Nsga-ii-based method for optimizing msr secondary reheat extraction flow of nuclear power unit

Abstract

The application discloses a kind of MSR secondary reheat extraction flow optimization methods of nuclear power unit based on NSGA-II, by establishing nuclear power unit conventional island thermodynamic system model, with secondary reheat extraction flow as design variable, with secondary reheat steam end difference and electric power as optimization goal optimization, to give the secondary reheat extraction flow of electric power most close to rated electric power and secondary reheat steam end difference most close to design end difference.This application has the advantages that: with secondary reheat extraction flow as design variable optimization, compared with the existing research focuses on reheat steam pressure, temperature and other design parameters optimization, directly controllable, easy for unit operation personnel to adjust unit operating condition.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of power systems, and particularly relates to a MSR secondary reheating extraction flow optimization method for a nuclear unit based on a fast and elitist non-dominated sorting genetic algorithm (NSGA-II). BACKGROUND

[0002] Nuclear fuel has extremely high energy density compared to fossil fuels, and nuclear reactions do not produce exhaust gas, dust and greenhouse gas, so it is a clean energy. Therefore, in the past more than half a century, nuclear power has been greatly applied and developed, and occupies an important position in the world energy structure. At present, China's nuclear power installed capacity ranks third in the world, and is expected to reach 51.03 million kilowatts in 2020. With the continuous rise of China's nuclear power installed capacity, more and more scholars focus on the optimization of the thermal performance of nuclear power units.

[0003] The moisture separator reheater (MSR) is an important auxiliary equipment of the conventional island of a nuclear power unit, and its performance will directly affect the efficiency and safe operation of the unit. The MSR is located between the high-pressure cylinder and the medium-pressure cylinder (or the high-pressure cylinder and the low-pressure cylinder) of the turbine, and is used to remove water from the high-pressure cylinder exhaust steam and heat the exhaust steam to make it superheated before entering the medium-pressure cylinder (or the low-pressure cylinder), so as to reduce the erosion of the low-pressure cylinder blades. In actual operation of the power plant, the MSR often cannot operate under the design condition, and the terminal temperature difference of the secondary reheater is higher or lower than the design terminal temperature difference, which affects the thermal system cycle efficiency of the turbine and the output electric power of the unit. At present, the research on the optimization of the MSR is focused on the optimization of the design parameters such as the inlet and outlet steam pressure and temperature of the reheater in the design stage, and from the perspective of the unit operation, the above parameters cannot be directly controlled.

[0004] In actual operation of the nuclear power unit, the MSR can adjust the secondary reheating steam flow by controlling the opening degree of the regulating valve (or adding a throttling device) on the secondary reheating extraction pipe, and change the MSR outlet steam temperature to match the operation requirements of the turbine equipment. Since the secondary reheating extraction of the MSR of the nuclear power unit is taken from the main steam system, the change of the new steam extraction flow will directly lead to the change of the output electric power of the turbine generator unit. Therefore, it is of great practical significance to establish a model of the conventional island thermal system of the nuclear power unit, take the secondary reheating extraction flow as a design variable, take the terminal temperature difference of the secondary reheater and the electric power as optimization objectives, and study the multi-objective optimization problem, for the operation optimization of the power plant. SUMMARY

[0005] The purpose of the present application is to provide a nuclear power unit MSR secondary reheating extraction flow optimization method based on NSGA-II, which is suitable for various nuclear power unit MSR secondary reheating extraction flow optimization, can be used to guide the operation control of the secondary reheating extraction flow of the nuclear power unit, so that the optimal flow value is reached, and the economic efficiency of the MSR equipment operation is kept best. Through the actual operation data verification calculation of the nuclear power unit, after the secondary reheating extraction flow of the MSR is optimized by the method, the electric power output by the nuclear power unit can be improved.

