Variable Speed Wind Turbine Pitch Angle Control Using Three-Term Fuzzy Controller
الموضوعات : مهندسی هوشمند برق
Ehsan Hosseini
1
(Najafabad Branch, Islamic Azad University)
Ghazanfar Shahgholian
2
(Department of Electrical Engineering, Najafabad Branch, Islamic Azad University, Isfahan, Iran)
Homayoun Mahdavi-Nasab
3
(Najafabad Branch, Islamic Azad University)
Farhad Mesrinejad
4
(Department of Electrical Engineering, Tiran Branch, Islamic Azad University, Tiran, Isfahan, Iran)
الکلمات المفتاحية: Fuzzy controller, PID Controller, Wind turbine, Pitch Angle,
ملخص المقالة :
Wind energy is one of the fastest sources of renewable energy. Based on different characteristics of wind conditions, the performance of wind turbines can be optimized by adjusting the parameters of the control system. The nonlinearity of the system model and high external uncertainties have made the control of wind turbines an important and necessary study. Pitch angle control is one of the most important controllers in wind turbines. In this paper, the aim is to adjust the pitch angle of the variable speed wind turbine. Fuzzy logic is used to control the Pitch angle, first the fuzzy controller is used as the automatic Pitch angle regulator, and then it is used to adjust the coefficients of the three-term controller (PID controller or three-period controller). Finally, the simulation results are obtained using Matlab software. The results show that the best answers are in using fuzzy logic in setting three-term control coefficients.
1 International Journal of Smart Electrical Engineering, Vol.10, No.1, Winter 2021 ISSN: 2251-9246
EISSN: 2345-6221
pp. 1:6 |
Variable Speed Wind Turbine Pitch Angle Control Using Three-Term Fuzzy Controller
Ehsan Hosseini1,3, Ghazanfar Shahgholian*1,3, Homayoun Mahdavi-Nasab1,4, Farhad Mesrinejad*2
1Department of Electrical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran
2Department of Electrical Engineering, Tiran Branch, Islamic Azad University, Tiran, Isfahan, Iran
3Smart Microgrid Research Center, Najafabad Branch, Islamic Azad University, Najafabad, Iran
4Digital Processing and Machine Vision Research Center, Najafabad Branch, Islamic Azad University, Najafabad, Iran
Abstract
Wind energy is one of the fastest sources of renewable energy. Based on different characteristics of wind conditions, the performance of wind turbines can be optimized by adjusting the parameters of the control system. The nonlinearity of the system model and high external uncertainties have made the control of wind turbines an important and necessary study. Pitch angle control is one of the most important controllers in wind turbines. In this paper, the aim is to adjust the pitch angle of the variable speed wind turbine. Fuzzy logic is used to control the Pitch angle, first the fuzzy controller is used as the automatic Pitch angle regulator, and then it is used to adjust the coefficients of the three-term controller (PID controller or three-period controller). Finally, the simulation results are obtained using Matlab software. The results show that the best answers are in using fuzzy logic in setting three-term control coefficients.
Keywords: Wind Turbine, Fuzzy Controller, PID controller, Pitch Angle
Article history: Received 20-Apr-2021; Revised 01-May-2021; Accepted 15-May-2021.
© 2021 IAUCTB-IJSEE Science. All rights reserved
1. Introduction
Problems with fossil fuel pollution and depletion of energy sources have led to the expansion of the use of renewable energy in the production of electricity energy [1-3].
Wind energy is one of the main types of renewable energy [4-6]. This type of energy is geographically vast, scattered, and decentralized, and is almost always available [7.8]. Kinetic energy in wind turbines is converted into mechanical energy and then into electrical energy [9,10].
High maneuverability in operation (from a few watts to several megawatts) is one of the advantages of wind energy. Wind energy in addition to meeting part of the electricity demand, has other benefits, such as no need for wind turbines to fuel, diversify energy sources and create a sustainable energy system, no need for water and no environmental pollution [11-14].
