CN117077528A - Ash box modeling method for ultra-low load operation of supercritical unit - Google Patents

Abstract

The invention discloses an ash box modeling method for ultra-low load operation of a supercritical unit. Firstly, constructing a wet state mechanism model according to the depth peak shaving requirement of a supercritical unit; then, combining an improved sparrow search algorithm with a Takagi-Sugeno fuzzy identification method to obtain unknown parameters of the model; and finally, verifying the effectiveness of the modeling method through a simulation experiment based on the power plant operation data. The modeling method has clear physical significance, has ideal precision under the ultralow load variable working condition operation of the unit, and lays a foundation for improving the deep adjustment capability of the unit.

Description

Ash box modeling method for ultra-low load operation of supercritical unit

Technical Field

The invention relates to the technical field of modeling of flexible operation of a thermal generator set, in particular to an ash box modeling method for ultra-low load operation of a supercritical unit.

Background

The development of efficient and available clean energy, the change of the power grid power structure configuration, the acceleration of the development of renewable energy generation to replace coal-fired power plants become an effective method for promoting the structural reform of electric energy in China. However, renewable energy sources are vulnerable to weather, making their output unstable and uncertain power generation characteristics present a significant challenge to the grid. In such a background, as an important component of the current energy structure, a coal-fired power plant must gradually realize a transformation from electric power energy supply to safety guarantee and flexible regulation of resources. Therefore, the existing coal-fired power plant is flexibly transformed, and the ultra-low load stable operation of the large-scale thermal power unit is researched to improve the deep peak regulation capability of the large-scale thermal power unit.

Compared with other widely applied thermal power units in the current stage, the supercritical (super) critical unit has the advantages of large power capacity, large load range, higher cyclic thermal efficiency, lower pollutant discharge and the like, and becomes a recognized main power unit suitable for participating in power grid peak regulation. Therefore, the technical improvement is carried out on the basis of the supercritical unit, and the operation flexibility and the peak shaving capacity of the traditional thermal power are obviously improved while the energy conservation and emission reduction requirements are met. The supercritical unit uses a once-through boiler, the main steam pressure reaches 24MPa during normal operation, the boiler is transited to a high rated working condition from below a self-generated load during starting, and the working medium in the boiler is in two forms of wet state and dry state. For a long time, the design and operation of the supercritical unit and the once-through boiler only need to carry basic load, and do not need to stay in a low-load stage for a long time. The dry mode operation of the unit usually comprises a basic load of the unit operation in the range of 30% -100% of rated load, so that many previous researches only perform model analysis and development on the dry mode of the unit, and few researches on the wet operation technology of the supercritical unit under the ultra-low load are performed. Today, in the face of the deep peak shaving task borne by the unit, the thermal power plant needs to operate in a lower load state, and is very important for model identification research of the supercritical unit in a wet state operation mode. Therefore, the invention takes the supercritical unit as a research object, adopts an ash box modeling strategy based on mechanism analysis and improved Takagi-Sugeno (T-S) fuzzy recognition, establishes an accurate mathematical model suitable for the unit to operate under ultra-low load, and has important significance for improving the deep peak shaving capacity of the supercritical unit.

The ash box modeling is a novel modeling method which organically integrates traditional mechanism modeling and data-driven modeling, and the idea is to identify unknown parameters in a mechanism model by means of a data-driven identification algorithm on the basis of constructing the mechanism model, so that a final model is obtained. In the face of the actual situation that the unit flexibility is especially aggravated by the working condition change under the deep peak shaving requirement, a certain lifting space exists for lengthy and complex mechanism modeling and data driving modeling with unclear physical significance, so that the establishment of an accurate model of a supercritical unit under the frequent negative working condition and the ultralow load mode by adopting an ash box modeling method with complementary mechanism and advantages of a digital driving modeling method has become the key point of current research. However, the gray box modeling approach does not completely eliminate the inherent drawbacks of the mechanism and data driven modeling approach. In order to balance the rapidity and the identification precision of the modeling algorithm as much as possible, the adjustment and optimization of each link of the ash box modeling method are needed to be carried out specifically from the internal mechanism and the external coordination of the two traditional modeling methods, so that the ash box modeling has a great development space. Firstly, in a mechanism modeling part, the complexity of a built model needs to be considered, wherein the number of parameters to be identified directly influences the calculation cost and effect of subsequent identification, but the model accuracy is reduced by excessive simplification. In addition, there are numerous alternatives in the data-based parameter identification section. The identification method based on the T-S fuzzy thought can process and approximate the nonlinear problem with any precision through the IF-THEN rule, and shows strong performance. Specifically, the parameter identification of the T-S fuzzy modeling method can be divided into a precondition part and a conclusion part, the clustering technology and the identification algorithm which are respectively relied on can be further discussed, and the links are accompanied with the development of the artificial intelligence technology and the swarm intelligence algorithm, so that infinite potential is displayed. Therefore, the T-S fuzzy recognition method fused with the group intelligent optimization algorithm can be fully utilized, and a dust box modeling method oriented to a supercritical unit wet state operation mode is formed by combining reasonably simplified mechanism analysis, so that a model foundation is provided for unit wet state stable operation research.

Disclosure of Invention

The invention aims to provide an ash box modeling method oriented to a supercritical unit wet state operation mode, fills the defect of wet state model identification of the unit during ultra-low load operation, and lays a foundation for maximally reducing the minimum output of a thermal power unit and the development of a corresponding control system in the wet state operation mode. The method fully considers the difference of the supercritical unit in the wet mode and the dry mode, models the mechanism, and then identifies the unknown parameters of the model based on the improved T-S fuzzy identification method. In the improved T-S fuzzy identification method, a precondition part of parameters adopts an improved K-means clustering method, a large amount of field operation data is input as a training set, K subspaces are obtained through a clustering algorithm, and the operation range contained in the corresponding data in the process is divided into K working conditions; carrying out parameter identification on the submodel of each typical working condition by adopting an improved sparrow search algorithm (Improved Sparrow Search Algorithm, ISSA) on the conclusion part of the parameters; and finally, weighting the output of the sub-model of the typical working condition by combining the membership degree of the fuzzy rule corresponding to each typical working condition so as to obtain the final global output. The method ensures that the identified unit model has ideal precision in the whole ultra-low load range.

The invention provides an ash box modeling method for ultra-low load operation of a supercritical unit, which comprises the following 4 steps:

s1: analyzing the operation characteristics and modeling difficulties of the supercritical unit in an ultralow-load wet mode;

s2: establishing a dust box modeling method flow aiming at ultra-low load operation of a supercritical unit;

s3: describing the ash bin modeling method steps combining mechanism analysis and data-driven T-S fuzzy recognition;

s4: and verifying and analyzing the effectiveness of the modeling method by combining a simulation experiment and a quantization index.

S1: the supercritical unit consists of three subsystems, namely a pulverizing system, a once-through boiler system and a steam turbine system. After raw coal is processed by the pulverizing system, mixed hot air is sent into a hearth for combustion, and chemical energy released in the process is converted into heat energy of working medium through a heating surface, so that the working medium is converted into state in the boiler evaporating system. Finally, the high-temperature and high-pressure steam output by the boiler enters a steam turbine, and blades of the steam turbine are driven to rotate to generate mechanical energy to drive a generator to rotate, so that the mechanical energy is converted into electric energy and is transmitted to a power grid. In a wet running mode of the supercritical unit, working medium parameters are in the sub-critical stateThe process of changing the water supply into the superheated steam still needs to go through three stages of heating, evaporating and superheating, and the working medium is in a gas-liquid two-phase flowing state when flowing out of the water wall pipe and can not directly enter the superheater. At this time, the steam-water separator arranged at the outlet of the water-cooled wall is equivalent to the steam drum of the subcritical unit in action, and plays a role in steam-water separation. The separated steam also enters the steam turbine to do work, and water flows into the water storage tank to be further recovered or discharged out of the whole cycle. The mass balance equation of the once-through boiler system in the wet mode is greatly different from that of the once-through boiler system in the dry mode, and the water level of the water storage tank is a key controlled quantity for the unit in the wet running mode. In addition, because the water-cooled wall outlet working medium is wet steam when in wet mode operation, the fuel quantity is directly increased at the moment, the temperature change of the middle point is not great, and the water-coal ratio control advanced signal used for the water-coal ratio control can possibly fail. Therefore, the invention does not set the middle point temperature which is usually used as the output variable of the unit model as the output of the wet mode model, and takes the water level of the water storage tank as the output variable of the wet mode model instead. Finally, a simplified model of the three-input three-output supercritical unit in a wet state operation mode can be constructed, wherein three input variables are the water supply quantity D _fw Quantity of fuel r _B And valve opening mu _T The three output variables are the unit load N and the main steam pressure p _st And the water level H in the water storage tank. In the analysis, the working medium flowing process of the wet running mode of the supercritical unit is more complex, and difficulties are brought to mechanism modeling analysis. Meanwhile, the fluctuation of the water level of the water storage tank is large, and compared with other outputs, ideal model fitting precision is difficult to obtain.

