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Topic Editors

Department of Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
Prof. Dr. Yanchi Zhang
School of Electrical Engineering, Shanghai Dianji University, Shanghai 201306, China
Prof. Dr. Dongdong Li
School of Electrical Engineering, Shanghai University of Electric Power, Shanghai 200090, China
Dr. Chenghong Gu
Department of Electronic and Electrical Engineering, University of Bath, Bath BA2 7AY, UK
Department of Electrical Engineering, ESTIA Institute of Technology, 64210 Bidart, France
Dr. Nan Zhao
School of Engineering, Lancaster University, Lancaster LA1 4YW, UK

Power System Dynamics and Stability

Abstract submission deadline
closed (29 February 2024)
Manuscript submission deadline
closed (31 May 2024)
Viewed by
21026

Topic Information

Dear Colleagues,

With the increase in power electronic components and equipment, the power electronization of new power systems will lead to fundamental changes in their structural characteristics, operating characteristics and control mode, thus causing complex electromagnetic transient processes and dynamic stability problems. These will challenge the safe and stable operation of power systems. In order to ensure the safe and stable operation of power electronic power systems, the goal of this Topic is to reveal the operation mechanism of the power electronic power system, establish the numerical simulation model of the power electronic power system, analyze and study the theory of instantaneous electrical parameters and electromagnetic transient stability theory, explore new control methods and new power equipment and realize more accurate analysis models, reasonable and stable analysis ideas, control technologies and intelligent management and control strategies for power electronic power systems.

The objective of this Topic is to encourage the dissemination of new concepts, ideas and novel methods for analyzing the modeling and dynamic stability of power electronic power systems. It aims to disseminate fundamental research, innovation and information exchange in these related fields. Application papers are also highly welcome. Topics of interest include, but are not limited to:

  1. Security and stability analysis of power electronic power systems;
  2. Research on the mechanism model of power electronic power systems;
  3. Research on electromagnetic transient simulation model of power electronic power systems;
  4. Analysis of the power electronic power system simulation method;
  5. Power electronic power system oscillation analysis and suppression measures;
  6. Power electronic power system oscillation control method;
  7. Power electronic power system stability and control based on cloud computing and artificial intelligence;
  8. Parameter optimization method for power electronic power system control;
  9. Research on grid connection control strategy and method;
  10. Mechanism analysis method of power electronic power system;
  11. Power electronic oscillation suppression device;
  12. Research on operation mode of power electronic power systems.

Prof. Dr. Da Xie
Prof. Dr. Yanchi Zhang
Prof. Dr. Dongdong Li
Dr. Chenghong Gu
Dr. Ignacio Hernando-Gil
Dr. Nan Zhao
Topic Editors

Keywords

  • power electronics
  • power system
  • modeling
  • dynamic stability analysis
  • mechanism analysis
  • simulation method
  • control strategy

Participating Journals

Journal Name Impact Factor CiteScore Launched Year First Decision (median) APC
Electricity
electricity
- 4.8 2020 27.2 Days CHF 1000
Electronics
electronics
2.6 5.3 2012 16.8 Days CHF 2400
Energies
energies
3.0 6.2 2008 17.5 Days CHF 2600
Processes
processes
2.8 5.1 2013 14.4 Days CHF 2400

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Published Papers (14 papers)

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18 pages, 4469 KiB  
Article
Identifying Weak Transmission Lines in Power Systems with Intermittent Energy Resources and DC Integration
by Anqi He, Jijing Cao, Shangwen Li, Lianlian Gong, Mingming Yang and Jiawei Hu
Energies 2024, 17(16), 3918; https://doi.org/10.3390/en17163918 - 8 Aug 2024
Viewed by 525
Abstract
Nowadays, intermittent energy resources, such as wind turbines, and direct current (DC) transmission have been extensively integrated into power systems. This paper proposes an identifying method for weak lines of novel power systems with intermittent energy resources and DC lines integration, which aims [...] Read more.
Nowadays, intermittent energy resources, such as wind turbines, and direct current (DC) transmission have been extensively integrated into power systems. This paper proposes an identifying method for weak lines of novel power systems with intermittent energy resources and DC lines integration, which aims to provide decision making for control strategies of novel power systems and prevent system blackouts. First, from the perspective of power system safety and stability, a series of risk indicators for the risk assessment of vulnerable lines is proposed. Then, lines in the system are tripped one by one. The calculation method for the proposed risk indicators is introduced. The impact of each line outage on system safety and stability can be fairly evaluated by these proposed risk indicators. On this basis, each risk assessment indicator is weighted to obtain a comprehensive risk assessment indicator, and then the risk caused by each line outage on the system can be quantified efficiently. Finally, the test system of a modified IEEE-39 bus system with wind farms and DC lines integration is used to verify the applicability of the proposed method, and the effectiveness of the proposed method is also demonstrated by comparing with existing methods. Full article
(This article belongs to the Topic Power System Dynamics and Stability)
Show Figures

Figure 1

Figure 1
<p>Risk assessment index system.</p>
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<p>Improved IEEE 39 bus system.</p>
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<p>Probability AC/DC power flow results: (<b>a</b>) bus voltage; (<b>b</b>) line transmission power.</p>
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<p>Risk of voltage violation and line overload after each line outage: (<b>a</b>) bus voltage violation risk; (<b>b</b>) line overload risk.</p>
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<p>Static security after each line outage.</p>
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<p>Static frequency stability after each line outage.</p>
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<p>Static rotor angle stability after each line outage.</p>
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<p>Static voltage stability after each line outage.</p>
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<p>Comprehensive index after each line outage.</p>
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17 pages, 2912 KiB  
Article
A Contoured Controller Bode-Based Iterative Tuning Method for Multi-Band Power System Stabilizers
by Hao Xu, Chongxi Jiang and Deqiang Gan
Energies 2024, 17(13), 3243; https://doi.org/10.3390/en17133243 - 1 Jul 2024
Viewed by 858
Abstract
An iterative tuning method for multi-band power system stabilizers is proposed, which utilizes the contoured controller Bode (CCBode) plot. The typical multi-band power system stabilizer, PSS4B, is conceptualized as a series connection of two filters: a band-pass filter and a phase compensator. The [...] Read more.
An iterative tuning method for multi-band power system stabilizers is proposed, which utilizes the contoured controller Bode (CCBode) plot. The typical multi-band power system stabilizer, PSS4B, is conceptualized as a series connection of two filters: a band-pass filter and a phase compensator. The tuning process involves a space searching approach for the phase compensator to ensure its phase–frequency response remains within acceptable bounds. Subsequently, the CCBode plot is employed to adjust the magnitude–frequency response of the band-pass filter, thereby enhancing stability performance across a broad frequency range. The method proposed can be applied to the parameter design of the multi-band power system stabilizer PSS4B in the power system to suppress the low-frequency oscillations of the local mode and inter-regional mode in the system. The effectiveness of this proposed method is demonstrated through case studies of the four -machine/two-area system and the North China Power Grid. Full article
(This article belongs to the Topic Power System Dynamics and Stability)
Show Figures

