RU2543256C2 - Solar heat photoelectric module with compound parabolic concentrator - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: solar heat photoelectric module with the compound parabolic concentrator consisting of the paraboloidal concentrator "Focon" and the heat photoelectric receiver located in a focal plane with uniform distribution of the concentrated radiation, differing in that the solar heat photoelectric module contains the compound parabolic concentrator and the cylindrical heat photoelectric receiver with the cooling device installed in the focal plane area, the concentrator representing a rotation body with smooth internal reflection surface, consisting of several zones (a-b, b-c, c-d) is designed compound using the principle of collecting of the reflected beams in two focal plane areas from separate zones of the concentrator: - the form of the reflecting surface of the zones a-b, b-c of the concentrator X (Y) is determined by the system of equations corresponding to the condition of uniform illumination of a surface of photo-electric part of the heat photoelectric receiver designed in the cylinder shape from the commutated high-voltage FEP with the length h_o and the radius r_o, Y_n=R_n ²/4f_o, X_n=R_n-(k-1)r_o, R_n=2f_o(tgα_n+cosα_n), Δα=α_o/N, α_n=Δα(n-N/2), X*=2f₁Q[(1+1/Q²)^l/₂-1], Q=B/r_o, B=h_o+h, Y*=X*²/4f₁, Y*_n=ΔY*n, X_n=[4f₁(Y*+Y*_n)]¹/₂, ΔY=P[1±(1-4R/P²)¹/₂]/2, P=L+Y_b, L=f_o+h+h_o/2, where α_n is an angle (in the zone of the working profile of the concentrator a-c) between the ordinate level in the point of coordinates X_n, Y_n and the beam reflected from the parabola surface with the focal length f_o arriving to focal plane area with the width h_o located on the radius r₀ of the cylindrical photo-electric receiver in Δα=α_o/N intervals where n is selected from a series of integers n=1, 2, 3…N, values of the parameters f_o, f₁, k are selected according to boundary conditions, and geometrical concentration of illumination of the photo-electric receiver K_n is equal in intervals of the concentrator radius ΔX_n=X_n-X_n-1: K_n=(R_n+1 ²-R_n ²)n/d_o, - shape of the reflecting surface of the zone c-d of the concentrator X (Y) is determined by the system of equations corresponding to the condition of uniform illumination of the surface of thermal part of the heat photoelectric receiver designed in the form of the truncated cone with a lateral surface with the length d*, upper radius r_ob and the lower radius r_b: X_c=2Y_c(1/codβ_b-tgβ_b), tgβ_b=(Y_c-H_b)(R_c-r_ob), f_b=Y_c-X_ctgβ_b, r_b=X_c-R_c, d*=h*/sinφ_o, d*_n=d*n/N, K_n=(R² _n+1-R² _n)/(r*_n+1+r*_n)Δd*, X_bn=2f_b(tgγ_bn+1/cosγ_bn), tgφ_o=h*/(r_o-r*_bo), where β_b - an angle (in the zone of the working profile of the concentrator c-d) between the ordinate level in the point of coordinates of X_c, Y_c, and the beam reflected from parabola surface with the focal length f_b arriving to focal plane area of the truncated cone with the radius r_b of the photo-electric receiver, γ_n - an angle (in the zone of the working profile of the concentrator c-d) between the ordinate level in the point of coordinates X_n, Y_n and the beam reflected from the parabola surface with the focal length f_b arriving to the focal plane area of the truncated cone with the width d* of the photo-electric receiver in the intervals Δd*=d*/N, where n is selected from a series of integers n=1, 2, 3…N. The values of the parameters f_b, k are selected according to boundary conditions, φ_o is an angle of inclination of the lateral surface of the truncated cone of the photo-electric receiver, and the geometrical concentration of illumination of the photo-electric K_n receiver is equal in intervals of the concentrator radius ΔX_n=X_n-X_n-1: Kn=(R=2n+1-R2n)/(r*n+1+r*n)Δd*.

EFFECT: improvement of efficiency, and decrease of cost of the generated energy.

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Description

The invention relates to solar technology and the design of solar modules with photovoltaic and thermal receivers of solar radiation and concentrators.

Known solar modules with photovoltaic converters (PECs) and solar radiation concentrators in the form of a paraboloid (Strebkov DS, Ross M.Yu., Dzhaylani AT, Mitina IV Solar installation with a concentrator. RF patent №2396493, Bull. No. 22, 2010).

