Active power control of wind turbine based on fuzzy pitch control

With the continuous increase in wind power penetration rate, wind turbine generators (referred to as WTGs or wind turbines) need to have the capability of active power control (APC) to respond to grid power commands. To reduce the burden of pitch control on wind turbines, existing studies have adopted a technological approach that uses variable-speed operation of the wind rotor instead of pitch control. Typically, pitch control is only initiated at the speed boundaries to limit variable-speed operation within the speed range. However, due to the influence of factors such as wind speed, rotor speed and control parameters, there is a noticeable saturation phenomenon in pitch control at the speed boundaries, which can affect the variable-speed process of the wind rotor and APC performance within the speed range. Therefore, this paper determines whether blade pitch adjustment needs to be performed in advance when the wind turbine operates within the speed range based on the rotor speed state. This avoids the pitch action at the speed boundaries and the associated pitch saturation problem. The results show that the proposed method in this paper reduces the frequency of the rotor speed reaching the speed boundaries by performing pitch actions within the speed range. This alleviates the influence of pitch saturation on the variable-speed process of the wind rotor, as well as the occurrence of overspeed and electromagnetic power drop, thereby improving the APC performance of the wind turbine.


Introduction
As wind power penetration continues to increase, wind turbines operating in maximum power point tracking (MPPT) mode, which aims to maximize individual unit power generation efficiency, exhibit severe fluctuations in output electromagnetic power, thereby significantly affecting grid frequency stability [1].Therefore, it is imperative for wind turbines (WTs) to possess active power control (APC) capabilities to adjust the electromagnetic power output based on grid power commands.[2].
The primary methods used for APC in wind turbines are blade pitch angle control (PAC) and rotor speed control (RSC).In [3], power control was discussed based on PAC and RSC separately.Compared to PAC methods, RSC methods utilize variable-speed operation of the wind turbine at zero pitch angle.As a result, when wind speed increases or grid power commands decrease, RSC methods degrade into constant-speed control solely relying on pitch adjustment.Consequently, both methods involve frequent pitch actions that can cause mechanical fatigue in the pitch actuation mechanism, which is detrimental to the long-term stable operation of wind turbine (WT) systems.In [4], an integrated APC method that combined rotor speed and pitch angle regulation was proposed.This method improves the rotor speed control loop, significantly reducing the number of pitch actions (IAPC).Typically, proportional-integral (PI) control is employed at the boundaries of the speed range to enable limited-speed operation and variable-speed operation at any pitch angle.However, the performance of pitch control at the range boundaries directly affects the variable-speed process of the wind turbine.Existing research on improvements to PAC and RSC methods regarding pitch control primarily focuses on enhancing power tracking or speed tracking performance.However, existing research overlooks the influence of pitch control at the boundaries.
Due to rate limitations in the pitch actuation mechanism of WTs, the pitch actuation mechanism is susceptible to rate saturation due to factors such as turbulent wind speed, rotor speed and control parameters.This saturation prevents the actual pitch angle from fully responding to the reference command, thereby affecting the subsequent passive variable-speed process of the WT.As a consequence, the rotor speed of the WT easily reaches the speed boundary, leading to overspeed and electromagnetic power drop.
To address this issue, this study examines whether preemptive blade pitch adjustment is necessary within the wind turbine's speed range based on the rotor speed state.This aims to prevent pitch actions at the speed boundaries and alleviate pitch saturation.The findings indicate that the proposed method significantly mitigates the impact of rate saturation on the WT's variable-speed process and reduces instances of overspeed and electromagnetic power drop.As a result, it enhances the APC performance of the WT.

Mathematical model of WT units and APC method
In this section, the focus is on presenting the mathematical model of variable-speed and variable-pitch WT units, as well as the basic principles of the IAPC method, which primarily relies on passive blade pitch control for regulation.

