Using a combination of four different strategies to increase the quality of current and power produced by multi-rotor wind turbine systems

Abstract

Using conventional controls often leads to undesirable results in the power and current quality of wind-based energy systems. To overcome the problem of low power/current quality, a combination of control strategies is an effective and convenient solution. In this study, it was proposed to combine the proportional-derivative regulator, proportional-integral regulator, super-twisting control, and fractional calculus to obtain a new controller characterized by high durability and distinctive performance. This proposed controller replaces traditional controllers for indirect fielded-oriented control of a doubly-fed induction generator. In this proposed approach, the pulse width modulation strategy was used to control the operation of the machine inverter. The proposed approach increases performance, and durability, and improves dynamic response to power. The proposed approach was used to control the generator inverter only to show how effective and efficient it is in improving the quality of power and current without resorting to controlling the grid inverter. This proposed strategy was implemented using MATLAB, where the effectiveness of the control strategy is evaluated under variable wind conditions and parameter changes, with the results compared to the traditional approach and some related work. The comparison with the conventional approach shows that the proposed approach reduces the total harmonic distortion of current by 97.24% and 91.81%. The simulation results show that the proposed approach significantly outperforms traditional control in terms of power and current quality, as active power ripples were reduced by 99.98% and 89.93%, current ripples were reduced by 99.74% and 99.38%, and reactive power ripples were reduced by 99.97% and 60.85%. Also, the proposed approach improves the steady-state error value by 96.85% and 99.98% for active power and by 67.55% and 96.59% for reactive power. These reduction ratios highlight the superiority and effectiveness of the proposed approach in improving the properties of the studied energy system, which makes it of interest in other industrial applications.

Introduction

Background

Renewable energy (RE) has become a widespread aspect of electricity generation, as several governments around the world use renewable sources such as solar energy, ¹ hydropower, and wind energy (WE) ² to provide energy and reduce the phenomenon of global warming. Also, these renewable sources, especially WE, contribute to overcoming the problem of the increasing demand for electrical energy (EE). According to the work done in Ref., ³ the economic emission transmission problem of electric power systems can be considered as one of the most popular multi-objective constrained optimization problems to minimize cost and emissions. On the other hand, power grids in remote areas often exhibit the characteristics of high inverter-fed power penetration, low grid power, poor maintenance forces, and high natural disaster risks. Therefore, enhancing the integrity and resilience of the vulnerable grid in remote areas is crucial for the long-term operation and expansion of the overall power system. ⁴ Although many approaches have been presented to deal with the power system problem, it is still a challenging problem especially when more and more renewable energy sources such as wind and solar are integrated into the system due to their intermittency and uncertainty. Using WE to generate electricity has many potential benefits; including reducing the use of traditional sources such as diesel, but there is growing concern about its use. Research indicates that the use of energy systems based on conventional wind turbines is associated with a range of negative consequences on the grid, including disruptions to power generation, especially in the case of weather disturbances such as strong winds. As is known, the resulting EE is closely related to the change in wind speed (WS). ⁵ Predicting WS is considered one of the most prominent challenges hindering energy systems based on WE. The author believes ⁶ that accurate and continuous prediction of WS leads to optimal operation and management of energy systems. According to the work done in Ref., ⁷ to obtain sufficient EE, giant turbines must be used, which allows for an increase in the costs and complexity of implementing these systems. Also, the quality of power and current are among the most prominent drawbacks of these energy systems, as this is due to the use of control strategies that are less effective and efficient. In addition, the use of some generators does not give satisfactory results in terms of the total costs of the system and the case of variable WSs. Choosing the right generator is extremely important. In this paper, the use of a double-fed induction generator (DFIG) has been chosen for the efficient generation of WE. This generator was relied upon due to its many characteristics mentioned in works.^8,9

Despite these negatives, the use of these turbine-based energy systems has positive effects on the environment and energy supply. These energy systems contribute significantly to increasing energy production and reducing production and consumption costs, which makes these energy systems useful, especially in remote and isolated areas. Given the pros and cons that characterize these energy systems, it is important to gain a better understanding of the mechanisms behind these effects. This study aims to use a new strategy to increase the effectiveness and efficiency of the energy system based on wind turbines, with a special focus on the quality of power and current. By using this proposed approach, we hope to reduce the drawbacks of energy systems and enhance durability.

Literature review

In the field of control, the strategies that have been proposed to control power can be classified into linear strategies, nonlinear strategies, intelligent strategies, and hybrid strategies. These strategies differ in terms of principle, performance, ease of implementation, durability, and ease of adjusting the dynamic response to power. Table 1 represents information about the most prominent strategies that have been used to control DFIG capabilities. In this table, the pros and cons of the control strategies used are given, along with the type of control used in the inverter.

Table 1.

Control technique of DFIG.

Ref.	Generator capacity	Turbine type	Control type	Controller used	Inverter control	Positives	Cons
Pura andIwański 10	2 MW	Single-rotor windturbine (SRWT)	Direct powercontrol (DPC)	Hysteresiscomparators (HCs)	Switching table (ST)	Simplicity Fast dynamic response Ease of completion Low cost	Energy ripples High total harmonic distortion (THD) of current Use capacity estimation Low robustness
Benbouhenniand Bizon 11	1.5 MW	Multi-rotor windturbine (MRWT)	Vector control (VC)	Proportional-integral(PI) regulator	Pulse widthmodulation (PWM)	Better response to suddenload changes as well as greatlyimproved torque at low speeds Better speed holding Not expensive	Current/power ripples Complexity Use the mathematical model High THD value of current Use capacity estimation Low durability
Sahri et al. 12	7.5 kW	SRWT	Direct torquecontrol (DTC)	HCs	ST	Fast dynamic response Simplicity Ease of completion Low cost	Energy ripples High THD value of current Use capacity estimation Low torque value at low speeds. Low robustness
Omaç and Erdem 13	Experimental: 350 W Simulation: 2.5 MW	SRWT	Field-orientedcontrol (FOC)	PI controller	PWM	Higher top speed Often just as importantly Higher machine drive efficiency Low-cost implementation	Current/power ripples Complexity Use the mathematical model High THD value of current Use capacity estimation Low robustness
Shiravani et al. 14	7.5 kW	SRWT	Predictivecontrol (PC)	PC controller	PWM	Durability Efficiency High performance	Current/power ripples Complexity Use the mathematical model High THD value of current Use power estimation Low durability
Mohamed et al. 15	1.5 MW	SRWT	Backsteppingcontrol (BC)	BC controller	PWM	Durability High performance Efficiency	Current/power ripples Complexity Use the mathematical model High THD value of current There is a significant number of gains Use power estimation Low durability
Zhang et al. 16	2 MW	SRWT	Sliding modecontrol (SMC)	SMC controllers	PWM	Durability High performance Efficiency	Complexity Use the mathematical model Current/energy ripples High THD value of current Use capacity estimation The phenomenon of chattering Low durability

This table gives a clear picture of some of the strategies used to control DFIG, as it is noted that power ripples, the THD value of current, the use of DFIG parameters, and low robustness are among the most prominent control drawbacks found in WE generation systems. To overcome the shortcomings of control strategies, several solutions have been proposed. Most of the solutions that were proposed included adding other strategies to traditional strategies, such as the use of genetic algorithms (GAs), fuzzy logic (FL) techniques, and neural networks (NNs). Table 2 represents the most prominent proposed works that used smart strategies, where the positives and negatives of each approach are mentioned.

Table 2.

Improved control technique of DFIG.