Known solar modules have concentrators that create high concentrations in the focal plane in the plane of the photoelectric converter, reaching 2000 times or more, which cannot be used by silicon planar solar cells.

Known solar photovoltaic module (prototype), consisting of a focon type paraboloid concentrator and a photovoltaic converter located in the focal plane with a uniform distribution of concentrated radiation (Arbuzov Yu.D., Babaev Yu.A., Evdokimov V.M., Levinskas A. L., Maiorov VA., Yasaytis D-Yu. Yu. Solar energy concentrator. USSR patent No. 1794254, 04/03/91).

The disadvantages of the known technical solutions are:

- reduction of efficiency by planar silicon photovoltaic photoelectric detectors at high solar radiation concentrations;

- the location of the optical focus on the axis of the photovoltaic module and the concentric distribution of the illumination of the surface of the photodetector limit the configuration and type of applied photoconductors (only circular planar photoconductors can be used);

- low voltages on one planar PEC (~ 0.5 V) lead to the need for sequential switching of a large number of PECs in the solar photovoltaic module in order to gain a voltage of 12 V or higher, acceptable for further use in electric batteries, DC inverters, and so on .P.

Serial switching of a large number of photomultipliers reduces the reliability of the system, because failure of one element of the circuit leads to a failure of the entire circuit.

The objective of the invention is to ensure the operation of the solar thermal photovoltaic module at high concentrations and uniform illumination of the photovoltaic receiver, obtaining a technically acceptable voltage (12 V and higher) on one PEC (module), increasing the conversion efficiency; obtaining hot water supply and reducing the cost of generated energy.

As a result of the use of the invention, on one part of the photovoltaic receiver on the surface of a cylindrical high-voltage photoelectric converter, uniform illumination of concentrated radiation is formed; on the other part of the photovoltaic receiver, illumination of concentrated radiation is formed to heat running water.

The above technical result is achieved in that in a solar photovoltaic module with a parabolotor concentrator, consisting of a Fokon type paraboloid concentrator and a thermophotovoltaic receiver located in the focal region with a uniform distribution of concentrated radiation, according to the invention, the thermophotovoltaic receiver contains a cooling device, the concentrator is a rotation body with a mirror internal reflection surface and consists of several zones (ab, bc, c -d) and is made integral according to the principle of collecting reflected rays in two focal regions from separate zones of the concentrator:

- the shape of the reflective surface of the zones ab, bc of the concentrator X (Y) is determined by a system of equations corresponding to the condition for uniform illumination of the surface of the photovoltaic part of the heat-photovoltaic receiver, made in the form of a cylinder of commutated high-voltage photomultipliers of length h _o and radius r _o :

Y _n = R _n ² / 4f _o , X _n = R _n - (k-1) r _o , R _n = 2f _o (tgα _n + cosα _n ), Δα = α _o / N, α _n = Δα (nN / 2), X * = 2f ₁ Q [(1 + 1 / Q ² ) ^l / ₂ -1], Q = B / r _o , B = h _o + h, Y * = X * ² / 4f ₁ , Y * _n = ΔY * _n, X _n = [4f _{1 (Y * + Y * n)} ] _^1/2, ΔY = P [1 ± (1-4R / P ^{2) _1/2]} / 2, P = L + Y _b , L = f _o + h + h _o / 2,

where y_n- the ordinate (in the main coordinate system XOY) of the calculated surface of the concentrator at point n, which is selected from a series of integers n = 1, 2, 3, ... N,

R _n is the radius of the calculated surface of the concentrator at point n,

F ₀ - the focal length of the calculated parabola,

X _n is the abscissa of the calculated surface of the concentrator,

K is an arbitrary coefficient, is selected in accordance with the boundary conditions,

α _n is the angle (in the area of the working profile of the concentrator a-c) between the ordinate level at the coordinate point X _n , Y _n and the beam reflected from the surface of the parabola with focal length f _o entering the focal region located at a radius r _{about the} photoelectric receiver in the intervals Δα = α _o / N, where n is selected from a series of integers n = 1, 2, 3 ... N,

where α₀- the angle between the reflected beam at a pointb and a reflected beam at a pointcsurface parabolas,

X * - parameter calculated by the formula

X * = 2f ₁ Q [(1 + 1 / Q ² ) ^l / ₂ -1],

where is the parameter f_oneselected in accordance with the boundary conditions:

Q is the parameter corresponding to the value Q = (h ₀ -h) / r ₀ ,

where h is the distance from the end surface of the photovoltaic part of the photovoltaic receiver to the focus of the calculated parabola,

r _{0 is the} radius of the photovoltaic part of the photovoltaic receiver,

Y * - function calculated by the formula:

Y * _n = ΔY * n,

where n is selected from a series of integers n = 1, 2, 3 ... N,

X _n - the abscissa of the calculated surface of the concentrator depending on the values of f _1, Y *, Y * _n ,

 ΔY - parameter calculated by the formula:

ΔY = P [1 ± (1-4R / P ^{2) _1/2]} / 2,

where P is the parameter corresponding to the value

P = L + Y _b ,

parameter R is selected in accordance with the boundary conditions,

L is the parameter corresponding to the value

L = f _o + h + h _o / 2,

where f _o - the focal length of the calculated parabola,

h _o - the length of the photomultiplier,

h - the distance from the end surface of the photovoltaic part of the photovoltaic receiver to the focus of the calculated parabola,

Y _b - the ordinate at the coordinate point X _b, Y _b parabola with focal length f _o ,

the values of the parameters f _o , f ₁ , k are selected in accordance with the boundary conditions, the geometric concentration of illumination of the photoelectric detector K _n in the intervals of the radius of the concentrator ΔX _n = X _n -X _n-1 is equal to:

K _n = (R _{n + 1} ² -R _n ² ) n / d _o ,

where R _{n + 1} is the radius of the calculated surface of the concentrator at the point n + 1,

R _n is the radius of the calculated surface of the concentrator at point n,

where n is selected from a series of integers n = 1, 2, 3 ... N,

d _o - the width of the focal region located on the radius r _{o of the} photoelectric receiver,

- the shape of the reflective surface of the cd zone of the concentrator X (Y) is determined by a system of equations corresponding to the condition for uniform illumination of the surface of the heat of the thermophotoelectric receiver, made in the form of a truncated cone with a side surface of length d *, upper radius r _s and lower radius r _in :

X _c = 2U _c (1 / codβ _in -tgβ _in ), tgβ _in = (Y _s -H _c ) (R _c -r _ov ), f _in = Y _c -X _c tgβ _in , r _in = X _c - R _c , d * = h * / sinφ _o , d * _n = d * n / N, K _n = (R ² _{n + 1} -R ² _n ) / (r * _{n + 1} + r * _n ) Δd * , X = 2f _{in the BN} (tgγ _BN + 1 / cosγ _{BN), tgφ o = h * /} (r o -r * _in)

where X _c is the abscissa (in the main coordinate system XOY) of the calculated surface of the concentrator at point c , which is selected from a series of integers n = 1, 2, 3 ... N,

_C is the ordinate (in the main coordinate system XOY) of the calculated surface of the concentrator at point c , which is selected from a series of integers n = 1, 2, 3 ... N,

β _in - the angle (in the zone of the working profile of the concentrator cd) between the ordinate level at the coordinate point X _s , Y _s and reflected from the surface of the parabola with the focal length f _{in the} beam coming in the focal region of the truncated cone of the photoelectric receiver,

H _in - the level of the location of the end part of the surface of the truncated cone of the photovoltaic receiver in coordinates X, Y,

R _c is the radius of the calculated surface of the concentrator at point c,

r _in - the radius of the end surface of the truncated cone of the photovoltaic receiver,

f _in - the focal length of the calculated parabola,

r _in - the distance from the axis OY to the focal length of the calculated parabola,

d * is the width of the truncated cone of the photovoltaic receiver,

h * is the height of the truncated cone,

φ _o - the angle of inclination of the generatrix of the truncated cone,

d * _n is the width of the truncated cone corresponding to the value d * _n = d * n / N, where n is selected from a series of integers n = 1, 2, 3 ... N,

the values of the parameters f _in, r _in are selected in accordance with the boundary conditions,

K _n - geometric concentration of illumination of the photoelectric receiver,

R _n is the radius of the surface of the concentrator at the point n, R _{n + 1} is the radius of the surface of the concentrator at the point n + 1,

r _n is the radius of the surface of the truncated cone of the photovoltaic receiver at point n,

r _{n + 1} is the radius of the surface of the truncated cone of the photovoltaic receiver at the point n + 1,

Δd * is the interval of the width of the truncated cone,

X _bn - abscissa of the calculated parabola (in the main coordinate system XOY) at point n,

f _in - the focal length of the parabola,

γ _bn is the angle between the ordinate level at V = f _in and the beam reflected from the surface of the parabola, arriving in the nth focal region within the radius from 0 to r _in on the surface of the truncated cone of the photovoltaic receiver,

φ _o - the angle of inclination of the generatrix of the truncated cone is determined by the ratio of the height of the truncated cone h * and the difference between the radius of the photovoltaic part of the photovoltaic receiver r _о and the radius of the end surface of the truncated cone r _in.

