CN111767646B - Tower type solar thermal power station receiver optimization design method - Google Patents
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Abstract
The invention discloses an optimal design method for a receiver of a tower type solar thermal power station. The method comprises the steps of firstly establishing a heat loss model in the heat exchange process of a receiver, and calculating to obtain the power generation efficiency and annual generating capacity of the power station by combining a lens field condensation model and an efficiency fitting formula of a power generation module under a non-rated working condition. The key parameters such as the size of the cavity of the receiver, the size of the heat exchange panel and the like are used as decision variables, the optimization proposition of minimizing the electrical cost of the leveling receiver is provided, and the self-adaptive particle swarm algorithm combined with intelligent Monte Carlo sampling is adopted for quick solving. The method can optimize and obtain the optimal receiver parameters, effectively reduce the construction cost of the receiver of the tower type solar thermal power station, can quickly and accurately solve the problem by using the optimization problem solving method, and is convenient for quick calculation in the design of the power station.
Description
Technical Field
The invention relates to the field of tower type solar thermal power stations, in particular to an optimal design method of a receiver of a tower type solar thermal power station.
Background
The tower type solar thermal power station is a large-scale condensation power generation device, and mainly comprises heliostats, a receiving tower, a receiver, a heat exchange device, a heat storage device and a thermal power generation device. Because of the advantages of large light concentration ratio (generally 300-1500) and high operating temperature (500-1500 ℃), tower-type solar thermoelectric systems are currently receiving more attention.
The receiver of the tower type solar thermal power station receives solar energy converged by the heliostat field and directly or indirectly transmits the solar energy to water vapor to realize photo-thermal conversion, and is an intermediate system for connecting the heliostat field and the power generation module. The receiver can be divided into an exposed type receiver and a cavity type receiver according to the physical structure, the panel of the exposed type receiver is directly exposed to the air, and the cavity type receiver is used for installing the receiver panel in the cavity of the tower top, so that the heat loss can be reduced; the receiver can be divided into a direct type receiver and an indirect type receiver according to the type of the heat transfer medium, the direct type receiver uses water/steam as the heat transfer medium, water is directly heated into steam in the receiver panel to drive the power generation module to generate power, the indirect type receiver uses molten salt or air and the like as the heat transfer medium, and the heated heat transfer medium in the receiver panel generates the steam through secondary heat transfer to participate in the subsequent power generation process.
The parameters of the receiver not only affect the optical efficiency of the heliostat field, but also affect the heat transfer efficiency and heat loss during the heat transfer process of the heat transfer medium, and determine the photo-thermal efficiency of the receiver and even affect the temperature of the heat transfer medium at the outlet of the receiver, thereby changing the efficiency of the subsequent power generation module. Therefore, the reasonable design of the receiver is important to improve the power generation efficiency of the power station.
Most of the existing researches focus on the research and development of novel materials and physical structures of the receiver to improve the heat exchange efficiency, reduce the heat loss, the equipment cost and the like, but for the receiver with specific materials and structures, how to optimally design key parameters such as the size of a cavity of the receiver, the size of a panel of the receiver, the pipe diameter of a heat exchange pipe and the like according to the requirements of the generating capacity, the input cost and the like of a power station, so as to improve the heat exchange efficiency, reduce the heat exchange loss, reduce the construction cost and the like, and the related researches are less. In fact, the receiver aperture area determines the field overflow efficiency, and the receiver panel size and receiver tube diameter determine the heat transfer efficiency of the receiver. Therefore, the parameter optimization of the receiver has important significance in the design and construction stage of the power station for improving the overall power generation efficiency of the power station and reducing the investment cost.
Disclosure of Invention
The invention provides an optimal design method of a receiver of a tower type solar thermal power station, which ensures that the highest power generation efficiency is obtained with the minimum cost in the design stage of the power station, the power generation requirement is met, and the average power generation cost of the receiver of the power station is reduced.
The technical scheme adopted by the invention is as follows:
(1) Under given heliostat field parameters, a model for calculating total energy reflected by the heliostat field at all times in the year is established based on a Monte Carlo ray tracing method.
The ray tracing method treats sunlight as non-parallel light by randomly scattering points on a mirror surface, namely, sunlight received and reflected by one point on the mirror surface is a group of light cones, and the energy of single light rays in the light cones is compliant with the distribution of a sun disc. According to the direction of the incident solar cone of the mirror surface point, the direction of the reflected solar cone is tracked, the energy of the solar rays and the intersection point of the reflected rays and the absorber plane are calculated, and the energy loss of the reflected rays in the propagation process and the energy when the reflected rays reach the receiver are calculated, so that the energy distribution on the receiver plane is obtained.
The Monte Carlo method is utilized to simulate the energy distribution in the solar cone, a sufficient number of rays are randomly selected in the solar cone, the energy of each ray is calculated through the solar disc distribution, and the energy of each ray is equivalent to representing the energy of the light cone at different points in a light spot formed on the absorber, so that the energy distribution on the plane of the receiver is obtained.
The process realizes parallel computation on the GPU by using the CUDA computing platform.
(2) The spill loss of heliostat reflected energy at any receiver parameter is calculated and the heat transfer loss of the receiver is calculated to obtain the energy transferred to the heat transfer medium.
And (3) calculating effective energy falling into the receiver panel according to the energy distribution on the receiver calculated in the step (1) and the parameters such as the length and the width of the receiver panel, the length and the width of the receiver cavity and the like, so as to obtain the overflow loss of the heliostat field reflected energy.
After the total effective energy on the receiver panel is obtained, the heat exchange loss on the receiver is calculated by the following method, thereby calculating the energy that is finally transferred to the heat transfer medium or water vapor.
