Adaptive PI Optimal Pitch Control for Wind Turbines with Tower Active Damping

Abstract

To avoid the waste of resources and improve the stability of generating power of early wind turbines. Aiming at the immature technical level of early wind turbine generators(WTGs), this paper proposes an adaptive PI control strategy for WTGs with variable pitch considering tower load shedding. First, to improve the adaptability of the pitch PI controller to different capacity units, the rotational inertia deviation normalization is used to realize the rotational inertia deviation auto-tuning. Second, to enhance the nonlinear compensation of wind turbine blades, the pitch gain scheduling module is designed. Then, two feedback links, anti-windup and tracking mode, are added on the basis of PI controller to avoid the problems of integral saturation and speed control failure of PI controller. In addition, to reduce the impact of wind load on the tower of the wind turbine, active damping control is added before and after the tower to suppress the vibration before and after the tower.

Keywords

wind turbine pitch-speed system PI damping variable pitch adaptive control

1 Introduction

Due to the limitations of technical level during the early construction period of the wind farm, there is a large safety margin in the design of wind turbines put into operation in the early stages. At the same time, the wind resources of wind turbines put into operation in the early stages are relatively good, and there is still some time before the wind turbines are retired. However, as the size of the WTG increases, the structural load of the unit increases, which had seriously threatened the safe and stable operation of the WTG (Rahman et al., 2019; Wang et al., 2024). Therefore, to avoid resource waste and reduce tower loads, adaptive optimal control methods considering tower loads need to be investigated to improve the load suppression capability while stabilizing the power output.

At present, the actual wind turbine control had been still mainly used in fixed-parameter PI control (Mostafa & Alireza, 2016), whose control parameters were usually determined based on theoretical design parameters and engineering experience, and can maintain a better control performance in the case of small changes in system parameters. However, in the actual operation of the wind turbine, with the changes in the external climate environment and the characteristics of the turbine itself, it will be difficult to ensure the smooth output of the turbine power under various disturbances. However, for the wind power generation system with strong nonlinearity and time-varying parameters (Akbarimajd et al., 2019; Luo et al., 2021; Ren et al., 2016), the nonlinearized constant model of the turbine had not been easy to establish. The wide range of random changes in wind speed also makes the control parameters less adaptable to the operating conditions, due to changes in external conditions or the action of the wind turbine itself, will make the wind turbine control process change (Guo et al., 2023; Liu et al., 2024). So that the PI control parameters are no longer applicable to the current controlled object, the control effect becomes worse, the need for PI control parameters with the wind speed and operating conditions change in real time. Therefore, this paper investigates the adaptive PI optimization control strategy for wind turbine with variable pitch considering tower load. When the dynamic characteristics of the wind turbine change, the PI parameters can be automatically adjusted online to adapt to different turbulent winds and different operating conditions based on considering the tower load.

To satisfy the dynamic characteristics of the real-time transformation of wind turbine controller parameters, Lee et al. (2014) had used time-delay estimation and nonlinear damping backpropagation to design a variable-gain PID controller, which had shown good control effect in solving the problem of unknown disturbances in the system. Sun et al. (2019) had designed a new adaptive PID controller using the A3C algorithm of deep reinforcement learning, which had approximated the value function using multi-layer neural networks to find the optimal control parameters and had solved the problems of slow convergence and low efficiency. Lin et al. (2013) based on multi-objective optimization technology and multi-attribute decision making technology, had put forward a PID parameter tuning method considering the balance of setting tracking, disturbance attenuation and robustness, and had applied it to the design of PID controller for wind turbine. Garmat et al. (2021) developed a multi-model predictive controller for variable-speed pitch-regulated wind turbines with enhanced PID-based parameter adaptation. However, the improved PID multi-model control validated in the literature only in 2MW units has limitations in scale applicability, and it is difficult to solve the risk of control instability brought by the complex nonlinear dynamics and extreme working conditions of large wind turbines. The above article uses a combination of reinforcement learning and PID controllers to regulate the controller parameters of wind turbines, but the time required to compute the controller parameters is long, making it difficult to apply to wind turbine pitch control.

Bekakra and Attous (2014) had used the Gray Wolf Optimization (GWO) algorithm to optimize the PI controller parameters of WTGs, but the GWO algorithm had relied heavily on the selection of the initial values, which had resulted in the algorithm failing to converge and affecting the control actions of WTGs. Xu et al. (2020) had proposed a method combining digital simulation and particle swarm algorithm for determining the optimal PI controller parameters for indirectly controlling the active and reactive power of doubly-fed wind turbines (DFIG). But only had considered solving the PI control parameters for a single operating condition and had not validated whether the method meets the operating conditions of WTGs, such as starting or stopping. Hasanien and Muyeen (2015) had combined the fuzzy control and PI control algorithm, had divided the fuzzy rules into four aspects, and had distinguished them according to the size of the error value between the generator's measured rotational speed and the rated rotational speed. Although it had improved the control accuracy, the standard of fuzzy division of the interval is not clear, and it had been difficult to cope with the sudden movements of the wind turbine for control. Gao and Wang (2016) had studied the adaptive genetic algorithm (AGA) used to optimize the PI control parameters of wind turbines; Echavarri et al. (2012) had applied the particle swarm algorithm in the PI control of wind turbine pitch, the above research mainly focused on the optimization of the initial value of the PI parameters, which resulted in the improvement of the system's control accuracy. But had not considered the real-time change of the PI parameters with the wind speed and operating conditions. Tian et al. (2012) had used small-signal analysis method in the DFIG to determine the operating point for linearization, based on which the controller was designed through the zero-pole configuration. But when the operating point of the system had been changed, the parameter-optimized controller control effect may deteriorate, and it was necessary to re-optimize the control parameters, and there was no discussion of the parameter optimization method of adaptive PI control that had been practically applied in the unit. The adjustment and optimization calculation of the controller parameters often take a lot of time, and it is difficult to ensure the real-time performance in practical application. The above method is mainly a combination of traditional PI controller parameter control and optimization methods, and its optimization effect depends on the number of iterations of particle swarm and the optimization results, and the model simulation environment is single, which is difficult to be applied to different types of wind turbines.

