CN105759611A - Pressurized water reactor (PWR) nuclear power plant reactor core power model predictive control method based on genetic algorithm - Google Patents

Abstract

The invention discloses a pressurized water reactor (PWR) nuclear power plant reactor core power model predictive control method based on a genetic algorithm. The method comprises the steps of establishing a mathematical state space model of a reactor core; linearizing the mathematical state space model of the reactor core; establishing a power predictive control model of the reactor core; and carrying out parameters setting for the power predictive control model based on a genetic algorithm. The invention combines operating parameters of the PWR core, sets the parameters in a controller by using an improved genetic algorithm, obtains a global optimal solution, and achieves self-adaptive adjustment of PWR nuclear power plant reactor core power control; also predicts a future deviation value by using the predictive model, determines a current optimal control strategy by rolling optimization, and enables minimum deviation between a future controlled variable and a value of expectation; and optimizes undetermined parameters in the reactor core power predictive control model by using the genetic algorithm, and obtains optimal values for the undetermined parameters.

Description

Pressurized-water reactor nuclear power plant core power model predictive control method based on genetic algorithm

Technical field

The present invention relates to pressurized-water reactor nuclear power plant core power to control, particularly relate to a kind of pressurized-water reactor nuclear power plant core power model predictive control method based on genetic algorithm.

Background technology

Pressurized water reactor core is one of capital equipment of pressurized-water reactor nuclear power plant, and its major function is by nuclear reaction, produces substantial amounts of heat.In pressurized-water reactor nuclear power plant running, if pressurized water reactor core power can not be well controlled, it is possible to shutdown can be caused, even major accident.Therefore the control of pressurized water reactor core power is particularly important.

At present, pressurized water reactor core power controls the control program adopted, and the PID being still traditional mostly controls.PID controller is the error according to system, proportion of utilization, integration and difference gauge calculate controlled quentity controlled variable and control actuator variation control core power.Owing to pressurized water reactor core is a nonlinear system, and multiple interference has uncertainty, load large-scope change brings certain unstability simultaneously, and especially in low-load conditions, traditional PID control system is difficult to quickly and stably control pressurized water reactor core power.

Summary of the invention

It is an object of the invention to overcome the shortcoming and defect of above-mentioned prior art, there is provided a kind of pressurized-water reactor nuclear power plant core power model predictive control method based on genetic algorithm, the impact that pressurized water reactor core power is controlled by the unstability etc. brought with the uncertainty that has because of multiple interference of elimination, load large-scope change.Precise and high efficiency of the present invention, capacity of resisting disturbance are strong, be adapted to load variations on a large scale.The present invention according to the difference of nuclear power station operating condition, can adjust and control parameter, it is achieved pressurized water reactor core power controls.

The present invention is achieved through the following technical solutions:

A kind of pressurized-water reactor nuclear power plant core power model predictive control method based on genetic algorithm, comprises the following steps:

S1, set up the mathematical state spatial model of reactor core, described mathematical state spatial model includes equivalence single group delayed neutron Point reactor kinetic equations, thermal-hydraulic model equation and reactive model equation, wherein said equivalence single group delayed neutron Point reactor kinetic equations, according to reactor simple group neutron diffusion theory, adopts equivalence single group delayed neutron to carry out approximate description many groups delayed neutron Point reactor kinetic equations and obtains；

S2, mathematical state spatial model to described reactor core carry out linearisation, this step according to the relational expression between core power and neutron density, the energy conservation equation in reactor, be approximately considered in heat transfer process coolant physical parameter and remain unchanged and the linearized theory of small perturbation near reactor equilibrium point, according to Differential Geometry knowledge, the mathematical state spatial model of described reactor core is carried out linearisation, draws the linear math expression formula between parameter in pressurized water reactor core；

S3, set up the power prediction Controlling model of reactor core, this step draws the expression formula of inearized model Predictive Control System according to Model Predictive Control Theory, by correctly choosing state space variable x, state space output y, Space-state control amount u, according to linear algebra knowledge, solve the matrix in inearized model Predictive Control System and system, after model predictive control system discretization, calculate predicted state space variable and the predicted state space output of system in prediction time domain；According to Model Predictive Control Theory, obtained the condition of optimal value by analytical model Predictive Control System, solve the state space output of system；

S4, based on genetic algorithm, described power prediction Controlling model is carried out parameter tuning, this step utilizes genetic algorithm the undetermined parameter in described reactor core power prediction Controlling model is carried out optimizing, draw the optimal value of undetermined parameter.

Preferably, described equivalence single group delayed neutron Point reactor kinetic equations is as follows:

$\frac{dn}{dt}=\frac{\mathrm{\ρ}-\mathrm{\β}}{\mathrm{\Λ}}n+\mathrm{\λ}c---\left(1\right)$

$\frac{dc}{dt}=\frac{\mathrm{\β}}{\mathrm{\Λ}}n-\mathrm{\λ}c---\left(2\right)$

In formula, n is neutron density, and ρ is global reactivity, and β is the share of effective delayed neutron, and Λ is neutron generation time, and t is the time, and λ is the single decay constant organizing delayed neutron of equivalence, and c is equivalence single group delayed-neutron precursor density；

Described thermal-hydraulic model equation is as follows:

$f_f{P}_a={\mathrm{\μ}}_f\frac{{\mathrm{dT}}_f}{dt}+P_c---\left(3\right)$

$(1-f_f)P_a+P_c={\mathrm{\μ}}_c\frac{{\mathrm{dT}}_l}{dt}+P_e---\left(4\right)$

In formula, f_fIt is fuel power share, μ_cIt is coolant thermal capacity, μ_fIt it is fuel heat capacity；

Described reactive model equation is as follows:

$\mathrm{\δ}\mathrm{\ρ}={\mathrm{\δ\ρ}}_r+{\mathrm{\α}}_f(T_f-T_{f0})+\frac{{\mathrm{\α}}_c(T_l-T_{l0})}{2}+\frac{{\mathrm{\α}}_c(T_e-T_{e0})}{2}---\left(5\right)$

$\frac{{\mathrm{d\δ\ρ}}_r}{dt}=G_r{Z}_r---\left(6\right)$

In formula, G_rThe value of representation unit length control rod, δ represents the deviation value of deviation poised state, Z_rRepresent and control stick speed, T_l0It is initial coolant outlet temperature, T_f0It is initial fuel mean temperature, T_e0It is initial coolant inlet temperature, ρ_rIt is that control rod moves introduced reactivity, α_fIt is fuel reaction property coefficient, α_cIt it is coolant reactivity coefficient.

Preferably, described step S2 the mathematical state spatial model of described reactor core is carried out linearisation particularly as follows:

Step S21, as follows according to the relation of core power Yu neutron density:

P_a=P₀n(7)

In formula, P_aFor actual core power；P₀For reactor core rated power, therefore the value of neutron density n can represent relative core power；

Law of conservation of energy is applied to presurized water reactor, obtains the energy conservation equation in reactor as follows:

P_c=Ω (T_f-T_c)(8)

P_e=M (T_l-T_e)(9)

In formula, P_cIt is the fuel heat that passes to coolant, P_eBeing the coolant heat that passes to secondary circuit, Ω is the heat transfer coefficient between fuel and coolant, and M is the mass flow thermal capacity of coolant, T_fIt is average fuel temperature, T_cIt is coolant mean temperature, T_eIt is coolant inlet temperature, T_lIt it is coolant outlet temperature；

In pressurized-water reactor nuclear power plant, generally, the inlet temperature of coolant is stable at 300 DEG C.The difference of coolant inlet temperature and outlet temperature is approximately in 30 DEG C, it can be assumed that coolant is with fuel heat transfer process, coolant physical parameter is constant, obtains:

$\left\{\begin{array}{c}{T}_c=\frac{1}{2}(T_l+T_e)\\ {\mathrm{\δT}}_e=0\end{array}\right.---\left(10\right);$

Step S22, linearized theory by perturbation small near equilibrium point, release the equilibrium valve of neutron density in pressurized-water reactor nuclear power plant and deviate the deviation value of poised state much larger than neutron density, be expressed as by neutron density n: n=n₀+ δ n, by differential knowledge, is expressed as formula (1):