Firstly, establishing an energy balance equation of a receiver heat exchange process as follows:
Q delivered ＝m f (h o -h i ) (1)
m f is the mass flow rate of the heat transfer medium, h i And h o Enthalpy values of the receiver inlet and outlet heat transfer medium, respectively. In addition, the basic heat exchange equation can be listed as follows:
A i ＝πd i L (4)
wherein T is wo Is the temperature of the outer wall of a heat exchange tube of the receiver, T wi Is the temperature of the inner wall of a heat exchange tube of the receiver, T f Is the average temperature of the heat transfer medium, d o ,d i ,d m Respectively the outer diameter and the inner diameter of the receiver pipeline and the average diameter, A m Is the average heat conduction area of the pipe wall of the receiver, A i Is the heat conduction area of the inner wall of the receiver tube, L is the characteristic length of the heat exchange tube, T i And T o Is the inlet and outlet temperature of the heat transfer medium, lambda is the heat conductivity coefficient of the heat exchange tube, alpha is the heat conductivity coefficient of the heat transfer medium in the receiver pipeline for convective heat transfer, and is calculated by using a dimensional analysis method, and the calculation mode is as follows:
first, the Reynolds number of the heat transfer medium flowing in the pipe is calculated:
d is the diameter of the tube (m), u is the flow rate of the heat transfer medium (m.s -1 ) ρ is the density of the heat transfer medium (kg.m -3 ) Mu is the dynamic viscosity (N.s.m -2 )；
And then judging the flowing state of the medium in the pipeline according to the Reynolds number, and calculating the corresponding heat transfer coefficient through an empirical formula of a dimensional analysis method.
Convection heat transfer coefficient alpha (W.m) -2 ·K -1 ) Mainly, mainlyAnd the flow velocity u (m.s) -1 ) Characteristic length L (m) of the heat transfer device, viscosity μ (N.s.m -2 ) Thermal conductivity lambda (W.m -1 ·K -1 ) Density ρ (kg.m) -3 ) Specific heat capacity C P (J·kg -1 ·K -1 ) And a volume expansion coefficient beta (K) -1 ) And (5) correlation. Thus, the convective heat transfer coefficient can be expressed as α=f (u, L, μ, λ, P, C P GβΔt). The dimensional analysis method combines the variables to design corresponding dimensionless numbers, so that the change data between the heat exchange coefficient and the numbers are measured through an experimental method, and a fitting equation is established. The dimensionless numbers are shown in table 1.
Table 1 dimensionless number table
The relationship between the convective heat transfer coefficient and the variables can be converted to N u ＝f(Re,Pr,Gr)。
Different Re correspond to different fluid flow states, and the convection heat transfer coefficients in the tube all have corresponding experimental data fitting equations.
When Re >10000, the flowing state is a complete turbulence state, and the corresponding empirical formula is:
Nu＝0.023Re 0.8 Pr 0.4 (7)
2300< Re <10000, the flow state belongs to the transition state, and the fitting equation is as follows:
f＝(1.82lgRe-1.64) -2 (9)
re <2300, when the flow state belongs to laminar flow, the contribution of natural convection to the heat exchange coefficient needs to be considered, so the basic empirical formula is as follows:
wherein mu w Is the viscosity of the fluid at the wall temperature, when Gr>25000, calculated according to the above formula, multiplied by a correction factor of 0.8 (1+0.015 Gr 1/3 ) When Gr<At 25000, natural convection is negligible.
A model of the heat loss of the heat exchange process occurring at the receiver is then built as shown in equation (1),
Q concentrated ＝Q loss,ref +Q loss,conv +Q loss,rad +Q loss,cond +Q delivered (11)
wherein Q is concentrated Representing the energy of convergence of heliostat fields, Q loss,ref 、Q loss,conv 、Q loss,rad And Q loss,cond Representing reflected energy loss, convective energy loss, radiant energy loss, and conductive energy loss, respectively, Q delivered Representing the energy transferred to the heat transfer medium.
The reflected energy loss is caused by the fact that part of the energy focused on the receiver by the heliostat is directly reflected by the receiver without being absorbed, calculated using equation (2), where ρ panel The reflectivity of the receiver panel is determined by the material and surface distribution of the receiver panel. For the cavity type receiver, due to the existence of the cavity, part of reflected energy is reflected in the cavity for multiple times and finally part of reflected energy is absorbed, and in order to simplify the calculation, a calculation method of correcting by using a visual factor, namely F in the formula (2), is directly adopted r The concrete definition is shown as a formula (3), wherein A rec And A ape The areas of the receiver heat exchange panel and the receiver aperture, respectively. For an exposed receiver, the visual factor is 1.
Q loss,ref ＝ρ panel Q concentraed F r (12)
The radiation heat loss is calculated as follows:
wherein ε w Is the emissivity of the wall of the receiver tube, which is corrected by the existence of the cavity, resulting in an average emissivity epsilon avg ，σ＝5.67×10 -8 W/(m 2 ·K 4 ) Is Boltzmann constant, T air Is the ambient air temperature in K.
The convective heat loss is calculated as follows:
Q loss.conv ＝h air (T rec -T air )A ape (16)
wherein T is rec Is the receiver surface temperature, h air The convection heat transfer coefficient of air is divided into natural convection heat transfer coefficient h air,nc And forced convection heat transfer coefficient h air,fc The method comprises the following steps:
h air ＝h air,nc +h air,fc (17)
the corresponding empirical formula is:
h air,nc ＝0.81(T wo -T air ) 0.426 (19)
wherein Nu air,fc 、Re air 、Pr air The knoop quasi-number, reynolds quasi-number and prandial quasi-number of forced convection heat transfer of air, respectively.
Conductive heat loss is primarily heat loss through the insulation.
Wherein T is insu ,δ insu ,λ insu The surface temperature, thickness and heat transfer coefficient of the heat insulation layer respectively. Wherein h is air,insu Is the heat transfer coefficient of air and the heat insulation layer. The corresponding empirical calculation formula is:
wherein Nu air Number of nucels to transfer heat for air convection.
