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Keywords = dual-area interconnected power system

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22 pages, 2704 KiB  
Article
Shanghai as a Model: Research on the Journey of Transportation Electrification and Charging Infrastructure Development
by Cong Zhang, Jingchao Lian, Haitao Min and Ming Li
Sustainability 2025, 17(1), 91; https://doi.org/10.3390/su17010091 - 26 Dec 2024
Viewed by 420
Abstract
As the world pivots to a greener paradigm, Shanghai emerges as an archetype in the sustainable urban transit narrative, particularly through the aggressive expansion and refinement of its electric vehicle (EV) charging infrastructure. This scholarly article provides a comprehensive examination of the current [...] Read more.
As the world pivots to a greener paradigm, Shanghai emerges as an archetype in the sustainable urban transit narrative, particularly through the aggressive expansion and refinement of its electric vehicle (EV) charging infrastructure. This scholarly article provides a comprehensive examination of the current state of charging infrastructure in Shanghai, highlighting the challenges that the existing infrastructure may face in light of the burgeoning electric vehicle market. This paper delves into the strategic development approaches adopted by Shanghai to address these challenges, particularly emphasizing the expansion of high-power charging infrastructure to meet the anticipated increase in future electric vehicle charging demands. It also discusses the implementation of co-construction and sharing models, the enhancement of interconnectivity and standardized management of charging facilities, and the continuous improvement and strengthening of infrastructure construction and operations. Furthermore, this article explores the implementation of time-of-use electricity pricing policies and the ongoing conduct of demand response activities, which are instrumental in creating conditions for vehicle-to-grid interaction. The aim of our presentation is to foster a keen understanding among policymakers, industry stakeholders, and urban planners of the mechanisms necessary to effectively navigate the emerging electric vehicle market, thereby encouraging harmonious development between metropolises and transportation systems. Future research endeavors should delve into the realms of fast-charging technologies, intelligent operation and maintenance of charging infrastructure, and vehicle-to-grid interaction technologies. These areas of study are pivotal in fostering the harmonious development of electric vehicles (EVs) and their charging infrastructure, thereby aligning with the dual objectives of advancing urban transportation systems and sustainable green city development. The findings presented herein offer valuable insights for policymakers, urban planners, and industry leaders, guiding them in crafting informed strategies that not only address the immediate needs of the EV market but also lay the groundwork for a scalable and resilient charging infrastructure, poised to support the long-term vision of sustainable urban mobility. Full article
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<p>EV registrations and sales share in Europe, 2015–2023.</p>
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<p>The new energy vehicle sales volume for China and the world.</p>
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<p>Shanghai’s stock of new energy vehicles.</p>
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<p>The stock of public chargers in Shanghai.</p>
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<p>Vehicle-to-charger ratios for Shanghai and typical countries.</p>
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<p>Shanghai new energy vehicle travel time distribution (24 h).</p>
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<p>Historical average charging duration/hours.</p>
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<p>Shanghai new energy vehicle average daily travel duration (hours).</p>
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<p>Shanghai new energy vehicle average daily travel distance (km) distribution.</p>
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<p>Distribution of electric vehicle travel time in different cities.</p>
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<p>Peak demand from NEV charging (year: 2023).</p>
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<p>Peak electricity load in Shanghai during the summer from 2018 to 2022.</p>
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<p>Spatial distribution of charging capacity.</p>
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<p>The time utilization efficiency of charging facilities in Shanghai.</p>
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<p>Compensation funds and prices for residential demand response.</p>
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36 pages, 6249 KiB  
Article
Multi-Objetive Dispatching in Multi-Area Power Systems Using the Fuzzy Satisficing Method
by Paspuel Cristian and Luis Tipán
Energies 2024, 17(20), 5044; https://doi.org/10.3390/en17205044 - 11 Oct 2024
Viewed by 668
Abstract
The traditional mathematical models for solving the economic dispatch problem at the generation level primarily focus on minimizing overall operational costs while ensuring demand is met across various periods. However, contemporary power systems integrate a diverse mix of generators from both conventional and [...] Read more.