Ref.	Type of study	Generator capacity	Target strategy	The type of strategy usedto improve performance	Inverter control	Positives	Cons
Chojaa et al. 17	1.5 kW	SRWT	DPC technique	NNs	Neural switchingtable	Simplicity Fast dynamic response Ease of completion Low cost	Energy ripples High THD of current Use power estimation Low robustness
Amraneand Chaiba 18	4 kw	SRWT	FOC technique	NNs-FLalgorithm	PWM technique	Dynamic performance is well improved Reducing power/current ripples Reduce the THD value of current Increased durability	Current/energy ripples Complexity Use the mathematical model High THD value of current Use capacity estimation Low durability
Boudjemaet al. 19	1.5 MW	SRWT	DTC technique	Super twistingcontrol (STC)	ST	Fast dynamic response Simplicity Ease of completion Low cost	Energy ripples High THD value of current Use capacity estimation Low torque value at low speeds. Low robustness
Labdai et al. 20	7.5 kW	SRWT	SMC control	FL technique	PWM	Higher top speed Often just as importantly Higher machine drive efficiency Low-cost implementation	Current/power ripples Complexity Use the mathematical model High THD value of current Use capacity estimation Low durability
Xiong and Sun 21	2 MW	SRWT	DPC technique	BC	PWM	Durability Efficiency High performance	Current/power ripples Complexity Use the mathematical model High THD value of current Use capacity estimation Low durability
Benbouhenniand Bizon 22	1.5 MW	MRWT	VC technique	Third-orderSMC technique	PWM	Durability High performance Efficiency	Current/power ripples Complexity Use the mathematical model High THD value of current There is a significant number of gains Use capacity estimation Low durability
Xiong et al. 23	Simulation: 2 MW Experimental: 2 kW	SRWT	DPCtechnique	SMC controllers	PWM	Durability High performance Efficiency	Complexity Use the mathematical model Current/power ripples High THD value of current Use capacity estimation The phenomenon of chattering Low durability
Kadi et al. 24	7.5 kW	SRWT	VC technique	Modified SMC	PWM technique	Durability Efficiency Simplicity High effectiveness	Estimating capabilities Energy ripples cannot be completely eliminated Using the mathematical model of the machine Affected by parameter changes Current quality

Among the most prominent nonlinear strategies that provide high performance, fractional-order control can be mentioned. This strategy is characterized by simplicity and high performance compared to many other strategies. ²⁵ Fractional-order control has greater design flexibility with randomized selections of fractional-order control and stronger robustness. Fractional order control has a wide range of applications in various fields such as renewable energies ²⁶ and control of electrical machines. ²⁷ According to the work done in Ref., ²⁸ using fractional-order control does not require knowledge of the mathematical model of the studied system precisely, which gives it high performance if the parameters of this system change. In Ref., ²⁹ it was proposed to use fractional-order control to improve the characteristics of the proportional tilt integral derivative plus one controller. The resulting controller is characterized by high performance and great robustness. Another application of the approach was proposed in, ³⁰ where a cascade fractional-order fuzzy proportional integral derivative-integral double derivative controller was used to improve the characteristics of tidal turbines. High durability and great efficiency are among the most prominent features of this controller. In Ref., ³¹ it is proposed to use a cascade combination of fractional order-based integral derivative and proportional integral derivative with a filter to control the multi-microgrid system. This proposed controller was compared with other controllers such as fractional-order integral derivative controller and proportional-integral derivative controller (PID). The simulation results showed that the proposed controller is superior to other controllers in terms of improving the characteristics of the multi-microgrid system. To improve the power quality of a network, it was proposed in Ref. ³² to combine fractional-order control and the FL technique. The use of the fractional-order FL control technique allows to significant improvement in the power quality compared to the traditional approach. This proposed strategy depends heavily on the number of FL technique rules used. Also, the proposed strategy improves the steady-state and transient performance of the solar-wind-grid integrated system. In Ref., ³³ it was proposed to use a fractional-order proportional-integral controller based on the grey wolf optimization algorithm to control the powers of the DFIG. This proposed strategy is characterized by simplicity, ease of implementation, and quick dynamic response. The simulation results showed that this proposed approach reduces the THD value by an estimated 70.59% compared to the PI control. Also, the proposed approach reduces the values of steady-state error (SSE), rise time, and settling time by percentages estimated at 100%, 91.40%, and 35.63%, respectively, compared to the PI approach. A simple dual-mode fractional order controller (SDMFOPI) tuned using a sine cosine optimization algorithm has been proposed to control the three-area hybrid power system. ³⁴ This studied energy system uses a storage system. The performance and efficiency of the SDMFOPI controller are compared with both PI, sine cosine optimization algorithm-based fractional-order proportional-integral controller, and sine cosine optimization algorithm-based dual-mode proportional-integral controller. The completed comparison showed that the proposed controller based on the sine cosine optimization algorithm significantly improves the values of settling time, overshoot, and undershoot compared to other controllers. The disadvantage of the proposed controller lies in the presence of a significant number of gains and complexity. In Ref., ³⁵ it was proposed to use a degrees of freedom-based fractional-order cascaded controller incorporating with derivative filter (N) to control an energy system consisting of as thermal unit, hydro unit, wind unit, diesel unit, and photovoltaic unit. This controller has been compared with different controllers such as PID controller in terms of time response and overshoot reduction. The simulation results showed the superiority of this proposed controller and its great ability to improve the value of undershoot, rise time, and settling time compared to other controllers. Despite the results obtained, the complexity and presence of a large number of gains are among the most prominent drawbacks that limit the use of this controller in other industrial applications. According to the work done in Ref., ³⁶ the main objectives of control are maximum power point tracking (MPPT) in the low WS region and WT protection in the high WS region using pitch angle control. Therefore, it is necessary to create an MPPT strategy characterized by high performance and great durability. Therefore, it was proposed to use an MPPT strategy based on a fractional-order PID controller to control wind turbines. Using this strategy allows for determining the reference value for the active power, which makes the current, power, and torque related to the shape of the WS change. This proposed strategy was compared with the strategy based on the PI controller, and MATLAB was used to implement this comparison. Simulation results showed the superiority of the proposed approach over the traditional approach in terms of response, overshoots, and indices performance. According to the work done in Ref., ³⁷ frequency and voltage are among the most important indicators in small AC networks. Therefore, the stability of the grid frequency and bus voltage must be maintained. A distributed secondary control scheme based on binomial smoothing is proposed for frequency recovery, average voltage recovery, and active and reactive power sharing between DGs in AC groups subject to irregular communication delays and actuator saturation. A state transformation-based strategy is designed under the prior information of control inputs to deal with irregular delays, which can completely mitigate the harmful effects of communication delay. In addition, a hyperbolic tangent function is introduced to approximate the non-smooth saturation function, and a time-invariant anti-saturation controller is designed, which can alleviate the effect caused by engine saturation. Also, the constant time stability of the closed-loop control system with motor saturation constraint is demonstrated. This proposed energy system was tested using MATLAB and the results were compared with other existing methods. The simulation and comparison results reveal the validity, robustness, and flexibility of the proposed method in recovering AC network frequency/average bus voltage and achieving accurate active/reactive power sharing.

In recent years, other new control strategies have been proposed that rely on combining different strategies, such as combining two or three different nonlinear strategies to obtain distinctive performance and significantly increasing robustness. Using a combination of several strategies to control DFIG reduces EE ripples and improves the quality of the current significantly, which is shown by reducing the THD value. In Table 3, most of the works that adopted the combination of several different strategies as a suitable solution are listed, where it is noted that modifications of different strategies such as the DPC strategy and FOC technique have been used. Therefore, the proposed solutions are always modifications of the traditional strategies and an attempt to add modifications to them, as these modifications sometimes lead to undesirable complexity. From the observation of Table 3, the use of merging creates several different negatives, as the most prominent negatives of the strategies resulting from merging are the high degree of complexity, the presence of a significant number of gains, which makes it difficult to control the dynamic response, the difficulty of implementation, and the high cost of implementation. However, looking at the results of these scientific works, it is noted that the results were excellent. Therefore, using a combination of different controls remains a reliable solution to overcome the drawbacks of low durability, current quality, and energy ripples.

Table 3.

Combined control strategies to improve the performance of DFIG.

Ref.	Type of study	Generator capacity	Target strategy	Strategies used in merging	Invertercontrol	Positives	Cons
Echiheb et al. 38	Simulation	10 kW	DPC technique	BC SMC	PWM	Outstanding performance High durability Reducing energy ripples Fast dynamic response	Complexity Difficulty of completion Having a significant number of gains Estimating capabilities Relying on the mathematical model of the machine
Benbouhenni 39	Simulation	1.5 MW	DPC technique	Third-order SMC NNs	PWM	Reducing energy ripples Fast dynamic response Robustness Reducing THD value of current	Estimating capabilities Reduced durability in the event of a malfunctions Number of interior layers needed Number of neurons in each layer Learning algorithm Relatively high degree of complexity
Habib 40	Simulation	1.5 MW	DTC technique	STA technique NNs	Modified spacevectormodulationtechnique	Minimizing torque/flux ripples Fast dynamic response Robustness Minimizing THD value of current	Estimating torque and flux Reduced durability in the event of a malfunctions Learning algorithm Number of interior layers needed Number of neurons in each layer Relatively high degree of complexity
Benbouhenni et al. 41	Simulation	1.5 MW	DPC technique	PI controller GAs Synergeticcontrol (SC)	PWM	Simplicity Ease of completion High durability Outstanding performance Reducing energy ripples Increasing the quality of the current	Estimating capabilities Reduced durability in the event of a change in the machine parameters The problem of power and current quality remains
Benbouhenniet al. 42	Simulation	1.5 MW	DPC technique	PI controller Terminal sliding mode technique GAs	PWM	Simplicity High durability Outstanding performance Reducing energy ripples Ease of completion Minimizing the THD value of current	Reduced durability in the event of a change in the machine parameters Estimating powers The problem of power and current quality remains
Gasmi et al. 43	Simulation	2 MW	DPC technique	STC technique Fractional-ordercontrol PI controller Particle swarm optimization (PSO)	PWM	High durability Outstanding performance Reducing energy ripples Ease of completion Minimizing the THD value of current	Complexity Difficulty of completion Having a large number of gains Estimating capabilities Reduced durability if DFIG parameters change.
Gasmi et al. 44	Simulation	2.4 MW Turbine type:single-rotor wind turbine	Indirect FOC technique	STC technique PSO	PWM	Reducing energy ripples Increased durability Reduce the THD value Improved dynamic response	Complexity Having a significant number of gains Estimating capabilities Difficulty of completion Its reliance on the mathematical model of the DFIG.
Benbouhenniet al. 45	Simulation	1.5 MW	DPC technique	NNs Fractional-ordercontrol	PWM	Precision It depends greatly on experience Simplicity Ease of completion Reducing energy ripples Reduce the THD of current Increased durability Significantly improve system performance	Estimating capabilities Having a significant number of gains Number of interior layers needed Number of nerve cells needed There is no mathematical rule to determine the number of the number of internal layers Control is affected by changes in DFIG parameters
Benbouhenniet al. 46	Simulation	1.5 MW	DPC technique	Fractional-order control FL	PWM		Number of FL rules needed There is no mathematical rule to determine the number of FL rules Control is affected by changes in DFIG parameters

