Internal Model Control (IMC)-Based Active and Reactive Power Control of Brushless Double-Fed Induction Generator with Notch Filter

The increase in demand for electricity and, in particular, green energy has put renewable energy systems at the focal point of energy policy worldwide. The higher reliability of brushless doubly fed induction generators (BDFIGs) makes them suitable for oﬀshore and remote wind energy generation (WEG) applications. Besides, controlling the active and reactive powers in an electrical power system is critical for optimal voltage regulation, reduced power losses, and enhanced utilization of installed equipment. However, the existing literature on BDFIG’s active and reactive power control highlights the poor dynamic response and high transients with harmonic generation during inductive load insertion. It is because the Ziegler technique was employed to select PI gains, and the instantaneous reactive power theory was used to mitigate harmonics. Considering that, this paper proposes a vector control (VC) method for BDFIGs in wind turbines, in which the proportional-integral (PI) gains for internal model control (IMC) are optimized to improve the dynamic response of the active and reactive power during inductive load insertion. The proposed method reduces the complexity, time consumption, and uncertainty in making the optimal choice. In addition, to reduce a double fundamental frequency component to the point-of-common-coupling (PCC) voltage, the excellent characteristics of the notch ﬁlter are utilized in the grid-side converter (GSC)-based vector control scheme. The simulation results in MATLAB/ Simulink show that the proposed IMC-based vector control scheme with a notch ﬁlter provides satisfactory results with a minimum peak value compared to existing techniques.


Introduction
As the global demand for electrical energy grows, renewable energy systems (RES) have become increasingly popular because of their eco-friendly nature [1]. Over the past decade, wind energy generation systems (WEGS)-based RES have gained considerable popularity for operating at a variable speed and constant frequency, with a broader range of aerodynamic efficiencies [2]. e doubly fed induction generator (DFIG)-based WEGS contains brush gears that get stuck in remote locations and prove challenging for offshore applications. On the other hand, the brushless double-fed induction generator (BDFIG) does not have brush gear, which is more reliable than the conventional induction generator [3]. Besides, the BDFIG has a simple structure (since the slip gear is not needed) and a lower cost than a comparable DFIG. It has led the BDFIGs to attract the attention of researchers and industries. A BDFIG consists of two separate sets of three-phase stator windings [4]. e stator winding connected with the grid is called the power winding (PW) and is responsible for generating electrical power.
e second stator winding, called the control winding (CW), is indirectly connected to the grid through a fractionally rated converter. e rotor is used to couple the two stator windings [5], whereas the pole pairs are different on each stator to avoid direct coupling between the two stator windings.
As part of the BDFIG control scheme, one of the primary objectives is to enhance the dynamic response, maintain constant power, and mitigate harmonics in the presence of loads [6]. In literature, researchers have attempted to control the BDFIG through different techniques that include model predictive virtual torque [7], power control [8], direct power controller (DPC) [9], and stator with indirect control quantities [10]. ese methods cannot offer an ideal control over the active and reactive powers with a suitable dynamic response. For this reason, the authors adopted one of the most prominent control schemes, termed vector control (VC) [11,12], which utilizes four PI regulators in its control structure to tackle the aforementioned problem.
is study uses the internal model control (IMC) approach to efficiently tune the PI regulators, leading to an optimal dynamic response of the proposed BDFIG. e proposed method eliminates the time constraints and complexity associated with conventional tuning approaches such as the trial and error and Ziegler-Nichols method [13,14]. e IMC is a way of selecting PI parameters analytically, which considers the system parameters based on the openloop poles of the PI controller to equalize them with the zeros in order to provide the desired closed-loop bandwidth and time constant [15]. Nonetheless, it simplifies the control design procedure and eliminates the need for time-consuming and inefficient trial and error testing that may be necessary [16]. e dynamic response of the proposed method is evaluated under inductive load conditions to demonstrate its efficacy. Further, it has been demonstrated that the voltage at the point of common coupling (PCC) was susceptible to fluctuation when the load variation was substantial, which affected the other loads connected to the PCC and caused torque pulsations. Besides, due to a power quality problem, voltage variations adversely affect both the generation and a variety of loads using electrical energy.
In addition, the BDFIG is controlled via a rotor-side converter (RSC) or grid-side converter (GSC) in the VC scheme. ese power electronic converters utilize the pulse width modulators and become the source of harmonics generation [17]. Besides, the nonlinear loads are also a major cause of harmonic generation in electrical power systems. ese harmonic currents are the main threat to the power system as they cause voltage stresses, low power factor, voltage drops, and increased heating in conductors at the PCC [18]. e active and passive filters have been used to remedy the above problem, but these are not preferred because of their large size, aging, and complexity of tuning. Another most common solution for the harmonic compensation is the use of inductance-capacitance-inductance (LCL) filters with power electronics converters. However, due to the LCL filters, the power system faces stability issues as the resonance region amplifies the unwanted harmonics [19,20]. Furthermore, many authors have used filters based on a certain theory to mitigate the harmonics. e most prominent theory is the IRP p-q theory which is widely applied in three-phase systems to compensate for the harmonics caused due to nonlinear loads [21,22]. Since the mentioned theory possesses the transformation method that increases the system's complexity, the system becomes unable to reject the narrowband frequency, ultimately resulting in suboptimal performance. Considering the above-raised problems, hence to mitigate the problem of double fundamental frequency components to the PCC voltage, this paper introduces a notch filter designed with a GSC-based VC scheme. e significant contributions of this paper are as follows: (i) A GSC-based VC scheme has been proposed to control PCC's active and reactive power during inductive load insertion (ii) An IMC-based approach has been adopted to evaluate the PI gains to enhance the dynamic response of the machine (iii) A notch filter has been designed to remove harmonics introduced due to inductive load insertion e literature related to the control of BDFIG under load conditions is presented in Table 1.
is paper is organized as follows: Section 1 provides a literature review, and Section 2 presents the BDFIG architecture. e proposed technique is described in Section 3. In Section 4, the results of the study are discussed. Finally, the paper is concluded in Section 5.