The traditional mathematical models for solving the economic dispatch problem at the generation level primarily focus on minimizing overall operational costs while ensuring demand is met across various periods. However, contemporary power systems integrate a diverse mix of generators from both conventional and renewable energy sources, contributing to economically efficient energy production and playing a pivotal role in reducing greenhouse gas emissions. As the complexity of power systems increases, the scope of economic dispatch must expand to address demand across multiple regions, incorporating a range of objective functions that optimize energy resource utilization, reduce costs, and achieve superior economic and technical outcomes. This paper, therefore, proposes an advanced optimization model designed to determine the hourly power output of various generation units distributed across multiple areas within the power system. The model satisfies the dual objective functions and adheres to stringent technical constraints, effectively framing the problem as a nonlinear programming challenge. Furthermore, an in-depth analysis of the resulting and exchanged energy quantities demonstrates that the model guarantees the hourly demand. Significantly, the system’s efficiency can be further enhanced by increasing the capacity of the interconnection links between areas, thereby generating additional savings that can be reinvested into expanding the links’ capacity. Moreover, the multi-objective model excels not only in meeting the proposed objective functions but also in optimizing energy exchange across the system. This optimization is applicable to various types of energy, including thermal and renewable sources, even those characterized by uncertainty in their primary resources. The model’s ability to effectively manage such uncertainties underscores its robustness, instilling confidence in its applicability and reliability across diverse energy scenarios. This adaptability makes the model a significant contribution to the field, offering a sophisticated tool for optimizing multi-area power systems in a way that balances economic, technical, and environmental considerations. Full article
(This article belongs to the Special Issue Energy, Electrical and Power Engineering 2024)
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<p>Multi-area economic dispatch.</p>
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<p>Pareto front example.</p>
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<p>Flowchart of the general multi-objective optimization model.</p>
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<p>Scheme of interconnected areas.</p>
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<p>Probability of wind resource use.</p>
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<p>Probability of use of the photovoltaic resource.</p>
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<p>Area demand.</p>
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<p>Autonomous dispatch area 1.</p>
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<p>Autonomous dispatch area 2.</p>
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<p>Autonomous dispatch area 3.</p>
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<p>Autonomous dispatch area 4.</p>
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<p>Energy by technology and area—case 1.</p>
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<p>Cost by technology and area—case 1.</p>
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<p>Emissions [tons CO<sub>2</sub>].</p>
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<p>Dispatch area 1—case 2.</p>
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<p>Energy interchange area 1—case 2.</p>
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<p>Dispatch area 2—case 2.</p>
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<p>Energy interchange area 2—case 2.</p>
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<p>Dispatch area 3—case 2.</p>
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<p>Energy interchange area 3—case 2.</p>
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<p>Energy dispatch area 4—case 2.</p>
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<p>Energy interchange area 4—case 2.</p>
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<p>Global sourcing dispatch—Case 2.</p>
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<p>Energy by technology and area—case 2.</p>
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<p>Cost by technology and area—case 2.</p>
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<p>Emissions [ton CO<sub>2</sub>].</p>
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<p>Pareto front—case 3.</p>
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<p>Dispatch area 1—case 3.</p>
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<p>Dispatch area 2—case 3.</p>
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<p>Energy interchange area 2—case 3.</p>
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<p>Dispatch area 3—case 3.</p>
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<p>Energy exchange area 3—case 3.</p>
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<p>Dispatch area 4—case 3.</p>
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<p>Energy interchanges area 4—case 3.</p>
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<p>Global sourcing dispatch—case 3.</p>
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<p>Energy by technology and area.</p>
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<p>Cost [millions USD] by technology and area.</p>
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<p>Emissions [<math display="inline"><semantics> <msub> <mi>CO</mi> <mn>2</mn> </msub> </semantics></math>]—case 3.</p>
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<p>Comparison of energetic parameters.</p>
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<p>Comparison of energetic parameters with energy variations.</p>
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19 pages, 2584 KiB  
Article
Robust Secondary Controller for Enhanced Frequency Regulation of Hybrid Integrated Power System
by Zahid Farooq, Shameem Ahmad Lone, Farhana Fayaz, Masood Ibni Nazir, Asadur Rahman and Saleh Alyahya
World Electr. Veh. J. 2024, 15(10), 435; https://doi.org/10.3390/wevj15100435 - 26 Sep 2024
Viewed by 742
Abstract
This present article examines the frequency control of a dual-area interconnected hybrid power system that integrates conventional as well as non-conventional sources with additional support from electric vehicles. The complicated, non-linear behavior of the system adds to the grid’s already high level of [...] Read more.
This present article examines the frequency control of a dual-area interconnected hybrid power system that integrates conventional as well as non-conventional sources with additional support from electric vehicles. The complicated, non-linear behavior of the system adds to the grid’s already high level of complexity. To navigate this complex environment, it becomes essential to develop a resilient controller. In this respect, a robust secondary controller is developed to handle the problem. The controller is developed while taking into account the intricate design of the contemporary power system. An extensive comparison between well-established controllers is presented to verify the efficacy of the proposed controller. An AI-based optimization technique, namely, COVID-19, is employed to obtain optimal values for different parameters of the controller. This work also investigates the effect of the FACTS device as a static synchronous series compensator (SSSC) on the dynamics of the system. Moreover, it also investigates the role of electric vehicles (EVs) and an SSSC on system stability. Further, the developed system is subjected to significant load variations and intermittent solar and wind disturbances to check the response of the optimal controller under dynamic conditions. The results demonstrate that the proposed controller reactions successfully handle system disturbances, highlighting the strength of the proposed controller design. Lastly, a case study on an IEEE-39 bus system is carried out to check the optimality of the proposed secondary controller. Full article
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<p>Model of multi-area power system (MAPS).</p>
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<p>EV simulation structure.</p>
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<p>Block diagram of MSPIDD controller.</p>
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<p>Diagram illustrating the influence of <span class="html-italic">SD</span> on <span class="html-italic">IR</span>.</p>
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<p>Diagram demonstrating the effect of masks in restricting disease transmission.</p>
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<p>Diagram depicting the action of T-cells on infected cells within the human body.</p>
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<p>Flowchart illustrating the COVID-19 algorithm.</p>
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<p>Diagram depicting the convergence characteristics.</p>
