CN109408895A - Fired power generating unit coordinates system mixing optimizing modeling method under depth peak regulation state - Google Patents

Abstract

Coordinate system the invention discloses fired power generating unit under depth peak regulation state and mix optimizing modeling method, the nonlinear model structure of system is established according to law of conservation, identification of Model Parameters is carried out by hybrid algorithm for optimization.Nonlinear Modeling can preferably reflect operational process of the extra-supercritical unit under depth peak regulation state when dynamic characteristic acute variation, hybrid algorithm for optimization combines limited teaching particle swarm algorithm, generation set searching algorithm, Polygon Algorithm, the area of space of set of feasible solution is quickly determined by limited teaching particle swarm algorithm, again using generation set searching algorithm, with relatively large step length searching optimal solution, if search failure uses Polygon Algorithm again.The problem of generating set based algorithm Premature Convergence, both can avoid using hybrid algorithm for optimization, also can solve the problem of Polygon Algorithm is not suitable for the optimization aim with noise, reduce the number of iterations of Polygon Algorithm, accelerate calculating speed.

Description

Fired power generating unit coordinates system mixing optimizing modeling method under depth peak regulation state

Technical field

The invention belongs to Thermal power engneerings and automatic control technology field, and in particular to thermal motor under depth peak regulation state Group coordination system mixes optimizing modeling method.

Background technique

For fired power generating unit, traditional modeling pattern is that basis does step response experiment acquisition input and output number at the scene According to the structure of model being determined according to step response characteristic, then by certain method, such as least square method, area-method, population Algorithm etc. recognizes the parameter of model, obtains the transfer function model of object.The model being fitted by this method belongs to line Property model, there is good precision in certain condition range, but unit is in Wide Range, especially in depth peak regulation Under state, when underload section is run, violent variation often occurs unit for the dynamic characteristic of object, and linear model is difficult to standard At this moment really description real process needs to establish nonlinear model by the actual characteristic for analyzing object, how to establish model, and The parameter of accurate identification model is the key that solve the problems, such as.

Summary of the invention

The technical problem to be solved by the present invention is to solve the above shortcomings of the prior art and to provide fiery under depth peak regulation state Electric unit cooperative system mixes optimizing modeling method.

To realize the above-mentioned technical purpose, the technical scheme adopted by the invention is as follows:

Fired power generating unit coordinates system mixing optimizing modeling method under depth peak regulation state, according to the conservation of mass, the conservation of energy Law establishes the differential equation of unit cooperative system, and is calculated by limited teaching particle swarm algorithm, generation set based algorithm, complex The hybrid algorithm for optimization that method combines recognizes model parameter, and the nonlinear model established can be well reflected the operation of unit Characteristic.

The modeling of the coordination system can be divided into pulverized coal preparation system modeling, boiler part modeling and steam turbine part modeling three Part.

Pulverized coal preparation system can be described with delay and inertial element, pure delay link are as follows:

In formula, u_B(kg/s) is instructed for fuel quantity；r′_BEnter coal amount (kg/s) for coal pulverizer；τ is delay time (s)；S is multiple Parameter.

It is available according to mass conservation law:

In formula, r_BFor the coal amount (kg/s) for actually entering burner hearth；M is coal amount (kg) in coal pulverizer.

According to coal pulverizer characteristic, the coal amount for actually entering burner hearth be can be written as:

In formula, c_BFor the basic power factor of coal pulverizer；f_HFor coal grindability correction factor；f_WFor moisture content of coal correction factor；f_R For fineness of pulverized coal correction factor；c₀Represent the inertia time (s) of powder processed.

Simultaneous (1) (2) (3), the transmission function of pulverized coal preparation system are as follows:

Boiler part modeling is according to Boiler of Ultra-supercritical Unit feature, when unit dry state is run, by economizer, water-cooling wall, The heating surfaces such as steam-water separator and superheater regard an entirety as.

Fluid properties are as lumped parameter at selection steam-water separator, because separator temperature (enthalpy) and coal-water ratio are close Correlation, while the variation of separator pressure reflection unit load.

