CN102682336B - Method for optimizing design on number of regulating stage nozzles of steam turbine based on improved genetic algorithm - Google Patents

Abstract

The invention specifically relates to a method for optimizing the design on the number of regulating stage nozzles of a steam turbine based on an improved genetic algorithm. The method disclosed by the invention aims at optimizing the number of the regulating stage nozzles of the steam turbine under multiple load points, so that a unit can stably run under different loads, and the nozzles can constitute more valve points as far as possible, thereby allowing the damper loss to be minimum and the intra-regulating-stage efficiency to be maximum. The method mainly comprises the following steps of: based on the improved genetic algorithm, determining the optimal nozzle number combination, the regulating-stage rear flow, the downstream pressure of each valve and the air flow force which can be achieved through outputting a load point in a situation that the deviation value Y between actual flow and theoretical flow is minimum: and through improved genetic codes and a fitness function, carrying out a genetic algorithm operation, and then outputting the optimal nozzle number combination achieved in the situation that the deviation value Y between the actual flow and the theoretical flow is minimum. The method disclosed by the invention can improve the speed of an optimization process and the accuracy of optimization results.

Description

Control Stage of Steam Turbine number of nozzle design optimization method based on improved genetic algorithms method

Technical field

The present invention relates to a kind of Control Stage of Steam Turbine number of nozzle design optimization method.

Background technology

Steam turbine is a kind ofly to take steam as power, the energy of steam is changed into the rotating machinery of mechanical work, is widely used in modern large generating system.As the typical process energy, the not storability of electric energy makes power of motor depend on to a great extent user's power consumption.Therefore steam turbine must often be adjusted its power, so that power of motor keeps balance with the load of extraneous change.Change steam turbine power the most directly, the most effective mode controls its air inflow exactly, carries out Steam Distribution of Steam Turbine.Current existing distribution way of steam has nozzle governing, throttling to join that vapour, sliding pressure are joined vapour, full electricity adjusts " management valve " formula to join vapour and bypass is joined vapour.Wherein, nozzle governing is that nozzle is divided into some groups (each nozzle sets is separate), by the different independent steam supplies of governing stage valve, according to the throttle flow that need to change steam turbine by aperture and the unlatching number of change governing stage valve of load.Only larger in the steam throttling loss of the valve place of standard-sized sheet not under specific load, and that the valve place steam throttling loss of all the other standard-sized sheets is reduced to is minimum, so its efficiency is high, good economy performance, is a kind of modal distribution way of steam.

The start and stop of steam turbine and power adjustments are the variations by control valve opening, thereby change, enter that the steam flow of steam turbine or steam parameter realize.Wherein, change steam turbine throttle flow and be called Steam Distribution of Steam Turbine, be determine steam turbine power main be also to hold most manageable mode.Consider that nozzle governing is little in the admission restriction loss of governing stage valve place, efficiency is high, and existing large steam turbine is mostly adopted and changed in this way steam turbine throttle flow.Control Stage of Steam Turbine static cascade is split into four admission segmental arcs, form successively in the direction of the clock the first vaporium, the second vaporium, the 3rd vaporium, the 4th vaporium, after each vaporium, be connected with several nozzles, vaporium is controlled to guarantee to the independent steam supply of each group nozzle by corresponding governing stage valve, need to realize steam turbine power with unlatching number by the aperture of change governing stage valve regulate according to actual load.

At present, the number of nozzle that in the nozzle of steam turbine device of domestic production, each vaporium is corresponding is normally identical, and mostly continue to use previous experiences data, in the time of can not well mating steam turbine work, basic load point, causes Qi working load district valve opening relatively little.And valve easily causes very large restriction loss in little aperture situation, its internal efficiency ratio is significantly declined, therefore in nozzle device structure design, should guarantee that working load point place governing stage valve keeps standard-sized sheet or full-shut position as far as possible.The working load point of general Steam Turbine can change with electrical network demand, when the given a plurality of load of reality, for making steam turbine reach desired working point, each organizes controlled stage valve on the spray nozzle device that number of nozzle is identical generally can not guarantee standard-sized sheet or full-shut position, thereby causes restriction loss to a certain degree.The conventional load point of current domestic unit is rated power 70%～80%, and its internal efficiency ratio only has 45% left and right, does not meet the themes of the times of current energy-conserving and environment-protective, is seriously restricting the raising of China's Turbo-generator Set economic benefit.

Summary of the invention

The present invention is in order to realize the optimization at multi-loading point tubine advanced technique group number of nozzle, make the unit all can steady operation under different loads, and allow nozzle form as far as possible more valve point, make throttling loss reduction, governing stage internal efficiency supreme good, and then a kind of Control Stage of Steam Turbine number of nozzle design optimization method based on improved genetic algorithms method has been proposed.

The present invention solves the problems of the technologies described above the technical scheme of taking to be: described optimization method is based on following model realization:

Y＝(xgz ₁-Ge ₁) ²+(xgz ₂-Ge ₂) ²+......+(xgz _l-Ge _l) ²，

L is the number of load point, obtains the combination of optimum number of nozzle under given load point: detailed process is as follows based on improved genetic algorithms method,

Step 1, initial population are set: set constraint condition:

First constraint condition: X ₁+ X ₂+ ...+X _n=X _z, X _z=const 2-2

Second constraint condition: X _min≤ X _i≤ X _max, i=1,2 ..., n; X _min=const, X _max=const 2-3

Xi represents i the number of nozzle that valve is corresponding, and const represents constant, adopts floating-point encoding, is [X between code area _min, X _max]

With the matrix of (n-1) * m, can represent initial population:

$\left[\begin{array}{c}{x}_{11},x_{12},...,x_{1(n-1)}\\ x_{21},x_{22},...,x_{2(n-1)}\\ .........................\\ x_{\mathrm{<figure-callout\; id="1"\; label="m"\; filenames="HDA00001640582600021.png"\; state="\{\{state\}\}">m</figure-callout>}1},x_{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="HDA00001640582600021.png"\; state="\{\{state\}\}">m</figure-callout>}2},...,x_{m(n-1)}\end{array}\right],$ x _i′j′∈R ₊，i′＝1，2，...，m，j′＝1，2，...，n-1. 2-4

