CN111767646A - Optimization design method for tower type solar thermal power station receiver - Google Patents
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Abstract
The invention discloses an optimization design method for a tower type solar thermal power station receiver. According to the method, a heat loss model of a receiver heat exchange process is established, and the power generation efficiency and the annual power generation amount of a power station are calculated and obtained by combining a mirror field light gathering model and an efficiency fitting formula of a power generation module under an un-rated working condition. The key parameters of the size of the hole cavity of the receiver, the size of a heat exchange panel and the like are used as decision variables, an optimization proposition for minimizing the electric power consumption cost of the leveling receiver is provided, and the self-adaptive particle swarm optimization combined with intelligent Monte Carlo sampling is adopted for fast solving. The method can be used for optimizing to obtain the optimal receiver parameters, the construction cost of the tower type solar thermal power station receiver is effectively reduced, the optimization problem solving method can be used for solving the problem quickly and accurately, and the rapid calculation during the power station design is facilitated.
Description
Technical Field
The invention relates to the field of tower type solar thermal power stations, in particular to an optimization design method of a tower type solar thermal power station receiver.
Background
The working principle of the tower type solar thermal power station is that sunlight is converged to a receiver at the top of a tower through a certain number of heliostats to generate high temperature, water flowing through the receiver is heated to directly generate high-temperature steam, or the heat transfer medium is heated and then the heat is transferred to steam through the heat transfer medium, and a steam turbine is pushed to generate power. Due to the advantages of large light condensation ratio (generally 300-1500) and high operation temperature (500-1500 ℃), the tower type solar thermoelectric system is widely concerned at present.
The receiver of the tower-type solar thermal power station receives solar energy converged by the heliostat field, directly or indirectly transmits the solar energy to water vapor, realizes photothermal conversion, and is an intermediate system for connecting the heliostat field and the power generation module. The receiver can be divided into an exposed receiver and a hole cavity receiver according to the physical structure, the panel of the exposed receiver is directly exposed in the air, and the hole cavity receiver installs the receiver panel in the hole cavity on the top of the tower, so that the heat loss can be reduced; the receiver can be divided into a direct receiver and an indirect receiver according to the type of the heat transfer medium, the direct receiver utilizes water/steam as the heat transfer medium, water in a receiver panel is directly heated into the steam to drive a power generation module to generate power, the indirect receiver utilizes molten salt or air and the like as the heat transfer medium, and the heat transfer medium heated in the receiver panel generates high-temperature 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 of the heat transfer medium in the heat exchange process, determine the photo-thermal efficiency of the receiver and even affect the temperature of the heat transfer medium at the outlet of the receiver so as to change the efficiency of the subsequent power generation module. Therefore, the reasonable design of the receiver is crucial to improving the power generation efficiency of the power station.
Most of the existing researches focus on research and development of novel materials and physical structures of receivers to improve heat exchange efficiency, reduce heat loss, equipment cost and the like, but for receivers made of specific materials and structures, according to the requirements of power generation capacity, input cost and the like of a power station, the key parameters of the sizes of cavities and cavities of the receivers, the sizes of panels of the receivers, the diameters of heat exchange tubes and the like are optimally designed to improve the heat exchange efficiency, reduce the heat exchange loss and reduce the construction cost, and related researches are few. In fact, the aperture area of the receiver determines the overflow efficiency of the mirror field, and the size of the receiver panel, the diameter of the receiver pipe and the like determine the heat exchange efficiency of the receiver. Therefore, the parameter optimization of the receiver has important significance for improving the overall power generation efficiency of the power station and reducing the investment cost in the design and construction stage of the power station.
Disclosure of Invention
The invention provides an optimization design method for a tower type solar thermal power station receiver, which can obtain the highest power generation efficiency at the minimum cost in the design stage of a power station, meet the power generation requirement and reduce the average power generation cost of the power station receiver.
The technical scheme adopted by the invention is as follows:
(1) under the given heliostat field parameters, a model for calculating the total reflection energy of the heliostat field at each moment in the whole 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 a single ray in each light cone is distributed according to a solar disc. And tracking the direction of the reflected sunlight cone according to the direction of the sunlight cone incident from the mirror surface point, calculating the energy of the sunlight and the intersection point of the reflected light and the plane of the absorber, and calculating the energy loss of the reflected light in the transmission process and the energy when the reflected light reaches the receiver, thereby obtaining the energy distribution on the plane of the receiver.
The energy distribution in the sunlight cone is simulated by using a Monte Carlo method, a sufficient number of rays are randomly selected in the sunlight cone, the energy of each ray is calculated through the distribution of the solar disc, 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 utilizes a CUDA computing platform to realize parallel computing on the GPU.
(2) And calculating the overflow loss of the reflection energy of the heliostat and the heat exchange loss of the receiver under any receiver parameter, and calculating to obtain the energy transferred to the heat transfer medium.
And (2) calculating effective energy falling in the receiver panel according to the energy distribution on the receiver calculated in the step (1) and parameters such as the length and the width of the receiver panel and the length and the width of a cavity of the receiver, so as to obtain the overflow loss of the reflected energy of the heliostat field.
After the total available energy on the receiver panel is obtained, the heat transfer loss on the receiver is calculated by the following method, and the energy finally transferred to the heat transfer medium or water vapor is calculated.
