tallakt / trptsim

A simulator for the Pyramid TRPT airborne wind energy [AWE] windmill

TRPT Simulator

This is a simulator for a particular kind of TRPT type. TRPT airborne wind energy is a class of windmills that are airborne and where the power of the flying part of the windmill is transferred using torque transfer through a tensile shaft. It means Tensile Rotary Power Transmission and the term was used first by Oliver Tulloch

This particular class of TRPT consists of a soft shaft (possibly with compression rods) and a number of kites rotating in a single layer, connected through a bridle, flying in a ring. And all the kites are of the same type.

To say what it isn't, no lifter kite is assumed, and the shaft is assumed to be mostly pure tether and not very long. Also there is only one layer, so not lower layers to expand the rotary shaft etc.

Why? Because these rigs are a simplest structure possible if the kite is very controllable. So some kind of computer control of the kite during the loop is assumed.

The simulator is intended for use with a stationary power plant as well as a power source on a moving vehicle.

Description of the simulation performed

The simulator is intended for quick prototyping of TRPT rigs without doing a complete detailed simulation. So

• The shape of the layer is assumes constant and all bridle lines tensioned. It is a goal of the simulator though, to verify that all bridle lines are tensioned
• Tether drag is using a simplified model disregarding dynamics
• The roll of the kites is set directly, dynamics in roll are not accounted for
• Pitch is not modelled, it is assumed that we can set pitch to achieve the desired lift coeficcient as needed

Install

In Julia, install from git with

pkg> add /path/to/TRPTSim#main

Then use with

using TRPTSim

Examples

First create a model/configuration

> cfg1 = ampyx_ap2()
> cfg2 = delft_lei_v3()
> cfg3 = eijkelhof()
> cfg4 = october_kite()
> cfg5 = wi_rigid_daisy()

Don't expect any detailed simulation. The models are coarse approximation based on available data. And the kites are not optimized for this kind of TRPT simulator.

You can convert a model to a Dict to allow Julia to pretty print the contents

> cfg |> config_to_dict
Dict{Symbol, Any} with 13 entries:
  :n              => 3
  :rho            => 1.225
  :gravity        => 9.81
  :elev           => 0.523599
  :l              => 6.7
  :safety_factor  => 3.0
  :c_d_tether     => 1.1
  :d              => 0.0012
  :s              => 0.2
  :design_c_l     => 0.635
  :c_d_fun_coeffs => [0.0148208, -0.0188157, 0.0381036, 0.0754882, 0.145568, -0.261428, -0.070654, 0.20734, -0.0597481]
  :m              => 0.42
  :radius         => 4.29

These values are what defines the kite parameters. To create a config with some different parameters, do

> cfg = config(wi_rigid_daisy(), n = 6, l = 15.0)

Or modify a confuration by scaling it

> cfg = scale_to_area(wi_rigid_daisy(), 40.0)

The basic unit of simulation is the solve function. There is a second version that is mostly more useful that wraps the result of the solve operation into a DataSet for easier analysis.

> wind_speed = 12.0
> psi = 0.0
> mtr = 0.1 # moment per tension per looping radius
> force_h = 0.0
> solution = solve_sector(cfg, wind_speed, psi, mtr, force_h)
> (dataframe, solver_input) = solve_sector_df(cfg, wind_speed, psi, mtr, force_h)

The inputs to the solver is some parameters that are not spesifically configuration, but more things that would notmally change. Wind speed is a good example. The inputs besides the configuration are

• wind_speed: The wind speed in m/s
• psi: the offset in azimuth relative to pointing the AWE rig directly downwind
• mtr: The moment that is be transferred for a given tension of the shaft, divided by the looping radius. Detailed explanation below.
• force_h: the force generated by the implemented algorithm in a direction horizontal in the direction perpendicular to the shaft centerline.

The parameter mtr requires more explanation. It represents the shafts ability to transfer torque given a certain tension. It is also divided by the looping radius to make the value constant during scaling, so that a mtr factor is similar across a wide range of designs and sizes.

To arrive at the actual moment transmitted through the shaft, use the formula:

moment = MTR * looping_radius * shaft_tension

The mtr factor also represents the induction factor of the rig. An mtr value of zero represents a shaft that is not transmitting any torque and the blades are rotating unloaded. Too high of an mtr factor and the rig will not perform well as the blades are slowed down.

Deciding the optimum mtr and tether tension is a hard optimization problem that takes a while to calculate. Luckily, the mtr value will not change much, so in this software, most times the mtr is just expected to be found by trial and error, and only the tension is optimized automatically every time.

The maximum possible mtr value depends on the shaft geometry. It may be calculated by calling

> radius1 = 1.0
> radius2 = 5.0
> length = 10.0
> mtr = shaft_section_mtr(radius1, radius2, length) 

The value of mtr is typically around 0.05. The maximum moment of a shoft shaft is usually applied when the shaft section has a twist of 90 degrees. For extending the upper wind range of a rig, the mtr may be increased as the kites will need to depower to account for maximum tether loading. The other option is to increase the tether diameter and strength. The first option requires making the shaft more stubby or adding compressive elements, while the latter will hurt low wind performance.

Values reported by solve... are usually reported per kite. For example the tension trace will report only the tension of a single kite during a full looping cycle. To get the sum of all tensions for all kites combined, use

> moment_of_all_kites = signal_sum_of_kites(dataframe.moment, solver_input[:config].n)

The flying speed may be estimated by this heuristic. This is used to initialize the solver with an initial flying speed.

> speed0 = heuristic_flying_speed(cfg, wind_speed, psi)

The optimal tension for a rig is estimated by iteration using. Optimal tension is the tension that gives the maximum power output.

> tension = optimal_tension(cnf, wind_speed, psi, mtr, force_h)

Once you have solved the kite motion, the solution can be plotted using

> plot_solution(dataframe, solver_input)

A complete power curve is made and plotted like this

> winds = 8:15
> pc = power_curve(cfg, winds, psi, mtr, force_h)
> plot_power_curves(pc)

To plot many curves in one chart

> plot_power_curves("First" => pc1, "Second" => pc2)
> plot_power_curves([("$mtr", power_curve(cfg, winds, psi, mtr, force_h)) for mtr = 0.01:0.01:0.08]...)

There is also a tension curve for mounting the windmill on a moving vessel

> plot_tension_curves(pc)

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