### Abstract

Original language | English |
---|---|

Journal | Wind Energy |

Volume | 18 |

Issue number | 6 |

Pages (from-to) | 991-1006 |

ISSN | 1095-4244 |

DOIs | |

Publication status | Published - 2015 |

### Keywords

- Wind power ramps
- Electrical grid integration
- Disturbance rejection
- Model predictive control
- Convex optimization
- Wind power control
- Energy storage
- Power output optimization

### Cite this

*Wind Energy*,

*18*(6), 991-1006. https://doi.org/10.1002/we.1742

}

*Wind Energy*, vol. 18, no. 6, pp. 991-1006. https://doi.org/10.1002/we.1742

**Model predictive control for wind power gradients.** / Hovgaard, Tobias Gybel; Boyd, Stephen; Jørgensen, John Bagterp.

Research output: Contribution to journal › Journal article › Research › peer-review

TY - JOUR

T1 - Model predictive control for wind power gradients

AU - Hovgaard, Tobias Gybel

AU - Boyd, Stephen

AU - Jørgensen, John Bagterp

PY - 2015

Y1 - 2015

N2 - We consider the operation of a wind turbine and a connected local battery or other electrical storage device, taking into account varying wind speed, with the goal of maximizing the total energy generated while respecting limits on the time derivative (gradient) of power delivered to the grid. We use the turbine inertia as an additional energy storage device, by varying its speed over time, and coordinate the flows of energy to achieve the goal. The control variables are turbine pitch, generator torque and charge/discharge rates for the storage device, each of which can be varied over given ranges. The system dynamics are quite non-linear, and the constraints and objectives are not convex functions of the control inputs, so the resulting optimal control problem is difficult to solve globally. In this paper, we show that by a novel change of variables, which focuses on power flows, we can transform the problem to one with linear dynamics and convex constraints. Thus, the problem can be globally solved, using robust, fast solvers tailored for embedded control applications. We implement the optimal control problem in a receding horizon manner and provide extensive closed-loop tests with real wind data and modern wind forecasting methods. The simulation results using real wind data demonstrate the ability to reject the disturbances from fast changes in wind speed, ensuring certain power gradients, with an insignificant loss in energy production.

AB - We consider the operation of a wind turbine and a connected local battery or other electrical storage device, taking into account varying wind speed, with the goal of maximizing the total energy generated while respecting limits on the time derivative (gradient) of power delivered to the grid. We use the turbine inertia as an additional energy storage device, by varying its speed over time, and coordinate the flows of energy to achieve the goal. The control variables are turbine pitch, generator torque and charge/discharge rates for the storage device, each of which can be varied over given ranges. The system dynamics are quite non-linear, and the constraints and objectives are not convex functions of the control inputs, so the resulting optimal control problem is difficult to solve globally. In this paper, we show that by a novel change of variables, which focuses on power flows, we can transform the problem to one with linear dynamics and convex constraints. Thus, the problem can be globally solved, using robust, fast solvers tailored for embedded control applications. We implement the optimal control problem in a receding horizon manner and provide extensive closed-loop tests with real wind data and modern wind forecasting methods. The simulation results using real wind data demonstrate the ability to reject the disturbances from fast changes in wind speed, ensuring certain power gradients, with an insignificant loss in energy production.

KW - Wind power ramps

KW - Electrical grid integration

KW - Disturbance rejection

KW - Model predictive control

KW - Convex optimization

KW - Wind power control

KW - Energy storage

KW - Power output optimization

U2 - 10.1002/we.1742

DO - 10.1002/we.1742

M3 - Journal article

VL - 18

SP - 991

EP - 1006

JO - Wind Energy

JF - Wind Energy

SN - 1095-4244

IS - 6

ER -