Firstly, establishing an energy balance equation of a heat exchange process of a receiver as follows:
Qdelivered＝mf(ho-hi) (1)
mfis the mass flow of the heat transfer medium, hiAnd hoThe enthalpy values of the receiver inlet and outlet heat transfer media, respectively. In addition, the basic heat exchange equation can be listed as follows:
Ai＝πdiL (4)
wherein, TwoIs the outer wall temperature, T, of the heat exchange tube of the receiverwiIs the temperature of the inner wall of the heat exchange tube of the receiver, TfIs the average temperature of the heat transfer medium, do,di,dmRespectively the outside diameter and the inside diameter of the receiver pipe, AmIs the average heat transfer area of the receiver tube wall, AiIs the heat conducting area of the inner wall of the receiver tube, L is the characteristic length of the heat exchange tube, TiAnd ToIs the inlet and outlet temperature of the heat transfer medium, lambda is the heat transfer coefficient of the heat exchange tube, α is the heat transfer coefficient of the heat transfer medium in the receiver tube for convective heat transfer, the use factor isThe method is obtained by calculation through an analytic method in the following way:
firstly, calculating the Reynolds number of the heat transfer medium flowing in the pipeline:
d is the diameter (m) of the pipe, and u is the flow velocity (m · s) of the heat transfer medium-1) ρ is the density (kg · m) of the heat transfer medium-3) And μ is the kinetic viscosity of the heat transfer medium (N.s.m)-2)；
Then, the flowing state of the medium in the pipeline is judged according to the Reynolds number, and the corresponding heat transfer coefficient is calculated through an empirical formula of a secondary analysis method.
Convective heat transfer coefficient α (W.m)-2·K-1) Mainly with the flow velocity u (m · s) of the fluid-1) Characteristic length L (m) of the heat transfer device, viscosity μ (N · s · m) of the fluid-2) Coefficient of thermal conductivity lambda (W.m)-1·K-1) Density rho (kg. m)-3) Specific heat capacity CP(J·kg-1·K-1) And coefficient of volume expansion β (K)-1) Accordingly, the convective heat transfer coefficient may be expressed as α ═ f (u, L, μ, λ, P, C)PG β Δ t), designing corresponding dimensionless norm by combining the above variables by an analytic equation, thereby experimentally measuring the variation data between the heat transfer coefficient and the norm, and establishing a fitting equation, the dimensionless norm being shown in table 1.
TABLE 1 dimensionless QUALITY TABLE
The relationship between the convective heat transfer coefficient and the above variables can be converted to Nu＝f(Re,Pr,Gr)。
Different Re corresponds to different fluid flowing states, and the convection heat transfer coefficient in the pipe has corresponding experimental data fitting equations.
When Re is greater than 10000, the flow state is a completely turbulent flow state, and the corresponding empirical formula is as follows:
Nu＝0.023Re0.8Pr0.4(7)
2300< Re <10000, the flow regime being in the transition regime, the fitting equation being as follows:
f＝(1.82lgRe-1.64)-2(9)
re <2300, where the flow regime is laminar, the contribution of natural convection to the heat transfer coefficient must be considered, and therefore the basic empirical formula is as follows:
wherein muwIs 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 is<At 25000, natural convection is negligible.
Then, a heat loss model of the heat exchange process of the receiver is established as shown in the formula (1),
Qconcentrated＝Qloss,ref+Qloss,conv+Qloss,rad+Qloss,cond+Qdelivered(11)
wherein Q isconcentratedRepresenting the energy, Q, converged by the heliostat fieldloss,ref、Qloss,conv、Qloss,radAnd Qloss,condRespectively representing reflection energy loss, convection energy loss, radiation energy loss and conduction energy loss, QdeliveredRepresenting the energy transferred to the heat transfer medium.
The reflected energy loss is caused by the fact that part of the energy concentrated on the receiver by the heliostat is directly reflected by the receiver without being absorbed, and is calculated by using the formula (2), wherein rhopanelThe reflectivity of the receiver panel is determined by the material and surface distribution of the receiver panel. For a cavity receiver, due to the existence of the cavity, a part of the reflected energy is reflected multiple times in the cavity, and finally a part of the reflected energy is absorbed, so that the calculation is simplified, and the calculation is directly carried outAdopts a calculation method corrected by a visual factor, namely F in an equation (2)rSpecifically defined as shown in formula (3), wherein ArecAnd AapeThe areas of the receiver heat exchange panel and the receiver bore, respectively. For an exposed receiver, the visual factor is 1.
Qloss,ref＝ρpanelQconcentraedFr(12)
The radiant heat loss is calculated as follows:
wherein the content of the first and second substances,wis the radiation coefficient of the receiver tube wall, which is corrected by the existence of the pore cavity to obtain the average radiation coefficientavg，σ＝5.67×10-8W/(m2·K4) Is the Boltzmann constant, TairIs the ambient air temperature in K.
Convective heat loss is calculated as follows:
Qloss.conv＝hair(Trec-Tair)Aape(16)
wherein, TrecIs the surface temperature of the receiver, hairThe heat transfer coefficient of air is divided into natural convection heat transfer coefficient hair,ncAnd forced convection heat transfer coefficient hair,fcNamely:
hair＝hair,nc+hair,fc(17)
the corresponding empirical formula is:
hair,nc＝0.81(Two-Tair)0.426(19)
wherein, Nuair,fc、Reair、PrairRespectively nusselt number, reynolds number and prank number of air forced convection heat transfer.
Conductive heat loss is primarily heat loss through the insulation.
