I will in the first part present to my framework. I will then give some earlier results. And actually I'd like to use the opportunity to be presenting to you guys from the different digital harness to somewhat trigger the discussion and look at the different outlooks and how I want to continue my work.

So starting with the framework, we've chosen a fairly simple model for the di-dynamics. We went from mass point model where we have the dynamics described by the different states.

So the states of our model are the position, the speed of the kite, its width coefficient, its roll angle. In the case of dry mode systems, we have a power coefficient and then the tether length, tethers, readouts, and tether acceleration. And this system is controlled by directly controlling the time derivatives of CL, roll angle, our kappa, and the tether trip.

And we have this in a, we model this using algebraic values. We have lambda, which is a measure for tension on the tether. And we solve this using index one and TAE.

So this is just in general states how we describe our model. And what we get with this, we use first trajectory optimization in a first part where we want to optimize the power output

in the trajectory. And in the next step, we do trajectory tracking using model predictive controller. And these last two parts, I use the ABOBS, which is an open source framework optimization of an orange system that is currently being developed at the University of York.

And so we're looking at large scale systems because the weights are expected to be larger. If you have larger weights, we have a comparable size to conventional wind turbines. And since we don't have these kind of systems developed yet, we wanted to go for quite generic design.

And also we're not trying to develop a new system, so we just want to simplify this part of the process. So by fitting manufacturing data from maybe McAnie and Amplex, we try to find the different aerodynamic coefficients, aerodynamic parameters of our system.

And so we came to the large scale system, so a weight span of about 60 meters, a wing area, corresponding to a wing area of about 120 km, a natural pressure of 26, which is very high, a wing mass of 8,000 kg, and in order to simplify aerodynamic modeling in this framework,

we choose an Ls of a wing with a airflow of SD 1722. So taking this design and plugging this into our optimizer, we came out with two optimal trajectories, the lift mode and the drag mode. And so starting with the lift mode on the left,

what we have here, we fly four loops for power generation, followed by a retraction phase. And so to give you some characteristics of this very optimal, very optimal trajectories,

we have a period of approximately 46 seconds, generating power of 7 MW for a loop time which is approximately 240 meters, flying at a very high speed of about 140 meters per second. So given the size of the aircraft, this can be discussed. And we have a maximum tether length of 660 meters.

For the drag mode, we fly single loops. We have a period of approximately 8 seconds, generating up to 9 MW power for a loop diameter of 325 meters at fairly the same maximum flight speed of about 24 meters per second and a tether length of 570 meters.

So this is when we plug the design into the optimizer. And the next step, the idea is to couple this with a flow simulation. So the flow simulation, we use larger simulation techniques, using the SD wind school that we've been developing at KU Leuven. And the idea there is that we model the atmospheric boundary layer as a pressure driven boundary layer.

I'm not going to go too much into the equation, so we use a compressible major stokes equation. And what I want to point out here is that we have the concentration of mass, concentration of momentum, and we add here this source term to model the effects of the drag.

So we're not modeling directly the flow around the airfoil, but we add this source term into our momentum equation for the flow. So that's this point here, so we add this using natural perspective method. And the idea is that we can, this solver is highly parallelized, and we can use high-performance computing techniques to do large simulations.

I have some keys about the implementation, we can discuss this after the lecture. The idea of this coupling is that we, as I mentioned before, we have a mass point to describe the dynamics,

but how we describe actually the guide into our LES field is that we discretize our wind into segments of area code length, given the platform that we have, and for each of these segments we can retrieve the local wind conditions given the LES flow field, and then compute geodynamic forces at these different locations.

The problem that we're dealing with here is that we have differences in length and time scales between the dynamics of the kite and the dynamics of the flow. So starting from maybe the difference in length scales is that the distance that the kite flies within one time step

is larger than the size of the different cells in our LES simulation. The second is that time steps of the kite dynamics are much smaller than time steps of the flow dynamics.

