Topologies and Controls for Optimal Energy Bifurcation in AC, DC, and Hybrid Microgrid

Topologies and Controls for Optimal Energy
Bifurcation in AC, DC, and Hybrid Microgrid
Pritam Bhowmik
Registration No: 1781001020
Department of Electrical Engineering
INSTITUTE OF TECHNICAL EDUCATION & RESEARCH
SIKSHA ‘O’ ANUSANDHAN
(Deemed to be UNIVERSITY)
Bhubaneswar, Odisha, India.
Jan 2021

Topologies and Controls for Optimal Energy
Bifurcation in an AC, DC and Hybrid Microgrid
Thesis submitted in partial fulfilment of the requirements
for the degree of
Doctor of Philosophy
by
Pritam Bhowmik
Registration No. 1781001020
Supervisor
Prof. (Dr.) Pravat Kumar Rout
Department of Electrical and Electronics Engineering,
Institute of Technical Education & Research,
Siksha ‘O’ Anusandhan Deemed to be University, Bhubaneswar, Odisha, India.
Department of Electrical Engineering
Institute of Technical Education and Research
(Deemed to be UNIVERSITY)
Jan 2021

(Deemed to be University)
(A Deemed to be University declared U/S 3 of the UGC Act, 1956)
Faculty of Engineering & Technology
Certificate
This is to certify that the dissertation entitled “Topologies and Controls for
Optimal Energy Bifurcation in an AC, DC and Hybrid Microgrid” submitted by
Pritam Bhowmik (Regd. No. 1781001020) is approved for the degree of Doctor
of Philosophy in Electrical Engineering from Institute of Technical Education
and Research, Siksha ‘O’ Anusandhan Deemed to be University, Bhubaneswar,
Odisha, India.
(External Examiner)
Prof. (Dr.) Pravat Kumar Rout,
(Supervisor)
Department of Electrical and
Electronics Engineering,
Institute of Technical Education and Research,
Siksha ‘O’ Anusandhan
Deemed to be University,
Prof. (Dr.) Renu Sharma,
(Head of the Department)
Department of Electrical Engineering,
Institute of Technical Education and Research,
Siksha ‘O’ Anusandhan
Deemed to be University,

Declaration
I, Pritam Bhowmik, declare that this written submission represents my ideas in
my own words and where others ideas or words have been included; I have
adequately cited and referenced the original sources. I also declare that I have
adhered to all principles of academic honesty and integrity and have not
represented, fabricated or falsified any idea/data/fact/source in my submission. I
understand that any violation of the above will cause for disciplinary action by
the Institute and can also evoke penal action from the sources which have thus
not been properly cited or from whom proper permission has not been taken when
needed.
Pritam Bhowmik,
Regd. No. 1781001020

Acknowledgement
At the very beginning, I would like to thank Head of the Department,
Electrical Engineering, and Siksha ‘O’ Anusandhan (Deemed to be University),
for providing me with the resources to carry out my research work. I am gratified
to my dear supervisor Prof. (Dr.) Pravat Kumar Rout for his endless support and
inspiration throughout the tenure. I would like to thank the Council of Scientific
and Industrial Research, Govt. of India, for providing me with the fellowship
(SRF-Direct, Ack. No. 143232/2K18/1) during the journey. I am highly obliged to
Prof. Josep M Guerrero, Aalborg University, Denmark, for enriching my research
work and coauthoring couples of the studies. I would like to express my gratitude
to the Villum Fonden (Grant-25920) for funding part of the research work. I am
highly obliged to Prof. Bikash C Pal, Imperial College, London for his valuable
technical inputs and endless support and endorsement throughout the period. I
am thankful to Prof. S. K. Padmanaban, Aalborg University, Esbjerg, Denmark,
and Prof. Abdullah Abusorrah, King Abdulaziz University, Saudi Arabia, for the
participation in the research work and coauthored few of the study. I am thankful
to Prof. Pietro Tricoli, Deputy Editor-in-Chief, IET Renewable Power Generation
for considering one of my research publication as the feature paper of the year
2020 and nominating me for the best paper award 2020 in his valuable periodical.
I am thankful to the publication houses like IEEE, IET, Elsevier, Wiley and
American Institute of Physics, for acknowledging, appreciating and endorsing my
research works.
I am thankful to my beloved wife for her sacrifice, patience and support
during this tough journey. I am grateful to my parents for their continuous effort
and inspiration throughout my life. Finally, I am thankful to my daughter for
inspiring me every time for many disappointments.
Pritam Bhowmik