BDFIG Architecture
e architecture of the system considered in this paper is shown in Figure 1. e BDFIG has two stator windings, the PW and the CW of the stator, respectively. e two windings of the BDFIG are coupled together by the rotor winding of the BDFIG.
ree-phase resistive-inductive RL load is connected to the PW of the stator and the grid (transformer). In a CW of the stator, two voltage source converters are connected back-to-back which are rotor-side converters (RSC) and grid-side converters (GSC). e DC-link is the bridging device between the two converters, which allows for an independent controller design for the RSC and the GSC based on the use of capacitors. e GSC is attached to the stator PW at the point of common coupling (PCC). It should be noted that R L and L L are, respectively, the equivalent load resistance and inductance of a load.
To enable VC of the machine, the PW and CW voltages are translated into the dq reference frame. Note that the dq reference frame is aligned with the PW flux orientation 2 International Transactions on Electrical Energy Systems [30,31]. e resulting dq components for PW are given as follows: where u p d and u pq denote the d and q components of PW voltage, while λ p d and λ pq symbolize the d and q components of PW ux. Similarly, the d and q components for CW are depicted as follows: λ cq L c i cq + L rc i rq , where u c d and u cq denote the d and q components of CW voltage, while λ c d and λ cq show the d and q components of CW ux. Similarly, for the d and q components for the rotor, given rotor current i r is given as λ rq L rp i pq + L rc i cq + L r i rq , where u r d and u rq denote the d and q components of rotor voltage, while λ r d and λ rq represent the d and q components of rotor ux. Finally, the rotor torque can be calculated as follows:   International Transactions on Electrical Energy Systems e VC scheme is designed for both RSC and GSC based on the preceding analytical model for the BDFIG-based wind turbine. Its purpose is to regulate the machine parameters at no load condition with the improved dynamic response.
is is achieved by selecting the PI regulators' gains by the IMC method. e notations set for this paper is listed in Table 2.