Simultaneous equations (1-21) can be solved to obtain the final heat transferred to the heat transfer medium when the heliostat aggregate energy is determined.
The simultaneous equations are solved by an iterative method, and the surface temperature of the receiver is calculated by setting the initial value of the energy transferred to the heat transfer medium, so that each heat loss is calculated, and the energy transferred to the heat transfer medium is calculated iteratively until convergence.
(3) The efficiency of the power generation module is calculated based on the energy transferred to the heat transfer medium.
The energy conversion efficiency of the power generation module under rated working conditions is determined by design parameters of the steam turbine and the generator, and the power generation module can be considered to be known. The efficiency calculation mode under the non-rated working condition adopts the following empirical fitting formula.
Efficiency eta of steam turbine under non-rated conditions turbine The calculation is as follows.
η turbine ＝(1-β)η turbine,norm (22)
β＝0.191-0.409r+0.218r 2 (23)
Wherein eta turbine,norm Is the turbine efficiency under rated working conditions, beta is the efficiency loss ratio, and r is the ratio of the turbine power to the rated power.
Efficiency eta of the generator generator The method comprises the following steps:
η generator ＝0.908+0.258r-0.3r 2 +0.12r 3 (24)
the pump efficiency changes are negligible.
Thus, the efficiency eta of the power generation module is obtained power Is that
η power ＝η turbine ×η generator (25)
The generated energy P at any moment is
P＝Q delivered η power (26)
Annual energy production is obtained by accumulation of energy production at various moments.
Through the three steps, under the condition that the parameters of the mirror field and the parameters of the power generation module are known, when the receiver selects different parameters, the efficiency and the total power generation efficiency of each module at any time of the power station can be calculated, and annual energy generation can be obtained after annual cumulative calculation.
(4) An optimization proposition of the receiver parameter design is established. The key parameters of the length and width of the cavity of the receiver, the length and width of the heat exchange panel, the diameter of the heat exchange tube and the like are selected as decision variables, an objective function LRCOE (Levelized Receiver Cost of Energy, leveling the electrical cost of the receiver) is designed, and the average power generation cost of the receiver in the whole life cycle is represented, and the specific calculation mode is shown as follows.
Wherein I is debt And I insurance For annual interest rate and insurance rate, C invest,receiver And C O&M,receiver The total investment cost and the operation maintenance cost of the receiver are represented by W, annual average power generation capacity and n, the whole life cycle of the power station, and the unit is year.
The established optimization model is as follows:
s.t. l re ≥l re,lb (28b)
w re ≥w re,lb (28c)
l aperture ≥l aperture,lb (28d)
w aperture ≥w aperture,lb (28e)
d tube ≥d tube,lb (28f)
l re ×w re ×0.5Flux limit ≥P N (28g)
W≥W design (28h)
wherein l re And w re Representing the length and width of the receiver panel, l aperture And w aperture Representing the length and width l of the bore aperture ,w aperture ，d tube The diameter of the heat exchange tube, subscript lb denotes the lower limit of each parameter, formulas 28b-28f denote the lower limit constraint of each parameter, formula 28g denotes the upper limit constraint of energy density on the receiver panel, P N Representing the average energy density of the receiver under rated conditions, flux limit Indicating an upper energy density safety limit on the receiver. Formula 28h represents the minimum annual energy production requirement, W design Representing the design annual energy production.
(5) And solving the optimization proposition by utilizing a self-adaptive particle swarm algorithm combined with an intelligent sampling Monte Carlo method. The specific solving mode is as follows:
step one: initializing population x= { X i I=1, 2, …, n }. Each individual x in the population i Are one possible solution to the optimization problem, and each x i All have a corresponding moving speed v i 。
Step two: the population is assessed. The current position and fitness of each particle in the population, namely, the objective function value, are stored as the optimal position of each particle, and the position and fitness of the optimal position fitness optimal individual in all particles are stored in the global optimal position.
Step three: the speed and position of each particle of the current population is updated. The calculation method is as follows:
wherein,and->The position and velocity of the d-th dimensional component of the i-th particle at the kth iteration are represented respectively,representing the self-historic optimal position found in k iterations of the ith particle,/for the particle>Represents the global optimal position found by the particle swarm in k iterations, omega is the inertia coefficient, and c 1 And c 2 Individual learning factors and global learning factors, < ->And->Is a random number within 0-1.
Step four: judging the iterative state of the algorithm, and updating the parameters of the particle swarm algorithm and the sampling precision when the reflected energy of the lens field is calculated according to the iterative state. The iterative state of the particle swarm algorithm is divided into four states of space exploration, detail description, gradual convergence and jump out of local optimum, and the evolution factor (evolutionary factor) F is used for helping to describe different states of the iterative process. First, the average distance d of the particle X from all other particles in the iterative process is defined i ：
Wherein D is the particle dimension. D of particles optimizing the objective function i Denoted as d g ，d min And d max Represents d i F can be defined as:
to characterize the distance of the current optimal point from all other points. And determining the corresponding iteration state when the F is different in value by adopting a fuzzy relation. When the F is a larger value, the algorithm is in a local optimal state, and when the F value is medium and large, the algorithm is in an exploration state; when the F value is moderate and small, the algorithm is in a detail describing state; the algorithm is in a convergence state when the F value tends to zero.
Parameter c of particle swarm algorithm in four states 1 And c 2 The adjustment mode is as follows:
space exploration state:
details depicting state:
gradually converging state:
and jumping out of the local optimal state:
wherein a and B are slow and fast increasing or decreasing speed factors, respectively, a and B are slow and fast increasing or decreasing random factors, respectively, and rand is a random number between (0, 1).