To address the issue of outdated control strategies in aging wind turbines, this paper proposes an adaptive PI pitch control strategy incorporating tower damping reduction. The main innovations of this study are as follows: 1) A rotational inertia deviation normalization method is developed to enable automatic adjustment of inertia deviations, significantly enhancing the pitch PI controller's adaptability to turbines with varying capacities. 2) A pitch gain scheduling module is designed to strengthen nonlinear compensation for turbine blades. Two supplementary feedback mechanisms (wind resistance and tracking modes) are integrated with the conventional PI controller, effectively resolving integral saturation issues, and preventing speed control failures. 3) An active damping control mechanism is implemented at both fore and aft tower positions, achieving vibration suppression in tower fore-aft directions to mitigate wind load impacts on turbine structures.

The rest of the paper is organized as follows. Section 2 describes the mathematical and dynamic models of wind turbines. The wind turbine adaptive PI pitch controller is designed in Section 3. Then, simulation results are given in Section 4 for different unit capacities and in different scenarios. Section 5 is the conclusion part of this paper.

2 Mathematical and Dynamic Models

2.1 Pitch Controller Model

Assuming that the drive shaft was a rigid shaft, the dynamic equations of the wind turbine and drive shaft were (Yesudhas et al., 2022):

\begin{aligned} T_{r} - N_{g} T_{g} & = (J_{r} + N_{g}^{2} J_{g}) \frac{d (ω_{r0} + Δ w_{r})}{d t} \\ = (J_{r} + N_{g}^{2} J_{g}) Δ {\dot{w}}_{r} \end{aligned}

(1)

Where, T_r represent pneumatic torque; N_g represent gearbox ratio; T_g represent generator torque; J_r represent rotational inertia of the wind turbine; J_g represent generator rotational inertia; w_r0 represent wind turbine rated rotational speed; Δw_r represent disturbance of wind turbine rotational speed with respect to the rated rotational speed; and Δ $\dot{w}$ _r represent angular acceleration of the wind turbine.

A first-order Taylor expansion is performed for generator torque and pneumatic torque:

\begin{aligned} T_{g} & = \frac{P_{0}}{N_{g} w_{r}} \approx \frac{P_{0}}{N_{g} w_{r0}} - \frac{P_{0}}{N_{g} w_{g 0}^{2}} Δ w_{r} \end{aligned}

(2)

\begin{aligned} T_{r} & = \frac{P (β, w_{r0})}{N_{g} w_{r0}} \approx \frac{P_{0}}{w_{r0}} + \frac{1}{w_{r0}} (\frac{\partial P}{\partial β}) Δ β \end{aligned}

(3)

Where, P₀ represent rated output power; P(β) represent mechanical power, where β is the pitch angle; w_g0 represent generator rated rotational speed; Δβ represent pitch angle perturbation about the operating point.

From this, the control relationship between the pitch angle perturbation and the wind turbine speed perturbation can be established and PI control can be applied:

\begin{aligned} Δ β = K_{P} N_{g} Δ w_{r} + K_{I} \int_{0}^{t} N_{g} Δ w_{r} d t + K_{D} N_{g} Δ {\dot{w}}_{r} \end{aligned}

(4)

Setting $\dot{φ} = Δ w_{r}$ , equation (5) combined with equation (2) ∼ equation (4) leads to equation (6):

\begin{aligned} \underset{{\bar{M}}_{φ}}{[I_{Drive} + \frac{1}{w_{r0}} (- \frac{\partial P}{\partial β}) N_{g} K_{D}]} \ddot{φ} + \underset{{\bar{C}}_{φ}}{[\frac{1}{w_{r0}} (- \frac{\partial P}{\partial β}) N_{g} K_{P} - \frac{P_{0}}{w_{r 0}^{2}}]} \dot{φ} \\ + \underset{{\bar{K}}_{φ}}{[\frac{1}{w_{r0}} (- \frac{\partial P}{\partial β}) N_{g} K_{I}]} φ = 0 \end{aligned}

(5)

Where, ∂P/∂β represent pitch angle sensitivity; I_Drive represent moment of inertia of the drive system; φ represent equivalent parameter.

The frequency ω_φ and damping ratio ζ_φ of this 2nd order system can be derived from equation (6):

\begin{aligned} {\begin{cases} ω_{φ} = \sqrt{\frac{K_{φ}}{M_{φ}}} \\ ζ_{φ} = \frac{C_{φ}}{2 \sqrt{K_{φ} M_{φ}}} = \frac{C_{φ}}{2 M_{φ} ω_{φ}} \end{cases} \end{aligned}

(6)

Where, M_φ, K_φ, C_φ represents equivalent mass, equivalent stiffness, equivalent damping.

For the pitch angle controller had designed, Feng et al. (2017) suggested that negative damping and differential gain should be ignored, and ω_φ = 0.6 rad/s and ζ_φ = 0.6∼0.7 are usually chosen for the second-order system, so that the controller parameters are shown in equation (7):

\begin{aligned} {\begin{cases} K_{P} = \frac{2 I_{Drive} w_{r0} ζ_{φ} ω_{φ}}{N_{g} (- \frac{\partial P}{\partial β})} \\ K_{I} = \frac{I_{Drive} w_{r0} ω_{φ}^{2}}{N_{g} (- \frac{\partial P}{\partial β})} \end{cases} \end{aligned}

(7)

Where, ω_φ represent equivalent system fundamental frequency. The PI gain calculated by equation (7) is obtained at a pitch angle of 0°. The above K_P and K_I are used as the initial values of the WTG model inputs.

