CN102678192B

CN102678192B - Optimized design method for nozzle number of nozzle sets considering turbine actual operation binding

Info

Publication number: CN102678192B
Application number: CN201210168056.9A
Authority: CN
Inventors: 刘金福; 万杰; 付云峰; 李飞; 张怀鹏; 张可浩; 游尔胜; 王一丰; 蔡鼎; 于达仁
Original assignee: Harbin Institute of Technology Shenzhen
Current assignee: Nanjing Power Horizon Information Technology Co ltd
Priority date: 2012-05-28
Filing date: 2012-05-28
Publication date: 2014-12-31
Anticipated expiration: 2032-05-28
Also published as: CN102678192A

Abstract

The nozzle number optimization design method of each nozzle group considering the actual operation constraints of the steam turbine relates to a nozzle number optimization design method of the steam turbine. The present invention aims at the problem that under the conditions of multiple common working load points of the existing units, the small opening of the valve at some of the working load points causes relatively large throttling loss and reduces the relative internal efficiency. Construct the nozzle number optimization model; calculate the actual flow rate of each given load point; calculate the theoretical flow rate of each given load point; construct the constraint conditions of the nozzle number optimization model; calculate the actual flow rate and the given load point based on the genetic algorithm theory The combination of the optimal number of nozzles corresponding to the minimum comprehensive deviation degree Y of the theoretical flow rate. When the unit reaches each load point, each valve of the control stage can be fully open or fully closed, and the throttling loss of the steam turbine control stage is minimized, and the optimal combination of the number of valve nozzles is optimized to make the unit Has the best economy.

Description

Optimal Design Method of Nozzle Number for Each Nozzle Group Considering the Actual Operating Constraints of Steam Turbine

技术领域 technical field

本发明涉及一种汽轮机的喷嘴数目优化设计方法。The invention relates to an optimal design method for the number of nozzles of a steam turbine.

背景技术 Background technique

汽轮机是一种以蒸汽为动力，将蒸汽的能量转化成机械功的旋转机械，是世界上最重要的原动机之一，在电厂、工业生产、舰船等行业有着极其广泛的应用。因此，对汽轮机进行优化改造在提高经济效益和节约能源方面都有很大的实际应用价值。A steam turbine is a rotating machine powered by steam and converts the energy of steam into mechanical work. It is one of the most important prime movers in the world and is widely used in power plants, industrial production, ships and other industries. Therefore, optimizing and transforming steam turbines has great practical application value in improving economic benefits and saving energy.

汽轮机的启停和功率的变化是通过调节阀的开度的变化，从而改变进入汽轮机的蒸汽流量或蒸汽参数来实现的。目前已有的配汽方式有喷嘴配汽、节流配汽、滑压配汽、全电调“阀门管理”式配汽和旁通配汽。其中喷嘴配汽是调节级的静叶栅被分隔为几个进气弧段，每个进气弧段由一定数目的喷嘴组成，不同的调节级阀门对各组喷嘴单独供汽，按照负荷的需要通过改变调节级阀门的开度和开启数目来改变汽轮机的进汽量。由于喷嘴配汽在调节级阀门处进汽节流损失小，效率高，它是应用最广泛的一种调节方式。现有大功率汽轮机大多采用这种方式改变汽轮机进汽量。已知各阀门在不全开的情况下会造成很大的节流损失，为减少汽轮机调节级的节流损失，应尽量保证各阀门全开或全闭。当实际给定多个负荷时，为达到所要求的工作点，相应的阀门一般不能保证全开或全闭状态，会造成很大的节流损失，造成汽轮机长期低效率运行，浪费了大量有效热能，使发电成本增加。国内机组的常用负荷点为额定功率的70％～80％左右，为减少甚至消除节流损失，我们设想根据先验的常用工作负荷点，对调节级各阀门对应的喷嘴数目进行优化设计，由此保证各阀门全开或全闭时能够组合出更多的常用工作负荷点，适应机组的经济运行。在优化设计过程中，考虑汽轮机的实际运行约束条件，对优化结果在实际工作中的应用具有重要的意义。汽轮机时常是在变负荷条件下运行，而在实际运行中，不同常用负荷点的运行频率不尽相同，有的负荷点运行的概率较高，有的负荷点运行概率相对较低，将各负荷点的运行频率作为约束之一；机组在实际运行中主蒸汽的压力一般是按照滑压曲线设定，汽轮机调门全开(或保持适当开度不变)，由锅炉调节主汽流量和压力(汽温基本保持不变)来调节负荷，这就使得汽轮机的调节级前主气流量和压力不为恒值，在喷嘴组设计中，加入滑压运行曲线，因此可以在单阀运行下提高调节级效率，可以进一步提高优化效果。具体方法则是在输入主蒸汽压力时将滑压曲线制成查表函数，根据机组不同的负荷点，得出相应的主蒸汽压力。将滑压运行方式作为约束二。考虑上述两种约束条件，按实际工作负荷来设计出汽轮机调节级最优阀门喷嘴数目组合，在更接近实际运行条件的基础上能够有效地提高汽轮机的综合效率，创造经济效益。The start and stop of the steam turbine and the change of power are realized by changing the opening degree of the regulating valve, thereby changing the steam flow rate or steam parameters entering the steam turbine. At present, the existing steam distribution methods include nozzle steam distribution, throttling steam distribution, sliding pressure steam distribution, full electric regulation "valve management" steam distribution and bypass steam distribution. Among them, the nozzle steam distribution is the adjustment stage, and the stationary blade cascade is divided into several intake arc sections, each intake arc section is composed of a certain number of nozzles, and different adjustment stage valves supply steam to each group of nozzles separately, according to the load It is necessary to change the steam intake of the steam turbine by changing the opening degree and opening number of the regulating stage valve. Because the nozzle steam distribution has small throttling loss and high efficiency at the regulating stage valve, it is the most widely used regulating method. Most of the existing high-power steam turbines use this method to change the steam intake of the steam turbine. It is known that each valve will cause a large throttling loss if it is not fully opened. In order to reduce the throttling loss of the regulating stage of the steam turbine, it is necessary to ensure that each valve is fully opened or fully closed. When multiple loads are actually given, in order to achieve the required operating point, the corresponding valves generally cannot be guaranteed to be fully open or fully closed, which will cause a large throttling loss, resulting in long-term low-efficiency operation of the steam turbine, wasting a lot of effective Thermal energy increases the cost of power generation. The common load point of the domestic unit is about 70% to 80% of the rated power. In order to reduce or even eliminate the throttling loss, we imagine that the number of nozzles corresponding to each valve of the regulating stage is optimally designed according to the prior common work load point. This ensures that when each valve is fully open or fully closed, more common working load points can be combined to adapt to the economical operation of the unit. In the optimization design process, considering the actual operating constraints of the steam turbine is of great significance to the application of the optimization results in actual work. Steam turbines often operate under variable load conditions, but in actual operation, the operating frequency of different commonly used load points is not the same, some load points have a higher probability of operation, and some load points have a relatively lower probability of operation, the load The operating frequency of the point is used as one of the constraints; the pressure of the main steam in the actual operation of the unit is generally set according to the sliding pressure curve, the steam turbine is fully opened (or the appropriate opening is kept unchanged), and the boiler adjusts the main steam flow and pressure ( The steam temperature remains basically unchanged) to adjust the load, which makes the main air flow and pressure before the regulating stage of the steam turbine not a constant value. In the design of the nozzle group, a sliding pressure operation curve is added, so the regulation can be improved under single valve operation. Level efficiency can further improve the optimization effect. The specific method is to make the sliding pressure curve into a look-up table function when the main steam pressure is input, and obtain the corresponding main steam pressure according to the different load points of the unit. The sliding pressure operation mode is taken as the second constraint. Considering the above two constraint conditions, the optimal number combination of valves and nozzles of the regulating stage of the steam turbine is designed according to the actual workload, which can effectively improve the overall efficiency of the steam turbine and create economic benefits on the basis of being closer to the actual operating conditions.

发明内容 Contents of the invention

本发明针对现有机组在多个常用工作负荷点条件下，对其中某些工作负荷点阀门开度小造成较大节流损失，相对内效率降低的问题，在考虑多个负荷点工作时长的概率和汽轮机滑压运行方式的实际运行约束条件下，提出了一种对汽轮机调节级喷嘴组的喷嘴数目进行优化的方法。The present invention aims at the problems of large throttling loss caused by the small valve opening of some of the working load points under the conditions of multiple common working load points of the existing unit, and the relative internal efficiency is reduced. Considering the long working hours of multiple load points Under the actual operating constraints of the probability and sliding pressure operation mode of the steam turbine, a method for optimizing the number of nozzles in the regulating stage nozzle group of the steam turbine is proposed.

本发明为解决上述技术问题采取的技术方案是：本发明所述方法是按照如下步骤来实现的：The technical scheme that the present invention takes for solving the problems of the technologies described above is: the method of the present invention is realized according to the following steps:

步骤一、构建喷嘴数目优化模型：Step 1: Construct the nozzle number optimization model:

Y＝W₁(xgz₁-Ge₁)²+W₂(xgz₂-Ge₂)²+......+W_l(xgz_l-Ge_l)² (2-10)Y＝W ₁ (xgz ₁ -Ge ₁ ) ² +W ₂ (xgz ₂ -Ge ₂ ) ² +...+W _l (xgz _l -Ge _l ) ² (2-10)

W₁、W₂......W_l表示各个负荷点运行时间百分比；W ₁ , W ₂ ...... W _l represent the percentage of running time of each load point;

xgz₁、xgz₂......xgz_l表示各个给定负荷点的实际流量；xgz ₁ , xgz ₂ ...... xgz _l represent the actual flow of each given load point;

Ge₁、Ge₂......Ge_l表示各个给定负荷点的理论流量；Ge ₁ , Ge ₂ ...... Ge _l represent the theoretical flow of each given load point;

实际流量与理论流量的综合偏离程度用Y表示；The comprehensive deviation degree between the actual flow and the theoretical flow is represented by Y;

步骤二、计算各个给定负荷点的实际流量：Step 2. Calculate the actual flow at each given load point:

由各阀门喷嘴数目及其对应的阀门开度计算1......l个给定负荷点的实际流量(与给定负荷点无关)：Calculate the actual flow of 1...l given load points from the number of nozzles of each valve and their corresponding valve openings (it has nothing to do with the given load point):

${xgz xgz}_{kj kj} = = \frac{0.648 0.648 {A A}_{nk nk}}{\sqrt{\frac{{p p}_{00 k k}}{{ρ ρ}_{00 k k}}}} \frac{{β β}_{11 k k}}{\frac{{p p}_{22}}{{p p}_{00 k k}}} {p p}_{22} = = {A A}_{k k} {μ μ}_{k k} {p p}_{22} - - - - - - ((11 - - 11))$

式中：j为阀门的开度组合形式，β_1k为第k个喷嘴组的调节级流量比，A_nk为第k个喷嘴组各个喷嘴喉部截面积之和，p_0k为第k个调节阀阀后的压力(即调节阀对应的喷嘴组前)，ρ_0k为第k个调节阀阀后的密度(即调节阀对应的喷嘴组前)， p_1k为第k个喷嘴组的喷嘴背压，p₂为调节级后汽室中的压力；In the formula: j is the opening combination form of the valve, β _1k is the flow ratio of the adjustment stage of the kth nozzle group, A _nk is the sum of the throat cross-sectional area of each nozzle of the kth nozzle group, p _0k is the kth adjustment The pressure behind the valve (that is, in front of the nozzle group corresponding to the regulating valve), _ρ0k is the density behind the valve of the kth regulating valve (that is, in front of the nozzle group corresponding to the regulating valve), p _1k is the nozzle back pressure of the kth nozzle group, p ₂ is the pressure in the steam chamber after the regulating stage;