Research gap and motivation

Although there have been a significant number of control strategies proposed in the field of DFIG control, several critical challenges remain. Most scientific research focuses on trying to create new controls that have high capabilities to control capabilities. These new strategies often use a mathematical model of the system under study. In addition, while simple strategies such as STC technique, PI regulator, and proportional derivative (PD) controller have been applied for power control, they often suffer from limitations such as high THD of current and low robustness when a fault occurs in the studied system. These defects create several unwanted problems at the network level and limit the spread of these energy systems. Another gap lies in the lack of control strategies that can significantly improve dynamic response and reduce power ripples. The combination of the two strategies showed promising results in improving durability, increasing power quality, and response time. The application of combining different strategies is still unexplored, as more than two strategies can be combined to obtain a new approach that has high robustness, especially under nonlinear operating conditions and different system parameters. Motivated by these shortcomings, this paper presents an integration of four different strategies for controlling the generated power present in a multi-wind turbine power system. This proposed approach aims to enhance the robustness of the studied energy system, overcome the problems of traditional strategies such as FOC, enhance system stability, and increase reliability by addressing the above-mentioned challenges. Also, providing superior performance compared to traditional strategy and related businesses. The study evaluates the efficiency and effectiveness of the proposed approach using several different tests in terms of improving the quality of power and current while highlighting the possibility of its application in other fields.

Challenges

Combining strategies as a solution is very efficient in reducing power ripples and reducing the THD of the current. In addition to increasing the robustness of the system and improving performance effectively compared to traditional strategies. But in some cases, the combination results in undesirable negative effects, as in the case of combining BC and SMC increases the degree of complexity, and the number of gains, requires a modification of the mathematical model of the machine, and raises the difficulty in performance. One of the challenges faced in this work is how to choose strategies that can be combined to obtain good results and maintain simplicity and ease of completion as much as possible. Moreover, reducing the number of gains and making the proposed control independent of system parameters is the second challenge faced in controlling DFIG.

Contribution

Therefore, four different strategies were chosen to obtain a new control characterized by high durability and distinctive performance. It was proposed to use fractional calculus, PD regulator, STA technique, and PI to obtain the proposed control. All of these strategies are characterized by simplicity, ease of adjustment, ease of implementation, not related to the mathematical model of the machine, and low cost, which makes the resulting control characterized by less complexity and greater robustness. So the main contribution of the paper can be identified as proposing a new nonlinear controller represented by the fractional-order PIPD super-twisting algorithm (FOPIPD-STA). This controller is used to improve the characteristics of the FOC, as the proposed control is considered the second contribution of the paper. Accordingly, the resulting control (FOC-FOPIPD-STA) is a control that differs from the FOC and several other works in terms of robustness, performance, and degree of complexity. MATLAB was used to implement this control, and it was applied to a 1.5 MW DFIG. In addition to using variable WS to complete the study. Several objectives were achieved from this completed study, which can be identified in the following points:

• Improving the performance and robustness of the FOC of DFIG.

• Overcoming the defects and problems of the PI controller.

• Underestimating the THD of current.

• Reducing steady-state error (SSE) and overshooting DFIG energy.

Paper organization

The work completed was divided into six different sections. In Section 2, the proposed system for generating energy from wind was discussed, where a model of both the turbine and the generator was given. The proposed controller is shown in Section 3. In Section 4, the proposed control for the RSC of DFIG was discussed, mentioning the pros and cons. The simulation results obtained are listed in Section 5, where several tests were used to study the characteristics of the FOC-FOPIPD-STA. Finally, the paper is concluded with the conclusions Section, where all the results obtained from this work were extracted.

Proposed energy system

In this section, the energy system proposed in this work is discussed, which is based on the use of WE as a source of EE generation. The studied energy system aims to reduce the emission of toxic gases and reduce the cost of producing EE. Also, reducing the use of traditional energy sources in generating EE and thus reducing the severity of global warming. In this section, the energy system proposed in this work is discussed, which is based on the use of WE as a source of EE generation. The studied energy system aims to reduce the emission of toxic gases and reduce the cost of producing EE. Also, reducing the use of traditional energy sources in generating EE and thus reducing the severity of global warming. The studied energy system is based on the use of multi-rotor turbines (MRWTs). This proposed system is characterized by simplicity, lower costs, and ease of implementation. The most prominent basic components of this studied energy system can be mentioned: MRWT, DFIG, and two inverters. In addition to these components, it is proposed to use a new control strategy, as the control strategy is considered one of the priorities that must be paid attention to because it is largely responsible for power quality. Figure 1 represents the system proposed for the study and used to generate EE from a renewable source, namely WE.

Figure 1.

The proposed power system.

To implement this proposed system, the mathematical model of its basic components must be known. These models are necessary to implement the system in MATLAB. In the next subsection, the mathematical modeling of the generator used to generate electrical power is discussed.

DFIG model

In this work, a DFIG generator was used to convert mechanical energy into electrical current. As is known, DFIG is considered among the suitable instruments in the case of variable WS due to its many advantages mentioned in Refs.^47,48 This generator is easy to control and any strategy can be applied easily, making it suitable for this work. The Park transform is used to provide a mathematical model for this generator. ⁴⁹ This modeling is an equation that expresses the mechanical and electrical parts of the DFIG. Using these equations, DFIG can be implemented in MATLAB. Depending on the work done in Ref., ⁵⁰ the mechanical part of the machine is expressed by equation (1). This equation gives the speed development of the machine in terms of torque. Through this equation, the operation of the DFIG, whether the engine or the generator is controlled.

$$T_e-T_r=J\frac{d\mathrm{\Omega }}{\mathrm{dt}}+f\mathrm{\Omega }$$

(1)

The expression for torque is represented in equation (2), where its value relates to flux and current. ⁵¹

$$T_e=1.5p\frac{M}{L_s}(-{\Psi }_{\mathrm{sd}}{I}_{\mathrm{rq}}+{\Psi }_{\mathrm{sq}}{I}_{\mathrm{rd}})$$

(2)

The flux is generated as a result of the current passing through the machine’s coils, where its value is related to both the intensity of the current and the values of the coils. Equation (3) expresses the flux depending on the machine currents. ⁵²

$$\{\begin{array}{c}{\Psi }_{\mathrm{dr}}=M{I}_{\mathrm{ds}}+L_r{I}_{\mathrm{dr}}\hfill \\ \multicolumn{1}{c}{{\Psi }_{\mathrm{qr}}=L_r{I}_{\mathrm{qr}}+M{I}_{\mathrm{qs}}}\\ \multicolumn{1}{c}{{\Psi }_{\mathrm{qs}}=M{I}_{\mathrm{qr}}+L_s{I}_{\mathrm{qs}}}\\ \multicolumn{1}{c}{{\Psi }_{\mathrm{ds}}=M{I}_{\mathrm{dr}}+L_s{I}_{\mathrm{ds}}}\end{array}$$

(3)

DFIG converts energy gained from the wind into voltage, and this voltage generates flux in the inductances. Equation (4) represents the relationship between flux and voltage. ⁵³

$$\{\begin{array}{c}\multicolumn{1}{c}{V_{\mathrm{dr}}=R_r{I}_{\mathrm{dr}}+\frac{d}{\mathrm{dt}}{\Psi }_{\mathrm{dr}}-w_r{\Psi }_{\mathrm{qr}}}\\ \multicolumn{1}{c}{V_{\mathrm{qr}}=R_r{I}_{\mathrm{qr}}+\frac{d}{\mathrm{dt}}{\Psi }_{\mathrm{qr}}+w_r{\Psi }_{\mathrm{dr}}}\\ \multicolumn{1}{c}{V_{\mathrm{qs}}=R_s{I}_{\mathrm{qs}}+\frac{d}{\mathrm{dt}}{\Psi }_{\mathrm{qs}}+w_s{\Psi }_{\mathrm{ds}}}\\ \multicolumn{1}{c}{V_{\mathrm{ds}}=R_s{I}_{\mathrm{ds}}+\frac{d}{\mathrm{dt}}{\Psi }_{\mathrm{sd}}-w_s{\Psi }_{\mathrm{qs}}}\end{array}$$

(4)

This generator needs mechanical energy to produce current. This mechanical energy is generated from wind using MRWT turbines. In the next subsection, the modeling of this turbine is discussed.

