A new approach for harmonic detection based on eliminating oscillatory coupling effects in microgrids

Received: 30 December 2022 Revised: 7 September 2023 Accepted: 9 October 2023 IET Renewable Power Generation DOI: 10.1049/rpg2.12867 ORIGINAL RESEARCH A new approach for harmonic detection based on eliminating oscillatory coupling effects in microgrids Mojtaba Ahmadi1Mohammad Hossein Mousavi1Hassan Moradi1 Kumars Rouzbehi2 1Department of Electrical Engineering, Razi University, Kermanshah, Iran 2Department of System Engineering and Automatic Control, University of Seville, Seville, Spain Correspondence Hassan Moradi, Department of Electrical Engineering, Razi University, Kermanshah, Iran. Email: [email protected].ir Abstract The primary goal of grid-connected microgrids is to control the active and reactive power, which is reachable by the inner current control loop in the control structure of power converters. However, when facing unbalanced conditions, the inner current control loop implemented in the dq frame does not function properly. In such conditions, the popular current control loop malfunctions since there is an oscillatory coupling between harmonic components. Therefore, in this study, a new harmonic detector based on decoupled double synchronous reference frame within the current control loop is proposed in which the oscillatory coupling between harmonic components is eliminated, and the overall performance of the power converter control system is significantly improved. The performance of the precisely developed mathematical models is verified by Matlab simulations, and the simulation results confirm the accuracy and proper operation of the proposed strategy. 1 INTRODUCTION In recent years, due to increasing energy consumption, limited fossil fuel resources, and related environmental issues, the use of distributed generation resources has been significantly increased [1]. Despite the numerous benefits associated with microgrids’ development, exploiting such grids has always posed challenges, such as, grid synchronization, voltage stability, power quality issues, and being low-inertia by nature that seems to be the root cause of several negative impacts on microgrids [2]. A major issue affecting power quality is harmonics. The presence of harmonics causes larger overall grid losses, increases electrically connected devices and equipment losses, failures in measuring instruments, torque disturbances in electric motors, and perturbations in electronic and telecommunication systems. Hence, the controlling, limiting, and compensating processes for grid harmonics have received immense attention from both industries and researchers [3]. There are effective strategies to compensate the harmonics in microgrids, including harmonic detection and extraction methods [4], primary controllers [5], and secondary controllers [6]. In the first approach, and sometimes even when using the second This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made. © 2023 The Authors. IET Renewable Power Generation published by John Wiley & Sons Ltd on behalf of The Institution of Engineering and Technology. and third ones, it is necessary to identify and extract harmonics for the purpose of compensation. In other words, harmonic characteristics such as amplitude and phase must be identified using a reliable and accurate method from the main current or voltage signal, and then harmonic components are neutralized within the harmonic compensation strategies. Therefore, the methods of separating and identifying harmonics are of special importance [7]. In general, harmonic isolation and identification can be classified into two groups of frequency-based and time-based methods. In the frequency-based structure, the Fourier series is used to separate the harmonic components from the original signal [8]. Other representations of Fourier series, such as Discrete Fourier Transform (DFT) [9] or Fast Fourier Transform (FFT) as well as Sliding Discrete Fourier Transform (SDFT) [10] are employed in control systems. Neural networks (NNs) or meta-heuristic algorithms are also employed to identify harmonic components. A novel approach for fault diagnosis, utilizing the total harmonic distortion (THD) of the voltage waveform as a key parameter for fault classification has been introduced in [11]. To achieve this, the authors employed a neural network trained with back propagation, genetic algorithm 3536 wileyonlinelibrary.com/iet-rpg IET Renew. Power Gener. 