The wind is oscillating and intermittent in nature and its wind is not constant. Half of the wind energy produced is generated in about 15% of the turbine's operating time, and a wind farm, like a fuel plant, does not produce sustainable energy [15,16].
Today, wind turbines play an important role in microgrids as sources of energy production [17-22]. The corresponding wind turbines can operate at both constant and variable speeds [23-25].
Various studies have been conducted on the application of wind energy and wind turbines [26-33].
A fuzzy logic-based pitch angle control strategy for variable speed wind turbine systems is presented in [34], in which the control input variables for the fuzzy logic controller are the power and output speed of the generator.
Microgrid load frequency control is proposed using model prediction controls in [35] so that the control of pitch angle of wind turbine generators and plug-in hybrid electric vehicles is coordinated. The simulation results show that this method is strong for changing system parameters compared to proportional and integral derivative controllers.
The performance of the stand-alone combined renewable energy system including three renewable energy sources, solar PV cells, wind turbines and fuel cells has been improved in [36] using an optimal PI controller for dynamic voltage restorer, which results in the application of the control method. In the system, by improving the voltage, current and power waveform for each source, improving the dynamic performance of the wind turbine generator and maintaining the continuous performance of three sources in fault conditions has been achieved.
The maximum power tracking method in the wind energy conversion system is proposed for the application of DC microgrids in [37], in which the induction generator operates in the self-excited state with the excitation capacitor in the stator. Also, a method for determining the duty ratio of dc-dc converter for the performance of the proposed system under MPPT conditions has been developed using wind turbine characteristics, steady state equivalent of induction generator and power balance in power converters, and the performance of the proposed algorithm for MPPT with results. Experimental with simulated values is shown.
The stability of a wind farm based on a dual-feed induction generator (DFIG) for variable wind speed power systems in strong and weak networks has been investigated in [38], which has the effect of power system stabilization (PSS) and static series synchronous compensator is analysed on the stability of the power system in the modified 14-bus IEEE test system.
A model for controlling the frequency of a wind farm connected to conventional units is presented in [39], in which a PID controller alerts the wind farm to power changes. Also, to improve the model performance, the defined frequency control parameters (in other words PID coefficients) are optimized based on a multi-objective function using a particle swarm optimization algorithm.
The problem of control the power capture of variable speed wind turbine systems with flexible shafts has been investigated in [40]. The purpose is to control the optimization of wind energy absorption by tracking the desired output power, and to compensate for errors caused by the steering filter and unknown control gains, a compensation dynamic is designed with compatible parameters.
One of the important issues in wind energy conversion systems is how to achieve the maximum output power of such systems at different wind speeds.
In this paper, the aim is to investigate the behavior of a wind turbine with a specific conversion function and the effect of the controller on the response of the wind turbine. First, the effects of three types of three-term controllers, in other words, proportional-integrator-derivative (PID) controller, are compared with each other. The coefficients of these controllers are adjusted using traditional methods. The fuzzy controller is then used to automatically adjust the angle. Finally, using this controller, the PID coefficients of the controller are adjusted. By changing the system input by one step, the results are compared to determine the fastest response at the output.
The remainder of this paper is organized as follows. Section 2 presents a brief overview of the wind turbine system model. The simulation results are presented in Section 3, and conclusions are drawn in Section 4.
2. Wind turbine system model
Wind energy is used as a sustainable energy. The kinetic energy of the wind is proportional to the square of the wind speed, and the strength of the wind is proportional to the cube of the wind speed. Therefore, with increasing wind speed, wind power will also increase.
The amount of power received by wind energy conversion systems from wind energy depends not only on the on-site wind characteristics but also on the control method used in wind energy conversion systems.