Based on the analysis of S1, complicated steam-water flow characteristics and fluctuation of water level of a water storage tank during operation in a wet mode of a supercritical unit bring difficulty to modeling, so that a gray box modeling method combining mechanism analysis and data-driven T-S fuzzy identification needs to be developed, and the accuracy of an identified model is improved. Step S2 may be embodied as:

s2.1: according to the operation characteristic analysis of the supercritical unit wet state operation mode, a simplified mechanism model is established for the unit wet state mode based on the mass and energy conservation law, unknown parameters in the mechanism model are reserved for subsequent identification, and the actual conditions of different model parameters under different working conditions are matched;

s2.2: for a nonlinear system, a linear relation exists between input data and output data in an incremental form, so that a T-S fuzzy identification structure in the incremental form is built for a nonlinear supercritical unit system in a parameter identification part in a data driving form;

S2.3: the precondition part of the T-S fuzzy recognition adopts an improved K-means clustering method, the data for model training is divided into a plurality of sub-data spaces, and the accuracy of the global model in the whole wet state operation range is ensured;

s2.4: the conclusion of the T-S fuzzy recognition is based in part on the recognition of sub-model unknown parameters by an improved sparrow search algorithm (Improved Sparrow Search Algorithm, ISSA);

after establishing a flow of an ash box modeling method aiming at ultra-low load operation of a supercritical unit, in S3, embodying a unit wet state mode mechanism model, a T-S fuzzy identification structure and a K-means clustering method and a conclusion part ISSA design improved by a precondition part thereof:

s3.1: a mechanism model is built for a wet running mode of the unit according to three subsystems of a pulverizing system, a once-through boiler system and a steam turbine system of the supercritical unit;

s3.1.1: powder making system

The powder making systems of different units are arranged approximately identically, and the dynamic characteristics of the powder making systems are generally described by adopting a first-order inertia and pure delay link:

wherein: r is (r) _B The coal amount in the furnace is expressed as kg/s; u (u) _B Indicating a coal feeding amount instruction, kg/s; c (C) ₀ The inertia coefficient of the pulverizing system; τ represents the time delay time of the pulverizing system, s; the delay time of the pulverizing system is not easy to identify, and the delay time is taken as a general empirical value tau=94 s;

The furnace powder then burns in the hearth to release heat, generally assuming heat generation Q ₁ Approximately proportional to the coal feed, there are:

Q ₁ ＝k ₀₁ r _B (2)

wherein: k (k) ₀₁ Is the unit calorific value coefficient of coal;

s3.1.2: DC boiler system

First, energy conservation analysis of the whole boiler part: the pulverized coal combustion analyzed in the coal preparation part releases heat, which can be about equal to working medium heat absorption for simplification, but in actual operation, the coal feeding and water feeding can not keep a fixed ratio, so that the heat absorption of the working medium and the heat release of combustion are mismatched, the influence is aggravated under low load, and then an energy mismatch function is increased, so that the heat Q absorbed by the working medium is obtained as follows:

wherein: n represents the load demand of the unit and MW; d (D) _fw Is the water supply flow rate, kg/s; b ₀ Representing the coal-water ratio in steady state and relating to load; mu, delta is a constant;

the conservation of energy for the whole boiler section can then be written as:

wherein: v (V) _b The volume of the heated working medium of the boiler is m3; ρ _m 、h _m The average density and specific enthalpy of the working medium of the boiler section are kg/m3 and kJ/kg; h is a _fw Is the specific enthalpy of water supply, kJ/kg; d (D) _st 、h _st The main steam flow and the specific enthalpy are kg/s and kJ/kg; q (Q) ₂ Represents the heat dissipation, kJ, of the water separated by the separator when it circulates internally; because the water level can be controlled in a certain range, the dissipated heat and the flow of the internal circulation working medium are related to the temperature difference between the external temperature, the two quantities are positively related to the current power of the unit, and the dissipated energy is indirectly related to the coal quantity:

Q ₂ ＝k ₀₂ r _B (5)

Wherein: k (k) ₀₂ Is a coefficient;

q and Q are as follows ₂ Combining, wherein the heat absorbed by the partial working medium of the final boiler is;

also, since the separator outlet steam density is difficult to obtain directly, the separator outlet pressure p is used _m Instead, the final energy conservation relationship may be written;

then analyzing the mass balance of the water storage tank, regarding the economizer, the water-cooled wall, the steam-water separator and the water storage tank as a whole evaporation system, wherein the mass input of the system is only water feeding, the mass output is separator outlet steam, and the mass capacity of a heating pipeline is ignored, so that the mass change of the system can be approximately represented by the change of the water level of the water storage tank, and the overflow valve is supposed to be closed when in stable wet operation, and has no hydrophobic flow loss, and the mass balance relation of the system is as follows:

wherein H is the water level of the water storage tank and m; c (C) ₂ ，C ₃ Representing the capacity coefficient of the water storage tank and the proportional coefficient of the pressure difference and the flow; p is p _st Is the main steam pressure, MPa;

further, based on unit dynamics and general empirical analysis, the specific enthalpy of feedwater and main steam is assumed to be the following expression:

h _fw ＝k ₃ N+b ₁ (9)

h _st ＝k ₄ p _st +k ₅ N+b ₂ (10)

wherein: k (k) ₃ 、k ₄ 、k ₅ 、b ₁ 、b ₂ Are parameters to be identified;

s3.1.3: steam turbine system

In a turbine system, superheated steam drives a turbine to produce mechanical work, which is converted into electrical energy in a generator, wherein the main steam flow into the turbine can be defined as:

D _st ＝μ _t f ₁ (p _st ,h _st ) (11)

Wherein: mu (mu) _t Opening of a main steam valve,%; correlation function f ₁ ＝(k ₆ p _st )/(h _st -b ₃ )；

The pressure difference of the steam in the boiler is expressed as Δp=g (p _m ) The method comprises the following steps:

g(p _m )＝k ₈ p _m -b ₅ (12)

wherein: k (k) ₈ 、b ₅ Is a parameter to be identified;

the dynamic process of the turbine is expressed as:

wherein: correlation function f ₂ ＝k ₇ p _st μ _t +b ₄ ；

In summary, the vector state space equation form of the supercritical unit dry state model can be written as:

Y ₁ ＝C ₁ (X ₁ ) (14)

in the analysis, the mechanism model contains 20 unknown parameters to be identified, namely C ₀ 、C ₁ 、C ₂ 、C ₃ 、C ₄ 、b ₀ 、b ₁ 、b ₂ 、b ₃ 、b ₄ 、b ₅ 、k ₀ 、k ₁ 、k ₂ 、k ₃ 、k ₄ 、k ₅ 、k ₆ 、k ₇ 、b ₈ ；

S3.2: aiming at the unknown parameters existing in the mechanism model deduced for the supercritical unit, a T-S fuzzy identification structure in an increment form is constructed:

wherein: r is R ⁱ Representing the ith fuzzy rule, namely the ith cluster; k is the number of clusters; n represents the total amount of data used for training; x (t) is a generalized input vector of sampling interval t, comprising three inputs and three output variables of the built mechanism model, defining x (t) = [ u ₁ (t),u ₂ (t),u ₃ (t),y ₁ (t),y ₂ (t),y ₃ (t)] ^T (t＝1,2,...,n)；c _i ，r _i Respectively corresponding to the clustering center and the radius in the ith rule; yv _i (t) represents an output vector in the form of a submodel increment in the ith rule;the parameter vector is the parameter vector of the sub model in the ith rule; v (t) is an input vector in delta form, defined as:

v(t)＝[Δu ₁ (t),Δu ₂ (t),Δu ₃ (t),Δy ₁ (t),Δy ₂ (t),Δy ₃ (t)] ^T (t＝1,2,...,n) (18)

wherein:and->Steady state values respectively representing the jth input and the zth output in the ith rule; in addition, in order to simplify the modeling process, the clustering center is regarded as a stable point, and the modeling algorithm performance is not affected by such simplification:

The ash box modeling method combines the mechanism with the data driving method, and is characterized in that unknown parameters of the deduced mechanism model are identified by a T-S fuzzy identification method, and the unknown parameters are identified by the T-S fuzzy identification methodAnd part of the input vector is written as an increment form of a parameter vector to be identified and a generalized input vector of the mechanism model, and finally, the output of the nonlinear submodel corresponding to each cluster is obtained through the following formula:

wherein:

in order to obtain a final global output, the final modeling result can be completed by carrying out fuzzy weighting on the submodel output under the corresponding rule, and the expression is as follows:

wherein: w (w) _i The fuzzy weighting corresponding to the sub-rule is calculated by the following formula:

s3.3: the structure of the T-S fuzzy recognition based on the increment form comprises a precondition part and a conclusion part, and the data processing of the precondition part is realized based on the simplicity and the maturity of a K-means clustering algorithm; in order to get rid of the complicated process of manually setting the cluster number, an improved K-means clustering algorithm capable of automatically searching the current most suitable cluster number is realized by adding two punishment items into an objective function on the basis of an original algorithm, and the objective function is defined as follows:

wherein: z _ti Membership of the data vector x (t) to the ith cluster; alpha _i Representing the probability that a point belongs to the ith cluster; according to the basic concept of the information theory,defined as information entropy, setting +.>The purpose of the items is to adjust the bias so that the partitioning of the clusters is as orderly as possible; to determine the number of clusters, a second entropy term is added

Further, a Lagrangian multiplier method is adopted to minimize an objective function, and a clustering center c is obtained _i Degree of membership z _ti And probability alpha _i The solution formulas of (a) are respectively as follows:

wherein j represents the iteration times of the clustering algorithm; from the probability alpha _i For the ith ratio alpha _i (j) If lnα _i (j) Less thanAlpha is then _i (j+1)<α _i (j) The method comprises the steps of carrying out a first treatment on the surface of the When alpha is _i <When 1/n, the number of data representing the cluster is too small, and the data is regarded as unreasonable cluster, and because the K-means algorithm takes all data as an initial cluster center, the ith candidate cluster center is automatically removed, and the current cluster number and the cluster center are updated;

in order to obtain the final cluster number and cluster center, the difference between the new cluster center obtained by each iteration of the algorithm and the previous time needs to be compared, and when the maximum difference is lower than a certain threshold value, the iteration is stopped and the current cluster center is output as a final result; the threshold can be set according to the requirement and recorded as a variable xi, C _i (t+1)-c _i (t) is less than or equal to ζ, wherein c _i (t+1) represents a new cluster center, c _i (t) represents a previous cluster center, and the calculation is considered to be completed;

after the clustering center is obtained through the process, the corresponding clustering radius can be further calculated; the initial cluster radius is first set to r _s =0 (s=1, 2,., k); then the distance between each group of data and the nearest clustering center is obtained according to the formula (27), and the clustering radius is updated according to the formula (28):

||x(t)-c _i ||＝min{||x(t)-c ₁ ||,||x(t)-c ₂ ||,...,|x(t)-c _k ||}(t＝1,2,...,n) (27)

r _i ＝max{||x(t)-c _i ||,r _i }(i＝1,2,...,k) (28)

repeating the above two formulas to obtain all cluster radii { r } ₁ ,r ₂ ,...,r _k }；

S3.4: in the conclusion part of the T-S fuzzy recognition, all unknown parameters in a mechanism model are required to be recognized, the modeling precision is directly affected by a parameter recognition result, and in consideration of more parameters to be recognized in an analyzed mechanism model, an ISSA is provided for carrying out model parameter recognition, and the main flow of an algorithm is as follows:

step one: initializing an algorithm, and setting the population scale of the algorithm as NP; the searching dimension Dim is equal to the number of parameters to be identified in the mechanism model; the maximum iteration number is L; the global optimum non-updated upper limit is l _max The method comprises the steps of carrying out a first treatment on the surface of the Recording the current iteration times l=1 and the global optimal unexplored times l _n =0; in addition, all individuals perform position initialization by the following formula;

wherein: lambda (lambda) _jmin And lambda (lambda) _jmax Forming upper and lower limits of the j-th dimensional parameter value; rand (0, 1) is a random number within (0, 1);

The model precision is a primary standard for judging the performance of the modeling method, so that the absolute error between the model output and the actual operation data of the unit is selected as an adaptability function of algorithm optimization, and the calculation formula is as follows:

wherein x is _i ＝{x _i,1 ,x _i,2 ,...,x _i,Dim }；Representing the modeled output; y (t) represents the actual running output of the unit; all individuals are ordered according to the ascending order of the fitness value, and the sequence label is marked as SortIndex;

step two: the fixed population proportion of an original Sparrow Search Algorithm (SSA) is improved, namely the proportion of discoverers, the proportion of detectors and the warning threshold value used for updating the discoverers are changed into parameters which change adaptively, and the corresponding calculation formula is (31);

wherein: pp represents the finder ratio; sp represents the proportion of the inspector; ST denotes an alert threshold; the angle marks min and max represent the upper limit and the lower limit of the corresponding measured values; the three parameters are adaptively changed along with the iteration times, so that the effects of increasing the searching range in the early stage and quickly converging in the later stage are achieved;

step three: after individual ranking, the individuals ranked in the first pp×np as discoverers update the location according to formula (32);

wherein:and R is ₂ Is of the type (0, 1)]Random numbers of (a); k is a random number obeying normal distribution; r is R ₂ <The update formula of ST part is composed of- >Modified to->The search range of a finder is enlarged, and the capability of an algorithm for solving the problem that an optimal solution is not at an origin is improved;

step four: the remaining individuals other than the finder are defined as followers, and the location update formula is (33);

wherein:is the current worst individual; />Is globally optimal; rand { -1,1} represents a random value of-1 or 1;

step five: after the discoverer and the follower complete the location update, all individuals have a probability of ST as a prober, and sp×np individuals in the random extraction population are then updated as the prober:

wherein:the optimal individual of the current iteration; xi quiltThe step control parameter is defined as a random number which obeys normal distribution with the mean value of 0 and the variance of 1; r is a member of the group [ 1,1 ]]Random numbers of (a); f (f) _i And f _w Respectively corresponding to the current optimal individual and the worst individual fitness value; ζ is a small constant to avoid a denominator of 0;

step six: calculating the fitness of the updated individual, selecting the minimum value of the current fitness to compare with the global optimal fitness, and updating the global optimal individual and the fitness if the current optimal fitness value is smaller than the global optimal fitness value; otherwise, the global optimal continuous times are not updated _n Adding 1;

step seven: the detection bee strategy of the artificial bee colony algorithm is combined, whether the global optimal continuous non-updated times reach a threshold value is judged, and if l _n >l _max The current global optimum and fitness are reserved, and then all individuals are updated according to a formula (29); otherwise, directly entering the next step;

step eight: if the iteration number reaches the upper limit L or the optimizing precision meets the requirement, the searching process is ended, otherwise, the next iteration is carried out in the second step.

Based on the ash box modeling scheme provided in the step S3, an accurate mathematical model is established for the wet running mode of the supercritical unit, and in the step S4, the effectiveness of the provided modeling scheme is verified and analyzed by means of a simulation experiment, and the specific process is as follows:

s4.1: firstly, the identification of model parameters is completed based on field operation data to obtain a complete wet model, 3000 groups are taken as training data sets for determining the model parameters according to actual operation data of a certain 350MW supercritical unit, actual operation conditions in a rated load range of 20% of the unit is covered, sampling intervals of the data are 5S, unknown parameters in the model are identified through a designed T-S fuzzy identification method, and fitting degree of model output and actual output is verified;

S4.2: based on the training model obtained in the step S4.1, verifying the universality of the model, selecting another 800 groups of field data under the rated load of 20% as a test data set, and judging whether the training model has the universality or not through the fitting effect;

s4.3: further verifying the performance of the ISSA on model parameter identification, replacing the conclusion part of the T-S fuzzy identification method with SSA and gray wolf optimization, performing a comparison experiment with the ISSA, and quantifying the identification result through performance indexes.