The inertia coefficient omega is adjusted by the following method:
the adjustment mode of the Monte Carlo simulation point number N adopted in the process of calculating the reflection energy of the lens field is as follows:
for particle x i The sampling point number n used in calculating the objective function i There are two part decisions, specifically as follows:
n i ＝n b ×η i (42)
wherein n is b Is the group sampling base number, which is correspondingly adjusted by different states in which the particle swarm algorithm is iterated, eta i Is the individual sampling coefficient of the particle, and is determined by the relationship between the current position of the particle and the currently obtained global optimal position.
n b The adjustment modes in different iteration states are shown in the formulas (41-44).
Space exploration state:
details depicting state:
gradually converging state:
and jumping out of the local optimal state:
where a and b are slow and fast increasing or decreasing speed factors, respectively, and rand is a random number between (0, 1). At the same time to n b The upper limit and the lower limit of the change process are set so as to ensure that the objective function calculation does not exceed the error limit because the simulation precision is too low, and the overall simulation calculation time is not too long.
Individual particle sampling coefficient eta i Is determined based on the distance of the current position of the particle from the current optimum point, defining particle x i From the current optimum point x gb Distance of (2)Wherein->And->Respectively representing the ith particle and the D-th dimensional component of the optimal particle in the kth iteration, wherein D is the particle dimension; calculating eta i The method comprises the following steps:
wherein delta min And delta max Delta respectively i Minimum and maximum of (2), soEpsilon is the balance factor and n' is the number of particles located in the feasible region.
Step five: and updating the individual optimal position and the global optimal position of each particle.
Step six: judging whether the maximum iteration times are reached or the convergence condition is reached, if so, outputting the position of the current global optimal individual; otherwise, turning to the third step.
The beneficial effects of the invention are as follows: according to the optimal design method of the receiver of the tower type solar thermal power station, enough sampling moments are selected, and the obtained optimal solution can ensure that annual energy generation of the power station meets design requirements and meanwhile average power generation cost of the receiver is lowest. Meanwhile, the self-adaptive particle swarm optimization method combined with the intelligent sampling Monte Carlo method can effectively reduce algorithm solving time and improve calculation efficiency in power station design.
Drawings
FIG. 1 is a flow chart of a method for optimizing the design of a receiver of a tower solar thermal power plant;
FIG. 2 is a flow chart of an iterative solution of a receiver heat exchange equation;
FIG. 3 is a block diagram of a PS10 power plant bore receiver;
FIG. 4 is a flow chart of an adaptive particle swarm algorithm that incorporates the intelligent Monte Carlo sampling method;
FIG. 5 is a graph of the variation of each parameter in the solution of the adaptive particle swarm algorithm incorporating the intelligent Monte Carlo sampling method;
fig. 6 is a graph of the number of particle samples versus the number of particle samples during a solution of an adaptive particle swarm algorithm that incorporates an intelligent monte carlo sampling method.
Detailed Description
Taking the receiver optimization process of spanish PS10 tower solar thermal power plant as an example in this example, the overall method flow is shown in fig. 1. The specific implementation process is as follows:
(1) And establishing a model for calculating total energy reflected by the lens field at all times in the whole year based on a Monte Carlo ray tracing method. Heliostat field parameters are shown in table 2 in this example.
Table 2 field parameters in examples
By using a ray tracing method, sunlight is treated as non-parallel light by randomly scattering points on a mirror surface, namely, sunlight received and reflected by one point on the mirror surface is a group of light cones, and the energy of single light rays in the light cones is compliant with the distribution of a sun disc. According to the direction of the incident solar cone of the mirror surface point, the direction of the reflected solar cone is tracked, the energy of the solar rays and the intersection point of the reflected rays and the absorber plane are calculated, and the energy loss of the reflected rays in the propagation process and the energy when the reflected rays reach the receiver are calculated, so that the energy distribution on the receiver plane is obtained.
The Monte Carlo method is utilized to simulate the energy distribution in the solar cone, a sufficient number of rays are randomly selected in the solar cone, the energy of each ray is calculated through the solar disc distribution, and the energy of each ray is equivalent to representing the energy of the light cone at different points in a light spot formed on the absorber, so that the energy distribution on the plane of the receiver is obtained. In order to ensure the simulation accuracy, the Monte Carlo sampling point number is 10000-15000.
The process realizes parallel computation on the GPU by using the CUDA computing platform. By using the method, the total reflection energy of the heliostat field at any moment can be obtained, and the calculated total reflection energy of the heliostat field is shown in table 3 by taking 12:00 of 21 days of 3 months of 2000 as an example, so that the result can be seen to be more accurate.
TABLE 3 simulation results of heliostat field reflection energy
(2) The spill loss of heliostat reflected energy at any receiver parameter is calculated and the heat transfer loss of the receiver is calculated to obtain the energy transferred to the heat transfer medium.
And (3) calculating effective energy falling into the receiver panel according to the energy distribution on the receiver calculated in the step (1) and the parameters such as the length and the width of the receiver panel, the length and the width of the receiver cavity and the like, so as to obtain the overflow loss of the heliostat field reflected energy.
After the total effective energy on the receiver panel is obtained, the heat exchange loss on the receiver is calculated by the following method, thereby calculating the energy that is finally transferred to the heat transfer medium or water vapor.