A. Wind energy conversion system
The wind energy conversion system can be illustrated by connecting several subsystems as shown in fig. 1, where Ft is the structural force that enters the tower. Also, shaft speed ωr, hub torque Tt, reaction torque Tg and PO show the consumer power, and β is the Pitch angle and βref is its reference value.
Fig. 1. Wind energy conversion system block diagram
B. Different work areas of wind speed
Wind speed is the determining factor of power reference, torque or turbine speed. Depending on the wind speed, the operation of the turbine can be divided into four general modes. Fig. 2 shows the mechanical output power of a wind turbine in terms of wind speed in four different regions.
Fig. 2. Wind turbine operating areas in terms of wind speed
C. Two-mass system
A simple structure of a rotating load motor drive system is shown in fig. 3. The system consists of a drive motor and once coupled to the motor via a shaft, where wM is the motor speed, wL is the loading speed and TS is the torsional torque of the shaft. The two input variables are motor torque (TM) and turbulent load torque (TL).
A two-mass model has been used in wind turbine modelling. As the Pitch’s rotate, the shaft connected to the gearbox rotates. Then, with the rotation of the gears, the rotor also starts to rotate in proportion to the gear ratio. By rotating the magnetic field generated by the coil, electrical energy is induced in the stator [41].
Fig. 3. Two-mass resonance system
D. Pitch angle control in wind turbine
The most common controller in variable speed wind turbines to get the desired output power is the Pitch angle controller [42,43]. Pitch angle control in wind turbines has a direct impact on machine dynamic performance and power system fluctuations. Wind turbines have a nonlinear and multivariate system, and it is important to design a controller that adapts to the system at all times.
The performance model shows the dynamic behavior between the angle demand (βd) of the controller and the amount taken from the Pitch angle (β). The differential equation of the Pitch angle changes is expressed as follows:
(1)
where the constant value of the Pitch angle actuator (Tβ) is calculated using the initial parameters of the wind turbine. In the Laplace area are:
(2)
The dynamic model of the modeled wind turbine system has been simulated in MATLAB software and a variety of controllers have been implemented to improve the output response.
E. PID controller
A proportional–integral–derivative (PID) controller or a three-period controller is a control loop mechanism that uses feedback [44,45]. This controller is widely used in industrial control applications and other systems that require continuous control to regulate pressure, flow, temperature, velocity and other process variables [46-48]. This controller continuously calculates the error value as the difference between the desired set point and the measured process variable and applies the necessary correction. There are several methods for tuning a PID loop [49,50].
2. Simulation results
The pitch angle in wind energy system is the angle at which a propeller, rotor, of turbine blade is set with respect to the plane of rotation. Pitch angle control is the most common means of adjusting the wind turbine aerodynamic torque. Pitch angles can have a significant effect on the power curve and turbine output [51-53].
In this section, the performance of three types of controllers to control the angle of the wind turbine blade is examined. The wind turbine parameters are given in table 1.
Table 1.
Wind turbine parameters
Value | Parameters |
1000 KW | Generator power rate |
1500 rpm | Generator speed rate |
20 rpm | Rotor turning speed |
35 m | The diameter of the blades |
0-90 degree | Reference angle of the pitch angle |
0.6 degree/sec | Rate angle change rate |
2 N.M/rad/sec | Damping coefficient |
0.75 N.M2 | Moment of inertia of the gearbox |
A. PID Fast controller
In this case, the transfer function of the PID controller is considered as follows:
(3)
The added component adds a degree of freedom to this controller compared to a normal PID, to achieve the appropriate phase limit.
In other words, it exerts its effect on the derivative gain in order to neutralize its effect in some moments or to increase its effect in moments.
Fig. 4 shows the blade angle control using this controller and a typical PID controller. The coefficients of this controller are determined using the Ziegrenickels test.
Fig. 4. Blade angle control using PID fast controller
B. PID Tuned controller
Therefore, different methods are proposed to optimize the PID controller coefficients. One of these methods is to add a time constant or add a zero and a pole.