Wherein T isinsu,insu,λinsuThe surface temperature, thickness and heat transfer coefficient of the thermal insulation layer are respectively. Wherein h isair,insuThe heat transfer coefficient of the air and the heat insulation layer. The corresponding empirical formula is:
wherein, NuairNusselt number for convective heat transfer to air.
Simultaneous equations (1-21) can be solved to obtain the amount of heat ultimately 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 an initial value of energy transferred to the heat transfer medium, so that heat losses are calculated, and the energy transferred to the heat transfer medium is iteratively calculated until convergence.
(3) The efficiency of the power generation module is calculated from the energy transferred to the heat transfer medium.
The energy conversion efficiency of the power generation module under rated conditions is determined by the design parameters of the steam turbine and the generator and can be considered to be known. The following empirical fitting formula is used for the efficiency calculation under the non-rated working condition.
Efficiency η of non-rated operating conditions of steam turbineturbineThe calculation is as follows.
ηturbine＝(1-β)ηturbine,norm(22)
β＝0.191-0.409r+0.218r2(23)
Wherein, ηturbine,normIs turbine efficiency at rated operating conditions, β is the efficiency loss ratio, and r is the ratio of turbine power to rated power.
Efficiency η of the generatorgeneratorComprises the following steps:
ηgenerator＝0.908+0.258r-0.3r2+0.12r3(24)
the change in pump efficiency is negligible.
Thus, the efficiency η of the power generation module is obtainedpowerIs composed of
ηpower＝ηturbine×ηgenerator(25)
The power generation amount at any time P is
P＝Qdeliveredηpower(26)
The annual generating capacity is obtained by accumulating the generating capacity at each moment.
Through the three steps, the efficiency of each module and the total power generation efficiency of the power station at any moment can be calculated when the receiver selects different parameters under the condition that the parameters of the mirror field and the parameters of the power generation modules are known, and the annual power generation can be obtained after the annual cumulative calculation.
(4) An optimization proposition for receiver parameter design is established. Key parameters such as the length and the width of a hole cavity of the receiver, the length and the width of a heat exchange panel, the diameter of a heat exchange tube and the like are selected as decision variables, a target function LRCOE (leveled received measured cost of Energy) is designed, average power generation cost of the receiver in the whole life cycle is represented, and a specific calculation mode is shown as follows.
Wherein, IdebtAnd IinsuranceFor annual interest and premium rates, Cinvest,receiverAnd CO&M,receiverThe total investment cost and the operation and maintenance cost of the receiver, W is the annual average generated energy, and n is the total power station costThe life cycle is in years.
The established optimization model is as follows:
s.t. lre≥lre,lb(28b)
wre≥wre,lb(28c)
laperture≥laperture,lb(28d)
waperture≥waperture,lb(28e)
dtube≥dtube,lb(28f)
lre×wre×0.5Fluxlimit≥PN(28g)
W≥Wdesign(28h)
wherein lreAnd wreLength and width of the receiver panel, /)apertureAnd wapertureIndicating the length and width l of the boreaperture,waperture，dtubeThe diameter of the heat exchange tubes, the subscript lb represents the lower limit of each parameter, equations 28b-28f represent the lower limit constraints of each parameter, equation 28g represents the upper limit constraint of the energy density on the receiver panel, PNIndicating the average energy density, Flux, of the receiver under nominal conditionslimitRepresenting a safe upper limit for energy density at the receiver. The formula 28h represents the minimum requirement of annual energy production, WdesignRepresenting 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 method is as follows:
the method comprises the following steps: initialization population X ═ XiI |, 1,2, …, n }. Each individual x in the populationiIs a feasible solution to the optimization problem and each xiAll have corresponding moving speeds vi。
Step two: the population was evaluated. And storing the current position and fitness of each particle in the population, namely the objective function value, as the optimal position of each particle, and storing the position and fitness of the optimal position and fitness individual in all the particles in the global optimal position.
Step three: the velocity and position of each particle of the current population are updated. The calculation method is as follows:
wherein the content of the first and second substances,
and
respectively representing the position and the velocity of the d-dimensional component of the ith particle at the kth iteration,
representing the self historical optimum position found in the ith particle for k iterations,
representing the global optimal position found by the particle swarm in k iterations, omega is the inertia coefficient, c1And c2Respectively an individual learning factor and a global learning factor,
and
is a random number within 0-1.
Step four: and judging the iterative state of the algorithm, and updating the parameters of the particle swarm algorithm and the sampling precision of the mirror field reflection energy calculated by the Monte Carlo sampling method according to the iterative state. Dividing the iterative state of the particle swarm algorithm into four states of space exploration, detail description, gradual convergence and local optimum jump, and evolution factor (evolutionary factor) F to help delineate the different states of the iterative process. First, an average distance d of a particle X from all other particles in an iterative process is definedi：
Wherein D is the particle dimension. D of particles for optimizing the objective functioniIs marked as dg，dminAnd dmaxRepresents diCan be defined as F:
to characterize the distance between the current optimal point and all other points. And determining the corresponding iteration states of different values of F by adopting a fuzzy relation. When F is a large value, the algorithm is in a jump-out local optimum state, and when the F value is medium and large, the algorithm is in an exploration state; when the F value is medium and slightly small, the algorithm is in a detail description state; the algorithm is in a converged state when the F value approaches zero.