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<p>Responses of PID, MSPID, and MSPIDD controllers. (<b>a</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mi>i</mi> <mi>e</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>Response against uneven load demand. (<b>a</b>) RLP pattern; (<b>b</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mi>i</mi> <mi>e</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>With and without EVs. (<b>a</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mi>i</mi> <mi>e</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>SSSC model.</p>
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<p>With and without SSSC. (<b>a</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mi>i</mi> <mi>e</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>Comparison with different combinations. (<b>a</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mi>i</mi> <mi>e</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>Response for random solar input. (<b>a</b>) Solar input; (<b>b</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mi>i</mi> <mi>e</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>Response for random solar input. (<b>a</b>) Solar input; (<b>b</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mi>i</mi> <mi>e</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>Response for random wind input. (<b>a</b>) Wind input; (<b>b</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mi>i</mi> <mi>e</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>Schematic of IEEE-39 bus system.</p>
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<p>Response of IEEE-39 bus system. (<b>a</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>3</mn> </msub> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mi>i</mi> <mi>e</mi> <mn>12</mn> </mrow> </msub> </mrow> </semantics></math>; (<b>e</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mi>i</mi> <mi>e</mi> <mn>23</mn> </mrow> </msub> </mrow> </semantics></math>; (<b>f</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mi>i</mi> <mi>e</mi> <mn>13</mn> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>Response of IEEE-39 bus system. (<b>a</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>3</mn> </msub> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mi>i</mi> <mi>e</mi> <mn>12</mn> </mrow> </msub> </mrow> </semantics></math>; (<b>e</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mi>i</mi> <mi>e</mi> <mn>23</mn> </mrow> </msub> </mrow> </semantics></math>; (<b>f</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mi>i</mi> <mi>e</mi> <mn>13</mn> </mrow> </msub> </mrow> </semantics></math>.</p>
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40 pages, 19433 KiB  
Article
Enhancing Load Frequency Control of Interconnected Power System Using Hybrid PSO-AHA Optimizer
by Waqar Younis, Muhammad Zubair Yameen, Abu Tayab, Hafiz Ghulam Murtza Qamar, Ehab Ghith and Mehdi Tlija
Energies 2024, 17(16), 3962; https://doi.org/10.3390/en17163962 - 9 Aug 2024
Cited by 1 | Viewed by 1264
Abstract
The integration of nonconventional energy sources such as solar, wind, and fuel cells into electrical power networks introduces significant challenges in maintaining frequency stability and consistent tie-line power flows. These fluctuations can adversely affect the quality and reliability of power supplied to consumers. [...] Read more.
The integration of nonconventional energy sources such as solar, wind, and fuel cells into electrical power networks introduces significant challenges in maintaining frequency stability and consistent tie-line power flows. These fluctuations can adversely affect the quality and reliability of power supplied to consumers. This paper addresses this issue by proposing a Proportional–Integral–Derivative (PID) controller optimized through a hybrid Particle Swarm Optimization–Artificial Hummingbird Algorithm (PSO-AHA) approach. The PID controller is tuned using the Integral Time Absolute Error (ITAE) as a fitness function to enhance control performance. The PSO-AHA-PID controller’s effectiveness is evaluated in two networks: a two-area thermal tie-line interconnected power system (IPS) and a one-area multi-source power network incorporating thermal, solar, wind, and fuel cell sources. Comparative analyses under various operational conditions, including parameter variations and load changes, demonstrate the superior performance of the PSO-AHA-PID controller over the conventional PSO-PID controller. Statistical results indicate that in the one-area multi-source network, the PSO-AHA-PID controller achieves a 76.6% reduction in overshoot, an 88.9% reduction in undershoot, and a 97.5% reduction in settling time compared to the PSO-PID controller. In the dual-area system, the PSO-AHA-PID controller reduces the overshoot by 75.2%, reduces the undershoot by 85.7%, and improves the fall time by 71.6%. These improvements provide a robust and reliable solution for enhancing the stability of interconnected power systems in the presence of diverse and variable energy sources. Full article
(This article belongs to the Special Issue Power Quality and Disturbances in Modern Distribution Networks)
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<p>Block diagram of speed governor.</p>
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<p>Transfer function model of turbine.</p>
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<p>Block structure of load mathematical model.</p>
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<p>One-area thermal energy network representation.</p>
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<p>Block diagram showing mechanical part of wind turbine.</p>
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<p>Block representation of PMSG wind energy network.</p>
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<p>P&amp;O MPPT approach.</p>
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<p>Circuit illustration of single-diode PV module.</p>
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<p>Circuit illustration of double-diode PV module.</p>
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<p>Schematic representation of fuzzy-based MPPT module.</p>
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<p>Fuzzy-based MPPT approach for PV.</p>
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<p>Block representation of dual-area IPS.</p>
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<p>Illustration of single-area multiple-source energy network.</p>
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<p>Fundamental illustration of PID controller.</p>
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<p>Flow chart of hybrid PSO-AHA optimizer.</p>
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<p>The frequency response of a single-area power network.</p>
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<p>One-area multiple-source frequency response to case 1.</p>
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<p>One-area multiple-source frequency response to case 2.</p>
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<p>Transient frequency response of dual-area tie-line IPS.</p>
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<p>Frequency response of dual-area case 1.</p>
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<p>Frequency response of dual-area case 2.</p>
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<p>Frequency response of dual-area case 3.</p>
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<p>Frequency response of dual-area case 4.</p>
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<p>Frequency response of dual-area case 5.</p>
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<p>Frequency response of dual-area case 6.</p>
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<p>Frequency responses of dual-area case 7.</p>
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<p>Frequency response of dual-area case 8.</p>
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<p>Frequency response of dual-area case 9.</p>
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<p>Frequency response of dual-area case 10.</p>
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<p>Frequency response of dual-area case 11.</p>
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<p>Frequency response of dual-area case 12.</p>
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<p>Frequency response of dual-area case 13.</p>
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<p>Frequency responses under load-variation case 1.</p>
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<p>Frequency responses under load-variation case 2.</p>
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<p>Frequency responses under load-variation case 3.</p>
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<p>Frequency responses under load-variation case 4.</p>
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24 pages, 6760 KiB  
Article
Novel Fractional-Order Proportional-Integral Controller for Hybrid Power System with Solar Grid and Reheated Thermal Generator
by Vadan Padiachy and Utkal Mehta
Solar 2023, 3(2), 298-321; https://doi.org/10.3390/solar3020018 - 1 Jun 2023
Cited by 3 | Viewed by 2300
Abstract
This paper presents a new fractional-order proportional-integral, (PI)λ (FO[PI]) type structure to investigate the load frequency control (LFC) problem. In the literature, some controllers’ extensive tuning options may slow or complicate the optimization process. Due to the intricacy of the tuning, even [...] Read more.