在实际计算过程中，p_1k与p₂的值不等，将喷嘴组流量方程改为：In the actual calculation process, the values of p _1k and p ₂ are not equal, so the flow equation of the nozzle group is changed to:

${xgz xgz}_{kj kj}^{' '} = = \frac{0.648 0.648 {A A}_{nk nk}}{\sqrt{\frac{{p p}_{00 k k}}{{ρ ρ}_{00 k k}}}} \frac{{β β}_{22 k k} {λ λ}_{k k}}{\frac{{p p}_{22}}{{p p}_{00 k k}}} {p p}_{22} - - - - - - ((11 - - 22)),,$

式中：β_2k为调节级的流量比，λ_k是调节级前后压力比的函数；In the formula: β _2k is the flow ratio of the regulating stage, and λ _k is the function of the pressure ratio before and after the regulating stage;

通过二分法计算p₂：步骤A、给定一个喷嘴后压力p_1k；步骤B、根据热力计算公式计算出喷嘴出口处蒸汽的焓h₁、蒸汽的速度c₁和动叶进口蒸汽的相对速度w₁，再通过公式(1-2)计算出一个喷嘴蒸汽的出口流量G_n；步骤C、然后假设一个动叶出口蒸汽的压力，即调节级后压力p₂；步骤D、通过热力计算公式得出动叶出口处蒸汽的焓h₂、出口处蒸汽的密度ρ₂、出口蒸汽的相对速度w₂和绝对速度c₂，再由公式计算出动叶出口蒸汽的流量G_b；步骤E、若G_b≠G_n，返回至步骤C继续计算，直到得到G_b＝G_n，得出调节级后压力p₂；G_b＝ρ₂w₂A_b，式中：ρ₂——动叶出口实际密度；A_b——动叶出口喉部面积；Calculate p ₂ by the dichotomy method: step A, given a pressure p _1k after a nozzle; step B, calculate the enthalpy h ₁ of the steam at the outlet of the nozzle, the velocity c ₁ of the steam and the relative velocity of the steam at the inlet of the moving blade according to the thermal calculation formula w ₁ , and then calculate the outlet flow G _n of a nozzle steam through the formula (1-2); step C, then assume the pressure of a moving blade outlet steam, that is, the pressure p ₂ after regulating the stage; step D, through the thermal calculation formula Obtain the enthalpy h ₂ of the steam at the outlet of the moving blade, the density ρ ₂ of the steam at the outlet, the relative velocity w ₂ and the absolute velocity c ₂ of the steam at the outlet, and then calculate the flow G _b of the steam at the outlet of the moving blade by the formula; step E, if G _b ≠G _n , return to step C and continue the calculation until G _b =G _n is obtained, and the pressure p ₂ after the regulating stage is obtained; G _b =ρ ₂ w ₂ A _b , where: ρ ₂ ——the actual Density; A _b ——throat area of the rotor blade outlet;

根据二分法计算得出的调节级后压力p₂代入到公式(1-2)中计算出实际流量xgz；According to the dichotomy method, the pressure p ₂ after the regulating stage is substituted into the formula (1-2) to calculate the actual flow rate xgz;

步骤三、计算各个给定负荷点的理论流量：Step 3. Calculate the theoretical flow at each given load point:

Ge_h＝Ge·ξ_h，其中Ge_h为负荷点的理论流量，Ge为汽轮机的额定流量，ξ_h为在负荷点下汽轮机运行功率占额定功率的百分比，h＝1，2，...l，l为工作负荷点的个数；Ge _h ＝Ge·ξ _h , where Ge _h is the theoretical flow at the load point, Ge is the rated flow of the steam turbine, ξ _h is the percentage of the operating power of the steam turbine at the load point to the rated power, h=1, 2,... l, l is the number of workload points;

步骤四、构建喷嘴数目优化模型的约束条件：Step 4. Constraints for constructing the nozzle number optimization model:

X₁+X₂+X₃+X₄＝X_z，X_z＝const (2-2)X ₁ +X ₂ +X ₃ +X ₄ =X _z , X _z =const (2-2)

X_min≤X_i≤X_max，i＝1，2，3，4；X_min＝const，X_max＝const (2-3)X _min ≤X _i ≤X _max , i=1, 2, 3, 4; X _min ＝const, X _max ＝const (2-3)

X₁，X₂，X₃，X₄表示四个喷嘴组的喷嘴数，X_z为总喷嘴数，const表示定值；X ₁ , X ₂ , X ₃ , X ₄ indicate the number of nozzles in the four nozzle groups, X _z is the total number of nozzles, and const indicates a fixed value;

步骤五、基于遗传算法理论求出给定负荷点下使得实际流量与理论流量的综合偏离程度Y最小时对应的最优喷嘴数目的组合，具体过程如下：Step 5. Based on the genetic algorithm theory, calculate the combination of the optimal number of nozzles corresponding to the minimum comprehensive deviation degree Y between the actual flow and the theoretical flow at a given load point. The specific process is as follows:

步骤五(一)、初始种群设定：Step five (1), initial population setting:

采用浮点数编码，编码区间为[X_min，X_max]，Using floating-point encoding, the encoding range is [X _min , X _max ],

$Chrom = [\begin{matrix} x_{11}, x_{12}, x_{13} \\ x_{21}, x_{22}, x_{23} \\ . . . . . . . . . . \\ x_{m 1}, x_{m 2}, x_{m 3} \end{matrix}],$ x_ij∈R₊，i＝1，2，...，m，j＝1，2，3.(2-4) $Chrome = [\begin{matrix} x_{11}, x_{12}, x_{13} \\ x_{twenty one}, x_{twenty two}, x_{twenty three} \\ . . . . . . . . . . \\ x_{m 1}, x_{m 2}, x_{m 3} \end{matrix}],$ x _ij ∈ R ₊ , i=1, 2,..., m, j=1, 2, 3.(2-4)

式中，m代表编码的个体数目；In the formula, m represents the number of individuals encoded;

对于一个个体，其每个染色体x_i1，x_i2，x_i3分别为前三个调节阀门对应的喷嘴组喷嘴数目X₁，X₂，X₃的编码，其对应关系为：For an individual, each of its chromosomes x _i1 , x _i2 , and x _i3 are the codes of the nozzle numbers X ₁ , X ₂ , and X ₃ of the nozzle group corresponding to the first three regulating valves, and the corresponding relationship is:

X_ij＝round(x_ij)，i＝1，2...m，j＝1，2，3(2-5)X _ij = round(x _ij ), i=1, 2...m, j=1, 2, 3(2-5)

round表示四舍五入取整，计算出X₁，X₂，X₃后，X₄为：round means rounding to an integer. After calculating X ₁ , X ₂ , and X ₃ , X ₄ is:

X_i4＝X_z-(X_i1+X_i2+X_i3) (2-7)X _i4 ＝X _z -(X _i1 +X _i2 +X _i3 ) (2-7)

步骤五(二)、构建适应度函数ObjV：通过适应度计算，实现个体的优化选择，同时使优化结果中第4个喷嘴组喷嘴数目满足约束条件(2-3)式，使不满足约束条件的个体(2-8)在迭代中舍弃：Step 5 (2): Build the fitness function ObjV: realize the optimal selection of individuals through fitness calculation, and at the same time make the number of nozzles in the fourth nozzle group in the optimization result satisfy the constraint condition (2-3), and make the constraint condition not satisfied Individuals (2-8) of are discarded in iterations:

X_i4＞X_max ORX_i4＜X_min (2-8)X _i4 > X _max OR X _i4 < X _min (2-8)

设适应度函数为：Let the fitness function be:

ObjV＝OBJ_func(Ge，Fa，X₁，X₂，X₃，X₄，others)ObjV=OBJ_func(Ge, Fa, X ₁ , X ₂ , X ₃ , X ₄ , others)

上述适应度函数没有显式的数学表达式，上述适应度函数的映射关系如下：The above fitness function has no explicit mathematical expression, and the mapping relationship of the above fitness function is as follows:

输入：enter:

1)、所有给定负荷点的流量Ge₁、Ge₂......Ge_l，以及每个负荷点运行时间百分比W₁、W₂......W_l；1), the flow rate Ge ₁ , Ge ₂ ... Ge _l of all given load points, and the operating time percentage W ₁ , W ₂ ... W _l of each load point;

2)、阀门开度(12种0，1组合)：[0000；0011；0101；1001；0110；1100；1010；1110；1101；1011；0111；1111]；2), valve opening (12 kinds of 0, 1 combination): [0000; 0011; 0101; 1001; 0110; 1100; 1010; 1110; 1101; 1011; 0111; 1111];

3)、阀门喷嘴组喷嘴数目组合X₁，X₂，X₃，X₄，通过一个个体的编码产生；3) The nozzle number combinations X ₁ , X ₂ , X ₃ , and X ₄ of the valve nozzle group are generated through an individual code;

4)、变工况计算的热力学参数：4) Thermodynamic parameters calculated under variable working conditions:

喷嘴出口蒸汽流速c₁、动叶进口相对速度w₁、喷嘴出口焓值h₁、绝对速度c₂、动叶出口的相对速度w₂、动叶出口焓值h₂、轮周效率η_u；Nozzle outlet steam velocity c ₁ , rotor blade inlet relative velocity w ₁ , nozzle outlet enthalpy value h _{1 , absolute velocity c 2} , rotor blade outlet relative velocity w ₂ , rotor blade outlet enthalpy value h ₂ , wheel circumference _efficiency η _u ;

调节级特性曲线：μ-ε、λ-ε、Ω_m-ε及η_u-x_a；Adjustment level characteristic curve: μ-ε, λ-ε, Ω _m -ε and η _u -x _a ;

u——动叶的圆周速度；u—circumferential speed of moving blade;

λ——系数， λ—coefficient,

Ω_m——级平均反动度；Ω _m - the average degree of reaction;

ε——级压力比；ε—stage pressure ratio;

η——轮周效率；η——wheel circumference efficiency;

x_a——速比；x _a - speed ratio;

μ——系数， μ—coefficient,

几何参数：各喷嘴喉部截面积A_nk，动叶出口截面积A_b；Geometric parameters: throat sectional area of each nozzle A _nk , rotor blade outlet sectional area A _b ;

滑压运行规律曲线：功率-主蒸汽压力；Sliding pressure operation law curve: power-main steam pressure;

映射：mapping:

1)、通过阀门喷嘴数目组合X₁，X₂，X₃，X₄和变工况计算的热力学参数(c₁、w₁、h₁、c₂、w₂、h₂、η_u)、调节级特性曲线(μ-ε、λ-ε、Ω_m-ε及η-x_a。)、几何参数(各喷嘴喉部截面积A_nk，动叶出口截面积A_b)、滑压运行规律曲线(功率-主蒸汽压力)，再加上12种阀门开度，代入步骤一至四所述的变工况计算函数；1), _the thermodynamic parameters (c ₁ _, w ₁ , h ₁ , c ₂ , w ₂ _, h ₂ , η _u ) _, Adjustment stage characteristic curve (μ-ε, λ-ε, Ω _m -ε and η-x _a .), geometric parameters (each nozzle throat cross-sectional area A _nk , rotor blade outlet cross-sectional area A _b ), sliding pressure operation law Curve (power-main steam pressure), plus 12 kinds of valve openings, substituted into the variable working condition calculation function described in steps 1 to 4;

步骤一至四的过程用下式表示，The process of steps 1 to 4 is represented by the following formula,

[Xgz，Xgz1，Xgz2，Xgz3，Xgz4，Xnri，Fux，Fuy]＝Changingstate(Ge₁，Fa，X₁，X₂，X₃，X₄，others)[Xgz, Xgz1, Xgz2, Xgz3, Xgz4, Xnri, Fux, Fuy] = Changing state (Ge ₁ , Fa, X ₁ , X ₂ , X ₃ , X ₄ , others)