Parameter c of particle swarm optimization in four states1And c2The adjustment mode is as follows:
the space exploration state is as follows:
detail description state:
gradual convergence state:
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 adjustment mode of the inertia coefficient omega is as follows:
the adjustment of the number N of monte carlo simulation points used in calculating the mirror field reflection energy is as follows:
for particle xiNumber n of sampling points used in calculating its objective functioniThere are two part decisions, specifically as follows:
ni＝nb×ηi(42)
wherein n isbIs the group sampling base number, is adjusted correspondingly by different states of the particle swarm algorithm iteration, ηiThe particle individual sampling coefficient is determined by the relationship between the current position of the particle and the currently obtained global optimal position.
nbThe adjustment at different iteration states is shown in equations (41-44).
The space exploration state is as follows:
detail description state:
gradual convergence state:
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). Simultaneously to nbAnd setting upper and lower limits of the variation process to ensure that the calculation of the objective function 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 ηiIs determined based on the distance between the current position of the particle and the current optimum point, and defines the particle xiX from the current optimum pointgbIs a distance of
Wherein
And
respectively representing the ith particle and the D-dimension component of the optimal particle in the kth iteration, D being the dimension of the particle, and ηiThe method comprises the following steps:
wherein the content of the first and second substances,minandmaxare respectively asiMinimum and maximum values of, so
For the balance factor, n' is the number of particles located within 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 or the convergence condition is reached, if so, outputting the position of the current global optimal individual; otherwise, turning to the third step.
The invention has the beneficial effects that: according to the optimization design method of the tower type solar thermal power station receiver, provided by the invention, enough sampling moments are selected, and the obtained optimal solution can ensure that the annual energy production of the power station meets the design requirement and the average power generation cost of the receiver is the lowest. Meanwhile, the self-adaptive particle swarm optimization method combined with the intelligent sampling Monte Carlo method can effectively reduce the algorithm solving time and improve the calculation efficiency in power station design.
Drawings
FIG. 1 is a flow chart of a method for optimizing design of a tower solar thermal power plant receiver;
FIG. 2 is a flow chart of iterative solution of receiver heat exchange equations;
FIG. 3 is a block diagram of a PS10 plant bore cavity receiver;
FIG. 4 is a flow chart of an adaptive particle swarm algorithm incorporating the smart Monte Carlo sampling method;
FIG. 5 is a graph of variation of parameters during a solution process of an adaptive particle swarm optimization incorporating the smart Monte Carlo sampling method;
FIG. 6 is a variation curve of the number of sampling points of particles in the adaptive particle swarm optimization solving process combined with the intelligent Monte Carlo sampling method.
Detailed Description
In this example, the receiver optimization process of a spanish PS10 tower type solar thermal power plant is taken as an example, and the overall method flow is shown in fig. 1. The specific implementation process is as follows:
(1) and establishing a model for calculating total reflection energy of the mirror field at each moment 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 mirror field parameters in the examples
The method is characterized in that sunlight is treated as non-parallel light by randomly scattering points on a mirror surface by using a ray tracing method, namely sunlight received and reflected by one point on the mirror surface is a group of light cones, and the energy of a single ray in each light cone obeys the distribution of a solar disc. And tracking the direction of the reflected sunlight cone according to the direction of the sunlight cone incident from the mirror surface point, calculating the energy of the sunlight and the intersection point of the reflected light and the plane of the absorber, and calculating the energy loss of the reflected light in the transmission process and the energy when the reflected light reaches the receiver, thereby obtaining the energy distribution on the plane of the receiver.
The energy distribution in the sunlight cone is simulated by using a Monte Carlo method, a sufficient number of rays are randomly selected in the sunlight cone, the energy of each ray is calculated through the distribution of the solar disc, 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 precision, the Monte Carlo sampling point number is between 10000-15000.
The process utilizes a CUDA computing platform to realize parallel computing on the GPU. By using the method, the total reflection energy of the heliostat field at any time can be obtained, taking 21/3/2000 as an example, and the total reflection energy of the heliostat field obtained by calculation is shown in table 3, so that the result can be seen to be more accurate.
TABLE 3 simulation result of heliostat field reflection energy
(2) And calculating the overflow loss of the reflection energy of the heliostat and the heat exchange loss of the receiver under any receiver parameter, and calculating to obtain the energy transferred to the heat transfer medium.
And (2) calculating effective energy falling in the receiver panel according to the energy distribution on the receiver calculated in the step (1) and parameters such as the length and the width of the receiver panel and the length and the width of a cavity of the receiver, so as to obtain the overflow loss of the reflected energy of the heliostat field.
After the total available energy on the receiver panel is obtained, the heat transfer loss on the receiver is calculated by the following method, and the energy finally transferred to the heat transfer medium or water vapor is calculated.
Firstly, establishing an energy balance equation of a heat exchange process of a receiver as follows:
Qdelivered＝mf(ho-hi) (1)
mfis the mass flow of the heat transfer medium, hiAnd hoThe enthalpy values of the receiver inlet and outlet heat transfer media, respectively. In addition, the basic heat exchange equation can be listed as follows:
Ai＝πdiL (4)
wherein, TwoIs the outer wall temperature, T, of the heat exchange tube of the receiverwiIs the temperature of the inner wall of the heat exchange tube of the receiver, TfIs the average temperature of the heat transfer medium, do,di,dmRespectively the outside diameter and the inside diameter of the receiver pipe, AmIs the average heat transfer area of the receiver tube wall, AiIs the heat conducting area of the inner wall of the receiver tube, L is the characteristic length of the heat exchange tube, TiAnd ToIs the inlet and outlet temperature of the heat transfer medium, lambda is the heat transfer coefficient of the heat exchange tube, α is the heat transfer coefficient of the heat transfer medium in the receiver tube for convective heat transfer, and is calculated by an analytic equation, the calculation method is as follows:
firstly, calculating the Reynolds number of the heat transfer medium flowing in the pipeline:
d is the diameter (m) of the pipe, and u is the flow velocity (m · s) of the heat transfer medium-1) ρ is the density (kg · m) of the heat transfer medium-3) And μ is the kinetic viscosity of the heat transfer medium (N.s.m)-2)；
Then, the flowing state of the medium in the pipeline is judged according to the Reynolds number, and the corresponding heat transfer coefficient is calculated through an empirical formula of a secondary analysis method.