The invention has the beneficial effects that:

the invention combines the transformation requirement of the power generation field of China on the new energy power consumption capability, and from the modeling perspective, provides a high-precision ash box modeling scheme combining a mechanism model and data driving identification aiming at the wet running mode of the supercritical unit, thereby laying a foundation for improving the deep peak regulation capability of the large-scale thermal generator unit.

The invention simplifies the supercritical unit in the wet state mode into a three-in three-out model in the mechanism modeling part, has obvious differences from the prior dry state mode model in the aspects of the selection of model output variables and the internal mass energy conservation analysis, and constructs a mechanism model more suitable for the wet state mode of the unit on the basis.

The invention provides an improved K-means algorithm and ISSA algorithm, and is used for solving the engineering problem in a power system. The method can get rid of the process of manually configuring the cluster number, and the method improves the global searching capability of the algorithm by combining the self-adaptive parameters and the ABC algorithm detection bee strategy. The designed identification algorithm can realize simultaneous identification of a large number of unknown parameters and meet the precision requirement of complex system modeling.

Detailed Description

Specific embodiments of the present invention will be further described below with reference to the drawings.

Referring to fig. 1 of the drawings, fig. 1 shows the condition of each section of the flow of steam and water in a wet mode of a once-through boiler; in a wet running mode of the supercritical unit, the process of changing the working medium parameters into superheated steam needs to undergo three stages of heating, evaporating and superheating, so that the working medium flows out of the water wall pipe and is in a gas-liquid two-phase flowing state, and the lengths of the three stages are changed along with the conditions of heat load, water supply flow and the like because the direct-current boiler has no fixed steam-water interface; when the water supply flow rate is increased, the length of the heating section is prolonged, and the lengths of the evaporating section and the superheating section are correspondingly shortened; therefore, when the supercritical unit is in a wet running mode, the steam-water separator acts like a steam drum of a natural circulation boiler, the water-cooling wall and the superheater can be separated, and a steam-water mixture at the outlet of the water-cooling wall is separated into steam and water so as to control the dryness of steam entering the superheater.

Referring to fig. 2 in the drawings, fig. 2 is a simplified structure and model diagram of a supercritical unit according to the present invention; after raw coal is processed by the pulverizing system, mixed hot air is sent into a hearth for combustion, and chemical energy released in the process is converted into heat energy of working medium through a heating surface, so that the working medium is converted into state in the boiler evaporating system. Finally, the high-temperature and high-pressure steam output by the boiler enters a steam turbine, and the blades of the steam turbine are driven to rotate so as to drive a generator to rotate, so that mechanical energy is converted into electric energy and is transmitted to a power grid. According to the supercritical unit operation principle, the wet mode is finally simplified into a three-input three-output model, wherein three output variables are unit load demand N and main steam pressure p _st And the water level H of the water storage tank, three input variables are D _fw Quantity of fuel r _B Valve opening mu _T 。

Referring to fig. 3 of the drawings, fig. 3 is a flow chart of a data driving type T-S fuzzy recognition method, wherein the T-S fuzzy recognition is an incremental structure, and both the precondition and conclusion parts adopt improved algorithms, so that the performance of the recognition method is improved from multiple aspects to obtain an optimal modeling effect;

referring to fig. 4 in the drawings of the specification, fig. 4 is a main flow of the proposed ISSA, the improvement is marked by a dotted line frame, the added adaptive parameters and the detection bee policy of the artificial bee colony algorithm enhance the ability of the algorithm to jump out of local optimum, and can improve the identification accuracy of the algorithm.

S1: analyzing the operation characteristics and modeling difficulties of the supercritical unit in an ultralow-load wet mode;

s2: establishing a dust box modeling method flow aiming at ultra-low load operation of a supercritical unit;

s3: describing the ash bin modeling method steps combining mechanism analysis and data-driven T-S fuzzy recognition;

s4: and verifying and analyzing the effectiveness of the modeling method by combining a simulation experiment and a quantization index.

S1: the supercritical unit consists of three subsystems, namely a pulverizing system, a once-through boiler system and a steam turbine system. After raw coal is processed by the pulverizing system, mixed hot air is sent into a hearth for combustion, and chemical energy released in the process is converted into heat energy of working medium through a heating surface, so that the working medium is converted into state in the boiler evaporating system. Finally, the high-temperature and high-pressure steam output by the boiler enters a steam turbine, and blades of the steam turbine are driven to rotate to generate mechanical energy to drive a generator to rotate, so that the mechanical energy is converted into electric energy and is transmitted to a power grid. In a wet running mode of the supercritical unit, working medium parameters are subcritical, the process of changing water into superheated steam still needs to be subjected to three stages of heating, evaporating and superheating, and when working medium flows out of the water wall pipe, the working medium is in a gas-liquid two-phase flowing state and cannot directly enter the superheater. At this time, the steam-water separator arranged at the outlet of the water-cooled wall is equivalent to the steam drum of the subcritical unit in action, and plays a role in steam-water separation. The separated steam also enters the steam turbine to do work, and water flows into the water storage tank to be further recovered or discharged out of the whole cycle. The mass balance equation of the once-through boiler system in the wet mode is greatly different from that of the once-through boiler system in the dry mode, and the water level of the water storage tank is a key controlled quantity for the unit in the wet running mode. In addition, because the water-cooled wall outlet working medium is wet steam when in wet mode operation, the fuel quantity is directly increased at the moment, the temperature change of the middle point is not great, and the water-coal ratio control advanced signal used for the water-coal ratio control can possibly fail. Therefore, the invention does not set the middle point temperature which is usually used as the output variable of the unit model as the output of the wet mode model, and takes the water level of the water storage tank as the output variable of the wet mode model instead. Finally, a simplified model of the three-input three-output supercritical unit in a wet state operation mode can be constructed, wherein three input variables are the water supply quantity D _fw Quantity of fuel r _B And valve opening mu _T The three output variables are the unit load N and the main steam pressure p _st And the water level H in the water storage tank. In combination with the analysis, the supercritical unit is wetThe working medium flowing process of the state operation mode is more complex, and difficulty is brought to mechanism modeling analysis. Meanwhile, the fluctuation of the water level of the water storage tank is large, and compared with other outputs, ideal model fitting precision is difficult to obtain.

Based on the analysis of S1, complicated steam-water flow characteristics and fluctuation of water level of a water storage tank during operation in a wet mode of a supercritical unit bring difficulty to modeling, so that a gray box modeling method combining mechanism analysis and data-driven T-S fuzzy identification needs to be developed, and the accuracy of an identified model is improved. Step S2 may be embodied as:

s2.1: according to the operation characteristic analysis of the supercritical unit wet state operation mode, a simplified mechanism model is established for the unit wet state mode based on the mass and energy conservation law, unknown parameters in the mechanism model are reserved for subsequent identification, and the actual conditions of different model parameters under different working conditions are matched;

s2.2: for a nonlinear system, a linear relation exists between input data and output data in an incremental form, so that a T-S fuzzy identification structure in the incremental form is built for a nonlinear supercritical unit system in a parameter identification part in a data driving form;

S2.3: the precondition part of the T-S fuzzy recognition adopts an improved K-means clustering method, the data for model training is divided into a plurality of sub-data spaces, and the accuracy of the global model in the whole wet state operation range is ensured;

s2.4: the conclusion of the T-S fuzzy recognition is based in part on the Improved Sparrow search algorithm (Improved Sparrow SearchAlgorithm, ISSA) to recognize unknown parameters of the sub-model;

after establishing a flow of an ash box modeling method aiming at ultra-low load operation of a supercritical unit, in S3, embodying a unit wet state mode mechanism model, a T-S fuzzy identification structure and a K-means clustering method and a conclusion part ISSA design improved by a precondition part thereof:

s3.1: a mechanism model is built for a wet running mode of the unit according to three subsystems of a pulverizing system, a once-through boiler system and a steam turbine system of the supercritical unit;

s3.1.1: powder making system

The powder making systems of different units are arranged approximately identically, and the dynamic characteristics of the powder making systems are generally described by adopting a first-order inertia and pure delay link:

wherein: r is (r) _B The coal amount in the furnace is expressed as kg/s; u (u) _B Indicating a coal feeding amount instruction, kg/s; c (C) ₀ The inertia coefficient of the pulverizing system; τ represents the time delay time of the pulverizing system, s; the delay time of the pulverizing system is not easy to identify, and the delay time is taken as a general empirical value tau=94 s;