2023;17:3536–3553. AHMADI ET AL.3537 (GA), and particle swarm optimization (PSO) methods, and subsequently compared their respective outcomes. In [12], a differential harmony search (DHS) algorithm combined with Wavelet Transform (WT) has been used for power quality categorization and to extract distorted signals. The study described in [13] explored a highly effective and economically viable strategy for mitigating harmonics and enhancing the power factor in power distribution networks. This approach involved the application of Shunt Hybrid Active Power Filters (SHAPF) driven by neural network algorithms. In [14], an adaptive harmonic segregation technique has been developed by integrating particle swarm optimization with a deep neural network. All these methods require large memory storage; while some of them do not show a reliable response in the transient state [15, 16] and need precise synchronization methods between the main component and the frequency sampling [17], the others exhibit acceptable transient response [18]. On the other hand, the time-based methods have more speed and less computational burden compared to the frequency-based methods. There are many articles to separate the harmonic components based on the time-based method, including [19], where the instantaneous power theory was exploited. In this article, a high-pass filter was used to identify the harmonics. Other timebased methods benefit from a proportional-resonance (PR) filter or second-order generalized integral filter (SOGI) [20, 21]. Some of these approaches were expanded in the articles and presented under the titles of double (DSOGI) [22], multiple (MSOGI) or SOGI-PLL control algorithm [23]inorderto improve the dynamics of the previous methods. Although the dynamic response waveforms of the 𝛼𝛽-frame PR controller are nearly analogous to the dq-frame PI controller when pursuing the positive sequence current references, they are less precise than those of the decoupled dq-frame PI scheme [24]. In fact, despite the non-cross-coupled structure of 𝛼𝛽-axes unlike dq-axes, the cross-coupling effects between the phase and amplitude of alternative current signals are still witnessed, leading to large transient errors and frequency sensitivity [25]. To overcome this major challenge, [24] has suggested the modified decoupled 𝛼𝛽-frame PR controller and compared it with the decoupled dq-frame PI control structure, confirming that both controllers yield similar performance. However, the presence of one more integrator in the 𝛼𝛽-frame PR controller, compared to the decoupled dq-frame PI scheme makes its structure more complicated and costly [26]. Besides, unbalanced sequence extraction methods can also be employed, aiming to identify harmonic components. Following dq transformation theory, synchronous controllers were implemented using a proportional-integral (PI) controller to segregate unbalanced components [27]. However, this method did not exhibit an optimal performance, so the researchers’ attention was drawn to another method called double synchronous reference frame (DSRF), which uses two separate frames to compensate for the unbalanced components. In this strategy, after transferring an unbalanced current or voltage to a synchronous reference frame by employing Park Transformation, a combination of DC component and oscillating components in the voltage or current range is obtained. When this combination passes through a low-pass filter, the oscillating component is removed and ready for using in the current/voltage control