The invention is illustrated figure 1-5.

Figure 1 presents the design diagram of a photovoltaic module with a composite parabolotoric concentrator with a uniform radial distribution of concentrated radiation on two surfaces of a thermophotovoltaic receiver.

Figure 2 presents the path of the rays from the parabolotoric concentrator to the photovoltaic receiver.

Figure 3 presents the shape of the reflective surface of the paraboloric concentrator.

Figure 4 presents a graph of the distribution of the concentration of illumination on the photoelectric part of the photovoltaic receiver module from the width of the focal region on the side surface of the cylinder.

Figure 5 presents a graph of the distribution of the concentration of illumination on the thermal part of the photovoltaic receiver module from the width of the focal region on the side surface of the photodetector.

The photovoltaic module in figure 1 consists of: a parabolotoric concentrator 1, which creates a focal region on the side surface of the photovoltaic module 2 on its cylindrical photovoltaic part 3 of height h _o , radius r _about ; the focal region on the surface of the thermal part 4 in the form of a truncated cone with a side surface of length d *, upper radius r _s , lower radius r _in and located in the lower part of the cooling device 5.

Parabolotoric concentrator 1 of the photovoltaic module in figure 2 consists of three zones with working profiles:

- zones a-b and b-c concentrate solar radiation in the focal region on the side surface of the photovoltaic receiver 2 of its cylindrical photoelectric part 3 of height h _o , radius r _o ;

- the c-d zone concentrates solar radiation in the focal region on the end surface in the form of a truncated cone 4 of the photovoltaic receiver 2.

Based on the above formulas, the shape of the reflecting surface of the concentrator is calculated — a graph of X (Y) (Fig. 3).

Figure 4 presents a graph of the distribution of the concentration of illumination (from zones a-b, b-c of the hub 1) on the lateral surface of the cylindrical photoelectric receiver 3 from the width of the focal region (from 0 to h _o ) in relative units (from 0 to 1).

With a decrease in the height h _{o of the} photoelectric receiver 3, i.e. with a decrease in the area of the photoelectric converters, there is an increase in the concentration of illumination of the photoelectric receiver 3.

Thus, it is possible to change the concentration of illumination of the photoelectric detector 3, without changing the overall dimensions of the hub 1 and the selected type of photoelectric converters.

Figure 5 presents a graph of the distribution of the illumination concentration (from the c-d zone of the concentrator 1) on the lateral surface of the thermal part of the end surface in the form of a truncated cone of the photodetector 4 of the photovoltaic receiver 2 from the width of the focal region in relative units (from 0 to 1).

From the above characteristics it is seen that the change in the concentration of illumination across the width of the focal region of the photovoltaic successor 2 does not exceed 40%, which does not affect the electrophysical and thermal characteristics of the solar module.

A solar thermal photovoltaic module with a hub operates as follows.

Solar radiation enters the surface of parabolotor concentrator 1, is reflected at angles of inclination α, β, γ, oriented in their zones (a-b, b-c, c-d) so that they provide a uniform concentration of rays:

- on the photovoltaic part 3 of the thermophotovoltaic receiver 2 of the module, made in the form of a cylinder of radius r _about from switched high-voltage photovoltaic converters of height h _o with a cooling device 5;

- on the thermal part 4 of the photovoltaic receiver 2 of the module, made in the form of a truncated cone with a maximum radius r _about and a minimum radius r _{s of the} side surface, heating the flowing water of a cylindrical cooling device 5.

An example of the implementation of a solar thermal photovoltaic module with a paraboloric concentrator.