Proposed RSC-Based Vector Control
is section presents the technique that has been proposed to improve the transient behavior when using a BDFIG. By employing a vector controller oriented on the frame of PW reference, a method has been proposed to control both active and reactive power independently. To determine the active power and reactive power analytically, the BDFIM mathematical model is used, while the IMC method is used to calculate the PI controller gains. In the vector control scheme, the reactive power and speed of the machine are controlled by regulating the dq components of the PW and CW currents. Figure 2 shows the controllers for the converters, namely, RSC and GSC. e per-phase steady-state equivalent circuit of a BDFIG is shown in Figure 3 [23,28]. Using the DC capacitance (C dc ), the RSC and GSC are decoupled.

IMC-Based Rotor-Side Converter.
e link between CW and RSC controls active and reactive powers across both by utilizing the d and q components, respectively. As a result of combining the mathematical expressions with the governing equations, a nonlinear dynamic model for the BDFIG can be derived, illustrating the a liation between both stator windings, which is governed by the cross-coupling between them. First, the CW current dq components are given as follows [32,33]: where β 1 , β 2 , β 3 , and β 4 symbolize the control for PW current coe cients of open loop. us, transfer function can now be obtained for the CW current as follows: Using a similar approach as above, we can derive the CW voltage, i.e., regulating CW voltage using the CW current [27]: where α 1 , α 1 ,. . ., α 5 represents the control for CW current coe cients of open loop. us, the transfer function for CW voltage is given by is is the mathematical model of the system with respect to voltage and current. e feed-forward compensation has been used to deal with external disturbances as it is one of the most common methods to handle them [15]. A  method of capturing external disturbances and improving the stability of systems based on IMC is proposed in this paper. e proposed RSC using the IMC method with a notch lter is shown in Figure 4. e standard IMC structure as given in [34] has been used to extract the PI gains.
In terms of the gain values suggested by this IMC approach, the following expressions have been used: where K PW p , K PW i and K CW p , K CW i denote the gain values for PW and CW current, respectively. Similarly, B p and B c represent the frequency bandwidth for PW and CW, respectively.

Control of Active and Reactive Power.
After selecting the PI gains through the IMC method, the methodology for controlling active and reactive power with NF is obtained from the single-phase equivalent circuit for the stand-alone BDFIG system, as shown in Figure 5. In Figure 5, i Ll is the a-phase load current for a-phase, u a and i a are the a-phase voltage and current at the PCC. Symbolizing the amplitudefrequency by U m and angular frequency of the phase voltage ω, respectively, e pa can be obtained as follows [23]: Converting equation (25) into the Laplace transform of, e pa can be obtained in the complex frequency domain as follows: Under normal conditions and at a natural speed i a 0, it can be assumed that the grid line resistance is negligible, and this assumption should be made without loss of generality. It is also important to note that when the load is attached, the switch will be closed, which will force the current into the stator as [23] i pa (s) U m s e ca (s)  International Transactions on Electrical Energy Systems 5 where L shows the total inductance and total resistance is indicated by R are given by It is necessary to de ne the magnitude and the angle of the total impedance in the following manner: Equation (27) can be rewritten as [23] i pa (s) Converting into the inverse Laplace transform, we get In equation (34), it shows that the current of the PW consists of two components. A fundamental frequency component is the rst of the two components, and the second is an exponential DC component. On the same principle, equations can be provided for the current in both the b and c phases of the stator PW. Consequently, active and reactive power for both the fundamental frequency and exponentially decaying DC component of the machine is given as e use of the above equations for power in the simulation will achieve the appropriate control within the vector control strategy. We observe a harmonic component at twice high of frequency despite this. Wang et al. in reference [23] made an attempt to avoid this component and also proposed the instantaneous reactive power (IRP) theory, which increases the complexity and results in suboptimal performance. e use of a notch lter has been proposed to eliminate the double fundamental frequency component in the voltage at the PCC following the reactive current compensation by the RSC. e notch lter has been used successfully in order to suppress harmonics.