loop [28]. However, this approach could not completely eliminate the components of the oscillatory coupling created between the dand qaxes, causing a poor performance of the current control loop and affecting the proper injection of active and reactive power [29]. On the other hand, the strategy can also be presented for the separation of harmonic components. Thus, an SRF-based harmonic detection algorithm was investigated in [30]. This method is used to separate harmonic components, performing the separation process via predetermined compensation angle changes, which has a large computational burden. In [31], this computational load is reduced using BPF as a separator of harmonic components. However, in this approach, only high-order harmonics, that is, 6n±1 are detected, and dominant harmonics such as 3rd harmonic are not separated. In addition, this method uses BPF, which is a second-order filter that slows down the system, and complicates the calculations. Furthermore, this filter can only separate one harmonic component, in other words, if two harmonic components need to be separated, two BPFs are required. For more components, a group of BPFs must be utilized, which increases the complexity of the control system. To address the weaknesses of the DSRF, a decoupled double synchronous reference frame (DDSRF) was introduced in [32]. Utilizing this enhanced method, the oscillating coupling between unbalanced components was completely eliminated. Moreover, one of the most explored strategies of harmonic detection is active power filters (APFs). Although the harmonic current injection through APFs to suppress the total and selective harmonic currents were studied in the literature [33], the complex configuration and imposing a high cost to the system [34] are yet the most important concerns in some applications. In this study, firstly, the performance of a DSRF-based controller is investigated facing harmonics in order to highlight its deficiency, then the DSRF system is enhanced, and a harmonic detector based on the DDSRF technique (HD-DDSRF) is presented as a decoupling structure to isolate and eliminate the harmonic fluctuations of the current. In the proposed technique, an unbalanced current vector is defined, which consists of the fifth and seventh harmonic components. Then, this vector is expressed in a DDSRF scheme to identify the harmonic components and remove the oscillatory coupling between them. Furthermore, in this approach, the injection of the current harmonic components is provided by the control loops, and the measured currents are utilized to separate the harmonic components. The contributions of this paper can be listed as follows: ∙Accurate identification of harmonic components in the current control system. ∙Improving the performance of the current controller using the HD-DDSRF approach. ∙Verifying the remarkable performance of the decoupled DSRF method over DSRF in detecting the harmonic components. 17521424, 2023, 14, Downloaded from https://ietresearch.onlinelibrary.wiley.com/doi/10.1049/rpg2.12867 by Universidad De Sevilla, Wiley Online Library on [07/11/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 3538 AHMADI ET AL. The article is organized as follows. In Section 2, the structure of HD-DDSRF is introduced in the presence of harmonic components, and a fair comparison is conducted with DSRF structure. Section 3presents the case study both for the control structure and power system. Simulation results are illustrated in Section 4. Limitations and future works are stated in Section 5, and finally, a conclusion is given in Section 6. 