The hub 1 with a maximum radius R _max = 485 mm, a minimum radius R _min = 67 mm and a height of 545.6 mm is made of an aluminum sheet with a thickness of 0.5 mm with a mirror-reflecting inner surface with a working profile:

in zones a-b, b-c providing a uniform concentration of the rays of the photovoltaic receiver 2 of the module on its photovoltaic part 3, made in the form of a cylinder with a radius r _o = 60 mm from a switched high-voltage solar cells with a height of h _o = 60 mm, a width of Δr = 10 mm and mounted on a cylindrical cooling device 5. The concentration of illumination on the surface of the photovoltaic part 3 of the photovoltaic receiver 2 of the module is K = 16 times;

in zone cd providing uniform concentration rays on the thermal part 4 teplofotoelektricheskogo receiver module 2, designed as a truncated cone with a maximum radius of r _o = 60 mm and the minimum radius r _s = 5 mm lateral surface mounted on a cylindrical cooling device 5. The average illuminance concentration on the thermal part 4 of the photovoltaic receiver 2 of the module will be K = 65 times. Thus, the proposed solar photovoltaic module of concentrated solar radiation with high-voltage photovoltaic converters and parabolotor concentrator 1 provides: a fairly uniform distribution of illumination with an average concentration of K = 16 times on the photovoltaic part 3 of the thermophotovoltaic receiver 2 modules from series-parallel connected high-voltage photovoltaic cells, increasing voltage and efficiency conversion of solar energy into electrical energy; and a fairly uniform distribution of the illumination of the thermal part 4 of the photovoltaic receiver 2 of the module with an average concentration of K = 65 times, heating the running water and thereby increasing the overall efficiency of solar energy conversion of the photovoltaic module.

Claims (1)

