damper openings and the adaptive adjustment value after the limiting operation are output;
[0025] If it is unreasonable, the second smoke damper opening sum adaptive adjustment value is limited by a second preset limit value, and the second smoke damper opening sum adaptive adjustment value after the limiting operation is output.
[0026] As a preferred solution of the flue gas damper adaptive adjustment control method taking into account the main steam temperature regulation of the present invention, the first preset function includes:
[0027] The first preset function is expressed as:
[0028] F(Pe)=a·Pe 2 +b·Pe+c
[0029] Wherein, F(Pe) represents the first preset function, Pe is the load instruction of the coal-fired unit, the unit is MW, a, b, c are the identification parameters of the coal-fired unit, and a<0.
[0030] As a preferred solution of the flue gas damper adaptive adjustment control method taking into account the main steam temperature regulation of the present invention, wherein: the adaptive adjustment value according to the sum of the reheat flue gas damper instruction and the flue gas damper opening, combined with the sum of the preset minimum flue gas damper openings, obtains the superheated flue gas damper instruction, including:
[0031] Obtaining the sum of the preset minimum smoke damper openings and the sum of the adaptive adjustment values of the smoke damper openings obtained after the second preprocessing;
[0032] Obtaining the difference between the sum of the preset minimum smoke damper openings and the sum of the adaptive adjustment values of the smoke damper openings obtained after the second preprocessing and the reheat smoke damper instruction obtained after the first preprocessing;
[0033] The difference between the sum of the preset minimum smoke damper openings and the adaptive adjustment value of the sum of the smoke damper openings obtained after the second preprocessing and the reheat smoke damper instruction obtained after the first preprocessing is used as the superheat smoke damper instruction.
[0034] In a second aspect, the present invention provides a flue gas damper adaptive adjustment control system taking into account main steam temperature regulation, comprising:
[0035] A data acquisition module is used to obtain the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler, the real-time value of the main steam temperature at the outlet of the coal-fired unit boiler, the set value of the reheat steam temperature of the coal-fired unit, and the set value of the main steam temperature of the coal-fired unit, and obtain a first deviation value according to the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler and the set value of the reheat steam temperature of the coal-fired unit;
[0036] A first preprocessing module is used to perform a first preprocessing on the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler and the set value of the reheat steam temperature of the coal-fired unit to obtain a reheat flue gas damper instruction;
[0037] The second preprocessing module is used to perform a second preprocessing on the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler, the real-time value of the main steam temperature at the outlet of the coal-fired unit boiler, the set value of the reheat steam temperature of the coal-fired unit, the set value of the main steam temperature of the coal-fired unit, and the first deviation value to obtain a flue gas damper opening and a self-adaptive adjustment value;
[0038] The instruction acquisition module is used to adaptively adjust the value according to the sum of the reheat smoke damper instruction and the smoke damper opening, combined with the sum of the preset minimum smoke damper openings, to obtain the superheat smoke damper instruction.
[0039] In a third aspect, the present invention provides a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the above-mentioned method when executing the computer program.
[0040] In a fourth aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program implements the steps of the method described above when executed by a processor.
[0041] Compared with the prior art, the beneficial effects of the present invention are as follows: the present invention proposes a flue gas damper adaptive adjustment control method and system taking into account main steam temperature regulation, obtaining the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler, the real-time value of the main steam temperature at the outlet of the coal-fired unit boiler, the reheat steam temperature setting value of the coal-fired unit and the main steam temperature setting value of the coal-fired unit, and obtaining a first deviation value according to the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler and the reheat steam temperature setting value of the coal-fired unit; the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler and the real-time value of the main steam temperature at the outlet of the coal-fired unit boiler The reheat steam temperature setting value of the coal-fired unit is pre-processed in the first place to obtain the reheat flue gas damper instruction; the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler, the real-time value of the main steam temperature at the outlet of the coal-fired unit boiler, the reheat steam temperature setting value of the coal-fired unit, the main steam temperature setting value of the coal-fired unit and the first deviation value are pre-processed in the second place to obtain the sum of flue gas damper openings and adaptive adjustment values; according to the reheat flue gas damper instruction and the sum of flue gas damper openings and adaptive adjustment values, combined with the sum of the preset minimum flue gas damper openings, the superheated flue gas damper instruction is obtained. The flexibility of adjusting the reheat steam temperature of the coal-fired unit under different operating conditions is improved, while optimizing the main steam temperature control, reducing the flue throttling loss, and improving the flexibility of the unit's transient operation.