This paper presents a new fractional-order proportional-integral, (PI)λ (FO[PI]) type structure to investigate the load frequency control (LFC) problem. In the literature, some controllers’ extensive tuning options may slow or complicate the optimization process. Due to the intricacy of the tuning, even if there are fewer tuning parameters, a robust structure can be obtained. The (PI)λ structure deviates from the standard FOPI, integer PID, or PI-PD controllers with the same or fewer tuning parameters. The efficacy of a tri-parametric fractional-order controller is examined on a two-area interconnected hybrid power system comprising a photovoltaic (PV) grid and a Reheated Thermal Generator (RTG). In order to obtain optimal performance with lower control efforts, a novel dual-performance index is developed for the LFC problem. Various analyses are also proven to perform better than other optimized controllers from the recent literature. The presented scheme is significantly robust to disturbance interruptions, non-linearities, and parameter perturbations. It is also observed that there are no stability issues due to communication time delays. It is highlighted that the improvement can be obtained without adding complex structure or controller parameters. Full article
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<p>PV-RTG interconnected power system.</p>
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<p>Linearized model of PV−RTG system.</p>
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<p>HVDC line illustration.</p>
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<p>New FO[PI] scheme.</p>
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<p>Dynamic disturbance signal.</p>
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<p>Scenario 1−PV frequency responses.</p>
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<p>Scenario 1−RTG frequency responses.</p>
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<p>Scenario 1−Tie-line power responses.</p>
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<p>Control signal movement in PV system.</p>
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<p>Scenario 2−PV frequency response.</p>
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<p>Scenario 2−RTG frequency response.</p>
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<p>Scenario 2−Tie-line power responses.</p>
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<p>Scenario 3−PV frequency responses in load.</p>
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<p>Scenario 3−RTG frequency responses in load.</p>
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<p>Scenario 3−Tie-line power responses in load.</p>
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<p>PV with 40% increased <inline-formula><mml:math id="mm58"><mml:semantics><mml:msub><mml:mi>T</mml:mi><mml:mi>g</mml:mi></mml:msub></mml:semantics></mml:math></inline-formula>.</p>
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<p>RTG with 40% increased <inline-formula><mml:math id="mm59"><mml:semantics><mml:msub><mml:mi>T</mml:mi><mml:mi>g</mml:mi></mml:msub></mml:semantics></mml:math></inline-formula>.</p>
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<p>Tie-line with 40% increased <inline-formula><mml:math id="mm60"><mml:semantics><mml:msub><mml:mi>T</mml:mi><mml:mi>g</mml:mi></mml:msub></mml:semantics></mml:math></inline-formula>.</p>
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<p>PV with 40% decreased <inline-formula><mml:math id="mm61"><mml:semantics><mml:msub><mml:mi>T</mml:mi><mml:mi>g</mml:mi></mml:msub></mml:semantics></mml:math></inline-formula>.</p>
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<p>RTG with 40% decreased <inline-formula><mml:math id="mm62"><mml:semantics><mml:msub><mml:mi>T</mml:mi><mml:mi>g</mml:mi></mml:msub></mml:semantics></mml:math></inline-formula>.</p>
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<p>Tie−line with 40% decreased <inline-formula><mml:math id="mm63"><mml:semantics><mml:msub><mml:mi>T</mml:mi><mml:mi>g</mml:mi></mml:msub></mml:semantics></mml:math></inline-formula>.</p>
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<p>PV with 40% increased <inline-formula><mml:math id="mm64"><mml:semantics><mml:msub><mml:mi>T</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:semantics></mml:math></inline-formula>.</p>
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<p>RTG with 40% increased <inline-formula><mml:math id="mm65"><mml:semantics><mml:msub><mml:mi>T</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:semantics></mml:math></inline-formula>.</p>
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<p>Tie−line with 40% increased <inline-formula><mml:math id="mm66"><mml:semantics><mml:msub><mml:mi>T</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:semantics></mml:math></inline-formula>.</p>
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<p>PV with 40% decreased <inline-formula><mml:math id="mm67"><mml:semantics><mml:msub><mml:mi>T</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:semantics></mml:math></inline-formula>.</p>
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<p>RTG with 40% decreased <inline-formula><mml:math id="mm68"><mml:semantics><mml:msub><mml:mi>T</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:semantics></mml:math></inline-formula>.</p>
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<p>Tie−line with 40% decreased <inline-formula><mml:math id="mm69"><mml:semantics><mml:msub><mml:mi>T</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:semantics></mml:math></inline-formula>.</p>
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<p>PV with nonlinearity.</p>
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<p>RTG with nonlinearity.</p>
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<p>Tie-line with nonlinearity.</p>
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<p>PV with CTD.</p>
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<p>RTG with CTD.</p>
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<p>Tie-line with CTD.</p>
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12 pages, 2140 KiB  
Article
Particle Swarm Optimization Algorithm-Tuned Fuzzy Cascade Fractional Order PI-Fractional Order PD for Frequency Regulation of Dual-Area Power System
by Mokhtar Shouran and Aleisawee Alsseid
Processes 2022, 10(3), 477; https://doi.org/10.3390/pr10030477 - 26 Feb 2022
Cited by 21 | Viewed by 2788
Abstract
This study proposes a virgin structure of Fuzzy Logic Control (FLC) for Load Frequency Control (LFC) in a dual-area interconnected electrical power system. This configuration benefits from the advantages of fuzzy control and the merits of Fractional Order theory in traditional PID control. [...] Read more.