The furnace powder then burns in the hearth to release heat, generally assuming heat generation Q ₁ Approximately proportional to the coal feed, there are:

Q ₁ ＝k ₀₁ r _B (36)

wherein: k (k) ₀₁ Is the unit calorific value coefficient of coal;

s3.1.2: DC boiler system

First, energy conservation analysis of the whole boiler part: the pulverized coal combustion analyzed in the coal preparation part releases heat, which can be about equal to working medium heat absorption for simplification, but in actual operation, the coal feeding and water feeding can not keep a fixed ratio, so that the heat absorption of the working medium and the heat release of combustion are mismatched, the influence is aggravated under low load, and then an energy mismatch function is increased, so that the heat Q absorbed by the working medium is obtained as follows:

wherein: n represents the load demand of the unit and MW; d (D) _fw Is the water supply flow rate, kg/s; b ₀ Representing the coal-water ratio in steady state and relating to load; mu, delta is a constant;

the conservation of energy for the whole boiler section can then be written as:

wherein: v (V) _b The volume of the heated working medium of the boiler is m3; ρ _m 、h _m The average density and specific enthalpy of the working medium of the boiler section are kg/m3 and kJ/kg; h is a _fw Is the specific enthalpy of water supply, kJ/kg; d (D) _st 、h _st The main steam flow and the specific enthalpy are kg/s and kJ/kg; q (Q) ₂ Represents the heat dissipation, kJ, of the water separated by the separator when it circulates internally; because the water level can be controlled in a certain range, the dissipated heat and the flow of the internal circulation working medium are related to the temperature difference between the external temperature, the two quantities are positively related to the current power of the unit, and the dissipated energy is indirectly related to the coal quantity:

Q ₂ ＝k ₀₂ r _B (39)

Wherein: k (k) ₀₂ Is a coefficient;

q and Q are as follows ₂ Combining, wherein the heat absorbed by the partial working medium of the final boiler is;

also, since the separator outlet steam density is difficult to obtain directly, the separator outlet pressure p is used _m Instead, the final energy conservation relationship may be written;

then analyzing the mass balance of the water storage tank, regarding the economizer, the water-cooled wall, the steam-water separator and the water storage tank as a whole evaporation system, wherein the mass input of the system is only water feeding, the mass output is separator outlet steam, and the mass capacity of a heating pipeline is ignored, so that the mass change of the system can be approximately represented by the change of the water level of the water storage tank, and the overflow valve is supposed to be closed when in stable wet operation, and has no hydrophobic flow loss, and the mass balance relation of the system is as follows:

wherein H is water in a water storage tankBit, m; c (C) ₂ ，C ₃ Representing the capacity coefficient of the water storage tank and the proportional coefficient of the pressure difference and the flow; p is p _st Is the main steam pressure, MPa;

further, based on unit dynamics and general empirical analysis, the specific enthalpy of feedwater and main steam is assumed to be the following expression:

h _fw ＝k ₃ N+b ₁ (43)

h _st ＝k ₄ p _st +k ₅ N+b ₂ (44)

wherein: k (k) ₃ 、k ₄ 、k ₅ 、b ₁ 、b ₂ Are parameters to be identified;

s3.1.3: steam turbine system

In a turbine system, superheated steam drives a turbine to produce mechanical work, which is converted into electrical energy in a generator, wherein the main steam flow into the turbine can be defined as:

D _st ＝μ _t f ₁ (p _st ,h _st ) (45)

Wherein: mu (mu) _t Opening of a main steam valve,%; correlation function f ₁ ＝(k ₆ p _st )/(h _st -b ₃ )；

The pressure difference of the steam in the boiler is expressed as Δp=g (p _m )：

g(p _m )＝k ₈ p _m -b ₅ (46)

Wherein: k (k) ₈ 、b ₅ Is a parameter to be identified;

the dynamic process of the turbine is expressed as:

wherein: correlation function f ₂ ＝k ₇ p _st μ _t +b ₄ ；

In summary, the vector state space equation form of the supercritical unit dry state model can be written as:

in the analysis, the mechanism model contains 20 unknown parameters to be identified, namely C ₀ 、C ₁ 、C ₂ 、C ₃ 、C ₄ 、b ₀ 、b ₁ 、b ₂ 、b ₃ 、b ₄ 、b ₅ 、k ₀ 、k ₁ 、k ₂ 、k ₃ 、k ₄ 、k ₅ 、k ₆ 、k ₇ 、b ₈ ；

S3.2: aiming at the unknown parameters existing in the mechanism model deduced for the supercritical unit, a T-S fuzzy identification structure in an increment form is constructed:

wherein: r is R ⁱ Representing the ith fuzzy rule, namely the ith cluster; k is the number of clusters; n represents the total amount of data used for training; x (t) is a generalized input vector of sampling interval t, comprising three inputs and three output variables of the built mechanism model, defining x (t) = [ u ₁ (t),u ₂ (t),u ₃ (t),y ₁ (t),y ₂ (t),y ₃ (t)] ^T (t＝1,2,...,n)；c _i ，r _i Respectively corresponding to the clustering center and the radius in the ith rule; yv _i (t) represents an output vector in the form of a submodel increment in the ith rule;the parameter vector is the parameter vector of the sub model in the ith rule; v (t) is an input vector in delta form, defined as:

v(t)＝[Δu ₁ (t),Δu ₂ (t),Δu ₃ (t),Δy ₁ (t),Δy ₂ (t),Δy ₃ (t)] ^T (t＝1,2,…,n) (52)

wherein:and->Steady state values respectively representing the jth input and the zth output in the ith rule; in addition, in order to simplify the modeling process, the clustering center is regarded as a stable point, and the modeling algorithm performance is not affected by such simplification:

The ash box modeling method combines the mechanism with the data driving method, and is characterized in that unknown parameters of the deduced mechanism model are identified by a T-S fuzzy identification method, and the unknown parameters are identified by the T-S fuzzy identification methodAnd part of the input vector is written as an increment form of a parameter vector to be identified and a generalized input vector of the mechanism model, and finally, the output of the nonlinear submodel corresponding to each cluster is obtained through the following formula:

wherein:

in order to obtain a final global output, the final modeling result can be completed by carrying out fuzzy weighting on the submodel output under the corresponding rule, and the expression is as follows:

wherein:w _i the fuzzy weighting corresponding to the sub-rule is calculated by the following formula:

s3.3: the structure of the T-S fuzzy recognition based on the increment form comprises a precondition part and a conclusion part, and the data processing of the precondition part is realized based on the simplicity and the maturity of a K-means clustering algorithm; in order to get rid of the complicated process of manually setting the cluster number, an improved K-means clustering algorithm capable of automatically searching the current most suitable cluster number is realized by adding two punishment items into an objective function on the basis of an original algorithm, and the objective function is defined as follows:

wherein: z _ti Membership of the data vector x (t) to the ith cluster; alpha _i Representing the probability that a point belongs to the ith cluster; according to the basic concept of the information theory,defined as information entropy, setting +.>The purpose of the items is to adjust the bias so that the partitioning of the clusters is as orderly as possible; to determine the number of clusters, a second entropy term is added

Further, a Lagrangian multiplier method is adopted to minimize an objective function, and a clustering center c is obtained _i Degree of membership z _ti And probability alpha _i The solution formulas of (a) are respectively as follows:

wherein j represents the iteration times of the clustering algorithm; from the probability alpha _i For the ith ratio alpha _i (j) If lnα _i (j) Less thanAlpha is then _i (j+1)<α _i (j) The method comprises the steps of carrying out a first treatment on the surface of the When alpha is _i <When 1/n, the number of data representing the cluster is too small, and the data is regarded as unreasonable cluster, and because the K-means algorithm takes all data as an initial cluster center, the ith candidate cluster center is automatically removed, and the current cluster number and the cluster center are updated;

in order to obtain the final cluster number and cluster center, the difference between the new cluster center obtained by each iteration of the algorithm and the previous time needs to be compared, and when the maximum difference is lower than a certain threshold value, the iteration is stopped and the current cluster center is output as a final result; the threshold can be set according to the requirement and recorded as a variable xi, C _i (t+1)-c _i (t) is less than or equal to ζ, wherein c _i (t+1) represents a new cluster center, c _i (t) represents a previous cluster center, and the calculation is considered to be completed;

after the clustering center is obtained through the process, the corresponding clustering radius can be further calculated; the initial cluster radius is first set to r _s =0 (s=1, 2, …, k); then, the distance between each group of data and the nearest clustering center is obtained according to a formula (61), and the clustering radius is updated according to a formula (62):

||x(t)-c _i ||＝min{||x(t)-c ₁ ||,||x(t)-c ₂ ||,...,|x(t)-c _k ||}(t＝1,2,…,n) (61)

r _i ＝max{||x(t)-c _i ||,r _i }(i＝1,2,…,k) (62)

repeating the above two formulas to obtain all cluster radii { r } ₁ ,r ₂ ,...,r _k }；