[0042] In addition, through the adaptive adjustment of the sum of the opening degrees of the dampers on the reheat side and the superheat side, the rapidity of the reheat steam temperature control can be improved while taking into account the main steam temperature control, reducing the flue throttling loss caused by the flue gas damper. According to the control method, for the operating condition where the reheat steam temperature is within a reasonable range and the main steam temperature is seriously under-temperature, the superheated flue gas damper can continue to be opened wide without being restricted by the fixed sum of the reheat side and superheat side damper openings while ensuring the reheat steam temperature is reasonable, so as to increase the main steam temperature and reduce the flue throttling loss of the flue gas damper; for the operating condition where the reheat steam temperature is seriously over-temperature, the reheated flue gas damper is closed small, the sum of the reheat side and superheat side damper openings is also increased, and finally the superheated flue gas damper is opened wide quickly; conversely, for the operating condition where the reheat steam temperature is seriously under-temperature, the reheated flue gas damper is opened wide, the sum of the reheat side and superheat side damper openings is reduced, and the superheated flue gas damper is closed wide quickly. Therefore, for the operating condition where the reheat steam temperature is seriously over-temperature or under-temperature, the reheated and superheated flue gas dampers are actuated simultaneously with a larger actuation amplitude, and the reheat steam temperature is adjusted faster. BRIEF DESCRIPTION OF THE DRAWINGS
[0043] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative labor. Among them:
[0044] Figure 1A method flow chart of a method and system for adaptively adjusting and controlling a flue gas damper taking into account main steam temperature regulation provided by an embodiment of the present invention;
[0045] Figure 2 A schematic diagram of a flue gas damper temperature regulation structure of a coal-fired unit flue, provided by an embodiment of the present invention, a flue gas damper adaptive adjustment control method and system taking into account main steam temperature regulation;
[0046] Figure 3 A control logic diagram of a flue gas damper adaptive adjustment control method and system taking into account main steam temperature regulation provided by an embodiment of the present invention;
[0047] Figure 4 A rendering of a flue gas damper adaptive adjustment control method and system taking into account main steam temperature regulation provided by an embodiment of the present invention;
[0048] Figure 5 An internal structural diagram of a computer device of a flue gas damper adaptive adjustment control method and system taking into account main steam temperature regulation provided by an embodiment of the present invention. DETAILED DESCRIPTION
[0049] In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the drawings of the specification. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in the art without creative work should fall within the scope of protection of the present invention.
[0050] Example 1
[0051] Reference Figure 1-Figure 5 , is the first embodiment of the present invention, which provides a method and system for adaptively adjusting a flue gas damper taking into account main steam temperature regulation, including a method for adaptively adjusting a flue gas damper taking into account main steam temperature regulation and a control system for adaptively adjusting a flue gas damper taking into account main steam temperature regulation, wherein the method for adaptively adjusting a flue gas damper taking into account main steam temperature regulation includes:
[0052] Before describing the embodiments of the present application in detail, some related concepts are first explained for the sake of clarity.
[0053] PID controller: The PID controller (Proportional-Integral-Derivative Controller) is a widely used closed-loop control strategy used to automatically adjust various industrial processes to ensure that the controlled variable (such as temperature, pressure, speed, etc.) closely tracks the set value. The PID controller works through three basic operations: Proportional (P): adjusts the output according to the current error size. The larger the error, the stronger the corrective action. Integral (I): Considers the effect of error accumulation over time to eliminate static errors. Even if there is a small but persistent error, the controller will gradually increase the output to correct it. Derivative (D): Predicts the trend of error change. If the error changes quickly, the controller will make larger adjustments in advance, which helps to reduce overshoot and oscillation.
[0054] Positive and negative action of PID controller: If the input deviation signal of the PID controller is defined as the real-time value minus the set value, then when the deviation increases, the PID controller whose output also increases is called a "positive action" PID controller; conversely, the PID controller whose output signal decreases as the deviation increases is called a "negative action" PID controller.
[0055] In the existing related technologies, the flue gas damper adjustment method of coal-fired units usually fixes the sum of the openings of the reheat side and superheat side dampers and connects the dampers on both sides in reverse linkage, that is, when the superheat side flue gas damper is closed, the reheat side flue gas damper will be opened to control the reheat steam temperature by changing the flue gas flow through the reheater flue. However, this traditional flue gas damper adjustment method cannot take into account the control of the main steam temperature, and has certain limitations in terms of response speed and system economy for the control of the reheat steam temperature.
[0056] The present application provides a method that can effectively solve the problems existing in the prior art. Next, multiple embodiments will be combined to explain in detail how to implement the flue gas damper adaptive adjustment control method that takes into account the main steam temperature regulation.