This study proposes a virgin structure of Fuzzy Logic Control (FLC) for Load Frequency Control (LFC) in a dual-area interconnected electrical power system. This configuration benefits from the advantages of fuzzy control and the merits of Fractional Order theory in traditional PID control. The proposed design is based on Fuzzy Cascade Fractional Order Proportional-Integral and Fractional Order Proportional-Derivative (FC FOPI-FOPD). It includes two controllers, namely FOPI and FOPD connected in cascade in addition to the fuzzy controller and its input scaling factor gains. To boost the performance of this controller, a simple and powerful optimization method called the Particle Swarm Optimization (PSO) algorithm is employed to attain the best possible values of the suggested controller’s parameters. This task is accomplished by reducing the Integral Time Absolute Error (ITAE) of the deviation in frequency and tie line power. Furthermore, to authenticate the excellence of the proposed FC FOPI-FOPD, a comparative study is carried out based on the obtained results and those from previously published works based on classical PID tuned by the Losi Map-Based Chaotic Optimization Algorithm (LCOA), Fuzzy PID Optimized by Teaching Learning-Based Optimization (TLBO) algorithm and Fuzzy PID with a filtered derivative mode tuned by PSO, which is employed in the same interconnected power system. The robustness of the suggested fuzzy structure is investigated against the parametric uncertainties of the testbed system. The simulation results revealed that the proposed FC FOPI-FOPD is robust, and it outperformed the other investigated controllers. For example, the drops in the frequency in area one and area two were improved by 89.785% and 97.590%, respectively, based on employing the proposed fuzzy configuration compared with the results obtained from the traditional PID. Full article
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<p>The block diagram of the two-area power system.</p>
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<p>The structural design of the proposed FC FOPI-FOPD controller.</p>
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<p>The membership functions of the proposed fuzzy design.</p>
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<p>Frequency drop in area one.</p>
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<p>Frequency drop in area two.</p>
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<p>Tie line power variation.</p>
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<p>Percentage of betterment with different controllers.</p>
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<p>Frequency variation in area one and area two under parametric uncertainty conditions with the proposed FC FOPI-FOPD controller.</p>
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<p>Tie line power deviation under the parametric uncertainty condition with the proposed FC FOPI-FOPD controller.</p>
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39 pages, 10884 KiB  
Article
Different Fuzzy Control Configurations Tuned by the Bees Algorithm for LFC of Two-Area Power System
by Mokhtar Shouran, Fatih Anayi, Michael Packianather and Monier Habil
Energies 2022, 15(2), 657; https://doi.org/10.3390/en15020657 - 17 Jan 2022
Cited by 14 | Viewed by 2660
Abstract
This study develops and implements a design of the Fuzzy Proportional Integral Derivative with filtered derivative mode (Fuzzy PIDF) for Load Frequency Control (LFC) of a two-area interconnected power system. To attain the optimal values of the proposed structure’s parameters which guarantee the [...] Read more.
This study develops and implements a design of the Fuzzy Proportional Integral Derivative with filtered derivative mode (Fuzzy PIDF) for Load Frequency Control (LFC) of a two-area interconnected power system. To attain the optimal values of the proposed structure’s parameters which guarantee the best possible performance, the Bees Algorithm (BA) and other optimisation tools are used to accomplish this task. A Step Load Perturbation (SLP) of 0.2 pu is applied in area one to examine the dynamic performance of the system with the proposed controller employed as the LFC system. The supremacy of Fuzzy PIDF is proven by comparing the results with those of previous studies for the same power system. As the designed controller is required to provide reliable performance, this study is further extended to propose three different fuzzy control configurations that offer higher reliability, namely Fuzzy Cascade PI − PD, Fuzzy PI plus Fuzzy PD, and Fuzzy (PI + PD), optimized by the BA for the LFC for the same dual-area power system. Moreover, an extensive examination of the robustness of these structures towards the parametric uncertainties of the investigated power system, considering thirteen cases, is carried out. The simulation results indicate that the contribution of the BA tuned the proposed fuzzy control structures in alleviating the overshoot, undershoot, and the settling time of the frequency in both areas and the tie-line power oscillations. Based on the obtained results, it is revealed that the lowest drop of the frequency in area one is −0.0414 Hz, which is achieved by the proposed Fuzzy PIDF tuned by the BA. It is also divulged that the proposed techniques, as was evidenced by their performance, offer a good transient response, a considerable capability for disturbance rejection, and an insensitivity towards the parametric uncertainty of the controlled system. Full article
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<p>Transfer function model of the testbed system.</p>
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<p>Structural diagram of Fuzzy PIDF controller of area 1.</p>
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<p>Membership functions of the two inputs and output.</p>
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<p>The Bees Algorithm flowchart.</p>
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<p>Frequency variation in area one (<math display="inline"><semantics> <mrow> <mo>∆</mo> <msub> <mi mathvariant="normal">F</mi> <mn>1</mn> </msub> </mrow> </semantics></math> in Hz).</p>
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<p>Frequency variation in area two (<math display="inline"><semantics> <mrow> <mo>∆</mo> <msub> <mi mathvariant="normal">F</mi> <mn>2</mn> </msub> </mrow> </semantics></math> in Hz).</p>
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<p>Tie-line power variation (<math display="inline"><semantics> <mrow> <mo>∆</mo> <msub> <mi mathvariant="normal">P</mi> <mrow> <mi>tie</mi> </mrow> </msub> </mrow> </semantics></math> in pu).</p>
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<p>Percentage of improvement with different techniques.</p>
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<p>Frequency deviation in area one (<math display="inline"><semantics> <mrow> <mo>∆</mo> <msub> <mi mathvariant="normal">F</mi> <mn>1</mn> </msub> </mrow> </semantics></math> in Hz) under parametric uncertainties of the testbed system.</p>