The controller transfer function is considered as follows:
(4)
where N is the filter coefficient and Ts is the time constant. In this function, by adding more degree of freedom to the controller, to reach the appropriate phase limit, considering the frequency stability, it tries to improve the coefficients. This operation is set automatically by taking feedback from the system output until the controller responds optimally. The considered coefficients are:
Kp=0.35906198503477
ki=2
kd=0.00196
N=100
Fig. 5 shows the angle control of the turbine blade using the above controller along with the conventional controller. As can be seen, the superiority of the adjusted controller is noticeable, because it is stable without any arousal.
Also, the interest limit is 17.2 decibels or 1.3 radians per second and the phase limit is 72.6 degrees or 0.236 radians, which indicates good stability for the system.
Fig. 5. Blade angle control using PID tuned controller
C. Fuzzy controller
In fuzzy logic, based on human experience, rules are expressed as linguistic variables.
With the help of these rules and by applying this logic to power systems, much better results can be achieved than conventional controllers. For this reason, the application of fuzzy logic in the power system has been mentioned in various studies [54-59]. Using this controller, the coefficients in the PID controller can be adjusted. In fuzzy control the parameters are fixed. So this controller is not suitable in unbalanced weather conditions and momentary change in wind speed [60].
To solve this problem and also to ensure the optimal performance of the controller, a PID fuzzy regulator is used. Fig. 6 shows the block diagram of the PID fuzzy adjuster for controlling the wind turbine blade angle.
As can be seen, the control coefficients depending on the fuzzy inputs have been modified. The system inputs are the blade angle changes and its derivative changes.
The PID coefficients are added together with the coefficients obtained from the fuzzy controller and form the new parameters of the PID controller. By taking feedback from the output and comparing it to the current angle, the system is adjusted at the moment:
Fig. 6. Fuzzy PID adjuster to control wind turbine blade angle
Fig. 7. Overview of system simulation with fuzzy PID controller
Fig. 8. Comparison of results of wind turbine blade angle controllers
Table 2.
Comparison of results of wind turbine blade angle controllers
Fuzzy adaptive PID controller | Fuzzy controller | Tuned PID controller | Conventional PID controller | Time domain specification |
4.74 | 5.68 | 5.16 | 4.93 | Delay time (sec) |
4.07 | 6.37 | 6 | 3.07 | Rise time (sec) |
10.7 | 21.3 | 11 | 26 | Settling time(sec) |
0 | 0 | 0 | 12.46 % | Peak overshoot |
(5)
(6)
(7)
In designing this fuzzy controller, the multiplication inference motor, single fuzzy generator and intermediate center inertia generator have been used.
The block diagram of the blade angle control simulation using the fuzzy adjusted PID controller is shown in Fig. 7.
The behavior of wind turbine blade controllers is given in Table 2. Fig. 8 shows the result of simulating a wind turbine blade using controllers. Frequency domain changes are shown in Fig. 9.
Fig. 9. Comparison time for wind turbine blade controllers
Fig. 10. Frequency ranges for wind turbine blade controllers
1. Conclusions and suggestions
The fuzzy controller has more peak time and less sitting time than the PID controller, and there is no overshot. In the adjuster of PID coefficients with fuzzy controller, compared to the previous two controllers, the sitting time is less but its ascent time is not as good as the PID controller.
References
[1]. M. Moradian, A. Soltani-Mohammadi, A. "A new control system for a dual stator-winding cage rotor induction generator in direct grid connected condition with maximum power point tracking of wind turbine”, Journal of Intelligent Procedures in Electrical Technology, vol. 9, no. 35, pp. 3-10, Dec. 2019.
[2]. N.P. Yengijeh, H. Moradi CheshmehBeigi, A. Hajizadeh, "Inertia emulation with the concept of virtual supercapacitor for islanded dc microgrid", Proceeding of the IEEE/IWEC, pp. 1-4, Shahrood, Iran, May 2021.