$\frac{d\mathrm{\δ}n}{dt}=\frac{-\mathrm{\β}}{\mathrm{\Λ}}\mathrm{\δ}n+\mathrm{\λ}\mathrm{\δ}c+\frac{\mathrm{\δ}\mathrm{\ρ}}{A}{n}_0---\left(11\right)$

In formula, n₀It it is the equilibrium valve of neutron density；δ n is the deviation value of actual neutron density deviation poised state；

The mathematic(al) representation that step S23, simultaneous formula (5) and formula (10) obtain δ ρ is as follows:

$\mathrm{\δ}\mathrm{\ρ}={\mathrm{\δ\ρ}}_r+{\mathrm{\α}}_f(T_f-T_{f0})+\frac{{\mathrm{\α}}_c(T_l-T_{l0})}{2}---\left(12\right);$

Step S24, simultaneous formula (11) and formula (12), use Differential Geometry knowledge, obtainWith δ n, δ c, δ T_f、δT_lAnd δ_ρrBetween relationship as follows:

$\frac{d\mathrm{\δ}n}{dt}=\frac{-\mathrm{\β}}{\mathrm{\Λ}}\mathrm{\δ}n+\mathrm{\λ}\mathrm{\δ}c+\frac{{\mathrm{\α}}_f}{\mathrm{\Λ}}{n}_0{\mathrm{\δT}}_f+\frac{{\mathrm{\α}}_c}{2\mathrm{\Λ}}{n}_0{\mathrm{\δT}}_l+\frac{n_0}{\mathrm{\Λ}}{\mathrm{\δ}}_{\mathrm{\ρ}r}---\left(13\right);$

Step S25, utilization Differential Geometry knowledge, obtained by formula (2)And the relationship between δ n and δ c is as follows:

$\frac{d\mathrm{\δ}c}{dt}=\frac{\mathrm{\β}}{\mathrm{\Λ}}\mathrm{\δ}n-\mathrm{\λ}\mathrm{\δ}c---\left(14\right);$

Step S26, simultaneous formula (3) and formula (7-8), use Differential Geometry knowledge, obtainWith δ n, δ T_fAnd δ T_lBetween relationship as follows:

$\frac{{\mathrm{dT}}_f}{dt}=\frac{f_f}{{\mathrm{\μ}}_f}{P}_0\mathrm{\δ}n-\frac{\mathrm{\Ω}}{{\mathrm{\μ}}_f}{\mathrm{\δT}}_f+\frac{\mathrm{\Ω}}{2{\mathrm{\μ}}_f}{\mathrm{\δT}}_l---\left(15\right);$

Step S27, simultaneous formula (4) and formula (7-9), use Differential Geometry knowledge, obtainWith δ n, δ T_fAnd δ T_lBetween relationship as follows:

$\frac{{\mathrm{d\δT}}_l}{dt}=\frac{1-f_f}{{\mathrm{\μ}}_c}{P}_0\mathrm{\δ}n+\frac{\mathrm{\Ω}}{{\mathrm{\μ}}_c}{\mathrm{\δT}}_f-\frac{2M+\mathrm{\Ω}}{2{\mathrm{\μ}}_c}{\mathrm{\δT}}_l---\left(16\right).$

Preferably, described step S3 set up reactor core power prediction Controlling model particularly as follows:

Step S31,

Theoretical according to model predictive control system, inearized model Predictive Control System can be obtained and be expressed as:

$\left\{\begin{array}{c}\stackrel{\·}{x}=A_{c}x+B_{c}u\\ y=Cx+Du\end{array}\right.---\left(17\right)$

In formula, x is state space variable；Y is state space output；U is Space-state control amount；Represent the derivative of state space variable；A_c、B_c, C, D be the matrix in model predictive control system respectively；

In this model predictive control system, take state space variable x respectively, state space output y, Space-state control amount u are:

$\left\{\begin{array}{c}x={\left[\begin{array}{ccccc}\mathrm{\δ}n& \mathrm{\δ}c& {\mathrm{\δT}}_f& {\mathrm{\δT}}_l& {\mathrm{\δ\ρ}}_r\end{array}\right]}^T\\ y=\[\mathrm{\δ}n\]\\ u=\[z_r\]\end{array}\right.---\left(18\right)$

In formula, state space variable x be 5 × 1 dimension matrixes, be made up of five variable element, they respectively δ n, δ c, δ T_f、δT_lAnd δ ρ_r；State space output y is made up of variable element δ n, Space-state control amount u is by variable element z_rComposition；

By formula (6), formula (13-16) and formula (18), according to linear algebra knowledge, solve model predictive control system (17), solve matrix A_c、B_c, C and D is respectively as follows:

$A_c=\left[\begin{array}{ccccc}-\frac{\mathrm{\β}}{\mathrm{\Λ}}& \frac{\mathrm{\β}}{\mathrm{\Λ}}& \frac{{\mathrm{\α}}_f}{\mathrm{\Λ}}{n}_0& \frac{{\mathrm{\α}}_c}{2\mathrm{\Λ}}{n}_0& \frac{n_0}{\mathrm{\Λ}}\\ \mathrm{\λ}& -\mathrm{\λ}& 0& 0& 0\\ \frac{f_f}{{\mathrm{\μ}}_f}{P}_0& 0& -\frac{\mathrm{\Ω}}{{\mathrm{\μ}}_f}& \frac{\mathrm{\Ω}}{2{\mathrm{\μ}}_f}& 0\\ \frac{1-f_f}{{\mathrm{\μ}}_f}{P}_0& 0& -\frac{\mathrm{\Ω}}{{\mathrm{\μ}}_c}& -\frac{2M+\mathrm{\Ω}}{2{\mathrm{\μ}}_c}& 0\\ 0& 0& 0& 0& 0\end{array}\right];B_c=\left[\begin{array}{c}0\\ 0\\ 0\\ 0\\ G_r\end{array}\right];$ D=[0]；C=[10000]；

Parameter G in matrix_r、n₀、λ、β、f_f、Λ、μ_f、P₀Provided by nuclear power plant, the running parameter α in matrix_f、α_c、μ_c, Ω, M be by n₀Determining, concrete calculating formula is as follows:

Step S32,

Described model predictive control system is carried out discretization, correctly choose sampling step length, described model predictive control system passes through current sample time k, it was predicted that following state space output, and the discrete form of described model predictive control system (17) is expressed as:

$\left\{\begin{array}{c}x(k+1|k)=Ax\left(k\right)+B\mathrm{\Δ}u\left(k\right)\\ y(k+1|k)=Cx(k+1|k)+Du\left(k\right)=CAx\left(k\right)+CB\mathrm{\Δ}u\left(k\right)\end{array}\right.---\left(19\right)$

In formula, the matrix A after system discretization and matrix B distinguish the matrix A before corresponding discretization_cAnd B_c；(k+1 | k) represent the predictive value in the current sample time k k+1 moment predicted；

Assuming to predict in described model predictive control system that time domain is Np, control time domain is Nc, is obtained by model predictive control system is theoretical, controls time domain less than or equal to prediction time domain, i.e. Np >=Nc；

Δ u (k+1)=u (k+1)-u (k), the dynamic prediction value of described model predictive control system future time instance is the actual value by current sample time, in whole prediction time domain, completes under the effect of Space-state control input quantity, therefore it is overseas when controlling, the controlled quentity controlled variable of state space remains unchanged, i.e. Δ u (k+i)=0, wherein i=Nc, Nc+1, Nc+2, Nc+3 ..., Np-1；

By current time k, state space variable value x (k) of system, it was predicted that in the k+m moment, the state space variable value of system is x (k+m | k), then the predicted state space variable of system is represented by:

X (k+m | k)=A^mx(k)+A^m-1BΔu(k)+A^m-2BΔu(k+1)+…+A^mBΔu(k+m)(20)

It is 0 controlling control variable Δ u beyond time domain Nc, formula (20) can obtain:

According to predicted state space variable, by y (k+1 | k)=Cx (k+1 | k)+Du (k)=CAx (k)+CB Δ u (k) in discretization model Predictive Control System (19), through type (21) can be tried to achieve the predicted state space of system and is output as:

Step S33,

According to Model Predictive Control Theory, for solving the optimal solution of system, objective function J is:

J=(R_s-Y)^T(R_s-Y)+ΔU^TR_wΔU(23)

In formula,

Y=[y (k+1 | k) y (k+2 | k) ... y (k+Np | k)]^T, it is the matrix of Np × 1 dimension；

Weight matrix R_wIt it is the diagonal matrix of Np × Np dimension；

Δ U=[Δ u (k) Δ u (k+1) ... Δ u (k+Nc-1)]^T, it is the matrix of Np × 1 dimension；

F=[CACA²…CA^Np]^T, it is the matrix of Np × 5 dimension；

R_s=[111 ... 1]^TR (k), wherein r (k) is given reference value, R_sIt it is the matrix of Np × 1 dimension；

$\mathrm{\Φ}=\left[\begin{array}{ccccc}CB& 0& 0& ...& 0\\ CAB& CB& 0& ...& 0\\ {\mathrm{CA}}^{2}B& CAB& CB& ...& 0\\ .& .& .& & .\\ .& .& .& & .\\ .& .& .& & .\\ {\mathrm{CA}}^{Np-1}B& {\mathrm{CA}}^{Np-2}B& {\mathrm{CA}}^{Np-3}B& ...& {\mathrm{CA}}^{Np-Nc}B\end{array}\right],$ It it is the matrix of Np × Nc dimension.

Thus can obtain:

Y=Fx (k)+Φ Δ U (24)

By Model Predictive Control Theory it can be seen that it is that object function J obtains minima that system obtains the condition of optimal solution, and the condition that object function J obtains minima is:By calculus and linear algebra knowledge, the value of the increment Delta U therefrom solving the Space-state control amount corresponding to optimal solution is:

Δ U=(Φ^TΦ+R_w)^-1Φ^T(R_s-Fx(k))

Δ u (k) is the first row of matrix Δ U, first row element, just can try to achieve state space output y according to described discretization model Predictive Control System (19).

Preferably, described step S4 based on genetic algorithm, described power prediction Controlling model is carried out parameter tuning particularly as follows:

Step S41, when certain sampling instant kT, generate comprise 3 undetermined parameter Np, Nc and R1 kth for chromosome, and calculate kth for the fitness function value indexJ corresponding to bar chromosome each in chromosome；

Step S42, according to kth for chromosomal fitness function value indexJ, through roulette wheel selection, intersection and variation, generate k+1 for chromosome, then calculate in kth+1 generation chromosome the fitness function value indexJ corresponding to each bar chromosome；

Step S43, so circulation go down, and according to fitness function value indexJ, constantly excellent genes are genetic to the next generation, constantly approach optimal solution,

If step S44 evolutionary generation is not up to set maximum evolutionary generation T, just obtain optimal solution；So genetic manipulation terminates at this moment；If evolutionary generation has reached set maximum evolutionary generation T, also do not draw optimal solution, then genetic manipulation terminates at this moment, and optimal solution is just drawn for chromosome by T.

Preferably, Model Predictive Control is predicted time domain be more than or equal to controlling time domain, i.e. Nc≤Np；And Nc and Np is integer, in GA, therefore set three parametric variable: N₁、k₁And R₁；To N₁、k₁Round, respectively obtain Nc and kk；Make Np=Nc+kk, just complete undetermined parameter Np, Nc and R₁Setting, then pass through genetic algorithm and carry out optimizing, draw Np, Nc and R₁Optimal value.

The present invention has such advantages as relative to prior art and effect:

(1) present invention is in conjunction with the operational factor of pressurized water reactor core, adopts Revised genetic algorithum that the parameters in controller is adjusted, draws globally optimal solution, it is achieved the self-adaptative adjustment that pressurized-water reactor nuclear power plant core power controls.Meanwhile, this invention accelerates convergence rate, has good robustness, controls response rapidly.

(2) present invention employs model predictive controller.Traditional PID controls to be according to the deviation between set-point and outputting measurement value, determines current control input.Compared with controlling with traditional PID, Model Predictive Control also utilizes forecast model to predict the deviation value in future, determines current optimal control policy by rolling optimization, makes the deviation between controlled variable and the expected value in future minimum.Model Predictive Control is the algorithm of a kind of optimum control, and its optimization process is not that an off-line completes, but is repeatedly optimized online in limited traveling time interval.

(3) present invention employs genetic algorithm.Genetic algorithm is not adopt Deterministic rules, but adopts the transition rule of probability to instruct its direction of search；Further, genetic algorithm has self-organizing, self adaptation and self-study habit.

Accompanying drawing explanation

Fig. 1 is PREDICTIVE CONTROL rolling optimization schematic diagram；

Fig. 2 is genetic algorithm flow chart；

Fig. 3 is the pressurized water reactor core power module PREDICTIVE CONTROL schematic diagram based on genetic algorithm.

Detailed description of the invention

For making the purpose of the present invention, technical scheme and advantage clearly, clearly, developing simultaneously referring to accompanying drawing, the present invention is described in more detail for embodiment.Should be appreciated that specific embodiment described herein is only in order to explain the present invention, is not intended to limit the present invention.

Embodiment

Pressurized water reactor core is one of capital equipment of pressurized-water reactor nuclear power plant, and its safety and stability is particularly significant；Traditional PID control system is difficult to quickly and stably control pressurized water reactor core power.The embodiment of the invention discloses a kind of pressurized-water reactor nuclear power plant core power model predictive control method based on genetic algorithm, said method comprising the steps of:

Step S1, set up the mathematical state spatial model of reactor core；

In pressurized-water reactor nuclear power plant, according to reactor simple group neutron diffusion theory, it can be deduced that many group delayed neutron Point reactor kinetic equations.But many group delayed neutron Point reactor kinetic equations, solve amount of calculation very big, and all need not solve many group delayed neutron Point reactor kinetic equations in a lot of occasions, therefore adopt equivalence single group delayed neutron to carry out approximate description many groups delayed neutron Point reactor kinetic equations.Equivalence single group delayed neutron Point reactor kinetic equations is as follows:

$\frac{dn}{dt}=\frac{\mathrm{\ρ}-\mathrm{\β}}{\mathrm{\Λ}}n+\mathrm{\λ}c---\left(1\right)$

$\frac{dc}{dt}=\frac{\mathrm{\β}}{\mathrm{\Λ}}n-\mathrm{\λ}c---\left(2\right)$

In formula, n is neutron density；ρ is global reactivity；β is the share of effective delayed neutron；Λ is neutron generation time；T is the time；λ is the single decay constant organizing delayed neutron of equivalence；C is equivalence single group delayed-neutron precursor density.Formula (1) indicates the relation that neutron density is worth over time between global reactivity, the share of effective delayed neutron, neutron generation time, neutron density, single decay constant and the equivalence list group delayed-neutron precursor density organizing delayed neutron of equivalence；Formula (2) indicates the relation that equivalence single group delayed-neutron precursor density is worth over time between effective share of delayed neutron, neutron generation time, neutron density, single decay constant and the equivalence list group delayed-neutron precursor density organizing delayed neutron of equivalence.

In pressurized-water reactor nuclear power plant, thermal-hydraulic model equation is as follows:

$f_f{P}_a={\mathrm{\μ}}_f\frac{{\mathrm{dT}}_f}{dt}+P_c---\left(3\right)$

$(1-f_f)P_a+P_c={\mathrm{\μ}}_c\frac{{\mathrm{dT}}_l}{dt}+P_e---\left(4\right)$

In formula, f_fIt it is fuel power share；μ_cIt is coolant thermal capacity；μ_fIt it is fuel heat capacity.Formula (3) indicates average fuel temperature and is worth over time and fuel heat capacity, fuel pass to the heat of coolant, relation between fuel power share and core power；Formula (4) indicates coolant outlet temperature and is worth over time and coolant thermal capacity, coolant pass to the heat of secondary circuit, fuel passes to the heat of coolant, relation between fuel power share and core power.

