Application of DPC to improve the integration of DFIG into wind energy conversion systems using FOPI controller

Abstract

While the direct power control (DPC) approach has proven effective in improving the efficiency of wind energy conversion systems (WECS) using doubly fed induction generators (DFIG), its applicability is currently confined to a single usage and has not been extended to meet numerous applications. This work aimed to modify the implementation of DPC in WECS-DFIG for several objectives. This is accomplished by updating the reference power of the conventional DPC method into an adapted one to achieve two goals independently. The first objective is to track the maximum power during wind speed variations. This tracking is performed by updating the reference power to match the maximum available power at the current wind speed. The second purpose is to ensure that the WECS remains connected to the grid and continues to operate smoothly even in the event of faults; supporting fault-ride through (FRT) capability. That is achieved by reducing the reference power during these faults. The discrimination between these two objectives is based on the voltage level at the point of connecting WECS to the grid. The controller provided is an improved fractional order PI controller developed using arithmetic optimization technique (AOA). A comparison between the AOA and cuckoo search is presented. The results demonstrate the efficacy of the suggested configuration and regulator in enhancing the performance of integrating DFIG into the WECS in the presence of wind fluctuations and short circuit faults occurring. It is worth noting that AOA is better than cuckoo search in fine-tuning the settings of the FOPI controller.

Keywords

Wind energy conversion system double-fed induction generator direct power control optimization fractional order PI

Introduction

Although solar PV has made notable advancements in the renewable energy sector, wind energy is generally considered more favorable when compared (‘Arnold et al., 2023). In 2022, wind energy sources comprised about 7.33% of global power output, indicating an increase from the 6.6% contribution in 2021. This was almost double the proportion compared to the levels seen in 2015 (‘Arnold et al., 2023). Wind energy is a reliable and potent factor in the continuous pursuit of sustainable energy solutions. It utilizes the boundless power of nature to fulfill the growing need for energy. Wind energy conversion systems (WECSs) consist of a wind turbine and an electrical generator. The Doubly-Fed Induction Generator (DFIG) is commonly employed, constituting 50% of the overall generators in use (Mosaad, Abu-Siada, and El-Naggar, 2019; Mosaad et al., 2022). DFIGs have the ability to operate at different speeds, allowing them to effectively capture wind energy over a broad range of wind velocities. This feature enhances efficiency as compared to generators with fixed-speed generators (Chojaa et al., 2022). DFIGs consist of interconnections between the windings of the rotor and stator, as well as the electrical grid. The rotor is often connected via a power converter, enabling the ability to modify the speed of operation and exercise control over it. DFIGs use a compact rotor-side power converter, often enabling the manipulation of the rotor current. This attribute improves the controllability (Alhato and Bouallègue, 2019). Two primary concerns occur when using these DFIGs in WECSs. One of the issues is the fluctuation in speed, which necessitates using a power controller to optimize the energy generated (Chojaa et al., 2021; Darvish Falehi, 2020; Luo and Niu, 2017). The second one is associated with the characteristics of the DFIG that are sensitive to grid failures (Mosaad et al., 2020; Mosaad et al., 2022).

These two challenges, MPPT and maintaining generator operation during failures, were successfully addressed by using flexible devices (Molinas et al., 2008; Mosaad and Sabiha, 2022; Mosaad et al., 2021; Siddique et al., 2018). These devices make remarkable contributions in these areas, but they also add costs to the system and increase its complexity via the inclusion of control mechanisms. Furthermore, the majority of these endeavors aimed to enhance the incorporation of DFIG into WECS by focusing on a single purpose (Karaipoom and Ngamroo, 2015), with just a few exceptions. An application with dual purposes, namely enhancing the power profile voltage profile and providing support for FRT, was introduced in Mosaad, Abu-Siada, and El-Naggar (2019). A flexible device called a superconductor was introduced to enhance the integration of DFIG into the WECS at two different modes (Benbouhenni et al., 2022; Mosaad, Abu-Siada, and El-Naggar, 2019). The first issue was a power fluctuation in the improvement mode caused by a strong gust of wind, while the second issue supported both fault ride-through (FRT) and low voltage ride-through (LVRT). The transition between these two modes was determined by the voltage level at the point of tying (POT) the generator to the grid (Mosaad, Abu-Siada and El-Naggar, 2019). However, this approach utilizes superconductors, which are still considered an expensive technology. Additionally, it does not take into account the maximum power as a reference for maximizing the energy generated from wind.