Mathematical model of wind turbine units
Rotor-side converter

Grid-side converter
The grid Generator  1 and referring to the explanation of aerodynamic power in [5], the aerodynamic power can be represented as: In the formula, R is the wind turbine radius, θ is the air density, v is the wind speed, ϖ is the rotor speed, P C represents the wind energy utilization coefficient, which is influenced by the pitch angle α and tip speed ratio κ .As one of the commonly used transmission chain models, the dual mass block model's low-speed side transmission shaft motion formula can be expressed as: where r J refers to the low-speed shaft's moment of inertia, r D represents the damping coefficient of the WT, a T is the aerodynamic torque of the WT, r ϖ is the WT speed, r ϖ % is the angular acceleration of the WT speed and ls T is the low-speed shaft torque.The motion formula of its high-speed measuring transmission shaft can be expressed as: where g J refers to the low-speed shaft's moment of inertia, g D represents the generator's damping coefficient, g T is the electromagnetic torque of the generator, g ϖ is the generator speed, and g ϖ % is the angular acceleration of the generator speed.hs T is the high-speed shaft torque, which can be expressed as Formula ( 5), where g n is the gearbox ratio.ls hs g gg ls hs ls ls

IAPC method for wind turbines
The IAPC method caches a portion of the aerodynamic power, which can utilize the variable speed of the WT at any pitch angle.In comparison to RSC, the IAPC strategy has a smaller pitch burden and more efficient utilization of wind energy.
The IAPC method can be structurally separated into three parts: the varying speed control part, the pitch control part and the MPPT part, as shown in Figure 2. Since the IAPC method is based on the PI loop for pitch adjustment at the boundaries within the speed range, it ignores the presence of saturation in the PI loop.However, integral saturation can affect the pitch action and subsequently have a detrimental effect on the variability of the speed process for the wind turbine.Among them, rate saturation affects the response of the pitch actuator to the reference command.Due to the cumulative and non-abrupt nature of the integral term in the Proportional-Integral (PI) control loop, when the pitch controller of a wind turbine experiences integral saturation, there is a process involved in accumulating and eliminating the integral term, during which a deviation occurs between the reference command and the actual pitch angle until the integrator exits the saturation state.

Pitch rate saturation phenomenon and its effects on the IAPC method
Therefore, the rate of change of the actual output value, denoted as du dt , is subject to limitations imposed by the influence of the integral term.

∋ ( ∋ (
To illustrate the phenomenon of rate saturation in wind turbine pitch control.The simulation uses a sinusoidal wind speed profile with parameters: amplitude of ∋ ( y=2sin 2 f +7. 5 ο , frequency of 0.048 Hz, and cmd =350kw P .In the process of raising the pitch angle, if we neglect the impact of pitch rate saturation in the IAPC strategy, the pitch angle at the speed limits of the operating speed range should remain in line with the steady-state pitch angle at the rated speed.At the rated speed, the WT has sufficient kinetic energy and the steady-state pitch angle corresponding to this wind speed is the smallest, which is most suitable for handling gradual decreases in gusty wind conditions.So, it is essential to compare the steady-state pitch angle at the rated speed with the pitch angle at the boundary of the operating speed range, taking into account the effects of rate saturation.Please refer to Figure 3  Figure 4. Phenomenon of electromagnetic power drop.Due to the influence of rate saturation on the pitching process at the boundary of the operating range, the pitch angle after entering the speed range becomes larger, reducing the wind-capturing capability of the turbine blades.At this point, the turbine switches from pitch regulation to speed regulation to cope with subsequent gradual decreases in gusty winds.The speed continues to decrease within the range.However, the larger pitch angle further exacerbates the speed decrease, making it more likely to reach the lower boundary of the range, resulting in a drop in electromagnetic power, as shown in Figure 4.
Therefore, to mitigate the detrimental impact of rate saturation on the wind turbine's passive speed regulation, this study adopts the proactive pitch adjustment method of pre-pitching before the rotor speed approaches the boundary of the operating range.By actively adjusting the pitch at the maximum pitching rate, the occurrence of pitch rate saturation is prevented.