2.2 Tower Front and Rear Active Damping Controller Models

Due to the small damping before and after the first-order modes of the tower, before and after vibration is easy to occur under the influence of wind load. For this reason, the active damping control of the tower front and rear is added to increase the equivalent damping to suppress the tower front and rear vibration. Since it is difficult to measure the velocity $\dot{x}$ at the top of the tower, it is usually chosen to measure the acceleration $\ddot{x}$ to obtain the velocity (Dong et al., 2018). The tower active damping control system is a new tower active damping control loop based on the original variable-speed pitch control loop, the pitch angle given command β_d transmitted to the pitch system by the main controller is the sum of the pitch angle output β_r of the pitch control loop and the pitch angle output Δβ of the tower active damping control loop. The principle of tower active damping control is to measure the acceleration $\ddot{x}$ of the top of the tower, get the speed $\dot{x}$ of the top of the tower through the integrator, and then multiply it by the appropriate gain coefficient K_a to get the additional pitch angle Δβ required by the tower active damping control.

In real wind turbines, tower top acceleration is measured directly by a triaxial piezoelectric acceleration sensor (e.g., PCB Piezotronics Type 356A15), which is usually mounted where the tower top flange meets the nacelle floor. The sensor range covers ±5 g and the frequency response range are 0.5–3000 Hz, which meets the vibration monitoring needs of the tower's first-order modes (0.2–0.3 Hz). To suppress high-frequency noise, the sensor signal is processed by a 4th-order Butterworth low-pass filter (cutoff frequency 10 Hz), and phase delays caused by sensor mounting position offsets are eliminated by a dynamic compensation module (Stoevesandt et al., 2022).

The block diagram of the working principle of the active damping control system for a large wind turbine tower is shown in Figure 1. The first-order dynamic response of the tower before and after had been expressed as a second-order damped resonant motion (Cao, 2021; Ying et al., 2015).

\begin{aligned} M_{i} {\ddot{x}}_{i} + D_{i} {\dot{x}}_{i} + K_{i} x_{i} = F_{i} + Δ F_{i} \end{aligned}

(8)

where M_i denotes the modal mass of the tower, D_i denotes the modal damping, K_i denotes the modal stiffness,

\ddot{x}

denotes the modal acceleration at the top of the tower.

\dot{x}

denotes the modal velocity at the top of the tower, x_i denotes the modal displacement at the top of the tower, F_i denotes the axial force of the rotor, and ΔF_i denotes the additional force due to the change in excitation. In these models, ΔF_i can be defined as (Liu et al., 2022; Qiao et al., 2017):

\begin{aligned} Δ F_{i} = - B {\dot{x}}_{i} \end{aligned}

(9)

where B denotes the additional damping provided by the rotor aerodynamic damping.

Figure 1.

Block Diagram of Active Damping Control for Large Wind Turbine Tower.

From equations (8) and (9), it can be deduced:

\begin{aligned} M_{i} {\ddot{x}}_{i} + (D_{i} + B) {\dot{x}}_{i} + K_{i} x_{i} = F_{i} \end{aligned}

(10)

Based on the derivation of the above equation, the equivalent damping of the tower is increased from D_i to (D_i + B). Subsequently, ΔF_i can be further expressed as:

\begin{aligned} Δ F_{i} = - B {\dot{x}}_{i} = \frac{\partial F_{i}}{\partial β_{i}} Δ β_{i} \end{aligned}

(11)

Based on equation (11), the relationship between the additional pitch angle and the velocity before and after the top of the tower can be derived as follows.

\begin{aligned} Δ β_{i} = \frac{- B}{\partial F_{i} / \partial β_{i}} {\dot{x}}_{i} = K_{a} {\dot{x}}_{i} \end{aligned}

(12)

Where, $\partial F_{i} / \partial β_{i}$ denotes the force and pitch angle curves and K_a denotes the active damping gain.

According to equation (12), aerodynamic damping B is needed to calculate the active damping gain. Therefore, the linear relationship between the load fluctuation q and wind speed fluctuation u acting on a blade of unit length can be expressed as:

\begin{aligned} q = \frac{1}{2} ρ ω r c (r) \frac{d C_{L}}{d α} u \end{aligned}

(13)

where ρ denotes the air density, ω denotes the rotor speed, c(r)denotes the airfoil chord at rotor radius r, and dC_L/dα denotes the rate of change of the lift coefficient C_L with respect to the angle of approach α.

Furthermore, the wind speed fluctuation u can be replaced by the blade fluctuation speed - ${\dot{x}}_{h}$ , and the aerodynamic damping $\dot{B}$ per unit length of the blade can be expressed as:

\begin{aligned} \dot{B} = \frac{q}{- {\dot{x}}_{h}} = \frac{1}{2} ρ ω r c (r) \frac{d C_{L}}{d α} \end{aligned}

(14)

Subsequently, the aerodynamic damping B of the rotor can be expressed as:

\begin{aligned} B = A \int \dot{B} d r = \frac{1}{2} A ρ ω \frac{d C_{L}}{d α} \int_{0}^{R} r c (r) d r \end{aligned}

(15)

where A denotes the number of wind turbine blades.

In this paper, the sensor signal processing process is improved by introducing a dynamic compensation module (see the phase correction method in literature [Stoevesandt et al., 2022] for details). Specifically, after the tower top acceleration signal is low-pass filtered by 4th order Butterworth, the dynamic gain compensation coefficient K_a is used for adaptive adjustment of the parameters, in which K_a is computed by innovatively combining the turbine capacity parameters.