The individual amount that wherein m representative is encoded, x _{i ' j '}for meeting the random number of second constraint condition, above-mentioned initial population adopts the formal construction of the constraint coding that meets second constraint condition; For body one by one, its each chromosome x _{i ' 1}, x _{i ' 2}, X _{i ' 3}... x _{i ' (n-1)}the nozzle sets number of nozzle X that before being respectively, (n-1) individual control valve is corresponding ₁, X ₂, X ₃... X _(n-1)coding, its corresponding relation is:

X _i′j′＝round(x _i′j′)，i′＝1，2...m，j′＝1，2，...，n-1 2-5

Round represents round, calculates X ₁, X ₂, X ₃... X _(n-1)after, and last number of nozzle calculates by following formula: X _nfor:

X _i′n＝X _z-(X _i′1+X _i′2+...+X _i′(n-1)) 2-7

Element in initial population is chosen at random in coding interval range, because second constraint condition is not well positioned to meet when initial population is encoded, can produce some insignificant individualities and make in cataloged procedure:

X _i′n＞X _max OR X _i′n＜X _min 2-8

By step 2, meet second constraint condition, the individuality that does not meet constraint condition given up in iteration,

Step 2: build the fitness function ObjV calculating based on Control Stage of Steam Turbine variable working condition, by fitness, calculate, realizing individual optimization selects, make in optimum results n nozzle sets number of nozzle also meet second constraint condition definition fitness function to be: ObjV=OBJ_func (Ge simultaneously, Fa, X ₁, X ₂..., X _n),

The mapping relations of this function are: the flow Ge, 2 that inputs to constant load point ⁿthe combination of individual valve opening, wherein valve opening is standard-sized sheet or complete shut-down, valve nozzle group number of nozzle combination X ₁, X ₂, X ₃... X _nwherein nozzle sets number of nozzle combination is by the unit parameter that coding produces, user sets of body one by one of initial population in step 1: the model of steam turbine, governing stage physical dimension, rated pressure and temperature after pressure, rated flow and governing stage after the pressure and temperature of live steam, governing stage, mapping: by valve nozzle number of combinations X ₁, X ₂, X ₃... X _n, thermodynamic parameter, governing stage family curve, geometric parameter and 2 ⁿindividual valve opening combination, obtains 2 by governing stage variable working condition computing method ⁿindividual flow value [Xgz ₁, Xgz ₂... .Xgz2 ⁿ]; Calculate steam turbine flow xgz after governing stage under this load point:

xgz＝Xgz _j 2-9

Xgz wherein _jsatisfy condition:

$|{\mathrm{Xgz}}_j-\mathrm{Ge}|=\min \left(\right|{\mathrm{Xgz}}_1-\mathrm{Ge}|,|{\mathrm{Xgz}}_2-\mathrm{Ge}|,......,|{\mathrm{Xgz}}_{2^n}-\mathrm{Ge}\left|\right),j=\mathrm{1,2},...,2^n,$

Ge is theoretical delivery after governing stage under this load point, to each given load point, all calculates an xgz,

Output: the comprehensive effect of the unit that definition 2-10 characterizes this Nozzle combination under load point operation, Y value is less, illustrates that this Nozzle combination is better,

Y＝(xgz ₁-Ge ₁) ²+(xgz ₂-Ge ₂) ²+......+(xgz _l-Ge ₁) ² 2-10

Finally being expressed as of fitness function:

For qualified individuality: X _min≤ X _n≤ X _max

$\mathrm{ObjV}=\frac{1}{Y}---2-11$

For ineligible individuality: X _n> X _maxoR X _n< X _min, adopt index measure transform (2-11)

Objective function

$\mathrm{ObjV}=\frac{1}{Y}/e^{\mathrm{\&alpha;\&delta;}}---2-12$

In formula 2-12, show not meet its fitness value of Nozzle combination of second constraint reduced e ^{α δ}doubly.

$\mathrm{\&delta;}=\left\{\begin{array}{cc}\frac{X_n-X_{\max }}{X_{\max }},\mathrm{if}& X_n>X_{\max }\\ \frac{X_{\min }-X_n}{X_{\min }},\mathrm{if}& X_n<X_{\min }\end{array}\right.---2-13$

Step 3, complete after step, then carry out selection, intersection, the mutation process of the genetic algorithm based on traditional; When genetic algebra reach end condition N for time, genetic process stops, output meets that actual flow and theoretical delivery deviation value Y this load point of output hour can reach that optimum number of nozzle combines, pressure, air-flow power after flow, each valve after governing stage.

The present invention has following beneficial effect: 1, the improvement of optimized algorithm: in optimizing process, solved problem with equality constraint,, fitness function has been revised meanwhile, greatly improved optimal speed and the accuracy of system;

2, can realize the interface that steam parameter is set, carries out governing stage variable working condition calculating is provided, can be adjusted the family curve curve of level flow.System, according to the deviation of actual flow and theoretical delivery, is constantly optimized to reduce deviation, obtains being applicable to the number of nozzle combination of this unit operation;

3, designer can limit the nozzle sets number of nozzle of every unit, with proof strength requirement.

Accompanying drawing explanation

Fig. 1 is the logic diagram of the Control Stage of Steam Turbine number of nozzle design optimization method based on improved genetic algorithms method, the #6 of Tu2Mou power plant unit number of nozzle Optimal Curve.

