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Research paper thumbnail of A Comprehensive Analysis into the Effects of Quasiperiodicity on the Swing Equation

WSEAS transactions on applied and theoretical mechanics, Dec 31, 2023

This research studies the case of quasiperiodicity occurring within the swing equation, a fundame... more This research studies the case of quasiperiodicity occurring within the swing equation, a fundamental model that characterises the behaviour of rotor of the machine in synchronous generators in electrical systems. Quasiperiodicity is explained by intricate patterns and understanding the stability of power systems. Bifurcation analysis, frequency domain techniques and numerical simulations are employed to study the swing equation in detail. The objective of this study is to provide a comprehensive understanding of the dynamical behaviour of the equation for the case of quasiperiodicity, using both analytical and numerical methods, when changes are made to the variables of the system. The results show the comparison of primary resonance and quasiperiodicity in the swing equation and analyses the rate at which stability is lost. This will help with the system losing its stability and identifies precursors to chaos which will prevent unavoidable circumstances in the real world.

Research paper thumbnail of Examining the Attainment Gap in Academic Performance of Minoritised Ethnic Groups for a STEM Related Subject, Discrete Mathematics

Research paper thumbnail of Addressing the Primary and Subharmonic Resonances of the Swing Equation

WSEAS TRANSACTIONS ON APPLIED AND THEORETICAL MECHANICS

A research investigation is undertaken to gain a more comprehensive understanding of the primary ... more A research investigation is undertaken to gain a more comprehensive understanding of the primary and subharmonic resonances exhibited by the swing equation. The occurrence of the primary resonance is characterised by amplified oscillatory reactions, voltage instability, and the possibility for system failure. The phenomenon of subharmonic resonance arises when the frequency of disturbance is a whole-number fraction of the natural frequency. This results in the occurrence of low-frequency oscillations and the potential for detrimental effects on equipment. The objective of this study is to expand upon the current literature regarding the impacts of primary resonance and enhance comprehension of subharmonic resonance in relation to the stability of a specific power system model. The analytical and numerical tools are utilised to investigate the fundamental principles of this resonant-related problem, aiming to provide an effective control solution. This choice is driven by the model’s...

Research paper thumbnail of Addressing the Primary and Subharmonic Resonances of the Swing Equation

A research investigation is undertaken to gain a more comprehensive understanding of the primary ... more A research investigation is undertaken to gain a more comprehensive understanding of the primary and subharmonic resonances exhibited by the swing equation. The occurrence of the primary resonance is characterised by amplified oscillatory reactions, voltage instability, and the possibility for system failure. The phenomenon of subharmonic resonance arises when the frequency of disturbance is a whole-number fraction of the natural frequency. This results in the occurrence of low-frequency oscillations and the potential for detrimental effects on equipment. The objective of this study is to expand upon the current literature regarding the impacts of primary resonance and enhance comprehension of subharmonic resonance in relation to the stability of a specific power system model. The analytical and numerical tools are utilised to investigate the fundamental principles of this resonant-related problem, aiming to provide an effective control solution. This choice is driven by the model's complex nonlinear dynamical behaviour, which offers valuable insights for further analysis. This analysis includes the Floquet Method, the Method of strained parameters, and the concept of tangent instability in order to provide an extension to existing literature relating to primary and subharmonic resonances, taking into account the dynamic and bifurcation characteristics of the swing equation. This objective will be achieved through the utilisation of both analytical and numerical methods, enabling the identification of specific indicators of chaos that can contribute to the safe operation of real-world scenarios.