S3.4: in the conclusion part of the T-S fuzzy recognition, all unknown parameters in a mechanism model are required to be recognized, the modeling precision is directly affected by a parameter recognition result, and in consideration of more parameters to be recognized in an analyzed mechanism model, an ISSA is provided for carrying out model parameter recognition, and the main flow of an algorithm is as follows:

step one: initializing an algorithm, and setting the population scale of the algorithm as NP; the searching dimension Dim is equal to the number of parameters to be identified in the mechanism model; the maximum iteration number is L; the global optimum non-updated upper limit is l _max The method comprises the steps of carrying out a first treatment on the surface of the Recording the current iteration times l=1 and the global optimal unexplored times l _n =0; in addition, all individuals perform position initialization by the following formula;

/>

wherein: lambda (lambda) _jmin And lambda (lambda) _jmax Forming upper and lower limits of the j-th dimensional parameter value; rand (0, 1) is a random number within (0, 1);

The model precision is a primary standard for judging the performance of the modeling method, so that the absolute error between the model output and the actual operation data of the unit is selected as an adaptability function of algorithm optimization, and the calculation formula is as follows:

wherein x is _i ＝{x _i,1 ,x _i,2 ,...,x _i,Dim }；Representing the modeled output; y (t) represents the actual running output of the unit; all individuals are ordered according to the ascending order of the fitness value, and the sequence label is marked as SortIndex;

step two: the fixed population proportion of an original Sparrow Search Algorithm (SSA) is improved, namely the proportion of discoverers, the proportion of detectors and the warning threshold value used for updating the discoverers are changed into parameters which change adaptively, and the corresponding calculation formula is (65);

wherein: pp represents the finder ratio; sp represents the proportion of the inspector; ST denotes an alert threshold; the angle marks min and max represent the upper limit and the lower limit of the corresponding measured values; the three parameters are adaptively changed along with the iteration times, so that the effects of increasing the searching range in the early stage and quickly converging in the later stage are achieved;

step three: after individual ranking, the individuals ranked in the top pp×np served as discoverers, updating the location according to equation (66);

wherein:and R is ₂ Is of the type (0, 1)]Random numbers of (a); k is a random number obeying normal distribution; r is R ₂ <The update formula of ST part is composed of- >Modified to->The search range of a finder is enlarged, and the capability of an algorithm for solving the problem that an optimal solution is not at an origin is improved;

step four: the remaining individuals other than the finder are defined as followers, and the location update formula is (67);

wherein:is the current worst individual; />Is globally optimal; rand { -1,1} represents a random value of-1 or 1;

step five: after the discoverer and the follower complete the location update, all individuals have a probability of ST as a prober, and sp×np individuals in the random extraction population are then updated as the prober:

/>

wherein:the optimal individual of the current iteration; ζ is defined as the step control parameter, which is a random number subject to a normal distribution with a mean of 0 and a variance of 1; r is a member of the group [ 1,1 ]]Random numbers of (a); f (f) _i And f _w Respectively corresponding to the current optimal individual and the worst individual fitness value; ζ is a small constant to avoid a denominator of 0;

step six: calculating the fitness of the updated individual, selecting the minimum value of the current fitness to compare with the global optimal fitness, and updating the global optimal individual and the fitness if the current optimal fitness value is smaller than the global optimal fitness value; otherwise, the global optimal continuous times are not updated _n Adding 1;

step seven: the detection bee strategy of the artificial bee colony algorithm is combined, whether the global optimal continuous non-updated times reach a threshold value is judged, and if l _n >l _max The current global optimum and fitness are reserved, and then all individuals are updated according to a formula (29); otherwise, directly entering the next step;

step eight: if the iteration number reaches the upper limit L or the optimizing precision meets the requirement, the searching process is ended, otherwise, the next iteration is carried out in the second step.

Based on the ash box modeling scheme designed in the step S3, an accurate mathematical model under the wet running mode of the supercritical unit is established, and feasibility of the proposed modeling scheme is verified and analyzed by means of a simulation experiment in the step S4, wherein the specific process is as follows:

the operating conditions of the unit according to this example at 20% and 30% rated load are as follows:

table 1350MW unit steady state values for different load operating points under wet state operation

All parameter setting values of the proposed data-driven fuzzy recognition algorithm are as follows:

table 2 parameter settings of the identification algorithm

S4.1: firstly, the identification of parameters is completed based on actual operation data of a unit to obtain a final wet state model, 3000 groups are taken as training data sets for determining model parameters according to the actual operation data of a certain 350MW supercritical unit, the operation working conditions within the range of 20% -30% of rated load of the unit are covered, the sampling interval of the used data is 5S, unknown parameters in the model are identified through a designed T-S fuzzy identification method, and the fitting effect between model output and actual output is judged through an average absolute error (MAE);

S4.2: based on the complete model obtained in the step S4.1, further verifying the universality of the model, selecting another 800 groups of field data under the rated load of 20% of the unit as a test data set, and verifying whether the model obtained by training has qualified modeling precision through fitting effects;

s4.3: further verifying the performance of the ISSA on model parameter identification, sequentially changing the conclusion part of the proposed T-S fuzzy identification method into SSA and GWO, performing comparison experiment with ISSA, and determining the model parameter identification by root mean square error (RSME) and fitting degree (f _d ) Quantifying the identification effect of different algorithms by the two performance indexes;

statistical results show that the ash box modeling method for the supercritical unit wet mode operation provided by the invention shows ideal modeling precision in the embodiment, and can provide an effective model foundation for improving the unit flexibility operation capability.

Claims (4)

1. The invention provides an ash box modeling method for ultra-low load operation of a supercritical unit, which comprises the following 4 steps:

s1: analyzing the operation characteristics and modeling difficulties of the supercritical unit in an ultralow-load wet mode;

s2: establishing a dust box modeling method flow aiming at ultra-low load operation of a supercritical unit;

S3: describing a gray box modeling method design step combining mechanism analysis and data-driven T-S fuzzy recognition;

s4: and verifying and analyzing the effectiveness of the modeling method by combining a simulation experiment and a quantization index.

S1: the supercritical unit consists of three subsystems, namely a pulverizing system, a once-through boiler system and a steam turbine system. After raw coal is processed by the pulverizing system, mixed hot air is sent into a hearth for combustion, and chemical energy released in the process is converted into heat energy of working medium through a heating surface, so that the working medium is converted into state in the boiler evaporating system. Finally, the high-temperature and high-pressure steam output by the boiler enters a steam turbine, and blades of the steam turbine are driven to rotate to generate mechanical energy to drive a generator to rotate, so that the mechanical energy is converted into electric energy and is transmitted to a power grid. In a wet running mode of the supercritical unit, working medium parameters are subcritical, the process of changing water into superheated steam still needs to be subjected to three stages of heating, evaporating and superheating, and when working medium flows out of the water wall pipe, the working medium is in a gas-liquid two-phase flowing state and cannot directly enter the superheater. At this time, the steam-water separator arranged at the water-cooled wall outlet is equivalent in functionAnd the steam-water separation function is achieved in the steam drum of the subcritical unit. The separated steam also enters the steam turbine to do work, and water flows into the water storage tank to be further recovered or discharged out of the whole cycle. The mass balance equation of the once-through boiler system in the wet mode is greatly different from that of the once-through boiler system in the dry mode, and the water level of the water storage tank is a key controlled quantity for the unit in the wet running mode. In addition, because the water-cooled wall outlet working medium is wet steam when in wet mode operation, the fuel quantity is directly increased at the moment, the temperature change of the middle point is not great, and the water-coal ratio control advanced signal used for the water-coal ratio control can possibly fail. Therefore, the invention does not set the middle point temperature which is usually used as the output variable of the unit model as the output of the wet mode model, and takes the water level of the water storage tank as the output variable of the wet mode model instead. Finally, a simplified model of the three-input three-output supercritical unit in a wet state operation mode can be constructed, wherein three input variables are the water supply quantity D _fw Quantity of fuel r _B And valve opening mu _T The three output variables are the unit load N and the main steam pressure p _st And the water level H in the water storage tank. In the analysis, the working medium flowing process of the wet running mode of the supercritical unit is more complex, and difficulties are brought to mechanism modeling analysis. Meanwhile, the fluctuation of the water level of the water storage tank is large, and compared with other outputs, ideal model fitting precision is difficult to obtain.