Embodiment

Embodiment one: in conjunction with Fig. 1, present embodiment is described, the optimization method of present embodiment is based on following model realization:

Y＝(xgz ₁-Ge ₁) ²+(xgz ₂-Ge ₂) ²+......+(xgz _l-Ge _l) ²，

L is the number of load point, obtains the combination of optimum number of nozzle under given load point: detailed process is as follows based on improved genetic algorithms method,

Step 1, initial population are set: set constraint condition:

First constraint condition: X ₁+ X ₂+ ...+X _n=X _z, X _z=const 2-2

Second constraint condition: X _min≤ X _i≤ X _max, i=1,2 ..., n; X _min=const, X _max=const 2-3

Xi represents i the number of nozzle that valve is corresponding, and const represents constant, adopts floating-point encoding, is [X between code area _min, X _max]

With the matrix of (n-1) * m, can represent initial population:

$\left[\begin{array}{c}{x}_{11},x_{12},...,x_{1(n-1)}\\ x_{21},x_{22},...,x_{2(n-1)}\\ .........................\\ x_{\mathrm{<figure-callout\; id="1"\; label="m"\; filenames="HDA00001640582600021.png"\; state="\{\{state\}\}">m</figure-callout>}1},x_{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="HDA00001640582600021.png"\; state="\{\{state\}\}">m</figure-callout>}2},...,x_{m(n-1)}\end{array}\right],$ x _i′j′∈R ₊，i′＝1，2，...，m，j′＝1，2，...，n-1. 2-4

The individual amount that wherein m representative is encoded, x _{i ' j '}for meeting the random number of second constraint condition, above-mentioned initial population adopts the formal construction of the constraint coding that meets second constraint condition; For body one by one, its each chromosome x _{i ' 1}, x _{i ' 2}, x _{i ' 3}... x _{i ' (n-1)}the nozzle sets number of nozzle X that before being respectively, (n-1) individual control valve is corresponding ₁, X ₂, X ₃... X _(n-1)coding, its corresponding relation is:

X _i′j′＝round(X _i′j′)，i′＝1，2...m，j′＝1，2，...，n-1 2-5

Round represents round, calculates X ₁, X ₂, X ₃... X _(n-1)after, and last number of nozzle calculates by following formula: X _nfor:

X _i′n＝X _z-(X _i′1+X _i′2+...+X _i′(n-1)) 2-7

Element in initial population is chosen at random in coding interval range, because second constraint condition is not well positioned to meet when initial population is encoded, can produce some insignificant individualities and make in cataloged procedure:

X _i′n＞X _max OR X _i′n＜X _min 2-8

By step 2, meet second constraint condition, the individuality that does not meet constraint condition given up in iteration,

Step 2: build the fitness function ObjV calculating based on Control Stage of Steam Turbine variable working condition, by fitness, calculate, realizing individual optimization selects, make in optimum results n nozzle sets number of nozzle also meet second constraint condition definition fitness function to be: ObjV=OBJ_func (Ge simultaneously, Fa, X ₁, X ₂..., X _n),

The mapping relations of this function are: the flow Ge, 2 that inputs to constant load point ⁿthe combination of individual valve opening, wherein valve opening is standard-sized sheet or complete shut-down, valve nozzle group number of nozzle combination X ₁, X ₂, X ₃... X _nwherein nozzle sets number of nozzle combination is by the unit parameter that coding produces, user sets of body one by one of initial population in step 1: the model of steam turbine, governing stage physical dimension, rated pressure and temperature after pressure, rated flow and governing stage after the pressure and temperature of live steam, governing stage, mapping: by valve nozzle number of combinations X ₁, X ₂, X ₃... X _n, thermodynamic parameter, governing stage family curve, geometric parameter and 2 ⁿindividual valve opening combination, obtains 2 by governing stage variable working condition computing method ⁿindividual flow value [Xgz ₁, Xgz ₂... .Xgz2 ⁿ];

Calculate steam turbine flow xgz after governing stage under this load point:

xgz＝Xgz _j 2-9

Xgz wherein _jsatisfy condition:

$|{\mathrm{Xgz}}_j-\mathrm{Ge}|=\min \left(\right|{\mathrm{Xgz}}_1-\mathrm{Ge}|,|{\mathrm{Xgz}}_2-\mathrm{Ge}|,......,|{\mathrm{Xgz}}_{2^n}-\mathrm{Ge}\left|\right),j=\mathrm{1,2},...,2^n,$

Ge is theoretical delivery after governing stage under this load point, to each given load point, all calculates an xgz, output: the comprehensive effect of the unit that definition 2-10 characterizes this Nozzle combination under load point operation, and Y value is less, illustrates that this Nozzle combination is better,

Y＝(xgz ₁-Ge ₁) ²+(xgz ₂-Ge ₂) ²+......+(xgz _l-Ge _l) ² 2-10

Finally being expressed as of fitness function:

For qualified individuality: X _min≤ X _n≤ X _max

$\mathrm{ObjV}=\frac{1}{Y}---2-11$

For ineligible individuality: X _n> X _maxoR X _n< X _min, adopt index measure transform (2-11)

Objective function

$\mathrm{ObjV}=\frac{1}{Y}/e^{\mathrm{\&alpha;\&delta;}}---2-12$

In formula 2-12, show not meet its fitness value of Nozzle combination of second constraint reduced e ^{α δ}doubly.

$\mathrm{\&delta;}=\left\{\begin{array}{cc}\frac{X_n-X_{\max }}{X_{\max }},\mathrm{if}& X_n>X_{\max }\\ \frac{X_{\min }-X_n}{X_{\min }},\mathrm{if}& X_n<X_{\min }\end{array}\right.---2-13$

α is constant coefficient, and target is to make when the Xn calculating surpasses setting threshold 100%, and its fitness value is greater than 1000 times of the lower fitness value that satisfies condition, i.e. δ=1, exp (α) > 1000, now α=6.9078;

Step 3, complete after step, then carry out selection, intersection, the mutation process of the genetic algorithm based on traditional; When genetic algebra reach end condition N for time, genetic process stops, output meets that actual flow and theoretical delivery deviation value Y this load point of output hour can reach that optimum number of nozzle combines, pressure, air-flow power after flow, each valve after governing stage.