[0006] The technical scheme of the present application is as follows: a nuclear power unit MSR secondary reheating extraction flow optimization method based on NSGA-II, comprising the following steps:

[0007] Step 1: obtaining unit normal operation condition data;

[0008] Step 2: calculating the main steam specific enthalpy and specific entropy according to the main steam pressure, temperature and dryness;

[0009] Step 3: taking the design efficiency of each stage as the initial iteration efficiency;

[0010] Step 4: determining the extraction pressure and extraction temperature of each extraction point, and calculating the extraction enthalpy of each extraction point;

[0011] Step 5: performing heat balance calculation on the regenerative system and the MSR;

[0012] Step 6: calculating the extraction flow of each extraction point and the stage power;

[0013] Step 7: calculating the turbine power;

[0014] Step 8: calculating the power error, if the error is less than the set value, output the thermal system model; otherwise,

[0015] Adjusting the efficiency of each stage, repeating steps 4 to 8;

[0016] Step 9: determining the design variable of the multi-objective optimization problem as the secondary reheating extraction flow Objective function

[0017] And the constraint condition is:

[0018]

[0019]

[0020] Wherein, T rh2d is the design end difference of the secondary reheater, is the end difference of the secondary reheater, P e0 is the rated electric power of the unit, is the electric power output by the unit, is the original secondary reheat extraction flow rate;

[0021] Step 10: randomly initialize N After binary coding, an initial parent population P0 is formed, and a child population Q0 is generated using crossover and mutation operations;

[0022] Step 11: non-dominated sorting is performed on the population R0 composed of P0 and Q0, and non-dominated solution sets F1, F2, F3... of all different levels are constructed;

[0023] Step 12: according to the non-dominated sequence from low to high, each layer population is sequentially put into the parent population P1 of the next iteration until the layer F j appears, the size of P1 exceeds the population size limit N, and P1 is continued to be filled according to the sorting of the crowding distance of individuals in F j from large to small until the population number reaches N;

[0024] Step 13: repeat steps 10 to 12 until the iteration number reaches the limit;

[0025] Step 14: among the final obtained population individuals, select the individual that makes the electric power closest to the rated electric power as the optimal secondary reheat extraction flow rate

[0026] In step 10, when selecting the parent for crossover, a tournament selection algorithm is used.

[0027] In step 11, the non-dominated sorting is a cyclic fitness grading process: first find the non-dominated solution set in the population, denoted as the first non-dominated layer F1, and assign all individuals in it a non-dominated sequence i rank =1, and remove them from the entire population; continue to find the non-dominated solution set in the remaining population, denoted as the second non-dominated layer F2, and assign the individuals a non-dominated sequence i rank =2; repeat the above operation until the entire population is layered, and the individuals in the same layer have the same non-dominated sequence i rank .

[0028] In step 12, the crowding distance of individual i refers to the distance between i and its adjacent individuals i+1 and i-1 in the target space, and the calculation steps are as follows:

[0029] Step 121: initialize the distance of individuals in the same layer, let L[i] d =0, and L[i] d represents the crowding distance of any individual i.

[0030] Step 122: arrange the individuals in the same layer in ascending order according to the mth objective function value.

[0031] Step 123: for the individual on the sequence edge, let its crowding distance be infinity.

[0032] Step 124: for the individual not on the sequence edge, its crowding distance is:

[0033]

[0034] where L[i+1] m is the m-th objective function value of the i+1-th individual, and are the maximum and minimum values of the m-th objective function in the set, respectively.

[0035] Step 125: repeat steps ii to iv for different objective functions to obtain the crowding distance L[i] d of the individual i.

[0036] The application has the advantages that the MSR secondary reheat extraction flow optimization method for nuclear power unit based on NSGA-II has the advantages of fast operation speed and good convergence of solution set. The secondary reheat extraction flow is taken as a design variable for optimization, compared with the existing research which focuses on the optimization of reheat inlet and outlet steam pressure, temperature and other design parameters, which is directly controllable and convenient for unit operation personnel to adjust the unit operation condition. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 is a flow chart of the thermal system modeling of the application;

[0038] Figure 2 is a flow chart of the MSR secondary reheat extraction flow optimization method for nuclear power unit based on NSGA-II provided by the application;

[0039] Figure 3 is a secondary reheat extraction flow optimization result graph in the embodiment of the application;

[0040] Figure 4 is a secondary reheat extraction flow and electric power relationship curve graph in the embodiment of the application;

[0041] Figure 5 is a hyper volume index (HV) change curve graph in the iteration process of the NSGA-II algorithm in the embodiment of the application;

[0042] Figure 6 is an inverted generation distance (IGD) change curve graph in the iteration process of the NSGA-II algorithm in the embodiment of the application. DETAILED DESCRIPTION

[0043] The application adopts a MSR secondary reheat extraction flow optimization method for nuclear power unit based on NSGA-II. A nuclear power unit conventional island thermal system model is established, the secondary reheat extraction flow is taken as a design variable, and the secondary reheat temperature difference and electric power are taken as optimization objectives for optimization, so that the secondary reheat extraction flow which considers the electric power closest to the rated electric power and the secondary reheat temperature difference closest to the design temperature difference is given.