2HD-DDSRF STRUCTURE Microgrids are designed to operate both in grid-connected and islanded modes. As mentioned before, the main goal of the control system in microgrids connected to the main grid is to properly control active and reactive power. In this case, because the scope of the research is to explore a new harmonic detection system, a constant voltage source has been used instead of DG sources in the studied microgrid. Furthermore, the control system mainly includes the current and voltage control loops. The detailed discussion about microgrid under study and the parameters and the specifications are given in Sections 3and 4, respectively. The first step to implementing the current control loop is transferring the three-phase voltage and current vectors into a SRF frame using Park Transformation. Considering balanced condition, these values are DC and without oscillation, in which case the PI controller can provide correct control commands for power control. Conversely, when an unbalanced condition occurs, the voltage and current contain fluctuations leading to disturbing the current control loop [35]. In this section, three-phase vectors are presented in dq frame and DSRF technique is introduced while facing harmonics. Although due to the predominance of 5th and 7th harmonics, it is assumed that the microgrid output current includes the fifth and seventh harmonics, the proposed method has the ability to eliminate other harmonics such as 3rd, 11th etc. in the same way. Here, iabc =ih1 abc +ih5 abc +ih7 abc (1) Due to ease of calculation, the above equation can be expressed in the alpha–beta frame as follows: i𝛼𝛽 =ih1 𝛼𝛽 +ih5 𝛼𝛽 +ih7 𝛼𝛽 =Ih1[cos (𝜔t+𝛿 ) sin (𝜔t+𝛿 )]+ Ih5⎡⎢⎢⎣ cos (5𝜔t+5𝛿) sin (5𝜔t+5𝛿)⎤⎥⎥⎦ +Ih7[cos (7𝜔t+7𝛿) sin (7𝜔t+7𝛿)](2) where Ih1,Ih5,Ih7are the amplitude of the main, fifth and seventh harmonics, respectively (See also Appendix 1). In order to present Equation (2)indq frame, Park Transformation is employed as follows [36]: e−J𝜃=[cos (𝜃) −sin (𝜃) sin (𝜃) cos (𝜃)](3) where 𝜃=𝜔t+𝜑 (4) 𝜑represents the phase of 𝜃. Then, ˜ i1 dq =e−J𝜃×i𝛼𝛽 =[cos (𝜃) −sin (𝜃) sin (𝜃) cos (𝜃)]× (Ih1[cos (𝜔t+𝛿 ) sin (𝜔t+𝛿 )]+Ih5[cos (5𝜔t+5𝛿) sin (5𝜔t+5𝛿)]+Ih7[cos (7𝜔t+7𝛿) sin (7𝜔t+7𝛿)]) (5) where ˜ i1 dq denotes the current main components in the dq frame, which consists of oscillatory terms. Using (4), (5)canbe expressed as: ˜ i1 dq =Ih1[cos (𝜑−𝛿 ) sin (𝜑−𝛿 )]+ Ih5[cos (4𝜔t+4𝜑)cos (5𝜑−5𝛿)+sin (4𝜔t+4𝜑)sin (5𝜑−5𝛿) sin (4𝜔t+4𝜑)cos (5𝜑−5𝛿)−cos (4𝜔t+4𝜑)sin (5𝜑−5𝛿)]+ Ih7[cos (6𝜔t+6𝜑)cos (7𝜑−7𝛿)+sin (6𝜔t+6𝜑)sin (7𝜑−7𝛿) sin (6𝜔t+6𝜑)cos (7𝜑−7𝛿)−cos (6𝜔t+6𝜑)sin (7𝜑−7𝛿)] (6) As it is clear from (6), expressions including cos(𝜑−𝛿) and other trigonometric terms whose arc is (𝜑−𝛿), represent DC terms because there is no frequency within their arc. Let’s assume that: ih1 d=Ih1×cos (𝜑−𝛿 ),ih1 q=Ih1×sin (𝜑−𝛿 ) ih5 d=Ih5×cos (5𝜑−5𝛿),ih5 q=Ih5×sin (5𝜑−5𝛿) ih7 d=Ih7×cos (7𝜑−7𝛿),ih7 q=Ih7×sin (7𝜑−7𝛿) (7) where ih1,5,7 d,qdenotes the DC value of 1st,5 th and 7th harmonics in dq frame. Considering (6)and(7), ˜ i1 dq =[ih1 d ih1 q]+[ih5 d.cos (4𝜔t+4𝜑)+ih5 q.sin (4𝜔t+4𝜑) ih5 d.sin (4𝜔t+4𝜑)−ih5 q.cos (4𝜔t+4𝜑)] +[ih7 d.cos (6𝜔t+6𝜑)+ih7 q.sin (6𝜔t+6𝜑) ih7 d.sin (6𝜔t+6𝜑)−ih7 q.cos (6𝜔t+6𝜑)] →˜ i1 dq =[ih1 d ih1 q] ←−−→ DC term +[ih5 d ih5 q] ←−−→ DC term .[cos (4𝜔t+4𝜑)+sin (4𝜔t+4𝜑) sin (4𝜔t+4𝜑)−cos (4𝜔t+4𝜑)] ←−−−−−−−−−−−−−−−−−−−−−→ AC term +[ih7 d ih7 q] ←−−→ DC term .[cos (6𝜔t+6𝜑)+sin (6𝜔t+6𝜑) sin (6𝜔t+6𝜑)−cos (6𝜔t+6𝜑)] ←−−−−−−−−−−−−−−−−−−−−→ AC term (8) can be summarized as follows: ˜ i1 dq =ih1 dq +ih5 dq .e−J4𝜃+ih7 dq .e−J6𝜃(9) 17521424, 2023, 14, Downloaded from https://ietresearch.onlinelibrary.wiley.com/doi/10.1049/rpg2.12867 by Universidad De Sevilla, Wiley Online Library on [07/11/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License AHMADI ET AL.3539 PI + - PI + - + - + + + + PI + - PI + - + - + + PI + - PI + - + - + + P I + - P I + - + + - + + + First harmonic current control loop P I + - P I + - + + - + + + P I + - P I + - + + - + + + − − − Fifth harmonic current control loop Seventh harmonic current control loop FIGURE 1 Current controller based on DSRF technique. Similarly, for the fifth and seventh harmonic components: ˜ i5 dq =ih1 dq .e−J4𝜃+ih5 dq +ih7 dq .e−J2𝜃(10) ˜ i7 dq =ih1 dq .e−J6𝜃+ih5 dq .e−J2𝜃+ih7 dq (11) From (9)–(11), it is obvious that when the three-phase voltage or current includes harmonics, after transferring to dq rotating reference frame, the harmonic