When set steady is safely operated, ignore the influence of desuperheating water, available:

q_{M, sm}=q_{M, fw} (5)

In formula, q_{M, sm}For the confluent (kg/s) for entering economizer；q_{M, fw}For total confluent (kg/s).

Related simplify and hypothesis is made to entire boiler heat-transfer process:

Fume side: (1) ignore the axial heat conduction between working medium, flue gas and tube wall；(2) boiler absorbs heat and fuel heat release It measures directly proportional；(3) ignore the dynamic changing process of fume side operating condition；(4) flue gas heat release is uniform.

Boiler side: (1) fluid behaviour on heat pipe cross section is uniform；(2) pressure p of steam-water separator is chosen_mAnd vapour Separator steam enthalpy h_mIt is approximately the p in model_mAnd h_m。

According to mass-conservation equation and energy conservation equation, have:

Q₁=k₁r_B (8)

In formula, s₁、s₂For dynamic parameter；ρ_mFor separator outlet vapour density (kg/m³)；q_{M, st}For main steam mass flow (kg/s)；h_mFor steam-water separator steam enthalpy (kJ/kg)；c_jFor heating section metal specific heat [kJ/ (kgK)]；m_jFor heating section gold Belong to quality (kg)；T_jFor heating section metal temperature (DEG C)；h_fwFor water supply enthalpy (kJ/kg)；h_stFor main steam enthalpy (kJ/kg)；Q₁For Boiler recepts the caloric (kJ/s)；k₁Gain (kJ/kg) is absorbed heat for working medium.

According to fume side assume (4) it is found thatT in formula_jmFor tube wall temperature (DEG C) at steam-water separator, and T_jm≈T_m, T in formula_mFor steam-water separator Temperature of Working (DEG C).

By formula (6) and formula (7) to p_m、h_mPartial differential calculating is done, available:

Wherein,

Joint type (9) and (10), can obtain:

Wherein,

According to pressure difference and flow equation:

In formula,For the initial volume flow (m of steam in superheater pipeline³/s)；Q₀The heat absorbed for steam through piping It measures (kJ)；Δ p=p_m-p_stThe pressure difference (MPa) generated for steam through piping, p_stFor main vapour pressure (MPa)；z₁, z₂For coefficient, It is related with the resistance of ducting, the specific heats of gases.

According toWherein v₀It is steam initially than volume (m³/ kg),For steam initial mass stream in superheater It measures (kg/s), formula (13) can be converted into

Wherein,Reflect coal-water ratio, h_mIts variation can be well reflected；p_mN can be reacted well_eVariation, Q₀With Unit load N_eIt is directly proportional；v₀=v (p_m, h_m).For simplified model, ignore h_mInfluence, have:

Δ p=g (p_m) (15)

Wherein, g () is a kind of functional relation.

Main steam flow equation is as follows:

In formula, ρ_stFor steam turbine inlet steam density (kg/m³)；μ_tFor steam turbine pitch aperture (%)；α is steam condition ginseng Number.

Again because of ρ_st=ρ (p_st, h_st), so formula (16) can be write as:

q_{M, st}=u_tf(p_st, h_st) (17)

Ignore h_stInfluence, therefore have:

q_{M, st}=u_tf(p_st) (18)

Wherein, f () is a kind of functional relation.

The hypothesis of steam turbine part: heat regenerative system (1) is regarded to a part of turbine system as；(2) ignore oxygen-eliminating device and Working medium quality, energy loss in condenser；(3) regard high, medium and low cylinder pressure Steam Turbine as an entirety；(4) it is used to ignore steam turbine Property and delay；(5) heat absorption of reheated steam is incorporated to steam turbine gain k₂Middle amendment；(6) steam turbine efficiency is considered as when unit operates normally It is constant.

Power expression:

N_e=k₂(q_{M, st}h_st-q_{M, st}h_fw) (19)

Wherein,

h_fw=h (p_m) (20)

L=l (r_B) (21)

k₂=k (r_B) (22)

Wherein, h (), l (), k () are a kind of functional relation.