Based on the aerodynamic damping model (equation 15) from literature (Liu et al., 2022), this study innovatively introduces the capacity correction factor η to improve the active damping gain as:

\begin{aligned} η & = 1.2 * R / D \end{aligned}

(16)

\begin{aligned} K_{a} & = \frac{- B \cdot η}{\partial F_{i} / \partial β_{i}} = η \frac{\frac{1}{2} A ρ ω \frac{d C_{L}}{d α} \int_{0}^{R} r c (r) d r}{\partial F_{i} / \partial β_{i}} \end{aligned}

(17)

Where, R is the impeller radius and D is the tower diameter.

3 Optimized Control of Wind Turbine Parameters with variable Pitch PI Controller

Since it is difficult to adapt the same set of variable pitch PI controller to wind turbines with different power levels and blade sizes, to reduce the task of adjusting parameter for different units, the method of normalizing the rotational speed deviation and compensating the blade nonlinearity is proposed. Because of the large deviation of large wind turbine units, the corresponding value of the controller should be increased synchronously, and the rotational inertia normalization can solve the problem of inconsistent step size of direct rotational inertia deviation of different models. Normalization of rated speed ensures that the controller responds proportionally to the percentage of rated speed error, which is the relative quantity, rather than the absolute error quantity. It reduces the variability of different WTG controllers’ tuning parameters and has a strong and consistent performance for different WTG input models. Figure 2 illustrates the PI pitch controller parameter optimization process.

Figure 2.

PI Pitch Controller Parameter Optimization Process.

3.1 Speed Deviation Self-Tuning

In this section, a rotational inertia deviation normalization method is proposed to automatically adjust the inertia deviation, which significantly improves the adaptability of the pitch PI controller to wind turbines of different capacities.

To ensure a good tracking speed in the transition section, the controller introduces a nonlinear compensation for speed deviation. So that the controller will have a stronger responsiveness to speed deviation, and thus more effective control. The nonlinear characteristic of the speed deviation reduces the amount of instantaneous fluctuation changes in the speed and makes it follow the speed reference value ω_ref stably. Equations (18)-–(21) represent the process of normalization and nonlinearity of rotor speed deviation of wind turbine. Firstly, speed deviation self-tuning is based on the relationship between speed and moment of inertia. Firstly, the speed deviation is converted into moment of inertia, as shown in formula (19). Unlike traditional direct use of speed deviation, the proposed moment of inertia includes parameters such as speed deviation, air density, gearbox ratio, and optimal power coefficient, considering the impact of various factors on wind turbine control, it has better applicability for wind turbines of different capacities. Secondly, set nonlinear coefficients, as shown in formula (21), which can reduce the impact of linearization on wind turbine control. Then, the deviation of the moment of inertia was multiplied by the nonlinear coefficient to achieve normalization and nonlinearity of the speed deviation. Based on this, a pitch gain scheduling was designed to compensate for the nonlinearity of the blades, reducing the deviation of the corresponding relationship between the pitch angle and torque in the lookup table method. Finally, by combining the nonlinear speed deviation L_err,_norm with the nonlinear compensation coefficient, the speed deviation was automatically adjusted.

\begin{aligned} ω_{err} & = ω - ω_{ref} \end{aligned}

(18)

\begin{aligned} L_{err} & = ω_{err} \frac{ρ π R^{5} C_{p max} ω_{g}}{2 λ_{o p t}^{3} G^{3} {\ddot{x}}^{2} I_{factor} ω_{rated}} \end{aligned}

(19)

\begin{aligned} L_{e r r, n o r m} & = L_{e r r} K_{e r r} \end{aligned}

(20)

\begin{aligned} K_{e r r} & = {\begin{cases} 2, & ω_{e r r} \leq - 0.3 \\ - ω_{e r r}, & - 0 .3 < ω_{e r r} \leq - 0.03 \\ 1, & - 0 .03 < ω_{e r r} \leq 0.03 \\ ω_{e r r}, & 0 .03 < ω_{e r r} \leq 0.3 \\ 2, & ω_{e r r} \geq 0.3 \end{cases} \end{aligned}

(21)

where ω is the actual rotor speed of the fan rotor, ω_ref is the reference rotor speed of the fan rotor, L_err is the rotor speed deviation, G, R, ω_g and I_factor denote the gearbox speed ratio, impeller radius, generator angular velocity, and moment of inertia gain coefficient, respectively. L_err,norm is the nonlinear rotor speed deviation, ω_rated is the rated rotor speed of the impeller of the fan,

\ddot{x}

denotes the tower top mode acceleration in rad/s, and K_err is the rotor speed nonlinear compensation coefficient. The segmented function of the speed deviation nonlinear compensation coefficient K_{_err} is shown in Figure 3.

Figure 3.

Segmental Function of the Nonlinear Compensation Coefficient K_{_err} for Speed Deviation.

As can be seen in Figure 3, the gain of the speed deviation is taken as 1 when the speed deviation is between +/-ω_err,1. If the speed deviation is beyond the transition between +/-ω_err,1, the gain is higher than 1. This allows the controller to be more responsive to the speed deviation, resulting in a more effective control.

The rotational speed deviation self-tuning principle is shown in Figure 4, in which β_opt, ω_rotor,opt and V_wind,opt denote the optimal pitch angle, optimal rotational speed and wind speed. k_p0 and k_i0 are the initial values of PI control parameters, which are obtained according to the empirical method. The purpose of the pitch gain scheduling method is to provide nonlinear compensation for wind turbine blades. The variable pitch gain scheduling method constructed in this paper is based on the look-up table method with the addition of blade nonlinear compensation, which can reduce the deviation of the correspondence between the pitch angle and the torque in the look-up table method, and the calculation process of this method is shown in eqs. (22)-(24).

\begin{aligned} K_{gain} & = max (- \frac{d T}{d β}, \frac{K_{p}}{β_{max} K_{gain\_min}}) \end{aligned}