[0057] Figure 1 A method flow chart of a flue gas damper adaptive adjustment control method and system taking into account main steam temperature regulation is shown, including:
[0058] S101, obtaining a real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler, a real-time value of the main steam temperature at the outlet of the coal-fired unit boiler, a set value of the reheat steam temperature of the coal-fired unit, and a set value of the main steam temperature of the coal-fired unit, and obtaining a first deviation value according to the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler and the set value of the reheat steam temperature of the coal-fired unit;
[0059] The first deviation value includes: the difference between the real-time value of the reheat steam temperature at the outlet of the boiler of the coal-fired unit and the set value of the reheat steam temperature of the coal-fired unit.
[0060] In the embodiment of the present application, the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler is R PV The reheat steam temperature setting value of the coal-fired unit is R SP The difference between the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler and the set value of the reheat steam temperature of the coal-fired unit is recorded as R E ;
[0061] Among them, R E =R SP -R PV .
[0062] In an optional embodiment, the reheat steam temperature setting value and the main steam temperature setting value of the coal-fired unit can be determined through the design specification and operating regulations of the coal-fired unit. The ideal temperature settings of the reheat steam and the main steam can be obtained when the coal-fired unit is operating normally through the design specification and operating regulations to ensure the stable operation and efficiency of the unit.
[0063] In an embodiment of the present application, the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler and the real-time value of the main steam temperature at the outlet of the coal-fired unit boiler can be obtained through a temperature sensor preset at the outlet of the coal-fired unit boiler.
[0064] In an optional embodiment, when a temperature sensor is set, if one temperature sensor is set, the temperature sensor is set at the center flow velocity of the main steam pipe or the reheat steam pipe, where the temperature can better represent the average temperature of the entire steam flow and is not easily affected by local hot spots or cold spots. This setting is conducive to reflecting the overall steam state.
[0065] In an optional embodiment, when setting the temperature sensor, if at least two temperature sensors are set, the sensors can be set at different positions of the steam pipe (such as the upper part, the middle part, and the lower part), and the sensor average value can be used as the real-time value. Sensors can also be set at important nodes of the steam flow, such as the boiler outlet, the superheater outlet, and the reheater outlet, and the real-time temperature value is calculated by different weights. This design can better monitor the efficiency and stability of the entire steam thermal cycle. Redundant sensors can also be set at key positions. Even if a sensor fails, it can continue to operate based on the data of other sensors, ensuring that the unit will not shut down due to a single sensor failure, etc., and setting temperature sensor operations.
[0066] It should be noted that by obtaining the real-time reheat steam temperature and main steam temperature, as well as the preset temperature setting value, the deviation between the current operating state and the target state can be reflected in real time, providing a basis for subsequent adaptive adjustment. The first deviation value reflects the control demand of the reheat steam temperature and is a key parameter for adjusting the flue gas damper opening.
[0067] S102, performing a first preprocessing on the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler and the set value of the reheat steam temperature of the coal-fired unit to obtain a reheat flue gas damper instruction;
[0068] Wherein, the first preprocessing includes:
[0069] Converting the load command of the coal-fired unit into a feedforward control signal of a reheat flue gas damper command of the coal-fired unit through a first preset function;
[0070] According to the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler and the set value of the reheat steam temperature of the coal-fired unit, in combination with the first PID controller, an output adjustment value of the real-time reheat steam temperature is obtained;
[0071] The sum of the feedforward control signal of the reheat flue gas damper instruction of the coal-fired unit and the output adjustment value of the real-time reheat steam temperature is obtained, and the reheat flue gas damper instruction is obtained according to the first preset limit value.
[0072] Specifically, the first preset function includes:
[0073] The first preset function is expressed as:
[0074] F(Pe)=a·Pe 2 +b·Pe+c
[0075] Wherein, F(Pe) represents the first preset function, Pe is the load instruction of the coal-fired unit, the unit is MW, a, b, c are the identification parameters of the coal-fired unit, and a<0.
[0076] In the embodiment of the present application, the load command of the coal-fired unit is recorded as Pe, and the feedforward control signal of the reheat flue gas damper command of the coal-fired unit is recorded as F fd ;
[0077] Among them, F fd =F(Pe).
[0078] In the embodiment of the present application, the first PID controller is a "reverse" PID controller, which obtains the reheat steam temperature setting value R SP and the real-time value of reheat steam temperature R PV Input to the "reverse action" PID controller to obtain the output adjustment value F of the real-time reheat steam temperature PID , and based on the obtained feedforward control signal F of the reheating flue gas damper command of the coal-fired unit fd , after passing the first preset limit, the final reheat flue gas damper instruction μ is obtained. R ; Feedforward control signal F fd is the steady-state control signal, F PIDis the dynamic control signal. The steady-state control signal is added to the dynamic control signal to obtain the total reheat flue gas damper command μ R . .