It is as follows by above available ultra-supercritical once-through boiler unit nonlinear model of analysis:

Wherein,

Further, the static parameter coordinated in mission nonlinear model structure can be by steady state data and non-linear Regression analysis is sought:

Wherein, subscript * represents variable and is in stable state.

Further, the Identifying Dynamical Parameters coordinated in mission nonlinear model structure use hybrid algorithm for optimization, I.e. comprehensive limited teaching particle swarm algorithm generates the advantages of set searching algorithm, Polygon Algorithm, carries out optimizing to model parameter Identification, optimization problem can be expressed as following formula:

In formula, f () is objective function, and A, b are respectively the coefficient matrix and constant vector of linear inequality constraint, and x is Optimized variable, g () are nonlinear complementary problem function, l₁, l₂Respectively superior vector up-and-down boundary constraint condition vector.

Further, the limited teaching particle swarm algorithm in the hybrid algorithm for optimization includes that tutorial section is mutually learned with particle Part is practised, process is as follows:

(1) initialization population makes it meet boundary constraint and linear restriction

(2) tutorial section

Calculate entire population average particleIt finds out optimal adaptation angle value particle and marks it for teacher's particleCalculating speed vectorRandom number r ∈ [0,1], T '_FIt is taken as 1 or 2 at random.

(3) the maximum feasible speed for not violating constraint is calculated

Renewal speed vector according to the following formula

Coefficient φ_jCalculation method it is as follows:

Determination may violate the velocity vector of linear restriction:

Wherein a_kFor the row k of matrix A.

It calculates along velocity vectorThe maximum coefficient of reduction in directionTo ensure not violate linear restriction:

Final speed vector value is as follows:

Update current particle position:

Particle mutually learns part are as follows:

For particle each in populationRandomly choose another particle

It repeats step (3) and determines maximum feasible velocity vectorIf update after particle fitness more preferably if receive, otherwise Keep original position constant.

Generation set searching algorithm basic thought in the hybrid algorithm for optimization is to pass through x^t+α^td^tUpdate current iteration X in step^t。α^tFor step-length, d^tFor direction vector, G^t, H^tFor direction set.Direction vector d^tBelong to two different set G^t, H^t, G^tDirection vector comprising solution space can be expanded, to guarantee ability of searching optimum, H^tComprising according to certain rule Other search direction vectors of selection, to acceleration figure of merit convergence rate.

Key step is as follows:

(1)G^tGeneration

If a. for optimal particle y_gNormal linear constrains non-ε active constraint, then G^t=D, D are coordinate direction set (mark Quasi- base vector and its opposite direction vector).ε active constraint is defined as:

I (x, ε)={ k ∈ { 1,2 ..., m }: b_k-a_kx≤ε} (33)

Wherein ε=α^t。

If b. for optimal particle y_gOnly there are ε active constraints for normal linear constraint, then define matrix Y, column vector For the row vector of the positive linear restriction of ε in corresponding linear constraint matrix A, to Y^TQR decomposition is carried out, orthogonal matrix Q is obtained, is solved Matrix Y^TRight inverse matrix J, Q and J column form G^t。

If c. for optimal particle y_gThere is ε active constraint with boundary constraint in normal linear constraint, by calculating Q in b, and Increase corresponding positive and negative unit norm base vector e_j(e_{J, k}=0, k ≠ j).

(2)H^tGeneration

If a. for optimal particle y_gNormal linear constrains non-ε active constraint, then H^t=D_TPPSO∪D_COM, wherein D_TPPSO The direction vector of optimal solution, D are successfully updated for the limited teaching particle swarm algorithm of last time_COMFor final step Polygon Algorithm Determining possibility descent direction.