iv
Table of Contents
Declaration...................................................................................................................................i
Acknowledgement......................................................................................................................ii
Abstract......................................................................................................................................iii
Table of Contents ......................................................................................................................iv
List of Figures.............................................................................................................................x
List of Tables............................................................................................................................xv
Introduction
1.1. Introduction .........................................................................................................................1
1.2. The alternative.....................................................................................................................3
1.3. Renewable energy................................................................................................................3
1.3.1. Wind energy..................................................................................................................4
1.3.2. Solar energy ..................................................................................................................5
1.4. Microgrid.............................................................................................................................5
1.4.1. Les Anglais (Haiti)........................................................................................................6
1.4.2. Mpeketoni (Kenya).......................................................................................................6
1.4.3. Bronsbergen Holiday Park (Netherland) ......................................................................6
1.5. Exploring the challenges in the framework of microgrid....................................................6
1.6. The motivation.....................................................................................................................9
1.7. Layout and the synopsis of the study ................................................................................10
1.7.1. Energy storage devices in microgrids.........................................................................10
1.7.2. State of charge and state of power management in dc microgrids .............................11
1.7.3. Filter less power allocation and regulation scheme for the dc microgrid...................11
1.7.4. Frequency superimposed energy bifurcation technology for dc microgrid................12
1.7.5. Robust coordinated control between dc and ac sub-grids...........................................12
1.7.6. Introductory concept of the auxiliary damping loop for the ac sub-grids ..................13
1.7.7. Non-directional synthetic inertial scheme for the hybrid islanded microgrid ............13
1.7.8. Direction sensitive synthetic inertial scheme for the hybrid microgrid......................13
1.7.9. Electric vehicle as a potential distributed load in hybrid microgrid ...........................14
1.7.10. Single phase virtual inertia emulation technique for hybrid microgrid through the
plug-in electric vehicle..........................................................................................................14

v
Energy storage devices in microgrids
2.1. Introduction .......................................................................................................................16
2.2. Modelling of energy storage devices.................................................................................16
2.2.1. Battery Energy Storage...............................................................................................17
2.2.2. Compressed Air Energy Storage.................................................................................18
2.2.3. Flywheel Energy Storage............................................................................................20
2.2.4. Supercapacitor Energy Storage...................................................................................22
2.2.5. Super Magnetic Energy Storage .................................................................................24
State of Charge and State of Power Management in DC
Microgrid
3.1. Introduction .......................................................................................................................26
3.2. Proposed self-tuned dynamic exponent based decentralised SoC management scheme ..28
3.2.1. Energy storage units with high specific energy..........................................................28
3.2.2. Designing of the self-tuned dynamic exponent ..........................................................29
3.2.3. Integrating BES & CAES system and deriving state variables ..................................29
3.2.4. SoC equalization time and the exponent.....................................................................32
3.2.5. Deriving the limits of the exponent ............................................................................32
3.3. Proposed FLC-DPI integrated decentralised SoP management scheme ...........................36
3.3.1. Energy storage units with high specific power...........................................................36
3.3.2. Integrating FES, SCES and SMES systems and deriving control variables...............36
3.4. Results and analysis...........................................................................................................39
3.4.1. System performance analysis under the dynamic loads .............................................39
3.4.2. System performance analysis under the fluctuating generations................................41
3.4.3. System performance analysis under the varying load and generations ......................42
3.5. Conclusion.........................................................................................................................44
Filter-less Power Allocation and Regulation Scheme for the
DC Microgrid
4.1. Introduction .......................................................................................................................46
4.2. Configuration of the test system........................................................................................49
4.3. Conceptualizing and designing of the proposed selected power component droop..........49
4.3.1. Bus capacitance and analogy with the selected power component droop ..................49
4.3.2. Demand allocation ......................................................................................................50

vi
4.3.3. Generalization of the concept .....................................................................................52
4.3.4. Selection of control parameters ..................................................................................52
4.4.1. Influence of coefficient selection on power allocation...............................................54
4.4.2. Incremental constant power load ................................................................................58
4.4.3. High-frequency demand bifurcation...........................................................................62
4.5. Prototyping ........................................................................................................................64
4.6. Real-time response and analysis........................................................................................66
4.7. Conclusion.........................................................................................................................68
Frequency Superimposed Energy Bifurcation Technology for
DC Microgrid
5.1. Introduction .......................................................................................................................69
5.2. Proposed virtual frequency based drooping ......................................................................71
5.2.1. Principle of conventional drooping in ac sub-grid......................................................71
5.2.2. Principle of conventional drooping in dc sub-grid .....................................................72
5.2.3. Frequency superimposition technique ........................................................................73
5.2.4. Maximum allowable limit of exchanged power .........................................................76
5.3.1. A comparative analysis of the maximum allowable exchanged power and stability .79
5.3.2. Power regulation within the dc sub-grid and SoC management.................................82
5.3.3. DC side compensation and circulating power ............................................................83
5.4. Conclusion.........................................................................................................................85
Hybrid Microgrid: Robust Coordinated Control between DC
and AC sub-grids
6.1. Introduction .......................................................................................................................87
6.2. Proposed demand driven virtual frequency based drooping approach..............................88
6.2.1. Functional Modes .......................................................................................................88
6.2.2. Integrated control layout of BES unit .........................................................................91
6.3. Principle operational layout of master-slave units ............................................................92
6.3.1. Proposed layout of control principle for the master converter ...................................94
6.3.2. Proposed layout of control principle for the slave converters ....................................94
6.3.3. Proposed layout of control principle for the photovoltaic unit...................................96
6.4. Stability of the integrated system ......................................................................................97

