Power Electronics in Renewable Energy Systems Teuvo Suntio and Tuomas Messo www.mdpi.com/journal/energies Edited by Printed Edition of the Special Issue Published in Energies Power Electronics in Renewable Energy Systems Power Electronics in Renewable Energy Systems Special Issue Editors Teuvo Suntio Tuomas Messo MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade Special Issue Editors Teuvo Suntio Tampere University of Technology Finland Tuomas Messo Tampere University of Technology Finland Editorial Office MDPI St. Alban-Anlage 66 4052 Basel, Switzerland This is a reprint of articles from the Special Issue published online in the open access journal Energies (ISSN 1996-1073) from 2018 to 2019 (available at: https://www.mdpi.com/journal/energies/special issues/power electronics) For citation purposes, cite each article independently as indicated on the article page online and as indicated below: LastName, A.A.; LastName, B.B.; LastName, C.C. Article Title. 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Contents About the Special Issue Editors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Preface to ”Power Electronics in Renewable Energy Systems” . . . . . . . . . . . . . . . . . . . xi Teuvo Suntio and Tuomas Messo Power Electronics in Renewable Energy Systems Reprinted from: Energies 2019 , 12 , 1852, doi:10.3390/en12101852 . . . . . . . . . . . . . . . . . . . 1 Teuvo Suntio, Tuomas Messo, Matias Berg, Henrik Alenius, Tommi Reinikka, Roni Luhtala and Kai Zenger Impedance-Based Interactions in Grid-Tied Three-Phase Inverters in Renewable Energy Applications Reprinted from: Energies 2019 , 12 , 464, doi:10.3390/en12030464 . . . . . . . . . . . . . . . . . . . . 6 Tuomas Messo, Roni Luhtala, Tomi Roinila, Erik de Jong, Rick Scharrenberg, Tommaso Caldognetto, Paolo Mattavelli, Yin Sun and Alejandra Fabian Using High-Bandwidth Voltage Amplifier to Emulate Grid-Following Inverter for AC Microgrid Dynamics Studies Reprinted from: Energies 2019 , 12 , 379, doi:10.3390/en12030379 . . . . . . . . . . . . . . . . . . . . 37 Yin Sun, E. C. W. (Erik) de Jong, Xiongfei Wang, Dongsheng Yang, Frede Blaabjerg, Vladimir Cuk and J. F. G. (Sjef) Cobben The Impact of PLL Dynamics on the Low Inertia Power Grid: A Case Study of Bonaire Island Power System Reprinted from: Energies 2019 , 12 , 1259, doi:10.3390/en12071259 . . . . . . . . . . . . . . . . . . . 55 Eyal Amer, Alon Kuperman and Teuvo Suntio Direct Fixed-Step Maximum Power Point Tracking Algorithms with Adaptive Perturbation Frequency Reprinted from: Energies 2019 , 12 , 399, doi:10.3390/en12030399 . . . . . . . . . . . . . . . . . . . . 71 Teuvo Suntio Dynamic Modeling and Analysis of PCM-Controlled DCM-Operating Buck Converters—A Reexamination Reprinted from: Energies 2018 , 11 , 1267, doi:10.3390/en11051267 . . . . . . . . . . . . . . . . . . . 87 Wajahat Ullah Khan Tareen, Muhammad Aamir, Saad Mekhilef, Mutsuo Nakaoka, Mehdi Seyedmahmoudian, Ben Horan, Mudasir Ahmed Memon and Nauman Anwar Baig Mitigation of Power Quality Issues Due to High Penetration of Renewable Energy Sources in Electric Grid Systems Using Three-Phase APF/STATCOM Technologies: A Review Reprinted from: Energies 2018 , 11 , 1491, doi:10.3390/en11061491 . . . . . . . . . . . . . . . . . . . 105 Xiaohe Wang, Liang Chen, Dan Sun, Li Zhang and Heng Nian A Modified Self-Synchronized Synchronverter in Unbalanced Power Grids with Balanced Currents and Restrained Power Ripples Reprinted from: Energies 2019 , 12 , 923, doi:10.3390/en12050923 . . . . . . . . . . . . . . . . . . . . 146 Arwindra Rizqiawan, Pradita 0. Hadi and Goro Fujita Development of Grid-Connected Inverter Experiment Modules for Microgrid Learning Reprinted from: Energies 2019 , 12 , 476, doi:10.3390/en12030476 . . . . . . . . . . . . . . . . . . . . 164 v Yingpei Liu, Yan Li, Haiping Liang, Jia He and Hanyang Cui Energy Routing Control Strategy for Integrated Microgrids Including Photovoltaic, Battery-Energy Storage and Electric Vehicles Reprinted from: Energies 2019 , 12 , 302, doi:10.3390/en12020302 . . . . . . . . . . . . . . . . . . . . 180 Daniel F. Opila, Keith Kintzley, Spencer Shabshab, and Stephen Phillips Virtual Oscillator Control of Equivalent Voltage-Sourced and Current-Controlled Power Converters † Reprinted from: Energies 2019 , 12 , 298, doi:10.3390/en12020298 . . . . . . . . . . . . . . . . . . . . 