B. if normal linear constraint is there are ε active constraint, except both direction set in a, also need to consider ε actively it is linear about The outer normal direction U of beam^tAnd their sum

H^t=D_TPPSO∪D_COM∪U^t∪{d_c}。

C. every step generates set based algorithm, need to be to solution space P^tCalculate extreme barrier function:

P^t={ x ∈ Rⁿ: x=y_g+α^tD, d ∈ G^t∪H^t, Ax≤b, l₁≤x≤l₂, g (x)≤0 } and (34)

Polygon Algorithm basic thought in the hybrid algorithm for optimization is with N_sIn the set of feasible solution S of a solution, than Compared with solution x worst in solution each in S_w, utilize the center x of remaining solution_cTo x_wCarry out reflection calculating, formula x_r=x_c+ρ(x_c- x_w),ρ is reflection coefficient, is usually taken to be 1.3.If new reflection solution

x_rIt is that simultaneously target function value is better than x to feasible solution_w, then x_rSubstitute x_wIf x_rIt is that infeasible solution or target function value be not excellent Change, then x_rTo center x_cMovement, above-mentioned reflection and contraction process can be repeated up to worst solution improvement or set S is punctured into a bit.

Further, the calculation method of the hybrid algorithm for optimization is as follows:

Step a: initialization, including population initialization and generation set searching algorithm initialization；

The population initialization includes: that N is randomly generated_PA feasible solution particleInitial velocityInitialize each The optimum solution of particleAnd population optimal particle y_g, initialize limited teaching particle swarm algorithm continuously unsuccessful iteration time Numerical value nui_P；

The generation set searching algorithm initialization includes: by disaggregation P⁰It is set as empty set, set D_TPPSOIt is initialized as last The successful solution of the limited teaching particle swarm algorithm of one step, D_COMThe feasible direction of search is determined by Polygon Algorithm, initialization generates set The continuous unsuccessful the number of iterations nui of algorithm_G。

Step b: mixing optimizing successively includes particle group hunting, generates Set-search and complex search；

The particle group hunting are as follows:

Based on current solution particleCalculate extreme barrier function f_nh:(35)；

1. updating single particle optimal solution value: ifThen

2. if population optimal value reduces, evenEnable nui_P=0；

3. calculatingAnd it is stored in D_TPPSOIn；

4. updating step-length

5. emptying set S in Polygon Algorithm^t；

6. Population Regeneration optimum particle position:

7. otherwise population search step fails, nui is enabled_P=nui_P+1；

The generation Set-search are as follows:

If nui_P≥nui_Pm, while α^t≥α_min, execute and generate Set-search, if x_GSSFor direction of search disaggregation P^tIn it is optimal Solution,

1. if f_nh(x_GSS) < f_nh(y_g), i.e. spanning set step search success updates optimal solution value y_g=x_GSS, enable nui_G= 0；

2. emptying set S in Polygon Algorithm^t；

3. increasing step-size in search α^t+1=min { 2 α^t, α_max}；

4. otherwise spanning set search failure, enables nui_G=nui_G+1；

5. reducing step-size in search

The complex search are as follows:

If nui_G≥nui_GmOr α^t< α_min, then complex search is executed, comprising:

1. initializing set of feasible solution S^t=P^t∪{y_g}；

2. if set of feasible solution S^tThe number N of middle solution_S< 2n, then in S^tIt is middle that 2n-N best in population search process is added_S A solution；

3. otherwise showing that population step and spanning set step are failed, disaggregation S is set^t=Z^t-1, Z^t-1For back The disaggregation of complex search process；

4. from S^tStart using Polygon Algorithm N_COMIteration reflection, Z^tIndicate the disaggregation that Polygon Algorithm returns, x_rIt is multiple Close the solution that shape search last time reflection generates, x_COM, x_wRespectively disaggregation Z^tMiddle optimal solution and worst solution；To standardize direction x_COM-x_w, x_COM-x_rWith meet f_nh(x_COM) < f_nh(y_g) direction vector x_COM-y_gIt is added to D_COMIn；

5. if f_nh(x_COM) < f_nh(y_g) then update optimal solution y_g=x_COMWith step-size in search α^t+1=min | | x_COM-y_g| |, max{α^t, α_min}}。

Step c: particle rapidity and current disaggregation are updated.

The update particle rapidity and current disaggregation are as follows:

1. generating new velocity vector to each particleAnd update each particle position

2. the number of iterations becomes t+1 from t and return step b is computed repeatedly.