components are also transferred to the destination frame. But, the expectation to attain the purely DC values of the dand qaxes is not met, which results in an unfavourable and weak performance of the current control loop. Hence, the DSRF-based current controller can be shown in Figure 1. In order to achieve optimal performance for active and reactive power injection, current fluctuations under unbalanced conditions should be avoided when using DSRF. To overcome the problems associated with the DSRF technique, here, a new structure called harmonic detector based on the decoupled double synchronous reference frame (HDDDSRF) is presented in this paper to minimize the fluctuations and their adverse effects. It can be seen from (9)–(11) that the range of fluctuations in each of the components is dependent on the other two components, so this mutual coupling effect between harmonic components can be eliminated by using the following formulation: i1 dq =ih1 dq ←−−−−→ DC term +ih5 dq .e−J4𝜃+ih7 dq .e−J6𝜃 ←−−−−−−−−−−−−−−−−−−−−−−−−−→ AC term − ⎛⎜⎜⎜⎝ ih5 dq .e−J4𝜃+ih7 dq .e−J6𝜃 ←−−−−−−−−−−−−−−−−−−−−−−−−→ Cross−coupling term ⎞⎟⎟⎟⎠(12) i5 dq =ih5 dq ←−−−−−→ DC term +ih1 dq .e−J4𝜃+ih7 dq .e−J2𝜃 ←−−−−−−−−−−−−−−−−−−−−−−−−−→ AC term − ⎛⎜⎜⎜⎝ ih1 dq .e−J4𝜃+ih7 dq .e−J2𝜃 ←−−−−−−−−−−−−−−−−−−−−−−−−→ Cross−coupling term ⎞⎟⎟⎟⎠(13) 17521424, 2023, 14, Downloaded from https://ietresearch.onlinelibrary.wiley.com/doi/10.1049/rpg2.12867 by Universidad De Sevilla, Wiley Online Library on [07/11/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 3540 AHMADI ET AL. Low Pass Filter Low Pass Filter PI + - PI + - + - + + + + PI + - PI + - + - + + PI + - PI + - + - + + Low Pass Filter + - - + - - + - - P I + - P I + - + + - + + + 1st harmonic current control loop P I + - P I + - + + - + + + 5th harmonic current control loop P I + - P I + - + + - + + + 7th harmonic current control loop − − − − − − − − − FIGURE 2 Current controller based on proposed HD-DDSRF technique. i7 dq =ih7 dq ←−−−−−→ DC term +ih1 dq .e−J6𝜃+ih5 dq .e−J2𝜃 ←−−−−−−−−−−−−−−−−−−−−−−−−→ AC term − ⎛⎜⎜⎜⎝ ih1 dq .e−J6𝜃+ih5 dq .e−J2𝜃 ←−−−−−−−−−−−−−−−−−−−−−−−−→ Cross−coupling term ⎞⎟⎟⎟⎠(14) where i1,5,7 dq shows the output HD-DDSRF in dq frame. In fact, in this strategy, the oscillating terms of the other harmonic components are created and subtracted from the original term to eliminate the coupling effects. Figure 2illustrates the structure of the proposed HD-DDSRF. 3MICROGRID UNDER STUDY AND THE PROPOSED CONTROL SYSTEM Figure 3shows the generalized structure of a distributed generation unit which is connected to the main grid through an LC filter along with the control system. As can be seen from the figure, a current controller based on HD-DDSRF is proposed to control the active and reactive power in the dq frame. Three current controllers have been used to inject harmonic components. When the harmonic components are completely separated by HD-DDSRF technique, they are now ready to be used in the current control loop. By employing KVL in the output filter of the distributed generation unit and transferring the relevant equations to the dq frame by using the HD-DDSRF, the following equations are obtained: Ldih1 d(t) dt +(R+ron)ih1 d(t)= Vh1 td (t)+Vh1 gd (t)+L𝜔0ih1 q(t) (15) Ldih1 q(t) dt +(R+ron)ih1 q(t)= Vh1 tq (t)−Vh1 gq (t)−L𝜔0ih1 d(t) (16) Ldih5 d(t) dt +(R+ron)ih5 d(t)= Vh5 td (t)+Vh5 gd (t)+L𝜔0ih5 q(t) (17) Ldih5 q(t) dt +(R+ron)ih5 q(t)= Vh5 tq (t)−Vh5 gq (t)−L𝜔0ih5 d(t) (18) Ldih7 d(t) dt +(R+ron)ih7 d(t)= Vh7 td (t)+Vh7 gd (t)+L𝜔0ih7 q(t) (19) 17521424, 2023, 14, Downloaded from https://ietresearch.onlinelibrary.wiley.com/doi/10.1049/rpg2.12867 by Universidad De Sevilla, Wiley Online Library on [07/11/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License AHMADI ET AL.3541 dq abc HD-DDSRF Current control loop based on HD-DDSRF Current control loop based on HD-DDSRF Current control loop based on HD-DDSRF dq abc dq abc + FIGURE 3 Schematic of distributed generation unit under study. TABLE 1 Specifications of the system