A comprehensive approach to closed-loop wind farm flow control using FLORIDyn

Abstract

Our planet is warming up with potentially disastrous consequences. The main cause of this climate change is the increase of greenhouse gases in the atmosphere, which are mainly emitted by burning fossil fuels to generate energy. Therefore, fossil fuels need to be substituted to reduce emissions from the energy sector. Renewable energies offer an alternative with reduced emissions. Among these, wind and solar energy are growing the fastest. This thesis investigates how the wind energy supply can be increased by improving its operational efficiency.

There are several reasons why a wind turbine may not generate its maximum capacity, one of them being its placement. Turbines are often placed in farms, which allows the collective use of infrastructure and minimizes land usage. The downside is that the turbines influence one another: As a turbine extracts energy from the wind, an area with lowered wind speed develops downstream. This area is called wake, and other turbines affected by it will generate less energy.

The ways to address this problem can be split into pre- and post-construction measures. Pre-construction the wind farm layout can be optimized, and post-construction control strategies are needed to operate the wind farm optimally. These strategies fall under the term wind farm flow control and aim to manipulate the flow between the turbines to optimize the farm performance. A turbine’s wake can be altered by changing the turbine’s resistance to the flow or by misaligning the turbine with the wind direction. The former leads to a faster wake recovery, and the latter results in a redirection of the wake, also called wake-steering.

The current state-of-the-art of wind farm flow control is to utilize wake-steering in an open-loop control configuration. To this end, steady-state engineering models of the wake are used to optimize the farm set points offline. This is done for a selection of atmospheric conditions and the set points are stored in a lookup table (LuT). During operation, the flow conditions are used to look up the precomputed turbine set points. A problem with this approach arises as open-loop control assumes a perfect match between the model and the actual conditions in the field. There are reasons why this might not be the case: (i) There is an inevitable modeling error, which creates a mismatch between the model and the reality; (ii) conditions can arise that are offline not accounted for, e.g., time-varying atmospheric conditions or layout changes due to turbine downtime.

These problems can be addressed by closing the loop. In closed-loop control, measurements are used to continuously correct the model and to adapt it to the current state of the true wind farm. Optimal set points are then found based on the current model state. The control strategy can, therefore, react to new conditions. A challenge is that the optimization needs to happen online and requires a way to incorporate sensor data into the model. Previous work has designed closed-loop approaches using the same computationally cheap steady-state models that were previously used for open-loop control. This was achieved by adapting the parameters of the model based on the mismatch between the observed and predicted measurements, like power generated. A core assumption these models make is that the flow is in a never changing steady state. However, flow conditions do change, and the large spacing between turbines leads to minutes of delay between the control action the upstream turbine takes and the effect that the downstream turbine experiences. The question arises: What could be achieved using dynamic wake models instead of steady-state ones? These can incorporate wake dynamics, which could lead to better decision-making.

This thesis designs a closed-loop model-predictive wind farm flow control strategy based on a dynamic wake model to maximize the energy generated by a wind farm under time-varying conditions. The thesis is comprised of three building blocks: (i) The development of a dynamic wake model, (ii) the derivation of a sensor fusion strategy to identify the state of the flow field, (iii) the composition of a control strategy that uses the model to optimize the control set points. The building blocks are then connected to form the closed-loop control strategy.

The model building is based on the further development of an existing model, which utilizes a steady-state wake model and reintroduces flow dynamics. In the first step, the underlying wake model is substituted by a three-dimensional one, and the formulation is adapted to heterogeneous flow conditions. In the second step, the model is reformulated as a framework that links to an arbitrary wake model. This is done to profit from advancements in the steady-state model development and to significantly decrease the computational cost of the model. In the third step, the dynamic model is compared to a steady-state one in a set of high-fidelity wind farm simulations under time-varying conditions based on field measurements. The results show that the dynamic model does provide a better match with a simulated wind farm.

In the second part of the thesis, a state estimation methodology is introduced. To this end, an ensemble approach is adopted, where the multiple versions of the model are simulated in parallel. The correlation between the ensembles is then used to correct them based on the predicted and measured wind direction and power measurements of the turbines. A byproduct of the ensemble approach is that each estimated state also has an uncertainty based on how much the ensembles agree on its value.

The third part of this thesis investigates the control and optimization problem. This part focuses on the cost function formulation and the behavior it leads to. In a steady-state frame, the delays do not have to be taken into account, but in a dynamic formulation, they become a challenge. We, therefore, propose a cost-function formulation that synchronizes the control actions with their effect at the downstream turbines. This leads to a series of smaller optimization problems instead of one larger one.

The three building blocks of this thesis are then tested in a case study: The closed-loop controller is employed to maximize the energy of a ten-turbine wind farm under time-varying conditions. Both the farm layout and wind direction time series are based on field conditions. The controller generates an overall energy gain of up to 4% over the baseline using noise-free wind direction measurements.
This is on par with the steady-state approach. However, the closed-loop approach is found to be more robust to disturbed wind direction measurements - Where the performance of the steady-state approach decreases to 1.7% due to the sensor noise; the closed-loop approach still achieves a 2.5% gain.

The conclusion of the work presented in this thesis is thereby: Closed-loop wind farm flow control based on a dynamic engineering surrogate model leads to a more accurate and robust state estimation of the wind farm flow field but, given no preview, does not necessarily lead to a higher energy generation than what can be achieved with steady-state models.