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<p>Frequency deviation in area two (<math display="inline"><semantics> <mrow> <mo>∆</mo> <msub> <mi mathvariant="normal">F</mi> <mn>2</mn> </msub> </mrow> </semantics></math> in Hz) under parametric uncertainties of the testbed system.</p>
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<p>Tie-line power deviation (<math display="inline"><semantics> <mrow> <mo>∆</mo> <msub> <mi mathvariant="normal">P</mi> <mrow> <mi>tie</mi> </mrow> </msub> </mrow> </semantics></math> in pu) under parametric uncertainties of the testbed system.</p>
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<p>Random load profile.</p>
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<p>Frequency deviation in area one: (<b>A</b>) based on BA tuning and (<b>B</b>) based on TLBO and PSO tuning.</p>
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<p>Frequency deviation in area two: (<b>A</b>) based on BA tuning and (<b>B</b>) based on TLBO and PSO tuning.</p>
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<p>Tie-line power deviation (<math display="inline"><semantics> <mrow> <mo>∆</mo> <msub> <mi mathvariant="normal">P</mi> <mrow> <mi>tie</mi> </mrow> </msub> </mrow> </semantics></math> in pu): (<b>A</b>) based on BA tuning and (<b>B</b>) based on TLBO and PSO tuning.</p>
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<p>Block diagram of Fuzzy Cascade PI − PD controller configuration equipped in area one.</p>
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<p>Block diagram of Fuzzy PI plus Fuzzy PD controller configuration equipped in area one.</p>
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<p>Block diagram of Fuzzy (PI + PD) controller configuration equipped in area one.</p>
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<p>Frequency deviation in area one (<math display="inline"><semantics> <mrow> <mo>∆</mo> <msub> <mi mathvariant="normal">F</mi> <mn>1</mn> </msub> </mrow> </semantics></math> in Hz).</p>
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<p>Frequency deviation in area two (<math display="inline"><semantics> <mrow> <mo>∆</mo> <msub> <mi mathvariant="normal">F</mi> <mn>2</mn> </msub> </mrow> </semantics></math> in Hz).</p>
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<p>Tie-line power deviation (<math display="inline"><semantics> <mrow> <mo>∆</mo> <msub> <mi mathvariant="normal">P</mi> <mrow> <mi>tie</mi> </mrow> </msub> </mrow> </semantics></math> in pu).</p>
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<p>Dynamic response of the testbed power system based on different fuzzy controllers under parametric uncertainty conditions, case 1. (<b>A</b>) Frequency variation in area 1; (<b>B</b>) frequency variation in area 2; (<b>C</b>) tie-line power variation.</p>
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<p>Dynamic response of the testbed power system based on different fuzzy controllers under parametric uncertainty conditions, case 2. (<b>A</b>) Frequency variation in area 1; (<b>B</b>) frequency variation in area 2; (<b>C</b>) tie-line power variation.</p>
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<p>Dynamic response of the testbed power system based on different fuzzy controllers under parametric uncertainty conditions, case 3. (<b>A</b>) Frequency variation in area 1; (<b>B</b>) frequency variation in area 2; (<b>C</b>) tie-line power variation.</p>
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<p>Dynamic response of the testbed power system based on different fuzzy controllers under parametric uncertainty conditions, case 4. (<b>A</b>) Frequency variation in area 1; (<b>B</b>) frequency variation in area 2; (<b>C</b>) tie-line power variation.</p>
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<p>Dynamic response of the testbed power system based on different fuzzy controllers under parametric uncertainty conditions, case 5. (<b>A</b>) Frequency variation in area 1; (<b>B</b>) frequency variation in area 2; (<b>C</b>) tie-line power variation.</p>
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<p>Dynamic response of the testbed power system based on different fuzzy controllers under parametric uncertainty conditions, case 6. (<b>A</b>) Frequency variation in area 1; (<b>B</b>) frequency variation in area 2; (<b>C</b>) tie-line power variation.</p>
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<p>Dynamic response of the testbed power system based on different fuzzy controllers under parametric uncertainty conditions, case 7. (<b>A</b>) Frequency variation in area 1; (<b>B</b>) frequency variation in area 2; (<b>C</b>) tie-line power variation.</p>
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<p>Dynamic response of the testbed power system based on different fuzzy controllers under parametric uncertainty conditions, case 8. (<b>A</b>) Frequency variation in area 1; (<b>B</b>) frequency variation in area 2; (<b>C</b>) tie-line power variation.</p>
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<p>Dynamic response of the testbed power system based on different fuzzy controllers under parametric uncertainty conditions, case 9. (<b>A</b>) Frequency variation in area 1; (<b>B</b>) frequency variation in area 2; (<b>C</b>) tie-line power variation.</p>
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<p>Dynamic response of the testbed power system based on different fuzzy controllers under parametric uncertainty conditions, case 10. (<b>A</b>) Frequency variation in area 1; (<b>B</b>) frequency variation in area 2; (<b>C</b>) tie-line power variation.</p>
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<p>Dynamic response of the testbed power system based on different fuzzy controllers under parametric uncertainty conditions, case 11. (<b>A</b>) Frequency variation in area 1; (<b>B</b>) frequency variation in area 2; (<b>C</b>) tie-line power variation.</p>
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<p>Dynamic response of the testbed power system based on different fuzzy controllers under parametric uncertainty conditions, case 12. (<b>A</b>) Frequency variation in area 1; (<b>B</b>) frequency variation in area 2; (<b>C</b>) tie-line power variation.</p>
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<p>Dynamic response of the testbed power system based on different fuzzy controllers under parametric uncertainty conditions, case 13. (<b>A</b>) Frequency variation in area 1; (<b>B</b>) frequency variation in area 2; (<b>C</b>) tie-line power variation.</p>
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19 pages, 4367 KiB  
Article
Water Cycle Algorithm Optimized Type II Fuzzy Controller for Load Frequency Control of a Multi-Area, Multi-Fuel System with Communication Time Delays
by Ch. Naga Sai Kalyan, B. Srikanth Goud, Ch. Rami Reddy, Haitham S. Ramadan, Mohit Bajaj and Ziad M. Ali
Energies 2021, 14(17), 5387; https://doi.org/10.3390/en14175387 - 30 Aug 2021
Cited by 36 | Viewed by 2289
Abstract
This paper puts forward the implementation of an intelligent type II fuzzy PID (T2-FPID) controller tweaked with a water cycle algorithm (WCA), subjected to an error multiplied with time area over integral (ITAE) objective index for regularizing the variations in frequency and interline [...] Read more.