3. Based on the analysis of S1, complicated steam-water flow characteristics and fluctuation of water level of a water storage tank during operation in a wet mode of a supercritical unit bring difficulty to modeling, so that a gray box modeling method combining mechanism analysis and data-driven T-S fuzzy identification needs to be developed, and the accuracy of an identified model is improved. Step S2 may be embodied as:

s2.1: according to the operation characteristic analysis of the supercritical unit wet state operation mode, a simplified mechanism model is established for the unit wet state mode based on the mass and energy conservation law, unknown parameters in the mechanism model are reserved for subsequent identification, and the actual conditions of different model parameters under different working conditions are matched;

s2.2: for a nonlinear system, a linear relation exists between input data and output data in an incremental form, so that a T-S fuzzy identification structure in the incremental form is built for a nonlinear supercritical unit system in a parameter identification part in a data driving form;

S2.3: the precondition part of the T-S fuzzy recognition adopts an improved K-means clustering method, the data for model training is divided into a plurality of sub-data spaces, and the accuracy of the global model in the whole wet state operation range is ensured;

s2.4: the conclusion of the T-S fuzzy recognition is based in part on the recognition of sub-model unknown parameters by an improved sparrow search algorithm (Improved Sparrow Search Algorithm, ISSA);

after establishing a flow of an ash box modeling method aiming at ultra-low load operation of a supercritical unit, in S3, embodying a unit wet state mode mechanism model, a T-S fuzzy identification structure and a K-means clustering method and a conclusion part ISSA design improved by a precondition part thereof:

s3.1: a mechanism model is built for a wet running mode of the unit according to three subsystems of a pulverizing system, a once-through boiler system and a steam turbine system of the supercritical unit;

s3.1.1: powder making system

The powder making systems of different units are arranged approximately identically, and the dynamic characteristics of the powder making systems are generally described by adopting a first-order inertia and pure delay link:

wherein: r is (r) _B The coal amount in the furnace is expressed as kg/s; u (u) _B Indicating a coal feeding amount instruction, kg/s; c (C) ₀ The inertia coefficient of the pulverizing system; τ represents the time delay time of the pulverizing system, s; the delay time of the pulverizing system is not easy to identify, and the delay time is taken as a general empirical value tau=94 s;

The furnace powder then burns in the hearth to release heat, generally assuming heat generation Q ₁ Approximately proportional to the coal feed, there are:

Q ₁ ＝k ₀₁ r _B (2)

wherein: k (k) ₀₁ Is the unit heat value of coalCoefficients;

s3.1.2: DC boiler system

First, energy conservation analysis of the whole boiler part: the pulverized coal combustion analyzed in the coal preparation part releases heat, which can be about equal to working medium heat absorption for simplification, but in actual operation, the coal feeding and water feeding can not keep a fixed ratio, so that the heat absorption of the working medium and the heat release of combustion are mismatched, the influence is aggravated under low load, and then an energy mismatch function is increased, so that the heat Q absorbed by the working medium is obtained as follows:

wherein: n represents the load demand of the unit and MW; d (D) _fw Is the water supply flow rate, kg/s; b ₀ Representing the coal-water ratio in steady state and relating to load; mu, delta is a constant;

the conservation of energy for the whole boiler section can then be written as:

wherein: v (V) _b The volume of the heated working medium of the boiler is m3; ρ _m 、h _m The average density and specific enthalpy of the working medium of the boiler section are kg/m3 and kJ/kg; h is a _fw Is the specific enthalpy of water supply, kJ/kg; d (D) _st 、h _st The main steam flow and the specific enthalpy are kg/s and kJ/kg; q (Q) ₂ Represents the heat dissipation, kJ, of the water separated by the separator when it circulates internally; because the water level can be controlled in a certain range, the dissipated heat and the flow of the internal circulation working medium are related to the temperature difference between the external temperature, the two quantities are positively related to the current power of the unit, and the dissipated energy is indirectly related to the coal quantity:

Q ₂ ＝k ₀₂ r _B (5)

Wherein: k (k) ₀₂ Is a coefficient;

q and Q are as follows ₂ Combining, wherein the heat absorbed by the partial working medium of the final boiler is;

also, since the separator outlet steam density is difficult to obtain directly, the separator outlet pressure p is used _m Instead, the final energy conservation relationship may be written;

then analyzing the mass balance of the water storage tank, regarding the economizer, the water-cooled wall, the steam-water separator and the water storage tank as a whole evaporation system, wherein the mass input of the system is only water feeding, the mass output is separator outlet steam, and the mass capacity of a heating pipeline is ignored, so that the mass change of the system can be approximately represented by the change of the water level of the water storage tank, and the overflow valve is supposed to be closed when in stable wet operation, and has no hydrophobic flow loss, and the mass balance relation of the system is as follows:

wherein H is the water level of the water storage tank and m; c (C) ₂ ，C ₃ Representing the capacity coefficient of the water storage tank and the proportional coefficient of the pressure difference and the flow; p is p _st Is the main steam pressure, MPa;

further, based on unit dynamics and general empirical analysis, the specific enthalpy of feedwater and main steam is assumed to be the following expression:

h _fw ＝k ₃ N+b ₁ (9)

h _st ＝k ₄ p _st +k ₅ N+b ₂ (10)

wherein: k (k) ₃ 、k ₄ 、k ₅ 、b ₁ 、b ₂ Are parameters to be identified;

s3.1.3: steam turbine system

In a turbine system, superheated steam drives a turbine to produce mechanical work, which is converted into electrical energy in a generator, wherein the main steam flow into the turbine can be defined as:

D _st ＝μ _t f ₁ (p _st ,h _st ) (11)

Wherein: mu (mu) _t Opening of a main steam valve,%; correlation function f ₁ ＝(k ₆ p _st )/(h _st -b ₃ )；

The pressure difference of the steam in the boiler is expressed as Δp=g (p _m ) The method comprises the following steps:

g(p _m )＝k ₈ p _m -b ₅ (12)

wherein: k (k) ₈ 、b ₅ Is a parameter to be identified;

the dynamic process of the turbine is expressed as:

wherein: correlation function f ₂ ＝k ₇ p _st μ _t +b ₄ ；

In summary, the vector state space equation form of the supercritical unit dry state model can be written as:

in the wet mode mechanism model, 20 unknown parameters are contained to be identified and are respectively C ₀ 、C ₁ 、C ₂ 、C ₃ 、C ₄ 、b ₀ 、b ₁ 、b ₂ 、b ₃ 、b ₄ 、b ₅ 、k ₀ 、k ₁ 、k ₂ 、k ₃ 、k ₄ 、k ₅ 、k ₆ 、k ₇ 、b ₈ ；