Firstly, establishing an energy balance equation of a receiver heat exchange process as follows:
Q delivered ＝m f (h o -h i ) (1)
m f is the mass flow rate of the heat transfer medium, h i And h o Enthalpy values of the receiver inlet and outlet heat transfer medium, respectively. In addition, the basic heat exchange equation can be listed as follows:
A i ＝πd i L (4)
wherein T is wo Is a receiverThe temperature of the outer wall of the heat exchange tube T wi Is the temperature of the inner wall of a heat exchange tube of the receiver, T f Is the average temperature of the heat transfer medium, d o ,d i ,d m Respectively the outer diameter and the inner diameter of the receiver pipeline and the average diameter, A m Is the average heat conduction area of the pipe wall of the receiver, A i Is the heat conduction area of the inner wall of the receiver tube, L is the characteristic length of the heat exchange tube, T i And T o Is the inlet and outlet temperature of the heat transfer medium, lambda is the heat conductivity coefficient of the heat exchange tube, alpha is the heat conductivity coefficient of the heat transfer medium in the receiver pipeline for convective heat transfer, and is calculated by using a dimensional analysis method, and the calculation mode is as follows:
first, the Reynolds number of the heat transfer medium flowing in the pipe is calculated:
d is the diameter of the tube (m), u is the flow rate of the heat transfer medium (m.s -1 ) ρ is the density of the heat transfer medium (kg.m -3 ) Mu is the dynamic viscosity (N.s.m -2 )；
And then judging the flowing state of the medium in the pipeline according to the Reynolds number, and calculating the corresponding heat transfer coefficient through an empirical formula of a dimensional analysis method.
Convection heat transfer coefficient alpha (W.m) -2 ·K -1 ) Mainly with the flow velocity u (m.s) -1 ) Characteristic length L (m) of the heat transfer device, viscosity μ (N.s.m -2 ) Thermal conductivity lambda (W.m -1 ·K -1 ) Density ρ (kg.m) -3 ) Specific heat capacity C P (J·kg -1 ·K -1 ) And a volume expansion coefficient beta (K) -1 ) And (5) correlation. Thus, the convective heat transfer coefficient can be expressed as α=f (u, L, μ, λ, P, C P GβΔt). The dimensional analysis method combines the variables to design corresponding dimensionless numbers, so that the change data between the heat exchange coefficient and the numbers are measured through an experimental method, and a fitting equation is established. The dimensionless numbers are shown in table 4.
Table 4 dimensionless number table
The relationship between the convective heat transfer coefficient and the variables can be converted to N u ＝f(Re,Pr,Gr)。
Different Re correspond to different fluid flow states, and the convection heat transfer coefficients in the tube all have corresponding experimental data fitting equations.
When Re >10000, the flowing state is a complete turbulence state, and the corresponding empirical formula is:
Nu＝0.023Re 0.8 Pr 0.4 (7)
2300< Re <10000, the flow state belongs to the transition state, and the fitting equation is as follows:
f＝(1.82lgRe-1.64) -2 (9)
re <2300, when the flow state belongs to laminar flow, the contribution of natural convection to the heat exchange coefficient needs to be considered, so the basic empirical formula is as follows:
wherein mu w Is the viscosity of the fluid at the wall temperature, when Gr>25000, calculated according to the above formula, multiplied by a correction factor of 0.8 (1+0.015 Gr 1/3 ) When Gr<At 25000, natural convection is negligible.
A model of the heat loss of the heat exchange process occurring at the receiver is then built as shown in equation (1),
Q concentrated ＝Q loss,ref +Q loss,conv +Q loss,rad +Q loss,cond +Q delivered (11)
wherein Q is concentrated Representing the energy of convergence of heliostat fields, Q loss,ref 、Q loss,conv 、Q loss,rad And Q loss,cond Representing reflected energy loss, convective energy loss, radiant energy loss, and conductive energy loss, respectively, Q delivered Representing the energy transferred to the heat transfer medium.
The reflected energy loss is caused by the fact that part of the energy focused on the receiver by the heliostat is directly reflected by the receiver without being absorbed, calculated using equation (2), where ρ panel The reflectivity of the receiver panel is determined by the material and surface distribution of the receiver panel. For the cavity type receiver, due to the existence of the cavity, part of reflected energy is reflected in the cavity for multiple times and finally part of reflected energy is absorbed, and in order to simplify the calculation, a calculation method of correcting by using a visual factor, namely F in the formula (2), is directly adopted r The concrete definition is shown as a formula (3), wherein A rec And A ape The areas of the receiver heat exchange panel and the receiver aperture, respectively. For an exposed receiver, the visual factor is 1.
Q loss,ref ＝ρ panel Q concentraed F r (12)
The radiation heat loss is calculated as follows:
wherein ε w Is the emissivity of the wall of the receiver tube, which is corrected by the existence of the cavity, resulting in an average emissivity epsilon avg ，σ＝5.67×10 -8 W/(m 2 ·K 4 ) Is Boltzmann constant, T air Is the ambient air temperature in K.
The convective heat loss is calculated as follows:
Q loss.conv ＝h air (T rec -T air )A ape (16)
wherein T is rec Is the receiver surface temperature, h air The convection heat transfer coefficient of air is divided into natural convection heat transfer coefficient h air,nc And forced convection heat transfer coefficient h air,fc The method comprises the following steps:
h air ＝h air,nc +h air,fc (17)
the corresponding empirical formula is:
h air,nc ＝0.81(T wo -T air ) 0.426 (19)
wherein Nu air,fc 、Re air 、Pr air The knoop quasi-number, reynolds quasi-number and prandial quasi-number of forced convection heat transfer of air, respectively.
Conductive heat loss is primarily heat loss through the insulation.
Wherein T is insu ,δ insu ,λ insu The surface temperature, thickness and heat transfer coefficient of the heat insulation layer respectively. Wherein h is air,insu Is the heat transfer coefficient of air and the heat insulation layer. The corresponding empirical calculation formula is:
wherein Nu air Noose for heat transfer for air convectionA benchmark number.
Simultaneous equations (1-21) can be solved to obtain the final heat transferred to the heat transfer medium when the heliostat aggregate energy is determined.
The simultaneous equations are solved by an iterative method, the surface temperature of the receiver is calculated by setting the initial value of the energy transferred to the heat transfer medium, and thus, each heat loss is calculated, so that the energy transferred to the heat transfer medium is calculated iteratively until convergence, and the iterative process is shown in fig. 2.