In pressurized-water reactor nuclear power plant, reactive model equation is as follows:

$\mathrm{\δ}\mathrm{\ρ}={\mathrm{\δ\ρ}}_r+{\mathrm{\α}}_f(T_f-T_{f0})+\frac{{\mathrm{\α}}_c(T_l-T_{l0})}{2}+\frac{{\mathrm{\α}}_c(T_e-T_{e0})}{2}---\left(5\right)$

$\frac{{\mathrm{d\δ\ρ}}_r}{dt}=G_r{Z}_r---\left(6\right)$

In formula, G_rThe value of representation unit length control rod；δ represents the deviation value of deviation poised state；Z_rRepresent and control stick speed；T_l0It it is initial coolant outlet temperature；T_f0It it is initial fuel mean temperature；T_e0It it is initial coolant inlet temperature；ρ_rIt is that control rod moves introduced reactivity；α_fIt it is fuel reaction property coefficient；α_cIt it is coolant reactivity coefficient.

Formula (6) indicates and is moved, by control rod, the relation that introduced reactivity is worth over time between value and the control stick speed of unit length control rod.Through type (6) can obtainWith Z_rBetween relationship, the foundation for reactor core power prediction Controlling model provides Mathematics Proof, is one of the linearizing important step of reactor core mathematical model.

In this step, according to reactor simple group neutron diffusion theory, adopt equivalence single group delayed neutron to carry out approximate description many groups delayed neutron Point reactor kinetic equations, obtain equivalence single group delayed neutron Point reactor kinetic equations in reactor.This step gives reactor thermo-hydraulics model equation and reactive model equation thereof, establishes the mathematical state spatial model of pressurized-water reactor nuclear power plant reactor core, and the control for pressurized-water reactor nuclear power plant core power provides Fundamentals of Mathematics.

S2, by the mathematical state spatial model linearisation of reactor core；

In order to reach to control the purpose of pressurized-water reactor nuclear power plant core power, it is necessary to the mathematical model of reactor core is carried out linearisation, and this step is intended to the mathematical state spatial model of reactor core obtained in step S1 is carried out linearisation.By the relational expression between core power and neutron density, the energy conservation equation in reactor, it is approximately considered in heat transfer process coolant physical parameter and remains unchanged and the linearized theory of small perturbation near reactor equilibrium point, according to Differential Geometry knowledge, reactor core mathematical model is carried out linearisation, and the foundation for reactor core power prediction Controlling model provides Mathematics Proof.

The linearisation of reactor core mathematical model is made up of following step:

Step S21:

In pressurized-water reactor nuclear power plant, core power is relevant with neutron density, and core power is as follows with the relation of neutron density:

P_a=P₀n(7)

In formula, P_aFor actual core power；P₀For reactor core rated power.According to formula (7), core power is directly proportional to neutron density, and reactor core power-handling capability is certain, and therefore the value of neutron density n can represent relative core power.

Law of conservation of energy is applied to presurized water reactor, obtains the energy conservation equation in reactor as follows:

P_c=Ω (T_f-T_c)(8)

P_e=M (T_l-T_e)(9)

In formula, P_cIt it is the fuel heat that passes to coolant；P_eIt it is the coolant heat that passes to secondary circuit；Ω is the heat transfer coefficient between fuel and coolant；M is the mass flow thermal capacity of coolant；T_fIt it is average fuel temperature；T_cIt it is coolant mean temperature；T_eIt it is coolant inlet temperature；T_lIt it is coolant outlet temperature.

In pressurized-water reactor nuclear power plant, generally, the inlet temperature of coolant is stable at 300 DEG C.The difference of coolant inlet temperature and outlet temperature is approximately in 30 DEG C, it can be considered that coolant is with fuel heat transfer process, coolant physical parameter is constant, so that

$\left\{\begin{array}{c}{T}_c=\frac{1}{2}(T_l+T_e)\\ {\mathrm{\δT}}_e=0\end{array}\right.---\left(10\right)$

This step primarily illustrates: core power is relevant with neutron density, and neutron density can represent relative power；Energy conservation equation in reactor；In pressurized-water reactor nuclear power plant, it is constant that the physical parameter of coolant can be approximately considered.This step is one of linearizing important step of reactor core mathematical model.

Step S22:

By the linearized theory of perturbation small near equilibrium point, in pressurized-water reactor nuclear power plant, the equilibrium valve of neutron density deviates the deviation value of poised state much larger than neutron density.Neutron density n can be expressed as:

N=n₀+δn.Therefore, by differential knowledge, formula (1) can be expressed as:

$\frac{d\mathrm{\δ}n}{dt}=\frac{-\mathrm{\β}}{\mathrm{\Λ}}\mathrm{\δ}n+\mathrm{\λ}\mathrm{\δ}c+\frac{\mathrm{\δ}\mathrm{\ρ}}{\mathrm{\Λ}}{n}_0---\left(11\right)$

In formula, n₀It it is the equilibrium valve of neutron density；δ n is the deviation value of actual neutron density deviation poised state.According to formula (7), the value of neutron density n can represent relative core power.Therefore, δ n can represent the side-play amount of relative power.

This step has drawn formula (11), it was shown thatAnd the mathematical relationship between δ n, δ c and δ ρ, has simplified formula (1), it it is one of the linearizing important step of reactor core mathematical model.

Step S23:

Simultaneous formula (5) and formula (10) can obtain:

$\mathrm{\δ}\mathrm{\ρ}={\mathrm{\δ\ρ}}_r+{\mathrm{\α}}_f(T_f-T_{f0})+\frac{{\mathrm{\α}}_c(T_l-T_{l0})}{2}---\left(12\right)$

This step obtains the mathematic(al) representation of δ ρ by simultaneous formula (5) and formula (10), and the simplification for formula (11) provides the foundation, and is one of the linearizing important step of reactor core mathematical model.

Step S24:

Simultaneous formula (11) and formula (12), use Differential Geometry knowledge, can obtain:

$\frac{d\mathrm{\δ}n}{dt}=\frac{-\mathrm{\β}}{\mathrm{\Λ}}\mathrm{\δ}n+\mathrm{\λ}\mathrm{\δ}c+\frac{{\mathrm{\α}}_f}{\mathrm{\Λ}}{n}_0{\mathrm{\δT}}_f+\frac{{\mathrm{\α}}_c}{2\mathrm{\Λ}}{n}_0{\mathrm{\δT}}_l+\frac{n_0}{\mathrm{\Λ}}{\mathrm{\δ}}_{\mathrm{\ρ}r}---\left(13\right)$

This step obtains formula (13) by simultaneous formula (11) and formula (12), it was shown thatWith δ n, δ c, δ T_f、δT_lAnd δ_ρrBetween relationship, the foundation for reactor core power prediction Controlling model provides Mathematics Proof, is one of the linearizing important step of reactor core mathematical model.

Step S25:

Using Differential Geometry knowledge, formula (2) is represented by:

$\frac{d\mathrm{\δ}c}{dt}=\frac{\mathrm{\β}}{\mathrm{\Λ}}\mathrm{\δ}n-\mathrm{\λ}\mathrm{\δ}c---\left(14\right)$

This step obtainsAnd the relationship between δ n and δ c, the foundation for reactor core power prediction Controlling model provides Fundamentals of Mathematics, is one of the linearizing important step of reactor core mathematical model.

Step S26:

Simultaneous formula (3) and formula (7-8), use Differential Geometry knowledge, can obtain:

$\frac{{\mathrm{dT}}_f}{dt}=\frac{f_f}{{\mathrm{\μ}}_f}{P}_0\mathrm{\δ}n-\frac{\mathrm{\Ω}}{{\mathrm{\μ}}_f}{\mathrm{\δT}}_f+\frac{\mathrm{\Ω}}{2{\mathrm{\μ}}_f}{\mathrm{\δT}}_l---\left(15\right)$

This step passes through simultaneous formula (3) and formula (7-8), obtainsWith δ n, δ T_fAnd δ T_lBetween relationship, the foundation for reactor core power prediction Controlling model provides Mathematics Proof, is one of the linearizing important step of reactor core mathematical model.