[3]. G. Shahgholian, “A brief review on microgrids: Operation, applications, modeling, and control”, International Trans. on Electrical Energy Systems, vol. 31, no. 6, Artiacl Number. e12885, 2021.
[4]. , Structural control and vibration issues in wind turbines: A review”, Engineering Structures, Vol. 2101, Article 110087, May 2020.
[5]. H. Haggi, F. Hasanzad, M. Golkar, “Security-constrained unit commitment considering large-scale compressed air energy storage (CAES) integrated with wind power generation”, International Journal of Smart Electrical Engineering, vol. 6, no. 4), pp. 127-134, Autumn 2017.
[6]. M. Mahdavian, N. Behzadfar, “A review of wind energy conversion system and application of various induction generators”, Journal of Novel Researches on Electrical Power, vol. 8, no. 4, pp. 55-66, 2020.
[7]. S. Abrazeh, A. Parvaresh, S.-R. Mohseni, M.J. Zeitouni, M. Gheisarnejad, M.H. Khooban, "Nonsingular terminal sliding mode control with ultra-local model and single input interval type-2 fuzzy logic control for pitch control of wind turbines", IEEE/CAA Journal of Automatica Sinica, vol. 8, no. 3, pp. 690-700, March 2021.
[8]. T. Senjyu, R. Sakamoto, N. Urasaki, T. Funabashi, H. Fujita, H. Sekine, "Output power leveling of wind turbine generator for all operating regions by pitch angle control", IEEE Trans. on Energy Conversion, vol. 21, no. 2, pp. 467-475, June 2006.
[9]. E. Hosseini, G. Shahgholian, "Partial- or full-power production in WECS: A survey of control and structural strategies", European Power Electronics and Drives, vol. 27, no. 3, pp. 125-142, Dec. 2017.
[10]. , , “A state-of-the-art review on the vibration mitigation of wind turbines”, Renewable and Sustainable Energy Reviews, Vol. 121, Article 109710, April 2020.
[11]. M. Tavoosi, B. Fani, E. Adib, “Stability analysis and control of dfig based wind turbine using FBC strategy”, Journal of Intelligent Procedures in Electrical Technology, vol. 4, no. 15, pp. 31-42, December 2013.
[12]. M. Fardamiri, S. Moussavi, “A fuzzy controlled PWM current source inverter for wind energy conversion system”, International Journal of Smart Electrical Engineering, vol. 3, no. 2, pp. 107-112, 2014.
[13]. I. Zangiabadi, A. Etesami, “Power management of a wind energy conversion system equipped by DFIG”, Journal of Intelligent Procedures in Electrical Technology, vol. 7, no. 26, pp. 23-34, Sept. 2016.
[14]. A. Nagizadeh Ghoogdareh, A. Doroudi, M. Poormonfared Azimi, “Investigation of reactive power control effects on flicker and harmonics emission of a DFIG wind turbine”, Journal of Intelligent Procedures in Electrical Technology, vol. 3, no. 12, pp. 47-54, March 2013.
[15]. E. Hosseini, G. Shahgholian, "Different types of pitch angle control strategies used in wind turbine system applications", Journal of Renewable Energy and Environment, vol. 4, no. 1, pp. 20-35, Winter 2017.
[16]. O. Feizollahzade, “Investigate and improve the reliability of small size wind energy conversion systems connected to the network”, International Journal of Smart Electrical Engineering, vol. 9, no. 2), pp. 69-77, 2020.
[17]. P. Kou, D. Liang, L. Gao, F. Gao, "Stochastic coordination of plug-in electric vehicles and wind turbines in microgrid: a model predictive control approach", IEEE Trans. on Smart Grid, vol. 7, no. 3, pp. 1537-1551, May 2016.