，得到12个流量值[Xgz₁，Xgz₂....Xgz₁₂]；, get 12 flow values [Xgz ₁ , Xgz ₂ ....Xgz ₁₂ ];

2)、计算各负荷点对应的阀门开度以及计算出的流量值；依次检验l个负荷点，则调节级阀门在全开或全关条件下的第h个负荷点的计算流量xgz_h为：2) Calculate the valve opening corresponding to each load point and the calculated flow value; check one load point in turn, then the calculated flow xgz _h of the hth load point of the regulating valve under the condition of fully open or fully closed is :

xgz_h＝Xgz_j使得|Xgz_j-Ge_h|＝m1n(|Xgz₁-Ge_h|，|Xgz₂-Ge_h|，......，|Xgz₁₂-Ge_h|)(2-9)xgz _h = Xgz _j such that |Xgz _j −Ge _h |=m1n(|Xgz ₁ −Ge _h |, |Xgz ₂ −Ge _h |, ..., |Xgz ₁₂ −Ge _h |) (2- 9)

h＝1，2，...，l；j＝1，2，...，12h=1, 2, ..., l; j = 1, 2, ..., 12

得到l个流量xgz₁，xgz₂......xgz_l Get l traffic xgz ₁ , xgz ₂ ...... xgz _l

输出：output:

式2-10表征该喷嘴组合的机组在不同负荷点运行下的综合效应，Y越小，说明该喷嘴组合越好；Equation 2-10 represents the comprehensive effect of the nozzle combination unit operating at different load points, the smaller Y is, the better the nozzle combination is;

Y＝W₁(xgz₁-Ge₁)²+W₂(xgz₂-Ge₂)²+......+W_l(xgz_l-Ge_l)²(2-10)Y＝W ₁ (xgz ₁ -Ge ₁ ) ² +W ₂ (xgz ₂ -Ge ₂ ) ² +...+W _l (xgz _l -Ge _l ) ² (2-10)

适应度函数的最终表达为：The final expression of the fitness function is:

当X_min≤X₄≤X_max时：When X _min ≤ X ₄ ≤ X _max :

$ObjV ObjV = = \frac{11}{Y Y} - - - - - - ((22 - - 1111))$

当X₄＞X_maxORX₄＜X_min时：When X ₄ >X _max OR X ₄ <X _min :

$ObjV ObjV = = \frac{11}{Y Y} / / {e e}^{αδ αδ} - - - - - - ((22 - - 1212))$

式2-12中表明不满足约束2-3的喷嘴组合其适应度值被缩小了e^αδ倍；Equation 2-12 shows that the fitness value of nozzle combinations that do not satisfy constraint 2-3 is reduced by e ^αδ times;

$δ δ = = \{\begin{matrix} \frac{{X x}_{44} - - {X x}_{max max}}{{X x}_{max max}},, if if & {X x}_{44} > > {X x}_{max max} \\ \frac{{X x}_{min min} - - {X x}_{44}}{{X x}_{min min}},, if if & {X x}_{44} < < {X x}_{min min} \end{matrix} - - - - - - ((22 - - 1313))$

α为缩小系数；α is the reduction factor;

步骤五(三)、完成上步骤后，再进行基于传统的遗传算法的选择、交叉、变异过程；当遗传代数达到终止条件N代时，遗传过程终止，输出满足实际流量与理论流量的综合偏离程度Y最小时对应的最优喷嘴数目的组合。Step 5 (3), after completing the above steps, proceed with the selection, crossover, and mutation processes based on the traditional genetic algorithm; when the genetic algebra reaches the termination condition N generations, the genetic process terminates, and the output satisfies the comprehensive deviation between the actual flow and the theoretical flow The combination of the optimal number of nozzles corresponding to the minimum degree Y.

本发明的有益效果是：The beneficial effects of the present invention are:

根据本发明方法，由用户给定汽轮机组的常用工作负荷点，在保证机组达到各负荷点时，调节级各阀门都能处于全开或全闭状态，最大限度地减少汽轮机调节级的节流损失的条件下，优化出最优的阀门喷嘴数目组合，使机组具有最佳的经济性。同时将常用负荷点运行的不同频率加以考虑，以类似加权的形式在优化中将该因素作为优化的一个条件，并考虑汽轮机滑压运行规律，以达到更加适应实际机组运行条件的优化效果。According to the method of the present invention, the common working load point of the steam turbine unit is given by the user, and when the unit reaches each load point, each valve of the regulating stage can be in a fully open or fully closed state, and the throttling of the regulating stage of the steam turbine can be minimized Under the condition of loss, optimize the combination of the number of valves and nozzles, so that the unit has the best economy. At the same time, the different frequencies of common load point operation are considered, and this factor is used as a condition for optimization in a similar weighted form, and the sliding pressure operation rule of the steam turbine is considered to achieve an optimization effect that is more suitable for the actual operating conditions of the unit.

本发明的的创新点具体表现在以下几个方面：The innovative points of the present invention are embodied in the following aspects:

1、利用本发明方法，用户能够根据实际情况自己给定汽轮机机组的常用工作负荷点，适用于各类机组；1. Utilizing the method of the present invention, the user can specify the common working load point of the steam turbine unit according to the actual situation, which is applicable to various units;

2、本发明方法考虑了汽轮机的变负荷条件运行条件，将常用负荷点的运行频率进行了加权处理，结合实际运行条件在保证调节级最小限度的节流损失的条件下，优化出最优的喷嘴数目组合；2. The method of the present invention considers the operating conditions of variable load conditions of the steam turbine, weights the operating frequency of common load points, and optimizes the optimal operating frequency under the condition of ensuring the minimum throttling loss of the regulating stage in combination with the actual operating conditions. Nozzle number combination;

3、本发明方法将汽轮机实际的滑压运行条件作为约束进行喷嘴组的数目优化；3. The method of the present invention uses the actual sliding pressure operating condition of the steam turbine as a constraint to optimize the number of nozzle groups;

4、本发明方法考虑了汽轮机组的实际运行约束，对汽轮机调节级阀门喷嘴进行优化改造，提高了调节阀的性能，使节流损失降到最低，提高了机组的经济性。4. The method of the present invention considers the actual operation constraints of the steam turbine unit, and optimizes and transforms the valve nozzle of the regulating stage of the steam turbine, improves the performance of the regulating valve, minimizes the throttling loss, and improves the economy of the unit.

本发明的经济性在于：汽轮机的入口蒸汽多由锅炉提供，通过本发明对汽轮机调节级的优化改造，可显著减少蒸汽节流损失，有效提高汽轮机的综合效率，进而降低锅炉的煤耗。据相关资料显示，在每度电节约2克煤耗的情况下，一台600MW的机组一年所创造的经济效益将增加约500万元。下面以250MW汽轮发电机组为例进一步本发明的经济价值和应用前景。The economy of the present invention lies in that the inlet steam of the steam turbine is mostly provided by the boiler, and through the optimization and transformation of the regulating stage of the steam turbine in the present invention, the steam throttling loss can be significantly reduced, the overall efficiency of the steam turbine can be effectively improved, and the coal consumption of the boiler can be further reduced. According to relevant data, in the case of saving 2 grams of coal consumption per kilowatt-hour, the economic benefits created by a 600MW unit will increase by about 5 million yuan a year. The economic value and application prospect of the present invention will be further described below by taking a 250MW turbogenerator set as an example.

试验以黑龙江牡丹江第二电厂#6机组为对照组：The test took Unit #6 of Heilongjiang Mudanjiang Second Power Plant as the control group:

由附图3可知：原始喷嘴组合的Y值为98，即理论流量与实际流量的偏差为98t/h。实际运行中如果要让机组在给定的负荷处稳定运行，则阀门开度需要有一个较大的变化。而通过遗传算法进行优化的结果显示，Y的取值从初始的接近80优化到15，即最终理论流量与实际流量之差仅有15t/h，则实际运行中阀门开度的变化很小，节流损失小。It can be seen from Figure 3 that the Y value of the original nozzle combination is 98, that is, the deviation between the theoretical flow rate and the actual flow rate is 98t/h. In actual operation, if the unit is to operate stably at a given load, the valve opening needs to have a large change. The result of optimization by genetic algorithm shows that the value of Y is optimized from the initial value of nearly 80 to 15, that is, the difference between the final theoretical flow rate and the actual flow rate is only 15t/h, and the change of the valve opening in actual operation is very small. The throttling loss is small.

喷嘴数目优化的实际效果可以由图2体现。在给定的5个带时间频率的负荷点下，优化出各个喷嘴组的数目。经过优化喷嘴组其调节级效率比原始喷嘴数目要高，综合来看，优化后调节级内效率提高了5％以上。这从另一个角度说明，优化过程是合理的，因为优化后实际流量与理论流量的偏差较小，降低了节流损失，因此在效率上得到了很大程度的提升。The actual effect of optimizing the number of nozzles can be reflected in Figure 2. Under the given 5 load points with time frequency, the number of each nozzle group is optimized. The efficiency of the adjustment stage of the optimized nozzle group is higher than that of the original number of nozzles. On the whole, the efficiency of the adjustment stage after optimization has increased by more than 5%. This shows from another perspective that the optimization process is reasonable, because after optimization, the deviation between the actual flow and the theoretical flow is small, reducing the throttling loss, and thus greatly improving the efficiency.

本发明的技术内容概述：Summary of technical content of the present invention:

本发明在用户给定相关参数的条件下，先随机产生一组喷嘴数目组合，然后进行循环迭代，以计算流量与理论流量的偏离程度作为度量依据，得出用户给定常用负荷下的最优的调节级喷嘴数目组合。其主要发明内容如下：Under the condition that the user sets relevant parameters, the present invention first randomly generates a group of nozzle number combinations, and then performs cyclic iterations, and uses the degree of deviation between the calculated flow rate and the theoretical flow rate as the measurement basis to obtain the optimal flow rate under the common load given by the user. The combination of the number of adjustment stage nozzles. Its main invention content is as follows:

1、用户给定汽轮机机组常用工作负荷点和调节级阀门喷嘴总数目的最大、最小值以及各相关的参数。1. The user specifies the maximum and minimum values of the common working load point of the steam turbine unit, the total number of regulating valve nozzles and related parameters.