vii
6.5.1. Grid power absorption and load shedding ..................................................................99
6.5.2. Under-loaded microgrid and grid side power injection ............................................101
6.5.3. Barred grid side injection and frequency regulation mode.......................................102
6.6. Conclusion.......................................................................................................................104
Introductory Concept of the Auxiliary Damping Loop for the
AC sub-grids
7.1. Introduction .....................................................................................................................105
7.2. Inertial response and the frequency.................................................................................107
7.3. Designing of the test environment...................................................................................108
7.4. Proposed superimposition technique of dynamic damping in the derivative control loop
................................................................................................................................................110
7.5. Results and analysis.........................................................................................................112
7.5.1. Individual impact-assessment of virtual inertia and virtual damping.......................113
7.5.2. Relative performance-assessment of II-DES............................................................115
7.5.3. Robustness and critical stability assessment.............................................................118
7.7. Conclusion.......................................................................................................................120
Non-directional Synthetic Inertial Scheme for the Hybrid
Islanded Microgrid
8.1. Introduction .....................................................................................................................121
8.2. Synthetic inertia emulation scheme.................................................................................123
8.2.1. Dynamic frequency regulation..................................................................................123
8.3. Proposed fuzzy tuned dynamic synthetic inertia.............................................................124
8.3.1. Analysis of the reference frequency tracking lag in an interfacing inverter.............124
8.3.2. Establishing the concept of virtual gyratory mass in a VSG ....................................124
8.3.3. Incorporation of the virtual PCL and SCL in the VSG.............................................124
8.3.4. Incorporation of fuzzy tuned dynamic synthetic inertia in the VSG ........................125
8.4. Undertaken test system....................................................................................................126
8.5. Analysis of the robustness and the stability ....................................................................127
8.6.1. Large load switching.................................................................................................131
8.6.2. Dynamic load............................................................................................................133
8.6.3. Large load switching over a small dynamic load......................................................135

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8.7. Prototyping and real-time analysis ..................................................................................136
8.8. Conclusion.......................................................................................................................138
Direction Sensitive Synthetic Inertial Scheme for the Hybrid
Microgrid
9.1. Introduction .....................................................................................................................139
9.2. Proposed direction sensitive dynamic inertia emulation technique ................................141
9.3. Assessment of the stability region...................................................................................144
9.4.1. Switching of static loads...........................................................................................148
9.4.2. Dynamic load............................................................................................................151
9.4.3. Dynamic asynchronous load.....................................................................................153
9.4.4. Multi source-based dual inertia module....................................................................155
9.4.5. Comparative stability analysis ..................................................................................157
9.5. Prototyping and the real-time performance assessment ..................................................159
9.6. Conclusion.......................................................................................................................161
Electric Vehicle: A Potential Distributed Load in Hybrid
Microgrid
10.1. Introduction ...................................................................................................................162
10.2. Proposed dual-layer cascaded control loop ...................................................................164
10.2.1. Designing of the primary control loop and the dynamics of the vehicle................164
10.2.2. Secondary control loop and establishing the cascaded dual-layer control .............166
10.3. Result and analysis ........................................................................................................167
10.3.1. Ideal propulsion unit and dynamics of the vehicle .................................................168
10.3.2. Improvement in the acceleration performance at the paddle to metal condition....170
10.3.3. Evaluation of the cruise control ability with respect to the random inclination .....172
10.4. Hardware-in-Loop test environment .............................................................................175
10.5. Conclusion.....................................................................................................................176
Plug-in Electric Vehicle: Single Phase Virtual Inertia
Emulation Technique for Hybrid Microgrid
11.1. Introduction ...................................................................................................................178
11.2. Proposed control mechanism and the hierarchy............................................................179
11.2.1. Signal processing unit.............................................................................................180

ix
11.2.2. Cascaded virtual reactance with the frequency and voltage droop.........................183
11.2.3. Virtual inertia and damping control based on the proposed ST-FOPI concept ......184
11.2.4. Voltage and current control loop ............................................................................187
11.3. Result and analysis ........................................................................................................187
11.3.1. Behavior and authentication of the test system ......................................................187
11.3.2. Instant of static load switching ...............................................................................190
11.3.3. Dynamic asynchronous load...................................................................................194
11.4. Prototyping ....................................................................................................................197
11.5. Real-time performance evaluation.................................................................................198
11.6. Conclusion.....................................................................................................................199
Conclusion
12.1. Conclusion.....................................................................................................................200
References..............................................................................................................................203
Publication.............................................................................................................................220

x
List of Figures
Fig. 1.1. Per capita power...........................................................................................................1
Fig. 1.2. Carbon deposition rate .................................................................................................2
Fig. 1.3. Concentration of carbon dioxide..................................................................................2
Fig. 1.4. Effect of fossil fuel on the global mortality .................................................................3
Fig. 1.5. Global wind power density ..........................................................................................4
Fig. 1.6. Growth in wind energy harnessing by region ..............................................................4
Fig. 1.7. Global solar irradiation measure ..................................................................................5
Fig. 2.1. Conceptualized schematic representation of the lead-acid battery ............................17
Fig. 2.2. Operational layout of compressed air energy storage system...................................19
Fig. 2.3. Structural layout of the flywheel storage system .......................................................20
Fig. 2.4. Structural modelling of supercapacitor ......................................................................22
Fig. 2.5. Equivalent mean model of SMES..............................................................................24
Fig. 3.1. Architecture of a dc microgrid ...................................................................................27
Fig. 3.2. Equivalent mean model of an energy storage unit .....................................................31
Fig. 3.3. Control principle of the proposed STDE technique...................................................35
Fig. 3.4. Control principle of the proposed FLC-DPI technique based SoP management
scheme ......................................................................................................................................38
Fig. 3.5. Fuzzy membership function.......................................................................................38
Fig. 3.6. System response under the dynamic loads.................................................................40
Fig. 3.7. System response under the fluctuating generation.....................................................42
Fig. 3.8. System response under the fluctuating load and generation ......................................43
Fig. 3.9. System stability ..........................................................................................................44
Fig. 4.1. Configured test-system...............................................................................................49
Fig. 4.2. Control loops of the SPC-D and the CL-D techniques ..............................................53
Fig. 4.3. Influence of coefficient ..............................................................................................55
Fig. 4.4. Response of power allocation ....................................................................................56
Fig. 4.5. Response of bus voltage in three different configurations.........................................57
Fig. 4.6. System response under incremental CPL (a) Selected power component droop, (b)
Conventional linear droop ........................................................................................................59
Fig. 4.7. Three-dimensional response of the bus voltage (a) Proposed SPC-D, (b)
Conventional CL-D ..................................................................................................................60
Fig. 4.8. Probability of the bus voltage ....................................................................................61
Fig. 4.9. Acquired power responses from the SPC-D under dynamic load profiles (a) BES (b)
SCES-A and SCES-B...............................................................................................................62