[0079] In the embodiment of the present application, the first preset limit value can be set by a high / low limit value monitor or other hardware limit.
[0080] In an optional embodiment, the specific value of the first preset limit can be determined by the following steps:
[0081] First, obtain the design specifications and safety operation manuals of the reference coal-fired unit (these materials may contain suggestions or requirements on the opening limit of the flue gas damper) and establish a mathematical model of the thermal system of the coal-fired unit;
[0082] Secondly, by establishing a mathematical model of the thermal system of a coal-fired unit and using simulation software (such as MATLAB / Simulink, Aspen HYSYS, etc.) for dynamic simulation, the performance of the PID controller can be tested under different operating conditions. During the simulation process, the range of the control signal can be observed, and then the appropriate limit value can be determined to ensure that the control output will not cause the system to exceed the limit or damage the equipment.
[0083] Again, in actual operation, by gradually adjusting the PID parameters and limits, observe the system response, especially pay attention to whether the controller output remains within a safe and effective range under various boundary conditions and abnormal conditions. This process often requires repeated trials and optimization to determine the optimal limits based on field commissioning data and operating experience.
[0084] Finally, when setting limits, leave a certain safety margin, that is, the upper and lower limits of the controller's output should be a certain percentage lower than the actual equipment operating limit to prevent control errors caused by unexpected situations.
[0085] In an optional embodiment, the specific value of the first preset limit value may also be directly set according to the operator's experience;
[0086] In the embodiment of the present application, the specific value of the first preset limit is 0%-100%, but other first preset limit values obtained according to the above steps or similar steps should be within the protection scope of the present application.
[0087] It should be noted that, through the first preprocessing, the load command of the coal-fired unit is combined with the real-time reheat steam temperature, taking into account the dual effects of feedforward control and feedback control. The feedforward control signal can pre-adjust the reheat flue gas damper according to the load change, while the PID controller makes real-time adjustments based on the deviation between the actual temperature and the set value to ensure accurate control of the reheat steam temperature. At the same time, the setting of the first preset limit value prevents equipment safety problems caused by excessive control signals, and ensures the stable operation of the coal-fired unit under various working conditions.
[0088] S103, performing a second preprocessing on the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler, the real-time value of the main steam temperature at the outlet of the coal-fired unit boiler, the set value of the reheat steam temperature of the coal-fired unit, the set value of the main steam temperature of the coal-fired unit, and the first deviation value to obtain a sum adaptive adjustment value of the flue gas damper opening;
[0089] Wherein, the second preprocessing includes:
[0090] According to the real-time value of the main steam temperature at the outlet of the coal-fired unit boiler and the set value of the main steam temperature of the coal-fired unit, in combination with the second PID controller, the sum of the openings of the first flue gas damper is obtained;
[0091] According to the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler and the set value of the reheat steam temperature of the coal-fired unit, in combination with the third PID controller, the sum of the opening degrees of the second flue gas damper is obtained.
[0092] Whether the first deviation value is reasonable is judged by the first preset deviation threshold, and an adaptive adjustment value of the sum of the corresponding smoke damper openings is output according to the judgment result.
[0093] Furthermore, the second preprocessing further includes:
[0094] Determining whether the first deviation value is reasonable by using a first preset deviation threshold;
[0095] If it is reasonable, the sum of the first smoke damper openings and the adaptive adjustment value are limited by the second preset limit value, and the sum of the first smoke damper openings and the adaptive adjustment value after the limiting operation are output;
[0096] If it is unreasonable, the second smoke damper opening sum adaptive adjustment value is limited by a second preset limit value, and the second smoke damper opening sum adaptive adjustment value after the limiting operation is output.
[0097] In the embodiment of the present application, the second PID controller is a "reverse action" PID controller, the third PID controller is a "positive action" PID controller, and the main steam temperature setting value of the coal-fired unit is recorded as S SP The real-time value of the main steam temperature at the outlet of the coal-fired unit boiler is recorded as S PV, the main steam temperature setting value S SP And the real-time value of main steam temperature S PV Input to the "reaction" PID controller to obtain the flue gas damper opening and adaptive adjustment value F that takes into account the main steam temperature regulation NPID , set the reheat steam temperature setting value R SP and the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler R PV Input to the "positive action" PID controller to obtain the flue gas damper opening and adaptive adjustment value F for rapid adjustment of the reheat steam temperature YPID .
[0098] In the embodiment of the present application, the first preset deviation threshold is set to ±4°C.