2、优化喷嘴数目：如果对用户给定的所有负荷点，都能在优化设计的喷嘴组条件下找到对应的调节阀开启(全开)组合，则达到了最优化的目的。分析计算中，以阀门全开或全闭时的计算流量与用户给定负荷的理论流量之间的偏离程度作为度量依据，过程中考虑不同常用负荷点的概率，将各负荷点的运行频率以类似加权的方式引入。若偏离程度最小，则结果最优，优化出的喷嘴数目组合即为最优的组合。具体实现过程如下：2. Optimize the number of nozzles: If for all the load points given by the user, the corresponding control valve opening (full opening) combination can be found under the condition of the optimally designed nozzle group, then the optimization goal has been achieved. In the analysis and calculation, the degree of deviation between the calculated flow rate when the valve is fully open or fully closed and the theoretical flow rate given by the user is used as the measurement basis, and the probability of different common load points is considered in the process, and the operating frequency of each load point is calculated as Introduced in a weighted manner. If the degree of deviation is the smallest, the result is optimal, and the optimized nozzle number combination is the optimal combination. The specific implementation process is as follows:

先随机产生一组喷嘴数目组合，计算在该情况下的计算流量与理论流量的偏离程度，然后对喷嘴数目组合进行迭代，找出在用户给定喷嘴总数目范围条件下，计算流量与理论流量的最小偏离程度，其所对应的喷嘴数目组合即为最优解。First randomly generate a group of nozzle number combinations, calculate the deviation between the calculated flow rate and the theoretical flow rate in this case, and then iterate the nozzle number combination to find out the calculated flow rate and theoretical flow rate under the condition of the total number of nozzles given by the user. The minimum degree of deviation, the corresponding nozzle number combination is the optimal solution.

a、计算理论流量：根据汽轮机组的实际运行参数及滑压运行规律曲线，由给定的负荷点可以计算出其对应的各理论流量G_ei；调查实际电厂运行情况，其常用的工作负荷点1个，所以本发明中给定i＝1，2，...1；a. Calculation of theoretical flow rate: According to the actual operating parameters of the steam turbine unit and the sliding pressure operation law curve, the corresponding theoretical flow rate G _ei can be calculated from the given load point; investigate the actual power plant operation situation, and its commonly used working load point 1, so i=1, 2,...1 is given in the present invention;

b、由各阀门喷嘴数目及其对应阀门开度，根据流量特性曲线计算流量G_ij：根据用户给定的喷嘴数目范围产生一组随机的喷嘴数目组合，假定调节阀都处于全开或全闭的最优状态。根据实际情况不存在一个阀门单开的情况，所以各阀门开度的组合会有2^4-4＝12种(j＝1，2，...12)。对每一种阀门开度组合计算流量XG_ij，b. From the number of nozzles of each valve and the corresponding valve opening, calculate the flow G _ij according to the flow characteristic curve: generate a group of random nozzle number combinations according to the range of nozzle numbers given by the user, assuming that the regulating valves are all fully open or fully closed optimal state. According to the actual situation, there is no single-opening situation of a valve, so there are 2^4-4=12 combinations of valve openings (j=1, 2, ... 12). Calculate the flow rate XG _ij for each valve opening combination,

令xG_i＝XG_ij使得|XG_ij-G_ei|＝min(|XG_I1-G_ei|，|XG_I2-G_ei|，...，|XG_I12-G_ei|，)；Let xG _i =XG _ij such that |XG _ij -G _ei |=min(|XG _I1 -G _ei |, |XG _I2 -G _ei |, ..., |XG _I12 -G _ei |,);

c、求给定喷嘴数目组合条件下，计算流量与理论流量的总偏差：考虑各负荷点的运行频率，进行加权处理：c. Calculate the total deviation between the flow rate and the theoretical flow rate under the condition of a given number of nozzle combinations: consider the operating frequency of each load point and perform weighted processing:

$Y Y = = {Σ Σ}_{i i = = 11}^{i i = = 66} {W W}_{i i} * * {((x x {G G}_{i i} - - {G G}_{i i}))}^{22}$

d、对喷嘴数目组合进行迭代计算，对每一组组合，都能算出一个计算流量与理论流量的最小总偏差。找出所有最小的总偏差，其对应的喷嘴数目组合即为最优的喷嘴数目组合。d. Carry out iterative calculation on the combination of the number of nozzles, and for each combination, a minimum total deviation between the calculated flow and the theoretical flow can be calculated. Find all the smallest total deviations, and the corresponding nozzle number combination is the optimal nozzle number combination.

附图说明 Description of drawings

图1是汽轮机喷嘴组的结构示意图(1-主蒸汽；2-调节阀；图1a是主视图，图1b是图1a的左视图)，如图1的喷嘴调节方式，调节级的静叶栅被分隔为几个进气弧段，每个进气弧段由一定数目的喷嘴组成，不同的调节级阀门对各组喷嘴单独供汽，按照负荷的需要通过改变调节级阀门的开度和开启数目来改变汽轮机的进汽量。中小型机组一般有4～7个调节阀，大型机组一般有4～6个调节阀；Fig. 1 is a schematic structural diagram of a steam turbine nozzle group (1-main steam; 2-regulating valve; Fig. 1a is a front view, and Fig. 1b is a left view of Fig. 1a), as shown in Fig. 1, the nozzle adjustment method, and the static blade cascade of the regulating stage It is divided into several intake arcs, and each intake arc is composed of a certain number of nozzles. Different regulating valves supply steam to each group of nozzles separately. According to the needs of the load, the opening and opening of the regulating valves Number to change the steam intake of the steam turbine. Small and medium-sized units generally have 4 to 7 regulating valves, and large units generally have 4 to 6 regulating valves;

图2是利用本发明方法开发的软件的喷嘴组设计界面截图，图3是优化指标曲线图；图4是根据热力计算公式计算各个参数的具体过程中利用的级速度三角形关系图。Fig. 2 is a screenshot of the nozzle group design interface of the software developed by the method of the present invention, and Fig. 3 is a curve diagram of an optimization index; Fig. 4 is a triangular diagram of stage speed utilized in the specific process of calculating each parameter according to the thermal calculation formula.

具体实施方式 Detailed ways

具体实施方式一：本实施方式所述的考虑汽轮机实际运行约束的各喷嘴组的喷嘴数目优化设计方法是按照如下步骤来实现的：Specific Embodiment 1: The optimal design method for the number of nozzles of each nozzle group considering the actual operation constraints of the steam turbine described in this embodiment is implemented according to the following steps:

X_min≤X_i≤X_max，i＝1，2，3，4；X_min＝const，X_max＝const(2-3)X _min ≤X _i ≤X _max , i=1, 2, 3, 4; X _min ＝const, X _max ＝const(2-3)

X_i4＝X_z-(X_i1+X_i2+X_i3) (2-7)X _i4 ＝X _z -(X _i1 +X _i2 +X _i3 ) (2-7)

X_i4＞X_max ORX_i4＜X_min (2-8)X _i4 > X _max OR X _i4 < X _min (2-8)

设适应度函数为：Let the fitness function be:

输入：enter:

喷嘴出口蒸汽流速c₁、动叶进口相对速度w₁、喷嘴出口焓值h₁、绝对速度c₂、动叶出口的相对速度w₂、动叶出口焓值h₂、轮周效率η_u；Nozzle outlet steam velocity c ₁ , rotor blade inlet relative velocity w ₁ , nozzle outlet enthalpy value h _{1 , absolute velocity c 2} , rotor blade outlet relative velocity _{w 2} _, rotor blade outlet enthalpy value h ₂ , wheel circumference efficiency η _u ;

u——动叶的圆周速度；u—circumferential speed of moving blade;

λ——系数， λ—coefficient,

Ω_m——级平均反动度；Ω _m - the average degree of reaction;

ε——级压力比；ε—stage pressure ratio;

η——轮周效率；η——wheel circumference efficiency;

x_a——速比；x _a - speed ratio;

μ——系数， μ—coefficient,

映射：mapping:

1)、通过阀门喷嘴数目组合X₁，X₂，X₃，X₄和变工况计算的热力学参数(c₁、w₁、h₁、c₂、w₂、h₂、η_u)、调节级特性曲线(μ-ε、λ-ε、Ω_m-ε及η-x_a。)、几何参数(各喷嘴喉部截面积A_nk，动叶出口截面积A_b)、滑压运行规律曲线(功率-主蒸汽压力)，再加上12种阀门开度，代入步骤一至四所述的变工况计算函数；1), _the thermodynamic parameters (c ₁ _, w ₁ , h ₁ , c ₂ , w ₂ _, h ₂ , η _u ) _, Adjustment stage characteristic curve (μ-ε, λ-ε, Ω _m -ε and η-x _a .), geometric parameters (each nozzle throat cross-sectional area A _nk , rotor blade outlet cross-sectional area A _b ), sliding pressure operation rule Curve (power-main steam pressure), plus 12 kinds of valve openings, substituted into the variable working condition calculation function described in steps 1 to 4;

[Xgz，Xgz1，Xgz2，Xgz3，Xgz4，Xnri，Fux，Fuy]＝Changingstate(Ge₁，Fa，X₁，X₂，X₃，X₄，others)，得到12个流量值[Xgz₁，Xgz₂....Xgz₁₂]；[Xgz, Xgz1, Xgz2, Xgz3, Xgz4, Xnri, Fux, Fuy]=Changingstate(Ge ₁ , Fa, X ₁ , X ₂ , X ₃ , X ₄ , others), get 12 flow values [Xgz ₁ , Xgz ₂ .... _Xgz12 ];

xgz_h＝Xgz_j使得|Xgz_j-Ge_h|＝min(|Xgz₁-Ge_h|，|Xgz₂-Ge_h|，......，|Xgz₁₂-Ge_h|)(2-9)xgz _h = Xgz _j such that |Xgz _j −Ge _h |=min(|Xgz ₁ −Ge _h |, |Xgz ₂ −Ge _h |, ..., |Xgz ₁₂ −Ge _h |) (2- 9)

h＝1，2，...，l；j＝1，2，...，12h=1, 2, ..., l; j = 1, 2, ..., 12

输出：output:

当X_min≤X₄≤X_max时：When X _min ≤ X ₄ ≤ X _max :

$ObjV ObjV = = \frac{11}{Y Y} - - - - - - ((22 - - 1111))$

当X₄＞X_maxORX₄＜X_min时：When X ₄ >X _max OR X ₄ <X _min :

α为缩小系数；α is the reduction factor;

在步骤二中，根据热力计算公式计算各个参数的具体过程为：In step 2, the specific process of calculating each parameter according to the thermal calculation formula is as follows:

1、喷嘴出口蒸汽流速c₁ 1. Steam flow rate at nozzle outlet c ₁

式中c_1s——喷嘴出口的汽流理想速度(m/s)；In the formula, c _1s ——the ideal velocity of the steam flow at the outlet of the nozzle (m/s);

——蒸汽在喷嘴中的滞止等熵焓降(J/Kg)； ——Stagnation isentropic enthalpy drop of steam in the nozzle (J/Kg);

——喷嘴的速度系数，取速度系数 - the velocity coefficient of the nozzle, Take the velocity coefficient

2、动叶进口相对速度w₁ 2. The relative velocity at the rotor blade inlet w ₁

动叶进出口速度三角形可参看图4，The velocity triangle of the rotor blade inlet and outlet can be seen in Fig. 4,

${w w}_{11} = = \sqrt{{c c}_{11}^{22} + + {u u}^{22} - - 22 {uc uc}_{11} cos cos {α α}_{11}} - - - - - - ((33 - - 1212))$

${γ γ}_{11} = = arcsin arcsin \frac{{c c}_{11} sin sin {α α}_{11}}{{w w}_{11}} - - - - - - ((33 - - 1313))$

u——动叶圆周速度u—circumferential speed of moving blade

γ₁——相对速度进入动叶栅的角γ ₁ ——The relative velocity enters the angle of moving blade cascade

3、喷嘴出口焓值h₁ 3. Nozzle outlet enthalpy h ₁

由于流动过程是绝热的，消耗与损失上的动能转化为热量又加热了蒸汽本身，所以喷嘴出口汽流的实际焓值h₁将大于理想焓值h_1s，即h₁＝h_1s+Δh_nξ。Since the flow process is adiabatic, the kinetic energy consumed and lost is converted into heat and heats the steam itself, so the actual enthalpy value h ₁ of the steam flow at the outlet of the nozzle will be greater than the ideal enthalpy value h _1s , that is, h ₁ = h _1s +Δh _nξ .