[18]. E. Mohammadi, R. Rasoulinezhad, G. Moschopoulos, "Using a supercapacitor to mitigate battery microcycles due to wind shear and tower shadow effects in wind-diesel microgrids", IEEE Trans. on Smart Grid, vol. 11, no. 5, pp. 3677-3689, Sept. 2020.
[19]. G. Aghajani, D. Mirabbasi, B. Alfi, H. S. Hatami, “Demand side management in a smart micro-grid in the presence of renewable generation and demand response”, Journal of Intelligent Procedures in Electrical Technology, vol. 8, no. 30, pp. 55-70, Sept. 2017.
[20]. R. Engleitner, A. Nied, M.S.M. Cavalca, J.P. da Costa, "Dynamic analysis of small wind turbines frequency support capability in a low-power wind-diesel microgrid", IEEE Trans. on Industry Applications, vol. 54, no. 1, pp. 102-111, Jan.-Feb. 2018.
[21]. Q. Wang, S. Niu, T. W. Ching, "A new double-winding vernier permanent magnet wind power generator for hybrid ac/dc microgrid application", IEEE Trans. on Magnetics, vol. 54, no. 11, pp. 1-5, Nov. 2018.
[22]. , , , Q. Wu, X. Jiang, "State variable technique islanding detection using time-frequency energy analysis for DFIG wind turbine in microgrid system", ISA Transactions, vol. 80, pp. 360-370, Sept. 2018.
[23]. M. Yin, Z. Yang, Y. Xu, J. Liu, L. Zhou, Y. Zou, “Aerodynamic optimization for variable-speed wind turbines based on wind energy capture efficiency”, Applied Energy, vol. 221, pp. 508-521, July 2018.
[24]. M. Yin, Y. Xu, C. Shen, J. Liu, Z. Y. Dong and Y. Zou, "Turbine stability-constrained available wind power of variable speed wind turbines for active power control", IEEE Trans. on Power Systems, vol. 32, no. 3, pp. 2487-2488, May 2017.
[25]. P. Novak, T. Ekelund, I. Jovik, B. Schmidtbauer, "Modeling and control of variable-speed wind-turbine drive-system dynamics", IEEE Control Systems Magazine, vol. 15, no. 4, pp. 28-38, Aug. 1995.
[26]. E. Ansari Nezhad, M. Najafi, “Optimal and intelligent designing of stand-alone hybrid photovoltaic/wind/fuel cell system considering cost and deficit load demand probability, Case study for Iran (Bushehr City)”, Signal Processing and Renewable Energy, vol. 4, no. 2, pp. 87-106, 2020.
[27]. V. Asadi Rad, S.B. Mozafari, S. Soleymani Morchehkhorti, “The application three-phase to single-phase z-source matrix converter in wind turbine”, Journal of Intelligent Procedures in Electrical Technology, vol. 7, no. 28, pp. 27-34, March 2017.
[28]. J.E. Sierra-García, M. Santos, "Improving wind turbine pitch control by effective wind neuro-estimators", IEEE Access, vol. 9, pp. 10413-10425, 2021.
[29]. M. Abdollahi, M. Moazzami, “Day-ahead coordination of vehicle-to-grid operation and wind power in security constraints unit commitment (SCUC)”, Journal of Intelligent Procedures in Electrical Technology, vol. 6, no. 22, pp. 49-56, Sept. 2015.
[30]. H. Badihi, Y. Zhang, P. Pillay, S. Rakheja, "Fault-tolerant individual pitch control for load mitigation in wind turbines with actuator faults", IEEE Trans. on Industrial Electronics, vol. 68, no. 1, pp. 532-543, Jan. 2021.
[31]. R. Prasad, N.P. Padhy, "Synergistic frequency regulation control mechanism for DFIG wind turbines with optimal pitch dynamics", IEEE Trans. on Power Systems, vol. 35, no. 4, pp. 3181-3191, July 2020.