Direct power control (DPC) is a crucial solution and feature that is now considered essential for integrating DFIG into WECS. It was employed and proven method that offers improved performance for DFIG-WECS applications (Benbouhenni, Bizon, et al., 2023). The DPC does not introduce any new devices to the system but instead utilizes the existing major components of the DFIG. The main advantage of DPC is its ability to leverage the current core components of the system without the need to add new devices, as opposed to flexible devices. The DPC approach is classified as a linear strategy since it utilizes a switching table to create control pulses in the inverter. The output power is controlled using two conventional hysteresis comparators. This control method is considered to be the most straightforward and uncomplicated control technique since it can be implemented in comparison to other strategies like backstepping and vector controllers. Despite its drawbacks, the typical DPC technique is associated with issues such as harmonic distortion of current and active power ripples. The crucial aspect of the traditional DPC approach is the precise choice of the rotor voltage vector. In contrast to vector control strategy and field-oriented control, DPC technology avoids the usage of inner loops, which may complicate the system and compromise the resilience of the approach (Nian et al., 2016). In order to control the power, two types of hysteresis comparators are used. A three-level hysteresis comparator is utilized to regulate the active power, while a two-level hysteresis comparator is employed to manage the reactive power (Zhi and Xu, 2007). The use of these conventional controls significantly contributes to the occurrence of harmonic distortions in voltage and current, hence restricting the dissemination of this approach. Furthermore, alongside these controllers, the active and reactive power rating is used, whereby the power rating is interconnected with the voltage and current measurement devices. Table 1 summarizes the DPC strategies for WECS-DFIGs.

Table 1.

Review about DPC methods for DFIGs.

Reference	DPC methodology	Disadvantages
(Zhi and Xu, 2007)	Using high-efficiency measurement equipment for voltage and current is necessary	• Rise in the cost of the system • One application, power smoothing against wind speed variations
(Sun and Wang, 2016)	Introducing hysteresis comparator	current quality and Power fluctuations were not considered
(Hu et al., 2010)	Sliding mode control	• Nonlinear control techniques increase the level of intricacy. • Increase the implementation cost
(Xiong and Sun, 2016)	Backstepping control
(Cheng et al., 2023)	Using PI controller	High response time
(Benbouhenni and Bizon, 2021)	Synergetic control	Necessitates precise and accurate measuring instruments
(Errouissi et al., 2017)	Model predictive control-based Taylor series expansion	Prone to changes in parameters and external disruptions
(Khateri-abri et al., 2019)	Fuzzy Logic Control	Lack of a definitive criterion for determining the number of rules

The PI controller is well-recognized in industrial automation for its straightforwardness and efficiency (El-Naggar et al., 2021). PI controllers are essential in the wind energy industry to optimize power production and ensure the system durability.

The Fractional Order PI (FOPI) controller offers various advantages over the PI controller as a result of its distinctive features. Management of complex systems with non-integer dynamics is improved by FOPI controller flexibility (Xiao et al., 2021). The FOPI controller reliably captures fractional-order system behavior, improving control precision and resilience. FOPI controllers are more transient-responsive and stable than PI controllers. FOPI controllers are appropriate for applications that need precise control across varied operating conditions because to their better control precision and disturbance rejection. Control theory breakthroughs like the FOPI controller improve performance and flexibility for many practical applications.