So we have within one time step of our flow simulation, we might have a hundred time steps for the kite dynamics. So we use spatial filtering to give the effect of the local forces to the next LES cells, and then when we have this distribution for all, say, our hundred sub-steps in the time step of the LES simulation,

we weight these different time steps and finally get a distribution of the force field inside our simulation, and we then add to the momentum equation. So that was the first part introducing the framework, and now I want to move on to some preliminary results.

So we've been first testing our controller. So what I'm plotting here is the difference, the different state that we have, the different controls for two different cases.

The first one being just considering the mass point model that we have for the MPC, and compare this with a discrete line that we use in SP-wind, our best relationship. So the idea here is that we can fairly track the three components of position, the components of the speed,

but we do have the difference between red and blue are differences in CL or more angles. So we cannot with this discrete model track the exact same performance as the master model. And so this leads to a drop in performance of about 50%,

so we cannot use as much power in our LES simulation as the optimal reference would actually predict. So that's the first point. For the drag mode system, we have the same characteristics, so we can track fairly well position and speed.

We do have some difficulties to track the aerodynamic coefficients, this leading into a drop of 40% of our performance. Plugging this then into our LES, coming to the setup of the farm, I'm looking at.

For this presentation today, I have fairly coarse simulations only using 250,000 windpoints, but we can scale up this to several millions. So here we only have a grid resolution of 12.5 to 25 meters, which is quite coarse given the size of the kite.

And the farm layer we're looking at is that we have the flow entering on the left side, flowing through the three kites which are positioned one behind each other. And so the idea is to look at how these kites influences themselves at the chance of performance. So looking first at the wind field that we're actually simulating here is,

again here we have a side view when the flow enters from the left, and we have a top view so the flow goes from the left to the right, here the high distribution, here the statewide distribution, so we see how the weight adds up and we interact with the different kites.

And actually given the asymmetric forcing that we have, so the lift force is not symmetric. And actually we have this forcing which is stronger in the bottom part of the kite, so this leads to bequeathes also in the performance. And so we can really see how the wind develops through the waveform,

and we can then assess the performance with several cycles. So what I show here in blue is the performance of the first row, in red the performance of the second row, and in green the performance of the green row. So we have what I described of 50%, 80% of the performance.

But we can also clearly see how this drops on the long end of the wave, through temperatures to the wind field. So these preliminary results are using very core simulations,

and the idea here was to have a discussion with you guys, so I prepared two main slides, some remarks that I want to share with you. So first is given the resolution of these simulations,

so they are quite coarse. If you increase the resolution of the flow simulation, you can get a better modeling actually of the force of the kite. So I show here some results from a previous study that we published earlier this year, where you can actually see also the lift mode systems, the nice bouncing features of the waves,

and in this case how this actually also mixes with the boundary layer. Also we have overestimated wave balance in deficit, because here our inflow condition is just over in the wind profile,

we don't have ambient turbulence. So looking at these wave profiles, for instance here where we have drop, drop in velocity to about 40 to 25 percent, these wave velocities are much smaller in real life when you have ambient turbulence, so this is what we're looking at at the moment. And the next part is actually some remarks on the trajectory that I'm currently using,

so we have a generic mask for the system, so the idea is also to adapt it to the difference between drag mode and lift mode systems. We are only using these other materials,

so knowing that in drag mode you should have also a conduction material in there. The optimizer gives us quite thick tethers, luckily the people of Dyema has shown us that they actually have these kind of tethers. So the idea is actually to see how we can improve our optimizer to actually get

to make more sense for instance, and I guess is are we too high value, so I hope we can have this discussion with you today. And what I want to work on next is to look at the different layouts, so how can we assess performance for changing the offset of the guides,

maybe looking at staggering the guides in the farm, and also one idea would be to re-optimize this reference trajectory that we have given the wake field, to see how we can maybe fly around the regions where we have the wake,

maybe fly higher, fly lower, even the wake from the upstream systems. Alright, so this brings me to my conclusion to the main three points of what I've shown today, is I presented this framework for my new optimal control techniques and simulation, that we have first performance mismatch between the model that we use

and the actual model that we fly into our earlier simulations, and that we have performance decrease within our wind farm, and that we want to investigate further layouts and also re-optimize our trajectories. Some references, also some operations, and thank you.