For step 3, be specifically described: by the fitness function of establishing in the initial population substitution step 2 of step 1 definition, each individuality all calculates corresponding fitness value:

ObjV ₁，ObjV ₂，...，ObjV _m

Then carry out selection, intersection, mutation process based on traditional genetic algorithm, produce the first generation new population identical with previous generation individual amount, by in the fitness function of establishing in first generation new population substitution step 2, each individuality all calculates corresponding fitness value again:

ObjV ₁，ObjV ₂，...，ObjV _m

Then carry out selection, intersection, mutation process based on traditional genetic algorithm, produce the second generation new population identical with previous generation individual amount, the like, until obtain N-Generation new population, wherein N is predefined genetic algebra, genetic process stops.

Embodiment two: the governing stage variable working condition computing method described in the step 2 of present embodiment are:

The theoretical delivery of step 2 one, each valve of calculating governing stage: G _i=G _eξ _k, G wherein _kfor the theoretical delivery of load point, G _efor the rated flow of steam turbine, ξ _kfor account for the number percent of rated power in load point tubine operate power, k=1,2 ... l, the number that k is working load point;

Step 2 two, by each valve nozzle number and corresponding valve opening thereof, calculate actual flow G _kj:

$G_{\mathrm{kj}}=\frac{0.648A_{\mathrm{nk}}}{\sqrt{\frac{p_{0k}}{{\mathrm{\&rho;}}_{0k}}}}\frac{{\mathrm{\&beta;}}_{1k}}{\frac{p_2}{p_{0\mathrm{<figure-callout\; id="2"\; label="k\; p"\; filenames="HDA00001640582600021.png"\; state="\{\{state\}\}">k</figure-callout>}}}}{p}_{}{}_2=A_k{\mathrm{\&mu;}}_k{p}_2---(1-1),$ In formula: the aperture array configuration that j is valve, β _1kbe the governing stage throughput ratio of k nozzle sets, A _nkbe each nozzle throat sectional area sum of k nozzle sets, p _0kbe the pressure (before being the nozzle sets that variable valve is corresponding) after k variable valve valve, ρ _0kbe the density (before being the nozzle sets that variable valve is corresponding) after k variable valve valve,

p _1kbe the nozzle back pressure of k nozzle sets, p ₂for the pressure in steam chest after governing stage;

In actual computation process, p _1kwith p ₂value not etc., nozzle sets flow equation is changed into:

$G_{\mathrm{kj}}=\frac{0.648A_{\mathrm{nk}}}{\sqrt{\frac{p_{0k}}{{\mathrm{\&rho;}}_{0k}}}}\frac{{\mathrm{\&beta;}}_{2k}{\mathrm{\&lambda;}}_k}{\frac{p_2}{p_{0k}}}{p}_2---(1-2),$

In formula: β _2kfor the throughput ratio of governing stage, λ _kit is the function of pressure ratio before and after governing stage;

Step 2 three, by dichotomy, calculate p ₂: pressure p after steps A, a given nozzle ₁; Step B, according to heating power computing formula, calculate the enthalpy h of nozzle exit steam ₁, steam speed c ₁relative velocity w with movable vane inlet steam ₁, then by formula (1-1), calculate the rate of discharge G of a nozzle steam _n; Step C, then suppose the pressure of movable vane outlet steam, i.e. pressure p after governing stage ₂; Step D, by heating power computing formula, draw the enthalpy h of movable vane exit steam ₂, density p ₂, outlet steam relative velocity w ₂with absolute velocity c ₂, then calculate by formula (1-1) the flow G that movable vane exports steam _b; If step e G _b≠ G _n, be back to step C and continue to calculate, until obtain G _b=G _n, draw pressure p after governing stage ₂;

Step 2 four, according to pressure p after the governing stage drawing in step 3 ₂be brought in formula (1-2) and calculate actual flow G with parameter _ij.In whole optimizing process, utilized the variable working condition of governing stage to calculate: to take into full account the model of steam turbine, the impact of the thermal parameter of the thermal parameter of the physical dimension of governing stage, main steam (temperature, pressure, enthalpy), governing stage outlet steam on governing stage steam flow, utilize the deviation of actual flow and theoretical delivery as the index of tolerance Nozzle combination quality, fully improved the accuracy of optimum results; Other implementation steps are identical with embodiment one.

Embodiment three:

One, the conventional working load point of the given steam-turbine unit of user, sliding pressure operation curve and governing stage valve nozzle sum, the span of single-nozzle group number of nozzle and the governing stage family curve that governing stage variable working condition calculates.

Two, optimize number of nozzle: if to the given all load point of user, can under the nozzle sets condition of optimal design, find corresponding variable valve to open (standard-sized sheet) combination, reach optimized object.In analytical calculation, calculated flow rate while usining valve wide open or full cut-off and give departure degree between the theoretical delivery of constant load as tolerance foundation, in process, take into full account the working time of different conventional load point, the running frequency of each load point is introduced in the mode of similar weighting.If departure degree is minimum, result is optimum, and the number of nozzle combination of optimization is optimum combination.

Specific implementation process is as follows: one group of number of nozzle combination of first random generation, calculate calculated flow rate in this case and the departure degree of theoretical delivery, then number of nozzle is combined into row iteration, find out under the given nozzle total number of user range of condition, the minimum departure degree of calculated flow rate and theoretical delivery, its corresponding number of nozzle combination is optimum solution.

(1) calculate theoretical flow: according to the actual operation parameters of Steam Turbine and sliding pressure operation law curve, by given load point, can be calculated each theoretical delivery Ge of its correspondence _i.Investigate actual power plant ruuning situation, its conventional working load point can be more than six, thus given i=1 in the present invention, 2 ... 6;

(2) by each valve nozzle number and corresponding valve opening thereof, according to rating curve calculated flow rate Xgz _ij, according to the given number of nozzle scope of user, produce one group of random number of nozzle combination, suppose all optimum states in standard-sized sheet or full cut-off of variable valve.The situation that does not exist a valve list to open due to actual conditions, thus the combination of each valve opening have 2^4-4=12 kind (j=1,2 ... 12).To each valve opening combination calculated flow rate G _ij.；

(3) ask under given number of nozzle combination condition the total departure of calculated flow rate and theoretical delivery: consider the running frequency of each load point, be weighted processing.