Implementing FOPI controllers in DPC for DFIGs has excellent potential to improve the efficiency and accuracy of wind energy conversion systems. FOPI controllers, unlike typical integer-order controllers, use fractional calculus features to enhance their ability to capture the intricate dynamics of DFIG systems (Benbouhenni, Mosaad, et al., 2023). FOPI controllers in DPC applications provide enhanced transient response, resilience, and flexibility to accommodate changing wind conditions. Their fractional order characteristic for a more refined manipulation of control parameters, resulting in enhanced performance in minimizing the effects of disturbances and improving power generation. The use of FOPI controllers in DPC for DFIG demonstrates the continual investigation of innovative control techniques to enhance the speed and dependability of wind energy systems, hence contributing to the continuous improvement of renewable energy technology. FOPI controller was implemented to enhance the field-oriented control (FOC) characteristics of DFIG-WECS (Li et al., 2020). This controller could significantly enhance the power quality compared to conventional strategies like the FOC technique. However, active power fluctuations continue, and the current total harmonic distortion (THD) shows a somewhat higher value (Li et al., 2020; Xiao et al., 2021). Calibrating parameters for the FOPI controller is necessary to achieve optimal performance in control systems with intricate and non-integer order dynamics. Optimizing the settings of the FOPI controller entails finding the optimal values for both the fractional order and the proportional and integral gains to achieve a precise equilibrium between the system responsiveness and stability (Kakkar et al., 2021). The tuning procedure usually depends on a blend of empirical techniques, simulations, and, occasionally, sophisticated optimization algorithms to modify the parameters progressively. The objective is to customize the FOPI controller to the particular attributes of the controlled system, guaranteeing adequate and resilient operation under various operating conditions (Ramadan et al., 2022). The dynamic and iterative tuning procedure exemplifies the adaptability and sophistication of FOPI controllers in effectively dealing with the complexities of real-world systems. Many optimization techniques were used to tune the FOPI controller settings (Guha et al., 2020). The aforementioned uses of FOPI controllers for DPC in WECS-DFIGs were researched for a single application. To the author, no research has been conducted for this FOPI controller for more than one application.

This work presents an optimized FOPI controller for modifying the DPC in DFIG-WECS. The optimization process is executed via an arithmetic optimization algorithm (AOA). The modification in the DPC is accomplished by utilizing various controller modes that are distinguished by the voltage level at the point of tying (POT) between the DFIG and the electrical grid. The first mode is triggered when the wind speed fluctuates and the POT voltage level remains above 0.9. In this mode, the reference power is adjusted based on the maximum power value, and the FOPI-DPC directs the generator to operate at this maximum point. The second mode is activated when the POT voltage level falls below 0.9 as a result of fault events. During this mode, the adaptation of DPC is accomplished by updating the reference power as a function of this low-level voltage. This implies that the reference power is decreased, and the FOPI-DPC will compel the generator power to match this diminished value. The DFIG will remain operational and facilitate FRT by decreasing its power output and reducing the current. Furthermore and to assess the effectiveness of the AOA in fine-tuning the settings of the FPOI controller, another optimization approach called cuckoo search (CS) will be used.

Control system and optimization

Historically, wind energy has relied chiefly on induction generators, especially DFIG, for electric power production owing to their notable efficiency and adaptable controllability. To create electric power, a generator, and a turbine are required to facilitate the rotation of the generator, and two inverters are needed to provide electricity to the generator. This system has the benefit of being both straightforward and cost-effective in comparison to the conventional method of producing electricity. The DFIG-WECS is shown in Figure 1. The comprehensive simulation of the wind turbine system is extensively described in Benbouhenni (2021) and Benbouhenni and Bizon (2021).

Figure 1.

DFIG-WECS.

