**1. Introduction**

Control algorithms for a wind turbine are generally designed to control both power and load [1]. The power control includes the maximum power region at wind speed lower than the rated wind speed, the rated power region at wind speed higher than the rated wind speed, and the transition region between the two mentioned power control regions. These control regions are named region 2, 3, and 2.5, respectively [2]. The load control is targeted to reduce loads that the wind turbine experiences and is distinguished on the basis of the load that is mostly reduced [3,4]. The tower damper is known to reduce the tower load and uses the acceleration signal of the nacelle to calculate the command to the pitch actuator to reduce loads [4–9]. This is used in region 3. The peak shaving is known to reduce the tower and blade loads at region 2.5 by slightly adjusting the pitch angle of the blade by a pre-designed pitch schedule [10]. The individual pitch control is used in region 3 to reduce the blade load due to imbalance loads caused by wind shear, tower shadow, etc. It uses the signals from strain sensors mounted on the blade roots to calculate the command to the pitch actuator [4,11]. The drivetrain damper is used in region 2 to reduce the low-speed shaft torque due to torsional modes from the drive train [12]. It uses the generator speed signal to calculate the torque command to the generator to cancel out the drivetrain mode in the torque command.

Power control for modern wind turbines is achieved by a combination of open-loop and closed-loop control. In region 2, the control strategy is to maximize the wind turbine power, and this is achieved by an open-loop torque control with a fixed pitch angle (known as fine pitch) to maximize the power coe fficient which is the aerodynamic conversion e fficiency of the rotor. Either a generator torque–speed lookup table or an optimal mode gain (optimal relationship between generator speed and torque) is used for this [13,14]. The power control in region 2.5 is an extension of the power control in region 2, and the control strategy just performs a smooth transition from region 2 to region 3. The control strategy in region 3 consists in regulating the power so that it does not exceed the rated power of the wind turbine. The generator speed is controlled by either a PI (proportional-integral) or a PID (proportional-integral-di fferential) control to achieve the rated wind speed. The generator torque is controlled by open-loop control and PI control [4,15].

Although many modern control algorithms, including the linear quadratic regulator (LQR), fuzzy control, and model predictive control (MPC) algorithms, have been proposed by researchers as control algorithms for wind turbines to improve their performance [16–20], no algorithm has been chosen as an alternative to the conventional PI or PID power control by wind turbine manufacturers or companies to provide wind turbine control solutions. This is because the conventional PI or PID control algorithms for wind turbines have been used for a long time as power control algorithms and found to be robust and e ffective. This practice is not likely to change fast, as manufacturers often adopt a conservative approach towards innovation in control system design.

E fforts have been made to improve the performance of the conventional PI or PID control algorithms by adding extra commands to the calculated pitch command [21,22]. These methods measure the wind speed by Light Detection and Ranging (LIDAR) or by other techniques; they commonly use the partial derivative of the pitch angle with respect to the generator speed to calculate the required pitch angle variation based on the current wind speed variation and add this, multiplied by a suitable proportional gain, to the pitch command from the conventional PI or PID control algorithm. Although these feed-forward controls could not be validated, they are considered to be applicable to the actual wind turbines because they use the conventional PI or PID control algorithms as a basis and integrate the feed-forward control in region 3.