By the method, the heat exchange efficiency of the receiver and the total energy transferred to the heat transfer medium under any receiver parameters can be calculated, taking the original receiver parameters of the PS10 power station as an example, the PS10 power station adopts a cavity type receiver, the structure of the cavity type receiver is shown in fig. 3, and the specific parameters are shown in table 5. The heat exchange result of the 12:00 receiver obtained by calculation in 3 months of 2000 is shown in table 6, and the calculation error is smaller, so that the model is more accurate.
(3) The efficiency of the power generation module is calculated based on the energy transferred to the heat transfer medium.
The energy conversion efficiency of the power generation module under rated working conditions is determined by design parameters of the steam turbine and the generator, and the power generation module can be considered to be known. The efficiency calculation mode under the non-rated working condition adopts the following empirical fitting formula.
Efficiency eta of steam turbine under non-rated conditions turbine The calculation is as follows.
η turbine ＝(1-β)η turbine,norm (22)
β＝0.191-0.409r+0.218r 2 (23)
Wherein eta turbine,norm Is the turbine efficiency under rated working conditions, beta is the efficiency loss ratio, and r is the ratio of the turbine power to the rated power.
Table 5 ps10 plant receiver parameters
Table 6 ps10 plant receiver heat exchange simulation results
Efficiency eta of the generator generator The method comprises the following steps:
η generator ＝0.908+0.258r-0.3r 2 +0.12r 3 (24)
the pump efficiency changes are negligible.
Thus, the efficiency eta of the power generation module is obtained power Is that
η power ＝η turbine ×η generator (25)
The generated energy P at any moment is
P＝Q delivered η power (26)
Through the three steps, under the condition that the parameters of the mirror field and the parameters of the power generation module are known, when the receiver selects different parameters, the efficiency and the total power generation efficiency of each module at any time of the power station can be calculated, and annual energy generation can be obtained after annual cumulative calculation.
(4) An optimization proposition of the receiver parameter design is established. The key parameters of the length and the width of the cavity of the receiver, the length and the width of the heat exchange panel, the diameter of the heat exchange tube and the like are selected as decision variables, an objective function LRCOE (Levelized Receiver Cost of Energy, leveling the electrical cost of the receiver) is designed, the average power generation cost of the receiver in the whole life cycle is represented, and the specific calculation mode is shown in (3).
Wherein I is debt And I insurance For annual interest rate and insurance rate, C invest,receiver And C O&M,receiver The total investment cost and the operation maintenance cost of the receiver are represented by W, annual average power generation capacity and n, the whole life cycle of the power station, and the unit is year. For PS10 plants, the above parameters are calculated as shown in table 7.
TABLE 7 LRCOE calculation parameters
The optimization model established for the PS10 plant receiver is as follows:
s.t. l re ≥0.1 (28b)
w re ≥0.1 (28c)
l aperture ≥0.1 (28d)
w aperture ≥0.1 (28e)
d tube ≥0.005 (28f)
l re ×w re ×375≥P N (28g)
W≥22GW (28h)
wherein l re And w re Representing the length and width of the receiver panel, l aperture And w aperture Representing the length and width l of the bore aperture ,w aperture ，d tube The diameter of the heat exchange tube, equations 26b-26f represent the lower limit constraints for each parameter, equation 26g represents the upper limit constraints for the energy density on the receiver panel, P N Representing the average energy density of the receiver under nominal conditions.
(5) And solving the optimization proposition by utilizing a self-adaptive particle swarm algorithm combined with an intelligent sampling Monte Carlo method. The solution flow is shown in fig. 4, and the specific solution mode is as follows:
step one: initializing population x= { X i I=1, 2, …, n }. Each individual x in the population i Are one possible solution to the optimization problem, and each x i All have a corresponding moving speed v i 。
Step two: the population is assessed. The current position and fitness of each particle in the population, namely, the objective function value, are stored as the optimal position of each particle, and the position and fitness of the optimal position fitness optimal individual in all particles are stored in the global optimal position.
Step three: the speed and position of each particle of the current population is updated. Calculation modes such as (5)
Wherein,and->The position and velocity of the d-th dimensional component of the i-th particle at the kth iteration are represented respectively,representing the self-historic optimal position found in k iterations of the ith particle,/for the particle>Represents the global optimal position found by the particle swarm in k iterations, omega is the inertia coefficient, and c 1 And c 2 An individual learning factor and a global learning factor, r 1 k And r 2 k Is a random number within 0-1.
Step four: judging the iterative state of the algorithm, and updating the parameters of the particle swarm algorithm and the sampling precision when the reflected energy of the lens field is calculated according to the iterative state. The iterative state of the particle swarm algorithm is divided into four states of space exploration, detail description, gradual convergence and jump out of local optimum, and the evolution factor (evolutionary factor) F is used for helping to describe different states of the iterative process. First, define particle X in the iterative process to be away from all other particlesAverage distance d of (2) i ：
D of particles optimizing the objective function i Denoted as d g ，d min And d max Represents d i F can be defined as:
to characterize the distance of the current optimal point from all other points. And determining the corresponding iteration state when the F is different in value by adopting a fuzzy relation. When the F is a larger value, the algorithm is in a local optimal state, and when the F value is medium and large, the algorithm is in an exploration state; when the F value is moderate and small, the algorithm is in a detail describing state; the algorithm is in a convergence state when the F value tends to zero.
Parameter c of particle swarm algorithm in four states 1 And c 2 The adjustment mode is as follows:
space exploration state:
/>
details depicting state:
gradually converging state:
and jumping out of the local optimal state:
wherein a and B are slow and fast increasing or decreasing speed factors, respectively, a and B are slow and fast increasing or decreasing random factors, respectively, and rand is a random number between (0, 1). Let a=a=0.1, b=b=0.05.