Y＝(xgz ₁-Ge ₁) ²+(xgz ₂-Ge ₂) ²+......+(xgz _l-Ge _l) ²

(4) to number of nozzle, combination utilizes genetic algorithm to carry out iterative computation, to each group combination, can calculate the total departure of a calculated flow rate and theoretical delivery.Find out the total departure of all minimums, its corresponding number of nozzle combination is optimum number of nozzle combination.

Three, algorithm is realized: genetic algorithm and improve and optimizate method: genetic algorithm is that to take natural selection and theory of heredity be basis, the efficient global optimization approach that survival of the fittest rule in biological evolution process is combined with the colony chromosomal random information exchanging mechanism in inside.Genetic algorithm has been abandoned traditional way of search, and the evolutionary process of simulation organic sphere adopts artificial evolution's mode to carry out random optimization search to object space.It regards the feasible solution in problem as body one by one in colony, and each coding is weaved into the form of symbol string, simulate the evolutionary process of Darwinian heredity selection and natural selection, colony is carried out to the operation (heredity, intersection, variation) based on hereditary repeatedly.According to the target fitness function of intended target, each individuality is evaluated, evolutionary rule according to the survival of the fittest, the survival of the fittest, constantly obtain optimum colony, in overall parallel search mode, search the optimum individual of optimizing in colony, in the hope of the optimum solution satisfying condition simultaneously.

The general process of genetic algorithm is: initial population (coding) is set, calculate fitness, select, intersect, variation, produce new population, recalculate fitness, successively loop iteration, until iterations reaches initial set value, heredity finishes, and last population obtaining is optimum population in generation, and the individuality in population is optimum individual.

(1) number of nozzle coding, variable load operation parameter and other parameters are determined

A. number of nozzle is encoded

In genetic algorithm, amount to be optimized is generally input in optimization system as random coded, but because optimized amount is often as actual production, operating parameter, there is actual physical meaning, can be subject to the restriction of extraneous all factors, value has certain constraint, can not directly bring as coding individual in initial population, need to carry out suitable conversion.So the requirement arranging for population is that each individuality must be the feasible solution of this optimization problem, optimizes and is just of practical significance like this.

In this example, the nozzle sets number of nozzle of optimizing not is that any value is all of practical significance.On the one hand, in Design of Steam Turbine manufacture process, / 4th segmental arcs of four corresponding governing stages of control valve difference, because the governing stage total area is fixed, each jet size is also setting value, and nozzle is evenly distributed on circumference, this just requires the number of nozzle in each segmental arc can not too much can not be very little.On the other hand, the nozzle of steam turbine is comprised of first stage stator blades grid and first order movable vane, governing stage (the steam turbine first order) has not only played acting effect, also played the guide functions to main steam, if therefore a certain segmental arc top nozzle number very little, does not have such effect, number is too many, and segmental arc can not be held any more.

Generally, when nozzle of steam turbine group designs, total number of nozzle is definite value, and each nozzle sets number of nozzle has minimum and maximum value.Constraint condition is:

First constraint condition: X ₁+ X ₂+ ...+X _n=X _z, X _z=const 2-2

Second constraint condition: X _min≤ X _i≤ X _max, i=1,2 ..., n; X _min=const, X _max=const 2-3

Genetic algorithm, due to its randomness, is difficult to solve the constraint of above-mentioned two equatioies, but can solve constraint condition by suitable conversion

Initial population adopts floating-point encoding, is [X between code area _min, X _max]

$\left[\begin{array}{c}{x}_{11},x_{12},...,x_{1(n-1)}\\ x_{21},x_{22},...,x_{2(n-1)}\\ .........................\\ {\mathrm{<figure-callout\; id="1"\; label="x\; m"\; filenames="HDA00001640582600021.png"\; state="\{\{state\}\}">x</figure-callout>}}_m,{\mathrm{<figure-callout\; id="2"\; label="x\; m"\; filenames="HDA00001640582600021.png"\; state="\{\{state\}\}">x</figure-callout>}}_m,...,x_{m(n-1)}\end{array}\right],$ x _i′j′∈R ₊，i′＝1，2，...，m，j′＝1，2，...，n-1. 2-4

The individual amount that wherein m representative is encoded, x _{i ' j '}for meeting the random number of second constraint condition, above-mentioned initial population adopts the formal construction of the constraint coding that meets second constraint condition; For body one by one, its each chromosome x _{i ' 1}, x _{i ' 2}, x _{i ' 3}... x _{i ' (n-1)}the nozzle sets number of nozzle X that before being respectively, (n-1) individual control valve is corresponding ₁, X ₂, X ₃... X _(n-1)coding, its corresponding relation is:

X _i′j′＝round(x _i′j′)，i′＝1，2...m，j′＝1，2，...，n-1 2-5

Round represents round, calculates X ₁, X ₂, X ₃... X _(n-1)after, and last number of nozzle calculates by following formula: X _nfor:

X _i′n＝X _z-(X _i′1+X _i′2+...+X _i′(n-1)) 2-7

Element in initial population is chosen at random in coding interval range, because second constraint condition is not well positioned to meet when initial population is encoded, can produce some insignificant individualities and make in cataloged procedure:

X _i′n＞X _max OR X _i′n＜X _min 2-8

These individualities are not actual meeting the demands, if but reject artificially these individualities, and can destroy the diversity of population, run counter to the optimization principles of genetic algorithm, therefore the constraint that need to take other modes to solve formula 2-3, concrete grammar will be introduced in (2) part.

(2) the fitness function design of calculating based on Control Stage of Steam Turbine variable working condition

In genetic algorithm, fitness function is for distinguishing the standard of individual in population quality, is unique foundation of carrying out natural selection.Fitness function characterizes a virtual physical environment, and the individuality in population is multiplied in virtual environment.The individuality wherein conforming will be retained, and maladjusted individuality will be eliminated.Fitness has quantized individual adaptedness in virtual environment, by calculating in individual substitution fitness function.