196 C. Anuradha, N. Chellammal, Md Saquib Maqsood and S. Vijayalakshmi Design and Analysis of Non-Isolated Three-Port SEPIC Converter for Integrating Renewable Energy Sources Reprinted from: Energies 2019 , 12 , 221, doi:10.3390/en12020221 . . . . . . . . . . . . . . . . . . . . 214 Hyung-Seok Park, Hong-Jun Heo, Bum-Seog Choi, Kyung Chun Kim and Jang-Mok Kim Speed Control for Turbine-Generator of ORC Power Generation System and Experimental Implementation Reprinted from: Energies 2019 , 12 , 200, doi:10.3390/en12020200 . . . . . . . . . . . . . . . . . . . . 246 Xiangwu Yan, Zijun Song, Yun Xu, Ying Sun, Ziheng Wang and Xuewei Sun Study of Inertia and Damping Characteristics of Doubly Fed Induction Generators and Improved Additional Frequency Control Strategy Reprinted from: Energies 2019 , 12 , 38, doi:10.3390/en12010038 . . . . . . . . . . . . . . . . . . . . 259 Teuvo Suntio Modeling and Analysis of a PCM-Controlled Boost Converter Designed to Operate in DCM Reprinted from: Energies 2019 , , 4, doi:10.3390/en12010004 . . . . . . . . . . . . . . . . . . . . . . 274 Ling Yang, Yandong Chen, Hongliang Wang, An Luo and Kunshan Huai Oscillation Suppression Method by Two Notch Filters for Parallel Inverters under Weak Grid Conditions Reprinted from: Energies 2018 , 11 , 3441, doi:10.3390/en11123441 . . . . . . . . . . . . . . . . . . . 290 Huadian Xu, Jianhui Su, Ning Liu and Yong Shi A Grid-Supporting Photovoltaic System Implemented by a VSG with Energy Storage Reprinted from: Energies 2018 , 11 , 3152, doi:10.3390/en11113152 . . . . . . . . . . . . . . . . . . . 310 Pan Hu, Hongkun Chen, Kan Cao, Yuchuan Hu, Ding Kai, Lei Chen and Yi Wang Coordinated Control of Multiple Virtual Synchronous Generators in Mitigating Power Oscillation Reprinted from: Energies 2018 , 11 , 2788, doi:10.3390/en11102788 . . . . . . . . . . . . . . . . . . . 329 Rongsheng Liu, Minfang Peng and Xianghui Xiao Ultra-Short-Term Wind Power Prediction Based on Multivariate Phase Space Reconstruction and Multivariate Linear Regression Reprinted from: Energies 2018 , 11 , 2763, doi:10.3390/en11102763 . . . . . . . . . . . . . . . . . . . 346 Yunlu Li, Junyou Yang, Haixin Wang, Weichun Ge and Yiming Ma Leveraging Hybrid Filter for Improving Quasi-Type-1 Phase Locked Loop Targeting Fast Transient Response Reprinted from: Energies 2018 , 11 , 2472, doi:10.3390/en11092472 . . . . . . . . . . . . . . . . . . . 363 vi Nadia Maria Salgado-Herrera, David Campos-Gaona, Olimpo Anaya-Lara, Aurelio Medina-Rios, Roberto Tapia-S ́ anchez and Juan Ramon Rodr ́ ıguez-Rodr ́ ıguez THD Reduction in Wind Energy System Using Type-4 Wind Turbine/PMSG Applying the Active Front-End Converter Parallel Operation Reprinted from: Energies 2018 , 11 , 2458, doi:10.3390/en11092458 . . . . . . . . . . . . . . . . . . . 382 Yalong Hu and Wei Wei Improved Droop Control with Washout Filter Reprinted from: Energies 2018 , 11 , 2415, doi:10.3390/en11092415 . . . . . . . . . . . . . . . . . . . 405 Adel Merabet Adaptive Sliding Mode Speed Control for Wind Energy Experimental System Reprinted from: Energies 2018 , 11 , 2238, doi:10.3390/en11092238 . . . . . . . . . . . . . . . . . . . 423 Rosario Miceli, Giuseppe Schettino and Fabio Viola A Novel Computational Approach for Harmonic Mitigation in PV Systems with Single-Phase Five-Level CHBMI Reprinted from: Energies 2018 , 11 , 2100, doi:10.3390/en11082100 . . . . . . . . . . . . . . . . . . . 437 Thuy Vi Tran, Seung-Jin Yoon and Kyeong-Hwa Kim An LQR-Based Controller Design for an LCL-Filtered Grid-Connected Inverter in Discrete-Time State-Space under Distorted Grid Environment Reprinted from: Energies 2018 , 11 , 2062, doi:10.3390/en11082062 . . . . . . . . . . . . . . . . . . . 457 Xing Li and Hua Lin Stability Analysis of Grid-Connected Converters with Different Implementations of Adaptive PR Controllers under Weak Grid Conditions Reprinted from: Energies 2018 , 11 , 2004, doi:10.3390/en11082004 . . . . . . . . . . . . . . . . . . . 485 Xiangwu Yan, Xueyuan Zhang, Bo Zhang, Zhonghao Jia, Tie Li, Ming Wu and Jun Jiang A Novel Two-Stage Photovoltaic Grid-Connected Inverter Voltage-Type Control Method with Failure Zone Characteristics Reprinted from: Energies 2018 , 11 , 1865, doi:10.3390/en11071865 . . . . . . . . . . . . . . . . . . . 502 Xiangwu Yan, Jiajia Li, Ling Wang, Shuaishuai Zhao, Tie Li, Zhipeng Lv and Ming Wu Adaptive-MPPT-Based Control of Improved Photovoltaic Virtual Synchronous Generators Reprinted from: Energies 2018 , 11 , 1834, doi:10.3390/en11071834 . . . . . . . . . . . . . . . . . . . 