Figure 1

Figure 1
<p>Standard IEEE model of PSS4B.</p>
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<p>Revised model of PSS4B.</p>
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<p>Controller <span class="html-italic">C</span>(<span class="html-italic">s</span>, <b>d</b>) matches a reference model <span class="html-italic">C<sub>r</sub></span>(<span class="html-italic">s</span>).</p>
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<p>Block diagram representing installing a PSS to the <span class="html-italic">k-</span>th generator of a multi-machine system.</p>
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<p>The Nyquist contour for: (<b>a</b>) Hurwitz stability; (<b>b</b>) D-stability.</p>
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<p>Iterative design process of PSS4B.</p>
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<p>Four-machine/two-area system.</p>
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<p>CCBode plots with <span class="html-italic">ζ</span> = 0: PSS4B(1).</p>
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<p>CCBode plots with <span class="html-italic">ζ</span> = 0: PSS4B(2).</p>
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<p>CCBode plots with <span class="html-italic">ζ</span> = 3%: PSS4B(2).</p>
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<p>CCBode plots with <span class="html-italic">ζ</span> = 3%: PSS4B(3).</p>
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<p>Simulation results of four-machine/two-area system.</p>
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<p>CCBode plots with <span class="html-italic">ζ</span> = 3%: PSS4B(4).</p>
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<p>CCBode plots with <span class="html-italic">ζ</span> = 3%: PSS4B(5).</p>
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30 pages, 16470 KiB  
Article
Research on Torque Characteristics of Vehicle Motor under Multisource Excitation
by Mingliang Yang, Yangyang Bao, Haibo Huang, Yalei Liu, Honglin Zhu and Weiping Ding
Electronics 2024, 13(11), 2019; https://doi.org/10.3390/electronics13112019 - 22 May 2024
Viewed by 653
Abstract
A hub motor is integrated into an electric wheel. The external excitation is complex and the heat dissipation conditions are poor. The working temperature of the hub motor easily becomes too high, resulting in large fluctuations in the output torque, which affect its [...] Read more.
A hub motor is integrated into an electric wheel. The external excitation is complex and the heat dissipation conditions are poor. The working temperature of the hub motor easily becomes too high, resulting in large fluctuations in the output torque, which affect its service life. Taking a four-wheel hub-driven electric vehicle as the research object and aiming to resolve the issue of inaccurate prediction of the output torque of the hub motor in the real operating environment of the vehicle, a method for analyzing the temperature rise and torque characteristics of the hub motor considering multisource excitation and magnetic–thermal bidirectional coupling is proposed. First, the multisource excitation transmission path of the hub motor and the coupling principle of the road-electric wheel-vehicle body suspension system are analyzed from three aspects: the electromagnetic effect of the hub motor itself, the tire-ground effect, and the interaction between suspension (body) and electric wheel. We concluded that the load torque and air gap change in the motor are the key factors of its torque characteristics. On this basis, a dynamic model of the road-electric wheel-suspension-vehicle body system, an electromagnetic field model of the hub motor, and a temperature field model are established, and the influence of load torque and air gap change on the loss of in-wheel motor under multisource excitation is analyzed. Furthermore, based on the magnetic–thermal bidirectional coupling method, the motor loss under the combined action of load torque and air gap change is introduced into the temperature field model, and combined with the electromagnetic field model of the hub motor, the temperature distribution law and torque characteristics of the hub motor are accurately predicted. Finally, the accuracy and effectiveness of the calculation results of the temperature and torque characteristics of the hub motor are verified via an electric wheel bench test. Full article
(This article belongs to the Topic Power System Dynamics and Stability)
Show Figures

Figure 1

Figure 1
<p>Multisource excitation transmission path of a hub-drive vehicle.</p>
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<p>Coupling principle of the road-electric wheel-suspension system.</p>
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<p>Force analysis of the electric wheel during rolling.</p>
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<p>Change rule of dynamic eccentricity <math display="inline"><semantics> <mrow> <msub> <mi>e</mi> <mi>d</mi> </msub> </mrow> </semantics></math>.</p>
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<p>Relationships between various models.</p>
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<p>(<b>a</b>) 1/4 suspension model principle. (<b>b</b>) 1/4 suspension dynamics model.</p>
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<p>Finite element model of the hub motor electromagnetic field.</p>
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<p>Relationship between the speed and output torque of the hub motor.</p>
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<p>Finite element model of the hub motor temperature field.</p>
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<p>Magnetic–thermal two-way coupling process.</p>
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<p>(<b>a</b>) Relationship between the output torque of the hub motor and the wheel speed under different working conditions. (<b>b</b>) Tire dynamic load under different working conditions.</p>
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<p>(<b>a</b>) Core loss of the hub motor; (<b>b</b>) eddy current loss of the hub motor; (<b>c</b>) winding loss of the hub motor; (<b>d</b>) output torque of the hub motors.</p>
Full article ">Figure 12 Cont.
<p>(<b>a</b>) Core loss of the hub motor; (<b>b</b>) eddy current loss of the hub motor; (<b>c</b>) winding loss of the hub motor; (<b>d</b>) output torque of the hub motors.</p>
Full article ">Figure 13
<p>(<b>a</b>) Change in the radial magnetic density at 600 rpm; (<b>b</b>) Change in the unbalanced magnetic pull <math display="inline"><semantics> <mrow> <msub> <mi>F</mi> <mi>y</mi> </msub> </mrow> </semantics></math> at 600 rpm.</p>
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<p>Equivalent stiffness <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mrow> <mi>U</mi> <mi>M</mi> <msub> <mi>P</mi> <mi>y</mi> </msub> </mrow> </msub> </mrow> </semantics></math> curves of the motor at different speeds.</p>
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<p>(<b>a</b>) Force between the stator and rotor; (<b>b</b>) relative offset of the stator and rotor.</p>
Full article ">Figure 16
<p>(<b>a</b>) Output torque of the hub motor caused by changes in the air gap at 600 rpm; (<b>b</b>) core loss of the hub motor caused by air gap changes at 600 rpm; (<b>c</b>) eddy current loss of the hub motor caused by air gap changes at 600 rpm; (<b>d</b>) winding loss of the hub motor caused by air gap changes at 600 rpm.</p>
Full article ">Figure 16 Cont.
<p>(<b>a</b>) Output torque of the hub motor caused by changes in the air gap at 600 rpm; (<b>b</b>) core loss of the hub motor caused by air gap changes at 600 rpm; (<b>c</b>) eddy current loss of the hub motor caused by air gap changes at 600 rpm; (<b>d</b>) winding loss of the hub motor caused by air gap changes at 600 rpm.</p>
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<p>Overall temperature cloud diagrams of the hub motor at 200 rpm, 400 rpm, and 600 rpm.</p>
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<p>(<b>a</b>) Temperature variation curves of the hub motor stator. (<b>b</b>) Temperature variation curves of the hub motor rotor. (<b>c</b>) Temperature variation curves of the hub motor winding. (<b>d</b>) Temperature variation curves of the hub motor permanent magnet.</p>
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<p>Changes in the output torque of the hub motor at 600 rpm.</p>
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<p>Temperature rise test system of the 1/4 suspension hub motor driven by the hub.</p>
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<p>Rotor and winding test temperature and calculated temperature curves at 600 rpm.</p>
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<p>Motor test torque with time at 600 rpm.</p>
Full article ">Figure A1
<p>(<b>a</b>) Change in the radial magnetic density at 200 rpm. (<b>b</b>) Change in unbalanced magnetic pull <math display="inline"><semantics> <mrow> <msub> <mi>F</mi> <mi>y</mi> </msub> </mrow> </semantics></math> at 200 rpm.</p>
Full article ">Figure A2
<p>(<b>a</b>) Change in the radial magnetic density at 200 rpm. (<b>b</b>) Change in unbalanced magnetic pull <math display="inline"><semantics> <mrow> <msub> <mi>F</mi> <mi>y</mi> </msub> </mrow> </semantics></math> at 400 rpm.</p>
Full article ">Figure A3
<p>(<b>a</b>) Output torque of the hub motor caused by changes in the air gap at 200 rpm. (<b>b</b>) Core loss of the hub motor caused by air gap changes at 200 rpm. (<b>c</b>) Eddy current loss of the hub motor caused by air gap changes at 200 rpm. (<b>d</b>) Winding loss of the hub motor caused by air gap changes at 200 rpm.</p>
Full article ">Figure A3 Cont.
<p>(<b>a</b>) Output torque of the hub motor caused by changes in the air gap at 200 rpm. (<b>b</b>) Core loss of the hub motor caused by air gap changes at 200 rpm. (<b>c</b>) Eddy current loss of the hub motor caused by air gap changes at 200 rpm. (<b>d</b>) Winding loss of the hub motor caused by air gap changes at 200 rpm.</p>
Full article ">Figure A4
<p>(<b>a</b>) Output torque of the hub motor caused by changes in the air gap at 400 rpm. (<b>b</b>) Core loss of the hub motor caused by air gap changes at 400 rpm. (<b>c</b>) Eddy current loss of the hub motor caused by air gap changes at 400 rpm. (<b>d</b>) Winding loss of the hub motor caused by air gap changes at 400 rpm.</p>
Full article ">Figure A5
<p>(<b>a</b>) Output torque change in the hub motor at 200 rpm. (<b>b</b>) Output torque change in the hub motor at 400 rpm.</p>
Full article ">Figure A6
<p>(<b>a</b>) Rotor and winding test temperature and calculated temperature curves at 200 rpm. (<b>b</b>) Rotor and winding test temperature and calculated temperature curves at 400 rpm.</p>
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<p>Motor test torque curve with time at 200 rpm.</p>
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<p>Motor test torque curve with time at 400 rpm.</p>
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16 pages, 6036 KiB  
Article
Analysis of Phase-Locked Loop Filter Delay on Transient Stability of Grid-Following Converters
by Chenglin Zhang, Junru Chen and Wenjia Si
Electronics 2024, 13(5), 986; https://doi.org/10.3390/electronics13050986 - 5 Mar 2024
Cited by 2 | Viewed by 1120
Abstract
To ensure precise phase estimation within the q-axis of the phase-locked loop (PLL), integrating a filter into the q-axis loop is essential to mitigate grid-voltage harmonics. Nevertheless, the intrinsic delay characteristics of this filter impede PLL synchronization during significant grid disturbances. This study [...] Read more.
To ensure precise phase estimation within the q-axis of the phase-locked loop (PLL), integrating a filter into the q-axis loop is essential to mitigate grid-voltage harmonics. Nevertheless, the intrinsic delay characteristics of this filter impede PLL synchronization during significant grid disturbances. This study begins by developing mathematical models for three types of filters—moving-average filter (MAF) for eliminating odd harmonic components, dq-frame cascaded delayed signal cancellation (dqCDSC) filter, and notch filter (NF). Following the reduction in filter orders, a third-order nonlinear large-signal model of the PLL, incorporating an additional q-axis internal filter, is formulated. Using phase plane analysis, this study investigates the transient synchronism of the grid-following converter (GFL) and explores the influence of delay time constants from the three PLL filters on its behavior while delineating the boundaries of their basins of attraction. Theoretical findings indicate that, relative to the traditional SRF-PLL, incorporating an internal filter into the PLL compromises the transient synchronous stability of GFL. Specifically, greater filter delay time constants exacerbate the GFL’s vulnerability to transient instability amid substantial grid disturbances. Hence, careful consideration is essential when using MAF-PLL and NF-PLL in situations demanding high synchronization stability. The theoretical analyses are validated using Matlab/Simulink to verify their accuracy. Full article
(This article belongs to the Topic Power System Dynamics and Stability)
Show Figures