MRWT model

In the field of renewable energy, the MRWT turbine is a new technology that has been proposed to overcome the disadvantages of conventional turbines. This turbine is different from ordinary turbines, as several turbines are used in one turbine. ⁵⁴ This method aims to increase the energy gained from the wind. The use of these turbines allows for reducing the severity of the global warming phenomenon and the high increase in energy demand. ⁵⁵ The use of MRWT allows for a significant reduction in the area of wind farms, which allows for a reduction in costs. Also, these turbines can overcome the winds generated between the turbines in wind farms, which allows for a significant increase in the farm’s output. ⁵⁶ MRWT turbine technology is constantly evolving; as new turbines have recently emerged that rely on merging a large number of turbines to obtain a single turbine, as this resulting turbine can withstand strong winds, which reduces material losses. ⁵⁷ According to the work done in Ref., ⁵⁸ MRWT is expensive compared to conventional turbines and is not widely used due to the advanced technology it uses. Also, MRWT has larger mechanical components than conventional turbines, which makes it need periodic maintenance. In this work, the focus was on using MRWT due to its many advantages compared to conventional turbines, where an MRWT consisting of two turbines (turbine 1 and turbine 2) was used. These two turbines are of different capacities. Therefore, the energy gained from the wind can be expressed by equation (5).^50,55 This energy gained is related to the size of each turbine and the WS.

$$P_t=P_2+P_1$$

(5)

Where, P_t is the total power, P₁ is the power of turbine 1, and P₂ is the power of turbine 2.

Equation (6) represents the torque generated by the MRWT turbine.

$$T_t=T_1+T_2$$

(6)

Where, T_t are the total torque, T₁ is the torque of turbine 1, and T₂ is the torque of turbine 2.

Equation (7) represents the expression for all the energy gained from the two turbines.

$$\{\begin{array}{c}{P}_2=\frac{C_p(\beta ,\lambda )}{2}\rho ·S_2·v_2^3\hfill \\ \multicolumn{1}{c}{P_1=\frac{C_p(\beta ,\lambda )}{2}\rho ·S_1·v_1^3}\end{array}$$

(7)

Where, λ is the tip speed ratio, ρ is the air density (kg/m³), β is the blade pitch angle (deg), v is the WS (m/s), and C_P is the power coefficient.

According to the work done in Ref., ⁵⁰ the torque value for each turbine can be expressed by equation (7). The torque value for each turbine depends on the WS of each turbine and its dimensions.

$$\{\begin{array}{c}{T}_2=\frac{C_p}{2{\lambda }_2^3}\rho ·\pi ·R_2^5·w_2^2\hfill \\ \multicolumn{1}{c}{T_1=\frac{C_p}{2{\lambda }_1^3}\rho ·\pi ·R_{11}^5·w_1^2}\end{array}$$

(8)

Where, R is the radius of the turbine (m).

The tip speed ration for each turbine is calculated by equation (9). The value of the tip speed ration is related to the radius of each turbine and the WS before each turbine.

$$\{\begin{array}{c}{\lambda }_1=\frac{w_1·R_1}{v_1}\hfill \\ \multicolumn{1}{c}{{\lambda }_2=\frac{w_2·R_2}{v_2}}\end{array}$$

(9)

The power gained from wind is related to the power coefficient. This is a very important coefficient, as it greatly affects the value of the power gained from wind. The largest value of this coefficient is 0.59. This coefficient can be expressed by the equation (10).

$$C_p(\beta ,\lambda )=\frac{1}{0.08\beta +\lambda }+\frac{0.035}{{\beta }^3+1}$$

(10)

In MRWT, each turbine has a different WS. The first turbine has a WS, and the second turbine has a WS different from the WS before the first turbine. According to the work done in Ref., ⁵⁷ the WS of the second turbine is affected by the dimensions of the first turbine and the WS before the first turbine. Also, this speed is affected by the distance between the two turbines (x). The value of the distance between the two turbines in this work is 15 m. equation (11) represents the WS before the second turbine.

$$v_2=v_1(1-\frac{1-\sqrt{(1-C_T)}}{2}(1+\frac{2x}{\sqrt{1+4x^2}}))$$

(11)

According to equation (11), the value of the WS before the second turbine is related to a constant factor (C_T) with a value less than 1. In the turbine used in this work, the value of this constant is equal to 0.9.

In the control field, several controllers have been proposed to control the powers of DFIG. These controllers have been proposed to replace the use of traditional controllers such as PI controllers. Most of these controllers proposed in the literature do not give satisfactory results in terms of power ripples and THD of current. Some of the proposed controls use the mathematical model of the studied system, which gives unsatisfactory results when the system parameters change, such as the BC-SMC approach. Therefore, a new approach is proposed that depends on integrating several control strategies and does not use the mathematical model of the studied system. This proposed approach is discussed in detail in the next section.

Proposed nonlinear controller

In the field of control, several controllers have been designed as a suitable solution for improving control strategies, where accuracy, robustness, simplicity, outstanding performance, no relation to the mathematical model of the system, and low cost are among the most prominent features that must be present in any proposed controller. The PI controller is considered one of the most prominent controllers, simple, less expensive, easy to implement, and easy to adjust. ⁵⁹ In addition to the presence of a small number of gains, it is one of the most prominent possible solutions that can be relied upon. This controller can be expressed by equation (8). ⁶⁰ However, this controller has a negative side, which is a decrease in performance if the machine parameters change, which is undesirable.

$$w(t)=K_p.e\left(t\right)+K_i.{\int }^e\left(t\right).\mathrm{dt}$$

(12)

Where, K_i and K_p are the constant gains and e(t) is the error (S = X*−X)

$$\frac{w(s)}{e(s)}=\frac{K_p.s+K_i}{s}$$

(13)

Another controller that belongs to the family of linear strategies has proven effective to some extent to improving the characteristics of systems, as it is characterized by ease of implementation, low cost, simplicity, and contains a small number of gains (only two gains), which makes it one of the easiest strategies to adjust the dynamic response. This controller is called a PD controller. The latter can be expressed by equation (15). ⁶¹ Despite the many advantages it has, its use is accompanied by drawbacks, as its use does not lead to a very significant reduction of ripples. Moreover, this controller is affected by changes in system parameters and gives unsatisfactory results, which makes it less common.

$$h(t)=K_3.\epsilon \left(t\right)+K_4.\frac{d\epsilon (t)}{\mathrm{dt}}$$

(15)

Where, $\epsilon$ (t) is the error, K₄ and K₃ are the constant gains.

$$\frac{h(s)}{\epsilon (s)}=K_4.s+K_3$$

(16)

In nonlinear strategies, the STA controller is considered one of the controllers that have shown great performance in improving the characteristics of the systems and significantly increasing their robustness compared to conventional techniques. ⁶² This controller depends on the PI controller in its structure, as it is a change in the structure of the PI controller, which makes it one of the simplest nonlinear strategies and the easiest to implement. ⁶³ In addition to having a small number of gains, it is easy to adjust and change the dynamic response.

The STA controller can be expressed by equation (17). ⁶⁴

$$u(t)={\lambda }_1(\left|S\right|{)}^r\mathrm{sign}(S)+{\lambda }_2\int \mathrm{sign}\left(S\right)\mathrm{dt}$$

(17)

Where, S is the surface, λ₂ and λ₁ are the gains.