[0044] The application adopts the following technical scheme:

[0045] The MSR secondary reheat extraction flow optimization method for nuclear power unit based on NSGA-II comprises the following steps:

[0046] Step 1: Obtain unit normal operation condition data.

[0047] Step 2: Calculate the main steam specific enthalpy and specific entropy according to the main steam pressure, temperature and dryness.

[0048] Step 3: Take the design efficiency of each stage as the iteration initial efficiency.

[0049] Step 4: Determine the extraction pressure and extraction temperature of each extraction point, and calculate the extraction enthalpy of each extraction point.

[0050] Step 5: Perform heat balance calculation on the regenerative system and the MSR.

[0051] Step 6: Calculate the extraction flow of each extraction point and the stage power.

[0052] Step 7: Calculate the turbine power.

[0053] Step 8: Calculate the power error, if the error is less than the set value, output the thermal system model; otherwise,

[0054] Repeat steps 4 to 8 after adjusting the efficiency of each stage.

[0055] Step 9: Determine the design variable of the multi-objective optimization problem as the secondary reheat extraction flow Objective function

[0056] And the constraint condition is:

[0057]

[0058] Wherein, T rh2d is the design temperature difference of the secondary reheat, is the temperature difference of the secondary reheat, P e0 is the rated electric power of the unit, is the electric power output by the unit, is the original secondary reheat extraction flow.

[0059] For NSGA-II algorithm, the secondary reheat extraction flow rate Corresponding to the population individual, the objective function corresponds to the fitness function. The secondary reheat extraction flow rate is substituted into the thermal system model, and the objective function value can be calculated.

[0060] Step 10: randomly initialize N After binary coding, an initial parent population P0 is formed, and crossover and mutation operations are used to generate the offspring population Q0.

[0061] Step 11: non-dominated sorting is performed on the population R0 composed of P0 and Q0, and non-dominated solution sets F1, F2, F3... of all different levels are constructed.

[0062] Step 12: according to the non-dominated sequence from low to high, the layered populations are sequentially placed into the parent population P1 of the next iteration until a layer F j is reached, and the size of P1 exceeds the population size limit N. According to the sorting of the crowded distance of individuals in F j from large to small, P1 is filled until the population size reaches N.

[0063] Step 13: repeat steps 10 to 12 until the iteration limit is reached.

[0064] Step 14: among the final population individuals, select the individual that makes the electric power closest to the rated electric power

[0065] Further, in step 10, when selecting the parent for crossover, the tournament selection algorithm is used.

[0066] Further, in step 11, the non-dominated sorting is a cyclic fitness grading process: first find the non-dominated solution set in the population, denoted as the first non-dominated layer F1, assign all individuals in it to the non-dominated sequence i rank = 1 (where i rank is the non-dominated sequence value of individual i), and remove it from the entire population; continue to find the non-dominated solution set in the remaining population, denoted as the second non-dominated layer F2, and assign the individual to the non-dominated sequence i rank = 2; repeat the above operation until the entire population is layered, and the individuals in the same layer have the same non-dominated sequence i rank .

[0067] Further, in step 12, the crowded distance of individual i refers to the distance between i+1 and i-1 adjacent to i in the objective space, and the calculation steps are as follows:

[0068] Step 121: initialize the distance of individuals in the same layer, let L[i] d = 0 (L[i] d represents the crowding distance of any individual i).

[0069] Step 122: arrange the individuals in the same layer in ascending order according to the mth objective function value.

[0070] Step 123: for the individuals on the sequence edge, let their crowding distance be infinite.

[0071] Step 124: for the individuals not on the sequence edge, their crowding distance is:

[0072]

[0073] where L[i+1] m is the mth objective function value of the i+1th individual, and are the maximum and minimum values of the mth objective function in the set, respectively.

[0074] Step 125: repeat steps ii to iv for different objective functions to obtain the crowding distance L[i] d of individual i.

[0075] The present application has the following advantages compared with the prior art: NSGA-II uses fast non-dominated sorting, reducing the computational complexity; the crowding distance of individuals is calculated to retain solutions with low similarity, maintaining the diversity of the solution space; the elite strategy is used to speed up convergence and remove inferior solutions faster. The MSR secondary reheat extraction flow optimization method for nuclear power unit based on NSGA-II has the advantages of fast running speed and good convergence of solution set. With the secondary reheat extraction flow as the design variable for optimization, compared with the existing research which focuses on optimizing the design parameters such as reheat inlet and outlet steam pressure and temperature, it is directly controllable and convenient for unit operation personnel to adjust the unit operating condition.