(22)

\begin{aligned} u & = \frac{L_{e r r, \; norm\;}}{K_{gain\;}} \\ = K_{e r r} \frac{ρ π R^{5} C_{p max} ω_{g}}{2 λ_{opt\;}^{3} G^{3} {\ddot{x}}^{2} I_{factor\;} ω_{rated\;} K_{gain\;}} ω_{e r r} \\ = K_{ratio\;} ω_{e r r} \end{aligned}

(23)

\begin{aligned} y (t) & = k_{p 0} e (t) + k_{i 0} \int e (t) d t \\ = k_{p 0} u + k_{i 0} \int u d t \\ = k_{p 0} K_{ratio} ω_{e r r} (t) + k_{i 0} K_{ratio} \int ω_{e r r} (t) d t \\ = K_{P} ω_{e r r} (t) + K_{I} \int ω_{e r r} (t) d t \end{aligned}

(24)

Where, dT/dβ is the torque parameter table, K_p is the pitch proportional control coefficient, β_max is the maximum pitch angle, K_{gain_main} is the pitch gain scheduling minimum scaling value in Nm/rad, L_err is the angular kinetic inertia deviation, and K_gain is the pitch scheduling gain coefficient. u represents the set value of the speed deviation, which serves as the input for the pitch PI controller.

Figure 4.

Self-tuning Principle for Speed Deviation.

3.2 Pitch PI Controller Optimization Design

In this section, A pitch gain scheduling module is designed to strengthen nonlinear compensation for turbine blades. Two supplementary feedback mechanisms (wind resistance and tracking modes) are integrated with the conventional PI controller, effectively resolving integral saturation issues, and preventing speed control failures.

The PI control system is unable to accurately control the wind turbine with serious nonlinearity due to its fixed control parameters. In response to this problem, many scholars have introduced the self-tuning control technology into the PI control and achieved good control results. Self-tuning control belongs to the category of variable gain control, which is mainly characterized by an online identification of the controlled object model, the purpose is to provide accurate real-time change information for determining the controller parameters, but it is still difficult to be realized in the core hardware of the wind power controller (programmable controller), and the calculation of many online tuning algorithms is large, which is difficult to ensure real-time performance in practical applications. Variable gain PI controller is utilized for variable gain control, and this algorithm is simple, fast and easy to implement.

In this paper, the pitch adaptive PI optimal control is used to dynamically adjust and optimize the PI parameters in order to find the optimal PI control parameters quickly and accurately. The pitch controller adds Anti-windup and tracking modes to the PI control. The ω_ref is calculated by the operating point set point module, and the output of the PI loop driven by the constant optimal tip speed ratio will be zero when the output of the integrator exceeds the boundary limit, and the Anti-windup can avoid the occurrence of integral saturation. Tracking mode enables the PI controller to track the pitch signal when it cannot control the speed, and is used to prevent smooth switching between torque and pitch controllers. u denotes the speed deviation trim value, which is used as an input to the pitch PI controller. T_s is set to 600 s, k_b and k_t denote the anti-windup signal gain value and the tracking signal gain value, respectively. The feedback signal can be adjusted quickly and effectively. The pitch PI controller schematic is shown in Figure 5.

Figure 5.

Optimized Design of Pitch PI Controller.

4 Example Analysis

4.1 Calculation Conditions

The Bladed software has been certified by Germanischer Lloyd (GL) and the International Electrotechnical Commission (IEC) and is widely recognized by researchers. Therefore, the physical models of 5MW and 10MW WTGs were established using Bladed software, and Table 1 demonstrates the design parameters of 5MW and 10MW WTGs. The simulation model established using Bladed consists of several main parts: blade, impeller, tower, nacelle, drive train, control system, pitch system, converter response, loss table and other related models. cp table and ct table are generated by bladed settings. The blade tip speed ratio is in the range of [0,20] with a step of 1. The pitch angle is in the range of [-5°,45°] with a step of 1°.

Table 1.
Main Design Parameters of 5MW and 10MW Wind Turbines.

Parameter name Reference point Reference point

Rated power 5MW 10MW

Impeller diameter 63m 126m

Cut in wind speed 3 m/s 3 m/s

Cut out wind speed 25 m/s 25 m/s

Gearbox speed ratio 97 105

Wind turbine moment of inertia 53 Kgm² 65 Kgm²

Minimum generator speed 100 rad/s 100 rad/s

Rated speed of generator 122.91 rad/s 122.91 rad/s

Tower first order frequency 0.219 Hz 0.219 Hz

Tower first order modal weight 269640 Kg 269640 Kg

Tower first order modal damping 144% 144%

Tower height 87.6 m 105 m

Optimum pitch angle 0deg 0deg

Maximum pitch rate 6deg/s 6deg/s

Minimum Pitch Rate −3deg/s −3deg/s

Rated torque 1.003 × 10⁶Nm 1.003 × 10⁶Nm

air density 1.225 kg/m³ 1.225 kg/m³

maximum torque 1.103 × 10⁶Nm 1.103 × 10⁶Nm

Parameter name	Reference point	Reference point
Rated power	5MW	10MW
Impeller diameter	63m	126m
Cut in wind speed	3 m/s	3 m/s
Cut out wind speed	25 m/s	25 m/s
Gearbox speed ratio	97	105
Wind turbine moment of inertia	53 Kgm²	65 Kgm²
Minimum generator speed	100 rad/s	100 rad/s
Rated speed of generator	122.91 rad/s	122.91 rad/s
Tower first order frequency	0.219 Hz	0.219 Hz
Tower first order modal weight	269640 Kg	269640 Kg
Tower first order modal damping	144%	144%
Tower height	87.6 m	105 m
Optimum pitch angle	0deg	0deg
Maximum pitch rate	6deg/s	6deg/s
Minimum Pitch Rate	−3deg/s	−3deg/s
Rated torque	1.003 × 10⁶Nm	1.003 × 10⁶Nm
air density	1.225 kg/m³	1.225 kg/m³
maximum torque	1.103 × 10⁶Nm	1.103 × 10⁶Nm

Figure 6.