[32]. S. Jenab, B. Fani, H. Ghasvari, “Transient performance improvement of wind turbines with doubly fed induction generators using fractional order control strategy”, Journal of Intelligent Procedures in Electrical Technology, vol. 4, no. 16, pp. 17-28, March 2014.
[33]. A. Hamidi, J. Beiza, T. Abedinzade, A. Daghigh, “Improving the dynamic stability of power grids including offshore wind farms and equipped with HVDC transmission system using adaptive neural controller”, Journal of Intelligent Procedures in Electrical Technology, vol. 11, no. 42, pp. 79-99, Sept. 2020.
[34]. T.L. Van, T.H. Nguyen, D. Lee, "Advanced pitch angle control based on fuzzy logic for variable-speed wind turbine systems", IEEE Transa. on Energy Conversion, vol. 30, no. 2, pp. 578-587, June 2015.
[35]. J. Pahasa, I. Ngamroo, "Coordinated control of wind turbine blade pitch angle and PHEVs using MPCs for load frequency control of microgrid", IEEE Systems Journal, vol. 10, no. 1, pp. 97-105, March 2016.
[36]. M. O. A. El-Raouf, M. I. Mosaad, M. A. Al-Ahmar, A. l. Mallawany, F. M. El Bendary, “Optimal PI controller of DVR to enhance the performance of hybrid power system feeding a remote area in Egypt”, Sustainable Cities and Society, vol. 47, Article Number: 101469, May 2019.
[37]. V. Nayanar, N. Kumaresan, N. Ammasai-Gounden, "A single-sensor-based MPPT controller for wind-driven induction generators supplying dc microgrid", IEEE Trans. on Power Electronics, vol. 31, no. 2, pp. 1161-1172, Feb. 2016.
[38]. J. Bhukya, V. Mahajan, "Optimization of damping controller for PSS and SSSC to improve stability of interconnected system with DFIG based wind farm", International Journal of Electrical Power and Energy Systems, vol. 108, pp. 314-335, June 2019.
[39]. V. Gholamrezaie, M.G. Dozein, H. Monsef, B. Wu, "An optimal frequency control method through a dynamic load frequency control (LFC) model incorporating wind farm", IEEE Systems Journal, vol. 12, no. 1, pp. 392-401, March 2018.
[40]. M. Huang, L. Tao, Z. Hu, "Command filter adaptive power capture control based on fuzzy rules emulated networks for variable speed wind turbines with flexible shaft", IEEE Access, vol. 9, pp. 91377-91386, April 2021.
[42]. X. Tang, M. Yin, C. Shen, Y. Xu, Z.Y. Dong, Y. Zou, "Active power control of wind turbine generators via coordinated rotor speed and pitch angle regulation", IEEE Trans. on Sustainable Energy, vol. 10, no. 2, pp. 822-832, April 2019.
[43]. R.R. Londero, C.M. Affonso, J.P.A. Vieira, "Effects of operational limits of DFIG wind turbines on long-term voltage stability studies", Electric Power Systems Research, v, pp. 134–140, Jan. 2017.
[44]. M. Lotfi-Forushani, B. Karimi, G. Shahgholian, “Optimal PID controller tuning for multivariable aircraft longitudinal autopilot based on particle swarm optimization algorithm”, Journal of Intelligent Procedures in Electrical Technology, vol. 3, no. 9, pp. 41-50, June 2012.
[45]. R. Shahedi, K. Sabahi, M. Tayana, A. Hajizadeh, “Self-tuning fuzzy PID controller for load frequency control in ac micro-grid with considering of input delay”, Journal of Intelligent Procedures in Electrical Technology, vol. 9, no. 35, pp. 19-26, December 2019.
[46]. H. Habibi, H. Rahimi Nohooji, I. Howard, "Adaptive PID control of wind turbines for power regulation with unknown control direction and actuator faults", IEEE Access, vol. 6, pp. 37464-37479, 2018.