Step S27:

Simultaneous formula (4) and formula (7-9), use Differential Geometry knowledge, can obtain:

$\frac{{\mathrm{d\δT}}_l}{dt}=\frac{1-f_f}{{\mathrm{\μ}}_c}{P}_0\mathrm{\δ}n+\frac{\mathrm{\Ω}}{{\mathrm{\μ}}_c}{\mathrm{\δT}}_f-\frac{2M+\mathrm{\Ω}}{2{\mathrm{\μ}}_c}{\mathrm{\δT}}_l---\left(16\right)$

This step passes through simultaneous formula (4) and formula (7-9), obtainsWith δ n, δ T_fAnd δ T_lBetween relationship, the foundation for reactor core power prediction Controlling model provides Mathematics Proof, is one of the linearizing important step of reactor core mathematical model.

S3, set up reactor core power prediction Controlling model；

In this step, reactor core power prediction Controlling model is based on Model Predictive Control Theory and sets up.The expression formula of inearized model Predictive Control System is drawn according to Model Predictive Control Theory；By correctly choosing state space variable x, state space output y, Space-state control amount u, according to linear algebra knowledge, solve the matrix in inearized model Predictive Control System (17) and system.After model predictive control system discretization, calculate predicted state space variable and the predicted state space output of system in prediction time domain.According to Model Predictive Control Theory, obtained the condition of optimal value by analytical model Predictive Control System, solve the state space output of system.

Step S31:

Theoretical according to model predictive control system, can obtain inearized model Predictive Control System can be expressed as:

$\left\{\begin{array}{c}\stackrel{\·}{x}=A_{c}x+B_{c}u\\ y=Cx+Du\end{array}\right.---\left(17\right)$

In formula, x is state space variable；Y is state space output；U is Space-state control amount；Represent the derivative of state space variable；A_c、B_c, C, D be the matrix in model predictive control system respectively.

In this model predictive control system, take state space variable x respectively, state space output y, Space-state control amount u are:

$\{\begin{array}{c}x={\left[\begin{array}{ccccc}\mathrm{\δ}n& \mathrm{\δ}c& {\mathrm{\δT}}_f& {\mathrm{\δT}}_l& {\mathrm{\δ\ρ}}_r\end{array}\right]}^T\\ y=\[\mathrm{\δ}n\]\\ u=\[z_r\]\end{array}---\left(18\right)$

In formula, state space variable x be 5 × 1 dimension matrixes, be made up of five variable element, they respectively δ n, δ c, δ T_f、δT_lAnd δ ρ_r；State space output y is made up of variable element δ n, Space-state control amount u is by variable element z_rComposition.

By formula (6), formula (13-16) and formula (18), according to linear algebra knowledge, it is possible to solve model predictive control system (17), solve matrix A_c、B_c, C and D is respectively as follows:

$A_c=\left[\begin{array}{ccccc}-\frac{\mathrm{\β}}{\mathrm{\Λ}}& \frac{\mathrm{\β}}{\mathrm{\Λ}}& \frac{{\mathrm{\α}}_f}{\mathrm{\Λ}}{n}_0& \frac{{\mathrm{\α}}_c}{2\mathrm{\Λ}}{n}_0& \frac{n_0}{\mathrm{\Λ}}\\ \mathrm{\λ}& -\mathrm{\λ}& 0& 0& 0\\ \frac{f_f}{{\mathrm{\μ}}_f}{P}_0& 0& -\frac{\mathrm{\Ω}}{{\mathrm{\μ}}_f}& \frac{\mathrm{\Ω}}{2{\mathrm{\μ}}_f}& 0\\ \frac{1-f_f}{{\mathrm{\μ}}_f}{P}_0& 0& -\frac{\mathrm{\Ω}}{{\mathrm{\μ}}_c}& -\frac{2M+\mathrm{\Ω}}{2{\mathrm{\μ}}_c}& 0\\ 0& 0& 0& 0& 0\end{array}\right];B_c=\left[\begin{array}{c}0\\ 0\\ 0\\ 0\\ G_r\end{array}\right];$ D=[0]；C=[10000].

Parameter G in matrix_rAnd n₀Value in different nuclear power plants or in the different operating region of same nuclear power plant, be not quite similar.Therefore, G_rAnd n₀Value provided by nuclear power plant.Parameter lambda in matrix, β, f_f、Λ、μ_f、P₀Also it is provided by nuclear power plant.Running parameter α in matrix_f、α_c、μ_c, Ω, M be by n₀Determining, concrete calculating formula is as follows:

This step is first theoretical according to model predictive control system, has drawn the expression formula of inearized model Predictive Control System；By correctly choosing state space variable x, state space output y, Space-state control amount u, according to linear algebra knowledge, solve the matrix A in system (17) and system_c、B_c, C and D.

Step S32:

Model predictive control system (17) is continuous print in time, in order to use computer to carry out computing, it is necessary to system (17) is carried out discretization.

Correctly choosing after sampling step length, system passes through current sample time k, it was predicted that following state space output.The discrete form of model predictive control system (17) is expressed as:

$\left\{\begin{array}{c}x(k+1|k)=Ax\left(k\right)+B\mathrm{\Δ}u\left(k\right)\\ y(k+1|k)=Cx(k+1|k)+Du\left(k\right)=CAx\left(k\right)+CB\mathrm{\Δ}u\left(k\right)\end{array}\right.---\left(19\right)$

In formula, the matrix A after system discretization and matrix B distinguish the matrix A before corresponding discretization_cAnd B_c；(k+1 | k) represent the predictive value in the current sample time k k+1 moment predicted.

Predicting in hypothesized model Predictive Control System that time domain is Np, control time domain is Nc.Can be obtained by model predictive control system theory, control time domain less than or equal to prediction time domain, i.e. Np >=Nc.

Δ u (k+1)=u (k+1)-u (k), the dynamic prediction value of system future time instance is the actual value by current sample time, under whole prediction time domain, completes under the effect of Space-state control input quantity.Therefore, controlling beyond time domain, the controlled quentity controlled variable of state space remains unchanged, i.e. Δ u (k+i)=0, wherein

By current time k, state space variable value x (k) of system, it was predicted that in the k+m moment, the state space variable value of system is x (k+m | k).Then the predicted state space variable of system is represented by:

X (k+m | k)=A^mx(k)+A^m-1BΔu(k)+A^m-2BΔu(k+1)+…+A^mBΔu(k+m)(20)

It is 0 controlling control variable Δ u beyond time domain Nc, formula (20) can obtain:

According to predicted state space variable, by y (k+1 | k)=Cx (k+1 | k)+Du (k)=CAx (k)+CB Δ u (k) in discretization model Predictive Control System (19), through type (21) can be tried to achieve the predicted state space of system and is output as:

In this step, after model predictive control system (17) is carried out discretization, obtain the model predictive control system (19) of discretization；Theoretical according to model predictive control system, calculate predicted state space variable and the predicted state space output of system in prediction time domain, the optimal solution for following solving system provides Fundamentals of Mathematics.

Step S33:

According to Model Predictive Control Theory, in order to solve the optimal solution of system, objective function J is:

J=(R_s-Y)^T(R_s-Y)+ΔU^TR_wΔU(23)

In formula,

Y=[y (k+1 | k) y (k+2 | k) ... y (k+Np | k)]^T, it is the matrix of Np × 1 dimension；

Weight matrix R_wIt it is the diagonal matrix of Np × Np dimension；

Δ U=[Δ u (k) Δ u (k+1) ... Δ u (k+Nc-1)]^T, it is the matrix of Np × 1 dimension；

F=[CACA²…CA^Np]^T, it is the matrix of Np × 5 dimension；

R_s=[111 ... 1]^TR (k), wherein r (k) is given reference value, R_sIt it is the matrix of Np × 1 dimension；

$\mathrm{\Φ}=\left[\begin{array}{ccccc}CB& 0& 0& ...& 0\\ CAB& CB& 0& ...& 0\\ {\mathrm{CA}}^{2}B& CAB& CB& ...& 0\\ .& .& .& & .\\ .& .& .& & .\\ .& .& .& & .\\ {\mathrm{CA}}^{Np-1}B& {\mathrm{CA}}^{Np-2}B& {\mathrm{CA}}^{Np-3}B& ...& {\mathrm{CA}}^{Np-Nc}B\end{array}\right],$ It it is the matrix of Np × Nc dimension.