519 Zakariya M. Dalala, Osama Saadeh, Mathhar Bdour and Zaka Ullah Zahid A New Maximum Power Point Tracking (MPPT) Algorithm for Thermoelectric Generators with Reduced Voltage Sensors Count Control † Reprinted from: Energies 2018 , 11 , 1826, doi:10.3390/en11071826 . . . . . . . . . . . . . . . . . . . 537 Yongli Wang, Yujing Huang, Yudong Wang, Haiyang Yu, Ruiwen Li and Shanshan Song Energy Management for Smart Multi-Energy Complementary Micro-Grid in the Presence of Demand Response Reprinted from: Energies 2018 , 11 , 974, doi:10.3390/en11040974 . . . . . . . . . . . . . . . . . . . . 553 Hui Liang, Long Guo, Junhong Song, Yong Yang, Weige Zhang and Hongfeng Qi State-of-Charge Balancing Control of a Modular Multilevel Converter with an Integrated Battery Energy Storage Reprinted from: Energies 2018 , 11 , 873, doi:10.3390/en11040873 . . . . . . . . . . . . . . . . . . . . 573 vii About the Special Issue Editors Teuvo Suntio received his PhD in electrical engineering from Helsinki University of Technology, Espoo, Finland, in 1992. He has worked in the power electronics-related industry for 22 years, and started his academic career in 1998. He is currently Professor in power electronics at Tampere University, Tampere, Finland. His research interests include the dynamic modeling and analysis of switched-mode converters in conventional and renewable energy applications. Tuomas Messo received his PhD in electrical engineering from Tampere University of Technology, Tampere, Finland, in 2014. He is currently working at GE Grid Solutions, Tampere, Finland, and holds the position of Adjunct Professor in power electronics at Tampere University, Tampere, Finland. His research interests include the dynamic modeling, analysis, and control design of grid-connected three-phase power converters in renewable energy applications and microgrids. ix Preface to ”Power Electronics in Renewable Energy Systems” The observed changes in weather conditions have accelerated the installation of renewable energy-based electricity systems around the world. Large-scale utilization of renewable energy sources in electricity production requires the use of power electronic converters to integrate the renewable energy systems into the power grids. This integration brings about certain challenges in terms of stability and robust performance of the power grids, which have to be solved before the wellbeing of the power grids can be guaranteed. This Special Issue of Energies aims to reveal the state-of-art in addressing interfacing problematics. According to the published papers, clear advancements have taken place, but the most critical issues remain unsolved. Direct power control with self-synchronizing synchronverters may be the most promising technique for solving the main stability problem, although many unsolved problems still persist. Another challenge in renewable energy production is the fluctuating nature of the available energy in renewable energy sources, which require utilization of stored energy to smooth the fluctuations. Different storage battery technologies are available, but their production may pose problems in the long term. Teuvo Suntio, Tuomas Messo Special Issue Editors xi energies Editorial Power Electronics in Renewable Energy Systems Teuvo Suntio * and Tuomas Messo Electrical Engineering Unit, Tampere University, Tampere 33720, Finland; tuomas.messo@tuni.fi * Correspondence: teuvo.suntio@tuni.fi; Tel.: + 358-400-828-431 Received: 13 May 2019; Accepted: 14 May 2019; Published: 15 May 2019 1. Introduction Renewable energy-based generation of electrical energy is currently experiencing rapid growth in electrical grids. The dynamics of electrical grids are starting to change due to the large-scale integration of power electronic converters into the grid for facilitating the utilization of renewable energy. The main problem with the use of grid-connected power electronic converters is the negative incremental resistor behavior observed in their input and output terminal impedances, which makes the grid prone to harmonic stability problems that are observed nowadays more and more often. This problem is di ffi cult or even impossible to remove because the converters have to be synchronized to the grid frequency, which actually creates the named output terminal-related problematic behavior. The input terminal-related problem is usually related to the output terminal feedback arrangement or to