The present invention has the advantage that compared with existing modeling method

1, the characteristic of analysis unit operation, establishing nonlinear model can more accurately reflect unit under depth peak regulation state The virtual condition of operation；

2, by reasonably assuming that and simplifying, it is easy to establish model；

3, more accurate to the identification of model parameter by hybrid algorithm for optimization.

Detailed description of the invention

Fig. 1 is the structural schematic diagram that the embodiment of the present invention controlled device simplifies.

Specific embodiment

The embodiment of the present invention is described in further detail below in conjunction with attached drawing.

Fig. 1 is the boiler-turbine structure chart that certain extra-supercritical unit simplifies, according to law of conservation, by reasonably false If establishing the nonlinear model of unit cooperative system with simplification:

Wherein,

According to the steady-state equation of system:

In conjunction with steam turbine power formula, can obtain:

Construct Optimization goal function:

Wherein, Δ p_st, Δ N_e, Δ T_sepRespectively main vapour pressure, unit in fact hair power, separator temperature actual value with The difference of model calculation value, p_st0, N_e0, T_sep0The respectively real stable state initial value for sending out power, separator temperature of main vapour pressure, unit.

By hybrid algorithm for optimization, optimization algorithm parameter is as follows:

1 hybrid optimization algorithm parameter of table

It is as follows that identification obtains dynamic parameter:

c₀=247, c₁=293760, c₂=53477, d₁=529, d₂=1835, τ=15

f(p_st)=41.2p_st+9.8

The model established is verified, the results showed that, error is up to 3.1%, minimum 0.5%, can be accurate The operation characteristic of description system.

The above is only the preferred embodiment of the present invention, protection scope of the present invention is not limited merely to above-described embodiment, All technical solutions belonged under thinking of the present invention all belong to the scope of protection of the present invention.It should be pointed out that for the art For those of ordinary skill, several improvements and modifications without departing from the principles of the present invention should be regarded as protection of the invention Range.

Claims (8)

1. fired power generating unit coordinates system mixing optimizing modeling method under depth peak regulation state, it is characterised in that: the following steps are included:

Step 1: according to law of conservation and machine unit characteristic, the nonlinear model structure of coordination system is established；

Step 2: by hybrid algorithm for optimization, model parameter is recognized.

2. fired power generating unit coordinates system mixing optimizing modeling method under depth peak regulation state according to claim 1, special Sign is: the nonlinear model structure for coordinating system described in step 1 is to pass through vacation according to the laws such as the conservation of mass, the conservation of energy If structure is as follows with foundation is simplified:

Wherein,

In above-mentioned formula: X,Respectively the state variable matrix of system and the differential matrix of state variable, r_B,p_m,h_mIt is respectively real Border enters the coal amount (kg/s) of burner hearth, the pressure (MPa) of steam-water separator, steam-water separator steam enthalpy (kJ/kg)；U, Y difference For the input variable matrix and output variable matrix of system, u_B,q_m,fw,u_tRespectively fuel quantity instructs (kg/s), total confluent (kg/s), steam turbine pitch aperture (%), p_st,h_m,N_eRespectively main vapour pressure (MPa), steam-water separator steam enthalpy (kJ/kg), Unit sends out power (MW) in fact；A, B (X), C (X), D (X) are respectively sytem matrix, input matrix, output matrix, transition matrix, k₁,k₂,l,h_fwFor static parameter, h_fwFor water supply enthalpy (kJ/kg), τ, c₀,c₁,c₂,d₁,d₂For dynamic parameter, τ prolongs for pulverized coal preparation system Slow time (s), e^-τsDelay link is represented, f (), g () are functional relation.

3. fired power generating unit coordinates system mixing optimizing modeling method under depth peak regulation state according to claim 2, special Sign is: the static parameter in the nonlinear model structure of the coordination system is asked by steady state data and nonlinear regression analysis It takes:

Wherein, subscript * represents variable and is in stable state, h_stFor main steam enthalpy (kJ/kg).

