Orientation of photovoltaic modules to minimize intercepted radiation in photovoltaic aglectric systems

1. A photovoltaic module assembly for generating electrical power on farmland while minimizing reduction of solar radiation incident on ground due to shadowing, comprising:

a photovoltaic module having a first photovoltaic face defining a first plane and a second, oppositely disposed photovoltaic face;

a first normal axis extending from the first plane;

a first motor operationally connected to pivot the photovoltaic module about a first tilt axis;

a second motor operationally connected to pivot the photovoltaic module about a second azimuth axis;

an electronic controller operationally connected to the respective first and second motors;

wherein the photovoltaic module has the capability for 180 degree rotation about the first tilt axis and 360 degree rotation about the second azimuth axis;

wherein an incident solar ray strikes the photovoltaic module at an angle of incidence defined as an intersection of the incident solar ray and the first tilt axis;

wherein the electronic controller is programmed to send signals to the respective motors to minimize the angle of incidence during a first predetermined period of time so as to minimize shadowing according to the following;

AOI=cos −1 [cos(T m )cos(Z s )+sin(T m )sin(Z s )cos(AZ s −AZ m )];

wherein:

AOI=Solar angle of incidence on the photovoltaic module (deg);

T m =Tilt angle of module (deg, wherein 0° is horizontal);

Z s =Solar zenith angle (deg);

AZ s =Solar azimuth angle (deg, wherein North=0° and East=90°);

AZ m =PV face azimuth angle (deg, wherein North=0° and East=90°);

wherein the total radiation available is given by

E

tot

=

∫

t

1

t

2

I

GHI

(

t

)

⁢

A

field

⁢

dt

;

wherein

I GHI =Global horizontal irradiance;

A field =Area of field;

wherein

the intercepted radiation by the PV module for a given AOI over a time period from t 1 to t 2 is given by the equations:

E

PV

,

dir

=

∫

t

1

t

2

I

DNI

(

t

)

⁢

A

PV

⁢

sin

⁡

(

AOI

⁡

(

t

)

)

⁢

□

⁡

(

AOI

)

⁢

dt

;

E

PV

,

dif

=

∫

t

1

t

2

I

DHI

(

t

)

⁢

A

PV

⁢

f

⁡

(

AOI

)

⁢

□

⁡

(

AOI

)

⁢

dt

;

E

PV

=

E

PV

,

dir

+

E

PV

,

dif

;

wherein:

E PV =Energy intercepted by the photovoltaic module;

E PV,dir =Energy intercepted by the photovoltaic module from direct solar rays;

E PV,dif =Energy intercepted by the photovoltaic module from diffuse solar rays;

I DNI =Direct normal irradiance;

I DHI =Diffuse horizontal irradiance;

A PV =Area of a PV module face;

□=Angular-dependent absorption coefficient of photovoltaic module;

f=Fraction of diffuse irradiance intercepted by the photovoltaic module;

E r,atmosphere =Reflected radiation from the PV panels into the atmosphere;

wherein the radiation available to the field is given by;

E field =E tot −E PV −E r,atmosphere: and

wherein the electronic minimizes the angle of incidence during a first predetermined period of time by sending a signal to set the angle of incidence at 0 degrees;

wherein the electronic controller sends signals to the respective motors to maintain the angle of incidence at ninety degrees during a second predetermined period of time to maximize power output by setting the angle of incidence at 90 degrees.

2. A photovoltaic system for generating electrical power on farmland while minimizing reduction of solar radiation incident on ground due to shadowing, comprising:

a photovoltaic module having a first photovoltaic face defining a first plane and a second, oppositely disposed photovoltaic face;

a normal axis extending from the first plane;

a first rotation axis extending through the photovoltaic module;

a second rotation axis extending through the photovoltaic module;

at least one motor operationally connected to rotate the photovoltaic module about at least one of respective first and second rotation axes;

an electronic controller operationally connected to at least one motor;

wherein an incident solar ray strikes the photovoltaic module at an angle of incidence defined as an intersection of the incident solar ray and the normal axis;

wherein during a first predetermined period of time corresponding to a growing season the electronic controller is programmed to send signals to the at least one motor to orient the photovoltaic module to minimize energy intercepted by the photovoltaic module by setting the angle of incidence equal to zero degrees; and

wherein during a second predetermined period of time outside the growing season the electronic controller is programmed to send signals to the at least one motor to maintain the angle of incidence of about ninety degrees to maximize energy intercepted by the photovoltaic module by setting the angle of incidence equal to ninety degrees;

wherein:

AOI=cos −1 [cos(T m )cos(Z s )+sin(T m )sin(Z s )cos(AZ s −AZ m )];

AOI=Solar angle of incidence on the photovoltaic module (deg);

T m =Tilt angle of module (deg, wherein 0° is horizontal);

Z s =Solar zenith angle (deg);

AZ s =Solar azimuth angle (deg, wherein North=0° and East=90°);