Figure 1

Figure 1
<p>Grid-following converter system structure.</p>
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<p>The PLL schematic diagram of the q-axis inner loop filter.</p>
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<p>Bode plots of the filter transfer function and its first-order counterpart. (<b>a</b>) Comparison of <span class="html-italic">G</span><sub>MAF</sub>(s) with approximate. (<b>b</b>) Comparison of dqCDSC<sub>n1,n2</sub>(s) with approximate. (<b>c</b>) Comparison of NF(s) with approximate.</p>
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<p>Time-Domain implementation of dqCDSC operator.</p>
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<p>The QSLS model of 3rd PLL.</p>
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<p>Surface plot of transient peak phase variation with <span class="html-italic">V</span><sub>g</sub> and <span class="html-italic">T</span>.</p>
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<p>The attraction domain of the SRF-PLL and PLLs with additional filters.</p>
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<p>Validation of the attraction domain.</p>
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<p>Phase trajectory plots of SRF-PLL and PLL with additional filters under fault conditions.</p>
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<p>The response curves of different filters for PLL with grid step of +3Hz and phase jump of +40 degrees. (<b>a</b>) <span class="html-italic">f</span><sub>pll</sub> (Hz). (<b>b</b>) Phase Error.</p>
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<p>GFL under fault conditions with PLL response curves for different inertia time constants. (<b>a</b>) Phase output. (<b>b</b>) Frequency deviation.</p>
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<p>Validation of the attraction domain. (<b>a</b>) Phase output. (<b>b</b>) Frequency deviation.</p>
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<p>Phase response of SRF-PLL and Additional Filter PLL at <span class="html-italic">V</span><sub>g</sub> = 0.35 p.u.</p>
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29 pages, 1596 KiB  
Article
Effect of a Large Proton Exchange Membrane Electrolyser on Power System Small-Signal Angular Stability
by Guy Wanlongo Ndiwulu, Eduardo Vasquez Mayen and Emmanuel De Jaeger
Electricity 2023, 4(4), 381-409; https://doi.org/10.3390/electricity4040021 - 1 Dec 2023
Viewed by 1162
Abstract
The dynamics of electrical systems have changed significantly with the increasing penetration of non-conventional loads such as hydrogen electrolysers. As a result, detailed investigations are required to quantify and characterize these loads’ effects on the dynamic response of interconnected synchronous machines after being [...] Read more.
The dynamics of electrical systems have changed significantly with the increasing penetration of non-conventional loads such as hydrogen electrolysers. As a result, detailed investigations are required to quantify and characterize these loads’ effects on the dynamic response of interconnected synchronous machines after being subjected to a disturbance. Many studies have focused on the effects of conventional static and dynamic loads. However, the impact of hydrogen electrolysers on the stability of power systems’ rotor angles is rarely studied. This paper assesses the effect of proton exchange membrane (PEM) electrolysers on small-disturbance rotor-angle stability. Dynamic modelling and the control of a PEM electrolyser as a load are first studied to achieve this. Then, the proposed electrolyser model is tested in the Amercoeur plant, which is part of the Belgian power system, to study its effect on the small-signal rotor-angle stability. Two approaches are considered to examine this impact: an analytical approach and time-domain simulations. The analytical approach consists of establishing a state-space model of the Belgian test system through linearisation around an operating point of the non-linear differential and the algebraic equations of the synchronous generators, the PEM electrolyser, the loads, and the network. The obtained state-space model allows for the determination of the eigenvalues, which are useful to evaluate the effect of the PEM electrolyser on the small-signal rotor-angle stability. This impact is investigated by examining the movement of the eigenvalues in the left complex half-plane. The obtained results show that the PEM electrolyser affects the electromechanical modes of synchronous machines by increasing their oscillation frequencies. The results also show that the effect of the electrolyser on these modes can be improved by adjusting the inertial constant and the damping coefficient of the synchronous machines. These results are consolidated through time-domain simulations using the software Matlab/Simscape from the version MatlabR2022a-academic use from Mathworks. Full article
(This article belongs to the Topic Power System Dynamics and Stability)
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Figure 1