DFIGs equipped with Rotor-Side Converters (RSC) and Grid-Side Converters (GSC) form a system designed for the efficient and adaptable conversion of wind energy. DFIGs are characterized by their ability to operate both the RSC and GSC independently, enabling variable speed operation and improved power quality. The RSC allows the electricity to flow in both directions between the rotor and the grid, permitting accurate regulation of the generator speed and torque. The GSC facilitates the connection between the generator and the electrical grid, guaranteeing smooth integration and reliable power transmission. The integration of DFIGs, RSCs, and GSCs showcases the advanced technology and effectiveness attainable in contemporary wind energy systems, bolstering the ongoing expansion and durability of renewable energy production. RSC provides several benefits compared to GSC in terms of control flexibility, efficiency, and system dependability. An important benefit of RSC is its capacity to manipulate the rotor current directly, facilitating accurate management of the generator speed and torque. This enables the wind turbine system to harvest the maximum amount of electricity from different wind speeds efficiently, hence enhancing its overall efficiency. Furthermore, RSCs facilitate the transmission of electricity in both directions, enabling a smooth connection with the electrical grid and improving the stability of the system. RSCs provide the benefit of being inherently simple and cost-effective when compared to GSCs (Mosaad et al. 2021). This work introduced a DPC approach by controlling the pulses of the RSC. This is achieved by allocating a predetermined set of active and reactive powers references, $P_{s}^{*}$ , $Q_{s}^{*}$ respectively, and the controller must precisely adhere to these values.

This paper presents a modification of the classical DPC to meet several objectives efficiently. This encompasses the MPPT mechanism when there are changes in wind speed, as well as maintaining the voltage level higher than 0.9 pu (Mosaad, Abu-Siada and El-Naggar, 2019). Furthermore, it provides support for the FRT and LVRT capabilities during a faulty occurrence at the POT where the voltage falls below 0.9 pu.

During the first mode, the MPPT algorithm adjusts the reference power to optimize power output when the wind speed varies, as long as the voltage remains at or above 0.9 pu. When the POT voltage falls below 0.9 in the second mode, namely outside the LVRT and FRT codes, it necessitates the disconnection of the DFIG from the system. In this scenario, the reference power is adjusted based on the decreased voltage level caused by the fault. The DFIG power will then align with this reduced reference power in order to maintain the generator operation until the faults are cleared. The system under study along with the proposed control block diagram is depicted in Figure 2.

Figure 2.

System control block diagram.

The reference power $P_{s}^{*}$ in this mode is reduced by a limiting factor KL (Salem et al., 2017; Mosaad et al., 2018).

K_{L} = (V_{p p t_p u})^{\frac{1}{V_{p o t_p u}}}

(1)

The presence of this limiting factor will decrease the reference real power during faults, as shown in Figure 3, in order to support LVRT capability. An issue emerges with this factor: during short circuit failures, when the POT voltage is zero, both the factor and the updated reference power will also be 0, thus making this mode inappropriate for supporting FRT. Hence, a sixth-order regression is employed to exclude these zero points, as explained in (14) and illustrated in Figure 3.

K_{L_f i t t e d} = 14.89 V_{{P O T}_{p u}}^{6} - 30.9 V_{{P O T}_{p u}}^{5} + 15.13 V_{{P O T}_{p u}}^{4} + 4.118 V_{{P O T}_{p u}}^{3} - 2.354 V_{{P O T}_{_p u}}^{2} + 0.21 V_{{P O T}_{p u}} + 0.009544

(2)

Figure 3.

Updated and fitted reference active power.

AOA optimization

The aim of this study is to improve the incorporation of DFIG into WECS by modifying DPC utilizing an optimized FOPI controller. The reactive power is adjusted to match the desired value of zero, ( $Q_{s}^{*})$ . While the active power will be monitored in two operational modes based on the voltage level of the POT.

The difference between the reference and actual reactive powers can be defined as:

ε_{Q} = Q_{s}^{*} - Q_{s}

(3)

While for the active powers is:

ε_{p} = P_{s}^{*} - P_{s}

(4)

This study utilizes the AOA to minimize the objective function $J$ , which is the integral of the squared error between the reference and actual real and reactive powers, provided as:

J = m i n \int_{0}^{\infty} (ε_{P}^{2} + ε_{Q}^{2}) d t

(5)

The use of arithmetic operators to solve arithmetic problems serves as the primary source of inspiration for the proposed AOA (Qiao et al. 2023; Abualigah et al. 2020). Exploration and exploitation are the two main stages of the AOA optimization process. The search agents of an algorithm cover a significant portion of the search space in order to prevent limiting solutions. The improvement in solution accuracy that follows the discovery stage is referred to as “exploitation.” We will look at the addition, subtraction, division, and multiplication operations as well as their results using arithmetic operators. The choice of search phase (exploration or exploitation) has to be determined before the AOA is started. The Math Optimizer Accelerated (MOA) function is a coefficient derived from:

M O A (C_{I t e r}) = M i n + C_{I t e r} * (\frac{M a x - M i n}{M_{I t e r}})

(6)

The AOA exploration operators randomly explore multiple regions and approaches within the search area to improve the solution. This is achieved through two main search strategies, namely the Division (D) search strategy and the Multiplication search strategy. The position updating equations for the exploration parts are as follows:

x i, j (C_{I t e r} + 1) = {\begin{matrix} \frac{b e s t (x j)}{M O P + ϵ} * ((U B j - L B j) * μ + L B j), r 2 < 0 \\ o t h e r w i s e, b e s t (x j) * M O P * ((U B j - L B j) * μ + L B j) \end{matrix}

(7)

The flow chart of the proposed AOA to optimize the FOPID controller for RSC of the DFIG is illustrated in Figure 4. This optimization approach is utilized to optimize the two FOPI controllers that are employed for regulating active and reactive powers. The performance took place twice, once for each mode.

Figure 4.

Flow chart of AOA.

In order to assess the effectiveness of the AOA in accurately adjusting the FPOI controller settings, we shall add another optimization approach called CS (Mosaad, Osama abed el-raouf, et al., 2019; Vinodkumar and Esakkiappan, 2022).

Results and discussions

This study introduces a DPC technique for achieving MPPT of wind power systems. The proposed technique also includes supporting LVRT and FRT capabilities. These two objectives were accomplished through the use of an optimized FOPI controller. Two FOPI controllers were presented, one for the active power control and the other for the reactive power control. They were optimized using AOA. The tuning process is conducted twice, once for the MPPT mode and once for the FRT mode. Another tuning process using CS for the MPPT mode is performed and the corresponding optimized FOPI parameters are given in Table 2. Table 2 provides also the FOPI optimized parameters for the FRT mode employing AOA.

Table 2.

FOPI controller parameters for MPPT and FRT modes.

	AOA		CS		AOA, FRT mode
	FOPI 1	FOPI 2	FOPI 1	FOPI 2	FOPI 1	FOPI 2
Kp	3.76	2.56	7.5	3.5	5.29	1.82
Ki	1.28	6.3	2.8	4.87	3.2	4.2
λ	0.89	0.45	1.05	0.78	0.93	0.32

The FOPI parameters will be applied to the DPC in both test scenarios (mode1 and 2), and the switching between each mode is performed according to the POT voltage level.

Test case 1: MPPT mode

This mode is activated when the POT voltage exceeds 0.9 pu during fluctuations in wind speed. The wind profile is depicted in Figure 5.

Figure 5.

wind speed pattern.

The wind speed variation does not significantly affect the POT voltage, resulting in voltage ranges exceeding 0.9 per unit, as shown in Figure 6. Consequently, the MPPT mode will be activated using the two FOPI parameters specified in Table 1 to maximize the energy produced by the DFIG.

Figure 6.

POV voltage at wind speed variation.

Without implementing DPC, the power will fluctuate at values that are not equivalent to the greatest one, as depicted in Figure 7(a). In this context, the reference power is updated to the maximum available value according to the wind speed. The DPC will strive to track this maximum power precisely while the wind speed fluctuates, as depicted in Figure 7(a). Two distinct sets of FOPI controllers were improved using both CS and AOA techniques. The maximum tracked active power is shown in Figure 7(a). The AOA surpasses the CS in terms of achieving the most value. The suggested controller, with a reference zero reactive power, can precisely track this reference power for both CS and AOA sets, with AOA demonstrating better performance, as seen in Figure 7(b).

Figure 7.

Reference and tracked active and reactive powers: (a) active power and (b) reactive power.

The proposed controller improves the real power profile with a THD of 2.88%, as shown in Figure 8. This improvement in the real power profile is accompanied by a THD excess, namely a THD of 13.83% and 12.66% as mentioned in Sahri et al. (2021).

Figure 8.

THD of the real power.