Convective heat transfer coefficient α (W.m)-2·K-1) Mainly with the flow velocity u (m · s) of the fluid-1) Characteristic length L (m) of the heat transfer device, viscosity μ (N · s · m) of the fluid-2) Coefficient of thermal conductivity lambda (W.m)-1·K-1) Density rho (kg. m)-3) Specific heat capacity CP(J·kg-1·K-1) And coefficient of volume expansion β (K)-1) Accordingly, the convective heat transfer coefficient may be expressed as α ═ f (u, L, μ, λ, P, C)PG β Δ t), designing corresponding dimensionless norm by combining the above variables by an analytic equation, thereby experimentally measuring the variation data between the heat transfer coefficient and the norm, and establishing a fitting equation.
TABLE 4 dimensionless QUALITY TABLE
The relationship between the convective heat transfer coefficient and the above variables can be converted to Nu＝f(Re,Pr,Gr)。
Different Re corresponds to different fluid flowing states, and the convection heat transfer coefficient in the pipe has corresponding experimental data fitting equations.
When Re is greater than 10000, the flow state is a completely turbulent flow state, and the corresponding empirical formula is as follows:
Nu＝0.023Re0.8Pr0.4(7)
2300< Re <10000, the flow regime being in the transition regime, the fitting equation being as follows:
f＝(1.82lgRe-1.64)-2(9)
re <2300, where the flow regime is laminar, the contribution of natural convection to the heat transfer coefficient must be considered, and therefore the basic empirical formula is as follows:
wherein muwIs 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 is<At 25000, natural convection is negligible.
Then, a heat loss model of the heat exchange process of the receiver is established as shown in the formula (1),
Qconcentrated＝Qloss,ref+Qloss,conv+Qloss,rad+Qloss,cond+Qdelivered(11)
wherein Q isconcentratedRepresenting the energy, Q, converged by the heliostat fieldloss,ref、Qloss,conv、Qloss,radAnd Qloss,condRespectively representing reflection energy loss, convection energy loss, radiation energy loss and conduction energy loss, QdeliveredIndicating delivery to a heat-transfer mediumEnergy.
The reflected energy loss is caused by the fact that part of the energy concentrated on the receiver by the heliostat is directly reflected by the receiver without being absorbed, and is calculated by using the formula (2), wherein rhopanelThe reflectivity of the receiver panel is determined by the material and surface distribution of the receiver panel. For the cavity receiver, because of the existence of the cavity, a part of the reflected energy is reflected in the cavity for a plurality of times, and finally a part of the reflected energy is absorbed, in order to simplify the calculation, a calculation method corrected by a visual factor is directly adopted, namely F in an equation (2)rSpecifically defined as shown in formula (3), wherein ArecAnd AapeThe areas of the receiver heat exchange panel and the receiver bore, respectively. For an exposed receiver, the visual factor is 1.
Qloss,ref＝ρpanelQconcentraedFr(12)
The radiant heat loss is calculated as follows:
wherein the content of the first and second substances,wis the radiation coefficient of the receiver tube wall, which is corrected by the existence of the pore cavity to obtain the average radiation coefficientavg，σ＝5.67×10-8W/(m2·K4) Is the Boltzmann constant, TairIs the ambient air temperature in K.
Convective heat loss is calculated as follows:
Qloss.conv＝hair(Trec-Tair)Aape(16)
wherein, TrecIs the surface temperature of the receiver, hairIs emptyThe convective heat transfer coefficient of gas is divided into natural convective heat transfer coefficient hair,ncAnd forced convection heat transfer coefficient hair,fcNamely:
hair＝hair,nc+hair,fc(17)
the corresponding empirical formula is:
hair,nc＝0.81(Two-Tair)0.426(19)
wherein, Nuair,fc、Reair、PrairRespectively nusselt number, reynolds number and prank number of air forced convection heat transfer.
Conductive heat loss is primarily heat loss through the insulation.
Wherein T isinsu,insu,λinsuThe surface temperature, thickness and heat transfer coefficient of the thermal insulation layer are respectively. Wherein h isair,insuThe heat transfer coefficient of the air and the heat insulation layer. The corresponding empirical formula is:
wherein, NuairNusselt number for convective heat transfer to air.
Simultaneous equations (1-21) can be solved to obtain the amount of heat ultimately 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 an initial value of the energy transferred to the heat transfer medium, so that the heat losses are calculated, the energy transferred to the heat transfer medium is iteratively calculated 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 parameter can be calculated, taking the original receiver parameter of the PS10 power station as an example, the PS10 power station adopts a cavity-type receiver, the structure of which is shown in FIG. 3, and the specific parameters are listed in Table 5. The calculated heat exchange results of the receiver at 21 st 12:00 rd 3/2000 are shown in table 6, and it can be seen that the calculation error is small and the model is accurate.