the grid synchronization actions. There are naturally many other problems, which can be related to the application of the renewable energy sources as an input source of the converters, and which can change their dynamic behavior profoundly. The Special Issue of Energies “Power Electronics in Renewable Energy Systems” was intended to disseminate new promising methods to tackle the stability problems observed to take place in power grids, and to provide new information to support the understanding of the origin of those problems. The particular topics of interest in the original call for papers included, but were not limited to: • Stability and modeling of large grid-connected PV and wind power plants; • Dynamic modeling and control design of renewable energy converters in grid feeding, supporting, and forming modes; • Impedance-based grid interaction studies; • Issues related to control, stability, diagnostics and interfacing of energy storage in renewable energy systems; • Voltage and frequency control of grids with high penetration of renewable distributed generation. This special issue of Energies contains four invited submissions [ 1 – 4 ], three review articles [ 5 – 7 ], and twenty-three research articles [ 8 – 30 ] covering di ff erent topics in renewable energy systems. The authors’ geographical distribution is: China (14); Finland (4); Korea (2); The Netherlands (1), Japan (1); Israel (1); USA (1); Canada (1); India (1); Jordan (1); Malaysia (1); Italy (1); UK (1). We thank the editorial sta ff and reviewers for their great e ff orts and help during the process. 2. Brief Overview of the Contributions to This Special Issue The main contributions of the paper are briefly reviewed in the following subsections. The first subsection reviews the invited papers, the second subsection reviews the review papers, and the third subsection reviews the article-type papers that are not reviewed in first subsection. No topic-specific classification is applied. Energies 2019 , 12 , 1852; doi:10.3390 / en12101852 www.mdpi.com / journal / energies 1 Energies 2019 , 12 , 1852 2.1. Invited Papers Suntio et al. [ 1 ] introduce the full picture of the source and load interaction formulations covering typical three-phase grid connected inverters, which are applied in renewable energy applications. The complexity of the analyses is obvious. The paper contains both simulated and experimental evidence to support the theoretical findings in the paper. It is clearly demonstrated that omitting the cross-coupling elements in the associated impedances will lead to very poor accuracy of the interaction analyses. Messo et al. [ 2 ] demonstrate that it is possible to implement an emulator for a grid-connected three-phase inverter by applying a high-bandwidth amplifier, which can be used e ff ectively to study the dynamic behavior of AC microgrids. Sun et al. [ 3 ] study the behavior of the phase locked loop (PLL) of the grid-connected power converter during a phenomenon known as rate of change of frequency (ROCOF) and its influence on the stability of the grid. Such a phenomenon has been observed to take place in the Bonaire Island power grid as a consequence of a grid fault. According to the study, the PLL control bandwidth has a crucial role in the well-being of the power grid. Amer et al. [ 4 ] studied the maximum power point (MPP) tracking process, where the perturbation frequency was adaptive instead of the step size to ensure a fast and trouble-free tracking process. The demonstrations show that the proposed technique works well. 2.2. Review Papers One of the review papers [ 1 ] was already reviewed in Section 2.1. Suntio [ 5 ] introduces the small-signal modeling and analysis of a peak-current-mode (PCM) controlled buck converter, which operates in discontinuous conduction mode (DCM). The modeling method is introduced already in 2001 but the given models are load-resistor a ff ected and do not contain the e ff ect of circuit parasitic elements. The paper shows that the load resistor hides the real location of the unstable pole, which is usually assumed to appear at the output–input voltage ratio of 2 / 3, but it can appear at the output–input voltage ratio of 1 / 2. It is also observed that the circuit elements have a significant contribution to the dynamic behavior as well. Tareen et al. [ 6 ] compare the use of static compensator (STATCOM) and active power filter (APF) in tackling the power quality issues in the case of high penetration of renewable energy sources in the power grid. The paper provides a comprehensive survey of the related topics and a wide list of key finds, which cannot be presented briefly in this overview. 