xi
Fig. 4.10. Acquired power responses from the CL-D under dynamic load profiles ................63
Fig. 4.11. Bus voltage density ..................................................................................................63
Fig. 4.12. Prototype hardware setup.........................................................................................65
Fig. 4.13. Acquired real-time response (a) Proposed SPC-D, (b) Conventional CL-D ...........66
Fig. 4.14. Noise power spectrum..............................................................................................67
Fig. 5.1. Control principle of the conventional ac sub-grid......................................................72
Fig. 5.2. Control principle of the interlinking converter ..........................................................74
Fig. 5.3. Control principle of the proposed dc-dc boost converter...........................................75
Fig. 5.4. Equivalent architecture of the hybrid microgrid ........................................................76
Fig. 5.5. Simulated undertaken model......................................................................................78
Fig. 5.6. A comparative analysis of the maximum allowable exchanged power limits...........79
Fig. 5.7. Maximum exchanged power and stability .................................................................80
Fig. 5.8. Power regulation within the dc sub-grid and SoC management ................................82
Fig. 5.9. DC side compensation and circulating power............................................................84
Fig. 6.1. System under study highlighting the sources and storages........................................89
Fig. 6.2. Proposed operational drooping mode.........................................................................90
Fig. 6.3. BES drooping characteristics .....................................................................................93
(a) Drooping state, (b) Full energy density, (c) Half energy density, (d) Zero energy density 93
Fig. 6.4. Control layouts...........................................................................................................95
(a) BES, (b) IC, (c) CAES, (d) PV ...........................................................................................95
Fig. 6.5. System stability ..........................................................................................................97
(a) HED, (b) FED .....................................................................................................................97
Fig. 6.6. System response under grid power absorption and load shedding...........................100
(a) Virtual frequency, (b) System voltage, (c) Current...........................................................100
Fig. 6.7. System response for under-loaded microgrid and grid side injection......................102
Fig. 6.8. System response under barred grid side injection....................................................103
Fig. 7.2. Established proposed inertia emulation scheme ......................................................112
Fig. 7.3. System observation (a) root-locus of increasing inertia (b) frequency response with
increasing inertia (c) root-locus of increasing damping co-efficient (d) frequency response
with increasing damping.........................................................................................................114
Fig. 7.4. Uncertainties in the test environment.......................................................................115
Fig. 7.5. System response.......................................................................................................116
Fig. 7.6. Control parameter of self-regulating PI ...................................................................117

xii
Fig. 7.7. System response delay .............................................................................................119
Fig. 7.8. Nyquist’s stability curves.........................................................................................120
Fig. 8.1. Schematic representation of PCL & SCL in a conventional VSG...........................125
Fig. 8.2. Schematic representation of proposed virtual gyratory mass integrated VSG.........126
Fig. 8.3. Schematic representation of designed test system highlighting the proposed RVSG
integration...............................................................................................................................127
Fig. 8.4. Responses of undertaken test model against uncertainties (a) Frequency, (b) Power
................................................................................................................................................128
Fig. 8.5. (a) Comparative bode response, (b) Root locus .......................................................129
Fig. 8.6. Detailed undertaken microgrid network...................................................................130
Fig. 8.7. System response and the stability under the large load switching scenario (a)
Frequency, (b) Power, (c) RoCoS, (d) Nyquist’s diagram .....................................................131
Fig. 8.8. Response delay.........................................................................................................133
Fig. 8.9. System response and the stability under the dynamic load scenario (a) Frequency, (b)
Power, (c) RoCoS, (d) Nyquist’s diagram..............................................................................134
Fig. 8.10. System response and the stability under the large load switching over a small
dynamic load scenario (a) Frequency, (b) Power, (c) RoCoS, (d) Nyquist’s diagram..........135
Fig. 8.11. Experimental prototype setup.................................................................................137
Fig. 8.12. Real-time frequency response from the prototype hardware setup........................137
Fig. 9.1. Concept of the low static inertial and the conventional dynamic inertial system...141
Fig. 9.2. Schematic representation of the proposed DSIE loop.............................................142
Fig. 9.3. Simulated test-system..............................................................................................145
Fig. 9.4. Effect of inertia on the frequency.............................................................................146
Fig. 9.5. Impedance response of the test-system....................................................................146
Fig. 9.6. Coupling effect of (a) active power, (b) reactive power ..........................................147
Fig. 9.7. Frequency response under the scenario of static load switching ............................148
Fig. 9.8. Response of coefficient of inertia under the scenario of static load switching.......149
Fig. 9.9. COI with respect to the power demand and the frequency .....................................150
Fig. 9.10. Density of acquired frequency response ................................................................151
Fig. 9.11. Response of frequency under the dynamic loading ..............................................151
Fig. 9.12. Dynamic frequency response in a three dimensional surface (a) DI, (b) DSIE.....152
Fig. 9.13. Probability vs. frequency .......................................................................................153
Fig. 9.14. Machine response...................................................................................................153
Fig. 9.15. Response of the microgrid .....................................................................................154
Fig. 9.16. Frequency response in contour surface ..................................................................154
Fig. 9.17. Frequency response of dual inertia module............................................................155