12 m/s Wind Speed and Acceleration Before and After the Wind Turbine Tower. (a) Turbulent Wind Speed of 12 m/s; (b) Acceleration Before and After the Tower.

Figure 7.

18 m/s Wind Speed and Acceleration Before and After the Wind Turbine Tower. (a) Turbulent Wind Speed of 18 m/s; (b) Acceleration Before and After the Tower.

4.2 Simulation of Tower Front and Rear Active Damping Controller

Parameters are provided by the bladed software. Therefore, the initial value of the tower active damping gain K_a can be obtained by equation (16). To better demonstrate the effectiveness of the adaptive PI pitch control considering the tower active damping control, Figures 6 and 7 respectively show the wind speed profiles and the tower before and after acceleration curves at 12 m/s and 18 m/s. The superiority of the adaptive PI pitch control considering the tower active damping control is verified by comparing the tower front and rear accelerations under the PI pitch control without considering the tower active damping control, the PI pitch control considering the tower active damping control and the adaptive PI pitch control considering the tower active damping control. In Figure 5, the turbulent wind is set to 12 m/s and the turbulence degree is set to 0.5. In Figure 6, the turbulent wind is set to 18 m/s and the turbulence degree is set to 1.5.

Figure 8.

Normal State Output Response of 5MW Wind Turbine. (a) Power; (b) Curve of Variation of k_p and k_i.

Figure 9.

Output Response Under Startup Condition of 5MW Wind Turbine. (a) Power; (b) Curve of Variation of k_p and k_i.

From Figure 6(b) and Figure 7(b), the range of acceleration fluctuation between the front and rear of the tower is significantly reduced after increasing the damping control, which verifies that increasing the equivalent damping can reduce the effect of wind load on the tower vibration.

Table 2.

5MW Wind Turbine Power Operation.

Condition	Control type	Power deviation	Deviation rate
Normal conditions	PI control	1.72 × 10⁵	3.44%
Normal conditions	Optimized PI control	1.95 × 10⁴	0.39%
Startup conditions	PI control	7.47 × 10⁴	1.49%
Startup conditions	Optimized PI control	3.56 × 10⁴	0.71%

4.3 Performance Testing of Units of Different Capacities Under Different Operating Conditions

4.3.1 Performance Test of 5MW Wind Turbine Under Different Working Conditions

In order to verify the effectiveness and accuracy of the adaptive PI optimization control for wind turbine pitch control, a wind turbine and controller model were constructed. Simulate and verify the adaptive PI optimization controller for variable pitch using NREL 5MW wind turbine. The power curves and PI parameter curves of the 5MW WTG under normal and startup conditions are shown in Figure 8 and Figure 9. In this paper, the relative standard deviation (RSD) is used as a criterion for judging the power fluctuation and torque fluctuation of the WTG, and the RSD is calculated as follows:

\begin{aligned} Y_{R S D} = \frac{Y_{real} - Y_{norm}}{\bar{Y}} \end{aligned}

(25)

Where, Y_real represent actual value, Y_norm represent, $\bar{Y}$ represent mean value.

Figure 8 and Figure 9 represent the corresponding outputs of the 5MW WTG under normal operating conditions and startup conditions for PI control and pitch adaptive PI optimization control, respectively. Figure 8(b) and Figure 9(b) show the k_p and k_i values of the different controllers for the wind turbine under normal operating conditions and startup conditions, respectively. In summary, the optimized PI control yields a smaller range of output power fluctuations and a more stable output for the wind turbine. Table 2 demonstrates the power deviation of the 5MW wind turbine under PI control and adaptive PI control.

From Table 2, the operating power deviation of the 5MW wind turbine based on adaptive PI control under normal and startup conditions is lower than that under PI control, which verifies the stability of adaptive PI control.

4.3.2 Performance Test of 10MW Wind Turbine Under Different Working Conditions

In order to verify that the pitch-adaptive PI optimization controller is suitable for different capacities of WTGs, this paper selects a 10MW WTG for simulation verification. The power curves and PI parameter curves of the 10MW WTG under normal and startup conditions are shown in Figure 10 and Figure 11. Table 3 demonstrates the power deviation of the 10MW wind turbine under PI control and adaptive PI control.

Figure 10.

Normal State Output Response of 5MW Wind Turbine. (a) Power at Normal Operating Conditions; (b) Curve of Variation of k_p and k_i.

Figure 11.

Output Response Under Startup Condition of 10MW Wind Turbine. (a) Power at Start-up; (b) Curve of Variation of k_p and k_i.

Table 3.

10MW Wind Turbine Power Operation.

Condition	Control type	Power deviation	Deviation rate
Normal conditions	PI control	2.10 × 10⁵	2.10%
Normal conditions	Optimized PI control	8.43 × 10⁴	0.84%
Startup conditions	PI control	1.82 × 10⁴	0.18%
Startup conditions	Optimized PI control	1.01 × 10⁴	0.10%

From Figure 10 and Figure 11, it can be seen that the power fluctuation of the turbine with adaptive pitch-variable PI optimization control is smaller and the output power is more stable, which can be well stabilized near the rated value under normal turbulent wind and startup conditions.

From Table 3, the operating power deviation of the 10MW wind turbine based on adaptive PI control under normal and startup conditions is lower than the operating power deviation under PI control. The simulation verification of 5MW and 10MW WTGs shows that the adaptive PI optimization control method proposed in this paper effectively reduces the power fluctuation and increases the stability of WTGs under different operating conditions.

4.4 Closed-Loop Stability Assessment of Adaptive PI Control

In this paper, an adaptive PI optimized controller is used, whose parameters change dynamically with the system conditions (e.g., wind speed and rotor inertia), so the traditional frequency domain Bode analysis cannot be directly applied. To assess the closed-loop stability of the system under adaptive control, a frozen-time linearization method is adopted (Chen et al., 2011; Wang et al., 2013).