[0076] The present application will be further described below with reference to the accompanying drawings and an embodiment of a 1000MW nuclear power unit secondary reheat extraction flow optimization. As shown in Figure 1 and Figure 2 , the present application provides a MSR secondary reheat extraction flow optimization method for nuclear power unit based on NSGA-II, specifically including the following steps:

[0077] (1) Obtain the unit normal operating condition data. In this embodiment, the operating data of a 1000MW nuclear power unit at a certain time on February 11, 2019 is obtained, and part of the data is shown in Table 1.

[0078] Table 1. Operation data of a 1000 MW nuclear power unit

[0079]

[0080] (2) Calculate the specific enthalpy and specific entropy of the main steam according to the main steam pressure, temperature and dryness. The dryness is 0.9951 at the design condition.

[0081] (3) Take the design efficiency of each stage as the initial efficiency of iteration.

[0082] (4) Determine the extraction pressure and extraction temperature of each extraction point, and calculate the extraction enthalpy of each extraction point.

[0083] (5) Perform heat balance calculation on the regenerative system and the MSR.

[0084] (6) Calculate the extraction flow rate of each extraction point and the stage power.

[0085] (7) Calculate the power of the steam turbine.

[0086] (8) Calculate the power error. If the error is less than the set value, output the thermal system model; otherwise, adjust the efficiency of each stage and repeat steps (4) to (8).

[0087] The program output is an electric power error of 0.02 MW, which is less than the maximum allowable error of 0.10 MW, and the established thermal system model is reliable.

[0088] (9) Determine the design variables of the multi-objective optimization problem as the secondary reheat extraction flow rate The objective function and the constraint condition are:

[0089]

[0090] where T rh2d is the design temperature difference of the secondary reheater, T rh2d = 11.3℃, is the temperature difference of the secondary reheater, P e0 is the rated electric power of the unit, P e0 = 1089 MW, is the output electric power of the unit, is the original secondary reheat extraction flow rate,

[0091] For the NSGA-II algorithm, the secondary reheat extraction flow rate corresponds to the population individual, and the objective function corresponds to the fitness function. Substituting the secondary reheat extraction flow rate into the thermal system model, the objective function value can be calculated.

[0092] (10) Randomly initialize N After being binary encoded, an initial parent population P0 is formed, and crossover and mutation operations are used to generate a child population Q0.

[0093] (11) Perform non-dominated sorting on the group R0 composed of P0 and Q0, and construct non-dominated solution sets F1, F2, F3... of all different levels.

[0094] (12) Following the non-dominated order from low to high, each stratified population is sequentially placed into the parent population P1 of the next iteration, until a certain stratum F is placed. j When the size of P1 exceeds the population size limit N, according to F j The individuals are sorted from largest to smallest crowding distance and P1 is filled until the population size reaches N.

[0095] (13) Repeat steps (10) to (12) until the number of iterations reaches the limit.

[0096] (14) Write a program to perform the calculation. The Pareto front calculated by the NSGA-II algorithm is as follows: Figure 3 As shown. Among the individuals in the final population, those with higher electrical power are selected. The individual closest to the rated electrical power This is the optimal second-stage reheat extraction steam flow rate. The relationship between the second-stage reheat extraction steam flow rate and electrical power is shown in the curve. Figure 4 As shown. In this embodiment, the optimal second-stage reheat extraction steam flow rate is... Compared to the original secondary reheat extraction steam flow rate The power decreased by 7.12%. The rated power is close to 1089MW, an increase of 1.68MW compared to the unoptimized power, and the terminal temperature difference of the second-stage reheater is... The temperature difference is 0.9℃ greater than the design temperature. Table 2 shows a comparison of the parameters before and after optimization. It can be concluded that the optimized parameters are closer to the design parameters, and the power output of the unit has been significantly improved.