4. fired power generating unit coordinates system mixing optimizing modeling method under depth peak regulation state according to claim 2, special Sign is: Identifying Dynamical Parameters in the nonlinear model structure of the coordination system use hybrid algorithm for optimization, that is, integrate by Limit teaching particle swarm algorithm generates set searching algorithm, Polygon Algorithm to model parameter progress optimizing identification, and optimization problem can To be expressed as following formula:

In formula, f () is objective function, and A, b are respectively the coefficient matrix and constant vector of linear inequality constraint, and x is optimization Variable, g () are nonlinear complementary problem function, l₁,l₂Respectively superior vector up-and-down boundary constraint condition vector.

5. fired power generating unit coordinates system mixing optimizing modeling method under depth peak regulation state according to claim 4, special Sign is: the calculation method of the hybrid algorithm for optimization is as follows:

Step a: initialization, including population initialization and generation set searching algorithm initialization；

Step b: mixing optimizing successively includes particle group hunting, generates Set-search and complex search；

Step c: particle rapidity and current disaggregation are updated.

6. fired power generating unit coordinates system mixing optimizing modeling method under depth peak regulation state according to claim 5, special Sign is: the initialization of population described in step a includes: that N is randomly generated_PA feasible solution particleInitial velocityInitialization is every The optimum solution of one particleAnd population optimal particle y_g, it is continuously unsuccessful to initialize limited teaching particle swarm algorithm The number of iterations value nui_P；

The generation set searching algorithm initialization includes: by disaggregation P⁰It is set as empty set, set D_TPPSOIt is initialized as final step The successful solution of limited teaching particle swarm algorithm, D_COMThe feasible direction of search is determined by Polygon Algorithm, initialization generates set based algorithm Continuous unsuccessful the number of iterations nui_G。

7. fired power generating unit coordinates system mixing optimizing modeling method under depth peak regulation state according to claim 5, special Sign is: particle group hunting described in step b are as follows:

Based on current solution particleCalculate extreme barrier function f_nh:(35)；

1. updating single particle optimal solution value: ifThen

2. if population optimal value reduces, evenEnable nui_P=0；

3. calculatingAnd it is stored in D_TPPSOIn；

4. updating step-length

5. emptying set S in Polygon Algorithm^t；

6. Population Regeneration optimum particle position:

7. otherwise population search step fails, nui is enabled_P=nui_P+1；

The generation Set-search are as follows:

If nui_P≥nui_Pm, while α^t≥α_min, execute and generate Set-search, if x_GSSFor direction of search disaggregation P^tMiddle optimal solution,

1. if f_nh(x_GSS) < f_nh(y_g), i.e. spanning set step search success updates optimal solution value y_g=x_GSS, enable nui_G=0；

2. emptying set S in Polygon Algorithm^t；

3. increasing step-size in search α^t+1=min { 2 α^t,α_max}；

4. otherwise spanning set search failure, enables nui_G=nui_G+1；

5. reducing step-size in search

The complex search are as follows:

If nui_G≥nui_GmOr α^t< α_min, then complex search is executed, comprising:

1. initializing set of feasible solution S^t=P^t∪{y_g}；

2. if set of feasible solution S^tThe number N of middle solution_S< 2n, then in S^tIt is middle that 2n-N best in population search process is added_SA solution；

3. otherwise showing that population step and spanning set step are failed, disaggregation S is set^t=Z^t-1, Z^t-1For back complex The disaggregation of search process；

4. from S^tStart using Polygon Algorithm N_COMIteration reflection, Z^tIndicate the disaggregation that Polygon Algorithm returns, x_rFor complex The solution that search last time reflection generates, x_COM,x_wRespectively disaggregation Z^tMiddle optimal solution and worst solution；To standardize direction x_COM- x_w,x_COM-x_rWith meet f_nh(x_COM) < f_nh(y_g) direction vector x_COM-y_gIt is added to D_COMIn；

5. if f_nh(x_COM) < f_nh(y_g) then update optimal solution y_g=x_COMWith step-size in search α^t+1=min | | x_COM-y_g||,max {α^t,α_min}}。

8. fired power generating unit coordinates system mixing optimizing modeling method under depth peak regulation state according to claim 5, special Sign is: update particle rapidity and current disaggregation described in step c are as follows:

1. generating new velocity vector to each particleAnd update each particle position

2. the number of iterations becomes t+1 from t and return step b is computed repeatedly.