4、动叶出口的相对速度w₂及绝对速度c₂ 4. The relative speed w ₂ and the absolute speed c ₂ of the rotor blade outlet

为了分析问题的方便，我们引入一个假想的速度c_a，与此相对应的动能等于级的理想焓降，即：For the convenience of analyzing the problem, we introduce an imaginary speed c _a , and the corresponding kinetic energy is equal to the ideal enthalpy drop of the stage, namely:

${Δh}_{s}^{*} = \frac{{c_{a}}^{2}}{2}$ (3-24) ${Δh}_{the s}^{*} = \frac{{c_{a}}^{2}}{2}$ (3-24)

${w w}_{22 s the s} = = \sqrt{22 Δ Δ {h h}_{b b} + + {w w}_{11}^{22}} = = \sqrt{22 {Ω Ω}_{m m} {Δh Δh}_{s the s}^{* *} + + {w w}_{11}^{22}} = = \sqrt{22 Δ Δ {h h}_{b b}^{* *}} - - - - - - ((33 - - 1616))$

式中Δh_b——动叶等熵焓降；In the formula, Δh _b ——isentropic enthalpy drop of moving blade;

w₁——动叶进口有效相对速度；w ₁ —effective relative speed at the inlet of the rotor blade;

——级滞止等熵焓降； ——stage stagnation isentropic enthalpy drop;

——动叶相对止滞等熵焓降， —— relative stagnation isentropic enthalpy drop of moving blade,

Ω_m——级平均反动度， Ω _m ——The average reaction degree of the stage,

w_2s——动叶出口的等熵速度w _2s —isentropic velocity at the outlet of the rotor blade

动叶栅的实际相对速度w₂可表示为：w₂＝ψw_2s The actual relative speed w ₂ of the moving blade cascade can be expressed as: w ₂ = ψw _2s

${c c}_{22} = = \sqrt{{w w}_{22}^{22} + + {u u}^{22} - - 22 u u {w w}_{22} cos cos ((180180 - - {β β}_{22}))} - - - - - - ((33 - - 1414))$

${α α}_{22} = = arcsin arcsin \frac{{w w}_{22} sin sin ((180180 - - {β β}_{22}))}{{c c}_{22} cos cos ((180180 - - {α α}_{22}))} - - - - - - ((33 - - 1515))$

α₂——出汽角α ₂ —— steam outlet angle

5、动叶出口焓值h₂ 5. The enthalpy value of the rotor blade outlet h ₂

动叶的出口焓值等于喷嘴出口焓值与焓降之差，即：The outlet enthalpy of the moving blade is equal to the difference between the nozzle outlet enthalpy and the enthalpy drop, namely:

h₂＝h_2s-Δh₂ h ₂ =h _2s -Δh ₂

1)动叶入口撞击损失Δh_β 1) Impingement loss at the inlet of the rotor blade Δh _β

${Δh Δh}_{β β} = = \frac{{(({w w}_{11} sin sin θ θ))}^{22}}{22} - - - - - - ((33 - - 1111))$

θ——动叶进口相对速度方向与动叶进口角方向的夹角θ——the angle between the relative velocity direction of the rotor blade inlet and the angle direction of the rotor blade inlet

2)动叶损失Δh_bξ 2) Blade loss Δh _bξ

动叶中的能量损失Δh_bξ也可以由表示，即：The energy loss Δh _bξ in the moving blade can also be expressed by, namely:

${Δh Δh}_{bξ bξ} = = \frac{11}{22} (({w w}_{22 s the s}^{22} - - {w w}_{22}^{22})) = = ((11 - - {ψ ψ}^{22})) Δ Δ {h h}_{b b}^{* *} - - - - - - ((33 - - 1818))$

ψ——动叶速度系数ψ——rotating blade velocity coefficient

3)余速损失Δh_c2 3) Residual speed loss Δh _c2

${Δh Δh}_{c c 22} = = \frac{{c c}_{22}^{22}}{22} - - - - - - ((33 - - 1919))$

焓降：Δh₂＝Δh_β+Δh_bξ+Δh_c2 Enthalpy drop: Δh ₂ = Δh _β + Δh _bξ + Δh _c2

6、轮周效率η_u 6. Wheel circumference efficiency η _u

考虑叶高损失后级的有用焓降为：The useful enthalpy drop of the rear stage considering leaf height loss is:

${Δh Δh}_{u u} = = {Δh Δh}_{s the s}^{* *} - - {Δh Δh}_{nξ nξ} - - {Δh Δh}_{β β} - - {Δh Δh}_{bξ bξ} - - {Δh Δh}_{c c 22} - - {Δh Δh}_{l l} - - - - - - ((33 - - 23 twenty three))$

故轮周效率为： $η_{u} = \frac{{Δh}_{u}}{{Δh}_{s}^{*}} - - - (3 - 21)$ Therefore, the cycle efficiency is: $η_{u} = \frac{{Δh}_{u}}{{Δh}_{the s}^{*}} - - - (3 - twenty one)$

具体实施方式二：本实施方式在步骤二的通过二分法计算p₂的过程中，所述喷嘴后压力p_1k的计算过程为：由汽轮机组在实际运行中得到的滑压运行规律曲线：功率-主蒸汽压力，再根据实际运行负荷，查得主蒸汽的压力，然后计算出p_1k。其它步骤与具体实施方式一相同。Specific implementation mode two: In the process of calculating _p2 by the dichotomy method in step two of this embodiment, the calculation process of the pressure _p1k after the nozzle is: the sliding pressure operation law curve obtained by the steam turbine unit in actual operation: power -The main steam pressure, and then check the main steam pressure according to the actual operating load, and then calculate p _1k . Other steps are the same as in the first embodiment.

针对本发明方法再进行如下详细阐述：Carry out following elaboration again for the inventive method:

1、遗传算法及其改进优化方法1. Genetic algorithm and its improved optimization method

遗传算法是以自然选择和遗传理论为基础，将生物进化过程中适者生存规则与群体内部染色体的随机信息交换机制相结合的高效全局寻优搜索算法。遗传算法摒弃了传统的搜索方式，模拟生物界的进化过程，采用人工进化的方式对目标空间进行随机优化搜索。它将问题中的可能解看做是群体中的一个个体，并将每个编码编成符号串的形式，模拟达尔文的遗传选择和自然淘汰的进化过程，对群体反复进行基于遗传的操作(遗传、交叉、变异)。根据预定目标的目标适应度函数对每个个体进行评价，依据适者生存、优胜劣汰的进化规则，不断得到最优的群体，同时以全局并行搜索方式来搜寻优化群体中的最优个体，以求得满足条件的最优解。Genetic Algorithm is an efficient global search algorithm based on natural selection and genetic theory, which combines the survival rule of the fittest in the process of biological evolution with the random information exchange mechanism of chromosomes within the population. The genetic algorithm abandons the traditional search method, simulates the evolution process of the biological world, and uses the artificial evolution method to carry out random optimization search on the target space. It regards the possible solutions in the problem as an individual in the group, and compiles each code into the form of a symbol string, simulating the evolution process of Darwin's genetic selection and natural elimination, and repeatedly performs genetic operations on the group (genetic , crossover, mutation). Evaluate each individual according to the target fitness function of the predetermined goal, and continuously obtain the optimal group according to the evolutionary rules of survival of the fittest and survival of the fittest, and at the same time search for the optimal individual in the optimized group with a global parallel search method, in order to The optimal solution that satisfies the conditions is obtained.

遗传算法的一般过程是：设置初始种群(编码)，计算适应度，选择，交叉，变异，产生新种群，重新计算适应度，依次循环迭代，直到迭代次数达到初始设定值，遗传结束，得到的最后一代种群为最优种群，种群里的个体为最优个体。The general process of the genetic algorithm is: set the initial population (coding), calculate the fitness, select, crossover, and mutate, generate a new population, recalculate the fitness, and iterate in turn until the number of iterations reaches the initial set value. The last generation population of is the optimal population, and the individual in the population is the optimal individual.

2、喷嘴数目编码，变负荷运行参数及其他参数确定2. Nozzle number coding, variable load operation parameters and other parameters determination

2.1考虑实际运行约束的喷嘴数目编码2.1 Coding of the number of nozzles considering the actual operating constraints

在遗传算法中，待优化的量一般作为随机编码输入到优化系统中，但由于优化量时常作为实际生产、运行中的参数，有实际的物理含义，会受到外界种种因素的制约，取值有一定的约束，不能直接拿来当做初始种群中个体的编码，需要进行适当的变换。所以对于种群设置的要求是，每个个体必须是该优化问题的可行解，这样优化才有实际意义。举例说明：In the genetic algorithm, the quantity to be optimized is generally input into the optimization system as a random code, but because the optimized quantity is often used as a parameter in actual production and operation, it has actual physical meaning and will be restricted by various external factors. Certain constraints cannot be directly used as the encoding of individuals in the initial population, and appropriate transformations are required. Therefore, the requirement for the population setting is that each individual must be a feasible solution to the optimization problem, so that the optimization has practical significance. for example:

寻找函数find function

$y the y = = f f (({x x}_{11},, {x x}_{22},, {x x}_{33},, {x x}_{44})) = = {x x}_{11}^{22} + + {x x}_{22}^{22} + + {x x}_{33}^{22} + + {x x}_{44}^{22} - - - - - - 22 - - 11$

的最小值，由于对于函数f，对任意实数其自变量x₁，x₂，x₃，x₄又是函数f的可行解，所以在编码的过程中x₁，x₂，x₃，x₄在实数范围内无任何约束条件，产生的随机编码符合优化条件，可以代入函数进行计算，得出相应的取值。The minimum value of the function f, since for any real number its independent variables x ₁ , x ₂ , x ₃ , x ₄ is the feasible solution of the function f, so in the encoding process x ₁ , x ₂ , x ₃ , x ₄ There are no constraints within the range of real numbers, and the generated random codes meet the optimization conditions, and can be substituted into functions for calculation to obtain corresponding values.

在本例中，所优化的喷嘴组喷嘴数目并不是任何取值都有实际意义的。一方面，在汽轮机设计制造过程中，四个调节阀门分别对应调节级的四分之一弧段，由于调节级总面积固定，各喷嘴大小也为设定值，且喷嘴均匀分布在圆周上，这就要求每个弧段上的喷嘴数目既不能太多也不能太少。另一方面，汽轮机的喷嘴是由第一级静叶栅和第一级动叶组成，调节级(汽轮机第一级)不仅起到了做功作用，也起到了对主蒸汽的导流作用，因此如果某一弧段上喷嘴数目太少则起不到这样的作用，数目太多，则弧段容纳不下。In this example, the number of nozzles in the optimized nozzle group is not practically meaningful for any value. On the one hand, in the design and manufacture process of the steam turbine, the four regulating valves correspond to a quarter of the arc section of the regulating stage. Since the total area of the regulating stage is fixed, the size of each nozzle is also the set value, and the nozzles are evenly distributed on the circumference. This requires that the number of nozzles on each arc segment can be neither too many nor too few. On the other hand, the nozzle of the steam turbine is composed of the first-stage static blade cascade and the first-stage moving blade. The regulating stage (the first stage of the steam turbine) not only plays the role of doing work, but also plays the role of guiding the main steam. Therefore, if If the number of nozzles on a certain arc is too small, this effect cannot be achieved, and if the number is too large, the arc cannot be accommodated.