xiii
Fig. 9.18. Compensated power and equalization error (a) DI (b) Proposed DSIE.................156
Fig. 9.19. Frequency density of dual inertia module..............................................................156
Fig. 9.20. Bode response of the system..................................................................................157
Fig. 9.21. Noise-Power spectrum ...........................................................................................158
Fig. 9.22. Nyquist’s stability response ...................................................................................158
Fig. 9.23. Experimental hardware setup................................................................................159
Fig. 9.24. Real-time frequency response (a) LSI Vs. DSIE, (b) DI Vs. DSIE ......................160
Fig. 10.1. Vector representation of acting forces on the vehicle............................................165
Fig. 10.2. Proposed dual-layer cascaded control mechanism.................................................167
Fig. 10.3. Dynamics of the vehicle with respect to the ideal propulsion unit ........................169
Fig. 10.4. Comparative vehicle dynamics ..............................................................................170
Fig. 10.5. Surface representation of dynamics .......................................................................171
Fig. 10.6. Inclination angle.....................................................................................................172
Fig. 10.7. Comparative vehicle dynamics (a) Velocity & acceleration (b) Propulsion torque &
power ......................................................................................................................................173
Fig. 10.8. Control parameters Kp & Ki in the time domain ....................................................174
Fig. 10.9. Control parameters of the DLCC loop ...................................................................174
Fig. 10.10. Layout of the Hardware-in-Loop test setup .........................................................175
Fig. 10.11. HIL test responses (a) paddle to metal condition (b) cruise control condition ....176
Fig. 11.1. Framework and the control hierarchy ....................................................................181
Fig. 11.2. Structural layout of the signal processing unit.......................................................182
Fig. 11.3. Magnitude and phase response of the designed SOGI...........................................182
Fig. 11.4. Structural layout of the cascaded droop control and the virtual reactance.............184
Fig. 11.5. Functional layout of ST-FOPI based virtual inertia and damping module ............185
Fig. 11.6. Cascaded voltage and current control loop ............................................................187
Fig. 11.7. Impedance of the test system .................................................................................188
Fig. 11.8. Coefficient of coupling (a) active power (b) reactive power .................................188
Fig. 11.9. Inertial effect on the test-system ............................................................................189
Fig. 11.10. Linearity of the test-system..................................................................................189
Fig. 11.11. Frequency response at the instant of static load switching ..................................191
Fig. 11.12. Computed control reference at the static load switching scenario.......................191
Fig. 11.13. Response of the proposed ST-FOPI at the instant of static load switching .........192
Fig. 11.14. Reference gate drive signals at the static load switching scenario.......................192
Fig. 11.15. Compensation of the transient power at the instant of static load switching .......193
Fig. 11.16. Computed density of the bus frequency...............................................................193

xiv
Fig. 11.17. Frequency response at dynamic load instances....................................................195
Fig. 11.18. Computed virtual power reference and phase angle at dynamic load instances ..195
Fig. 11.19. Response of proportional and integral coefficient at dynamic load instances .....196
Fig. 11.20. Reference gate drive signals at dynamic load instances ......................................196
Fig. 11.21. Probability of the system frequency.....................................................................197
Fig. 11.22. Architecture of the prototype ...............................................................................198
Fig. 11.23. Acquired real-time frequency response of the prototype....................................199