Another strategy that is no less important than other strategies in the field of control, fractional-order control is considered one of the strategies that appeared in the field of mathematics and has given excellent results in the field of control. ⁶⁵ This strategy is based on fractional calculus, as it is characterized by simplicity, ease of application, and outstanding performance compared to classical controls. ³⁵ In addition to its lack of connection to the mathematical model of the system, this makes it one of the most prominent solutions that can be relied upon in the field of control. It has been used in several different fields.^66,67

In this part, a new controller will be given that is based on the strategies mentioned (PD, PI, fractional calculus, and STA) to obtain a controller that has high characteristics and maintains ease of implementation and simplicity as much as possible. This proposed controller can be expressed by the mathematical model represented in equation (18).

$$\begin{array}{l}y\left(t\right)=\left(K_1\times \frac{e\left(t\right)}{s^{\beta }}+K_2\times e\left(t\right)\right)\left(K_3\times \frac{d\epsilon {\left(t\right)}^{\alpha }}{dt}+K_4\epsilon \left(t\right)\right)\\ (K_5\times {\left(\left|\delta \left(t\right)\right|\right)}^{r}sign(\delta \left(t\right))+K_6{\displaystyle \underset{0}{\overset{t}{\int }}sign}(\delta \left(t\right).dt)\end{array}$$

(18)

Where, β and α are the gains of fractional-order control, K₁ to K₆ are the gains of the proposed controller. Using the latter, the dynamic response is adjusted and changed. The proposed controller (FOPIPD-STA) can become another controller (PIPD-STA) if the values of both β and α are 1. This is a good feature that makes the controller operate as two different controllers, where the condition must be taken that the gains β and α do not take the value 0. Equation (19) expresses the proposed controller when both β and α take the value 1.

$$\begin{array}{l}y\left(t\right)=\left(K_1\times \frac{e\left(t\right)}{s}+K_2\times e\left(t\right)\right)\left(K_3\times \frac{d\epsilon \left(t\right)}{dt}+K_4\epsilon \left(t\right)\right)\\ (K_5\times {\left(\left|\delta \left(t\right)\right|\right)}^{r}sign(\delta \left(t\right))+K_6{\displaystyle \underset{0}{\overset{t}{\int }}sign}(\delta \left(t\right).dt)\end{array}$$

(19)

The proposed controller represented in the equation can be expressed using Figure 2 to simplify understanding and give a clear picture of the idea, as simplicity is one of the most prominent features. From observing Figure 2 and equation (18), it can be said that the number of gains is one of the most prominent features of this new controller. As is known, a large number of gains make it difficult to adjust the dynamic response and to use artificial intelligence techniques to determine these values.

Figure 2.

The proposed controller.

Proposed indirect FOC technique of DFIG

Traditional indirect FOC technique

The indirect FOC technique is a strategy that relies on the use of a PI controller to control the characteristic quantities, as the technique uses the PWM strategy for the purpose of controlling the RSC of DFIG. This strategy is based on the idea of flux ray orientation, as the principle of this technique is explained in the works.^68,69 According to these works, the components of the current can be written according to the equation (20).

$$\{\begin{array}{c}{I}_{\mathrm{ds}}=-\frac{M}{N}{I}_{\mathrm{dr}}+\frac{{\phi }_s}{L_s}\hfill \\ \multicolumn{1}{c}{I_{\mathrm{qs}}=-\frac{M}{L_s}{I}_{\mathrm{qr}}}\end{array}$$

(20)

The rotor voltage written in equation (21) becomes as follows:

$$\{\frac{V_{\mathrm{dr}}=R_r.I_{\mathrm{dr}}-w_r{L}_r\sigma I_{\mathrm{qr}}}{V_{\mathrm{qr}}=R_r.I_{\mathrm{qr}}+w_r{L}_r\sigma I_{\mathrm{dr}}+g\frac{M.V_s}{L_s}}$$

(21)

The rotor a flux written in equation (22) becomes as follows ⁷⁰ :

$$\{\frac{{\phi }_{\mathrm{dr}}=L_r\sigma I_{\mathrm{dr}}+\frac{M.V_s}{L_s.w_s}}{{\phi }_{\mathrm{qr}}=L_r\sigma I_{\mathrm{qr}}}$$

(22)

Both error in the quadrature rotor current and the error in Ps can be written using the equation (23).

$$\{\frac{e(I_{\mathrm{qr}})=I_{\mathrm{qr}}^{*}-I_{\mathrm{qr}}}{e(P_s)=P_s^{*}-P}$$

(23)

The reference value for quadrature rotor current can be written as follows ⁷¹ :

$$I_{\mathrm{qr}}^{*}=[K_{p}e(P_s)+K_i\int e(P_s)\mathrm{dt}]X\left[\frac{-L_s}{M{V}_s}\right]$$

(24)

Both error in the direct rotor current and the error in Qs can be written using the equation (25).

$$\{\frac{e(I_{\mathrm{dr}})=I_{\mathrm{dr}}^{*}-I_{\mathrm{dr}}}{e(Q_s)=Q_s^{*}-Q_s}$$

(25)

The reference value for direct rotor current can be written as follows:

$$I_{\mathrm{dr}}^{*}=[[K_{p}e(Q_s)+K_i\int e(Q_s)\mathrm{dt}]-\left[\frac{V_s^2}{w_s{L}_s}\right]]X\left[\frac{-L_s}{M{V}_s}\right]$$

(26)

Using the above equations, the reference value of the rotor voltage can be written according to the following equation ⁶⁹ :

$$\{\frac{V_{\mathrm{qr}}^{*}=[K_{p}e(I_{\mathrm{qr}})+K_i\int e(I_{\mathrm{qr}})\mathrm{dt}]-I_{\mathrm{dr}}g{w}_s\sigma }{V_{\mathrm{dr}}^{*}=[K_{p}e(I_{\mathrm{dr}})+K_i\int e\left(I_{\mathrm{dr}}\right)\mathrm{dt}]-I_{\mathrm{qr}}g{w}_s\sigma }$$

(27)

In the indirect FOC technique, four PI-type controls are used, which makes them greatly affected if the machine parameters change, which is undesirable. Moreover, using these controls makes the indirect FOC technique less efficient, robust, and performant than some strategies such as backstepping and SMC. Therefore, a new strategy for the indirect FOC technique will be presented in Sub-section 4.2 of the paper.

Proposed indirect FOC technique

The strategy proposed in this part depends on the traditional strategy in principle and structure, as the controller proposed in Section3 is used for this purpose. So the proposed strategy is a change to the FOC strategy with the use of the FOPIPD-STA to control the distinct amounts. In this proposed strategy, four FOPIPD-STA controllers are used along with the PWM for the purpose of generating control pulses in the RSC of DFIG. This proposed technique is characterized by high durability and outstanding performance compared to the FOC. In addition to the great efficiency and effectiveness in improving system characteristics, such as increasing power quality and minimizing the THD of current. Figure 3 represents the strategy proposed in this paper.

Figure 3.

The proposed technique of DFIG.

The FOC-FOPIPD-STA aims to calculate the reference values of the voltage, as these reference values are used by the PWM for the purpose of controlling the RSC. Therefore, good results are obtained and this will be proven in Section 5 of the paper. Using the FOPIPD-STA controller will significantly increase the performance of the FOC and overcome existing problems. On the other hand, the MPPT is used in this proposed control to obtain the reference value for the Ps and thus the value of the maximum energy from the WS.

The reference values of effort in this proposed strategy can be expressed by equation (27).

$$\{\begin{array}{c}{V}_{dr}^{\ast }=\left(K_1\frac{e\left(t\right)}{s}+K_{2}e\left(t\right)\right)\left(K_3\times \frac{d\epsilon \left(t\right)}{dt}+K_4\epsilon \left(t\right)\right)\\ \left(K_5\times {\left(\left|\delta \left(t\right)\right|\right)}^{r}sign\left(\delta \left(t\right)\right)+K_6{\displaystyle {\int }_0^{t}sign}(\delta \left(t\right).dt\right)\\ -I_{qr}g{w}_s\sigma \\ V_{qr}^{\ast }=\left(K_1\frac{e\left(t\right)}{s}+K_{2}e\left(t\right)\right)\left(K_3\times \frac{d\epsilon \left(t\right)}{dt}+K_4\epsilon \left(t\right)\right)\\ (K_5\times {\left(\left|\delta \left(t\right)\right|\right)}^{r}sign(\delta \left(t\right))+K_6{\displaystyle {\int }_0^{t}sign}(\delta \left(t\right).dt)\\ -I_{dr}g{w}_s\sigma \end{array}$$

(28)

The proposed strategy requires measured values of power, as to know these values, the flux must be estimated. Therefore, to estimate the flux, voltage and current are measured. Both the current and the estimated flux values are used to estimate both Ps and Qs. Equation (28) is used to estimate the flux.