Notch Filter Design.
In its default con guration, a notch lter (NF) allows only frequencies in a narrow band and rejects frequencies outside of it. In addition to their conventional applications as band reject or band-stop lters, NFs may also be employed as pre lters to reject harmonics that feedback controllers do not eliminate.
is type of rejection is needed to improve the system's response time or improve the bandwidth. e nonlinearities coming from switched components and their unpredictable functioning are a challenge when designing for complex systems. Upon nding the lightly damped mode, the complex pair of poles that cause the harmonics are derived from a linearized system. A complex pair of zeros with slightly higher damping must be placed rst in the s-plane, followed by one with a slightly lower natural frequency. Doing so will ensure that the root-locus stays out of the right half of the plane [21]. Following the design guidelines of [24], we exploit a secondorder band-stop digital NF with a transfer function that is as follows: Here, f 0 is the center frequency and BW is the 3 dB bandwidth. e NF parameters are given in Table 3. e notch lter utilized in the GSC is shown in Figure 6. e block diagram implementation of an NF with the parameters in Table 3 and equation (24) is shown in Figure 6.
One such NF is included as a pre lter for each phase as indicated by blocks labeled NF in Figure 7. An illustration of the frequency response of the NF can be seen in Figure 8. e successful rejection of the unwanted frequency can be attributed to the high-quality factor Q f 0 /BW 50.