一般在汽轮机喷嘴组设计时，总的喷嘴数目为定值，且每个喷嘴组喷嘴数目有最大和最小值。约束条件为：Generally, when designing a steam turbine nozzle group, the total number of nozzles is a fixed value, and each nozzle group has a maximum and a minimum number of nozzles. The constraints are:

X₁+X₂+X₃+X₄＝X_z，X_z＝const 2-2X ₁ +X ₂ +X ₃ +X ₄ =X _z , X _z =const 2-2

X_min≤X_i≤X_max，i＝1，2，3，4；X_min＝const，X_max＝const 2-3X _min ≤ X _i ≤ X _max , i=1, 2, 3, 4; X _min ＝const, X _max ＝const 2-3

遗传算法由于其随机性，很难解决上述两个等式的约束，但可以通过适当的变换解决约束条件；Due to its randomness, genetic algorithm is difficult to solve the constraints of the above two equations, but it can solve the constraints by appropriate transformation;

采用浮点数编码，编码区间为[X_min，X_max]Using floating-point encoding, the encoding range is [X _min , X _max ]

$Chrom = [\begin{matrix} x_{11}, x_{12}, x_{13} \\ x_{21}, x_{22}, x_{23} \\ . . . . . . . . . . \\ x_{m 1}, x_{m 2}, x_{m 3} \end{matrix}],$ x_ij∈R₊，i＝1，2，...，m，j＝1，2，3. 2-4 $Chrome = [\begin{matrix} x_{11}, x_{12}, x_{13} \\ x_{twenty one}, x_{twenty two}, x_{twenty three} \\ . . . . . . . . . . \\ x_{m 1}, x_{m 2}, x_{m 3} \end{matrix}],$ x _ij ∈ R ₊ , i=1, 2,..., m, j=1, 2, 3. 2-4

式中，m代表编码的个体数目，优化前系统设定，m越大，优化系统进入最优稳定解的迭代次数越少，但每次迭代的计算量越大耗时越多，一般情况下，在系统进入最优解稳定区间时，尽量让迭代结束，故个体数目与迭代次数是通过多次试验调试得出，以保证优化效率最高。In the formula, m represents the number of individuals encoded, which is set by the system before optimization. The larger m is, the fewer iterations it takes for the optimization system to enter the optimal stable solution, but the larger the calculation amount of each iteration, the more time-consuming it is. , when the system enters the stable interval of the optimal solution, try to let the iteration end, so the number of individuals and the number of iterations are obtained through multiple experiments and debugging to ensure the highest optimization efficiency.

对于一个个体，其每个染色体x_i1，x_i2，x_i3，分别为前三个调节阀门对应的喷嘴组喷嘴数目X₁，X₂，X₃的编码，其对应关系为：For an individual, each of its chromosomes x _i1 , x _i2 , and x _i3 are the codes of the nozzle numbers X ₁ , X ₂ , and X ₃ of the nozzle group corresponding to the first three regulating valves, and the corresponding relationship is:

X_ij＝round(x_ij)，i＝1，2...m，j＝1，2，3 2-5X _ij = round(x _ij ), i=1, 2...m, j=1, 2, 3 2-5

round表示四舍五入取整。计算出X1，X2，X3后，X4为：round means rounding off. After calculating X1, X2, X3, X4 is:

X_i4＝X_z-(X_i1+X_i2+X_i3) 2-7X _i4 ＝X _z -(X _i1 +X _i2 +X _i3 ) 2-7

这样初始种群的设置在一个范围内是随机的，第一个约束条件(式2-2)也很好的满足了。但是对于式(2-3)，初始种群进行编码的时候不能很好的满足，也就是说，编码过程中会产生一些无意义的个体使得：In this way, the setting of the initial population is random within a certain range, and the first constraint condition (Formula 2-2) is also well satisfied. But for formula (2-3), the initial population cannot be well satisfied when encoding, that is to say, some meaningless individuals will be generated during the encoding process so that:

X_i4＞X_maxORX_i4＜X_min 2-8X _i4 > X _max OR X _i4 < X _min 2-8

这些个体并不是实际满足要求的，但如果人为地剔除这些个体，则会破坏种群的多样性，违背了遗传算法的优化原则，因此需要采取其他方式解决式2-3的约束，具体方法将在2.2部分介绍。These individuals do not actually meet the requirements, but if these individuals are artificially eliminated, the diversity of the population will be destroyed, which violates the optimization principle of the genetic algorithm. Therefore, other methods need to be adopted to solve the constraints of formula 2-3. The specific method will be in 2.2 Section introduction.

2.2变负荷运行参数及其它参数2.2 Variable load operating parameters and other parameters

优化过程中喷嘴数目不仅作为待优化量(输出量)，也是优化系统的输入量，从文章第一部分可知，通过汽轮机调节级变工况计算可以得到汽轮机调节级特性曲线，四个调节阀门对应的各股气流同时作用下的调节级阀后压力、各阀门对应流量、内效率、气流力等参数。这些输出的热力学参数在后面的优化过程中起到了至关重要的作用，考虑到这是变负荷运行下调节级喷嘴数目优化，优化前需要的参数为变负荷运行参数和调节级变工况计算的所有参数。优化前，用户输入(变工况计算的参数)，给定的各负荷点以及各负荷点对应的运行时间百分比，输出在各负荷点下的调节级阀后压力、各阀门对应流量、内效率、气流力等。In the optimization process, the number of nozzles is not only used as the quantity to be optimized (output), but also the input quantity of the optimization system. From the first part of the article, it can be seen that the characteristic curve of the steam turbine regulation stage can be obtained through the calculation of the steam turbine regulation stage change working condition. The four regulation valves correspond to Parameters such as the pressure behind the regulating valve, the corresponding flow rate of each valve, internal efficiency, and air flow force under the simultaneous action of each air flow. These output thermodynamic parameters play a crucial role in the subsequent optimization process. Considering that this is the optimization of the number of adjustment stage nozzles under variable load operation, the parameters required before optimization are the variable load operating parameters and the calculation of the adjustment stage variable working conditions. all parameters of . Before optimization, the user inputs (parameters calculated under variable working conditions), given each load point and the percentage of running time corresponding to each load point, and outputs the post-valve pressure of the regulating stage at each load point, the corresponding flow rate of each valve, and the internal efficiency , air flow, etc.

在之前的变工况计算中，主蒸汽压力一般是定值，通过改变主汽阀和调节阀开度来改变主蒸汽流量的。而滑压运行中，主汽阀和调节阀门开度不变，通过改变主蒸汽的压力以达到调节主蒸汽流量的作用。在实际运行中，两者往往是同时进行的：主汽阀和调节阀的开度随着汽轮机功率的改变而改变，并且主蒸汽的压力也随着功率改变而改变，这样就可以达到在阀门全开或全关的条件下改变主蒸汽的压力等参数使机组在给定的负荷点运行，降低了节流损失。通过滑压运行曲线(功率-主蒸汽压力)可以查出在某一负荷点(功率)处的主蒸汽的压力。滑压曲线是通过机组实际试验得到的。In the previous variable working condition calculation, the main steam pressure is generally a fixed value, and the main steam flow is changed by changing the opening of the main steam valve and the regulating valve. In sliding pressure operation, the opening of the main steam valve and the regulating valve remain unchanged, and the main steam flow can be adjusted by changing the pressure of the main steam. In actual operation, the two are often carried out at the same time: the opening of the main steam valve and the regulating valve change with the power of the steam turbine, and the pressure of the main steam also changes with the power, so that it can be achieved at the valve Change the main steam pressure and other parameters under the condition of fully open or fully closed to make the unit run at a given load point and reduce the throttling loss. The pressure of the main steam at a certain load point (power) can be found out through the sliding pressure operation curve (power-main steam pressure). The sliding pressure curve is obtained through the actual test of the unit.

给定负荷点1：Given load point 1:

[Xgz₁，Xgz1₁，Xgz2₁，Xgz3₁，Xgz4₁，Xnri₁，Fux₁，Fuy₁]＝Changingstate(Ge₁，P₁，Fa，X₁，X₂，X₃，X₄，others)[Xgz ₁ , Xgz1 ₁ , Xgz2 ₁ , Xgz3 ₁ , Xgz4 ₁ , Xnri ₁ , Fux ₁ , Fuy ₁ ]=Changingstate(Ge ₁ , P ₁ , Fa, X ₁ , X ₂ , X ₃ , X ₄ , others)

给定负荷点2：Given load point 2:

[Xgz₂，Xgz1₂，Xgz2₂，Xgz3₂，Xgz4₂，Xnri₂，Fux₂，Fuy₂]＝Changingstate(Ge₂，P₂，Fa，X₁，X₂，X₃，X₄，others)[Xgz ₂ , Xgz1 ₂ , Xgz2 ₂ , Xgz3 ₂ , Xgz4 ₂ , Xnri ₂ , Fux ₂ , Fuy ₂ ]=Changingstate(Ge ₂ , P ₂ , Fa, X ₁ , X ₂ , X ₃ , X ₄ , others)

给定负荷点1：Given load point 1:

[Xgz_l，Xgz1_l，Xgz2_l，Xgz3_l，Xgz4_l，Xnri_l，Fux_l，Fuy_l]＝Changingstate(Ge_l，P_l，Fa，X₁，X₂，X₃，X₄，others)[Xgz _l , Xgz1 _l , Xgz2 _l , Xgz3 _l , Xgz4 _l , Xnri _l , Fux _l , Fuy _l ]=Changingstate(Gel _, P _l , Fa, X ₁ , X ₂ , X ₃ , X ₄ , others)

对于每个负荷点，其输入值的符号含义分别为：负荷点的实际流量，主蒸汽压力(在输入主蒸汽压力时将滑压曲线制成查表函数，根据机组不同的负荷点，得出相应的主蒸汽压力)，阀门开度，阀门1对应喷嘴组喷嘴数目，阀门2对应喷嘴组数目，阀门3对应喷嘴组数目，阀门4对应喷嘴组数目，其他参数。其输出的值符号含义从左向右依次为：调节级后流量、阀门1后流量、阀门2后流量、阀门3后流量、阀门4后流量、相对内效率、水平气流力、竖直气流力。For each load point, the symbolic meanings of the input values are: the actual flow of the load point, the main steam pressure (when the main steam pressure is input, the sliding pressure curve is made into a look-up table function, and according to the different load points of the unit, the obtained Corresponding main steam pressure), valve opening, valve 1 corresponds to the number of nozzle groups, valve 2 corresponds to the number of nozzle groups, valve 3 corresponds to the number of nozzle groups, valve 4 corresponds to the number of nozzle groups, and other parameters. The meanings of the output value symbols from left to right are: flow after regulating stage, flow after valve 1, flow after valve 2, flow after valve 3, flow after valve 4, relative internal efficiency, horizontal airflow force, vertical airflow force .

汽轮机在满负荷运转下的功率为额定功率，其主蒸汽流量为额定流量。功率与流量成正比，因此只要给定额定流量和不同负荷点下的汽轮机功率占额定功率的百分比，则可以得出汽轮机在该负荷点下的主蒸汽流量(输入量第一项)。Fa为阀门的开度，X1，X2，X3，X4为汽轮机4阀门对应的喷嘴数目，在优化中，各阀门喷嘴数目由系统通过编码自动产生，阀门开度也由优化系统产生。对于同一台机组，其他参数基本保持不变，用户可以根据需要自行设定这些参数。The power of the steam turbine at full load is the rated power, and its main steam flow is the rated flow. The power is proportional to the flow rate, so as long as the rated flow rate and the percentage of the steam turbine power at different load points to the rated power are given, the main steam flow rate of the steam turbine at the load point (the first item of the input amount) can be obtained. Fa is the opening of the valve, X1, X2, X3, X4 are the number of nozzles corresponding to the 4 valves of the steam turbine. During optimization, the number of nozzles of each valve is automatically generated by the system through coding, and the valve opening is also generated by the optimization system. For the same unit, other parameters basically remain unchanged, and users can set these parameters according to their needs.

3、考虑实际运行约束的基于汽轮机调节级变工况计算的适应度函数的确定3. Determination of the fitness function based on the calculation of the steam turbine regulation step change condition considering the actual operation constraints

在遗传算法中，适应度函数是用来区分群体中个体好坏的标准，是进行自然选择的唯一依据。适应度函数表征一个虚拟的自然环境，种群中的个体在虚拟环境中进行繁衍。其中适应环境的个体将被保留下来，不适应环境的个体将被淘汰。适应度量化了个体在虚拟环境中的适应程度，通过将个体代入适应度函数中计算得到。In the genetic algorithm, the fitness function is the standard used to distinguish good and bad individuals in the group, and is the only basis for natural selection. The fitness function represents a virtual natural environment, and the individuals in the population reproduce in the virtual environment. Among them, the individuals who adapt to the environment will be retained, and the individuals who are not adapted to the environment will be eliminated. The fitness measure quantifies the adaptability of the individual in the virtual environment, which is calculated by substituting the individual into the fitness function.