Figure 1
<p>Test grid around the Belgian Amercoeur plant, in which 100 MW of PEM electrolysers are connected to the grid through a 12-pulse thyristor rectifier. The number of each busbar is given in red.</p>
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<p>Dynamic response of the cell voltage of each of the four electrochemical models proposed in the literature as a function of the cell current. The cell input current is set to 5 A.</p>
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<p>Transient response of the cell voltage of each of the four electrochemical models proposed in the literature as a function of the cell current. The cell input current is set to 5 A.</p>
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<p>Hydrogen PEM electrolyser model connected to the grid through a 12-pulse thyristor rectifier.</p>
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<p>Electrical model of a PEM electrolyser and 12-pulse thyristor rectifier.</p>
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<p>Physical system of the 12-pulse thyristor rectifier associated with the electrolyser model in the s domain.</p>
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<p>Complete control structure composed of an internal current control loop and an external voltage control loop.</p>
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<p>Steady-state conditions of the PEM electrolyser connected to <math display="inline"><semantics> <mrow> <mi>B</mi> <mi>u</mi> <mi>s</mi> <mi>b</mi> <mi>a</mi> <mi>r</mi> <mspace width="3.33333pt"/> <mn>4</mn> </mrow> </semantics></math>: (<b>a</b>) DC electrolyser current; (<b>b</b>) firing angle; (<b>c</b>) DC voltage.</p>
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<p><span class="html-italic">n</span> PEM electrolyser models connected to the grid through a 12-pulse thyristor rectifier.</p>
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<p>Fractions of constant impedance load and constant current load dependent on the number of electrolysers connected in parallel on the DC rectifier side.</p>
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<p>Firing angle associated with the parameters of the proportional-integral controller.</p>
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<p>The modelled system’s modes in the complex plane: (<b>a</b>) without connecting the PEM electrolyser to test system; (<b>b</b>) with 100 MW of PEM electrolysers connected to the grid. The modes in the absence of the electrolyzer are depicted in blue, while those incorporating the electrolyzer are illustrated in red.</p>
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<p>Movement of modes <math display="inline"><semantics> <msub> <mi>λ</mi> <mn>1</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>λ</mi> <mn>2</mn> </msub> </semantics></math> caused by changes in the inertial constant value of the synchronous generator connected to <math display="inline"><semantics> <mrow> <mi>B</mi> <mi>u</mi> <mi>s</mi> <mi>b</mi> <mi>a</mi> <mi>r</mi> <mspace width="3.33333pt"/> <mn>4</mn> </mrow> </semantics></math>: <math display="inline"><semantics> <msub> <mi>H</mi> <mn>1</mn> </msub> </semantics></math> = 3 to 7 s. The modes in the absence of the electrolyzer are depicted in blue, while those incorporating the electrolyzer are illustrated in red.</p>
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<p>Movement of- the <math display="inline"><semantics> <msub> <mi>λ</mi> <mn>3</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>λ</mi> <mn>4</mn> </msub> </semantics></math> modes caused by changes in the inertial constant value of the synchronous generator connected to <math display="inline"><semantics> <mrow> <mi>B</mi> <mi>u</mi> <mi>s</mi> <mi>b</mi> <mi>a</mi> <mi>r</mi> <mspace width="3.33333pt"/> <mn>6</mn> </mrow> </semantics></math>: <math display="inline"><semantics> <msub> <mi>H</mi> <mn>2</mn> </msub> </semantics></math> = 2.6 to 7 s. The modes in the absence of the electrolyzer are depicted in blue, while those incorporating the electrolyzer are illustrated in red.</p>
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<p>Movement of the <math display="inline"><semantics> <msub> <mi>λ</mi> <mn>5</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>λ</mi> <mn>6</mn> </msub> </semantics></math> modes caused by changes in the inertial constant value of the synchronous generator connected to <math display="inline"><semantics> <mrow> <mi>B</mi> <mi>u</mi> <mi>s</mi> <mi>b</mi> <mi>a</mi> <mi>r</mi> <mspace width="3.33333pt"/> <mn>11</mn> </mrow> </semantics></math>: <math display="inline"><semantics> <msub> <mi>H</mi> <mn>3</mn> </msub> </semantics></math> = 3 to 7 s. The modes in the absence of the electrolyzer are depicted in blue, while those incorporating the electrolyzer are illustrated in red.</p>
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<p>Movement of the <math display="inline"><semantics> <msub> <mi>λ</mi> <mn>1</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>λ</mi> <mn>2</mn> </msub> </semantics></math> modes caused by changes in the damping torque coefficient value of the synchronous generator connected to <math display="inline"><semantics> <mrow> <mi>B</mi> <mi>u</mi> <mi>s</mi> <mi>b</mi> <mi>a</mi> <mi>r</mi> <mspace width="3.33333pt"/> <mn>4</mn> </mrow> </semantics></math>: <math display="inline"><semantics> <msub> <mi>D</mi> <mn>1</mn> </msub> </semantics></math> = 0.5 to 0.8. The modes in the absence of the electrolyzer are depicted in blue, while those incorporating the electrolyzer are illustrated in red.</p>
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<p>Movement of the <math display="inline"><semantics> <msub> <mi>λ</mi> <mn>3</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>λ</mi> <mn>4</mn> </msub> </semantics></math> modes caused by changes in the damping torque coefficient value of the synchronous generator connected to <math display="inline"><semantics> <mrow> <mi>B</mi> <mi>u</mi> <mi>s</mi> <mi>b</mi> <mi>a</mi> <mi>r</mi> <mspace width="3.33333pt"/> <mn>4</mn> </mrow> </semantics></math>: <math display="inline"><semantics> <msub> <mi>D</mi> <mn>2</mn> </msub> </semantics></math> = 0.5 to 0.8. The modes in the absence of the electrolyzer are depicted in blue, while those incorporating the electrolyzer are illustrated in red.</p>
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<p>Movement of the <math display="inline"><semantics> <msub> <mi>λ</mi> <mn>5</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>λ</mi> <mn>6</mn> </msub> </semantics></math> modes caused by changes in the damping torque coefficient value of a synchronous generator connected to <math display="inline"><semantics> <mrow> <mi>B</mi> <mi>u</mi> <mi>s</mi> <mi>b</mi> <mi>a</mi> <mi>r</mi> <mspace width="3.33333pt"/> <mn>4</mn> </mrow> </semantics></math>: <math display="inline"><semantics> <msub> <mi>D</mi> <mn>3</mn> </msub> </semantics></math> = 0.5 to 0.8. The modes in the absence of the electrolyzer are depicted in blue, while those incorporating the electrolyzer are illustrated in red.</p>
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<p>(<b>a</b>) Dynamic response of the rotor speed deviations (<math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>ω</mi> <mi>i</mi> </msub> </mrow> </semantics></math>) and (<b>b</b>) the dynamic response of the rotor angle deviations (<math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>θ</mi> <mi>i</mi> </msub> </mrow> </semantics></math>).</p>
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<p>Dynamic response of electromechanical state variables of <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>G</mi> <mspace width="3.33333pt"/> <mn>1</mn> </mrow> </semantics></math> when 100 MW of PEM electrolysers are connected to the grid at 15 s: (<b>a</b>) rotor angle deviation and (<b>b</b>) rotor speed deviation with the impact of modelling the electrolyser as a load.</p>
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<p>Dynamic response of electromechanical state variables of <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>G</mi> <mspace width="3.33333pt"/> <mn>2</mn> </mrow> </semantics></math> when 100 MW of PEM electrolysers are connected to the grid at 15 s: (<b>a</b>) rotor angle deviation and (<b>b</b>) rotor speed deviation with the impact of modelling the electrolyser as a load.</p>
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<p>Dynamic response of electromechanical state variables of <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>G</mi> <mspace width="3.33333pt"/> <mn>3</mn> </mrow> </semantics></math> when 100 MW of PEM electrolysers are connected to the grid at 15 s: (<b>a</b>) rotor angle deviation and (<b>b</b>) rotor speed deviation with the impact of modelling the electrolyser as a load.</p>
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<p>Dynamic responses of electromechanical state variables of <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>G</mi> <mspace width="3.33333pt"/> <mi>i</mi> </mrow> </semantics></math> of electrolyser current: (<b>a</b>) DC electrolyser current and (<b>b</b>) rotor speed deviations <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>ω</mi> <mi>i</mi> </msub> </mrow> </semantics></math>.</p>
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15 pages, 2485 KiB  
Article
Supplementary Control of Conventional Coordinated Control for 1000 MW Ultra-Supercritical Thermal Power Plant Using One-Step Ahead Control
by Hyuk Choi, Yeongseok Choi, Un-Chul Moon and Kwang Y. Lee
Energies 2023, 16(17), 6197; https://doi.org/10.3390/en16176197 - 25 Aug 2023
Cited by 2 | Viewed by 1183
Abstract
The intermittence of renewable energy sources increases the importance of the effective load-tracking ability of power plants. Coordinated control between boiler and turbine systems is the uppermost layer of a thermal power plant control to follow the load demand. In this paper, a [...] Read more.