(3) The efficiency of the power generation module is calculated from the energy transferred to the heat transfer medium.
The energy conversion efficiency of the power generation module under rated conditions is determined by the design parameters of the steam turbine and the generator and can be considered to be known. The following empirical fitting formula is used for the efficiency calculation under the non-rated working condition.
Efficiency η of non-rated operating conditions of steam turbineturbineThe calculation is as follows.
ηturbine＝(1-β)ηturbine,norm(22)
β＝0.191-0.409r+0.218r2(23)
Wherein, ηturbine,normIs turbine efficiency at rated operating conditions, β is the efficiency loss ratio, and r is the ratio of turbine power to rated power.
TABLE 5 PS10 plant receiver parameters
TABLE 6 PS10 plant receiver Heat transfer simulation results
Efficiency η of the generatorgeneratorComprises the following steps:
ηgenerator＝0.908+0.258r-0.3r2+0.12r3(24)
the change in pump efficiency is negligible.
Thus, the efficiency η of the power generation module is obtainedpowerIs composed of
ηpower＝ηturbine×ηgenerator(25)
The power generation amount at any time P is
P＝Qdeliveredηpower(26)
Through the three steps, the efficiency of each module and the total power generation efficiency of the power station at any moment can be calculated when the receiver selects different parameters under the condition that the parameters of the mirror field and the parameters of the power generation modules are known, and the annual power generation can be obtained after the annual cumulative calculation.
(4) An optimization proposition for receiver parameter design is established. Key parameters such as the length and the width of a hole cavity of the receiver, the length and the width of a heat exchange panel, the diameter of a heat exchange tube and the like are selected as decision variables, a target function LRCOE (leveled received measured cost of Energy) is designed, average power generation cost of the receiver in the whole life cycle is represented, and the specific calculation mode is shown in (3).
Wherein, IdebtAnd IinsuranceFor annual interest and premium rates, Cinvest,receiverAnd CO&M,receiverThe total investment cost and the operation and maintenance cost of the receiver are shown, W is the annual average generated energy, and n is the full life cycle of the power station, and the unit is year. For the PS10 plant, the above parameters calculation method is shown in table 7.
TABLE 7 LRCOE calculation parameters
The optimization model established for the PS10 plant receiver is as follows:
s.t. lre≥0.1 (28b)
wre≥0.1 (28c)
laperture≥0.1 (28d)
waperture≥0.1 (28e)
dtube≥0.005 (28f)
lre×wre×375≥PN(28g)
W≥22GW (28h)
wherein lreAnd wreLength and width of the receiver panel, /)apertureAnd wapertureIndicating the length and width l of the boreaperture,waperture，dtubeThe diameter of the heat exchange tube, equations 26b-26f represent the lower bound for each parameter, equation 26g represents the upper bound for the energy density on the receiver panel, PNIndicating the average energy density of the receiver at nominal operating conditions.
(5) And solving the optimization proposition by utilizing a self-adaptive particle swarm algorithm combined with an intelligent sampling Monte Carlo method. The solving flow is shown in fig. 4, and the specific solving method is as follows:
the method comprises the following steps: initialization population X ═ XiI |, 1,2, …, n }. Each individual x in the populationiIs a feasible solution to the optimization problem and each xiAll have corresponding moving speeds vi。
Step two: the population was evaluated. And storing the current position and fitness of each particle in the population, namely the objective function value, as the optimal position of each particle, and storing the position and fitness of the optimal position and fitness individual in all the particles in the global optimal position.
Step three: the velocity and position of each particle of the current population are updated. The calculation method is as (5)
Wherein the content of the first and second substances,
and
respectively representing the position and the velocity of the d-dimensional component of the ith particle at the kth iteration,
representing the self historical optimum position found in the ith particle for k iterations,
representing the global optimal position found by the particle swarm in k iterations, omega is the inertia coefficient, c1And c2Are an individual learning factor and a global learning factor, r, respectively1 kAnd r2 kIs a random number within 0-1.
Step four: and judging the iterative state of the algorithm, and updating the parameters of the particle swarm algorithm and the sampling precision of the mirror field reflection energy calculated by the Monte Carlo sampling method 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 local optimum jumping out, and an evolution factor (evolution factor) F is used for helping to describe different states of the iterative process. First, an average distance d of a particle X from all other particles in an iterative process is definedi：
D of particles for optimizing the objective functioniIs marked as dg，dminAnd dmaxRepresents diCan be defined as F:
to characterize the distance between the current optimal point and all other points. And determining the corresponding iteration states of different values of F by adopting a fuzzy relation. When F is a large value, the algorithm is in a jump-out local optimum state, and when the F value is medium and large, the algorithm is in an exploration state; when the F value is medium and slightly small, the algorithm is in a detail description state; the algorithm is in a converged state when the F value approaches zero.
Parameter c of particle swarm optimization in four states1And c2The adjustment mode is as follows:
the space exploration state is as follows:
detail description state:
gradual convergence state:
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). And taking A as 0.1 and B as 0.05.
The adjustment mode of the inertia coefficient omega is as follows:
the adjustment of the number N of monte carlo simulation points used in calculating the mirror field reflection energy is as follows:
for particle xiNumber n of sampling points used in calculating its objective functioniThere are two part decisions, specifically as follows:
ni＝nb×ηi(42)
wherein n isbIs the group sampling base number, is adjusted correspondingly by different states of the particle swarm algorithm iteration, ηiThe particle individual sampling coefficient is determined by the relationship between the current position of the particle and the currently obtained global optimal position.
nbThe adjustment at different iteration states is shown in equations (43-46).