2.3. Article Papers Wang et al. [ 7 ] proposes a modified self-synchronized synchronverter, which works better in an unbalanced grid compared to the conventional self-synchronized synchronverters. The main benefit of the synchronverters is that there is no need for PLL function, which would eliminate the negative incremental resistor phenomenon in the output impedance of the grid-connected converter. Rizqiawan et al. [8] introduce the development of grid-connected inverter modules intended for teaching microgrid issues to electrical engineering students. Liu et al. [ 9 ] introduce issues related to the concept known as Energy Internet, where microgrid control is implemented based on the internet by utilizing the concept of an energy router. In this study, the primary energy sources are considered to be a photovoltaic array, an energy storage battery, and the battery of an electric vehicle. Opila et al. [10] introduce virtual oscillator control of voltage-sourced and current-controlled power converters. The paper is highly theoretical and lacks a direct practical connection to the real world. Anuradha et al. [11] introduce the design and analysis of a non-isolated three-port single ended primary inductance converter (SEPIC) for renewable energy source applications, where the input section of the converter is used as a modular section for interfacing di ff erent renewable energy sources. The problem in the paper is that the PV interfacing is not considered correctly, which is still quite a common issue in renewable energy interfacing studies. Park et al. [ 12 ] introduce the methods to control the speed of a turbine generator, where the energy of the system is extracted from di ff erent heat sources. The control algorithm indirectly estimates the required speed of the generator. The rest of the converter system is 2 Energies 2019 , 12 , 1852 similar to the full-power converter systems used in wind power interfacing. Yan et al. [ 13 ] study the inertia and damping characteristics of a doubly-fed induction generator (DFIC) during a grid fault. The paper proposes methods to control the frequency in such a manner that the system stability is improved. Suntio [ 14 ] provides small-signal models for a peak current mode-controlled boost converter, which operates in discontinuous operation mode with all the power stage parasitic elements included. It is shown that the modeling technique developed in the early 2000s yields accurate models for the boost converter as well when the load resistor e ff ect is removed. Yang et al. [ 15 ] study the oscillation phenomenon observed to take place between the parallel-connected grid-tied inverters in weak grid conditions. The damping method is based on adding two virtual impedances in series and in parallel with the original output impedance of the inverter. The practical experiments show that the proposed technique works. Xu et al. [ 16 ] introduce methods to provide grid-supporting functions in photovoltaic systems by utilizing battery energy storage to create a virtual synchronous generator. The power system is claimed to be able to operate without phase locked loop grid synchronizing. The concept is validated with simulations. Hu et al. [17] study the coordinated control of virtual synchronous generators. The developed strategy is validated by simulations. Liu et al. [ 18 ] study the ultra-short-term wind power prediction methods, which are based on multivariate phase–space reconstruction and linear regression. The developed method is shown to be more accurate than earlier developed methods. Li et al. [ 19 ] study the design of phase lock loop-based grid synchronizing aiming for fast transient behavior. The proposed concept is based on the application of adaptive notch filtering and moving average filtering as the inner loop of the phase locked loop. The experimental validation proves the improvement of the proposed technique. Salgado-Herrera et al. [ 20 ] study the total harmonic distortion (THD) in wind energy systems showing that the utilization of an active front-end converter to provide the DC-link voltage will reduce the overall THD. The concept is verified by simulation. Hu et al. [ 21 ] propose an improved droop control method