[0097] Table 2. Comparison of parameters before and after optimization

[0098]

[0099] Figure 5 and Figure 6The figure is the variation curve of the hypervolume (HV) and the inverted generational distance (IGD) in the iteration process of the NSGA-II algorithm in this embodiment. The HV represents the volume of the region in the objective space enclosed by the non-dominated solution set obtained by the algorithm and the reference point. The IGD represents the average value of the distance from each reference point to the nearest solution. The larger the HV value and the smaller the IGD value, the better the comprehensive performance of the algorithm. As can be seen from the figure, after 500 iterations, the HV value is close to 0.84, and the IGD value is close to 0, so the solution set obtained by using the NSGA-II algorithm has good convergence and diversity. The MSR secondary reheat extraction flow optimization method based on the NSGA-II has a fast running speed, and the convergence of the solution set is good, and can be used to guide the actual operation of the nuclear power unit, adjust the secondary reheat extraction flow to reach the optimal operation value, and improve the output electric power of the unit.

Claims

1. A method for optimizing the second-stage reheat extraction steam flow rate of nuclear power unit MSR based on NSGA-II, characterized in that, Includes the following steps: Step 1: Obtain normal operating condition data of the unit; Step 2: Calculate the specific enthalpy and specific entropy of the main steam based on the main steam pressure, temperature, and dryness fraction; Step 3: Take the design efficiency of each stage as the initial efficiency for iteration; Step 4: Determine the extraction pressure and temperature at each extraction point, and calculate the extraction enthalpy at each extraction point; Step 5: Perform heat balance calculations for the regenerative system and MSR; Step 6: Calculate the extraction steam flow rate and stage power at each extraction point; Step 7: Calculate the turbine power; Step 8: Calculate the power error. If the error is less than the set value, output the thermodynamic system model; otherwise, After adjusting the efficiency of each stage, repeat steps 4 to 8; Step 9: Determine the design variable for the multi-objective optimization problem as the second-stage reheat extraction steam flow rate. The objective function and constraints are as follows: Among them, T rh2d Design a differential pressure for the secondary reheater. For the secondary reheater terminal temperature difference, P e0 The rated electrical power of the unit, The electrical power output of the unit. This is the original secondary reheat extraction steam flow rate; Step 10: Randomly initialize N After binary encoding, an initial parent population P0 is formed, and crossover and mutation operations are used to generate a child population Q0. Step 11: Perform non-dominated sorting on the population R0 composed of P0 and Q0, and construct all non-dominated solution sets F1, F2, F3... of different levels; Step 12: Following the non-dominated sorting from low to high order, sequentially place each stratified population into the parent population P1 of the next iteration, until a certain stratum F is placed. j When the size of P1 exceeds the population size limit N, according to F j The individuals are sorted from largest to smallest crowding distance and P1 is filled until the population size reaches N; Step 13: Repeat steps 10 to 12 until the number of iterations reaches the limit; Step 14: Among the individuals in the final population, select those that have the highest electrical power. The individual closest to the rated electrical power This is the optimal second-stage reheat extraction steam flow rate.

2. The method for optimizing the second-stage reheat extraction steam flow rate of nuclear power unit MSR based on NSGA-II as described in claim 1, characterized in that: In step 10, when selecting the parent generation for the crossover, the tournament selection algorithm is used.

3. The method for optimizing the second-stage reheat extraction steam flow rate of nuclear power unit MSR based on NSGA-II as described in claim 1, characterized in that: In step 11, the non-dominated ranking is a cyclic fitness hierarchical process: first, find the non-dominated solution set in the population, denoted as the first non-dominated layer F1, and assign a non-dominated order i to all individuals in it. rank =1, and remove it from the entire population; continue to find the non-dominated solution set in the remaining population, denoted as the second non-dominated layer F2, and assign the non-dominated order i to the individual. rank =2; Repeat the above operation until the entire population is stratified, and individuals within the same stratum have the same non-dominated order i. rank .

4. The method for optimizing the second-stage reheat steam extraction flow rate of nuclear power unit MSR based on NSGA-II as described in claim 1, characterized in that: In step 12, the crowding distance of individual i refers to the distance between two adjacent individuals i+1 and i-1 in the target space, and its calculation steps are as follows: Step 121: Initialize the distance between individuals in the same layer, let L[i] d =0, L[i] d Let i represent the crowding distance for any individual i; Step 122: Sort individuals in the same layer in ascending order based on the m-th objective function value; Step 123: For individuals on the edge of the sequence, set their crowding distance to infinity; Step 124: For individuals on the non-sequence edge, their crowding distance is: In the formula, L[i+1] m Let m be the objective function value of the (i+1)th individual. and Let be the maximum and minimum values ​​of the m-th objective function in the set, respectively; Step 125: For different objective functions, repeat steps 122 to 124 to obtain the crowding distance L[i] for individual i. d .

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