The space exploration state is as follows:
detail description state:
gradual convergence state:
jumping out of the local optimal state:
wherein a and b are slow and fast increases, respectivelyThe large or small speed factor is a random number between (0,1) and 0.3 as a, and 0.2 as b. Simultaneously to nbSet the upper and lower limits of the course of change [5000,15000]Therefore, the calculation of the objective function 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 ηiIs determined based on the distance between the current position of the particle and the current optimum point, and defines the particle xiX from the current optimum pointgbIs a distance of
Wherein
And
representing the D-dimension component of the ith particle and the optimal particle, D being the dimension of the particle, at the kth iteration, respectively, computing ηiThe method comprises the following steps:
wherein the content of the first and second substances,minandmaxare respectively asiMinimum and maximum values of, so
Take 0.8 and n' as the number of particles within 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 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 change of the particle group parameters and the historical optimal values in the iterative process of the algorithm is shown in fig. 5, and it can be seen that the algorithm parameters are dynamically adjusted in the iterative process to adapt to different iterative processes, so that convergence is accelerated. In the iterative process, the particle sampling base number and the sampling number change of each particle individual are shown in fig. 6, and it can be seen that the sampling base number dynamically changes to adopt different overall sampling accuracies at each stage, so that the calculation time is reasonably distributed; the individual calculation time of each particle is different and is continuously changed along with the iteration process, so that the time and the precision of the calculation of the objective function are more accurately balanced. The optimization solving process runs for 2000 and 2500 seconds on a computer with a 4-core Intel Xeon silver 4110@2.1GHz CPU, a 20G memory and a NivdiaTesla P4 display card, and the solving efficiency is high.
The optimal parameters of the receiver obtained by the optimization algorithm and the optimized LRCOE are shown in Table 8, and it can be seen that the annual power generation amount 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 obvious.
TABLE 8 receiver optimization results
Claims (7)
1. An optimal design method for a tower type solar thermal power station receiver is characterized by comprising the following steps:
(1) under given heliostat field parameters, establishing a model for calculating the distribution of the mirror field reflection energy on a receiver plane at different moments based on a ray tracing method;
(2) calculating the overflow loss of heliostat field reflection energy and the heat exchange loss of the receiver under any receiver parameter, and calculating to obtain the energy transferred to the heat transfer medium;
(3) calculating the efficiency of the power generation module according to the energy transferred to the heat transfer medium, thereby calculating the power generation amount at any moment and the total power generation amount all year round;
(4) establishing an optimization problem of receiver parameter design by taking the lowest receiver accuracy electricity generation cost as a target;
(5) and (4) 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 tower solar thermal power plant receiver optimal design method according to claim 1, characterized in that the step (1) is specifically: the method comprises the steps of randomly scattering points on a mirror surface, treating sunlight as a sunlight cone, simulating energy distribution in the sunlight cone by using a Monte Carlo method, randomly selecting a sufficient number of rays in the sunlight cone, calculating the energy of each ray through solar disc distribution, and tracking and calculating the energy loss of each ray in the reflection and convergence process, thereby obtaining the energy distribution on a receiver plane.
3. The method for optimizing design of tower solar thermal power plant receiver according to claim 1, wherein the step (2) first obtains the spillover loss of heliostat field reflected energy by calculating the effective energy falling within the receiver area under specific receiver size parameters through the energy distribution on the receiver plane obtained in the step (1); based on the effective energy in the receiver region, a simultaneous equation method is adopted to calculate the heat exchange loss of the receiver, and the method specifically comprises the following steps:
the energy balance equation of the heat exchange process of the receiver is established as follows
Qdelivered＝mf(ho-hi) (1)
QdeliveredRepresenting the energy transferred to the heat transfer medium, mfIs the mass flow of the heat transfer medium, hiAnd hoThe enthalpy values of the receiver inlet and outlet heat transfer media, respectively;
the basic heat exchange equation is established as follows:
Ai＝πdiL (4)
wherein Q isdeliveredRepresenting the energy transferred to the heat transfer medium, TwoIs the outer wall temperature, T, of the heat exchange tube of the receiverwiIs the temperature of the inner wall of the heat exchange tube of the receiver, TfIs the average temperature of the heat transfer medium, do,di,dmRespectively the outer diameter, the inner diameter and the average diameter of the receiver pipe, AmIs the average heat transfer area of the receiver tube wall, AiIs the heat conducting area of the inner wall of the receiver tube, L is the characteristic length of the heat exchange tube, TiAnd ToIs the inlet and outlet temperature of the heat transfer medium, lambda is the heat transfer coefficient of the heat exchange tube, α is the heat transfer coefficient of the heat transfer medium in the receiver tube for convective heat transfer, and is calculated by the use of an analytic equation;
the heat loss during the heat exchange process occurring at the receiver is modeled as follows:
Qconcentrated＝Qloss,ref+Qloss,conv+Qloss,rad+Qloss,cond+Qdelivered(6)
Qloss,ref＝ρpanelQconcentraedFr(7)
Qloss.conv＝hair(Trec-Tair)Aape(11)
hair＝hair,nc+hair,fc(12)
hair,nc＝0.81(Two-Tair)0.426(14)
wherein Q isconcentratedRepresenting the energy, Q, converged by the heliostat fieldloss,ref、Qloss,conv、Qloss,radAnd Qloss,condRespectively representing reflection energy loss, convection energy loss, radiation energy loss and conduction energy loss, QdeliveredRepresenting the energy transferred to the heat transfer medium; rhopanelRepresenting the reflectivity of the receiver panel, FrIs a visual factor, ArecAnd AapeThe areas of the heat exchange panel of the receiver and the pore chamber of the receiver are respectively;wis the emissivity of the receiver tube wall,avgis the mean emissivity coefficient, σ is 5.67 × 10- 8W/(m2·K4) Is the Boltzmann constant, TrecIs the receiver surface temperature, TairIs the ambient air temperature; h isairThe heat transfer coefficient of air is divided into natural convection heat transfer coefficient hair,ncAnd forced convection heat transfer coefficient hair,fc，Nuair,fc、Reair、PrairRespectively are Nusselquan number, Reynolds number and Prandlor number of air forced convection heat transfer;Tinsu,insu,λinsusurface temperature, thickness and heat transfer coefficient of the heat-insulating layer, respectively, wherein hair,insuNu for heat transfer coefficient of air and heat insulation layer by air convectionairTo calculate;
solving simultaneous equations (1) - (21) to obtain the heat finally transferred to the heat transfer medium when the heliostat convergence energy is determined; the simultaneous equations are solved by an iterative method, and the surface temperature of the receiver is calculated by setting an initial value of energy transferred to the heat transfer medium, so that heat losses are calculated, and the energy transferred to the heat transfer medium is iteratively calculated until convergence.