AZ m =PV face azimuth angle (deg, wherein North=0° and East=90°);

wherein the total radiation available is given by

E

t

⁢

o

⁢

t

=

∫

t

1

t

2

I

GHI

(

t

)

⁢

Λ

field

⁢

dt

;

wherein

I GHI =Global horizontal irradiance;

A field =Area of field;

the intercepted radiation by the PV module for a given AOI over a time period from t 1 to t 2 is given by the equations:

E

PV

,

dir

=

∫

t

1

t

2

I

DNI

(

t

)

⁢

A

PV

⁢

sin

⁡

(

AOI

⁡

(

t

)

)

⁢

□

⁡

(

AOI

)

⁢

dt

;

E

PV

,

dif

=

∫

t

1

t

2

I

DHI

(

t

)

⁢

A

PV

⁢

f

⁡

(

AOI

)

⁢

□

⁡

(

AOI

)

⁢

dt

;

E

PV

=

E

PV

,

dir

+

E

PV

,

dif

;

wherein:

E PV =Energy intercepted by the photovoltaic module;

E PV,dir =Energy intercepted by the photovoltaic module from direct solar rays;

E PV,dif =Energy intercepted by the photovoltaic module from diffuse solar rays;

I DNI =Direct normal irradiance;

I DHI =Diffuse horizontal irradiance;

A PV =Area of a PV module face;

□=Angular-dependent absorption coefficient of photovoltaic module;

f=Fraction of diffuse irradiance intercepted by the photovoltaic module;

E r,atmosphere =Reflected radiation from the PV panels into the atmosphere;

wherein the radiation available to the field is given by; and

E field =E tot −E PV −E r,atmosphere .

3. The system of claim 2 wherein the first pivot axis defines tilt of the photovoltaic module and wherein the second rotation axis defines azimuthal orientation of the photovoltaic module.

4. The system of claim 3 wherein the module is pivotable about the first rotation axis.

5. The system of claim 3 wherein the module is pivotable about the second rotation axis.

6. The system of claim 5 wherein the module is pivotable about the first rotation axis and about the second rotation axis and the at least one motor includes a first motor operationally connected to the module for pivoting the module about the first rotation axis and a second motor operationally connected to the module for pivoting the module about the second rotation axis.

7. The system of claim 3 wherein the electronic controller is programmed with a first algorithm for controlling the first motor and a second algorithm for controlling the second motor.

8. A method for generating electric power on active use farmland while minimizing shadow disruption, comprising:

a) installing a photovoltaic module having a first generally planar photovoltaic face, a second, oppositely disposed photovoltaic face, a tilt axis, and an azimuth axis, wherein the photovoltaic module casts a shadow on active use farmland; and

b) using an electronic controller operationally connected to the photovoltaic module, the electronic controller programmed to automatically pivot the photovoltaic module about at least one respective axis to orient the photovoltaic face parallel to a line extending from the sun to the photovoltaic module according to:

AOI=cos −1 [cos(T m )cos(Z s )+sin(T m )sin(Z s )cos(AZ s −AZ m )];

wherein:

AOI=Solar angle of incidence on the photovoltaic module (deg);

T m =Tilt angle of module (deg, wherein 0° is horizontal);

Z s =Solar zenith angle (deg);

AZ s =Solar azimuth angle (deg, wherein North=0° and East=90°);

AZ m =PV face azimuth angle (deg, wherein North=0° and East=90°);

wherein the total radiation available is given by

E

tot

=

∫

t

1

t

2

I

GHI

(

t

)

⁢

A

field

⁢

dt

;

wherein

I GHI =Global horizontal irradiance;

A field =Area of field;

the intercepted radiation by the PV module for a given AOI over a time period from t 1 to t 2 is given by the equations:

E

PV

,

dir

=

∫

t

1

t

2

I

DNI

(

t

)

⁢

A

PV

⁢

sin

⁡

(

AOI

⁡

(

t

)

)

⁢

□

⁡

(

AOI

)

⁢

dt

;

E

PV

,

dif

=

∫

t

1

t

2

I

DHI

(

t

)

⁢

A

PV

⁢

f

⁡

(

AOI

)

⁢

□

⁡

(

AOI

)

⁢

dt

;

E

PV

=

E

PV

,

dir

+

E

PV

,

dif

;

wherein:

E PV =Energy intercepted by the photovoltaic module;

E PV,dir =Energy intercepted by the photovoltaic module from direct solar rays;

E PV,dif =Energy intercepted by the photovoltaic module from diffuse solar rays;

I DNI =Direct normal irradiance;

I DHI =Diffuse horizontal irradiance;

A PV =Area of a PV module face;

□=Angular-dependent absorption coefficient of photovoltaic module;

f=Fraction of diffuse irradiance intercepted by the photovoltaic module;

E r,atmosphere =Reflected radiation from the PV panels into the atmosphere;

wherein the radiation available to the field is given by;

E field =E tot −E PV −E r,atmosphere .