The inertia coefficient omega is adjusted by the following method:
the adjustment mode of the Monte Carlo simulation point number N adopted in the process of calculating the reflection energy of the lens field is as follows:
for particle x i The sampling point number n used in calculating the objective function i There are two part decisions, specifically as follows:
n i ＝n b ×η i (42)
wherein n is b Is the group sampling base number, which is correspondingly adjusted by different states in which the particle swarm algorithm is iterated, eta i Is the individual sampling coefficient of the particle, and is determined by the relationship between the current position of the particle and the currently obtained global optimal position.
n b Adjustment modes in different iteration statesAs shown in formulas (43-46).
Space exploration state:
details depicting state:
gradually converging state:
and jumping out of the local optimal state:
where a and b are slow and fast increasing or decreasing speed factors, respectively, taking a=0.3 and b=0.2 rand as a random number between (0, 1). At the same time to n b Setting upper and lower limits of the change process [5000,15000 ]]The method ensures that the objective function calculation does not exceed the error limit because the simulation precision is too low, and the overall simulation calculation time is not too long.
Individual particle sampling coefficient eta i Is determined based on the distance of the current position of the particle from the current optimum point, defining particle x i From the current optimum point x gb Distance of (2)Wherein->And->Respectively represent the ith particle and the optimal particle at the kth iterationD is the particle dimension; calculating eta i The method comprises the following steps:
wherein delta min And delta max Delta respectively i Minimum and maximum of (2), soEpsilon takes 0.8 and n' is the number of particles located in the feasible region.
Step five: and updating the individual optimal position and the global optimal position of each particle.
Step six: judging whether the maximum iteration times are reached or the convergence condition is reached, if so, outputting the position of the current global optimal individual; otherwise, turning to the third step.
By adopting the optimization method, the variation of the particle swarm parameters and the historical optimal values in the iterative process of the algorithm is shown in fig. 5, and the algorithm parameters can be dynamically adjusted in the iterative process to adapt to different iterative processes so as to accelerate convergence. In the iterative process, the sampling base of particles and the sampling number of each particle are changed as shown in fig. 6, and it can be seen that the sampling base is dynamically changed to adopt different overall sampling precision at each stage, so that the calculation time is reasonably distributed; the calculation time of each particle is different and is changed continuously along with the iterative process, so that the time and the precision of the calculation of the objective function are more accurately balanced. The time of the optimization solving process running on the computers of the 4 cores Intel Xeon silver 4110@2.1GHz CPU, the 20G memory and the Nivdia Tesla P4 display card is 2000-2500 seconds, and the solving efficiency is high.
The optimal parameters of the receiver and the optimized LRCOE obtained by solving the optimization algorithm are shown in the table 8, and it can be seen that the annual energy production of the optimized power station is increased by 5.41%, the average power generation cost of the receiver is reduced by 5.72%, and the optimization effect is remarkable.
Table 8 receiver optimization results
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Claims (5)
1. The receiver optimization design method for the tower type solar thermal power station is characterized by comprising the following steps of:
1) Under given heliostat field parameters, a model for calculating the distribution of the mirror field reflection energy at different moments on a receiver plane is established based on a ray tracing method; the step 1) specifically comprises the following steps: the method comprises the steps of randomly scattering points on a mirror surface, treating sunlight as a solar cone, simulating energy distribution in the solar cone by using a Monte Carlo method, randomly selecting a sufficient number of light rays in the solar cone, calculating the energy of each light ray by using solar disc distribution, and tracking and calculating the energy loss of each light ray in the reflection and convergence process, so that the energy distribution on a receiver plane is obtained;
2) Calculating the overflow loss of heliostat field reflection energy under any receiver parameter and the heat exchange loss of the receiver, and calculating the energy transferred to the heat transfer medium;
step 2) firstly obtaining the overflowing loss of the reflected energy of the heliostat field by calculating the effective energy falling in the receiver area under the specific receiver size parameter through the energy distribution on the receiver plane obtained in step 1); based on the effective energy in the receiver area, the simultaneous equation method is adopted to calculate the heat exchange loss of the receiver, specifically:
the energy balance equation for establishing the receiver heat exchange process is as follows
Q delivered ＝m f (h o -h i ) (1)
Q delivered Represents the energy transferred to the heat transfer medium, m f Is the mass flow rate of the heat transfer medium, h i And h o Enthalpy values of the receiver inlet and outlet heat transfer medium, respectively;
the basic heat exchange equation is established as follows:
A i ＝πd i L (4)
wherein Q is delivered Represents the energy transferred to the heat transfer medium, T wo Is the temperature of the outer wall of a heat exchange tube of the receiver, T wi Is the temperature of the inner wall of a heat exchange tube of the receiver, T f Is the average temperature of the heat transfer medium, d o ,d i ,d m Respectively the outer diameter, the inner diameter and the average diameter of the receiver pipeline, A m Is the average heat conduction area of the pipe wall of the receiver, A i Is the heat conduction area of the inner wall of the receiver tube, L is the characteristic length of the heat exchange tube, T i And T o Is the inlet and outlet temperature of the heat transfer medium, lambda is the heat conductivity coefficient of the heat exchange tube, alpha is the heat conductivity coefficient of the heat transfer medium in the receiver pipeline for convective heat transfer, and is calculated by using a dimensional analysis method;
the heat loss of the heat exchange process occurring at the receiver is modeled as follows:
Q concentrated ＝Q loss,ref +Q loss,conv +Q loss,rad +Q loss,cond +Q delivered (6)
Q loss,ref ＝ρ panel Q concentraed F r (7)
Q loss.conv ＝h air (T rec -T air )A ape (11)
h air ＝h air,nc +h air,fc (12)
h air,nc ＝0.81(T wo -T air ) 0.426 (14)