The intermittence of renewable energy sources increases the importance of the effective load-tracking ability of power plants. Coordinated control between boiler and turbine systems is the uppermost layer of a thermal power plant control to follow the load demand. In this paper, a supplementary controller is proposed based on the One-Step Ahead strategy for coordinated control of thermal power plants. After a plant model is developed offline from a step response test, the optimized control of the One-Step Ahead strategy is applied to the boiler feed-forward (BFF) signal to control the electric power output and the main steam pressure simultaneously. Simulation with a 1000 MW ultra-supercritical (USC) once-through type power plant is performed. The results show that the error of Mega-Watt Output (MWO) was reduced to 78~95%, and settling time was reduced to 64~79% from conventional coordinated control by adding the proposed supplementary controller. Full article
(This article belongs to the Topic Power System Dynamics and Stability)
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<p>A schematic of a 1000 MW ultra-supercritical once-through type power plant.</p>
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<p>Conventional boiler combustion control system configuration.</p>
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<p>Proposed One-Step Ahead control structure.</p>
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<p>(<b>a</b>) Step response data of Mega-Watt Output (<span class="html-italic">MWO</span>). (<b>b</b>) Step response data of Main Steam Pressure (<span class="html-italic">MSP</span>).</p>
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<p>(<b>a</b>) Comparison between step response data and model output of <span class="html-italic">MWO</span>. (<b>b</b>) Comparison between step response data and model output of <span class="html-italic">MSP</span>.</p>
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<p>Flow chart of proposed supplementary One-Step Ahead Control.</p>
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<p>Power load demand scenario of 1000 MW USC power plant.</p>
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<p>(<b>a</b>) Comparison of the <span class="html-italic">MWO</span> with the conventional CC and the CC with proposed supplementary control. (<b>b</b>) Zoom of the step-up response. (<b>c</b>) Zoom of the step-down response.</p>
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<p>(<b>a</b>) Comparison of the <span class="html-italic">MSP</span> with the conventional CC and the CC with proposed supplementary control. (<b>b</b>) Zoom of the step-up response. (<b>c</b>) Zoom of the step-down response.</p>
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<p>Variation of the supplementary BFF signal of the proposed controller.</p>
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30 pages, 10154 KiB  
Article
New Technology and Method for Monitoring the Status of Power Systems to Improve Power Quality—A Case Study
by Rahim Ildarabadi and Mahmoud Zadehbagheri
Processes 2023, 11(8), 2468; https://doi.org/10.3390/pr11082468 - 16 Aug 2023
Cited by 2 | Viewed by 1194
Abstract
The identification and analysis of harmonics, frequency, and transient events are essential today. It is necessary to have available data relating to harmonics, frequency, and transient events to understand power systems and their proper control and analysis. Power quality monitoring is the first [...] Read more.
The identification and analysis of harmonics, frequency, and transient events are essential today. It is necessary to have available data relating to harmonics, frequency, and transient events to understand power systems and their proper control and analysis. Power quality monitoring is the first step in identifying power quality disturbances and reducing them and, as a result, improving the performance of the power system. In this paper, while presenting different methods for measuring these quantities, we have made some corrections to them. These reforms have been obtained through the analysis of power network signals. Finally, we introduce a new monitoring system capable of measuring harmonics, frequency, and transient events in the network. In addition, these values are provided for online and offline calculations of harmonics, frequency, and transient events. In this paper, two new and practical methods of the “algebraic method” are used to calculate network harmonics and wavelet transform to calculate transient modes in the network. Furthermore, the proposed monitoring system is able to reduce the amount of data-storage memory. The results of the simulations performed in this article show the superiority of using the new method presented for online and offline monitoring of power quality in electric power systems. Full article
(This article belongs to the Topic Power System Dynamics and Stability)
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<p>System voltage waveform.</p>
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<p>Monitoring system: (<b>a</b>) simplified block diagram; (<b>b</b>) simulated structure.</p>
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<p>Voltage signal, scaling factor, and wavelet factor for voltage signal.</p>
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<p>Algorithm of the algebraic method.</p>
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<p>Simulation of the first harmonic frequency (actual and simulated signals).</p>
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<p>Simulation of voltage V(t) (algebraic method).</p>
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<p>(<b>a</b>) First harmonic amplitude; (<b>b</b>) first harmonic phase in rad/(blue curves are actual, and red curves are simulated).</p>
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<p>(<b>a</b>) 3rd harmonic amplitude; (<b>b</b>) 15th harmonic amplitude (blue curves are actual, and red curves are simulated) (algebraic method).</p>
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<p>Algorithm of DFT method for calculating harmonics.</p>
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<p>Simulation of the frequency of the first harmonic (DFT Method).</p>
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<p>The actual value (blue) and the simulated value (red) of the voltage waveform.</p>
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<p>(<b>a</b>) Amplitude of the first harmonic (<b>b</b>) Phase of the first harmonic in terms of radians (the blue curves are actual, and the red curves are simulated).</p>
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<p>(<b>a</b>) 3rd harmonic amplitude; (<b>b</b>) 15th harmonic amplitude (blue curves are actual, and red curves are simulated).</p>
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<p>Windowing of <math display="inline"><semantics> <mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> by <math display="inline"><semantics> <mrow> <mo> </mo> <mo> </mo> <msub> <mi>P</mi> <mrow> <mi>K</mi> <mo> </mo> <mo>,</mo> <mo> </mo> <mo>Δ</mo> <mi>T</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> in the time.</p>
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<p>Limiter for wavelet factor (<math display="inline"><semantics> <mrow> <msub> <mi>d</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>).</p>
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<p>Waveform under compressing.</p>
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<p>Algorithm of recursive algebraic method for steady-state approximation.</p>
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<p>Harmonics recovery algorithm.</p>
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<p>The waveform of the signal when the fault.</p>
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<p>The waveform of the signal when the fault occurs.</p>
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<p>The fault occurred when the size of the derivative of the signal is minimum at that moment. (<b>a</b>) The signal itself; (<b>b</b>) the derivative of the signal.</p>
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<p>The fault occurred when the size of the derivative of the signal at that moment is maximum. (<b>a</b>) The signal itself; (<b>b</b>) the derivative of the signal.</p>
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<p>Wavelet transform of the signal under analysis.</p>
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<p>The fault occurred when the size of the derivative of the signal is minimum at that moment. (<b>a</b>) Signal itself; (<b>b</b>) scaling factor; (<b>c</b>) wavelet factor.</p>
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<p>The fault occurred when the size of the derivative of the signal is maximum at that moment. (<b>a</b>) Signal itself; (<b>b</b>) scaling factor; (<b>c</b>) wavelet factor.</p>
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<p>(<b>a</b>) Actual and simulated signals. (<b>b</b>) Absolute error between actual and simulated signals.</p>
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<p>(<b>a</b>) Actual and simulated signals. (<b>b</b>) Absolute error between actual and simulated signals.</p>
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17 pages, 4540 KiB  
Article
Impact Mechanisms of Commutation Failure Caused by a Sending-End AC Fault and Its Recovery Speed on Transient Stability
by Yifeng Lin, Jiawei Hu, Tong Wang and Zengping Wang
Electronics 2023, 12(16), 3439; https://doi.org/10.3390/electronics12163439 - 14 Aug 2023
Cited by 1 | Viewed by 773
Abstract
A sending-end AC fault may lead to commutation failure (CF) in a line-commutated converter high-voltage direct current (LCC-HVDC) system. In this paper, a theoretical analysis of the impact mechanisms of a CF and its recovery speed on the transient stability of a sending-end [...] Read more.