A 5 MW wind turbine is selected for simulation verification at a wind speed of 12 m/s. The adaptive PI parameter optimization method proposed in this paper is compared with the conventional PI parameter method at 12 m/s corresponding to the fixed values of k_p and k_i parameters. Their Bode and pole plots are given in Figure 12.

Figure 12.

Bode Plots and Pole Plots. (a) Bode Plots; (b) Pole Plots.

As can be seen in Figure 12, the phase margin is improved to 45° (30° for ordinary PI), and the gain decay slope at the cutoff frequency of 0.6 rad/s is accelerated to −40 dB/dec, which effectively eliminates the 2 dB resonance peak of the ordinary PI in the low-frequency band (10⁻² rad/s) and suppresses the risk of tower vibration. The pole distribution shows that the optimized pole damping ratio is improved by 35% (0.51→0.69), the real part is left shifted to −0.92 s⁻¹ (−0.55 s⁻¹ for ordinary PI), and the dynamic convergence speed is accelerated by 41%, which meets the stringent stability requirements of wind turbines for fast pitch change and turbulence disturbance resistance.

4.5 Sensitivity Analysis of Controller Parameters

To verify the robustness of the proposed adaptive PI control strategy, the key parameters of the controller are analyzed with ±20% perturbation in this section. The tower active damping gain K_a, the speed normalization factor K_err, and the PI initial gain k_p0 are selected for sensitivity analysis to test the effects of parameter deviations on the standard deviation of the power (σP) and the tower top acceleration (σa) of the 5MW wind turbine. The simulation condition is 18 m/s turbulent wind (IEC Class B) and the results are shown in Table 4.

Table 4.
Sensitivity Analysis of 5MW Wind Turbine Unit Controller Parameters.

Value Bias σP(kW) Change rate σa(m/s²) Change rate

Reference value - 195 - 0.078 -

K _a +20% 203 +4.1% 0.081 +3.8%

−20% 210 +7.7% 0.085 +9.0%

K _err ±30% 198 +1.5% 0.079 +1.3%

k _p0 +20% 224 +14.9% 0.091 +16.7%

−20% 231 +18.5% 0.096 +23.1%

Value	Bias	σP(kW)	Change rate	σa(m/s²)	Change rate
Reference value	-	195	-	0.078	-
K _a	+20%	203	+4.1%	0.081	+3.8%
−20%	210	+7.7%	0.085	+9.0%
K _err	±30%	198	+1.5%	0.079	+1.3%
k _p0	+20%	224	+14.9%	0.091	+16.7%
−20%	231	+18.5%	0.096	+23.1%

It is clear from the analysis in the table: (1)

The low sensitivity of the active damping gain K_a, with a power fluctuation increase of <8% for ±20% perturbation, verifies the robustness of the aerodynamic damping model of equation (16).

(2)

The segmental threshold adjustment of the rotational speed nonlinearity compensation coefficient K_err has a weak impact on the system (<2%), thanks to the design of the moment of inertia normalization in Section 3.1.

(3)

The sensitivity of the initial PI parameter k_p0 is high, but it is corrected in real time during actual operation by the gain scheduling module in Figure 4, and the field data show that the adaptive mechanism can make the dynamic adjustment range of k_p up to ±35%, which effectively compensates the initial parameter deviation.

5 Conclusion

In this paper, an adaptive PI optimization control method for pitch control of wind turbines considering tower load is proposed for the technical transformation of old wind turbines. The method solves the control parameter problem in pitch control, and at the same time considers the influence of tower load on pitch control. The conclusions drawn in this paper are as follows: (1)

increasing the tower active damping controller, the tower front and rear acceleration and thus the tower displacement are reduced, and the tower load is reduced.

(2)

Through the simulation verification of 5MW and 10MW wind turbines under normal turbulent wind conditions and startup wind conditions. The results show that the power deviation of the 5MW wind turbine decreased by 88.95% under normal operation conditions, 52.34% under startup conditions. The 10MW wind turbine decreased by 59.86% under normal operation conditions, and 44.51% under startup conditions. The effectiveness of the proposed method is verified. The adaptive PI optimization control method proposed in this paper can achieve stable power output with small power deviation and is not limited by the capacity of the turbine, operating conditions and wind speed.

This paper proposes a control strategy improvement method for old wind turbines, compared with the latest intelligent control methods, although there is a theoretical performance gap, but more practical and economic advantages, for the stock of units to provide a higher feasibility of the solution.

Footnotes

ORCID iD

Xiaodong Wang

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Science and Technology Project of SGCC, (grant number 4000-202355454A-3-2-ZN).

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

References

Akbarimajd

Olyaee

Sobhani

Shayeghi

(2019). Nonlinear multi-agent optimal load frequency control based on feedback linearization of wind turbines. IEEE Transactions on Sustainable Energy, 10(1), 66–74. https://doi.org/10.1109/TSTE.2018.2823062

Bekakra

Attous

D. B.

(2014). Optimal tuning of PI controller using PSO optimization for indirect power control for DFIG based Wind turbine with MPPT. International Journal of System Assurance Engineering & Management, 5(3), 219–229. https://doi.org/10.1007/s13198-013-0150-0

Cao

(2021). Seismic performance analysis and safety assessment of wind turbine tower system. Proceedings of the 2021 7th International Conference on Hydraulic and Civil Engineering & Smart Water Conservancy and Intelligent Disaster Reduction Forum (ICHCE & SWIDR), Nanjing, China, 6–8 November 2021; pp.1024–1030.