Research paper thumbnail of Comparison of Online Learning during the COVID-19 Pandemic against the Traditional Face-to-Face Learning Experience for a STEM Related Subject, Analytical Mathematics

Journal of education, society and behavioural science, Jul 5, 2022

The Coronavirus (Covid-19) pandemic put a halt provisionally to face-to-face teaching throughout ... more The Coronavirus (Covid-19) pandemic put a halt provisionally to face-to-face teaching throughout the educational sector impeding in addition, university students from receiving their traditional on campus teaching learning experience. Educators, academics, and the higher institutional authorities had to act fast and change their mode of teaching delivery to online platforms, with many students transferring their learning habits and customs to various online mediums and tools. In view of the struggles and adjustments many students underwent with this new method of teaching, a research study was conducted to identify whether online learning had an effect on student performance for a Science, Technology, Engineering and Mathematics (STEM) related module. On this purpose, this paper evaluates different statistical test measures to compare the two different teaching techniques adopted by a university foundation level module, Analytical Mathematics. Results from the pursued quantitative analysis show a decrease in the success of students' performance whilst receiving online teaching, suggesting a lesser impact on improved learning compared to the customary face-to-face delivery for this specific module. With regards to engagement, observations from the qualitative analysis of the study show a lack of involvement and participation from students with their lecturer and peers whilst in an online environment, echoing its influence on student performance. The deductions of the analyses of this study, emphasize that the necessary transition to online delivery and learning during the pandemic did lead to a challenging and negative experience on students and their performance for this STEM related subject.

Research paper thumbnail of Investigating the Attainment Gap in Academic Performance of Minoritised Ethnic Groups for a STEM Related Subject

Journal of Education, Society and Behavioural Science

This paper addresses the attainment gap in academic performance for students of Minoritised and n... more This paper addresses the attainment gap in academic performance for students of Minoritised and non-minoritised ethnicity, studying Discrete Mathematics, an undergraduate university level module, whereby an investigation of the effect of an intervention in one of the assessments is undertaken and statistically analysed. The attainment gap faced by the students of the UK higher education sector is concerning and between students of minoritised ethnic background and their counterparts, there is a sizeable achievement disparity in the education system. These groups' divergent academic performance is referred to as the attainment, and socioeconomic disadvantage, cultural hurdles, and institutional bias have all acted as a setback for the students from Black, Asian, and Minority Ethnic communities. However, there are obstacles to putting this strategy into practise, such as the need for suitable pedagogical techniques and assistance for students from different ethnic circumstances. C...

Research paper thumbnail of An Investigation into the Primary and Subharmonic Resonances of the Swing Equation

WSEAS TRANSACTIONS ON SYSTEMS AND CONTROL

A study is conducted to obtain a deeper insight into the primary and subharmonic resonances of th... more A study is conducted to obtain a deeper insight into the primary and subharmonic resonances of the swing equation. The primary resonance, which can result in increased oscillatory responses, voltage instability, and potential system collapse, happens when the external disturbance frequency coincides with the natural frequency of the system. Subharmonic resonance occurs when the disturbance frequency is an integer fraction of the natural frequency, leading to low-frequency oscillations and possible equipment damage. The purpose of this study is to provide an extension of the existing literature of the effects of primary resonance and further provide a thorough understanding of subharmonic resonance on the stability of a certain power system paradigm. Motivated by the rich nonlinear dynamical behaviour exhibited by this evergreen model, analytical and numerical techniques are employed to examine the underlying principles, creating an efficient control solution for this resonant-relate...

Research paper thumbnail of Comparison of Online Learning during the COVID-19 Pandemic against the Traditional Face-to-Face Learning Experience for a STEM Related Subject, Analytical Mathematics

Journal of Education, Society and Behavioural Science

The Coronavirus (Covid-19) pandemic put a halt provisionally to face-to-face teaching throughout ... more The Coronavirus (Covid-19) pandemic put a halt provisionally to face-to-face teaching throughout the educational sector impeding in addition, university students from receiving their traditional on campus teaching learning experience. Educators, academics, and the higher institutional authorities had to act fast and change their mode of teaching delivery to online platforms, with many students transferring their learning habits and customs to various online mediums and tools. In view of the struggles and adjustments many students underwent with this new method of teaching, a research study was conducted to identify whether online learning had an effect on student performance for a Science, Technology, Engineering and Mathematics (STEM) related module. On this purpose, this paper evaluates different statistical test measures to compare the two different teaching techniques adopted by a university foundation level module, Analytical Mathematics. Results from the pursued quantitative a...