[0099] In an optional embodiment, the first preset deviation threshold is implemented by a high / low limit monitor, which can be obtained by building a system mathematical model or a simulation tool or expert experience.
[0100] In an embodiment of the present application, the first flue gas damper opening sum adaptive adjustment value is the flue gas damper opening sum adaptive adjustment value that takes into account the main steam temperature regulation, and the second flue gas damper opening sum adaptive adjustment value is the flue gas damper opening sum adaptive adjustment value that quickly adjusts the reheat steam temperature.
[0101] In an optional embodiment, the specific step of obtaining the value of the second preset limit may be the same as or different from the specific step of obtaining the value of the first preset limit.
[0102] In the embodiment of the present application, the real-time deviation value R of the reheat steam temperature is determined. E Whether it is within a reasonable range, select the adaptive adjustment value μA of the sum of the smoke damper openings;
[0103] If R E If it is within a reasonable range, select F. NPID , after being limited by the second preset limit value, μA is formed, that is:
[0104] μA=F NPID ;
[0105] If R E If it exceeds the reasonable range, select F YPID , after being limited by the second preset limit value, μA is formed, that is:
[0106] μA=F YPID ;
[0107] In the embodiment of the present application, the specific values of the large and small clipping operations of the second preset limit are 0 to 80%, but other second preset limit values obtained according to the above steps or similar steps should be within the protection scope of the present application.
[0108] It should be noted that by combining the real-time and set values of the main steam temperature and the reheat steam temperature, and adopting PID controllers with different characteristics, accurate and flexible adjustment of the flue gas damper opening is achieved. The adaptive adjustment value of the sum of the first flue gas damper openings mainly focuses on the stability of the main steam temperature, while the adaptive adjustment value of the sum of the second flue gas damper openings focuses on rapid response to changes in the reheat steam temperature. Through the judgment of the first preset deviation threshold, the first flue gas damper opening or the second flue gas damper opening is selected as the adaptive adjustment value, and then through the limiting operation, it can be ensured that during the control process, whether it is normal operating conditions or abnormal operating conditions, it can effectively prevent the equipment operation due to excessive control signals from exceeding the safety range, thereby improving the safety and stability of the operation of the entire coal-fired unit.
[0109] In addition, by setting different limit thresholds, dynamic adjustments can be made according to actual operating conditions and equipment performance, increasing the adaptability of the system. This adaptive adjustment not only takes into account the operating limits of the equipment, but also takes into account possible environmental changes and the experience of operators, making the control method more intelligent and reliable. This innovative control method significantly improves the thermal efficiency and operating life of coal-fired units and reduces maintenance costs, which has important practical significance for the safe and efficient operation of large-scale thermal power systems.
[0110] S104, obtaining a superheated smoke damper instruction according to the reheated smoke damper instruction and the sum of the smoke damper openings, adaptively adjusting the value, and combining the sum of the preset minimum smoke damper openings.
[0111] According to the reheat smoke damper instruction and the adaptive adjustment value of the sum of the smoke damper openings, combined with the sum of the preset minimum smoke damper openings, the superheat smoke damper instruction is obtained, including:
[0112] Obtaining the sum of the preset minimum smoke damper openings and the sum of the adaptive adjustment values of the smoke damper openings obtained after the second preprocessing;
[0113] Obtaining the difference between the sum of the preset minimum smoke damper openings and the sum of the adaptive adjustment values of the smoke damper openings obtained after the second preprocessing and the reheat smoke damper instruction obtained after the first preprocessing;
[0114] The difference between the sum of the preset minimum smoke damper openings and the adaptive adjustment value of the sum of the smoke damper openings obtained after the second preprocessing and the reheat smoke damper instruction obtained after the first preprocessing is used as the superheat smoke damper instruction.
[0115] In the embodiment of the present application, the sum of the minimum flue gas damper openings μmin manually set by the unit operation operator is added to the obtained flue gas damper opening sum adaptive adjustment value μA, and the real-time flue gas damper opening sum μ can be obtained, that is:
[0116] μ=μ A +μ min ;
[0117] According to the sum of the flue gas damper openings μ obtained above and the reheat flue gas damper command μ R The final superheated flue gas damper command μ is obtained by subtracting S ,Right now
[0118] μ S =μ-μ R ;
[0119] It should be noted that the flue gas damper adjustment control that takes into account the main steam temperature regulation can be completed based on the obtained superheated flue gas damper instruction, and the unit is percentage. For example, when the superheated flue gas damper instruction obtained is 30%, the damper is opened to 30% of the full stroke (0~100%).