Results and Discussion
e results to assess the e ectiveness of the proposed controller are presented in this section. One of the contributions of current research work is that it has developed a e pa R p L p i pa i a u a R L L L Figure 5: Single-phase equivalent circuit from PW.  Table 4. A wind turbine model is considered constant with maximum power point tracking (MPPT) control that causes an increase in its power with a corresponding increase in wind speed. MPPT is used to extract the maximum available power from the wind energy, which is then served as the reference active power to be attained from the considered BDFIG-based wind turbine. e wind speed Vw is considered constant (12m/s) throughout the simulation run. In order to control the BDFIG's generator, the VC scheme is simulated along with International Transactions on Electrical Energy Systems its RSC and GSC controls under inductive load conditions. Besides, the PI gains for controllers are calculated using the IMC method. e active power and volt-ampere reactive (VAR) controllers receive the error signals of P 1 and Q 1 to output v c d and v cq . e dq components of PW and CW current components are regulated to obtain the desired active and reactive powers. e signals to the PWM generator are being applied by the CW reference voltage after transforming dq components into three-phase components. e PWM will generate a signal to switch the universal bridge, and CW will be supplied with a variable supply frequency, as shown in Figure 4.
A VC scheme is based on inner and outer control loops that can be implemented according to PI regulators. In terms of performance, the choice of the gains for these regulators plays an important role. It is commonly referred to use the "Ziederger method" to choose these gains [35]. In this case, the WECS could undergo a large overshoot followed by a long settling period. e IMC technique is used in this paper to tune the PI regulators in order to adjust the BDFIG's dynamic response to a desirable level. us, we compared the performance of the proposed technique with the technique such as Ziegler method-based PI regulators gains with the addition of reactive power theory to remove the harmonics that increase the system's complexity due to the involvement of the transformation method. us, the system cannot reject the narrowband frequency, which ultimately results in suboptimal performance. e frequency response of the voltage drops with NF and reactive power theory is plotted in Figure 9. A double fundamental frequency harmonic is observed without any ltering. However, the double frequency harmonic has been compensated signi cantly using the proposed NF. It can be observed that the NF reduces the double fundamental frequency harmonic signi cantly to near rejection.
To assess the performance of the proposed technique, inductive load with three di erent reactive power levels, 30, 45, and 55 kVArs, is considered. e load's active power is set at 4.5 KW, and the inductive load is allowed to connect at 3 ms. e objective is to control active and reactive power with a less transient response while eliminating the double frequency harmonic using the notch lter. It is observed that the proposed technique-based controller signi cantly reduced the transients in both active and reactive powers. e comparison shows that the proposed technique outperformed the existing method, as it attained machine parameters such as PW voltage, CW current, PW current, machine speed, and active and reactive power far better than     International Transactions on Electrical Energy Systems the present levels. Besides, it is also observed that the IMCbased PI tuning improves the dynamic response while the notch lter signi cantly reduces the double fundamental frequency harmonic. e PW voltage's response with and without the proposed technique is shown in Figure 10.
Note: e proposed technique employs IMC-based PI gains calculations with a notch lter design, whereas the technique 1 uses Ziegler method-based PI regulators gains with the addition of reactive power theory. Figure 10 shows that the PW voltage is reduced to 0.8 pu with the IRP method, which may cause the disconnection of load. However, the PW voltage remains close to 1 p.u with the proposed method when the inductive load having 30 KVAr is added to the grid-connected system. It has already been mentioned that the machine has a control winding current that must be su cient to control the converter.
e technique used in this paper successfully maintains a 13.1 A current compared to the CW's 11.3 A current; see Figure 11(a). e PW is connected directly to the grid through the PCC; it should remain close to its rated value when the inductive load is inserted into the system. e PW will be close to the cut-o value, which increases the chances of load disconnection if the proper control system is not provided. Figure 12(a) shows that the proposed control technique reduced the PW current by 113 A compared to the most recent technique's 63 A. e improved results obtained for PW voltage, CW current, and PW current with the proposed technique are shown in Table 5. e speed of the machine plays an important role in determining the machine's performance. e electrical machines in WECS need to provide consistent power output despite the continuous variations in wind speed. e wind speed decides the amount of power that can be extracted from WECS. In this way, it leads to generating a frequency with variable characters. is situation becomes problematic when the wind turbines are connected to a synchronized frequency grid system. e connection of variable frequency with xed grid frequency raises the issues of power ickering, unstable situations, and system disconnection. Hence, the machine speed maintains its value even if an inductive load is inserted with less transients and overshoot, as shown in Figure 13(a) with the proposed control technique. However, the speed is found to have more       settling time. Active and reactive power control at the instant of multilevel inductive load integration is crucial since it contributes to the smooth electrical power supply. Although the active power is set at 4.5 kW, a comparison with the IRP technique may be seen in terms of the controller's transient response and ability to revert to its original value when the reactive power of the load is altered, shown in Figure 14.
Likewise, the reactive power values such as 30 kVAr, 45 kVAr, and 55 kVAr are also seen in Figure 15 and compared with the IRP technique. e active power and reactive power for three types of loads are shown in Figures 14 and 15, along with the comparison with technique 1. e proposed technique appears to control the active and reactive power with better dynamic ability when inductive loads add to the BDFIG system. is is evident from its performance in regulating BDFIG's power. Adding a notch filter removes the double fundamental harmonics that further improves the power system. Compared with that particular technique 1, the results obtained with the proposed work meet the expectations. e improvements achieved by the proposed technique are delineated obviously in Table 7.
It can be seen that in all three cases, the proposed technique offers an improvement in the case of obtaining less peak value for the active and reactive power during inductive load insertion.

Conclusion
is paper presented a method for improving the transient behavior of a BDFIG's RSC when an inductive load is abruptly applied to the PCC. e IMC approach was used to calculate the PI gains for the BDFIG in order to help the machine improve its dynamic response. Based on the analysis of the voltage drop at the PCC using the power equations as a reference, a double fundamental frequency harmonic appears to exist, and a notch filter is designed to remove this double fundamental frequency harmonic. Simulations were performed in MATLAB/Simulink to evaluate the proposed controller thoroughly. e results suggest that the proposed technique can reduce the overshoot and the peak value while simultaneously controlling the active and reactive power.

Data Availability
No data were used to support this study.

Conflicts of Interest
e authors declare that they have no conflicts of interest.