xv
List of Tables
Table 3.1. Rule base .................................................................................................................38
Table 3.2. System response under the dynamic loads..............................................................40
Table 3.3. System response under the fluctuating generation ..................................................42
Table 3.4. System response under the fluctuating load and generation ...................................44
Table 4.1. Derived statistical information for multiple KSPC-D.................................................57
Table 4.2. Derived statistical information for incremental CPL ..............................................60
Table 4.3. Derived statistical information under dynamic load profile....................................64
Table 4.4. Derived statistical information from real-time response.........................................67
Table 5.1. System evolution .....................................................................................................81
Table 5.2. Evolution of SoC management scheme...................................................................83
Table 5.3. Evolution of circulating power................................................................................85
Table 6.1. Selected system parameters.....................................................................................98
Table 6.2. System observation under grid power absorption and load shedding...................100
Table 6.3. System observation for under-loaded microgrid and grid side injection ..............102
Table 6.4. System observation under barred grid side injection ............................................104
Table 7.1. Model specification ...............................................................................................109
Table 7.3. Statistics of uncertainties.......................................................................................116
Table 7.4. Statistics of frequency deflection ..........................................................................118
Table 7.5. Statistics of inertial power.....................................................................................118
Table 8.1. Model parameters for designing microgrid testbed...............................................128
Table 8.2. System statistics for the large load switching scenario .........................................132
Table 8.3 System statistics for the dynamic load scenario.....................................................134
Table 8.4 System statistics for the scenario of large load switching over a small dynamic load
................................................................................................................................................136
Table A. Types of micro sources and controller parameters..................................................138
Table B. Line parameters........................................................................................................138
Table C. Additional system recreation parameter ..................................................................138
Table 9.1. Fundamental concept of the proposed DSIE.........................................................143
Table 9.2. Control parameters ................................................................................................146
Table 9.3. Statistics of frequency under static load switching ...............................................149
Table 9.4. Statistics of coefficient of inertia under static load switching...............................149
Table 9.5. Statistics of frequency under the dynamic loading................................................152
Table 9.6. Statistics of frequency under dual inertia module.................................................155

xvi
Table 9.7. Statistics of real-time frequency response.............................................................160
Table 10.1. Statistics of the vehicle dynamics........................................................................169
Table 10.2. Comparative statistics of vehicle dynamics ........................................................172
Table 10.3. Comparative statistics of the cruise control ability .............................................173
Table 11.1. Parameters of the ST-FOPI control loop.............................................................186
Table 11.2. Statistical parameter of the test-system...............................................................190
Table 11.3. Statistics of frequency at the instant of static load switching..............................190
Table 11.4. Statistics of power compensation at the instant of static load switching ............194
Table 11.5. Statistics of frequency density at the instant of static load switching .................194
Table 11.6. Statistics of frequency at dynamic load instances ...............................................196
Table 11.7. Statistics of real-time frequency..........................................................................199

INTRODUCTION
Chapter 1
Topologies and Controls for Optimal Energy Bifurcation in an AC, DC and Hybrid
Microgrid
Pritam Bhowmik

Chapter 1
Introduction
1.1. Introduction
In ancient Egyptian literature, a phrase Thunderer of the Nile had been mentioned to
describe the electric fish in 2750 BCE. The roman physician Scribonius Largus had described
the effect of the electric shock in his book De compositione medicamentorum liber in 47 AD
[1]. This is a piece of clear evidence that the knowledge about the electricity and the
conductivity existed in the ancient culture. In 1646, the term electricity has been first coined by
Thomas Browne in his book Pseudodoxia Epidemica [2]. Later in 1752, Benjamin Franklin
introduced the Leyden Jar for the storage of static electricity, which was the pioneering concept
of modern batteries today [3]. Scientist James Clerk Maxwell fundamentally developed the
relationship between the electricity and the magnetism in his book On Physical Lines of Force
in 1862 [4]. In the late 19th
century, progress in electrical science is noteworthy. Thomas Edison
and Nikola Tesla have taken the concept beyond the scientific curiosity and with some great
technology transfer made it an essential gizmo for modern society [5]. The 20th
century was all
about turning fossil fuel into the electricity to ensure the easy transportation of energy. In
today’s world, the average power per capita is the measure of the wellbeing of a country. The
per capita power of developed countries like the United States, Canada, Russia, etc. has been
comparatively shown against the developing country-India in Fig. 1.1 [6]. The per capita power
visualize the impact of the electrical energy on the modern society.
Fig. 1.1. Per capita power
0
200
400
600
800
1000
1200
1400
1600
1800
Unitaed
States
Russia Japan Germany Canada India
Watt/Person

P. Bhowmik
2
Fig. 1.2. Carbon deposition rate [7]
Fig. 1.3. Concentration of carbon dioxide [8]
The fossil fuel is the primary source of electrical energy. In thermal plants, coal, petroleum, and
natural gases are burned to produce heat. Eventually, the heat energy is converted to the
electrical energy through turbines and alternators. With the increasing demand for electric
power, the use of fossil fuel is also increasing with the time, which ultimately deposits carbon
on the surface of the planet. Figure 1.2 illustrates the carbon deposition rate in metric tons per
year [7]. During the process of burning fossil fuels, and the deposited carbon emits the huge
amount of carbon dioxide, which directly impure the air. The concentration of carbon dioxide
in the air is showcased in Fig. 1.3. It is observed that, in the late nineteen hundred century, while
the electricity became the necessity for the society, exponential growth in the CO2 concentration
is started. [8]. In 2014, a scientific society, Our World in Data had carried