[0120] In summary, the present invention proposes a flue gas damper adaptive adjustment control method taking into account the main steam temperature regulation, obtaining the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler, the real-time value of the main steam temperature at the outlet of the coal-fired unit boiler, the reheat steam temperature setting value of the coal-fired unit and the main steam temperature setting value of the coal-fired unit, and obtaining a first deviation value according to the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler and the reheat steam temperature setting value of the coal-fired unit; the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler and the reheat steam temperature setting value of the coal-fired unit The temperature setting value is pre-processed for the first time to obtain the reheat flue gas damper instruction; the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler, the real-time value of the main steam temperature at the outlet of the coal-fired unit boiler, the reheat steam temperature setting value of the coal-fired unit, the main steam temperature setting value of the coal-fired unit and the first deviation value are pre-processed for the second time to obtain the sum of the flue gas damper openings adaptive adjustment value; according to the reheat flue gas damper instruction and the sum of the flue gas damper openings adaptive adjustment value, combined with the preset minimum flue gas damper openings, the superheated flue gas damper instruction is obtained. The flexibility of adjusting the reheat steam temperature of the coal-fired unit under different operating conditions is improved, while optimizing the main steam temperature control, reducing the flue throttling loss, and improving the flexibility of the unit's transient operation. In addition, through the adaptive adjustment of the sum of the damper openings on the reheat side and the superheat side, the rapidity of the reheat steam temperature control can be improved while taking into account the main steam temperature control, reducing the flue throttling loss of the flue gas damper. According to the control method, for the operating condition where the reheat steam temperature is within a reasonable range and the main steam temperature is seriously under-temperature, the superheated flue gas damper can continue to be opened wide without being restricted by the fixed sum of the reheat side and superheat side damper openings while ensuring the reheat steam temperature is reasonable, so as to increase the main steam temperature and reduce the flue throttling loss of the flue gas damper; for the operating condition where the reheat steam temperature is seriously over-temperature, the reheated flue gas damper is closed small, the sum of the reheat side and superheat side damper openings is also increased, and finally the superheated flue gas damper is opened wide quickly; conversely, for the operating condition where the reheat steam temperature is seriously under-temperature, the reheated flue gas damper is opened wide, the sum of the reheat side and superheat side damper openings is reduced, and the superheated flue gas damper is closed wide quickly. Therefore, for the operating condition where the reheat steam temperature is seriously over-temperature or under-temperature, the reheated and superheated flue gas dampers are actuated simultaneously with a larger actuation amplitude, and the reheat steam temperature is adjusted faster.
[0121] This embodiment also provides a flue gas damper adaptive adjustment control system that takes into account main steam temperature regulation, including:
[0122] A data acquisition module is used to obtain the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler, the real-time value of the main steam temperature at the outlet of the coal-fired unit boiler, the set value of the reheat steam temperature of the coal-fired unit, and the set value of the main steam temperature of the coal-fired unit, and obtain a first deviation value according to the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler and the set value of the reheat steam temperature of the coal-fired unit;
[0123] A first preprocessing module is used to perform a first preprocessing on the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler and the set value of the reheat steam temperature of the coal-fired unit to obtain a reheat flue gas damper instruction;
[0124] The second preprocessing module is used to perform a second preprocessing on the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler, the real-time value of the main steam temperature at the outlet of the coal-fired unit boiler, the set value of the reheat steam temperature of the coal-fired unit, the set value of the main steam temperature of the coal-fired unit, and the first deviation value to obtain a flue gas damper opening and a self-adaptive adjustment value;
[0125] The instruction acquisition module is used to adaptively adjust the value according to the reheat smoke damper instruction and the sum of the smoke damper openings, and obtain the superheat smoke damper instruction in combination with the sum of the preset minimum smoke damper openings.
[0126] The above-mentioned unit modules may be embedded in or independent of a processor in a computer device in the form of hardware, or may be stored in a memory in a computer device in the form of software, so that the processor can call and execute operations corresponding to the above-mentioned modules.
[0127] This embodiment also provides a computer device, which may be a terminal, and its internal structure diagram may be as shown in FIG. Figure 5 As shown. The computer device includes a processor, a memory, a communication interface, a display screen and an input device connected through a system bus. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The communication interface of the computer device is used to communicate with an external terminal in a wired or wireless manner, and the wireless manner can be achieved through WIFI, an operator network, NFC (near field communication) or other technologies. When the computer program is executed by the processor, a smoke damper adaptive adjustment control method that takes into account the main steam temperature regulation is implemented. The display screen of the computer device can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer device can be a touch layer covered on the display screen, or a button, trackball or touchpad set on the computer device housing, or an external keyboard, touchpad or mouse.