Fuzzy algorithm-based advanced pitch control strategy
This section designs an advanced pitch control strategy based on different speed ranges.When approaching the boundary of the range, the pitch actuator is advanced at the maximum speed to avoid rate saturation and improve the performance of the wind turbine APC.
Design objective.Firstly, the speed range is segmented, denoted as 1 lim,u = ϖ ϖϖ ,Χ , 2 lim,l =+ ϖ ϖϖ Χ , and ∋ ( ϖϖ   ， and the speed acceleration continues to decrease, the pitch actuation mechanism adjusts downward at the maximum pitch adjustment rate.
Case 5: In all other cases, the pitch angle remains constant.Outside the speed range, the PI control loop is still used for pitch adjustment at the boundary.
Considering that the division of the speed range is significantly influenced by the turbulence intensity in actual turbulent wind conditions, fuzzy control with its nonlinearity and strong robustness can effectively handle the variation of rotor speed under turbulent wind speed conditions.Therefore, this paper adopts a fuzzy algorithm to design the pitch controller, as shown in Figure 5. .The fuzzy rules can be found in Table 1 Table 1.The fuzzy rules.

∋ (
The design idea of fuzzy rules is as follows: 1) When the speed deviation is in the PB and PM intervals, if the acceleration change is PB or PM, the speed tends to exceed the upper boundary of the interval.To reduce the speed as soon as possible, it is necessary to adjust the pitch upward at the maximum pitch rate.In this case, the output value M is set to + 2. If the acceleration change is PS, it is necessary to adjust the pitch upward at half of the maximum pitch rate.At this time, the output value M is set to +1.
2) When the speed deviation is in the PS, Z and NS intervals, if the acceleration change is PB or PM, it is necessary to perform advance pitch adjustment.The output M is set to +1.
3) When the speed deviation is in the range NB and NM if the acceleration changes to PB or PM, there is a tendency for the speed to exceed the lower boundary of the range.To increase the speed as soon as possible, it is necessary to pitch downwards at the maximum pitch rate.At this time, the output value M is set to -2; If the acceleration changes to PS, it is necessary to pitch downwards at half the maximum pitch rate and the output value M is set to -1 which doesn't need to pitch in other situations.

Simulation verification
The speed limit of the WT is 4.9 deg/s and cmd =350kw P .The proposed measure was verified through simulation under turbulent wind speeds and compared with IAPC.The evaluation metrics for assessing the APC performance of the WT include pitch action amount sum α Χ , accumulated time of overspeed U (s) t , accumulated time of maximum power output L (s) t , number of speed reaching boundaries S, and electromagnetic power instruction deviation e P ρ [5].Finally, as shown in Figure 6, based on the simulation results, an analysis was conducted from three aspects: pitch performance, variable-speed performance and power instruction response performance.The results are shown in Table 2:  In the proposed method in this paper, although the advance pitch adjustment increases the pitch action within the speed range, it improves the utilization of the passive variable speed of the WT, significantly reduces the pitch adjustment for speed limitation outside the range and mitigates the excessive pitch adjustment caused by rate saturation.As depicted in Table 2, the strategy proposed in this study can reduce the pitch action of the actuator from 136.41° to 125.31°, enhancing the wind turbine's speed regulation performance while reducing the burden on the actuator.
b. Variable-speed Regulation Performance In this paper, the U t and L t both are reduced to 0. This is because the advanced pitch adjustment avoids saturation and excessive pitch adjustment, fully utilizing the passive variable-speed process of the wind turbine.By implementing advanced pitch adjustment, not only is the overspeed time reduced but also the time when the speed is below the lower limit of the range is reduced.c.The Performance of Power Command Response As shown in Table 2, compared to the IAPC method, the value of e P ρ decreases from 5.58 kW to 0 in the proposed method.This is because when the speed becomes too low and approaches the lower boundary of the range, the actuator adjusts the pitch at the maximum pitch rate, increasing the windcapturing capacity of the wind turbine and preventing the speed from falling to the lower boundary.