Chen

Gao

(2011). Closed-Loop analysis and cascade control of a nonminimum phase boost converter. IEEE Transactions on Power Electronics, 26(4), 1237–1252. https://doi.org/10.1109/TPEL.2010.2070808

Dong

Wang

Qiu

(2018). A wireless multifunctional monitoring system of tower body running state based on MEMS acceleration sensor. 2018 19th International Symposium on Quality Electronic Design (ISQED), Santa Clara, CA, USA, pp. 357–363.

Echavarri

F. O.

Zulueta

Hernanz

J. R.

Guede

J. L.

Lesaka

J. M. L.

(2012). Particle swarm optimization based tuning for a small wind turbine pitch control. International Journal on Technical and Physical Problems of Engineering (IJTPE), 4(13), 164–170.

Feng

Zheng

L. I.

Yue-qiang

L. I.

(2017). Torque-pitch coordinated control for improving the power production of wind energy conversion system. Proceedings of the CSEE, 37(19), 5622–5632. https://doi.org/10.13334/j.02588013.pcsee.162125

Gao

Wang

(2016). Parameters tuning and optimization of Variable-gain PI controller of wind turbine based on immune genetic algorithm. Chinese Society for Power Engineering, 36, 22–29.

Garmat

Azzouzi

Bouchekima

(2021). Comparison between improved PID and LQ multimodel optimal controllers for variable-speed wind turbines. Electric Power Components and Systems, 48(18), 1875–1887. https://doi.org/10.1080/15325008.2021.1908453

10.

Guo

Schlipf

Cheng

P. W.

(2023). Evaluation of lidar-assisted wind turbine control under various turbulence characteristics. Wind Energy Science, 8(2), 149–171. https://doi.org/10.5194/wes-8-149-2023

11.

Hasanien

H. M.

Muyeen

S. M.

(2015). Affine projection algorithm based adaptive control scheme for operation of variable-speed wind generator. IET Generation, Transmission & Distribution, 9(16), 2611–2616. https://doi.org/10.1049/iet-gtd.2014.1146

12.

Lee

J. Y.

Jin

Chang

P. H.

(2014). Variable PID gain tuning method using back stepping control with time-delay estimation and nonlinear damping. lEEE Transactionson Industrial Electronics, 61(12), 6975–6985. https://doi.org/10.1109/TIE.2014.2321353

13.

Lin

Y. S.

Song

F. F.

Teng

D. W.

(2013). Multi-Objective optimization and parameter tuning for turbine PID controller. Advanced Materials Research, 779, 971–976. https://doi.org/10.4028/www.scientific.net/AMR.779-780.971

14.

Liu

Wang

(2024). Independent pitch adaptive control of large wind turbines using state feedback and disturbance accommodating control. Energies, 17(18), 4619. https://doi.org/10.3390/en17184619

15.

Liu

Zhang

Wang

Xie

Cao

(2022). Optimization of pitch control parameters for a wind turbine based on tower active damping control. Energies, 15(22), 8686. https://doi.org/10.3390/en15228686

16.

Luo

Wang

Chen

(2021). H-infinity state estimation for coupled stochastic complex networks with periodical communication protocol and intermittent nonlinearity switching. IEEE Transactions on Network Science and Engineering, PP(99), 1–1.

17.

Mostafa

Alireza

(2016). Nonlinear model identification and PI control of wind turbine using neural network adaptive frame wavelets. Journal of Wavelet Theory and Applications, 10(2), 131–146.

18.

Qiao

Han

Deng

Liu

Dong

Pan

Zhao

(2017). Research on variable pitch control strategy of wind turbine for tower vibration reduction. The Journal of Engineering, 2017(13), 2005–2008. https://doi.org/10.1049/joe.2017.0680

19.

Rahman

Ong

Z. C.

Chong

W. T.

Julai

X. W.

(2019). Wind turbine tower modeling and vibration control under different types of loads using ant colony optimized PID controller. Arabian Journal for Science & Engineering, 44(2), 707–720. https://doi.org/10.1007/s13369-018-3190-6

20.

Ren

Brindley

Jiang

(2016). Nonlinear PI control for variable pitch wind turbine. Control Engineering Practice, 50, 84–94. https://doi.org/10.1016/j.conengprac.2016.02.004

21.

Stoevesandt

Schepers

Fuglsang

Sun

(2022). Handbook of wind energy aerodynamics. Springer Nature.

22.

Sun

Ren

Duan

Yan

(2019-10-24). The Adaptive PlD Controlling Using Algorithm Advantage Actor Critic Asynchronous Learning Method. Springer International Publishing.

23.

Tian

X. S.

Huang

Y. H.

X. Y.

Wang

W. S.

(2012). Comparison of the frequency control strategy of wind turbines and its optimization scheme. Advanced Materials Research, 608, 494–499. https://doi.org/10.4028/www.scientific.net/AMR.608-609.494

24.

Wang

Cui

Zhou

Chen

Cheng

(2024). Structural load inversion and state analysis of floating wind turbine tower based on joint input-state estimation. Chinese Journal of Ship Research, 19(4), 167–175.

25.

Wang

Yang

Zhao

(2013). Robust stability analysis for an enhanced ILC-based PI controller. Journal of Process Control, 23(2), 201–214. https://doi.org/10.1016/j.jprocont.2012.08.004

26.

Yuan

Liu

Jiang

Gao

Shen

Cai

(2020). A pitch angle controller based on novel fuzzy-PI control for wind turbine load reduction. Energies, 13(22), 6086. https://doi.org/10.3390/en13226086

27.

Yesudhas

A. A.

Joo

Y. H.

Lee

S. R.

(2022). Reference model adaptive control scheme on PMVG-based WECS for MPPT under a real wind speed. Energies, 15(9), 3091. https://doi.org/10.3390/en15093091

28.

Ying

Zhu

Yang

G. D.

(2015). Development of active tower damping control on wind turbines. Acta Energy. Sol. Sin, 36, 54–60.