[0128] This embodiment further provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the following steps are implemented:
[0129] Obtaining a real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler, a real-time value of the main steam temperature at the outlet of the coal-fired unit boiler, a set value of the reheat steam temperature of the coal-fired unit, and a set value of the main steam temperature of the coal-fired unit, and obtaining a first deviation value according to the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler and the set value of the reheat steam temperature of the coal-fired unit;
[0130] Performing a first preprocessing on the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler and the set value of the reheat steam temperature of the coal-fired unit to obtain a reheat flue gas damper instruction;
[0131] Performing a second preprocessing on the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler, the real-time value of the main steam temperature at the outlet of the coal-fired unit boiler, the set value of the reheat steam temperature of the coal-fired unit, the set value of the main steam temperature of the coal-fired unit, and the first deviation value to obtain a sum adaptive adjustment value of the flue gas damper opening;
[0132] The superheated smoke damper instruction is obtained according to the reheated smoke damper instruction and the sum of the smoke damper openings, and the adaptive adjustment value is combined with the sum of the preset minimum smoke damper openings.
[0133] Example 2
[0134] Reference Figure 2-Figure 4 , which is an embodiment of the present invention, provides a flue gas damper adaptive adjustment control method and system taking into account main steam temperature regulation. In order to verify the beneficial effects of the present invention, scientific demonstration is carried out through experiments.
[0135] In this embodiment, a coal-fired unit has a rated load of 600MW, a primary intermediate reheat unit, a main steam temperature setting value of 571°C, and a reheat steam temperature setting value of 569°C. When the traditional control method is adopted, that is, the sum of the openings of the reheat flue gas damper and the superheat flue gas damper is fixed at 120%, in a certain transient process, when the real-time value of the reheat steam temperature is lower than 569°C, and the main steam temperature is lower than the set value of 571°C, the reheat flue gas damper is fully opened, that is, the opening is 100%. At this time, the superheat flue gas damper cannot take into account the adjustment of the main steam temperature, that is, the opening of the superheat flue gas damper remains unchanged at 20%. When the control method of the present application is used in this transient process, because the superheated flue gas damper also adjusts the main steam temperature, the main steam temperature is lower than the set value of 571°C, the flue gas damper adaptive adjustment value increases, so that the superheated flue gas damper continues to open to 50%, so that the main steam temperature is increased by 2°C; and the reheated steam temperature is within a reasonable range (i.e., within ±4°C of the set value) during the process. At this time, the opening of the reheated flue gas damper is still maintained at 100%, and the sum of the two openings is 150%, and the flue throttling loss is reduced.
[0136] In summary, the control method of the present application can improve the rapidity of reheat steam temperature control while taking into account the main steam temperature control through adaptive adjustment of the sum of the damper openings on the reheat side and the superheat side, thereby reducing the flue throttling loss caused by the flue gas damper.
[0137] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.
[0138] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of complete hardware embodiments, complete software embodiments, or embodiments in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code. The scheme in the embodiments of the present application can be implemented in various computer languages, for example, object-oriented programming language Java and literal scripting language JavaScript, etc.
[0139] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.
[0140] These computer program instructions may also be stored in a computer readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture including an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.
[0141] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.
[0142] Although the preferred embodiments of the present application have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present application.
[0143] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.
Claims
1. A flue gas damper adaptive adjustment control method taking into account main steam temperature regulation, characterized in that: include: Obtaining a real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler, a real-time value of the main steam temperature at the outlet of the coal-fired unit boiler, a set value of the reheat steam temperature of the coal-fired unit, and a set value of the main steam temperature of the coal-fired unit, and obtaining a first deviation value according to the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler and the set value of the reheat steam temperature of the coal-fired unit; Performing a first preprocessing on the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler and the set value of the reheat steam temperature of the coal-fired unit to obtain a reheat flue gas damper instruction; Performing a second preprocessing on the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler, the real-time value of the main steam temperature at the outlet of the coal-fired unit boiler, the set value of the reheat steam temperature of the coal-fired unit, the set value of the main steam temperature of the coal-fired unit, and the first deviation value to obtain a sum adaptive adjustment value of the flue gas damper opening; The superheated smoke damper instruction is obtained according to the reheated smoke damper instruction and the sum of the smoke damper openings adaptively adjusted value, combined with the sum of the preset minimum smoke damper openings.
2. The method for adaptively adjusting and controlling the flue gas damper taking into account the main steam temperature regulation according to claim 1, characterized in that: The first deviation value includes: the difference between the real-time value of the reheat steam temperature at the outlet of the boiler of the coal-fired unit and the set value of the reheat steam temperature of the coal-fired unit.