4. The tower solar thermal power plant receiver optimal design method according to claim 1, characterized in that the calculation of the efficiency of the power generation module in step (3) is based on a fitting formula under an off-rated condition,
efficiency η of non-rated operating conditions of steam turbineturbineThe calculation method is
ηturbine＝(1-β)ηturbine,norm(17)
β＝0.191-0.409r+0.218r2(18)
Wherein, ηturbine,normIs the turbine efficiency under rated operating conditions, β is the efficiency loss ratio, r is the ratio of the turbine power to the rated power;
efficiency η of the generatorgeneratorComprises the following steps:
ηgenerator＝0.908+0.258r-0.3r2+0.12r3(19)
ignoring pump efficiency variations;
thus, the efficiency η of the power generation module is obtainedpowerIs composed of
ηpower＝ηturbine×ηgenerator(20)
The power generation amount at any time P is
P＝Qdeliveredηpower(21)
The annual generating capacity is obtained by accumulating the generating capacity at each moment.
5. The method for the optimal design of a tower solar thermal power plant receiver according to claim 1, characterized in that the optimization problem established in step (4) is as follows:
s.t. lre≥lre,lb(22b)
wre≥wre,lb(22c)
laperture≥laperture,lb(22d)
waperture≥waperture,lb(22e)
dtube≥dtube,lb(22f)
lre×wre×0.5Fluxlimit≥PN(22g)
W≥Wdesign(22h)
wherein lreAnd wreLength and width of the receiver panel, /)apertureAnd wapertureIndicating the length and width of the bore, dtubeDenotes the diameter of the heat exchange tube, the subscript lb denotes the lower limit of each parameter, LRCOE is (leveled Receiver Cost of energy), IdebtAnd IinsuranceFor annual interest and premium rates, Cinvest,receiverAnd CO&M,receiverFor the total investment cost and the operation and maintenance cost of the receiver, W is the annual energy production, n is the full life cycle of the power station, the unit is year, FluxlimitRepresents a safe upper limit of energy density, P, at the receiverNRepresents the average energy density, W, of the receiver under rated conditionsdesignRepresenting the design annual energy production.
6. The tower solar thermal power plant receiver optimal design method of claim 1, characterized in that the adaptive particle swarm algorithm used in step (5) divides the iteration state into four, and adopts different parameter adjustment methods in different states, specifically:
the space exploration state is as follows:
detail description state:
gradual convergence state:
jumping out of the local optimal state:
wherein, c1And c2The individual learning factor and the global learning factor are respectively, the superscript k represents the iteration number, A and B are respectively the slow and fast increasing or decreasing speed factor, a and B are respectively the slow and fast increasing or decreasing random factor, and rand is a random number between (0, 1).
7. The optimal design method for the tower-type solar thermal power plant receiver of claim 1, wherein the adaptive particle swarm algorithm in the step (5) is combined with an intelligent Monte Carlo sampling method, the number of sampling points during the calculation of the mirror field reflection energy is dynamically adjusted according to the iteration state, and specifically, the method comprises the following steps:
for particle xiNumber n of sampling points used in calculating its objective functioniIs defined as
ni＝nb×ηi(31)
Wherein n isbIs the population sampling cardinality, ηiIs the particle individual sampling coefficient;
nbthe adjustment mode in different iteration states is shown as the formula (32-35);
the space exploration state is as follows:
detail description state:
gradual convergence state:
jumping out of the local optimal state:
wherein, a and b are respectively the speed factors of slow speed and fast increasing or decreasing, and rand is a random number between (0, 1);
individual particle sampling coefficient ηiIs determined based on the distance between the current position of the particle and the current optimum point, and defines the particle xiX from the current optimum pointgbIs a distance of
Wherein
And
respectively representing the ith particle and the D-dimension component of the optimal particle in the kth iteration, D being the dimension of the particle, and ηiThe method comprises the following steps:
wherein the content of the first and second substances,minandmaxare respectively asiIs a balance factor, and n' is the number of particles located within the feasible region.
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