Test case 2: FRT and LVRT mode

Two different fault conditions will be simulated in this case. The first case involves a three-phase to-ground fault occurring between 2 and 2.15 seconds. The second instance involves a 50% voltage sag occurring between 3.5 and 3.75 seconds. Both of these faulty conditions result in a decrease in the voltage level of the POT to a value lower than 0.9 pu, as illustrated in Figure 9.

Figure 9.

POT voltage at fault events.

Within this particular context, the generator will be disconnected from the grid. This disconnection can occur because of protection devices or the voltage ranges within the disconnecting zone, as required by certain grid codes. Failure to update the reference power will not alleviate the problem, but rather make it worse, especially since the controller will try to adhere to this constant reference value. The second mode, when triggered, will update the reference power based on the voltage level as presented in equation (14). Put simply, these errors will cause a fall in the voltage level at POT, resulting in a decrease in the reference power. Therefore, the controller will monitor and adjust the updated (reduced) reference power, resulting in a decrease in the DFIG. This will ensure that the generator remains connected to the grid during these fault events. When the fault occurrences cause the voltage level to drop below 0.9 pu, the second mode will be activated using the FOPI controller gains specified in Table 1, mode 2. The reduced reference power is updated at the fault time intervals where the second mode is activated according to (14). Two different faults will be discussed, three-phase to ground fault and 50% sagging.

Three-phase fault conditions

A three-phase to ground fault between 2 and 2.15 seconds is simulated in this case. The voltage level dropped to zero as a result of this fault. This will require disconnecting the DFIG from the system. The purpose of the modified DPC is to decrease the injected power from the DFIG during fault intervals in order to maintain the generator in operation. The reference power is adjusted based on (14), as illustrated in Figure 10. The controller real power attempts to closely align with the updated reference power, but with minor deviations. In order to maintain the DFIG in service during a failure interval, it is necessary to reduce the power and retain the POT voltage level at values higher than zero. This is in accordance with certain grid codes, and the example shown in Figure 11 is based on the code used in Spain. The FOPI-DPC, with the optimized gains of the second mode, successfully increased the POT voltage during fault intervals and complied with the Spain code to maintain the generator in service and thereby support FRT.

Figure 10.

Reference and updated power at three-phase fault.

Figure 11.

POT voltage at three-phase fault conditions.

Voltage sag event

In order to assess the capacity of the second mode to track the updated reference power, a test case will be conducted. This test case will involve simulating a 50% voltage drop between 3.5 and 3.75 seconds. The updated reference and tracked power, as determined by FOPI-DPC, is illustrated in Figure 12. The controller successfully achieved accurate tracking of the reference power. This decrease in the reference power and subsequent increase in controller power marginally raises the POT voltage to a value greater than 0.5 per unit, as depicted in Figure 13.

Figure 12.

Reference and updated power at 50% sagging condition.

Figure 13.

POT voltage at 50% sagging condition.

Conclusions

The primary concerns of DFIG-based WECS are power fluctuations and limited fault ride-through capability. This work aims to address these two concerns by adapting the classical DPC without adding any auxiliary devices. The two concerns are resolved by implementing a FOPI controller, which has been fine-tuned using AOA. The discrimination between power fluctuations and FRT/LVRT modes is accomplished by detecting the voltage level of the POT. In response to this discrimination, the FOPI group adjusted parameters using AOA. In power fluctuation mode, the reference power was updated to its maximum value, and the AOA-FOPI-DPC precisely tracks this reference power to achieve MPPT. It is important to note that the wind speed profile selected was a random one rather than a step change. For the second mode, when failures lead to a decrease in the POT voltage level, the reference power is updated based on this diminished voltage. This has decreased the injected power from the DFIG and hence allows the generator to remain operational even during faults. The FRT test case was examined in this study, and the proposed AOA-FOPI-DPC demonstrated the ability to decrease power and uphold voltage within the allowed level as specified by the Spain code. Furthermore, the sag criteria are fulfilled in this study by the proposed modified DPC.

Footnotes

Appendix

Declaration of conflicting interests

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

Funding

The author received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Mohamed I. Mosaad

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