S3.2: aiming at the unknown parameters existing in the mechanism model deduced for the supercritical unit, a T-S fuzzy identification structure in an increment form is constructed:

wherein: r is R ⁱ Representing the ith fuzzy rule, namely the ith cluster; k represents the number of clusters; n represents the total amount of data used for training; x (t) is a generalized input vector of sampling interval t, comprising three inputs and three output variables of the built mechanism model, defined as x (t) = [ u ] ₁ (t),u ₂ (t),u ₃ (t),y ₁ (t),y ₂ (t),y ₃ (t)] ^T (t＝1,2,...,n)；c _i ，r _i Respectively corresponding to the clustering center and the radius in the ith rule; yv _i (t) represents an output vector in the form of a submodel increment in the ith rule;the parameter vector is the parameter vector of the sub model in the ith rule; v (t) is an input vector in delta form, defined as:

v(t)＝]Δu ₁ (t),Δu ₂ (t),Δu ₃ (t),Δy ₁ (t),Δy ₂ (t),Δy ₃ (t)] ^T (t＝1,2,...,n) (18)

wherein:and->Steady state values respectively representing the jth input and the zth output in the ith rule; in addition, in order to simplify the modeling process, the clustering center is regarded as a stable point, and the modeling algorithm performance is not affected by such simplification: the ash box modeling method combines the mechanism with the data driving method, and is characterized in that unknown parameters of the deduced mechanism model are identified by a T-S fuzzy identification method, and +. >And part of the input vector is written as an increment form of a parameter vector to be identified and a generalized input vector of the mechanism model, and finally, the output of the nonlinear submodel corresponding to each cluster is obtained through the following formula:

wherein:

in order to obtain a final global output, the final modeling result can be completed by carrying out fuzzy weighting on the submodel output under the corresponding rule, and the expression is as follows:

wherein: w (w) _i The fuzzy weighting corresponding to the sub-rule is calculated by the following formula:

s3.3: the structure of the T-S fuzzy recognition based on the increment form comprises a precondition part and a conclusion part, and the data processing of the precondition part is realized based on the simplicity and the maturity of a K-means clustering algorithm; in order to get rid of the complicated process of manually setting the cluster number, an improved K-means clustering algorithm capable of automatically searching the current most suitable cluster number is realized by adding two punishment items into an objective function on the basis of an original algorithm, and the objective function is defined as follows:

wherein: z _ti Membership of the data vector x (t) to the ith cluster; alpha _i Representing the probability that a point belongs to the ith cluster; according to the basic concept of the information theory,defined as information entropy, setting +. >The purpose of the items is to adjust the bias so that the partitioning of the clusters is as orderly as possible; to determine the number of clusters, a second entropy term is added

Further, a Lagrangian multiplier method is adopted to minimize an objective function, and a clustering center c is obtained _i Degree of membership z _ti And probability alpha _i The solution formulas of (a) are respectively as follows:

wherein j represents the iteration times of the clustering algorithm; from the probability alpha _i For the ith ratio alpha _i (j) If lnα _i (j) Less thanAlpha is then _i (j+1)<α _i (j) The method comprises the steps of carrying out a first treatment on the surface of the When alpha is _i <When 1/n, the number of data representing the cluster is too small, and the data is regarded as unreasonable cluster, and because the K-means algorithm takes all data as an initial cluster center, the ith candidate center is automatically removed, and the current cluster number and the cluster center are updated; in order to obtain the final cluster number and cluster center, the difference between the new cluster center obtained by each iteration of the algorithm and the previous time needs to be compared, and when the maximum difference is lower than a certain threshold value, the iteration is stopped and the current cluster center is output as a final result; the threshold can be set according to the requirement and recorded as a variable xi, C _i (t+1)-c _i (t) is less than or equal to ζ, wherein c _i (t+1) represents a new cluster center, c _i (t) represents a previous cluster center, and the calculation is considered to be completed;

after the clustering center is obtained through the process, the corresponding clustering radius can be further calculated; the initial cluster radius is first set to r _s =0 (s=1, 2,., k); then the distance between each group of data and the nearest clustering center is obtained according to the formula (27), and the clustering radius is updated according to the formula (28):

||x(t)-c _i ||＝min{||x(t)-c ₁ ||,||x(t)-c ₂ ||,...,|x(t)-c _k ||}(t＝1,2,...,n) (27)

r _i ＝max{||x(t)-c _i ||,r _i }(i＝1,2,…,k) (28)

repeating the above two formulas to obtain all cluster radii { r } ₁ ,r ₂ ,...,r _k }；

S3.4: in the conclusion part of the T-S fuzzy recognition, all unknown parameters in a mechanism model are required to be recognized, the modeling precision is directly affected by a parameter recognition result, and in consideration of more parameters to be recognized in an analyzed mechanism model, an ISSA is provided for carrying out model parameter recognition, and the main flow of an algorithm is as follows:

step one: initializing an algorithm, and setting the population scale of the algorithm as NP; the searching dimension Dim is equal to the number of parameters to be identified in the mechanism model; the maximum iteration number is L; the global optimum non-updated upper limit is l _max The method comprises the steps of carrying out a first treatment on the surface of the Recording the current iteration times l=1 and the global optimal unexplored times l _n =0; in addition, all individuals perform position initialization by the following formula;

wherein: lambda (lambda) _jmin And lambda (lambda) _jmax Forming upper and lower limits of the j-th dimensional parameter value; rand (0, 1) is a random number within (0, 1); the model precision is a primary standard for judging the performance of the modeling method, so that the absolute error between the model output and the actual operation data of the unit is selected as an adaptability function of algorithm optimization, and the calculation formula is as follows:

Wherein x is _i ＝{x _i,1 ,x _i,2 ,...,x _i,Dim }；Representing the modeled output; y (t) represents the actual running output of the unit; all individuals are ordered according to the ascending order of the fitness value, and the sequence label is marked as SortIndex;

step two: the fixed population proportion of an original Sparrow Search Algorithm (SSA) is improved, namely the proportion of discoverers, the proportion of detectors and the warning threshold value used for updating the discoverers are changed into parameters which change adaptively, and the corresponding calculation formula is (31);

wherein: pp represents the finder ratio; sp represents the proportion of the inspector; ST denotes an alert threshold; the angle marks min and max represent the upper limit and the lower limit of the corresponding measured values; the three parameters are adaptively changed along with the iteration times, so that the effects of increasing the searching range in the early stage and quickly converging in the later stage are achieved;

step three: after individual ranking, the individuals ranked in the first pp×np as discoverers update the location according to formula (32);

wherein:and R is ₂ Is of the type (0, 1)]Random numbers of (a); k is a random number obeying normal distribution; r is R ₂ <The update formula of ST part is composed of->Modified to->The search range of a finder is enlarged, and the capability of an algorithm for solving the problem that an optimal solution is not at an origin is improved;

step four: the remaining individuals other than the finder are defined as followers, and the location update formula is (33);

Wherein:for the current worst individuals；/>Is globally optimal; rand { -1,1} represents a random value of-1 or 1;

step five: after the discoverer and the follower complete the location update, all individuals have a probability of ST as a prober, and sp×np individuals in the random extraction population are then updated as the prober:

wherein:the optimal individual of the current iteration; ζ is defined as the step control parameter, which is a random number subject to a normal distribution with a mean of 0 and a variance of 1; r is a member of the group [ 1,1 ]]Random numbers of (a); f (f) _i And f _w Respectively corresponding to the current optimal individual and the current worst individual fitness value; ζ is a small constant to avoid a denominator of 0;

step six: calculating the fitness of the updated individual, selecting the minimum value of the current fitness to compare with the global optimal fitness, and updating the global optimal individual and the fitness if the current optimal fitness value is smaller than the global optimal fitness value; otherwise, the global optimal continuous times are not updated _n Adding 1;

step seven: the detection bee strategy of the artificial bee colony algorithm is combined, whether the global optimal continuous non-updated times reach a threshold value is judged, and if l _n >l _max The current global optimum and fitness are reserved, and then all individuals are updated according to a formula (29); otherwise, directly entering the next step;

Step eight: if the iteration number reaches the upper limit L or the optimizing precision meets the requirement, the searching process is ended, otherwise, the next iteration is carried out in the second step.

4. Based on the ash box modeling scheme provided in the step S3, an accurate mathematical model is established for the wet running mode of the supercritical unit, and in the step S4, the effectiveness of the provided modeling scheme is verified and analyzed by means of a simulation experiment, and the specific process is as follows:

s4.1: firstly, the identification of model parameters is completed based on field operation data to obtain a complete wet model, 3000 groups are taken as training data sets for determining the model parameters according to actual operation data of a certain 350MW supercritical unit, actual operation conditions in a rated load range of 20% of the unit is covered, sampling intervals of the data are 5S, unknown parameters in the model are identified through a designed T-S fuzzy identification method, and fitting degree of model output and actual output is verified;

s4.2: based on the training model obtained in the step S4.1, verifying the universality of the model, selecting another 800 groups of field data under the rated load of 20% as a test data set, and judging whether the training model has the universality or not through the fitting effect;

s4.3: further verifying the performance of the ISSA on model parameter identification, replacing the conclusion part of the T-S fuzzy identification method with SSA and gray wolf optimization, performing a comparison experiment with the ISSA, and quantifying the identification result through performance indexes.