under study. Parameters Value Unit Peak phase voltage 311 [V] DC-link voltage 650 [V] Grid frequency 50 [Hz] Switching frequency 10 [kHz] Inductance 1.8 [mH] Capacitance 25 [μF] Resistance 1.19 [mΩ] Switch resistance 0.88 [mΩ] Filter damping ratio 0.707 – Ldih7 q(t) dt +(R+ron)ih7 q(t)= Vh7 tq (t)−Vh7 gq (t)−L𝜔0ih7 d(t) (20) where Vh1,5,7 tdq (t)=Vdc 2mh1,5,7 dq (21) Rand Lare the resistance and inductance of output filter, respectively. ron denotes switch internal resistance and 𝜔0is grid frequency. Also, Vt,Vdc and mdq sequentially denote inverter terminal voltage, inverter DC side voltage, and control command applied to the inverter gate. Equations (15)–(20) show that there is a coupling between Idand Iqin the harmonic sequences. To remove this coupling, according to Figure 4, a feed-forward compensator is applied. According to Figure 5, to design the controllers, the simpli- − − − FIGURE 4 Block diagram of harmonic sequences current controllers based on HD-DDSRF. _ + FIGURE 5 Simplified block diagram of closed-loop current control system based on HD-DDSRF for LCL filter. fied block diagram of the current sequences closed-loop control system is considered. PI controller is implemented to equalize the steady state error of the closed loop system to zero. Thus, kh1,5,7 d,qI =kp+ki s(22) kh1.5.7 d.qI represents the coefficients of PI controllers for the 1st,5 th and 7th harmonics in d-q frame. kpand kiare the pro- 17521424, 2023, 14, Downloaded from https://ietresearch.onlinelibrary.wiley.com/doi/10.1049/rpg2.12867 by Universidad De Sevilla, Wiley Online Library on [07/11/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 3542 AHMADI ET AL. FIGURE 6 MATLAB schematic of simulation scenarios. TABLE 2 Scenario one specifications. Current references injection time Harmonic component Current amplitude t=0.8 s h1- daxis 4 A t=1s h1-qaxis −2A t=1.1 s h5- daxis −1A t=1.2 s h5- qaxis 2 A t=1.3 s h7- daxis 2 A t=1.4 s h7- qaxis −1A portional and integral coefficients, respectively. The open loop transfer function of the current control system is as follows: Toli (s)=(kp Ls )⎛⎜⎜⎜⎝ s+ki kp s+R+ron L⎞⎟⎟⎟⎠ (23) Based on (23), the open loop transfer function has a pole close to the origin. The zero of the PI controller is selected to eliminate this pole. Then: ki kp =R+ron L(24) Finally, the closed-loop transfer function of the current control system can be written as follows: Gi(s)= ih1,5,7 d,q(s) ih1,5,7 d,qref (s) =1 𝜏is+1(25) where 𝜏iindicates the time constant of the closed loop system: kp L=1 𝜏i (26) To achieve a fast system response, 𝜏ishould be small and for this purpose, according to (26), a large value for kpshould be adopted. On the other hand, according to (25), the closed loop system of current control acts like a first-order low-pass filter; hence, by reducing 𝜏i(increasing the value of kp), the bandwidth of the closed loop control system increases. To control active and reactive power, according to instantaneous power theory in the dq frame for fundamental components [37]: P1 s(t)=3 2[V1 d(t)i1 d(t)+V1 q(t)i1 q(t)](27) Q1 s(t)=3 2[−V1 d(t)i1 q(t)+V1 q(t)i1 d(t)](28) If the PLL is in the steady-state V1 q≈0that is why: P1 s(t)=3 2[V1 d(t)i1 d(t)](29) Q1 s(t)=3 2[−V1 d(t)i1 q(t)](30) Therefor based on above equations P1 sand Q1 scan be controlled by i1 dand i1 qrespectively, thus: i1 dre f (t)=2 3V1 d P1 s(t)(31) i1 qre f (t)=−2 3V1 d Q1 s(t)(32) The above equations state that changes in the current references will result in changes in the active and reactive power loop. 17521424, 2023, 14, Downloaded from https://ietresearch.onlinelibrary.wiley.com/doi/10.1049/rpg2.12867 by Universidad De Sevilla, Wiley Online Library on [07/11/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License AHMADI ET AL.3543 4SIMULATION RESULTS The system shown in Figure 3has been simulated using the Simscape toolbox in Matlab/Simulink. To evaluate the effectiveness of the proposed HD-DDSRF method, it is compared with DSRF approach. Two scenarios have been simulated in this study. For the first scenario, variation of current references at different times is considered to create harmonic currents in the inverter output. The specifications of the studied system components are listed in Table 1. In the second scenario, to show the robustness of the proposed detection scheme under harsh harmonic conditions, in addition to reference harmonic current injection, a nonlinear load [38] has been added to the system. Figure 6illustrates the MATLAB schematic of simulated scenarios. 