Research paper thumbnail of Capturing Student Satisfaction: A Case Study on the National Student Survey Results to Identify the Needs of Students in STEM Related Courses for a Better Learning Experience

Education Sciences, 2020

The UK higher education has been one of the top destinations for international students over the ... more The UK higher education has been one of the top destinations for international students over the last few decades, and it is beneficial to the UK local and national economy. However, recent changes of the governmental policies on the way UK universities are funded and the recession that still affects economies around the world have left many universities around the UK at financial survival risk. With relatively limited access to reduced research funds, student recruitment has a vital importance for most universities. It has been well established in the literature that academic reputation and the level of services have the most significant impact on national and international students. Thus, universities, to maintain their market share, must spend much energy and resources to improve the level of services offered to their students. The recently introduced National Student Survey (NSS) has become one of the most important metrics to assess student satisfaction that influences directly...

Research paper thumbnail of An Insight into the Dynamical Behaviour of the Swing Equation

WSEAS TRANSACTIONS ON MATHEMATICS

Motivated by the nonlinear dynamics of mathematical models encountered in power systems, an inves... more Motivated by the nonlinear dynamics of mathematical models encountered in power systems, an investigation into the dynamical behaviour of the swing equation is carried out. This paper examines analytically and numerically the development of oscillatory periodic solutions, whereby increases of the control parameter, lead to a cascade of period doubling bifurcations, before eventually loss in stability is exhibited and effective forerunners to chaos revealed. Gaining an understanding on the dynamical behaviour of the system can help to produce a deeper insight of the bifurcations entailed, with the appearance of the triggered sequence of the first period doubling’s acting as precursors of imminent danger and difficult operations of a practical system.

Research paper thumbnail of A Comprehensive Analysis into the Effects of Quasiperiodicity on the Swing Equation

WSEAS transactions on applied and theoretical mechanics, Dec 31, 2023

This research studies the case of quasiperiodicity occurring within the swing equation, a fundame... more This research studies the case of quasiperiodicity occurring within the swing equation, a fundamental model that characterises the behaviour of rotor of the machine in synchronous generators in electrical systems. Quasiperiodicity is explained by intricate patterns and understanding the stability of power systems. Bifurcation analysis, frequency domain techniques and numerical simulations are employed to study the swing equation in detail. The objective of this study is to provide a comprehensive understanding of the dynamical behaviour of the equation for the case of quasiperiodicity, using both analytical and numerical methods, when changes are made to the variables of the system. The results show the comparison of primary resonance and quasiperiodicity in the swing equation and analyses the rate at which stability is lost. This will help with the system losing its stability and identifies precursors to chaos which will prevent unavoidable circumstances in the real world.

Research paper thumbnail of Examining the Attainment Gap in Academic Performance of Minoritised Ethnic Groups for a STEM Related Subject, Discrete Mathematics

Research paper thumbnail of Addressing the Primary and Subharmonic Resonances of the Swing Equation

WSEAS TRANSACTIONS ON APPLIED AND THEORETICAL MECHANICS

A research investigation is undertaken to gain a more comprehensive understanding of the primary ... more A research investigation is undertaken to gain a more comprehensive understanding of the primary and subharmonic resonances exhibited by the swing equation. The occurrence of the primary resonance is characterised by amplified oscillatory reactions, voltage instability, and the possibility for system failure. The phenomenon of subharmonic resonance arises when the frequency of disturbance is a whole-number fraction of the natural frequency. This results in the occurrence of low-frequency oscillations and the potential for detrimental effects on equipment. The objective of this study is to expand upon the current literature regarding the impacts of primary resonance and enhance comprehension of subharmonic resonance in relation to the stability of a specific power system model. The analytical and numerical tools are utilised to investigate the fundamental principles of this resonant-related problem, aiming to provide an effective control solution. This choice is driven by the model’s...