based on the conventional droop control with a washout filter controller. The proposed method is validated by utilizing the hardware-in-the-loop (HIL) method. Merabet [ 22 ] studies the application of adaptive sliding mode speed control of a wind energy generator. The proposed technique is validated experimentally by utilizing a small-scale prototype system. Miceli et al. [23] study harmonic mitigation by means of computational methods in a single-phase five-level cascaded H-bridge multilevel inverter. The developed method is experimentally validated with a small-scale prototype. Tran et al. [ 24 ] study the control design of a grid-connected inverter under distorted grid conditions based on the linear-quadratic regulator technique. The proposed control technique is based on the internal model control principle. The experimental validation shows that the proposed technique works well. Li et al. [ 25 ] study the e ff ect of adaptive resonant controllers on the stability of the grid-connected inverters under weak grid conditions. The validation of the studies is performed experimentally. The paper provides useful tips for implementing adaptive resonant controllers to avoid problems. Yan et al. [ 26 ] study the control methods of grid-connected inverters to make them mimic the characteristics of a synchronous generator. The proposed techniques are validated by simulations, which do not necessarily convince the readers. Yan et al. [ 27 ] study the adaptive maximum power point tracking-based control to create the properties of a synchronous generator. The reader may have problems understanding the proposed techniques because the authors have not explicitly specified in which operation mode the system is working. Dalala et al. [ 28 ] propose an algorithm for thermoelectric generators to track the maximum power point (MPP). The method is based on indirectly detecting the open-circuit voltage and estimating short circuit current, which are then used for tracking the MPP. The experimental waveforms show that the proposed technique tracks the MPP very quickly. Wang et al. [ 29 ] study the energy management in a micro-grid based on demand response. An optimization strategy is developed for minimizing the operating costs. The strategy is tested on a real case study. Liang et al. [ 30 ] study the balancing of the charges of embedded storage batteries in series-connected switching modules. The proposed control strategy is experimentally tested and shown to work well. 3 Energies 2019 , 12 , 1852 2.4. Discussions The published papers represent the current main topics related to renewable energy. The lack of full understanding of the dynamics of the converters, which are applied in a renewable energy system, still dominates the discussions in this field even if hundreds of papers have already been published where the true nature has been explicitly presented. The lack of experimental validation will also usually reduce the acceptance of the information. Conflicts of Interest: The authors declare no conflict of interest. References 1. Suntio, T.; Messo, T.; Berg, M.; Alenius, H.; Reinikka, T.; Luhtala, R.; Zenger, K. Impedance-based interactions in grid-tied three-phase inverters in renewable energy applications. Energies 2019 , 17 , 464. [CrossRef] 2. Messo, T.; Luhtala, R.; Roinila, T.; de Jong, E.; Scharrenberg, R.; Calddognetto, T.; Mattavelli, P.; Sun, Y.; Fabian, A. Using high-bandwidth voltage amplifier to emulate grid-following inverter for ac microgrid dynamics studies. Energies 2019 , 12 , 379. [CrossRef] 3. Sun, Y.; de Jong, E.; Wang, X.; Yang, D.; Blaabjerg, F.; Cuk, V.; Cobben, J. The impact of PLL dynamics on the low inertia power grid: A case study of Bonaire Island power system. Energies 2019 , 12 , 1259. [CrossRef] 4. Amer, E.; Kuperman, A.; Suntio, T. Direct fixed-step power point tracking algorithms with adaptive perturbation frequency. Energies 2019 , 12 , 399. [CrossRef] 5. Suntio, T. Dynamic modeling and analysis of PCM-controlled DCM-operating buck converters—A reexamination. Energies 2018 , 11 , 1267. [CrossRef] 6. Tareen, W.; Aamir, M.; Mekhilef, S.; Nakaoka, M.; Seyedmahmoudian, M.; Horan, B.; Memon, M.; Baig, N. Mitigation of power quality issues due to high penetration of renewable energy sources in Electric gride systems using three-phase APF / STATCOM technologies: A review. Energies 2018 , 11 , 1491. [CrossRef] 7. Wang, X.; Chen, L.; Sun, D.; Zhang, L.; Nian, H. A modified