Method for designing the layout of turbines in a windfarm

A computer program product for optimizing the layout of turbines on a grid, said grid representing a land parcel, to maximize energy yield produced by the turbines comprising:

• a non-transitory storage medium readable by a processor and storing instructions for operation by the processor for performing a method comprising:
• a) receiving wind data for each possible location of placement of a turbine on said grid;
• b) calculating an energy yield for a given layout of turbines on said grid as a nonlinear objective function, said function constrained by said wind data;
• c) implementing a bounding heuristic, said bounding heuristic comparing said calculated energy yield for said given layout of turbines to a current lower bound, and if said calculated energy yield is greater than the current lower bound, replacing the current lower bound with the calculated energy yield;
• and
• d) repeating steps a to c for different layouts of turbines on the grid, wherein the objective function computes the energy yield for the given layout according to:
• max
• ⁢
• ⁢
• P
• ′
• =
• ∑
• p
• ⁢
• ⁢
• {
• x
• p
• *
• ∑
• wdir
• ⁢
• ⁢
• {
• P
• ⁢
• ⁢
• 0
• wdir
• *
• (
• 1
• -
• ∑
• pi
• ∈
• I
• p
• ,
• wdir
• ⁢
• ⁢
• (
• x
• pi
• *
• δ
• ⁢
• ⁢
• V
• wdir
• ,
• pi
• ,
• p
• 2
• )
• )
• 3
• }
• }
• wherein P′=power, p=a location on the grid, xp=0 or 1, wdir=wind direction, P0wdir=power produced by turbine at location p due to wind from wind direction wdir in the absence of wake interference from other turbines, pi=ith element of set I, xpi=0 or 1, and δV=wind deficit.

A system for optimizing the layout of turbines on a grid, said grid representing a land parcel, said system operable to maximize an energy yield produced by the turbines placed on said grid comprising a processor operable to:

• a) receive wind data and cost data for each possible location of placement of a turbine on said grid;
• b) calculate an energy yield for a given layout of turbines on said grid as a nonlinear objective function, said function constrained by said wind data and said cost data
• c) implement a bounding heuristic, said bounding heuristic comparing said calculated energy yield for said given layout of turbines to an lower bound, and if said calculated energy yield is greater than the current lower bound, replacing the current lower bound with the calculated energy yield;
• and
• d) repeat steps a to c for different layouts of turbines on the grid, wherein the objective function computes the energy yield for the given layout according to:
• max
• ⁢
• ⁢
• P
• ′
• =
• ∑
• p
• ⁢
• ⁢
• {
• x
• p
• *
• ∑
• wdir
• ⁢
• ⁢
• {
• P
• ⁢
• ⁢
• 0
• wdir
• *
• (
• 1
• -
• ∑
• pi
• ∈
• I
• p
• ,
• wdir
• ⁢
• ⁢
• (
• x
• pi
• *
• δ
• ⁢
• ⁢
• V
• wdir
• ,
• pi
• ,
• p
• 2
• )
• )
• 3
• }
• }
• wherein P′=power, p=a location on the grid, xp=0 or 1, wdir=wind direction, P0wdir=power produced by turbine at location p due to wind from wind direction wdir in the absence of wake interference from other turbines, pi=ith element of set I, xpi=0 or 1, and δV=wind deficit.

A method for finding a minimum area required for production of a given energy yield, said area associated with a layout of turbines on a grid, said grid representing a land parcel, comprising:

• a) defining a first area for the grid;
• b) calculating an energy yield according to a nonlinear objective function produced by placement of a fixed amount of the wind turbines on the grid defined by the first area;
• c) determining if the calculated energy yield for the first area is greater than a threshold value, and if the calculated energy yield is greater than the threshold value then defining a second area for the grid, said second area smaller in size than the first area;
• d) calculating an energy yield according to a nonlinear objective function produced by placement of the fixed amount of turbines on the grid defined by the second area;
• e) determining if the calculated energy yield for the second area is greater than the threshold value, and if the calculated energy yield for the second area is greater than the threshold value selecting the second area;
• and
• f) repeating steps a to e for subsequently smaller first and second areas using the same fixed amount of turbines until the minimum area required for production of the given energy yield is discovered, wherein the nonlinear objective function is constrained by a budget constraint according to:
• ∑
• p
• ⁢
• ⁢
• x
• p
• *
• cost
• p
• ≤
• B
• and
• x
• p
• ∈
• {
• 0
• ,
• 1
• }
• ⁢
• ⁢
• ∀
• p
• wherein xp is a location on the grid and costp is an installation cost associated with the location defined by xp,wherein a programmed processing unit performs said defining, energy yield calculating steps b) and d) and determining steps c) and e), and said repeating.