在本例中，优化的目标是使得在最优喷嘴组喷嘴数目的组合下，调节级的节流损失最小。节流损失是由于汽轮机在进气过程中调节阀门不完全开启造成的，当调节阀门全开或全关的条件下，节流损失最小。如果有某种阀门喷嘴组喷嘴数目的组合，使得各阀门在开度为1或0下能在给定的负荷点处运行(即计算出的流量Xgz_i等于其给定负荷的流量Ge_i)，则说明该喷嘴组合为最优组合。实际上，这样完美的喷嘴组合并不存在，计算出的流量和给定负荷对应的流量必然有一定的差值。但如果差值越小，则也能说明该喷嘴组合能达到较优的组合。机组实际运行中，调节阀门会开启或关闭少许来弥补上述流量的差值，产生的节流损失较小。In this example, the goal of optimization is to minimize the throttling loss of the regulating stage under the combination of the number of nozzles in the optimal nozzle group. The throttling loss is caused by the incomplete opening of the regulating valve during the intake process of the steam turbine. When the regulating valve is fully opened or fully closed, the throttling loss is the smallest. If there is a certain combination of the number of nozzles in the valve nozzle group, each valve can operate at a given load point when the opening is 1 or 0 (that is, the calculated flow Xgz _i is equal to the flow Ge _i of its given load) , it means that the nozzle combination is the optimal combination. In fact, such a perfect nozzle combination does not exist, and there must be a certain difference between the calculated flow and the flow corresponding to the given load. But if the difference is smaller, it can also show that the nozzle combination can achieve a better combination. In the actual operation of the unit, the regulating valve will be opened or closed a little to make up for the above flow difference, and the resulting throttling loss is small.

考虑到变负荷运行，一种喷嘴组合要在多个负荷点都能较好的运行，产生的节流损失较小，并且阀门开度尽可能趋于1或0，则需要提出一种综合指标来衡量该喷嘴数目在这些负荷点运行下的效果。Considering the variable load operation, if a nozzle combination can operate well at multiple load points, the resulting throttling loss is small, and the valve opening tends to be 1 or 0 as much as possible, it is necessary to propose a comprehensive index to measure the effect of the number of nozzles operating at these load points.

通过上述分析，适应度函数的结构可以基本确定了。该适应度函数是由编码等多个调节级相关参数作为输入，通过不断反复迭代到各负荷点的变工况计算中计算调节级后流量，再通过相应的法则将计算得到流量和给定的流量比较，得到综合各负荷点下效果最好的喷嘴组合。在四个阀门全开或全关的条件下组合出的阀门开度有种组合，由于在实际运行过程中，不存在只开启一个阀门的情况，故剩下12中阀门开度的组合。Through the above analysis, the structure of the fitness function can be basically determined. The fitness function is input by a number of adjustment level related parameters such as coding, and calculates the flow rate after the adjustment level through repeated iterations to the calculation of variable working conditions at each load point, and then uses the corresponding rules to calculate the calculated flow rate and the given Comparing the flow rates, the combination of nozzles with the best effect under all load points can be obtained. The combined valve opening under the condition of four valves fully open or fully closed has Since there is no situation in which only one valve is opened in the actual operation process, there are 12 combinations of valve openings left.

设适应度函数为：Let the fitness function be:

该函数没有显式的数学表达式，下面详细阐述该函数的映射关系：This function has no explicit mathematical expression, and the mapping relationship of this function is elaborated below:

输入：enter:

1)所有给定负荷点的流量Ge₁、Ge₂......Ge_l，以及每个负荷点运行时间百分比W₁、W₂......W_l 1) The flow rate Ge ₁ , Ge ₂ ...Ge _l of all given load points, and the operating time percentage of each load point W ₁ , W ₂ ...W _l

2)阀门开度(12种0，1组合)：[0000；0011；0101；1001；0110；1100；1010；1110；1101；1011；0111；1111]；2) Valve opening (12 combinations of 0 and 1): [0000; 0011; 0101; 1001; 0110; 1100; 1010; 1110; 1101; 1011; 0111; 1111];

3)阀门喷嘴组喷嘴数目组合X1，X2，X3，X4，通过一个个体的编码产生3) Valve nozzle group nozzle number combination X1, X2, X3, X4, generated by an individual code

4)由变工况计算的热力学参数(c₁、w₁、h₁、c₂、w₂、h₂、η_u)、调节级特性曲线(μ-ε、λ-ε、Ω_m-ε及η-x_a。)、几何参数(各喷嘴喉部截面积A_nk，动叶出口截面积A_b)、滑压运行规律曲线(功率-主蒸汽压力)等.4) Thermodynamic parameters (c ₁ , w ₁ , h ₁ , c ₂ , w ₂ , h ₂ , η _u ) calculated from variable working conditions, adjustment level characteristic curves (μ-ε, λ-ε, Ω _m -ε and η-x _a .), geometric parameters (throat cross-sectional area of each nozzle A _nk , rotor blade outlet cross-sectional area A _b ), sliding pressure operation law curve (power-main steam pressure), etc.

映射：mapping:

1)通过阀门喷嘴数目组合X1，X2，X3，X4和其它参数，再加上12种阀门开度，代入变工况计算函数1) Combining X1, X2, X3, X4 and other parameters through the number of valve nozzles, plus 12 kinds of valve openings, substituting into the variable working condition calculation function

得到12个流量值[Xgz₁，Xgz₂....Xgz₁₂]Get 12 flow values [Xgz ₁ , Xgz ₂ ....Xgz ₁₂ ]

2)计算各负荷点对应的阀门开度以及计算出的流量值。依次检验1个负荷点，则调节级阀门在全开或全关条件下的第i个负荷点的计算流量xgz_i为：xgz_i＝Xgz_j使得|Xgz_j-Ge_i|＝min(|Xgz₁-Ge_i|，|Xgz₂-Ge_i|，......，|Xgz₁₂-Ge_i|)2-9i＝1，2，...，l；j＝1，2，...，122) Calculate the valve opening corresponding to each load point and the calculated flow value. Check one load point in turn, then the calculated flow xgz _i of the i-th load point of the regulating valve under the condition of fully open or fully closed is: xgz _i =Xgz _j such that |Xgz _j -Ge _i |=min(|Xgz ₁ -Ge _i |,|Xgz ₂ -Ge _i |,...,|Xgz ₁₂ -Ge _i |) 2-9i=1, 2,..., l; j=1, 2,. . . ., 12

得到1个流量xg₁，xgz₂......xgz_l Get 1 traffic xg ₁ , xgz ₂ ...... xgz _l

输出：output:

各个机组在实际运行条件下，各负荷的运行时间频率不同，在喷嘴数目优化模型中将运行时间概率进行加权处理。式2-10表征该喷嘴组合的机组在不同负荷点运行下的综合效应，Y越小，说明该喷嘴组合越好。Under the actual operating conditions of each unit, the operating time frequency of each load is different, and the operating time probability is weighted in the nozzle number optimization model. Equation 2-10 characterizes the comprehensive effect of the nozzle combination unit operating at different load points, and the smaller Y is, the better the nozzle combination is.

Y＝W₁(xgz₁-Ge₁)²+W₂(xgz₂-Ge₂)²+......+W_l(xgz_l-Ge_l)² 2-10Y＝W ₁ (xgz ₁ -Ge ₁ ) ² +W ₂ (xgz ₂ -Ge ₂ ) ² +...+W _l (xgz _l -Ge _l ) ² 2-10

在遗传算法中，适应度函数越大，遗传到下一代的概率越大，并且适应度函数的取值非负，在本例中Y取值越小是我们越希望得到的。所以Y不是适应度函数的最终表达。另一方面，2.1.1中式2-3的约束并没有在编码中被解决，如果按照上述过程进行优化，则一些不满足约束条件2-3的喷嘴组合也被代入到计算中并且可能随着计算出较大的适应度被遗传到下一代中，造成优化错误。因此我们需要在适应度函数定义时，采用适当的变换将没有意义的个体在迭代中逐渐淘汰，以保留符合条件的个体。In the genetic algorithm, the greater the fitness function, the greater the probability of inheritance to the next generation, and the value of the fitness function is non-negative. In this example, the smaller the value of Y is, the more we hope to obtain. So Y is not the final expression of the fitness function. On the other hand, the constraints of Equation 2-3 in 2.1.1 have not been solved in the coding. If the optimization is carried out according to the above process, some nozzle combinations that do not satisfy the constraints 2-3 will also be substituted into the calculation and may follow The calculated greater fitness is inherited to the next generation, resulting in optimization errors. Therefore, when defining the fitness function, we need to use appropriate transformations to gradually eliminate meaningless individuals in iterations to retain eligible individuals.

当X_min≤X₄≤X_max时：When X _min ≤ X ₄ ≤ X _max :

$ObjV ObjV = = \frac{11}{Y Y} - - - - - - 22 - - 1111$

当X₄＞X_maxORX₄＜X_min时：When X ₄ >X _max OR X ₄ <X _min :

$ObjV ObjV = = \frac{11}{Y Y} / / {e e}^{αδ αδ} - - - - - - 22 - - 1212$

式2-12中表明不满足约束2-3的喷嘴组合其适应度值被缩小了e^αδ倍。Equation 2-12 shows that the fitness value of nozzle combinations that do not satisfy constraint 2-3 is reduced by e ^αδ times.

$δ δ = = \{\begin{matrix} \frac{{X x}_{44} - - {X x}_{max max}}{{X x}_{max max}},, if if & {X x}_{44} > > {X x}_{max max} \\ \frac{{X x}_{min min} - - {X x}_{44}}{{X x}_{min min}},, if if & {X x}_{44} < < {X x}_{min min} \end{matrix} - - - - - - 22 - - 1313$

上式说明，X4越偏离设计值，适应度值相对没有偏离设计值的缩小倍数越大。α为缩小系数，在优化前设定。我们在实验时设计当X4偏离设计值100％时适应度值缩小1000倍。此时α＝6.9078。这样，被缩小了适应度值的个体将在遗传迭代过程中被逐渐淘汰掉，达到了实现约束条件2-3的目的。The above formula shows that the more X4 deviates from the design value, the greater the reduction factor of the fitness value relative to the value that does not deviate from the design value. α is the reduction factor, which is set before optimization. We design in the experiment that when X4 deviates from the design value by 100%, the fitness value is reduced by 1000 times. At this time, α=6.9078. In this way, the individuals whose fitness value has been reduced will be gradually eliminated in the genetic iteration process, and the purpose of realizing the constraints 2-3 is achieved.