A sending-end AC fault may lead to commutation failure (CF) in a line-commutated converter high-voltage direct current (LCC-HVDC) system. In this paper, a theoretical analysis of the impact mechanisms of a CF and its recovery speed on the transient stability of a sending-end power system (TSSPS) is performed. Firstly, the models of the sending-end power system and DC power of CF are established; the ramp function is utilized to characterize the DC power recovery process. Secondly, the swing direction of the relative rotor angle caused by a sending-end AC fault is discussed, and the DC power flow method is employed to theoretically analyze the impacts of CF and its recovery speed on TSSPS. Next, the mathematic relations between parameters of the voltage-dependent current order limiter (VDCOL) and DC power recovery speed are further derived. It is concluded that the impacts of CF and its recovery speed on transient stability are related to the swing direction caused by a sending-end AC fault, the inertia of generators, and the location of the rectifier station. Finally, the theoretical analysis is validated by Kundur’s two-area system and IEEE 68-bus-based AC/DC asynchronous interconnection test power systems, respectively. Full article
(This article belongs to the Topic Power System Dynamics and Stability)
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<p>Equivalent model of sending-end power system.</p>
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<p>Simulation results of CF.</p>
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<p>Chain of fault events.</p>
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<p>Swing direction of relative rotor angle when the sending-end fault occurs.</p>
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<p>Equivalent reactance diagram of the sending-end power system.</p>
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<p>Impact of CF on the TSSPS: (<b>a</b>) swing forward; (<b>b</b>) swing backward.</p>
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<p>Impact of improving the DC power recovery speed on the TSSPS: (<b>a</b>) swing forward; (<b>b</b>) swing backward.</p>
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<p>Mathematical model of VDCOL.</p>
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<p>Parameters of VDCOL: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>U</mi> </mrow> <mrow> <mi mathvariant="normal">d</mi> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math> changes; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>I</mi> </mrow> <mrow> <mi mathvariant="normal">o</mi> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math> changes.</p>
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<p>Kundur’s two-area-based test power system.</p>
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<p>Impact of CF on the TSSPS: (<b>a</b>) swing forward; (<b>b</b>) swing backward.</p>
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<p>Impact of increasing <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>k</mi> </mrow> <mrow> <mi mathvariant="normal">d</mi> </mrow> </msub> </mrow> </semantics></math> on the TSSPS: (<b>a</b>) swing forward; (<b>b</b>) swing backward.</p>
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<p>IEEE 68-bus-based test power system.</p>
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<p>Scenario I: (<b>a</b>) relative rotor angle; (<b>b</b>) DC power.</p>
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<p>Scenario II: (<b>a</b>) relative rotor angle; (<b>b</b>) DC power.</p>
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<p>Scenario III: (<b>a</b>) relative rotor angle; (<b>b</b>) DC power.</p>
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<p>Scenario IV: (<b>a</b>) relative rotor angle; (<b>b</b>) DC power.</p>
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<p>Simulation results of different fault locations: (<b>a</b>) impact of CF on TSSPS; (<b>b</b>) impact of increasing <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>k</mi> </mrow> <mrow> <mi mathvariant="normal">d</mi> </mrow> </msub> </mrow> </semantics></math> on TSSPS.</p>
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16 pages, 1089 KiB  
Article
Novel Heuristic Optimization Technique to Solve Economic Load Dispatch and Economic Emission Load Dispatch Problems
by Nagendra Singh, Tulika Chakrabarti, Prasun Chakrabarti, Martin Margala, Amit Gupta, S. Phani Praveen, Sivaneasan Bala Krishnan and Bhuvan Unhelkar
Electronics 2023, 12(13), 2921; https://doi.org/10.3390/electronics12132921 - 3 Jul 2023
Cited by 21 | Viewed by 1994
Abstract
The fundamental objective of economic load dispatch is to operate the available generating units such that the needed load demand satisfies the lowest generation cost and also complies with the various constraints. With proper power system operation planning using optimized generation limits, it [...] Read more.
The fundamental objective of economic load dispatch is to operate the available generating units such that the needed load demand satisfies the lowest generation cost and also complies with the various constraints. With proper power system operation planning using optimized generation limits, it is possible to reduce the cost of power generation. To fulfill the needs of such objectives, proper planning and economic load dispatch can help to plan the operation of the electrical power system. To optimize the economic load dispatch problems, various classical and new evolutionary optimization approaches have been used in research articles. Classical optimization techniques are outdated due to many limitations and are also unable to provide a global solution to the ELD problem. This work uses a new variant of particle swarm optimization techniques called modified particle swarm optimization, which is effective and efficient at finding optimum solutions for single as well as multi-objective economic load dispatch problems. The proposed MPSO is used to solve single and multi-objective problems. This work considers constraints like power balance and power generation limits. The proposed techniques are tested for three different case studies of ELD and EELD problems. (1) The first case is tested using the data of 13 generating unit systems along with the valve point loading effect; (2) the second case is tested using 15 generating unit systems along with the ramp rate limits; and (3) the third case is tested using the economic emission dispatch (EELD) as a multi-objective problem for 6 generating unit systems. The outcomes of the suggested procedures are contrasted with those of alternative optimization methods. The results show that the suggested strategy is efficient and produces superior optimization outcomes than existing optimization techniques. Full article
(This article belongs to the Topic Power System Dynamics and Stability)
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<p>Effect of the valves’ loading on generation cost function.</p>
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<p>Power generation limits due to ramp rate limits.</p>
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<p>Pseudo code for the NPSO.</p>
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<p>Convergence characteristic of the MPSO plotted between the objective functions and the iteration.</p>
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20 pages, 9687 KiB  
Article
Research on the Access Planning of SOP and ESS in Distribution Network Based on SOCP-SSGA
by Yuxin Jia, Qiong Li, Xu Liao, Linjun Liu and Jian Wu
Processes 2023, 11(6), 1844; https://doi.org/10.3390/pr11061844 - 19 Jun 2023
Cited by 3 | Viewed by 1385
Abstract
This paper proposes a two-stage planning model for soft open point (SOP) and energy storage system (ESS) that considers the cost of faults in response to the current issue of SOP and ESS systems not considering the impact of SOP access on load [...] Read more.
This paper proposes a two-stage planning model for soft open point (SOP) and energy storage system (ESS) that considers the cost of faults in response to the current issue of SOP and ESS systems not considering the impact of SOP access on load transfer in the event of a fault in the distribution network. Firstly, considering the uncertainty of “PV-load”, typical scenarios of PV and load are constructed based on the clustering algorithm. Secondly, aiming at the economic performance of the distribution network and the capacity of PV access, a two-stage optimization model is established for the joint integration of SOP and ESS into the distribution network (normal and fault operation) under typical scenarios. The model is solved by using the second-order cone programming algorithm and steady-state genetic algorithm (SOCP-SSGA). Stage one involves planning for the integration capacity and location of SOP and ESS into the distribution network under each scenario within a period based on SOCP with the goal of minimizing economic costs. In stage two, the PV access capacity of the distribution network is optimized using SSGA with the goal of enhancing the PV accommodation capability. Finally, verification and analysis are conducted on an improved IEEE33 node system. The results show that when the system optimizes access to a group of SOP and ESS, the total economic cost is reduced by RMB 61,729 compared to random access, and the accessible PV capacity is increased by 0.5278 MW. Moreover, optimizing access to two sets of SOP and ESS can further reduce the total economic cost by RMB 107,048 compared to the optimized access group and increase accessible PV capacity by 1.5751 MW. Therefore, the proposed plan for SOP and ESS planning in this paper can significantly reduce the economic cost of distribution networks, enhance the absorption capacity of distributed photovoltaics, improve the voltage level of power grid operation, and, thereby, improve the economic and reliability of distribution network operation. Full article
(This article belongs to the Topic Power System Dynamics and Stability)
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<p>The basic structure of back-to-back SOP.</p>
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<p>Two-stage programming-model solution flowchart.</p>
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<p>Improving the IEEE33 node distribution-network system.</p>