Research paper thumbnail of Addressing the Primary and Subharmonic Resonances of the Swing Equation

A research investigation is undertaken to gain a more comprehensive understanding of the primary ... more A research investigation is undertaken to gain a more comprehensive understanding of the primary and subharmonic resonances exhibited by the swing equation. The occurrence of the primary resonance is characterised by amplified oscillatory reactions, voltage instability, and the possibility for system failure. The phenomenon of subharmonic resonance arises when the frequency of disturbance is a whole-number fraction of the natural frequency. This results in the occurrence of low-frequency oscillations and the potential for detrimental effects on equipment. The objective of this study is to expand upon the current literature regarding the impacts of primary resonance and enhance comprehension of subharmonic resonance in relation to the stability of a specific power system model. The analytical and numerical tools are utilised to investigate the fundamental principles of this resonant-related problem, aiming to provide an effective control solution. This choice is driven by the model's complex nonlinear dynamical behaviour, which offers valuable insights for further analysis. This analysis includes the Floquet Method, the Method of strained parameters, and the concept of tangent instability in order to provide an extension to existing literature relating to primary and subharmonic resonances, taking into account the dynamic and bifurcation characteristics of the swing equation. This objective will be achieved through the utilisation of both analytical and numerical methods, enabling the identification of specific indicators of chaos that can contribute to the safe operation of real-world scenarios.

Research paper thumbnail of Comparison of Online Learning during the COVID-19 Pandemic against the Traditional Face-to-Face Learning Experience for a STEM Related Subject, Analytical Mathematics

Journal of education, society and behavioural science, Jul 5, 2022

The Coronavirus (Covid-19) pandemic put a halt provisionally to face-to-face teaching throughout ... more The Coronavirus (Covid-19) pandemic put a halt provisionally to face-to-face teaching throughout the educational sector impeding in addition, university students from receiving their traditional on campus teaching learning experience. Educators, academics, and the higher institutional authorities had to act fast and change their mode of teaching delivery to online platforms, with many students transferring their learning habits and customs to various online mediums and tools. In view of the struggles and adjustments many students underwent with this new method of teaching, a research study was conducted to identify whether online learning had an effect on student performance for a Science, Technology, Engineering and Mathematics (STEM) related module. On this purpose, this paper evaluates different statistical test measures to compare the two different teaching techniques adopted by a university foundation level module, Analytical Mathematics. Results from the pursued quantitative analysis show a decrease in the success of students' performance whilst receiving online teaching, suggesting a lesser impact on improved learning compared to the customary face-to-face delivery for this specific module. With regards to engagement, observations from the qualitative analysis of the study show a lack of involvement and participation from students with their lecturer and peers whilst in an online environment, echoing its influence on student performance. The deductions of the analyses of this study, emphasize that the necessary transition to online delivery and learning during the pandemic did lead to a challenging and negative experience on students and their performance for this STEM related subject.

Research paper thumbnail of Investigating the Attainment Gap in Academic Performance of Minoritised Ethnic Groups for a STEM Related Subject

Journal of Education, Society and Behavioural Science

This paper addresses the attainment gap in academic performance for students of Minoritised and n... more This paper addresses the attainment gap in academic performance for students of Minoritised and non-minoritised ethnicity, studying Discrete Mathematics, an undergraduate university level module, whereby an investigation of the effect of an intervention in one of the assessments is undertaken and statistically analysed. The attainment gap faced by the students of the UK higher education sector is concerning and between students of minoritised ethnic background and their counterparts, there is a sizeable achievement disparity in the education system. These groups' divergent academic performance is referred to as the attainment, and socioeconomic disadvantage, cultural hurdles, and institutional bias have all acted as a setback for the students from Black, Asian, and Minority Ethnic communities. However, there are obstacles to putting this strategy into practise, such as the need for suitable pedagogical techniques and assistance for students from different ethnic circumstances. C...