In this example, the target of optimization is to make under the combination of optimum nozzle sets number of nozzle, and the restriction loss of governing stage is minimum.Restriction loss is because steam turbine control valve in intake process is not exclusively opened and caused, and under the condition of control valve standard-sized sheet or complete shut-down, restriction loss is minimum.If there is the combination of certain valve nozzle group number of nozzle, making each valve is that 1 or 0 time energy is at given load point place operation (the flow Xgz calculating in aperture _iequal it to the flow Ge of constant load _i, illustrate that this Nozzle combination is optimum combination.In fact, so perfect Nozzle combination does not exist, the flow calculating and must have certain difference to flow corresponding to constant load.But if difference is less, also can illustrate that this Nozzle combination can reach preferably combination.In unit actual motion, the difference that a little makes up above-mentioned flow can be opened or close to control valve, and the restriction loss of generation is less.

Consider variable load operation, a kind of Nozzle combination will can move preferably in a plurality of load point, the restriction loss producing is less, and valve opening is tending towards 1 or 0 as far as possible, needs to propose a kind of overall target and weighs the effect of this number of nozzle under these load point operations.

By above-mentioned analysis, the structure of fitness function can be substantially definite.This fitness function is as input by a plurality of governing stage correlation parameters such as codings, flow after governing stage is calculated in variable working condition by each load point that constantly iterates in calculating, by corresponding rule, will calculate flow and given throughput ratio again, obtain the best Nozzle combination of effect under comprehensive each load point.If fitness function is:

ObjV＝OBJ_func(Ge，Fa，X ₁，X ₂，X ₃，X ₄，others)

This function does not have explicit mathematic(al) representation, elaborates the mapping relations of this function below:

Input to the flow Ge, 2 of constant load point ⁿindividual valve opening combination, wherein valve opening is standard-sized sheet or complete shut-down, valve nozzle group number of nozzle combination X1, X2, ..., Xn, wherein nozzle sets number of nozzle combination is by the unit parameter that coding produces, user sets of body (model of steam turbine, governing stage physical dimension, after the pressure and temperature of live steam, governing stage after pressure, rated flow, governing stage rated pressure and temperature) one by one of initial population in step 1

Mapping: by valve nozzle number of combinations X1, X2 ..., Xn, above-mentioned middle thermodynamic parameter, geometric parameter and 2 ⁿindividual valve opening combination, obtains 2 by governing stage variable working condition computing method ⁿindividual flow value [Xgz ₁, Xgz ₂... .Xgz2 ⁿ];

Calculate steam turbine flow xgz after governing stage under this load point:

xgz＝Xgz _j 2-9

Xgz wherein _jsatisfy condition:

$|{\mathrm{Xgz}}_j-\mathrm{Ge}|=\min \left(\right|{\mathrm{Xgz}}_1-\mathrm{Ge}|,|{\mathrm{Xgz}}_2-\mathrm{Ge}|,......,|{\mathrm{Xgz}}_{2^n}-\mathrm{Ge}\left|\right),j=\mathrm{1,2},...,2^n,$

Ge is theoretical delivery after governing stage under this load point, to each given load point, all calculates an xgz, output: the comprehensive effect of the unit that definition 2-10 characterizes this Nozzle combination under load point operation, and Y value is less, illustrates that this Nozzle combination is better,

Y＝(xgz ₁-Ge ₁) ²+(xgz ₂-Ge ₂) ²+......+(xgz _l-Ge _l) ² 2-10

In genetic algorithm, fitness function is larger, is genetic to follow-on probability larger, and the value of fitness function is non-negative, and Y value is less is in this example that we more wish to obtain.So Y is not the final expression of fitness function.On the other hand, (1) constraint of Chinese style 2-3 is not solved in coding, if be optimized according to said process, the Nozzle combination that does not more meet constraint condition 2-3 is also updated in calculating and may be genetic in the next generation along with calculating larger fitness, causes optimization mistake.Therefore we need to, when fitness function defines, adopt suitable conversion that nonsensical individuality is eliminated gradually in iteration, to retain qualified individuality.

Finally being expressed as of fitness function:

For qualified individuality: X _min≤ X _n≤ X _max

$\mathrm{ObjV}=\frac{1}{Y}---2-11$

For ineligible individuality: X _n> X _maxoR X _n< X _min, adopt index measure transform (2-11)

Objective function

$\mathrm{ObjV}=\frac{1}{Y}/e^{\mathrm{\&alpha;\&delta;}}---2-12$

In formula 2-12, show not meet its fitness value of Nozzle combination of second constraint reduced e ^{α δ}doubly.

$\mathrm{\&delta;}=\left\{\begin{array}{cc}\frac{X_n-X_{\max }}{X_{\max }},\mathrm{if}& X_n>X_{\max }\\ \frac{X_{\min }-X_n}{X_{\min }},\mathrm{if}& X_n<X_{\min }\end{array}\right.---2-13$

Above formula explanation, X _nget over off-design value, fitness value does not have the minification of off-design value larger relatively.α is coefficient of reduction, before optimization, sets.We dwindle 1000 times by design fitness value when X4 off-design is worth 100% when experiment.α=6.9078 now.Like this, the individuality of reduced fitness value will be eliminated gradually in genetic iteration process, reach the object that realizes constraint condition 2-3.

(3) select, intersect and variation

A. select. select with certain probability selection defect individual, to form new population in operation Cong Jiu colony, to breed, obtain individuality of future generation.Individual selected probability is relevant with fitness value, and ideal adaptation degree is higher, and selected probability is larger.Adopt roulette method herein, i.e. the selection strategy based on fitness ratio, individual selected probability is:

$p_i=\frac{F_i}{{\mathrm{\&Sigma;}}_j^N{F}_j}---2-14$

Fi is this individual fitness value,

for all ideal adaptation degree value sums.

B. interlace operation.Owing to adopting floating-point encoding herein, therefore choosing arithmetic, corresponding Crossover Strategy intersects, be to produce two new individualities by two individual linear combinations.Suppose at two individual X _a, X _bbetween carry out arithmetic intersection, by two new individualities that produce after arithmetical operation, be:

X′ _A＝aX _B+(1-a)X _A 2-15

X′ _B＝aX _A+(1-a)X _B

Wherein a is a parameter, and a can be a constant, can be also the variable being determined by evolutionary generation.Adopting herein a is set is a constant 0.8.