Thus can obtain:

Y=Fx (k)+Φ Δ U (24)

By Model Predictive Control Theory it can be seen that it is that object function J obtains minima that system obtains the condition of optimal solution.Object function J obtains the condition of minima:By calculus and linear algebra knowledge, the value of the increment Delta U therefrom solving the Space-state control amount corresponding to optimal solution is:

Δ U=(Φ^TΦ+R_w)^-1Φ^T(R_s-Fx(k))

Δ u (k) is the first row of matrix Δ U, first row element, just can try to achieve state space output y according to system (19).

In this step, according to Model Predictive Control Theory, obtaining the condition of minima by analyzing object function, namely model predictive control system obtains the condition of optimal value, solves the state space output of system.Model Predictive Control is the algorithm of a kind of optimum control, and its optimization process is not that an off-line completes, but is repeatedly optimized online in limited traveling time interval, as shown in Figure 1.

S4, Predictive Control System parameter tuning based on genetic algorithm

In this step, the advantage utilizing genetic algorithm, the undetermined parameter in reactor core power prediction Controlling model designed in step S3 is carried out optimizing, draws their optimal value.After adding genetic algorithm, designed reactor core power prediction Controlling model can be applied to various working, and practicality is higher.

Genetic algorithm is the computation model of the biological evolution process of the simulation natural selection of Darwinian evolutionism and genetic mechanisms, is a kind of method searching for optimal solution by simulating nature evolutionary process.

With reference to Fig. 2, the elementary operation process of genetic algorithm is as follows:

(1) initialize: arranging maximum evolutionary generation is T, and the initial value of evolutionary generation enumerator is 0, and stochastic generation individuality is as initial population.

(2) individual evaluation: according to fitness function, calculates the fitness function value of each individuality in colony P (t).

(3) Selecting operation: selection opertor is acted on colony.Selection is in order to the individuality optimized is genetic directly to the next generation, or by after matching and intersecting and produce new individuality, then it is genetic to the next generation.Selecting operation is based on the Fitness analysis of individual in population.

(4) crossing operation: crossover operator is acted on colony.Crossover operator plays the role of a nucleus in genetic algorithm.

(5) mutation operator: mutation operator is acted on colony.Genic value on some locus of individual in population string is changed.Colony P (t) obtains colony P (t+1) of future generation after selection, intersection, mutation operator.

(6) end condition judges: if t=T, then exported as optimal solution by the individuality with maximum adaptation degree obtained in evolutionary process, and terminates calculating.

In model predictive control system designed above, it was predicted that time domain Np, control time domain Nc and penalty coefficient R₁Carry out assignment according to actual condition, these three undetermined parameter choose on control system output performance impact bigger.Considering the sensitivity of such parameter, the present invention proposes the Predictive Control System parameter tuning method based on GA.

Genetic algorithm utilizes computer exactly, in given undetermined parameter span, institute's likely value of simulation undetermined parameter, and calculate the fitness function value indexJ corresponding to each value, after simulation many times, finally according to the size of fitness function value indexJ, draw the optimal value of undetermined parameter.In the present invention, the effect of genetic algorithm is: the advantage utilizing genetic algorithm, to prediction time domain Np, controls time domain Nc and penalty coefficient R₁Carry out optimizing, draw their optimal value so that designed reactor core power prediction Controlling model can be applied to various working.The optimizing principle of this tuning process is as follows:

Step S41: when certain sampling instant kT, generate comprise 3 undetermined parameter Np, Nc and R1 kth for chromosome, and calculate kth for the fitness function value indexJ corresponding to bar chromosome each in chromosome.

Step S42: according to kth for chromosomal fitness function value indexJ, through roulette wheel selection, intersection and variation, generates k+1 for chromosome.Calculate the fitness function value indexJ corresponding to each bar chromosome in kth+1 generation chromosome again.

Step S43: so circulation is gone down, and according to fitness function value indexJ, constantly excellent genes is genetic to the next generation, constantly approaches optimal solution.

Step S44: if evolutionary generation is not up to set maximum evolutionary generation T, just obtain optimal solution；So genetic manipulation terminates at this moment.If evolutionary generation has reached set maximum evolutionary generation T, also do not draw optimal solution, then genetic manipulation terminates at this moment, and optimal solution is just drawn for chromosome by T.

It is to be noted that predict time domain in Model Predictive Control be more than or equal to controlling time domain, i.e. Nc≤Np；And Nc and Np is integer.Therefore in GA, set three parametric variable: N₁、k₁And R₁；To N₁、k₁Round, respectively obtain Nc and kk；Make Np=Nc+kk, just complete 3 undetermined parameter Np, Nc and R₁Setting.Np, Nc and R is drawn by genetic algorithm₁Optimal value.

In sum, present invention employs the model predictive control method based on genetic algorithm pressurized water reactor core power is controlled, utilize the advantages such as the self-organizing of genetic algorithm, self adaptation and self-study habit, and the advantage such as the rolling optimization of Model Predictive Control and feedback compensation, stablize, efficiently control pressurized water reactor core power, it is ensured that pressurized-water reactor nuclear power plant runs safely and steadly.Pressurized water reactor core power module PREDICTIVE CONTROL schematic diagram based on genetic algorithm of the present invention, as shown in Figure 3.The present invention is by the model predictive control method based on genetic algorithm, draw the optimal solution of control system, the control rod direction of motion and movement velocity are adjusted, are finally reached the purpose controlling pressurized-water reactor nuclear power plant core power, it is ensured that pressurized water reactor core safe and stable operation.The impact that pressurized water reactor core power is controlled by the unstability etc. that the present invention has considered the uncertainty that has due to multiple interference, load large-scope change brings, it is provided that a kind of precise and high efficiency, capacity of resisting disturbance are strong, be adapted to the model predictive controller of load variations on a large scale.

Above-described embodiment is the present invention preferably embodiment; but embodiments of the present invention are also not restricted to the described embodiments; the change made under other any spirit without departing from the present invention and principle, modification, replacement, combination, simplification; all should be the substitute mode of equivalence, be included within protection scope of the present invention.

Claims (6)

1. the pressurized-water reactor nuclear power plant core power model predictive control method based on genetic algorithm, it is characterised in that comprise the following steps:

S1, set up the mathematical state spatial model of reactor core, described mathematical state spatial model includes equivalence single group delayed neutron Point reactor kinetic equations, thermal-hydraulic model equation and reactive model equation, wherein said equivalence single group delayed neutron Point reactor kinetic equations, according to reactor simple group neutron diffusion theory, adopts equivalence single group delayed neutron to carry out approximate description many groups delayed neutron Point reactor kinetic equations and obtains；

S2, mathematical state spatial model to described reactor core carry out linearisation, this step according to the relational expression between core power and neutron density, the energy conservation equation in reactor, be approximately considered in heat transfer process coolant physical parameter and remain unchanged and the linearized theory of small perturbation near reactor equilibrium point, according to Differential Geometry knowledge, the mathematical state spatial model of described reactor core is carried out linearisation, draws the linear math expression formula between parameter in pressurized water reactor core；

S3, set up the power prediction Controlling model of reactor core, this step draws the expression formula of inearized model Predictive Control System according to Model Predictive Control Theory, by correctly choosing state space variable x, state space output y, Space-state control amount u, according to linear algebra knowledge, solve the matrix in inearized model Predictive Control System and system, after model predictive control system discretization, calculate predicted state space variable and the predicted state space output of system in prediction time domain；According to Model Predictive Control Theory, obtained the condition of optimal value by analytical model Predictive Control System, solve the state space output of system；

S4, based on genetic algorithm, described power prediction Controlling model is carried out parameter tuning, this step utilizes genetic algorithm the undetermined parameter in described reactor core power prediction Controlling model is carried out optimizing, draw the optimal value of undetermined parameter.