[47]. H. Ren, B. Hou, G. Zhou, L. Shen, C. Wei, Q. Li, "Variable pitch active disturbance rejection control of wind turbines based on bp neural network PID", IEEE Access, vol. 8, pp. 71782-71797, 2020.
[48]. M. Safaei, S. Hosseinia, M. Hosseini Toodeshki, “A general method for designing fractional order PID controller”, Journal of Intelligent Procedures in Electrical Technology, vol. 3, no. 12, pp. 25-34, March 2013.
[49]. N. Taheri, H. Orojlo, F. Ebrahimi, "Damping controller design in offshore wind power plants to improve power system stability using fractional order PID controllers based on optimized exchange market algorithm", Journal of Intelligent Procedures in Electrical Technology, vol. 13, no. 51, pp. 91-110, Dec. 2022.
[50]. R. Shahedi, K. Sabahi, M. Tayana, A. Hajizadeh, “Self-tuning fuzzy PID controller for load frequency control in ac micro-grid with considering of input delay”, Journal of Intelligent Procedures in Electrical Technology, Vol. 9, No. 35, pp. 19-26, Dec. 2019.
[51]. J. Zhang, M. Cheng, Z. Chen, X. Fu, "Pitch angle control for variable speed wind turbines", Proceeding of the IEEE/DRPT, pp. 2691-2696, Nanjing, China, April 2008.
[52]. D. Palejiya, D. Chen, "Performance improvements of switching control for wind turbines", IEEE Trans. on Sustainable Energy, vol. 7, no. 2, pp. 526-534, April 2016.
[53]. P. Chen, D. Han, F. Tan, J. Wang, "Reinforcement-based robust variable pitch control of wind turbines", IEEE Access, vol. 8, pp. 20493-20502, 2020.
[54]. M. Rahmani, F. Faghihi, H. Moradi-Cheshmeh-Beigi, S. Hosseini, “Frequency control of islanded microgrids based on fuzzy cooperative and influence of STATCOM on frequency of microgrids”, Journal of Renewable Energy and Environment, vol. 5, no. 4, pp. 27-33, 2018.
[55]. M. Abbasi, M. Nafar, M. Simab, "Management and control of microgrids connected to three-phase network with the approach of activating current limitation under unbalanced errors using fuzzy intelligent method with the presence of battery, wind, photovoltaic and diesel sources", Journal of Intelligent Procedures in Electrical Technology, vol. 13, no. 49, pp. 59-71, June 2022.
[56]. H. Moradi CheshmehBeigi, A. Mohamadi, “Torque ripple minimization in srm based on advanced torque sharing function modified by genetic algorithm combined with fuzzy PSO”, International Journal of Industrial Electronics Control and Optimization, vol. 1, no. 1, pp. 71-80, Spring 2018.
[57]. A. Shoulaie, M. Bayati-Poudeh, G. Shahgholian, “Damping torsional torques in turbine-generator shaft by novel PSS based on genetic algorithm and fuzzy logic”, Journal of Intelligent Procedures in Electrical Technology, vol. 1, no. 2, pp. 3-10, Sept. 2010.
[58]. H. Ghorbani, R. Kardehi Moghaddam, S. Razavi, “Regulating the output voltage of buck-boost converters using general type2 fuzzy controller”, Signal Processing and Renewable Energy, vol. 4, no. 2, pp. 37-51, 2020.
[59]. R. Zamani, M. Siahi, A. Ramezani, “Robust type-2 fuzzy control for glucose-level regulation in type-i diabetic patients”, International Journal of Smart Electrical Engineering, vol. 10, no. 2, pp. 87-94, 2021.
[60]. V. Calderaro, C. Cecati, A. Piccolo, P. Siano, “Adaptive fuzzy control for variable speed wind systems with synchronous generator and full scale converter”, Wind Power Systems. Green Energy and Technology, vol 0, pp. 337-388, Springer, Berlin, Heidelberg, 2010.