3. The flue gas damper adaptive adjustment control method taking into account main steam temperature regulation according to claim 2 is characterized in that: The first preprocessing comprises: Converting the load command of the coal-fired unit into a feedforward control signal of a reheat flue gas damper command of the coal-fired unit through a first preset function; According to the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler and the set value of the reheat steam temperature of the coal-fired unit, in combination with the first PID controller, an output adjustment value of the real-time reheat steam temperature is obtained; The sum of the feedforward control signal of the reheat flue gas damper instruction of the coal-fired unit and the output adjustment value of the real-time reheat steam temperature is obtained, and the reheat flue gas damper instruction is obtained according to the first preset limit value.
4. The method for adaptively adjusting and controlling the flue gas damper taking into account the main steam temperature regulation as claimed in claim 3, characterized in that: The second preprocessing comprises: According to the real-time value of the main steam temperature at the outlet of the coal-fired unit boiler and the set value of the main steam temperature of the coal-fired unit, in combination with the second PID controller, the sum of the openings of the first flue gas damper is obtained; According to the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler and the set value of the reheat steam temperature of the coal-fired unit, in combination with the third PID controller, the sum of the opening degrees of the second flue gas damper is obtained. Whether the first deviation value is reasonable is judged by the first preset deviation threshold, and an adaptive adjustment value of the sum of the corresponding smoke damper openings is output according to the judgment result.
5. The method for adaptively adjusting and controlling the flue gas damper taking into account the main steam temperature regulation according to claim 4, characterized in that: The second preprocessing further comprises: Determining whether the first deviation value is reasonable by using a first preset deviation threshold; If it is reasonable, the sum of the first smoke damper openings and the adaptive adjustment value are limited by the second preset limit value, and the sum of the first smoke damper openings and the adaptive adjustment value after the limiting operation are output; If it is unreasonable, the second smoke damper opening sum adaptive adjustment value is limited by a second preset limit value, and the second smoke damper opening sum adaptive adjustment value after the limiting operation is output.
6. The method for adaptively adjusting and controlling the flue gas damper taking into account the main steam temperature regulation according to claim 5, characterized in that: The first preset function includes: The first preset function is expressed as: F(Pe)=a·Pe 2 +b·On+c Wherein, F(Pe) represents the first preset function, Pe is the load instruction of the coal-fired unit, the unit is MW, a, b, c are the identification parameters of the coal-fired unit, and a<0.
7. The method for adaptively adjusting and controlling the flue gas damper taking into account the main steam temperature regulation according to claim 6, characterized in that: The adaptive adjustment value of the sum of the reheated smoke damper instruction and the smoke damper opening, combined with the sum of the preset minimum smoke damper openings, to obtain the overheated smoke damper instruction includes: Obtaining the sum of the preset minimum smoke damper openings and the sum of the adaptive adjustment values of the smoke damper openings obtained after the second preprocessing; Obtaining the difference between the sum of the preset minimum smoke damper openings and the sum of the adaptive adjustment values of the smoke damper openings obtained after the second preprocessing and the reheat smoke damper instruction obtained after the first preprocessing; The difference between the sum of the preset minimum smoke damper openings and the adaptive adjustment value of the sum of the smoke damper openings obtained after the second preprocessing and the reheat smoke damper instruction obtained after the first preprocessing is used as the superheat smoke damper instruction.
8. A flue gas damper adaptive adjustment control system taking into account main steam temperature regulation, characterized in that: include: A data acquisition module is used to obtain the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler, the real-time value of the main steam temperature at the outlet of the coal-fired unit boiler, the set value of the reheat steam temperature of the coal-fired unit, and the set value of the main steam temperature of the coal-fired unit, and obtain a first deviation value according to the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler and the set value of the reheat steam temperature of the coal-fired unit; A first preprocessing module is used to perform a first preprocessing on the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler and the set value of the reheat steam temperature of the coal-fired unit to obtain a reheat flue gas damper instruction; The second preprocessing module is used to perform a second preprocessing on the real-time value of the reheat steam temperature at the outlet of the coal-fired unit boiler, the real-time value of the main steam temperature at the outlet of the coal-fired unit boiler, the set value of the reheat steam temperature of the coal-fired unit, the set value of the main steam temperature of the coal-fired unit, and the first deviation value to obtain a flue gas damper opening and a self-adaptive adjustment value; The instruction acquisition module is used to adaptively adjust the value according to the sum of the reheat smoke damper instruction and the smoke damper opening, combined with the sum of the preset minimum smoke damper openings, to obtain the superheat smoke damper instruction.
9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.
Citation Information
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