4.1 Scenario 1 In this scenario, to evaluate the performance of HD-DDSRF in harmonic component detection and control, the reference values are changed from zero to the determined values presented in Table 2. The simulation first scenario while injecting harmonic components are expressed as follows: Figure 7shows the current of main harmonic component in dand qaxes for both methods. As can be seen, after applying (a) (b) FIGURE 7 Main component current waveform (a) d-axis with ih1 dre f =4Aatt=0.8 s, (b) q-axis with ih1 qre f =−2Aatt=1s. (a) (b) FIGURE 8 Injected power for both DSRF and HD-DDSRF methods: (a) active, (b) reactive. the reference values at t=1.1 s and t=1.3 s for the 5th harmonic as well as t=1.2 s and t=1.4 s for the 7th harmonic in both dand qaxes, the main component current in d-axis follows its reference value which is 4 A. There is also a same trend in the q-axis. It is clear that the control method based on DSRF exhibits a wide range of oscillations in both dq axes leading to weak performance of current controllers in injecting active and reactive power, according to Figure 8. In the d–q frame, the current signals are not purely DC and contain oscillations with frequencies of 2𝜔, 4𝜔and 6𝜔. Hence, using FFT analysis, a new definition is presented to display the frequency spectrum as an index relative the DC components of the signal, called Magnitude of DC% (shown as THD% in the graphs). Here, to maintain MATLAB standard FFT analysis outputs, magnitude of DC is shown as THD% in the figures, but they differ from three-phase THD% definition. This THD% shows the oscillations in DC signals. In order to compare the range of these oscillations, the current harmonic spectrum is depicted in Figure 9. As can be observed, the magnitude of DC%, when using DSRF-based controller in dand qaxes, is 38.06% and 23.02%, respectively. In addition, the sixth and fourth harmonics have appeared in the dq frame, which can be proved using (12). The suggested HD-DDSRF control structure reduces the range of other component variations on the main harmonic and guarantees the proper injection of active and reactive power. According to Figure 10, the magnitude of 17521424, 2023, 14, Downloaded from https://ietresearch.onlinelibrary.wiley.com/doi/10.1049/rpg2.12867 by Universidad De Sevilla, Wiley Online Library on [07/11/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 3550 AHMADI ET AL. (a) (b) (c) (d) FIGURE 22 Evaluating fifth harmonic component in abc frame. (a) DSRF three-phase waveform, (b) HD-DDSRF three-phase waveform, (c) DSRF THD%, (d) HD-DDSRF THD%. separate the harmonic components and control the current of the main, fifth, and seventh harmonic sequences. The precise mathematical analysis and simulation results showed that the synchronous controller in the dq frame, DSRF, malfunctions when harmonic components are injected, and mutual oscillatory couplings appear in the dq current. The frequency of these oscillations was proved by using mathematical computations. Additionally, investigating the harmonic spectrum clarified these oscillatory terms. It was also found that the current controller based on the DSRF method could not compensate for fluctuations in any of the references. On the other hand, the results of the HD-DDSRF proposed method showed that the magnitude of DC (MoDC) value was within the acceptable limit and the mutual oscillatory couplings were eliminated (a) (b) (c) (d) FIGURE 23 Evaluating seventh harmonic component in abc frame. (a) DSRF three-phase