This paper puts forward the implementation of an intelligent type II fuzzy PID (T2-FPID) controller tweaked with a water cycle algorithm (WCA), subjected to an error multiplied with time area over integral (ITAE) objective index for regularizing the variations in frequency and interline power flow of an interconnected power system during load disturbances. The WCA-based T2-FPID is tested on a multi-area (MA) system comprising thermal-hydro-nuclear (THN) (MATHN) plants in each area. The dynamical behavior of the system is analyzed upon penetrating area 1 with a step load perturbation (SLP) of 10%. However, power system practicality constraints, such as generation rate constraints (GRCs) and time delays in communication (CTDs), are examined. Afterward, a territorial control scheme of a superconducting magnetic energy storage system (SMES) and a unified power flow controller (UPFC) is installed to further enhance the system performance. The dominancy of the presented WCA-tuned T2-FPID is revealed by testing it on a widely used dual-area hydro-thermal (DAHT) power system model named test system 1 in this paper. Analysis reveals the efficacy of the presented controller with other approaches reported in the recent literature. Finally, secondary and territorial regulation schemes are subjected to sensitivity analysis to deliberate the robustness. Full article
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<p>Dual-area conventional hydro-thermal plant (DAHT) (test system 1) [<a href="#B24-energies-14-05387" class="html-bibr">24</a>].</p>
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<p>Model of a MATHN plant with CTDs (test system 2) [<a href="#B21-energies-14-05387" class="html-bibr">21</a>].</p>
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<p>MFs implemented for the FLC.</p>
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<p>Structure of the T2-FPID controller.</p>
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<p>UPFC damping controller [<a href="#B21-energies-14-05387" class="html-bibr">21</a>].</p>
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<p>WCA approach flowchart.</p>
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<p>Responses for case 1: (<b>a</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> </mrow> </semantics> </math> (<b>b</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mi>i</mi> <mi>e</mi> <mn>12</mn> </mrow> </msub> </mrow> </semantics> </math> and (<b>c</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> </mrow> </semantics> </math>.</p>
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<p>Responses for case 1: (<b>a</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> </mrow> </semantics> </math> (<b>b</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mi>i</mi> <mi>e</mi> <mn>12</mn> </mrow> </msub> </mrow> </semantics> </math> and (<b>c</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> </mrow> </semantics> </math>.</p>
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<p>Responses for case 2: (<b>a</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> </mrow> </semantics> </math> (<b>b</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mi>i</mi> <mi>e</mi> <mn>12</mn> </mrow> </msub> </mrow> </semantics> </math> and (<b>c</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> </mrow> </semantics> </math>.</p>
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<p>Responses for case 3: (<b>a</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> </mrow> </semantics> </math> (<b>b</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mi>i</mi> <mi>e</mi> <mn>12</mn> </mrow> </msub> </mrow> </semantics> </math> and (<b>c</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> </mrow> </semantics> </math>.</p>
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<p>Responses for case 3: (<b>a</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> </mrow> </semantics> </math> (<b>b</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mi>i</mi> <mi>e</mi> <mn>12</mn> </mrow> </msub> </mrow> </semantics> </math> and (<b>c</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> </mrow> </semantics> </math>.</p>
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<p>Responses for case 4: (<b>a</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> </mrow> </semantics> </math> (<b>b</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mi>i</mi> <mi>e</mi> <mn>12</mn> </mrow> </msub> </mrow> </semantics> </math> and (<b>c</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> </mrow> </semantics> </math>.</p>
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<p>Responses for case 5: (<b>a</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> </mrow> </semantics> </math> (<b>b</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mi>i</mi> <mi>e</mi> <mn>12</mn> </mrow> </msub> </mrow> </semantics> </math> and (<b>c</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> </mrow> </semantics> </math>.</p>
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<p>Responses for case 5: (<b>a</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> </mrow> </semantics> </math> (<b>b</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mi>i</mi> <mi>e</mi> <mn>12</mn> </mrow> </msub> </mrow> </semantics> </math> and (<b>c</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> </mrow> </semantics> </math>.</p>
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<p>Responses for case 6 for load variations: (<b>a</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> </mrow> </semantics> </math> (<b>b</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mi>i</mi> <mi>e</mi> <mn>12</mn> </mrow> </msub> </mrow> </semantics> </math> and (<b>c</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> </mrow> </semantics> </math>.</p>
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<p>Responses for case 6 for load variations: (<b>a</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> </mrow> </semantics> </math> (<b>b</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mi>i</mi> <mi>e</mi> <mn>12</mn> </mrow> </msub> </mrow> </semantics> </math> and (<b>c</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> </mrow> </semantics> </math>.</p>