Claims

1. consider a number of nozzle Optimization Design for each nozzle sets that steam turbine actual motion retrains, it is characterized in that: described method realizes in accordance with the following steps:

Step one, structure number of nozzle Optimized model:

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

W ₁, W ₂w _lrepresent each loading point percentage working time;

Xgz ₁, xgz ₂xgz _lrepresent the actual flow of each given loading point;

Ge ₁, Ge ₂ge _lrepresent the theoretical delivery of each given loading point;

The comprehensive departure degree Y of actual flow and theoretical delivery represents;

Step 2, calculate the actual flow of each given loading point:

1 is calculated by the valve opening of each valve nozzle number and correspondence thereof ... the actual flow of l given loading point:

{xgz}_{kj} = \frac{0.648 A_{nk}}{\sqrt{\frac{p_{0 k}}{ρ_{0 k}}}} \frac{β_{1 k}}{\frac{p_{2}}{p_{0 k}}} p_{2} = A_{k} μ_{k} p_{2} - - - (1 - 1)

In formula: j is the aperture combining form of valve, β _1kfor the governing stage flow-rate ratio of a kth nozzle sets, A _nkfor each nozzle throat sectional area sum of a kth nozzle sets, p _0kfor the pressure after a kth modulating valve valve, ρ _0kfor the density after a kth modulating valve valve, p _1kfor the nozzle back pressure of a kth nozzle sets, p ₂for the pressure in steam chest after governing stage;

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

{xgz}_{kj}^{'} = \frac{0.648 A_{nk}}{\sqrt{\frac{p_{0 k}}{p_{0 k}}}} \frac{β_{2 k} λ_{k}}{\frac{p_{2}}{p_{0 k}}} p_{2} - - - (1 - 2),

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

P is calculated by dichotomy ₂: pressure p after steps A, a given nozzle _1k; Step B, enthalpy h according to thermodynamic computing formulae discovery delivery nozzle outlet port steam ₁, steam speed c ₁with the relative velocity w of movable vane inlet steam ₁, then the rate of discharge G of a nozzle steam is calculated by formula (1-2) _n, the detailed process according to thermodynamic computing formulae discovery parameters is:

Jet expansion steam flow rate c ₁:

C in formula _1s---the steam flow ideal velocity (m/s) of jet expansion;

---the stagnation isentropic enthalpy drop, ideal enthalpy drop (J/Kg) of steam in nozzle;

---the velocity coefficient of nozzle, get velocity coefficient 2, movable vane import relative velocity w ₁

Movable vane imports and exports speed,

w_{1} = \sqrt{c_{1}^{2} + u^{2} - 2 u c_{1} \cos α_{1}} - - - (3 - 12)

γ_{1} = \arcsin \frac{c_{1} \sin α_{1}}{w_{1}} - - - (3 - 13)

U---movable vane peripheral velocity

γ ₁---relative velocity enters the angle of moving blades

Jet expansion enthalpy h ₁:

Because flow process is adiabatic, consuming with the kinetic transformation in loss is that heat heated again steam itself, so the actual enthalpy h of jet expansion steam flow ₁desirable enthalpy h will be greater than _1s, i.e. h ₁=h _1s+ △ h _{n ξ};

The pressure of step C, then a hypothesis movable vane outlet vapor, i.e. pressure p after governing stage ₂; Step D, drawn the enthalpy h of movable vane outlet port steam by thermodynamic computing formula ₂, outlet port steam density p ₂, outlet vapor relative velocity w ₂with absolute velocity c ₂, then the flow G of movable vane outlet vapor is gone out by formulae discovery _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; G _b=ρ ₂w ₂a _b, in formula: ρ ₂---movable vane outlet actual density; A _b---movable vane outlet throat area;

The relative velocity w of movable vane outlet ₂and absolute velocity c ₂:

In order to the convenience of problem analysis, we introduce an imaginary speed c _a, corresponding kinetic energy equals the isentropic enthalpy drop of level, that is:

Δ h_{s}^{*} = \frac{{c_{a}}^{2}}{2} - - - (3 - 24)

w_{2 s} = \sqrt{2 Δ h_{b} + w_{1}^{2}} = \sqrt{2 Ω_{m} Δ h_{s}^{*} + w_{1}^{2}} = \sqrt{2 Δ h_{b}^{*}} - - - (3 - 16)

△ h in formula _b---movable vane isentropic enthalpy drop, ideal enthalpy drop;

W ₁---the effective relative velocity of movable vane import;

---level stagnation isentropic enthalpy drop, ideal enthalpy drop;

---movable vane is stagnant isentropic enthalpy drop, ideal enthalpy drop relatively only,

Ω _m---the average degree of reaction of level,

W _2s---the constant entropy speed of movable vane outlet

The actual relative velocity w of moving blades ₂be expressed as: w ₂=ψ w _2s

c_{2} = \sqrt{w_{2}^{2} + u^{2} - 2 u w_{2} \cos (180 - β_{2})} - - - (3 - 14)

α_{2} = \arcsin \frac{w_{2} \sin (180 - β_{2})}{c_{2} \cos (180 - α_{2})} - - - (3 - 15)

α ₂---flow outlet angle

Movable vane outlet enthalpy h ₂:

The outlet enthalpy of movable vane equals the difference of jet expansion enthalpy and enthalpy drop, that is:

h ₂＝h _2s-△h ₂

1) movable vane entrance clashes into loss △ h _β

Δ h_{β} = \frac{{(w_{1} \sin θ)}^{2}}{2} - - - (3 - 11)

The angle in θ---movable vane import relative velocity direction and movable vane inlet angle direction

2) moving blade loss △ h _{b ξ}

Energy loss △ h in movable vane _{b ξ}be expressed as:

{Δh}_{bξ} = \frac{1}{2} ({w_{2 s}}^{2} - {w_{2}}^{2}) = (1 - ψ^{2}) Δ h_{b}^{*} - - - (3 - 18)

ψ---movable vane velocity coefficient

3) leaving loss △ h _c2

Δ h_{c 2} = \frac{{c_{2}}^{2}}{2} - - - (3 - 19)

Enthalpy drop: △ h ₂=△ h _β+ △ h _{b ξ}+ △ h _c2

According to pressure p after the governing stage that dichotomy calculates ₂be updated in formula (1-2) and calculate actual flow xgz;

Step 3, calculate the theoretical delivery of each given loading point:

Ge _h=Ge ξ _h, wherein Ge _hfor the theoretical delivery of loading point, Ge is the rated flow of steam turbine, ξ _hfor accounting for the percentage of rated power in loading point tubine operate power, h=1,2 ... l, l are the number of working load point;

The constraint conditio of step 4, structure number of nozzle Optimized model:

X ₁+X ₂+X ₃+X ₄＝X _z,X _z＝const (2-2)

X _min≤X _i≤X _max,i＝1,2,3,4；X _min＝const,X _max＝const (2-3)

X ₁, X ₂, X ₃, X ₄represent the nozzle number of four nozzle sets, X _zfor total nozzle number, const represents definite value;

Step 5, obtain given loading point based on Genetic Algorithms Theory under the combination of optimum number of nozzle corresponding when making actual flow and the comprehensive departure degree Y of theoretical delivery minimum, detailed process is as follows:

Step 5 (one), initial population set:

Adopting floating-point encoding, is [X between code area _min, X _max],

Chrom = [\begin{matrix} x_{11}, x_{12}, x_{13} \\ x_{21}, x_{22}, x_{23} \\ . . . . . . . . . . . . . . . . . \\ x_{m 1}, x_{m 2,} x_{m 3} \end{matrix}], x_{ij} &Element; R_{+}, i = 1,2, . . ., m, j = 1,2,3 . - - - (2 - 4)

In formula, the individual amount of m representative coding;

For body one by one, its each chromosome x _i1, x _i2, x _i3, be respectively the nozzle sets number of nozzle X that first three regulating valve is corresponding ₁, X ₂, X ₃coding, its corresponding relation is:

X _ij＝round(x _ij),i＝1,2...m,j＝1,2,3 (2-5)

Round represents round, calculates X ₁, X ₂, X ₃after, X ₄for:

X _i4＝X _z-(X _i1+X _i2+X _i3) (2-7)

Step 5 (two), structure fitness function ObjV: calculated by fitness, realize individual optimum choice, make the 4th nozzle sets number of nozzle in optimum results meet constraint conditio (2-3) formula simultaneously,

The individuality (2-8) not meeting constraint conditio is given up in iteration:

X _i4>X _max OR X _i4<X _min (2-8)

If fitness function is:

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

Above-mentioned fitness function does not have explicit mathematic(al) representation, and the mapping relations of above-mentioned fitness function are as follows:

Input:

1), the flow Ge of all given loading point ₁, Ge ₂ge _l, and each loading point percentage working time W ₁, W ₂w _l;

2), 12 kinds of valve openings: [0 000; 0011; 0101; 1001; 0110; 1100; 1010; 1110; 1101; 1011; 0111; 111 1];

3), valve nozzle group number of nozzle combination X ₁, X ₂, X ₃, X ₄, produced by the coding of body one by one;

4), the thermodynamic parameter of variable condition calculation:

Jet expansion steam flow rate c ₁, movable vane import relative velocity w ₁, jet expansion enthalpy h ₁, absolute velocity c ₂, movable vane outlet relative velocity w ₂, movable vane outlet enthalpy h ₂, wheel efficiency η _u;

Governing stage characteristic curve: μ-ε, λ-ε, Ω _m-ε and η _u-x _a;

The peripheral velocity of u---movable vane;

λ---coefficient,

λ = \frac{β_{1}}{β_{2}};

Ω _m---the average degree of reaction of level;

ε---stage pressure ratio;

η---wheel efficiency;

X _a---speed ratio;

μ---coefficient,

μ = \frac{β_{2} λ}{ϵ};

Fa---valve opening;

Geometric parameter: each nozzle throat sectional area A _nk, movable vane discharge area A _b;

Sliding pressure operation law curve: power-main steam pressure;

Map:

1), by valve nozzle number of combinations X ₁, X ₂, X ₃, X ₄be c with the thermodynamic parameter of variable condition calculation ₁, w ₁, h ₁, c ₂, w ₂, h ₂, η _u, governing stage characteristic curve is μ-ε, λ-ε, Ω _m-ε and η-x _a, geometric parameter is each nozzle throat sectional area A _nk, movable vane discharge area A _b, sliding pressure operation law curve, adds 12 kinds of valve openings, substitutes into the variable condition calculation function described in step one to four;

The process of step one to four represents with following formula,

[Xgz, Xgz1, Xgz2, Xgz3, Xgz4, Xnri, Fux, Fuy]=Changingstate (Ge ₁, Fa, X ₁, X ₂, X ₃, X ₄, others), obtain 12 flow value [Xgz ₁, Xgz ₂.Xgz ₁₂], what Xnri, Fux, Fuy represented respectively is internal efficiency ratio, horizontal gas flow power, vertically air-flow power;

2) flow value, calculating valve opening corresponding to each loading point and calculate; Check l loading point, then the calculated flow rate xgz of h the loading point of governing stage valve under standard-sized sheet or complete shut-down condition successively _hfor:

Xgz _h=Xgz _jmake | Xgz _j-Ge _h|=min (| Xgz ₁-Ge _h|, | Xgz ₂-Ge _h| ..., | Xgz ₁₂-Ge _h|) (2-9)

h＝1,2,...,l；j＝1,2,...,12

Obtain l flow xgz ₁, xgz ₂... xgz _l

Export:

Formula 2-10 characterizes the comprehensive effect of unit under different load point runs of this Nozzle combination, and Y is less, illustrates that this Nozzle combination is better;

Finally being expressed as of fitness function:

Work as X _min≤ X ₄≤ X _maxtime:

ObjV = \frac{1}{Y} - - - (2 - 11)

Work as X ₄>X _maxoR X ₄<X _mintime:

ObjV = \frac{1}{Y} / e^{αδ} - - - (2 - 12)

Show not meet the reduced e of its fitness value of Nozzle combination of constraint 2-3 in formula 2-12 ^{α δ}doubly;

α is coefficient of reduction;

Step 5 (three), complete step after, then carry out based on the selection of traditional genetic algorithm, intersection, mutation process; When genetic algebra reach end condition N for time, genetic process stops, export meet actual flow minimum with the comprehensive departure degree Y of theoretical delivery time corresponding optimum number of nozzle combination.

2. the number of nozzle Optimization Design of each nozzle sets of consideration steam turbine actual motion according to claim 1 constraint, is characterized in that: calculate p in step 2 by dichotomy ₂process in, pressure p after described nozzle _1kcomputational process be: the sliding pressure operation law curve obtained in actual motion by steam turbine set: power-main steam pressure, then according to actual motion load, check in the pressure of main steam, then calculate p _1k.