This study was performed to develop a new power control algorithm to be applied to a 100 kW medium-capacity wind turbine to improve its performance using a similar approach to the previous feed-forward control. The target wind turbine is not a multi-megawatt wind turbine and cannot afford a LIDAR to measure the wind speed, therefore a wind speed estimator was chosen for this study. Also, to calculate the feed-forward pitch command signal, contributions from other measured parameters as well as the estimated wind speed were considered for fine adjustment of the pitch angle command that was added to the command from the conventional PI or PID control algorithm. Therefore, an LQR controller was finally selected for this purpose. The LQR control uses wind speed estimators to estimate the representative wind speed experienced by that wind turbines and determine the magnitude of the control command [21,23–26]. Reference [24] constructed a tower and blade state estimator using accelerometers and strain gauges arranged along structural members and used it to estimate the wind state. The demonstration was conducted through an aerosol-servo-elastic simulator, which suggested that the individual blade fatigue and load could be reduced. Reference [25] demonstrated power curve tracking through a model-based control using a wind schedule for 3 MW wind turbines with blade tip speed constraints in simulated environments. In Reference [26], a wind observer was tested using field test data collected from NREL CART3 wind turbines. The results showed that the rotor equivalent wind speed estimated by the proposed observer correlated with the meteorological data and was much more accurate than the speed measured by an onboard wind vane. The wind speed estimator used in this study used a three-dimensional (3D) lookup table based on the two-mass drivetrain model with measured generator speed, torque, and pitch angle [4,21]. In [16], an LQR controller was designed for a megawatt (MW)-class wind turbine, and simulations were performed to test its performance. The simulation results showed that the performance of the wind turbine was improved by the proposed

LQR controller compared to that obtained with the conventional PI control, and the blade and tower loads were also reduced. Reports in the literature show that LQR controllers are e ffective as wind turbine controllers [16], but their performance relies on the accuracy of the wind speed estimators, so they are vulnerable to the noise or unexpected events influencing the measurement signal that is used for wind speed estimation. The reason is that the sensitivity varies with the wind speed. This issue has not been studied.

The purpose of this paper was to improve the performance of a PI control algorithm by virtue of an LQR controller which has a good control performance but is vulnerable to uncertainties in wind speed estimation. Therefore, a hybrid controller is newly proposed in this study. A PI control was used as the conventional power control, and an LQR control was used as a feed-forward controller to improve the control performance. This new control algorithm minimizes changes in the conventional PI control algorithm so that it could be relatively easily adopted by wind turbine manufacturers as a new control algorithm for modern wind turbines. Also, the proposed algorithm was expected to limit the contribution from the LQR controller which was significantly a ffected by wind speed estimation errors because the LQR controller was used as a feed-forward controller. For this, a new hybrid controller, which is a combination of the conventional PI and LQR controllers, was designed for a 100 kW wind turbine. It is di fficult to validate wind turbine control algorithms in a field test with multi-MW-class wind turbines. Therefore, numerical modeling is generally used to validate the performance of a single wind turbine or in wind farms [27–32]. The target wind turbine had a permanent-magnet synchronous generator (PMSG) without a gearbox and blades with a substantially smaller rotor moment of inertia and faster rotational speed compared to those of MW-class wind turbines. The proposed LQR-PI controller was tested with dynamic simulations, and the performances were compared with those of a PI and an LQR control algorithms with and without noise in the measured generator speed signal.

#### **2. Target Wind Turbine**

The target wind turbine used in this study is a PMSG horizontal-axis wind turbine. An overview of the specifications and an image of the target wind turbine are presented in Table 1 and Figure 1, respectively. The wind turbine is installed on an onshore test bed located in Gimnyeong-ri, Jeju-do, South Korea.


**Table 1.** Specifications of the target wind turbine.

**Figure 1.** Image of the target wind turbine.

## **3. Numerical Modeling**

The commercial code DNVGL-Bladed (4.6, DNV·GL, Oslo, Norway) was used for numerical modeling. DNVGL-Bladed was used to extract linear models, blade power coefficients, and thrust coefficients for the wind turbine. The in-house code includes control algorithms, wind speed estimators, and wind turbine numerical models. This section describes the wind speed estimator and wind turbine numerical models, and the next section introduces the control algorithm. From a control system perspective, a wind turbine numerical model includes aerodynamics, drive trains, generators, towers, and pitch actuators.

A block diagram of the overall functional scheme of a wind turbine is shown in Figure 2. The blue box indicates the control algorithm, the green box indicates the wind speed estimator, and the yellow box presents the wind turbine numerical model.

**Figure 2.** Block diagram of the in-house code.