C. variation.Variation can improve the local search ability of genetic algorithm and can maintain the diversity of population.Conventional Mutation Strategy has basic bit mutation, evenly variation, border variation etc.Thermoelectricity load distribution problem is complicated nonlinear problem, can there is good effect to approach optimum solution, but be difficult to determinacy and must search optimum solution, in order to address this problem, adopted Gaussian approximation variation herein, can improve the local search ability of genetic algorithm to focussing search region, and have certain probability to make algorithm jump out local minimum point.During concrete operations, with meeting average, be original parameter value, variance is that a random number of the normal distribution of original parameter value square is replaced original genic value, and from the characteristic of normal distribution, Gaussian mutation is also near the regional area original individuality of focussing search.Concrete formula is as follows:

$f\left(x\right)=\frac{1}{\sqrt{2\mathrm{\&pi;}}{q}^2}{e}^{-\frac{{(x-q)}^2}{2q^2}}---2-16$

Wherein q is original genic value.

(4) genetic iteration is optimized number of nozzle

Initial population substitution fitness function is also selected, is produced new population after crossover and mutation according to fitness value, and be again updated to fitness function and produce third generation population according to above-mentioned rule, the like.When genetic algebra reaches setting value, heredity finishes, and the population finally obtaining is optimum population, i.e. optimum number of nozzle combination.By optimum number of nozzle, carry out governing stage variable working condition calculating, obtain the characterisitic parameter such as pressure after efficiency, air-flow power, governing stage.

For step 3, be specifically described: by the fitness function of establishing in the initial population substitution step 2 of step 1 definition, each individuality all calculates corresponding fitness value:

ObjV ₁，ObjV ₂，...，ObjV _m

Then carry out selection, intersection, mutation process based on traditional genetic algorithm, produce the first generation new population identical with previous generation individual amount, by in the fitness function of establishing in first generation new population substitution step 2, each individuality all calculates corresponding fitness value again:

ObjV ₁，ObjV ₂，...，ObjV _m

Then carry out selection, intersection, mutation process based on traditional genetic algorithm, produce the second generation new population identical with previous generation individual amount, the like, until obtain N-Generation new population, wherein N is predefined genetic algebra, genetic process stops.

Concrete quantification effect: the test #6 of Yi Mou power plant unit is control group, at steam turbine geometric parameter, rating curve is all in identical situation, take actual nozzle of steam turbine number for one group is input parameter, it is input that another group adopts new Nozzle combination of number of nozzle optimization method optimization, calculate final steam turbine under given some loads two kinds of nozzle sets and working condition.As shown in Figure 2: the Y value of original Nozzle combination is 96, its physical significance for the deviation of theoretical flow and actual flow be 96t/h.In actual motion, if allow unit in given load place stable operation, valve opening need to have a larger variation.And the result being optimized by genetic algorithm shows, the value of Y approaches 50 and is optimized to 8.7 from initial, and the difference of final theoretical delivery and actual flow only has 8.7t/h, and in actual motion, the variation of valve opening is very little, restriction loss is little, and above-mentioned experiment parameter used is referring to subordinate list one.

Subordinate list one: number of nozzle Optimal Parameters

Claims (2)

1. the Control Stage of Steam Turbine number of nozzle design optimization method based on improved genetic algorithms method, is characterized in that described optimization method is based on following model realization:

Y=(xgz ₁-Ge ₁) ²+(xgz ₂-Ge ₂) ²+......+(xgz _l-Ge _l) ²，

L is the number of load point, obtains the combination of optimum number of nozzle under given load point: detailed process is as follows based on improved genetic algorithms method,

Step 1, initial population are set: set constraint condition:

First constraint condition: X ₁+ X ₂+ ...+X _n=X _z, X _z=const 2 2

Second constraint condition: X _min≤ X _i≤ X _max, i=1,2 ..., n; X _min=const, X _max=const 2 3Xi represent i the number of nozzle that valve is corresponding, const represents constant, adopts floating-point encoding, is [X between code area _min, X _max] with the matrix of (n-1) * m, can represent initial population:

$\left[\begin{array}{c}{x}_{11},x_{12},...,x_{1(n-1)}\\ x_{21},x_{22},...,x_{2(n-1)}\\ .........................\\ x_{m1},x_{m2},...,x_{m(n-1)}\end{array}\right],x_{i^{\&prime;}{j}^{\&prime;}}\&Element;R_{+},i^{\&prime;}=\mathrm{1,2},...,m,j^{\&prime;}=\mathrm{1,2},...,n-1.---2-4$

The individual amount that wherein m representative is encoded, x _{i ' j '}for meeting the random number of second constraint condition, above-mentioned initial population adopts the formal construction of the constraint coding that meets second constraint condition; For body one by one, its each chromosome x _{i ' 1,}x _{i ' 2,}x _{i ' 3}... x _{i ' (n-1)}(n 1) nozzle sets number of nozzle X that individual control valve is corresponding before being respectively _1,x _2,x ₃... X _(n-1)coding, its corresponding relation is:

X _i′j′=round(x _i′j′),i′=1,2...m,j′=1,2,...,n-1 2-5

Round represents round, calculates X _1,x _2,x ₃... X _(n-1)after, and last number of nozzle calculates by following formula: X _nfor:

X _i′n=X _z-(X _i′1+X _i′2+...+X _i′(n-1)) 2-7

Element in initial population is chosen at random in coding interval range, because second constraint condition is not well positioned to meet when initial population is encoded, can produce some insignificant individualities and make in cataloged procedure:

X _i′n>X _max OR X _i′n<X _min 2-8

By step 2, meet second constraint condition, the individuality that does not meet constraint condition given up in iteration,

Step 2: build the fitness function ObjV calculating based on Control Stage of Steam Turbine variable working condition, by fitness, calculate, realizing individual optimization selects, make in optimum results n nozzle sets number of nozzle also meet second constraint condition definition fitness function to be: ObjV=OBJ_func (Ge, Fa, X1 simultaneously, X2, ..., Xn)