$$\{\begin{array}{c}{\phi }_{s\beta }=\sigma I_{r\beta }{L}_r\hfill \\ \multicolumn{1}{c}{{\phi }_{s\alpha }=\sigma I_{r\alpha }{L}_r+{\phi }_s\frac{M}{L_s}}\end{array}$$

(29)

With: $\sigma =1-\frac{M^2}{L_s{L}_r}$

The equation (29) is used to estimate the capabilities in this work.

$$\{\begin{array}{c}{P}_s=-\frac{3}{2}{V}_s{\phi }_{s\beta }\frac{L_m}{\sigma .L_r.L_s}\hfill \\ \multicolumn{1}{c}{Q_s=-\frac{3}{2}(\frac{V_s}{\sigma L_s}{\phi }_{\beta s}-\frac{V_s{L}_m}{\sigma L_r{L}_s})}\end{array}$$

(30)

In Figure 4, it is shown how to calculate reference voltage values using the proposed strategy, where the proposed controller is used for this purpose. These voltage reference values are calculated based on I_dr and I_qr. These reference values are used to generate the pulses needed to operate the machine’s inverter. Alternatively, the gain values of these controls can be found using simulation and experimentation, or by employing intelligent strategies such as genetic algorithms. The MATLAB format of this controller is listed in Appendix 1.

Figure 4.

Voltage reference values.

The stability of the proposed approach can be proven using Lyapunov’s theorem. This theorem relies on derivative calculations to prove stability, making it somewhat complex. In some cases, the calculations do not yield satisfactory results. Another reliable method for demonstrating the stability of the proposed approach is the Bode curve. The Bode curve is a frequency study, where both magnitude (dB) and phase (deg) are extracted using MATLAB. The Bode curve method does not require complex calculations, as it is a graphical method characterized by simplicity and minimal effort.

Figure 5(a) represents the Bode curve for the conventional approach. From this figure, it is observed that the values of Magnitude (dB) and Phase (deg) for the conventional approach (PI controller) change with frequency. The value of Magnitude (dB) varies from 10 dB to −60 dB, while the value of Phase (deg) varies from 0° to −90°. Therefore, both Magnitude (dB) and Phase (deg) have negative values. From Figure 5(a), it is observed that when the value of Magnitude (dB) is 0 dB, the value of Phase (deg) is approximately −90 °, so the phase margin is 90°. Since the phase margin is positive, this system is stable.

Figure 5.

Bode curve: (a) PI controller and (b) FOPIPD-STA controller.

Figure 5(b) represents the Bode curve for the proposed approach (FOPIPD-STA controller). This figure shows the variation of both phase (deg) and magnitude (dB) as a function of voltage. The value of phase (deg) varies from 0° to −360° and the value of magnitude (dB) for the proposed approach varies from 0 dB to −30 dB. Therefore, both phase (deg) and magnitude (dB) take negative values. From Figure 5(b), it can be seen that the gain at −180° is −2.5 dB, so the gain margin is 2.5 dB. Since the phase margin is positive, this system is stable.

Results

In this part, a numerical simulation of the FOC-FOPIPD-STA technique is given using MATLAB, where a 1.5 MW DFIG is used for this purpose. The parameters of this generator are in Refs.^42,43 A variable WS is used to complete the study, where two different tests are proposed and a study is made to compare the graphical and numerical results of the two controls to show the extent of the superiority of the indirect FOC-FOPIPD-STA technique.

Reference tracking test

In this test, a variable WS is used to study the characteristics of the FOC-FOPIPD-STA technique compared to the FOC-PI technique, where the results obtained are represented in Tables 4 and 5 as well as Figures 6 and 7. From Figure 7 it is noted that the capacities take the nature of the references well with the presence of ripples, where the Ps changes according to the change in WS. However, the Qs do not change according to the change in WS, as it takes the value 0 VAR throughout the simulation period. In addition, the current of both techniques has the same shape as the WS, where the higher the value of the WS, the higher the value of the current, and vice versa. Also, the current has a sinusoidal shape with ripples. In Figure 6(e) and (f), the THD of the current value for the strategies is shown where the THD value for the FOC-PI technique is 1.10% and 0.09% for the FOC-FOPIPD-STA technique. Accordingly, the FOC-FOPIPD-STA technique minimized the THD value compared to the FOC-PI technique by an estimated rate of 91.81%, as this percentage proves the high quality of the current in the FOC-FOPIPD-STA technique compared to the FOC-PI technique. Figure 7 represents Zoom in the results of the first test. This figure gives a clear picture of the superiority of the FOC-FOPIPD-STA technique in terms of ripples compared to the FOC-PI technique. The values and percentages of these ripples are in Table 4, where it is noted that the values and percentages of ripple reduction show that the FOC-FOPIPD-STA technique has a high ability to significantly overcome the problem of power and current ripples. The FOC-FOPIPD-STA technique minimized the ripples of Qs, current, and Ps by percentages estimated at 60.85%, 99.38%, and 89.93%, respectively, compared to the FOC-PI technique.

Table 4.

Ratios/Values of the power and currents ripples.

Controllers and ratios	Qs (VAR)	Ia (A)	Ps (W)
PI	22,917	16.2	30,800
FOPIPD-STA	8970	0.1	3100
Ratios	60.85%	99.38%	89.93%

Table 5.

Value/Ratios of SSE, overshoot, rise time, and response time in the test-1 case.

Controllers and ratios	Characteristics	Ps (W)	Qs (VAR)
PI	Rise time	0.00925 s	0.00078 s
	Overshoot	23,400	19,140
	SSE	19,100	13,060
	Response time	0.0095 s	0.00975 s
FOPIPD-STAtechnique	Rise time	0.02825 s	0.0005 s
	Overshoot	6600	14,580
	SSE	600	4273
	Response time	0.0425 s	0.00925 s
Ratios	Rise time	67.25%	35.89%
	Overshoot	71.79%	23.82%
	SSE	96.85%	67.55%
	Response time	−77.64%	5.12%

Figure 6.

Results of the first test: (a) active power, (b) reactive power, (c) current (PI), (d) current (FOPIPD-STA), (e) THD of the current (traditional technique), and (f) THD of the current (proposed technique).

Figure 7.

Zoom in the results of the first test: (a) active power, (b) reactive power, (c) current (PI), and (d) current (FOPIPD-STA).

In Table 5, the numerical results of this test are given for the two power controls in terms of response time, SSE, rise time, and overshoot. This table gives a clear picture of the superiority of the FOC-FOPIPD-STA technique over the FOC-PI technique in terms of response time, SSE, rise time, and overshoot, and this appears through the relatively high reduction rates. But there is a negative to this FOC-FOPIPD-STA technique, which is the rise time and response time of Ps. The FOC-FOPIPD-STA technique minimized the values of overshoot, SSE, and rise time of Ps by percentages estimated at 71.79%, 96.85%, and 67.25%, respectively, compared to the FOC-PI technique. Regarding Qs, the percentages of response time, overshoot, SSE, and response time were reduced by percentages estimated at 35.89%, 23.82%, 67.55%, and 5.12%, respectively, compared to the FOC-PI technique. The conventional FOC-PI technique yielded better results compared to the FOC-FOPIPD-STA technique in terms of Ps response time, with the conventional approach reducing the response time by approximately 77.74%. Therefore, the active power response time can be considered a drawback of the proposed approach in this test. This drawback can be attributed to the gain values of the FOPIPD-STA controller. This drawback could be overcome in the future by using smart strategies to calculate these gain values, such as Grey Wolf optimization.

Robustness test

This test is different from the first test, as the same WS is used to study the performance of strategies in terms of changing machine parameters. So, in this test, the machine parameters are changed to study the robustness of the techniques used in this work, where the values of the resistances are multiplied by 2 and the values of the coils are multiplied by 2. Figures 8 and 9 represent the graphical results of this test, and Tables 6 and 7 show the numerical results. Obtained from durability testing. Despite the change in the machine parameters, it is noted that the powers continue to follow the references well (Figure 8(a) and (b)), with the presence of ripples. Also, the Ps keeps changing according to the change in WS, as its value increases as the WS increases and decreases as it decreases. However, the Qs are not affected by the change in WS and remain 0 VAR for the two strategies. The current for the two controls is represented in Figure 8(c) and (d), where it is noted that the current is affected by the change in WS, as it takes the form of a change in WS with the presence of ripples. The shape of the current in the case of both controls is sinusoidal, with an advantage to the FOC-FOPIPD-STA technique in terms of quality, and this is what Figure 9 shows. The THD value of the current of both techniques is represented in Figure 8(e) and (f), where it is noted that the THD value was 2.18% and 0.06% for both the FOC-PI strategy and the FOC-FOPIPD-STA technique, respectively. So, the FOC-FOPIPD-STA technique minimized the value of THD by an estimated 97.24% compared to the FOC-PI technique. Therefore, the quality of the current is very high in this test despite the change in parameters when using the FOC-FOPIPD-STA technique compared to the FOC-PI technique.