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<p>Photovoltaic and load scenarios with daily output curves: (<b>a</b>) photovoltaic; (<b>b</b>) load.</p>
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<p>Voltage change chart of each node: (<b>a</b>) PV not connected; (<b>b</b>) Access PV.</p>
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<p>Voltage change chart of each node: (<b>a</b>) PV not connected; (<b>b</b>) Access PV.</p>
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<p>SOP running active and reactive power: (<b>a</b>) SOP active power; (<b>b</b>) SOP reactive power.</p>
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<p>The operating power of ESS.</p>
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<p>Voltage change chart of each node: (<b>a</b>) PV not connected; (<b>b</b>) Access PV.</p>
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<p>SOP running active and reactive power: (<b>a</b>) SOP active power; (<b>b</b>) SOP reactive power.</p>
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<p>Operating power of ESS.</p>
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<p>Voltage change chart of each node: (<b>a</b>) PV not connected; (<b>b</b>) Access PV.</p>
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<p>SOP running active and reactive power: (<b>a</b>) SOP active power; (<b>b</b>) SOP reactive power.</p>
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<p>Operating power of ESS.</p>
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15 pages, 1179 KiB  
Article
A Gray-Box Stability Analysis Method of Grid-Connected Inverter Considering Synchronization Dynamics
by Tianzhi Zheng, Fannie Kong, Guojin Li, Zhenmin Wang and Yanming Chen
Electronics 2023, 12(11), 2509; https://doi.org/10.3390/electronics12112509 - 2 Jun 2023
Cited by 1 | Viewed by 1010
Abstract
The Grid-Connected Inverter (GCI) can be considered a gray box when circuit and controller parameters are missing due to intellectual property rights or parameter variations caused by aging, which poses an impediment to assessing the stability of the system. This paper presents a [...] Read more.
The Grid-Connected Inverter (GCI) can be considered a gray box when circuit and controller parameters are missing due to intellectual property rights or parameter variations caused by aging, which poses an impediment to assessing the stability of the system. This paper presents a gray-box stability analysis method based on impedance identification of GCI considering the synchronization dynamics. The impedance frequency responses of GCI are measured by the frequency scanning method on the dq-frame. Meanwhile, the influence of synchronization dynamics and background harmonics is theoretically investigated. A vector fitting (VF) algorithm, co-designed with impedance identification, is then applied to generate polynomial transfer functions. Based on the obtained transfer functions, the stability of the GCI can be judged by the distance relationship between the prohibited area boundary and the center of the gershgorin-circle through the distance formula. Finally, the experiments of both RT-LAB and experimental prototypes are conducted to verify the feasibility of the proposed method. Full article
(This article belongs to the Topic Power System Dynamics and Stability)
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<p>Three-phase grid-connected inverter and its control structure.</p>
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<p>The dq-frames under PLL dynamics.</p>
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<p>The improvement of PLL structure for impedance measurement.</p>
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<p>Forbidden region of FRBC.</p>
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<p>Forbidden region of proposed method.</p>
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<p>RT-LAB test platform.</p>
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<p>Impedance of GCI based on different measurement methods.</p>
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<p>The results of fitting based on measured impedance.</p>
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<p>Curves with different SCRs based the GCI analytical model: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>C</mi> <mi>R</mi> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>C</mi> <mi>R</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math>. (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>C</mi> <mi>R</mi> <mo>=</mo> <mn>3.5</mn> </mrow> </semantics></math>.</p>
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<p>Curves with different SCRs based the measured model: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>C</mi> <mi>R</mi> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>C</mi> <mi>R</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math>. (<b>c</b>)<math display="inline"><semantics> <mrow> <mspace width="3.33333pt"/> <mi>S</mi> <mi>C</mi> <mi>R</mi> <mo>=</mo> <mn>3.5</mn> </mrow> </semantics></math>.</p>
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<p>Nyquist curves of the characteristic values of <math display="inline"><semantics> <mrow> <mi mathvariant="bold">L</mi> <mo>(</mo> <mi mathvariant="bold">s</mi> <mo>)</mo> </mrow> </semantics></math> in dq frame (<math display="inline"><semantics> <mrow> <mi>S</mi> <mi>C</mi> <mi>R</mi> <mo>=</mo> <mn>3.5</mn> </mrow> </semantics></math>).</p>
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<p>Experimental platform of grid-connected inverter.</p>
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<p>The dynamic experiment of a phase in GCI.</p>
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<p>Experiment results of GCI with <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>C</mi> <mi>R</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math>. (<b>a</b>) Output current waveforms of GCI; (<b>b</b>) THD of output current.</p>
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<p>Experiment results of GCI with <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>C</mi> <mi>R</mi> <mo>=</mo> <mn>3.8</mn> </mrow> </semantics></math>. (<b>a</b>) Output current waveforms of GCI; (<b>b</b>) THD of output current.</p>
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19 pages, 1981 KiB  
Review
Review of RoCoF Estimation Techniques for Low-Inertia Power Systems
by Xiaoyu Deng, Ruo Mo, Pengliang Wang, Junru Chen, Dongliang Nan and Muyang Liu
Energies 2023, 16(9), 3708; https://doi.org/10.3390/en16093708 - 26 Apr 2023
Cited by 6 | Viewed by 3744
Abstract
As the traditional generation is gradually replaced by inverter-based resources, a lack of rotational inertia is now a common issue of modern power systems, which leads to an increasingly larger rate of change of frequency (RoCoF) following contingencies and may result in frequency [...] Read more.
As the traditional generation is gradually replaced by inverter-based resources, a lack of rotational inertia is now a common issue of modern power systems, which leads to an increasingly larger rate of change of frequency (RoCoF) following contingencies and may result in frequency collapse. As a crucial index of the frequency security and stability of power systems, the accurate estimation of the RoCoF can be a foundation for the development of advanced operations and control techniques of the future power system. This paper firstly analyzes the role of the RoCoF in typical blackouts occurring in recent years and discusses the physical and numerical nature of the RoCoF; then, by introducing the frequency spatial distribution of the power system, the paper discusses the concept of the “center” RoCoF that can present the frequency security and stability of the entire system. The estimation and prediction techniques of the maximal power system RoCoF following a contingency and the existing real-time tracking techniques of the power system RoCoF are comprehensively reviewed. Finally, the open questions and related research topics of the RoCoF estimation are discussed. Full article
(This article belongs to the Topic Power System Dynamics and Stability)
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<p>Frequency security problems of low-inertia systems.</p>
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<p>Typical frequency evolution of a power system.</p>
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<p>Taxonomy of offline RoCoF estimation techniques for power systems.</p>
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<p>Taxonomy of real-time RoCoF tracking techniques.</p>
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<p>The control block diagram of the PI filter.</p>
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18 pages, 3935 KiB  
Article
Circuit Breaker Fault Diagnosis Method Based on Coil Current Time Sequence Phase Trajectory Characteristics
by Yaqi Chen, Qiong Li, Yang Zou, Guohua Long, Nianping Yan and Ruixiang Fan
Processes 2023, 11(4), 1241; https://doi.org/10.3390/pr11041241 - 17 Apr 2023
Cited by 1 | Viewed by 1276
Abstract
The traditional circuit breaker fault diagnosis method suffers from insufficient feature information extraction and is easily affected by abnormal signal acquisition. To address this, this paper introduces the phase space reconstruction algorithm to reconstruct the current signal for fault diagnosis based on phase [...] Read more.
The traditional circuit breaker fault diagnosis method suffers from insufficient feature information extraction and is easily affected by abnormal signal acquisition. To address this, this paper introduces the phase space reconstruction algorithm to reconstruct the current signal for fault diagnosis based on phase trajectory features. The proposed method uses a first-order forward differencing method and mutual information method to process abnormal data and select the parameters of the reconstruction, then extract overall and local inflection point features to construct a fault feature set. The support vector machine algorithm-based model is trained and tested using actual samples, and the results show that the proposed method can adaptively sample anomalous signals, exhibit strong robustness, and significantly improve the accuracy of fault classification. Full article