Research paper thumbnail of An Investigation into the Primary and Subharmonic Resonances of the Swing Equation

WSEAS TRANSACTIONS ON SYSTEMS AND CONTROL

A study is conducted to obtain a deeper insight into the primary and subharmonic resonances of th... more A study is conducted to obtain a deeper insight into the primary and subharmonic resonances of the swing equation. The primary resonance, which can result in increased oscillatory responses, voltage instability, and potential system collapse, happens when the external disturbance frequency coincides with the natural frequency of the system. Subharmonic resonance occurs when the disturbance frequency is an integer fraction of the natural frequency, leading to low-frequency oscillations and possible equipment damage. The purpose of this study is to provide an extension of the existing literature of the effects of primary resonance and further provide a thorough understanding of subharmonic resonance on the stability of a certain power system paradigm. Motivated by the rich nonlinear dynamical behaviour exhibited by this evergreen model, analytical and numerical techniques are employed to examine the underlying principles, creating an efficient control solution for this resonant-relate...

Research paper thumbnail of Comparison of Online Learning during the COVID-19 Pandemic against the Traditional Face-to-Face Learning Experience for a STEM Related Subject, Analytical Mathematics

Journal of Education, Society and Behavioural Science

The Coronavirus (Covid-19) pandemic put a halt provisionally to face-to-face teaching throughout ... more The Coronavirus (Covid-19) pandemic put a halt provisionally to face-to-face teaching throughout the educational sector impeding in addition, university students from receiving their traditional on campus teaching learning experience. Educators, academics, and the higher institutional authorities had to act fast and change their mode of teaching delivery to online platforms, with many students transferring their learning habits and customs to various online mediums and tools. In view of the struggles and adjustments many students underwent with this new method of teaching, a research study was conducted to identify whether online learning had an effect on student performance for a Science, Technology, Engineering and Mathematics (STEM) related module. On this purpose, this paper evaluates different statistical test measures to compare the two different teaching techniques adopted by a university foundation level module, Analytical Mathematics. Results from the pursued quantitative a...

Research paper thumbnail of Capturing Student Satisfaction: A Case Study on the National Student Survey Results to Identify the Needs of Students in STEM Related Courses for a Better Learning Experience

Education Sciences, 2020

The UK higher education has been one of the top destinations for international students over the ... more The UK higher education has been one of the top destinations for international students over the last few decades, and it is beneficial to the UK local and national economy. However, recent changes of the governmental policies on the way UK universities are funded and the recession that still affects economies around the world have left many universities around the UK at financial survival risk. With relatively limited access to reduced research funds, student recruitment has a vital importance for most universities. It has been well established in the literature that academic reputation and the level of services have the most significant impact on national and international students. Thus, universities, to maintain their market share, must spend much energy and resources to improve the level of services offered to their students. The recently introduced National Student Survey (NSS) has become one of the most important metrics to assess student satisfaction that influences directly...

Research paper thumbnail of An Insight into the Dynamical Behaviour of the Swing Equation

WSEAS TRANSACTIONS ON MATHEMATICS

Motivated by the nonlinear dynamics of mathematical models encountered in power systems, an inves... more Motivated by the nonlinear dynamics of mathematical models encountered in power systems, an investigation into the dynamical behaviour of the swing equation is carried out. This paper examines analytically and numerically the development of oscillatory periodic solutions, whereby increases of the control parameter, lead to a cascade of period doubling bifurcations, before eventually loss in stability is exhibited and effective forerunners to chaos revealed. Gaining an understanding on the dynamical behaviour of the system can help to produce a deeper insight of the bifurcations entailed, with the appearance of the triggered sequence of the first period doubling’s acting as precursors of imminent danger and difficult operations of a practical system.