Introduction
3
Fig. 1.4. Effect of fossil fuel on the global mortality
out one study on the world mortality rate and the sensitive elements. According to the study,
there is a certain relationship between human health and CO2 concentration. Further, it has been
claimed in the study that the total mortality in the world is highly influenced by the burning of
fossil fuel [9]. The statistics have been graphically represented in Fig. 1.4. It is clear from the
observation that the effect of the coal and the oil is the most severe and highly influence the
mortality rate worldwide.
1.2. The alternative
It is the evidential truth that prior to the technological improvement in the mining sector
to extract underground oar in early 19th
century, the use of biomass existed to fuel the fire. From
the ice age to the doorstep of industrialization, the only known fuel for the human being was
the biomass which is a renewable energy source [10]. The second most evidential use of
renewable energy found hundreds of years ago is the wind energy to drive ships [11]. The use
of geothermal energy is also one of the oldest culture found in the Paleolithic culture to prefer
hot spring water for bathing and swimming [12]. In the literature of the Roman culture, the
concept of space heating is observed. In 1860 and 1870, due to the industrialization in Europe,
there was fear that the civilization would struggle in near future to fuel the fire for civilization.
In the year of 1956, the first wind turbines were developed to produce electricity followed by
the solar farm in 1980 [13].
1.3. Renewable energy
With suitable policies and technological infrastructure, renewable energy has a huge
potential scope to grow over a few decades. The primary reason is the availability of renewable
energy over a wide geographical area where fossil fuel is limitedly available in few countries.
Dramatic growth in the renewable energy share is expected by 2030 to ensure energy security
and to avail the economic assistance. As it has been stated earlier, the growth
Brown Coal
Coal
Oil
Biomass
Gas Nuclear
Brown Coal Coal Oil Biomass Gas Nuclear

P. Bhowmik
4
Fig. 1.5. Global wind power density [20]
Fig. 1.6. Growth in wind energy harnessing by region [21]
in the renewable sector will eventually reduce air pollution and the premature mortality from
the intoxication of the high carbon dioxide concentration [14]. Renewable energy farms which
cultivate the energy from the water or wind are indirectly deriving the available heat energy on
the surface of the planet received from the sunlight [15]. At least for the one billion years, the
present perception of renewable energy will exist [16]. According to a hypothetical study, the
temperature of the surface after a billion year will increase to a level where water will not be
available in the liquid form [17].
1.3.1. Wind energy
The present installed capacity of the wind energy is approximately 650 GW which is
4% of the total electricity demand in the world [18]. The most advance wind turbines are

Introduction
5
capable to produce the peak power of 9 MW at the desired environmental condition [19]. In the
high altitude, preferably wind farms are developed to avail the peak power. On average, the
operational period of the wind farm is 16 hours a day and which is available for more than 200
days a year [20]. The Technical University of Denmark has studied the average potential of the
wind energy 100 meters above the surface and released one map which is illustrated in Fig. 1.5.
The growth in wind energy harvesting in the last 40 years has been shown in Fig. 1.6 [21]. It is
observed in the illustration that the growth in the last 20 years is exponential.
1.3.2. Solar energy
The solar farms are growing rapidly throughout the world. The installed capacity has
already reached 600 GW in 2020 [18]. With the massive improvement in material science, the
cost of photovoltaic panels is reducing day by day. It is expected that, in every five years, the
installed capacity will be double the prior [22]. At present, 2% of the total load demand in the
world is supplied from solar energy [23]. The concept of concentrated solar power has recently
taken a momentum, where an optical lens is used to converge the sunlight into a light-beam.
This technique is comparatively very cost-effective as the cost of the lens is approximately a
tenth of the panel. The commercial implementation of the solar beam based farm is established
in 1980 [24]. Italy has the largest penetration level of solar power in the national grid by 7.7%
in 2015 [25]. The world irradiation atlas has been shown in Fig. 1.7 [26].
1.4. Microgrid
Renewable energy is distributed in a huge geographical area and to harness the wind or
solar power from nature, the distributed micro-generator is required [27]. The concept of the
micro-generators are such that it can operate individually with some local controls but can feed
power to either a local load or it can feed power to the wide-area grid network. The network
which integrates these small scale micro-generation units with local loads is known as
microgrid [28]. The responsibility of the microgrid is not limited only to the integration of micro
Fig. 1.7. Global solar irradiation measure [26]

P. Bhowmik
6
generators through some electrical feeder, but a microgrid is to also ensure the controls of micro
sources either locally or through some communication channel [29]. A microgrid invariably
integrates energy storage systems in the network to assure the power consumer an uninterrupted
service and to ensure the high short circuit capacity for the network [30]. As it has been already
stated, a microgrid can feed only the local load, which is specified as the islanded microgrid.
Community microgrid, Remote off-grid microgrid and Military based microgrids are the few
examples of the islanded microgrid [31]. When a microgrid electrically coupled to a wide grid
network, it is called as the grid-connected microgrid or the grid following microgrid.
Sometimes, the islanded microgrid is also referred to as the grid forming microgrid.
1.4.1. Les Anglais (Haiti)
In the outskirts of the city, a cloud-based microgrid has been developed in Les Anglais,
Haiti to power 52 numbers of buildings [32]. The topology adopted for this microgrid is a mess
network-based architecture. The system adopts a communication channel based monitoring and
control scheme. In the architecture of the microgrid, there is the provision of local gateway
based smart meter which transmits and receives command through the cloud [33]. The smart
meters are also capable to detect energy theft to keep the energy loss as minimum as 12
percentage [34].
1.4.2. Mpeketoni (Kenya)
In Kenya, a diesel-fuelled microgrid has been developed by the Mpeketoni Electricity
Project [35]. The microgrid is an islanded microgrid to power the rural area which was initially
not connected to any nationalized grid due to the geographical position. The control of the
micro-generator units is based on the optical fibre based communication channel. The midpoint
energy theft protection for the system is also present which is developed based on the signal
processing based approach.
1.4.3. Bronsbergen Holiday Park (Netherland)
To harness the energy available from the sunlight, a rooftop based integrated solar
microgrid has been deployed in Netherland to power an amusement park. Besides the grid-
connected mode, the microgrid can sustain as in the autonomous mode with the facility of
battery energy storage systems integrated. In the islanded mode of operation, in association
with the storage system, the microgrid can handle 150 kW of peak demand in a clear sunny day
[36]. The centralized control scheme which makes use of the communication channel is
responsible to regulate the amount of active and reactive power feeding in the wide grid
network.
1.5. Exploring the challenges in the framework of microgrid
The microgrid is a close network which integrates renewable resources through micro-
generators. As the renewable energy is distributed in nature, it is always expected to have the
distributed micro-generation units in the network, preferably near to the load end to reduce the
transmission losses [37]-[38]. The harnessing of renewable energy is not difficult if one