The mapping relations of this function are: the flow Ge, 2 that inputs to constant load point ⁿthe combination of individual valve opening, wherein valve opening is standard-sized sheet or complete shut-down, valve nozzle group number of nozzle combination X _1,x _2,x ₃... X _nwherein nozzle sets number of nozzle combination is by the unit parameter that coding produces, user sets of body one by one of initial population in step 1: the model of steam turbine, governing stage physical dimension, rated pressure and temperature after pressure, rated flow and governing stage after the pressure and temperature of live steam, governing stage

Mapping: by valve nozzle number of combinations X _1,x _2,x ₃... X _n, thermodynamic parameter, governing stage family curve, geometric parameter and 2 ⁿindividual valve opening combination, obtains 2 by governing stage variable working condition computing method ⁿindividual flow value [Xgz _1,xgz ₂.Xgz2 ⁿ]; Calculate steam turbine flow xgz after governing stage under this load point:

xgz=Xgz _j 2-9

Xgz wherein _jsatisfy condition:

$|{\mathrm{Xgz}}_j-\mathrm{Ge}|=\min \left(\right|{\mathrm{Xgz}}_1-\mathrm{Ge}|,|{\mathrm{Xgz}}_2-\mathrm{Ge}|,......|{\mathrm{Xgz}}_{2^n}-\mathrm{Ge}\left|\right),j=\mathrm{1,2},...,2^n,$

Ge is theoretical delivery after governing stage under this load point, to each given load point, all calculates an xgz,

Output: the comprehensive effect of the unit that definition 2-10 characterizes this Nozzle combination under load point operation, Y value is less, illustrates that this Nozzle combination is better,

Y=(xgz ₁-Ge ₁) ²+(xgz ₂-Ge ₂) ²+......+(xgz _l-Ge _l) ² 2-10

Finally being expressed as of fitness function:

For qualified individuality: X _min≤ X _n≤ X _max

$\mathrm{ObjV}=\frac{1}{Y}---2-11$

For ineligible individuality: X _n>X _maxoR X _n<X _min, adopt index measure transform (2-11) objective function

$\mathrm{ObjV}=\frac{1}{Y}/e^{\mathrm{\&alpha;\&delta;}}---2-12$

In formula 2-12, show not meet its fitness value of Nozzle combination of second constraint reduced e ^{α δ}doubly;

$\mathrm{\&delta;}=\left\{\begin{array}{cc}\frac{X_n-X_{\max }}{X_{\max }},\mathrm{if}& X_n>X_{\max }\\ \frac{X_{\min }-X_n}{X_{\min }},\mathrm{if}& X_n<X_{\min }\end{array}\right.---2-13$

Step 3, complete after step, then carry out selection, intersection, the mutation process of the genetic algorithm based on traditional; When genetic algebra reach end condition N for time, genetic process stops, output meets that actual flow and theoretical delivery deviation value Y this load point of output hour can reach that optimum number of nozzle combines, pressure, air-flow power after flow, each valve after governing stage.

2. the Control Stage of Steam Turbine number of nozzle design optimization method based on improved genetic algorithms method according to claim 1, is characterized in that the governing stage variable working condition computing method described in step 2 are: step 2 one, calculate the theoretical delivery of each valve of governing stage: G _i=G _eξ _k, G wherein _kfor the theoretical delivery of load point, G _efor the rated flow of steam turbine, ξ _kfor account for the number percent of rated power in load point tubine operate power, k=1,2 ... l, the number that k is working load point;

Step 2 two, by each valve nozzle number and corresponding valve opening thereof, calculate actual flow G _kj:

$G_{\mathrm{kj}}=\frac{0.648A_{\mathrm{nk}}}{\sqrt{\frac{p_{0k}}{{\mathrm{\&rho;}}_{0k}}}}\frac{{\mathrm{\&beta;}}_{1k}}{\frac{p_2}{p_{0k}}}{p}_2=A_k{\mathrm{\&mu;}}_k{p}_2---(1-1),$ In formula: the aperture array configuration that j is valve, β _1k

Be the governing stage throughput ratio of k nozzle sets, A _nkbe each nozzle throat sectional area sum of k nozzle sets, p _0kbe the pressure (before being the nozzle sets that variable valve is corresponding) after k variable valve valve, ρ _0kbe the density (before being the nozzle sets that variable valve is corresponding) after k variable valve valve,

p _1kbe the nozzle back pressure of k nozzle sets, p2 is the pressure in steam chest after governing stage;

In actual computation process, the value of p1k and p2 not etc., does not change nozzle sets flow equation into:

$G_{\mathrm{kj}}=\frac{0.648A_{\mathrm{nk}}}{\sqrt{\frac{p_{0k}}{{\mathrm{\&rho;}}_{0k}}}}\frac{{\mathrm{\&beta;}}_{2k}{\mathrm{\&lambda;}}_k}{\frac{p_2}{p_{0k}}}{p}_2---(1-2),$

In formula: β _2kfor the throughput ratio of governing stage, λ _kit is the function of pressure ratio before and after governing stage;

Step 2 three, by dichotomy, calculate p ₂: pressure p after steps A, a given nozzle ₁; Step B, according to heating power computing formula, calculate the enthalpy h of nozzle exit steam ₁, steam speed c ₁relative velocity w with movable vane inlet steam ₁, then by formula (1-1), calculate the rate of discharge G of a nozzle steam _n; Step C, then suppose the pressure of movable vane outlet steam, i.e. pressure p after governing stage ₂; Step D, by heating power computing formula, draw the enthalpy h of movable vane exit steam ₂, density p ₂, outlet steam relative velocity w ₂with absolute velocity c ₂, then calculate by formula (1-1) the flow G that movable vane exports steam _b; If step e G _b≠ G _n, be back to step C and continue to calculate, until obtain G _b=G _n, draw pressure p after governing stage ₂;

Step 2 four, according to pressure p after the governing stage drawing in step 3 ₂be brought in formula (1-2) and calculate actual flow G with parameter _ij.

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