Figure 8.

Results of the robustness test: (a) active power, (b) reactive power (second test), (c) current (PI), (d) current (FOPIPD-STA), (e) THD of the current (traditional technique), and (f) THD of the current (proposed technique).

Figure 9.

Zoom in the results of the robustness test: (a) active power, (b) reactive power, (c) current (PI), and (d) current (FOPIPD-STA).

Table 6.

Value and ratios of current and energy ripples (robustness test).

Techniques and ratios	Qs (VAR)	Ia (A)	Ps (W)
PI	52,940	38.5	85,800
FOPIPD-STA	11	0.1	10
Ratios	99.97%	99.74%	99.98%

Table 7.

Ratios of SSE, response time, overshoot, and rise time in the robustness test case.

Ratios and strategies		Ps (W)	Qs (VAR)
FOC-PI	Rise time	0.00575 s	0.005
	Overshoot	53,500	41,540
	SSE	39,600	41,810
	Response time	0.00625 s	0.00575 s
FOC-FOPIPD-STAtechnique	Rise time	0.02825 s	0.0035 s
	Overshoot	5300	24,560
	SSE	5	1422
	Response time	0.04225	0.00425 s
Ratios	Rise time	−59.29%	30%
	Overshoot	90.09%	40.87
	SSE	99.98%	96.59
	Response time	−85.20%	26.08%

The ripples are shown in Figure 9, as this figure gives a clear picture of the superiority of the FOC-FOPIPD-STA technique in terms of reducing energy and current ripples compared to the FOC-PI. The values and ratios of these ripples are present in Table 6, where it is noted that the FOC-FOPIPD-STA technique reduced the ripple values of Qs, current, and Ps by percentages estimated at 99.97%, 99.74%, and 99.98%, respectively, compared to the FOC-PI technique. So, these high percentages give the extent of the efficiency and high ability of the FOC-FOPIPD-STA technique in overcoming ripples and improving the quality of current and energy for the studied energy system.

In Table 7, the values and percentages of minimization of response time, SSE, rise time, and overshoot of DFIG power are given. So, it is noted that the FOC-FOPIPD-STA technique outperformed the FOC-PI technique in terms of minimizing the values of response time, SSE, rise time, and overshoot compared to the FOC-PI technique. However, it is noted that there are drawbacks represented in the values of both the response time and the rise time of Ps, as the FOC-FOPIPD-STA technique provided undesirable results. Regarding the reactive power, it is noted that the FOC-FOPIPD-STA technique minimized the values of rise time, overshoot, SSE, and response time by percentages estimated at 30%, 40.87%, 96.59%, and 26.08%, respectively, compared to the FOC-PI technique. In the case of active power, the FOC-FOPIPD-STA technique minimized the values of both SSE and overshoot by percentages estimated at 90.09% and 99.98%, respectively, compared to the FOC-PI technique. Therefore, these percentages demonstrate the high performance of the FOC-FOPIPD-STA technique despite changing the machine parameters, as the aforementioned drawbacks can be overcome by using smart techniques such as GAs to calculate the parameters of the FOC-FOPIPD-STA technique.

In Table 8, the percentage change in the THD value of current between the two tests is given, as it is noted that the value of THD increased significantly in the FOC-PI technique compared to the FOC-FOPIPD-STA technique. This increase was estimated at 49.54%, which indicates that the FOC-PI technique has lower performance compared to the FOC-FOPIPD-STA strategy, which reduced the THD value despite changing the DFIG parameters. Therefore, the ratios of reduction in the THD value in the two tests were 33.33%. This percentage indicates that the FOC-FOPIPD-STA technique has outstanding performance and great effectiveness in improving the quality of the current.

Table 8.

Study of the effect of the THD value between the second and first tests for two control techniques.

Characteristics	THD value of current
Techniques	FOC-PI	FOPIPD-STA
Test 1	1.10	0.09
Test 2	2.18	0.06
Test 2 – Test 1	+1.08	−0.03
Ratios (%)	49.54	−33.33

Table 9 represents a study of the change in the amplitude value of the fundamental signal (50 Hz) between the first test and the durability test for the two techniques. From this table, it is noted that the value of this amplitude was greatly affected in the second test (durability) compared to the first test due to the change in the machine parameter values. The amplitude value increased significantly in the second test compared to the first test for the two approaches. Therefore, it can be said that changing the values of the instrument parameters affects the amplitude value of the fundamental signal (50 Hz). The difference in amplitude value was estimated at +45.70 and +47 A for both the traditional FOC-PI approach and the proposed approach, respectively. So the proposed approach provided the largest difference in the amplitude of the fundamental signal (50 Hz) compared to the traditional FOC-PI strategy. The influence rate of the amplitude value was estimated at 6.10% and 6.26% for both the traditional FOC-PI technique and the proposed approach, respectively. Therefore, the proposed approach provided the largest percentage of change in the amplitude value of the fundamental signal (50 Hz), which highlights its ability to improve the amplitude value, which is a good thing.

Table 9.

Study of the effect of the amplitude value of fundamental signal (50 Hz) between the second and first tests for the two control techniques.

Characteristics	Amplitude value (A) of fundamental signal (50 Hz)
Strategies	FOC-PI	FOPIPD-STA
Test 1	703.30	703.20
Test 2	749	750.20
Test 2 – Test 1	+45.70	+47
Ratios (%)	6.10	6.26

Third test: Steps wind speed profile test

This test uses step-wise WS, making this third test different from the previous two tests. The results of this test are presented in Figures 10 to 12. The numerical results are presented in Tables 10 and 11.

Figure 10.

Third test results: (a) active power (third test), (b) reactive power (third test), (c) stator current (FOPIPD-STA controller), and (d) stator current (PI controller).

Figure 11.

Zoom in the third test results: (a) active power, (b) reactive power, (c) stator current (FOPIPD-STA controller), and (d) stator currents (PI).

Figure 12.

Current THD of both techniques: (a) THD (PI) and (b) THD (FOPIPD-STA).

Table 10.

Value and ratios of current and energy ripples (third test).

Techniques and ratios	Qs (VAR)	Isa (A)	Ps (W)
PI	21,803	15.9	29,700
FOPIPD-STA	8840	0.1	2900
Ratios (%)	59.45	99.3	90.23

Table 11.

Ratios/Values of SSE, response time, overshoot, and rise time in the second test case.

Techniques	Characteristics	Ps (W)	Qs (VAR)
PI	Rise time (s)	0.0809	0.00063
	Overshoot	22,900	18,090
	SSE	18,500	12,120
	Response time (s)	0.0060	0.00850
FOPIPD-STAtechnique	Rise time (s)	0.02512	0.00044
	Overshoot	5900	12,340
	SSE	550	4120
	Response time (s)	0.00814	0.00812
Ratios (%)	Rise time (s)	68.94	30.15
	Overshoot	74.23	31.78
	SSE	97.02	66.00
	Response time (s)	−35.66	4.47

Figure 10 represents the graphical results of the controls implemented in this paper when the WS is in step-wise motion. Figure 10(a) represents the change in active power over time for the two controls.

This figure shows that the change in this power is the same as the change in WS, with a rapid dynamic response in both cases. The active power follows the reference well, with undulations. These undulations, as shown in Figure 11(a), are lower in the designed approach compared to the conventional approach.

Figure 10(b) represents the reactive power of two controllers. This power does not change with changes in WS, remaining constant and following the reference value well for both controllers. Furthermore, ripples are observed in this power, and as shown in Figure 11(b), these ripples are higher in the case of using the conventional approach compared to the proposed approach. Therefore, the proposed approach significantly reduces power ripples, making it a reliable solution in the field of renewable energy.

Figure 10(c) and (d) represent the current variation for the two approaches. This current varies with WS, and its value is related to the active power. It is also noted that there are ripples in this current. These ripples are lower in the proposed approach compared to the conventional approach, as shown in Figure 11(c) and (d).

Figure 12 represents the THD of current for two controllers. According to Figure 12, this value was estimated to be 1.07% and 0.07% for the conventional and proposed approaches, respectively. These values demonstrate that the proposed approach yielded a better THD value than the conventional approach. Therefore, the proposed approach reduces the THD value by 93.45% compared to the conventional approach. On the other hand, Figure 12 shows that the fundamental (50 Hz) current amplitude value was estimated to be 741.20 A for both controls. Therefore, both controls provided the same fundamental (50 Hz) signal amplitude value. These results reflect the ability and effectiveness of the proposed approach to improve current quality.