self-synchronized synchronverter in unbalanced power grids with balanced currents and restrained power ripples. Energies 2019 , 12 , 923. [CrossRef] 8. Rizqiawan, A.; Hadi, P.; Fujita, G. Development of grid-connected inverter experiment modules for microgrid learning. Energies 2019 , 12 , 476. [CrossRef] 9. Liu, Y.; Li, Y.; Liang, H.; He, J.; Cui, H. Energy routing control strategy for integrated microgrids including photovoltaic, battery-energy storage and electric vehicles. Energies 2019 , 12 , 302. [CrossRef] 10. Opila, D.; Kintzley, K.; Shabshab, S.; Phillips, S. Virtual oscillator control of equivalent voltage-sourced and current-controlled power converters. Energies 2019 , 12 , 298. [CrossRef] 11. Anuradha, C.; Chellamma, N.; Maqsood, S.; Viljayalakshmi, S. Design and analysis of non-isolated three-port SEPIC converter for integrating renewable energy sources. Energies 2019 , 12 , 221. [CrossRef] 12. Park, H.-S.; Heo, H.-J.; Choi, B.-S.; Kim, K.-C.; Kim, J.-M. Speed control for turbine-generator of ORC power generation system and experimental implementation. Energies 2019 , 12 , 200. [CrossRef] 13. Yan, X.; Song, Z.; Xu, Y.; Sun, Y.; Wang, Z.; Sun, X. Study of inertia and damping characteristics of doubly fed induction generators and improved additional frequency control strategy. Energies 2019 , 12 , 38. [CrossRef] 14. Suntio, T. Modeling and analysis of a PCM-controlled boost converter designed to operate in DCM. Energies 2019 , 12 , 4. 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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http: // creativecommons.org / licenses / by / 4.0 / ). 5 energies Review Impedance-Based Interactions in Grid-Tied Three-Phase Inverters in Renewable Energy Applications Teuvo Suntio 1, *, Tuomas Messo 1 , Matias Berg 1 , Henrik Alenius 1 , Tommi Reinikka 1 , Roni Luhtala 2 and Kai Zenger 3 1 Laboratory of Electrical Engineering, Tampere University, 33720 Tampere, Finland; tuomas.messo@tuni.fi (T.M.); matias.berg@tuni.fi (M.B.); henrik.alenius@tuni.fi (H.A.); tommi.reinikka@tuni.fi (T.R.) 2 Laboratory of Automation and Hydraulics, Tampere University, 33720 Tampere, Finland; roni.luhtala@tuni.fi 3 Department of Electrical Engineering and Automation, Aalto University, 02150 Espoo, Finland; kai.zenger@aalto.fi * Correspondence: teuvo.suntio@tuni.fi; Tel.: +358-400-828-431 Received: 12 December 2018; Accepted: 28 January 2019; Published: 31 January 2019 Abstract: Impedance-ratio-based interaction analyses in terms of stability and performance of DC-DC converters is well established. Similar methods are applied to grid-connected three-phase converters as well, but the multivariable nature of the converters and the grid makes these analyses very complex. This paper surveys the state of the interaction analyses in the grid-connected three-phase converters, which are used in renewable-energy applications. The surveys show clearly that the impedance-ratio-based stability assessment are usually performed neglecting the cross-couplings between the impedance elements for reducing the complexity of the analyses. In addition, the interactions, which affect the transient performance, are not treated usually at all due to the missing of the corresponding analytic formulations. This paper introduces the missing formulations as well as explicitly showing that the cross-couplings of the impedance elements have to be taken into account for the stability assessment to be valid. In addition, this paper shows that the most accurate stability information can be obtained by means of the determinant related to the associated multivariable impedance ratio. The theoretical findings are also validated by extensive experimental measurements. Keywords: source and load impedance; transient dynamics; stability; grid synchronization; power electronics; power grid 1. Introduction The negative-incremental-resistor oscillations were observed to take place, in practice, already in the early 1970s when an LC-type input filter was connected at the input terminal of regulated converters as reported in References [ 1 , 2 ]. The development of the dynamic modeling method known as state-space averaging (SSA) in the early 1970s [ 3 – 5 ] enabled the theoretical studies of the origin of the input-filter interactions, which were published in the mid 1970s [ 6 , 7 ] by Middlebrook. He stated later that he applied the extra-element-theorem-based (EET) method [ 8 , 9 ] when developing the