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<p>Responses for case 6 for variations in the tie-line coefficient: (<b>a</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> </mrow> </semantics> </math> (<b>b</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mi>i</mi> <mi>e</mi> <mn>12</mn> </mrow> </msub> </mrow> </semantics> </math> and (<b>c</b>) <math display="inline"> <semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> </mrow> </semantics> </math>.</p>
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28 pages, 7437 KiB  
Article
Load Frequency Control Based on the Bees Algorithm for the Great Britain Power System
by Mokhtar Shouran, Fatih Anayi, Michael Packianather and Monier Habil
Designs 2021, 5(3), 50; https://doi.org/10.3390/designs5030050 - 2 Aug 2021
Cited by 34 | Viewed by 4462
Abstract
This paper focuses on using the Bees Algorithm (BA) to tune the parameters of the proposed Fuzzy Proportional–Integral–Derivative with Filtered derivative (Fuzzy PIDF), Fractional Order PID (FOPID) controller and classical PID controller developed to stabilize and balance the frequency in the Great Britain [...] Read more.
This paper focuses on using the Bees Algorithm (BA) to tune the parameters of the proposed Fuzzy Proportional–Integral–Derivative with Filtered derivative (Fuzzy PIDF), Fractional Order PID (FOPID) controller and classical PID controller developed to stabilize and balance the frequency in the Great Britain (GB) power system at rated value. These controllers are proposed to meet the requirements of the GB Security and Quality of Supply Standard (GB-SQSS), which requires frequency to be brought back to its nominal value after a disturbance within a specified time. This work is extended to employ the proposed fuzzy structure controller in a dual-area interconnected power system. In comparison with controllers tuned by Particle Swarm Optimization (PSO) and Teaching Learning-Based Optimization (TLBO) used for the same systems, simulation results show that the Fuzzy PIDF tuned by BA is able to significantly reduce the deviation in the frequency and tie-line power when a sudden disturbance is applied. Furthermore, the applied controllers tuned by BA including the Fuzzy PIDF prove their high robustness against a wide range of system parametric uncertainties and different load disturbances. Full article
(This article belongs to the Section Electrical Engineering Design)
Show Figures

Figure 1

Figure 1
<p>Frequency fluctuations following the loss of generation up to 1800 MW [<a href="#B1-designs-05-00050" class="html-bibr">1</a>].</p>
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<p>GB simplified power system.</p>
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<p>Structural diagram of fuzzy PIDF controller.</p>
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<p>Membership functions of the two inputs and output.</p>
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<p>The Bees Algorithm flowchart.</p>
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<p>Change in frequency in the GB power system for 0.035 pu load disturbance with tuned PID-based ISE.</p>
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<p>Change in frequency in the GB power system for 0.035 pu load disturbance with tuned PID-based ITAE.</p>
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<p>Change in frequency in the GB power system for 0.035 pu load disturbance with tuned FOPID-based ISE.</p>
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<p>Change in frequency in the GB power system for 0.035 pu load disturbance with tuned FOPID-based ITAE.</p>
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<p>Change in frequency in the GB power system for 0.035 pu load disturbance with tuned Fuzzy PIDF-based ISE.</p>
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<p>Change in frequency in the GB power system for 0.035 pu load disturbance with tuned Fuzzy PIDF-based ITAE.</p>
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<p>Comparison of the dynamic response of GB power model with parameter uncertainties of scenarios 1 and 2 with no secondary control loop.</p>
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<p>Comparison of three controllers tuned by BA based on ISE for scenario 2.</p>
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<p>Comparison of three controllers tuned by BA based on ITAE for scenario 2.</p>
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<p>Comparison of three controllers tuned by BA based on ITAE for LFC of the GB system in the nominal scenario with 0.053 pu load disturbance.</p>
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<p>Comparison of three controllers tuned by BA based on ITAE for LFC of the GB system in scenario 2 with 0.053 pu load disturbance.</p>
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<p>Transfer function model of the investigated dual-area power system.</p>
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<p>Frequency deviation in area 1 (∆F<sub>1</sub>).</p>
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<p>Frequency deviation in area 2 (∆F<sub>2</sub>).</p>
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<p>Tie-line power deviation (∆P<sub>tie</sub>).</p>
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<p>Frequency deviation in area 1 (∆F<sub>1</sub>) under parametric uncertainties.</p>
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<p>Frequency deviation in area 1 (∆F<sub>2</sub>) under parametric uncertainties.</p>
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<p>Tie-line power deviation (∆P<sub>tie</sub>) under parametric uncertainties.</p>
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<p>The primary frequency response of GB power system with and without the feedback gain of electrical vehicles.</p>
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<p>The primary frequency response of GB power system with various values of Tg.</p>
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<p>The primary frequency response of GB power system with various values of H.</p>
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<p>The primary frequency response of GB power system with various values of D.</p>
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<p>The primary frequency response of GB power system with various values of R.</p>
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