waveform, (b) HD-DDSRF three-phase waveform, (c) DSRF THD%, (d) HD-DDSRF THD%. by using the HD-DDSRF. In summary, the key findings from simulation scenarios are as below: - In the first scenario, a comparative simulation was performed to assess the effectiveness of the proposed method. This simulation aimed to highlight the differences between the DSRF and HD-DDSRF methods in mitigating dq axis harmonic oscillations. The DSRF detection method exhibited harmonic fluctuations of 38.06%, 37.07%, and 16.46% in the d-axis for the main, fifth, and seventh harmonic components, respectively. For the q-axis, these fluctuations measured 23.02%, 20.82%, and 75.79%. In contrast, the implementation of the proposed method significantly reduced the amplitude of these fluctuations. Specifically, the d-axis harmonic fluctuations 17521424, 2023, 14, Downloaded from https://ietresearch.onlinelibrary.wiley.com/doi/10.1049/rpg2.12867 by Universidad De Sevilla, Wiley Online Library on [07/11/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License AHMADI ET AL.3551 (a) (b) FIGURE 24 Evaluating fifth and seventh harmonic component in abc frame for HD-DDSRF method (Scenario B). (a) Fifth harmonic, (b) seventh harmonic. were minimized to 0.23%, 1.48%, and 0.32% for the main, fifth, and seventh components, respectively. Furthermore, the q-axis showed a noticeable reduction, reaching 0.47% for the main component, 0.86% for the fifth component, and 0.77% for the seventh component. - In the second scenario, having established the effectiveness of the proposed method in comparison with the other approach, we sought to assess its robustness under more challenging conditions. In addition to the prevailing conditions from the first scenario, we introduced a non-linear load to the system. Although the amplitude of harmonic fluctuations increased to some extent, they still remained within an acceptable range, demonstrating the resilience of the proposed method and its ability to maintain satisfactory detection performance even in the presence of non-linear loads. - Finally, to verify the results obtained from the proposed HDDDSRF method, comparisons were made with IEEE-519 Standard. The outcome confirms that the THD values for harmonic three-phase waveforms are below the maximum permitted value of (4% THD). AUTHOR CONTRIBUTIONS Mojtaba Ahmadi: conceptualization: methodology: software: writing original draft. Mohammad Hossein Mousavi:investigation phase: Software: validation: and data curation. Hassan Moradi: supervision: reviewing and editing of the manuscript. Kumars Rouzbehi: supervision and editing of the manuscript. 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Power Gener. 17, 3536–3553 (2023). https://doi.org/10.1049/rpg2.12867 Suppose that the amplitude of 5th and 7th harmonic components are 20% and 10% of the fundamental amplitude, respectively. ia=sin (t)+0.2sin(5t)+0.1sin(7t)(A1) ib=sin (t−2𝜋 3)+0.2sin(5t−2𝜋 3)+0.1sin(7t−2𝜋 3) (A2) ic=sin (t+2𝜋 3)+0.2sin(5t+2𝜋 3)+0.1sin(7t+2𝜋 3) (A3) Considering Clarke transformation: [i𝛼 i𝛽]=2 3⎡⎢⎢⎣ 1−1 2−1 2 0√3 2−√3 2⎤⎥⎥⎦⎡⎢⎢⎢⎣ ia ib ic ⎤⎥⎥⎥⎦ (A4) If ia,ib,andicfrom (A4) are replaced with (A1)–(A3), after simplification, we have: i𝛼=2 15 sin (5t)+1 15 sin (7t)−1 15 sin(5t−2𝜋 3) −1 15 sin (5t+2𝜋 3)−1 30 sin (7t−2𝜋 3)−1 30 (7t+2𝜋 3) +2 3sin (t)−1 3sin (t−2𝜋 3)−1 3sin (t+2𝜋 3)(A5) 17521424, 2023, 14, Downloaded from https://ietresearch.onlinelibrary.wiley.com/doi/10.1049/rpg2.12867 by Universidad De Sevilla, Wiley Online Library on [07/11/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License AHMADI ET AL.3553 i𝛽=1 3[√3 5sin(5t−2𝜋 3)+1 10 sin (7t−2𝜋 3) +sin (t−2𝜋 3)] −1 3[√3 5sin (5t+2𝜋 3)+1 10 sin (7t+2𝜋 3)+sin (t+2𝜋 3) (A6) As can be observed from (A5)and(A6), 1st, 5th, and 7th harmonic orders are appeared in 𝛼𝛽 frame. 17521424, 2023, 14, Downloaded from https://ietresearch.onlinelibrary.wiley.com/doi/10.1049/rpg2.12867 by Universidad De Sevilla, Wiley Online Library on [07/11/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License