input-filter-design rules in References [6,7] for the cascaded input-filter-converter system. According to the EET method, the source or load-system-affected transfer function G S/L org ( s ) of the converter can be given by G S/L org = 1 + Z n − 1 Y n − 2 1 + Z d − 1 Y d − 2 × G org (1) Energies 2019 , 12 , 464; doi:10.3390/en12030464 www.mdpi.com/journal/energies 6 Energies 2019 , 12 , 464 where G org ( s ) denotes the original or unterminated transfer function of the converter, Z n − 1 Y n − 2 denotes the impedance-admittance product of the numerator polynomial, and Z d − 1 Y d − 2 denotes the impedance-admittance product of the denominator polynomial, respectively. The formulation in Equation (1) is very useful, because it defines automatically the correct order of the impedance-like elements in the numerator and denominator impedance-admittance products, to perform the source/load analysis in a correct manner as instructed in References [ 10 – 12 ] and implied in Figure 1. The most crucial factor in the analysis of the cascaded systems is to recognize that the duality must be valid at the interface between the upstream and downstream subsystems. This means that the only valid source-sink pairs are Figure 1a,d as well as Figure 1b,c, respectively. The cascaded system will not be proper with the other source-sink combinations at the interface between the subsystems because of violating Kirchhoff’s laws. Figure 1. The source/sink equivalent circuits: ( a ) Thevenin’s source, ( b ) Norton’s source, ( c ) Thevenin’s sink, and ( d ) Norton’s sink. As Equation (1) indicates, the theoretical formulation in Equation (1) does not contain impedance ratios, but it is sometimes easier to understand the behavior of the impedance-admittance products, when the product is considered as an impedance ratio as in References [ 6 , 7 ]. The minor-loop gain launched by Middlebrook in References [6,7] actually denotes the denominator product Z d − 1 Y d − 2 as minor-loop gain, which can be given equally as Z d − 1 / Z d − 2 , because Z d − 2 = Y − 1 d − 2 . The minor-loop gain actually equals Z TH Y N according to Figure 1, which indicates explicitly that the numerator impedance of the impedance ratio (i.e., minor-loop gain) always equals the internal impedance of the voltage-type subsystem, and the denominator impedance equals the internal impedance of the current-type subsystem, respectively [10]. Stability of the cascaded system can be assessed based on Z TH Y N by applying Nyquist stability criterion [ 13 ], because ( 1 + Z TH Y N ) − 1 forms an impedance-based sensitivity function similarly as ( 1 + L x ) − 1 in control engineering [ 14 , 15 ], where L x denotes the feedback-loop gain. If the phase or gain margin of the feedback loop is low then the sensitivity function will exhibit peaking, which affects the corresponding closed-loop transfer function, and it may cause deterioration in transient response or may make the converter more prone to instability [ 14 , 15 ]. The similar phenomena will take place also in case of ( 1 + Z TH Y N ) − 1 The impedance-admittance product ( Z n − 1 Y n − 2 ) of the numerator polynomial is not directly related to the system stability similarly as Z TH Y N is. One of the elements in Z n − 1 Y n − 2 equals either Z TH or Y N depending on the type of the source/load system (cf. Figure 1), and the other element (i.e., Z n − 1 or Y n − 2 ) is a certain special impedance-like parameter, which will be introduced for the grid-tied three-phase inverters in Section 2. The special parameters of the DC-DC converters are defined in general and given also explicitly for a number of converters in Reference [ 12 ]. The impedance-based interactions via the numerator polynomial in Equation (1) may affect the control-related transfer functions or the internal input or output impedances that may deteriorated the transient behavior of the converter as demonstrated in Reference [11]. The input-filter-design rules, introduced in References [ 6 , 7 ], have been later extended to apply for stability and performance assessment in arbitrary systems as well, where the robust stability and performance are defined in the form of forbidden regions out of which the minor-loop gain ( Z TH Y N ) should stay for the robust stability to exist [ 10 , 16 – 19 ] as illustrated in Figure 2. The forbidden region induced by the input-filter-design rules [ 6 , 7 ] is assumed to be outside of the circle, which has 7