A solar photovoltaic module with a parabolotor concentrator, consisting of a Fokon type paraboloid concentrator and a thermophotovoltaic receiver located in the focal region with a uniform distribution of concentrated radiation, characterized in that the solar thermophotovoltaic module contains a parabolotor concentrator and a thermophotovoltaic receiver with a cooling device installed in the focal region , a hub representing a body of revolution with a mirror internal overhnostyu reflection, consisting of several zones (a-b, b-c, c-d), formed integral on the principle of collecting the reflected beams in the focal regions of two separate zones concentrator:
- the shape of the reflecting surface of zones a-b, b-c of the concentrator X (U) is determined by a system of equations corresponding to the condition for uniform illumination of the surface of the photovoltaic part of the photovoltaic receiver, made in the form of a cylinder of commutated high-voltage photovoltaic cells with length h_o and radius r_o,
Y_n= R_n ²/ 4f_o, X_n= R_n- (k-1) r_o, R_n= 2f_o(tgα_n+ cosα_n), Δα = α_o/ N, α_n= Δα (n-N / 2), X * = 2f_oneQ [(1 + 1 / Q²)^l/₂-1], Q = B / r_o, B = h_o+ h, Y * = X *²/ 4f_one, Y *_n= ΔY * n, X_n= [4f_one(Y * + Y *_n)]^one/₂, ΔY = P [1 ± (1-4R / P²)^one/₂] / 2, P = L + Y_b, L = f_o+ h + h_o/ 2,
where y_{n -}the ordinate (in the main coordinate system XOY) of the calculated surface of the concentrator at point n, which is selected from a series of integers n = 1, 2, 3, ... N,
R_nis the radius of the calculated surface of the concentrator at point n,
F₀- the focal length of the calculated parabola,
X_n- the abscissa of the calculated surface of the concentrator,
K is an arbitrary coefficient, is selected in accordance with the boundary conditions,
α_n - the angle (in the zone of the working profile of the concentrator a-s) between the ordinate level at the coordinate point X_n, U_n and reflected from the surface of the parabola with focal length f_o ray arriving in the focal region located at a radius r_about photoelectric receiver in the intervals Δα = α_o/ N, where n is selected from a series of integers n = 1, 2, 3 ... N,
where α₀- the angle between the reflected beam at a pointb and a reflected beam at a pointcsurface parabolas,
X * - parameter calculated by the formula
X * = 2f_oneQ [(1 + 1 / Q²)^l/₂-one],
where is the parameter f_oneselected in accordance with the boundary conditions:
Q is the parameter corresponding to the value Q = (h₀-h) / r₀,
where h is the distance from the end surface of the photovoltaic part of the photovoltaic receiver to the focus of the calculated parabola,
 r₀- the radius of the photovoltaic part of the photovoltaic receiver,
Y * - function calculated by the formula:
Y *_n= ΔY * n,
where n is selected from a series of integers n = 1, 2, 3 ... N,
X_n- abscissa of the calculated surface of the concentrator depending on the values of f_one,Y *, Y *_n,
 ΔY - parameter calculated by the formula:
ΔY = P [1 ± (1-4R / P²)^one/₂] / 2,
where P is the parameter corresponding to the value
P = L + Y_b,
parameter R is selected in accordance with the boundary conditions,
L is the parameter corresponding to the value
L = f_o+ h + h_o/ 2,
where f_o- the focal length of the calculated parabola,
h_o- the length of the photomultiplier,
h - the distance from the end surface of the photovoltaic part of the photovoltaic receiver to the focus of the calculated parabola,
Y_b- ordinate at the coordinate point X_bY_bfocal length parabolas_o,
parameter values f_of_one, k are selected in accordance with the boundary conditions, the geometric concentration of illumination of the photoelectric detector K_n in the intervals of the radius of the concentrator ΔX_n= X_n-X_n-1 is equal to:
K_n= (R_{n + 1} ²-R_n ²) n / d_o,
where r_{n + 1}is the radius of the calculated surface of the concentrator at the point n + 1,
R_nis the radius of the calculated surface of the concentrator at point n,
where n is selected from a series of integers n = 1, 2, 3 ... N,
 d_o- the width of the focal region located at a radius r₀photoelectric receiver
- the shape of the reflecting surface of the c-d zone of the concentrator X (Y) is determined by a system of equations corresponding to the condition for uniform illumination of the surface of the thermal part of the heat-photovoltaic receiver, made in the form of a truncated cone with a side surface of length d *, upper radius r_ov and lower radius r_at:
X_c= 2U_c(1 / codβ_at-tgβ_at), tgβ_at= (Y_from-H_at) (R_c-r_ov), f_at= Y_c-X_ctgβ_at, r_at= X_c-R_c, d * = h * / sinφ_o, d *_n= d * n / N, K_n= (R² _{n + 1}-R² _n) / (r *_{n + 1}+ r *_n) Δd *, X_bn= 2f_at(tgγ_bn+ 1 / cosγ_bn), tgφ_o= h * / (r_o-r *_in),
where x_c- abscissa (in the main coordinate system XOY) of the calculated surface of the concentrator at a pointc, which is selected from a series of integers n = 1, 2, 3 ... N,
At_c- ordinate (in the main coordinate system XOY) of the calculated surface of the concentrator at a pointc, which is selected from a series of integers n = 1, 2, 3 ... N,
β_at - the angle (in the zone of the working profile of the concentrator c-d) between the ordinate level at the coordinate point X_from, U_from and reflected from the surface of the parabola with focal length f_at a beam arriving at the focal region of the truncated cone of the photoelectric receiver,
N_at- the location level of the end part of the surface of the truncated cone of the photovoltaic receiver in coordinates X, Y,
R_c - radius of the calculated surface of the concentrator at a pointc
r_in- the radius of the end surface of the truncated cone of the photovoltaic receiver,
f_at- the focal length of the calculated parabola,
r_at- the distance from the axis OY to the focal length of the calculated parabola,
d * is the width of the truncated cone of the photovoltaic receiver,
h * is the height of the truncated cone,
φ_o- the angle of inclination of the generatrix of the truncated cone,
d *_n- the width of the truncated cone corresponding to the value of d *_n= d * n / N, where n is selected from a series of integers n = 1, 2, 3 ... N,
parameter values f_at,r_inare selected in accordance with the boundary conditions,
K_n- geometric concentration of illumination of the photoelectric receiver,
R_nis the radius of the surface of the concentrator at the point n, R_{n + 1}is the radius of the surface of the concentrator at the point n + 1,
r_n- the radius of the surface of the truncated cone of the photovoltaic receiver atn
r_{n + 1}- the radius of the surface of the truncated cone of the photovoltaic receiver atn + 1,
Δd * is the interval of the width of the truncated cone,
X_bn- abscissa of the calculated parabola (in the main coordinate system XOY) at the pointn
f_at- the focal length of the parabola,
γ_bn - the angle between the level of the ordinate in Y = f_atand a ray reflected from the surface of the parabolanfocal region within the radius from 0 to r_inon the surface of a truncated cone of a photovoltaic receiver,
 φ_o- the angle of inclination of the generatrix of the truncated cone is determined by the ratio of the height of the truncated cone h * and the difference between the radius of the photovoltaic part of the photovoltaic receiver r_aboutand the radius of the end surface of the truncated cone r_in.

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