2. the pressurized-water reactor nuclear power plant core power model predictive control method based on genetic algorithm according to claim 1, it is characterised in that

Described equivalence single group delayed neutron Point reactor kinetic equations is as follows:

$\frac{dn}{dt}=\frac{\mathrm{\ρ}-\mathrm{\β}}{\mathrm{\Λ}}n+\mathrm{\λ}c---\left(1\right)$

$\frac{dc}{dt}=\frac{\mathrm{\β}}{\mathrm{\Λ}}n-\mathrm{\λ}c---\left(2\right)$

In formula, n is neutron density, and ρ is global reactivity, and β is the share of effective delayed neutron, and Λ is neutron generation time, and t is the time, and λ is the single decay constant organizing delayed neutron of equivalence, and c is equivalence single group delayed-neutron precursor density；

Described thermal-hydraulic model equation is as follows:

$f_f{P}_a={\mathrm{\μ}}_f\frac{{\mathrm{dT}}_f}{dt}+P_c---\left(3\right)$

$(1-f_f)P_a+P_c={\mathrm{\μ}}_c\frac{{\mathrm{dT}}_l}{dt}+P_e---\left(4\right)$

In formula, f_fIt is fuel power share, μ_cIt is coolant thermal capacity, μ_fIt it is fuel heat capacity；

Described reactive model equation is as follows:

$\mathrm{\δ}\mathrm{\ρ}={\mathrm{\δ\ρ}}_r+{\mathrm{\α}}_f(T_f-T_{f0})+\frac{{\mathrm{\α}}_c(T_l-T_{l0})}{2}+\frac{{\mathrm{\α}}_c(T_e-T_{e0})}{2}---\left(5\right)$

$\frac{{\mathrm{d\δ\ρ}}_r}{dt}=G_r{Z}_r---\left(6\right)$

In formula, G_rThe value of representation unit length control rod, δ represents the deviation value of deviation poised state, Z_rRepresent and control stick speed, T_l0It is initial coolant outlet temperature, T_f0It is initial fuel mean temperature, T_e0It is initial coolant inlet temperature, ρ_rIt is that control rod moves introduced reactivity, α_fIt is fuel reaction property coefficient, α_cIt it is coolant reactivity coefficient.

3. the pressurized-water reactor nuclear power plant core power model predictive control method based on genetic algorithm according to claim 2, it is characterised in that described step S2 the mathematical state spatial model of described reactor core is carried out linearisation particularly as follows:

Step S21, as follows according to the relation of core power Yu neutron density:

P_a=P₀n(7)

In formula, P_aFor actual core power；P₀For reactor core rated power, the value of neutron density n is represented relative core power；

Law of conservation of energy is applied to presurized water reactor, obtains the energy conservation equation in reactor as follows:

P_c=Ω (T_f-T_c)(8)

P_e=M (T_l-T_e)(9)

In formula, P_cIt is the fuel heat that passes to coolant, P_eBeing the coolant heat that passes to secondary circuit, Ω is the heat transfer coefficient between fuel and coolant, and M is the mass flow thermal capacity of coolant, T_fIt is average fuel temperature, T_cIt is coolant mean temperature, T_eIt is coolant inlet temperature, T_lIt it is coolant outlet temperature；

By assuming that coolant is with fuel heat transfer process, coolant physical parameter is constant, obtains:

$\left\{\begin{array}{c}{T}_c=\frac{1}{2}(T_l+T_e)\\ {\mathrm{\δT}}_e=0\end{array}\right.---\left(10\right);$

Step S22, linearized theory by perturbation small near equilibrium point, release the equilibrium valve of neutron density in pressurized-water reactor nuclear power plant and deviate the deviation value of poised state much larger than neutron density, be expressed as by neutron density n: n=n₀+ δ n, by differential knowledge, is expressed as formula (1):

$\frac{d\mathrm{\δ}n}{dt}=\frac{-\mathrm{\β}}{\mathrm{\Λ}}\mathrm{\δ}n+\mathrm{\λ}\mathrm{\δ}c+\frac{\mathrm{\δ}\mathrm{\ρ}}{\mathrm{\Λ}}{n}_0---\left(11\right)$

In formula, n₀It it is the equilibrium valve of neutron density；δ n is the deviation value of actual neutron density deviation poised state；

The mathematic(al) representation that step S23, simultaneous formula (5) and formula (10) obtain δ ρ is as follows:

$\mathrm{\δ}\mathrm{\ρ}={\mathrm{\δ\ρ}}_r+{\mathrm{\α}}_f(T_f-T_{f0})+\frac{{\mathrm{\α}}_c(T_l-T_{l0})}{2}---\left(12\right);$

Step S24, simultaneous formula (11) and formula (12), use Differential Geometry knowledge, obtainWith δ n, δ c, δ T_f、δT_lAnd δ_ρrBetween relationship as follows:

$\frac{d\mathrm{\δ}n}{dt}=\frac{-\mathrm{\β}}{\mathrm{\Λ}}\mathrm{\δ}n+\mathrm{\λ}\mathrm{\δ}c+\frac{{\mathrm{\α}}_f}{\mathrm{\Λ}}{n}_0{\mathrm{\δT}}_f+\frac{{\mathrm{\α}}_c}{2\mathrm{\Λ}}{n}_0{\mathrm{\δT}}_l+\frac{n_0}{\mathrm{\Λ}}{\mathrm{\δ}}_{\mathrm{\ρ}r}---\left(13\right);$

Step S25, utilization Differential Geometry knowledge, obtained by formula (2)And the relationship between δ n and δ c is as follows:

$\frac{d\mathrm{\δ}c}{dt}=\frac{\mathrm{\β}}{\mathrm{\Λ}}\mathrm{\δ}n-\mathrm{\λ}\mathrm{\δ}c---\left(14\right);$

Step S26, simultaneous formula (3) and formula (7-8), use Differential Geometry knowledge, obtainWith δ n, δ T_fAnd δ T_lBetween relationship as follows:

$\frac{{\mathrm{dT}}_f}{dt}=\frac{f_f}{{\mathrm{\μ}}_f}{P}_0\mathrm{\δ}n-\frac{\mathrm{\Ω}}{{\mathrm{\μ}}_f}{\mathrm{\δT}}_f+\frac{\mathrm{\Ω}}{2{\mathrm{\μ}}_f}{\mathrm{\δT}}_l---\left(15\right);$

Step S27, simultaneous formula (4) and formula (7-9), use Differential Geometry knowledge, obtainWith δ n, δ T_fAnd δ T_lBetween relationship as follows:

$\frac{{\mathrm{d\δT}}_l}{dt}=\frac{1-f_f}{{\mathrm{\μ}}_c}{P}_0\mathrm{\δ}n+\frac{\mathrm{\Ω}}{{\mathrm{\μ}}_c}{\mathrm{\δT}}_f-\frac{2M+\mathrm{\Ω}}{2{\mathrm{\μ}}_c}{\mathrm{\δT}}_l---\left(16\right).$

4. the pressurized-water reactor nuclear power plant core power model predictive control method based on genetic algorithm according to claim 3, it is characterised in that described step S3 set up reactor core power prediction Controlling model particularly as follows:

Step S31,

Theoretical according to model predictive control system, inearized model Predictive Control System can be obtained and be expressed as:

$\left\{\begin{array}{c}\stackrel{\·}{x}=A_{c}x+B_{c}u\\ y=Cx+Du\end{array}\right.---\left(17\right)$

In formula, x is state space variable；Y is state space output；U is Space-state control amount；Represent the derivative of state space variable；A_c、B_c, C, D be the matrix in model predictive control system respectively；

In this model predictive control system, take state space variable x respectively, state space output y, Space-state control amount u are:

$\left\{\begin{array}{c}x={\left[\begin{array}{ccccc}\mathrm{\δ}n& \mathrm{\δ}c& {\mathrm{\δT}}_f& {\mathrm{\δT}}_l& {\mathrm{\δ\ρ}}_r\end{array}\right]}^T\\ y=\[\mathrm{\δ}n\]\\ u=\[z_r\]\end{array}\right.---\left(18\right)$

In formula, state space variable x be 5 × 1 dimension matrixes, be made up of five variable element, they respectively δ n, δ c, δ T_f、δT_lAnd δ ρ_r；State space output y is made up of variable element δ n, Space-state control amount u is by variable element z_rComposition；

By formula (6), formula (13-16) and formula (18), according to linear algebra knowledge, solve model predictive control system (17), solve matrix A_c、B_c, C and D is respectively as follows:

$A_c=\left[\begin{array}{ccccc}-\frac{\mathrm{\β}}{\mathrm{\Λ}}& \frac{\mathrm{\β}}{\mathrm{\Λ}}& \frac{{\mathrm{\α}}_f}{\mathrm{\Λ}}{n}_0& \frac{{\mathrm{\α}}_c}{2\mathrm{\Λ}}{n}_0& \frac{n_0}{\mathrm{\Λ}}\\ \mathrm{\λ}& -\mathrm{\λ}& 0& 0& 0\\ \frac{f_f}{{\mathrm{\μ}}_f}{P}_0& 0& -\frac{\mathrm{\Ω}}{{\mathrm{\μ}}_f}& \frac{\mathrm{\Ω}}{2{\mathrm{\μ}}_f}& 0\\ \frac{1-f_f}{{\mathrm{\μ}}_c}{P}_0& 0& \frac{\mathrm{\Ω}}{{\mathrm{\μ}}_c}& -\frac{2M+\mathrm{\Ω}}{2{\mathrm{\μ}}_c}& 0\\ 0& 0& 0& 0& 0\end{array}\right];B_c=\left[\begin{array}{c}0\\ 0\\ 0\\ 0\\ G_r\end{array}\right];$ D=[0]；C=[10000]；

Parameter G in matrix_r、n₀、λ、β、f_f、Λ、μ_f、P₀Provided by nuclear power plant, the running parameter α in matrix_f、α_c、μ_c, Ω, M be by n₀Determining, concrete calculating formula is as follows:

Step S32,

Described model predictive control system is carried out discretization, correctly choose sampling step length, described model predictive control system passes through current sample time k, it was predicted that following state space output, and the discrete form of described model predictive control system (17) is expressed as:

$\left\{\begin{array}{c}x(k+1|k)=Ax\left(k\right)+B\mathrm{\Δ}u\left(k\right)\\ y(k+1|k)=Cx(k+1|k)+Du\left(k\right)=CAx\left(k\right)+CB\mathrm{\Δ}u\left(k\right)\end{array}\right.---\left(19\right)$

In formula, the matrix A after system discretization and matrix B distinguish the matrix A before corresponding discretization_cAnd B_c；(k+1 | k) represent the predictive value in the current sample time k k+1 moment predicted；

Assuming to predict in described model predictive control system that time domain is Np, control time domain is Nc, is obtained by model predictive control system is theoretical, controls time domain less than or equal to prediction time domain, i.e. Np >=Nc；

Δ u (k+1)=u (k+1)-u (k), the dynamic prediction value of described model predictive control system future time instance is the actual value by current sample time, in whole prediction time domain, complete under the effect of Space-state control input quantity, therefore overseas when controlling, the controlled quentity controlled variable of state space remains unchanged, i.e. Δ u (k+i)=0, wherein i=Nc, Nc+1, Nc+2, Nc+3, ..., Np-1；

By current time k, state space variable value x (k) of system, it was predicted that in the k+m moment, the state space variable value of system is x (k+m | k), then the predicted state space variable of system is represented by:

X (k+m | k)=A^mx(k)+A^m-1BΔu(k)+A^m-2BΔu(k+1)+…+A^mBΔu(k+m)(20)

It is 0 controlling control variable Δ u beyond time domain Nc, formula (20) can obtain:

According to predicted state space variable, by y (k+1 | k)=Cx (k+1 | k)+Du (k)=CAx (k)+CB Δ u (k) in discretization model Predictive Control System (19), through type (21) can be tried to achieve the predicted state space of system and is output as:

Step S33,

According to Model Predictive Control Theory, for solving the optimal solution of system, objective function J is:

J=(R_s-Y)^T(R_s-Y)+ΔU^TR_wΔU(23)

In formula,

Y=[y (k+1 | k) y (k+2 | k) ... y (k+Np | k)]^T, it is the matrix of Np × 1 dimension；

Weight matrix R_wIt it is the diagonal matrix of Np × Np dimension；

Δ U=[Δ u (k) Δ u (k+1) ... Δ u (k+Nc-1)]^T, it is the matrix of Np × 1 dimension；

F=[CACA²…CA^Np]^T, it is the matrix of Np × 5 dimension；

R_s=[111 ... 1]^TR (k), wherein r (k) is given reference value, R_sIt it is the matrix of Np × 1 dimension；

$\mathrm{\Φ}=\left[\begin{array}{ccccc}CB& 0& 0& \mathrm{...}& 0\\ CAB& CB& 0& \mathrm{...}& 0\\ {\mathrm{CA}}^{2}B& CAB& CB& \mathrm{...}& 0\\ .& .& .& & .\\ .& .& .& & .\\ .& .& .& & .\\ {\mathrm{CA}}^{Np-1}B& {\mathrm{CA}}^{Np-2}B& {\mathrm{CA}}^{Np-3}B& \mathrm{...}& {\mathrm{CA}}^{Np-Nc}B\end{array}\right],$ It it is the matrix of Np × Nc dimension；

Thus can obtain:

Y=Fx (k)+Φ Δ U (24)

By Model Predictive Control Theory it can be seen that it is that object function J obtains minima that system obtains the condition of optimal solution, and the condition that object function J obtains minima is:By calculus and linear algebra knowledge, the value of the increment Delta U therefrom solving the Space-state control amount corresponding to optimal solution is:

Δ U=(Φ^TΦ+R_w)^-1Φ^T(R_s-Fx(k))

Δ u (k) is the first row of matrix Δ U, first row element, just can try to achieve state space output y according to described discretization model Predictive Control System (19).

5. the pressurized-water reactor nuclear power plant core power model predictive control method based on genetic algorithm according to claim 4, it is characterised in that described step S4 based on genetic algorithm, described power prediction Controlling model is carried out parameter tuning particularly as follows:

Step S41, when certain sampling instant kT, generate comprise 3 undetermined parameter Np, Nc and R1 kth for chromosome, and calculate kth for the fitness function value indexJ corresponding to bar chromosome each in chromosome；

Step S42, according to kth for chromosomal fitness function value indexJ, through roulette wheel selection, intersection and variation, generate k+1 for chromosome, then calculate in kth+1 generation chromosome the fitness function value indexJ corresponding to each bar chromosome；

Step S43, so circulation go down, and according to fitness function value indexJ, constantly excellent genes are genetic to the next generation, constantly approach optimal solution；

If step S44 evolutionary generation is not up to set maximum evolutionary generation T, just obtain optimal solution；So genetic manipulation terminates at this moment；If evolutionary generation has reached set maximum evolutionary generation T, also do not draw optimal solution, then genetic manipulation terminates at this moment, and optimal solution is just drawn for chromosome by T.

6. the pressurized-water reactor nuclear power plant core power model predictive control method based on genetic algorithm according to claim 5, it is characterised in that

Described power prediction Controlling model is carried out in the Model Predictive Control of parameter tuning prediction time domain be more than or equal to controlling time domain, i.e. Nc≤Np by described step S4 based on genetic algorithm；And Nc and Np is integer, in GA, therefore set three parametric variable: N₁、k₁And R₁；To N₁、k₁Round, respectively obtain Nc and kk；Make Np=Nc+kk, just complete undetermined parameter Np, Nc and R₁Setting, then pass through genetic algorithm and carry out optimizing, draw Np, Nc and R₁Optimal value.