Conclusion
While the existing IAPC strategy improves the utilization of passive variable speed through coordinating speed regulation and pitch adjustment, it fails to consider the impact of rate saturation at the boundaries on the wind turbine's variable-speed process.Pitch rate saturation affects the pitch action at the boundaries, which in turn influences the variable-speed process and APC performance of the wind turbine.Therefore, this study determines, based on the wind turbine's speed state, whether preemptive pitch adjustment is necessary within the speed range to prevent pitch actions and associated saturation issues at the speed boundaries.The simulation results demonstrate that the proposed method mitigates the effect of rate saturation on the WT's variable-speed process, as well as reduces the occurrences of overspeed and electromagnetic power drop, thereby improving the APC performance of the wind turbine.

Figure 1 .
Figure 1.Wind turbine transmission chain model.Using the transmission chain model of the WT shown in the Figure1and referring to the explanation of aerodynamic power in[5], the aerodynamic power can be represented as:

Figure 2 .
Figure 2. Schematic diagram of the structure of the IAPC controller.Since the IAPC method is based on the PI loop for pitch adjustment at the boundaries within the speed range, it ignores the presence of saturation in the PI loop.However, integral saturation can affect the pitch action and subsequently have a detrimental effect on the variability of the speed process for the wind turbine.Among them, rate saturation affects the response of the pitch actuator to the reference command.
Based on the definition of pitch rate saturation in [8], the pitch angle reference command output by the PI-based pitch controller is: α represents the proportional term of the reference command and term of the reference command.

Figure 3 .
Figure 3.Comparison between con α and steady α .Figure4.Phenomenon of electromagnetic power drop.Due to the influence of rate saturation on the pitching process at the boundary of the operating range, the pitch angle after entering the speed range becomes larger, reducing the wind-capturing capability of the turbine blades.At this point, the turbine switches from pitch regulation to speed regulation to cope with subsequent gradual decreases in gusty winds.The speed continues to decrease within the range.However, the larger pitch angle further exacerbates the speed decrease, making it more likely to reach the lower boundary of the range, resulting in a drop in electromagnetic power, as shown in Figure4.Therefore, to mitigate the detrimental impact of rate saturation on the wind turbine's passive speed regulation, this study adopts the proactive pitch adjustment method of pre-pitching before the rotor speed approaches the boundary of the operating range.By actively adjusting the pitch at the maximum pitching rate, the occurrence of pitch rate saturation is prevented.
the need for proactive pitch adjustment is determined based on the deviation of the rotor speed and its acceleration in different speed range segments.The following five cases are generally considered: Case 1: When the speed is in range 1 lim,u ϖϖ   ， and the speed acceleration continues to increase, the pitch actuation mechanism adjusts upward at the maximum pitch adjustment rate.Case 2: When the speed is in range Ζ ∴ z1 ϖϖ ， and the speed acceleration continues to increase, the pitch actuation mechanism adjusts upward at half the maximum pitch adjustment rate.Case 3: When the speed is in range Ζ ∴ 2z ϖϖ ， and the speed acceleration continues to decrease, the pitch actuation mechanism adjusts downward at half the maximum pitch adjustment rate.Case 4: When the speed is in range l i m , l2

Figure 5 .
Figure 5.The proposed controller in this paper.The two input domains of fuzzy control are denoted as Ζ ∴ 0.5,0.5 , and Ζ ∴ 0.25, 0.25 , , and the output

Figure 6 .
Figure 6.Comparison of two APC methods under turbulent wind speed.Table 2. Evaluation metrics of two APC methods under turbulent wind speed.

Table 2 .
Evaluation metrics of two APC methods under turbulent wind speed.