Table 10 presents the power ripple values and reduction ratios. This table shows that the active power ripple values were estimated at 29,700 and 2900 W for the conventional and proposed approaches, respectively. These values demonstrate that the proposed approach reduced the active power ripple values compared to the conventional approach, with a reduction ratio estimated at 90.23%. The reactive power ripples in this test were estimated to be 21,803 VAR and 8840 VAR for the traditional and proposed approaches, respectively. These values indicate that the ripples are 59.45% lower in the proposed approach compared to the traditional strategy. On the other hand, the current ripples were 15.9 and 0.1 A for the traditional and designed approaches, respectively. The proposed approach produced 99.3% lower current ripples than the conventional approach. These ratios demonstrate the effectiveness and efficiency of the approach in improving current and power quality. These results approach a potential future target for other industrial applications.

Table 11 presents the numerical values and reduction ratios for SSE, response time, overshoot, and rise time using the proposed controls. This table demonstrates that the proposed approach yielded satisfactory results compared to the conventional approach, with rise time, overshoot, and SSE values of active power reduced by 68.94%, 74.23%, and 97.02%, respectively. Furthermore, the proposed approach reduces the rise time, overshoot time, sse, and response time of reactive power by 30.15%, 31.78%, 66%, and 4.47%, respectively, compared to the PI controller-based traditional control approach. These results demonstrate the effectiveness, efficiency, and robustness of the proposed approach in improving the system properties, making it a promising and reliable solution. Despite this high performance, the proposed approach yielded unsatisfactory results in terms of active power response time compared to the conventional approach. In this test, the proposed approach yielded an average response time of 35.66% greater than the conventional approach, suggesting that the active power response time is a drawback of the approach designed for this test. This drawback can be attributed to the controller’s gain values, which can be overcome in the future using algorithms such as grey wolf optimization.

Tables 12 and 13 represent a study of the extent to which the values of the basic signal amplitude (50 Hz) and the THD of current were affected between the first and third tests. Table 12 shows that the THD value decreased significantly in the third test for both controls compared to the first test, which can be said that the wind variability pattern significantly affects the THD value. This effect was estimated to be 2.72% and 22.22% for the conventional and proposed approaches, respectively. Thus, the proposed approach yielded a greater reduction in current THD than the conventional approach, demonstrating the effectiveness and power of the proposed approach in improving current THD. Furthermore, using wind speed in steps significantly reduces current THD.

Table 12.

Study of the effect of the THD value between the third and first tests for two methods.

Characteristics	Current THD (%)
Techniques	FOC-PI	FOPIPD-STA
Test 1	1.10	0.09
Test 3	1.07	0.07
Test 3 – Test 1	−0.03	−0.02
Ratios (%)	−2.72	−22.22

Table 13.

Study of the effect of the amplitude value of fundamental signal (50 Hz) between the third and first tests for the two methods.

Characteristics	Amplitude value of fundamental signal (50 Hz)
Strategies	FOC-PI	FOPIPD-STA
Test 1	703.30	703.20
Test 3	741.20	741.20
Test 3 – Test 1	+38	+38
Ratios (%)	5.12	5.12

Table 13 shows that the amplitude value increased in the third test compared to the first test for both controls. Therefore, it can be concluded that the wind speed variation significantly affects the amplitude value. This increase in amplitude value was estimated at 5.12% for both controls. Therefore, the proposed approach exhibited a similar effect to the conventional approach. The results presented in Tables 12 and 13 demonstrate the high performance, robustness, and effectiveness of the proposed approach, making it a promising solution.

Table 14 represents a comparison of the completed work with some related works in terms of the percentage of reduction in the value of overshoot of power. By observing this table, the proposed approach gave a better percentage of reduction in overshoot than several works, where in work ⁷⁰ the percentage of reduction in overshoot reached 6.05% and 9.19% for both the reactive and active power, respectively. Also, in work, ⁷³ the overshoot reduction ratios in the second test case were 22.77% and 32.49% for both active and reactive power respectively. These works presented lower ratios than those presented by the proposed approach, which highlights its effectiveness and strength in improving the overshoot value. Another comparison is made in Table 15 between the IFOC-FOPIPD-STA strategy and other related works. This comparison was made in terms of the response time to the powers. This table shows that the IFOC-FOPIPD-STA strategy gave much better time than several other papers. In work, ³⁸ the response time was estimated to be 33.8 and 34.5 ms for the active and reactive powers, respectively. Also, in work, ⁸¹ the response time was estimated to be 12.15 and 10.08 ms for the active and reactive powers, respectively. These times are much larger than the times provided by the proposed approach in the first test, which confirms the effectiveness of the proposed approach in improving the dynamic response.

Table 14.

Comparing the IFOC-FOPIPD-STA strategy with some works in terms of the minimization rates obtained for DFIG power overshoot.

References	Ratios (%)
	Qs (VAR)	Ps (W)
Benbouhenni et al. 70	6.44	25.07
	6.05	9.19
Sami et al. 71	16.59	7.23
Habib et al. 72	37.42	80
Yessef et al. 73	44.06	32.20
	22.77	32.49
Habib et al. 74	60.93	67.74
Habib et al. 75	60.93	67.74
Benbouhenni et al. 76	48.38	73.87
	49.32	20.10
Designed approach (IFOC-FOPIPD-STA)	23.82	71.79
	40.87	90.09
	31.78	74.23

Table 15.

A comparison between the IFOC-FOPIPD-STA strategy and related papers in terms of DFIG power response time.

References	Response time (ms)
	Ps	Qs
Ibrahim et al. 77	17	18
	9	5
Alami et al. 78	15	80
Ardjal et al. 79	1.78	8.50
Chojaa et al. 80	-	28
Echiheb et al. 38	33.8	34.5
Benbouhenni et al. 81	12.15	10.08
	11.25	9.85
	11.85	10.05
Designed approach(IFOC-FOPIPD-STA)	4.25	9.25
	42.25	4.25
	8.14	8.12

Table 16 compares the current THD of the approach designed in this paper with some other papers. In work, ⁸⁴ the THD value was estimated to be 2.57% and 0.98%. Also, the THD value was estimated to be 4.88% and 4.19% in. ⁸⁸ These and other values listed in Table 16 are very high compared to the THD values given by the proposed approach (0.07%, 0.06%, and 0.09%). The results presented in Table 16 demonstrate the robustness of the proposed approach in improving THD and current quality compared to other work. This comparison makes the proposed approach a potential future target for other industrial applications.

Table 16.

Comparison with related works in terms of current THD.

References		THD (%)
Quan et al. 82		9.7
		3.2
Yaichi et al. 83		1.66
Boudjema et al. 84		2.57
		0.98
Boudjema et al. 85		3.1
Mahfoud et al. 86		4.80
Ayrir et al. 87		6.70
		2.04
Mohd Yusoff et al. 88		4.88
		4.19
Amrane and Chaiba18’		1.14
Mossa et al. 89		0.77
		2.15
Mahfoud et al. 90		12
		7.19
Younes et al. 91		8.87
		2.91
		2.72
Alhato and Bouallègue 92		10.79
		4.05
Yahdou et al. 93		3.13
Amrane et al. 94		3.70
Sayeh et al. 95		8.80
		2.27
		2.31
Chojaa et al. 80		1.39
		0.88
Sayeh et al. 96	DPC	6.26
		6.42
		8.74
	Fuzzy 12sectors DPC	1.47
		2.09
		2.15
Designedapproach(IFOC-FOPIPD-STA)		0.09
		0.06
		0.07

Conclusions

In this study, a novel control was implemented based on the use of the FOC-FOPIPD-STA technique to control powers and improve the robustness and efficiency of the FOC strategy. The proposed control is characterized by high performance and is distinguished by improving the quality of the current despite changing the machine parameters (see Tables 8 and 9). Also, robustness is one of the most prominent features of this proposed technique compared to the FOC-PI technique. This suggested technique was implemented and its performance was verified in the MATLAB environment, where a 1.5 MW DFIG was used for this purpose. The simulation results showed the superiority of the proposed control in terms of improving the system characteristics, and this is shown by the ratios in Tables 4 to 7. In addition, the study was restricted to simulation and in specific operating conditions only, as the study of the proposed control behavior will be expanded in the future in other working conditions such as the presence of network flaws. An attempt will also be made to implement this proposed strategy experimentally, with the addition of smart techniques such as genetic algorithm techniques to calculate gains to overcome the existing drawbacks.