(This article belongs to the Topic Power System Dynamics and Stability)
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<p>Model of HP550B2 breaking solenoid with coil equivalent circuit diagram and its closing current waveform: (<b>a</b>) split-close solenoid model; (<b>b</b>) coil solenoid equivalent circuit diagram; (<b>c</b>) coil current waveform.</p>
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<p>Normal state multi-cycle current signal with corresponding Lyapunov exponential spectrum: (<b>a</b>) multi-cycle current signal; (<b>b</b>) Lyapunov index spectrum.</p>
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<p>Phase trajectory at delay time Ï„ = 9 with the characteristics corresponding to the critical point of the current signal.</p>
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<p>Phase trajectory with delay time Ï„ = 3, 15: (<b>a</b>) Ï„ = 3; (<b>b</b>) Ï„ = 15.</p>
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<p>Current signals containing data fluctuation anomalies and corresponding reconstructed phase trajectory: (<b>a</b>) current signal; (<b>b</b>) reconstructed phase trajectory.</p>
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<p>Frequency histogram distribution of the absolute value of the first-order forward difference.</p>
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<p>Abnormal overrun data detection.</p>
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<p>Mutual information function curve: (<b>a</b>) normal; (<b>b</b>) contains abnormal data; (<b>c</b>) after abnormal data processing.</p>
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<p>Phase trajectory comparison chart: (<b>a</b>) normal; (<b>b</b>) contains abnormal data; (<b>c</b>) after abnormal data processing.</p>
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<p>Current signals in different states and corresponding multi-period phase planes: (<b>a</b>) comparison of time-domain waveforms of current signals under different states; (<b>b</b>) normal state phase trajectory; (<b>c</b>) core card astringent phase track; (<b>d</b>) core empty travel large phase trajectory; (<b>e</b>) inter-turn short-circuit phase trajectory; (<b>f</b>) supply voltage too low phase track.</p>
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<p>Overall characteristics of different fault phase trajectories <span class="html-italic">D</span>, <span class="html-italic">E</span> distribution: (<b>a</b>) association dimension <span class="html-italic">D</span>; (<b>b</b>) origin moment <span class="html-italic">E</span>.</p>
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<p>Distribution of local features <span class="html-italic">M</span><sub>1</sub>, <span class="html-italic">M</span><sub>3</sub> and <span class="html-italic">M</span><sub>5</sub> for different fault phase trajectories: (<b>a</b>) amplitude <span class="html-italic">M</span><sub>1</sub> under <span class="html-italic">T</span><sub>1</sub> phase space; (<b>b</b>) amplitude <span class="html-italic">M</span><sub>3</sub> under <span class="html-italic">T</span><sub>3</sub> phase space; (<b>c</b>) amplitude <span class="html-italic">M</span><sub>5</sub> under T5 phase space.</p>
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<p>Overall fault identification process.</p>
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<p>Current waveform with noise.</p>
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17 pages, 2052 KiB  
Article
Improved Repetitive Control for an LCL-Type Grid-Tied Inverter with Frequency Adaptive Capability in Microgrids
by Hongwei Zhang, Qiangsong Zhao, Shuanghong Wang and Xuebin Yue
Electronics 2023, 12(7), 1736; https://doi.org/10.3390/electronics12071736 - 5 Apr 2023
Cited by 1 | Viewed by 1669
Abstract
Repetitive control (RC), which can track any periodic signal with a known integer period with zero steady-state error, is widely used for current control of grid-tied inverters in microgrids. However, the inherent one fundamental period time delay, leads to poor dynamic performance. Furthermore, [...] Read more.
Repetitive control (RC), which can track any periodic signal with a known integer period with zero steady-state error, is widely used for current control of grid-tied inverters in microgrids. However, the inherent one fundamental period time delay, leads to poor dynamic performance. Furthermore, the performance of conventional RC (CRC) will degrade when operating at a high variation grid frequency. Therefore, this paper proposes a frequency adaptive improved RC (FA-IRC) for grid-tied inverters. The improved RC (IRC) consists of a repetitive controller with a modified internal model filter, plus a proportional controller. In comparison to the CRC, the IRC has a good dynamic response, because it provides a higher gain and a wider bandwidth at the resonant frequency. Moreover, to achieve the frequency adaptability of the IRC, a fractional delay, based on a finite impulse response (FIR) filter, is built into the IRC system, to ensure that the resonant frequency of the IRC is approximately equal to the actual grid frequency and harmonic frequency. Stability analysis and characteristic analysis of the FA-IRC system are reported in this paper. Simulations are conducted, to demonstrate the validity of the proposed method. Full article
(This article belongs to the Topic Power System Dynamics and Stability)
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<p>Model structure diagram of a single-phase LCL-type grid-tied inverter.</p>
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<p>Block diagram of CRC.</p>
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<p>Block diagram of the PIMR-RC system.</p>
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<p>Block diagram of the proposed modified RC.</p>
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<p>Bode diagram of modified RC and CRC.</p>
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<p>Magnitude response of modified RC and CRC.</p>
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<p>Block diagram of the proposed IRC system.</p>
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<p>Frequency responses of Lagrange-interpolation-based FD filters.</p>
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<p>Block diagram of the FA-IRC system.</p>
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<p>Distribution of the dominant poles of <math display="inline"><semantics> <msub> <mi>P</mi> <mn>0</mn> </msub> </semantics></math>(z) with different <math display="inline"><semantics> <msub> <mi>k</mi> <mi>p</mi> </msub> </semantics></math>.</p>
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<p>Bode diagram of <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> with <math display="inline"><semantics> <mrow> <mi>Q</mi> <mo>(</mo> <mi>z</mi> <mo>)</mo> <mo>=</mo> <mn>0.99</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>Q</mi> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>0.25</mn> <mi>z</mi> <mo>+</mo> <mn>0.5</mn> <mo>+</mo> <mn>0.25</mn> <msup> <mi>z</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>.</p>
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<p>Bode diagrams of IRC (<span class="html-italic">N</span> = 200) and FA-IRC (<span class="html-italic">N</span> = 198.4 and 201.6).</p>
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<p>Magnitude characteristics of IRC (<span class="html-italic">N</span> = 200) and FA-IRC (<span class="html-italic">N</span> = 198.4 and 201.6) at the fundamental frequency.</p>
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<p>Output waveforms of the PIMR-RC system and spectrum analysis of the output current when <math display="inline"><semantics> <msub> <mi>f</mi> <mi>g</mi> </msub> </semantics></math> = 50 Hz.</p>
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<p>Output waveforms of the FA-IRC system and spectrum analysis of the output current when <math display="inline"><semantics> <msub> <mi>f</mi> <mi>g</mi> </msub> </semantics></math> = 50 Hz.</p>
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<p>Output waveforms of the PIMR-RC system and spectrum analysis of the output current when <math display="inline"><semantics> <msub> <mi>f</mi> <mi>g</mi> </msub> </semantics></math> = 49.6 Hz.</p>
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<p>Output waveforms of the FA-IRC system and spectrum analysis of the output current when <math display="inline"><semantics> <msub> <mi>f</mi> <mi>g</mi> </msub> </semantics></math> = 49.6 Hz.</p>
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<p>Output waveforms of the PIMR-RC system and spectrum analysis of the output current when <math display="inline"><semantics> <msub> <mi>f</mi> <mi>g</mi> </msub> </semantics></math> = 50.4 Hz.</p>
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<p>Output waveforms of the FA-IRC system and spectrum analysis of the output current when <math display="inline"><semantics> <msub> <mi>f</mi> <mi>g</mi> </msub> </semantics></math> = 50.4 Hz.</p>
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<p>Transient waveforms and current errors of different control systems when reference current changes, with grid frequency <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mi>g</mi> </msub> <mo>=</mo> <mn>49.6</mn> </mrow> </semantics></math> Hz. (<b>a</b>) FA-IRC system. (<b>b</b>) PIMR-RC system.</p>
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<p>Transient waveforms and current errors of different control systems when reference current changes, with grid frequency <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mi>g</mi> </msub> <mo>=</mo> <mn>50.4</mn> </mrow> </semantics></math> Hz. (<b>a</b>) FA-IRC system. (<b>b</b>) PIMR-RC system.</p>
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