wherein Q is concentrated Representing the energy of convergence of heliostat fields, Q loss,ref 、Q loss,conv 、Q loss,rad And Q loss,cond Representing reflected energy loss, convective energy loss, radiant energy loss, and conductive energy loss, respectively, Q delivered Representing the energy transferred to the heat transfer medium; ρ panel Representing the reflectivity of the receiver panel, F r As a visual factor, A rec And A ape The areas of the receiver heat exchange panel and the receiver cavity are respectively; epsilon w Is the emissivity of the receiver tube wall, ε avg Is the average emissivity, σ=5.67×10 - 8 W/(m 2 ·K 4 ) Is Boltzmann constant, T rec Is the receiver surface temperature, T air Is the ambient air temperature; h is a air The convection heat transfer coefficient of air is divided into natural convection heat transfer coefficient h air,nc And forced convection heat transfer coefficient h air,fc ，Nu air,fc 、Re air 、Pr air A knowler's standard number, a reynolds standard number, and a prandtl standard number, respectively, of forced convection heat transfer of air; t (T) insu ,δ insu ,λ insu The surface temperature, thickness and heat transfer coefficient of the heat insulation layer are respectively, wherein h is air,insu Nuceyer criterion number Nu for heat transfer by air convection for heat transfer coefficient of air and heat insulating layer air Calculating;
solving simultaneous equations (1) - (21) to obtain the final heat transferred to the heat transfer medium when the heliostat focused energy is determined; the simultaneous equations are solved through an iteration method, and the surface temperature of a receiver is calculated by setting an initial value of energy transferred to a heat transfer medium, so that heat loss of each item is calculated, and the energy transferred to the heat transfer medium is calculated iteratively until convergence;
3) According to the energy transferred to the heat transfer medium, calculating the efficiency of the power generation module, so as to calculate the power generation amount at any moment and the total annual power generation amount;
4) The method comprises the steps of establishing an optimization problem of receiver parameter design by taking the lowest receiver accuracy electric power generation cost as a target;
5) And (3) rapidly solving the optimization problem in the step (4) by adopting a self-adaptive particle swarm algorithm combined with an intelligent Monte Carlo sampling method to obtain the optimal design parameters of the receiver.
2. The method for optimizing design of a receiver of a tower solar thermal power plant according to claim 1, wherein the step 3) of calculating the efficiency of the power generation module is based on a fitting formula under non-rated conditions,
efficiency eta of steam turbine under non-rated conditions turbine The calculation mode is that
η turbine ＝(1-β)η turbine,norm (17)
β＝0.191-0.409r+0.218r 2 (18)
Wherein eta turbine,norm Is the turbine efficiency under the rated working condition, beta is the efficiency loss ratio, and r is the ratio of the turbine power to the rated power;
efficiency eta of the generator generator The method comprises the following steps:
η generator ＝0.908+0.258r-0.3r 2 +0.12r 3 (19)
ignoring the pump efficiency variation;
thus, the efficiency eta of the power generation module is obtained power Is that
η power ＝η turbine ×η generator (20)
The generated energy P at any moment is
P＝Q delivered η power (21)
Annual energy production is obtained by accumulation of energy production at various moments.
3. The method for optimizing the design of the receiver of the tower type solar thermal power station according to claim 1, wherein the optimization problem established in the step 4) is as follows:
s.t.l re ≥l re,lb (22b)
w re ≥w re,lb (22c)
l aperture ≥l aperture,lb (22d)
w aperture ≥w aperture,lb (22e)
d tube ≥d tube,lb (22f)
l re ×w re ×0.5Flux limit ≥P N (22g)
W≥W design (22h)
wherein l re And w re Representing the length and width of the receiver panel, l aperture And w aperture Represents the length and width of the bore, d tube Indicating the diameter of the heat exchange tube, subscript lb indicating the lower limit of each parameter, LRCOE being (Levelized Receiver Cost of Energy) normalized receiver electrical cost, I debt And I insurance For annual interest rate and insurance rate, C invest,receiver And C O&M,receiver For the total investment cost and operation and maintenance cost of the receiver, W is annual energy production, n is the total life cycle of the power station, and the unit is annual Flux limit Representing an upper energy density safety limit, P, at the receiver N Representing the average energy density, W, of the receiver under rated conditions design Representing the design annual energy production.
4. The method for optimizing the design of the receiver of the tower type solar thermal power station according to claim 1, wherein the adaptive particle swarm algorithm used in the step 5) divides the iteration state into four types, and adopts different parameter adjustment methods in different states, specifically:
space exploration state:
details depicting state:
gradually converging state:
and jumping out of the local optimal state:
wherein c 1 And c 2 The individual learning factors and the global learning factors are respectively, the upper mark k represents the iteration times, A and B are respectively the slow and fast increasing or decreasing speed factors, a and B are respectively the slow and fast increasing or decreasing random factors, and rand is a random number between (0, 1).
5. The optimization design method of the tower type solar thermal power station receiver according to claim 1, wherein the adaptive particle swarm algorithm in the step 5) is combined with an intelligent monte carlo sampling method, and the number of sampling points in the process of calculating the reflection energy of the mirror field is dynamically adjusted according to the iteration state, and specifically comprises the following steps:
for particle x i The sampling point number n used in calculating the objective function i Is defined as
n i ＝n b ×η i (31)
Wherein n is b Is the base of group sampling, η i Is the individual sampling coefficient of the particles;
n b the adjustment modes in different iteration states are shown in formulas (32-35);
space exploration state:
details depicting state:
gradually converging state:
and jumping out of the local optimal state:
wherein a and b are slow and fast increasing or decreasing speed factors, respectively, and rand is a random number between (0, 1);
individual particle sampling coefficient eta i Is determined based on the distance of the current position of the particle from the current optimum point, defining particle x i From the current optimum point x gb Distance of (2)Wherein->And->Respectively representing the ith particle and the D-th dimensional component of the optimal particle in the kth iteration, wherein D is the particle dimension;
calculating eta i The method comprises the following steps:
wherein delta min And delta max Delta respectively i Epsilon is the balance factor and n' is the number of particles in the feasible region.
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