Introduction
7
assumes a single micro source. In a framework of microgrid, it becomes challenging to maintain
synchronization among multiple interconnected micro-generation units [39]-[40]. The first
difficulty comes from nature. Nature is always very difficult to predict through our
technological development. Nature often surprises us with uncertainties and the prediction of
cloud coverage, solar irradiation and wind speed is not practically possible [41]. Therefore, the
power generation in such micro sources which harnesses solar or wind energy does not remain
constant. The fluctuation in the power generation introduces the problem of unstable frequency
and voltage [42].
Therefore, maintaining the synchronization among the micro-generation unit becomes
difficult and precise power-sharing among the microgeneration units becomes a challenging
issue in the control engineering [43]. The power flow in the ac network depends on the
frequency. The frequency is a global parameter in the electrical system which means the
measures of the frequency in point 1 is equal to the measures in point 2. Taking use of this
global parameter frequency, communication channels are often used to interlink interfacing
converters of distributed sources to command and take control of active power regulation from
a centrally established control centre. However, the major problem in this scheme is the
communication channel itself. Establishment of the communication network is a huge
economic burden for the microgrid. Therefore, preferably a communication channel based
central control should be avoided to keep the establishment cost of microgrid low [44]. There
is a certain probability of the communication failure which eventually lead the complete system
to the blackout. Even a small delay in receiving the signal in the other end becomes dangerous
and put the converter on electrical and thermal stress [45]. The alternative technique is the
communication less distributed control which is technically referred to as droop control [46].
The droop control technique locally measures the frequency and active power and computes
the gate pulse for the converter locally without any signal level clock frequency
synchronization. According to the character of network impedance, there are some variants of
droop control technique available [47]. The concept of the droop control is already an
established technique and the practical implementation is evidenced. However, there is another
side of the coin where the active power is closely coupled with the voltage [48]. In this case,
either the effect of frequency on the active power is insignificant or completely abolished. The
reactance plays the role here. While the ratio between the reactance to the resistance declines
the effect of the voltage on the active power becomes more prominent. In low and medium
voltage microgrid where the operational voltage is below 11 kV, it becomes quite difficult to
regulate the active power in the ac network [49]. The measure of voltage on point 1 and point
2 are not equal due to the line resistance. In that case, droop control becomes unstable. However,
there is a concept of virtual impedance in the ac microgrid which eventually can manipulate the
characteristics of the network impedance to strengthen the coupling between the frequency and
active power [49]. However, in dc microgrid, there is no concept of frequency. The active power
in dc network is solely dependent on the voltage. As the voltage is a local parameter and cannot
be used as a global reference, power-sharing in the dc network is the crucial issue.
The energy storage system is an invariable part of the microgrid [50]. The primary
responsibility of the energy storage system is to ensure the uninterrupted service. The downtime

P. Bhowmik
8
of renewable sources is considered a big factor. At the downtime period, while there is no
renewable power available in the network, it is the responsibility of the energy storage system
to satisfy the whole load demand without an interruption [51]. Therefore, multiple numbers of
energy storage units are required in the microgrid frame. There is a technical challenge to ensure
the equal utilization of the resources without burdening a single unit. It means that the storage
unit is expected to be exhausted at the same time [52]. The simplest way to solve this issue is
by ensuring the equal power-sharing among the storage unit, which mat eventually drain the
energy at the same rate and the storage unit will die down at the same time. But, this simple
trick does not work in a practical situation due to the unequal storage capacity of the units. If
all the storage unit supplies the equal amount of power at some instant of time, the unit with a
smaller capacity will be exhausted earlier. Therefore, the state of charge (SoC) management is
a challenge in this field [51]. The SoC management becomes even more complex when different
categories of storage units are present in a network which has different response time.
The renewable power generators and the storage systems are mostly operating in dc
system, while the load at the consumers' end are mostly ac in nature. There are some bulk power
industrial consumers who prefer to buy power in dc. Therefore, the microgrids are mostly
hybrid in nature where two or many sub-grids existed. Categorically, there are two types of sub-
grids are present, dc and ac [53]. In the ac sub-grid, it is obvious that the real power will be
regulated by the frequency and in the dc sub-grid it will be through the voltage. The
coordination and the power flow between the two topologically different sub-grids are complex
[54]. In one sub-grid, the active power is influenced by voltage and in another, it is by
frequency. Therefore, it is difficult to compare the two set of references i.e. voltage and
frequency which are not identically similar [55]. The amount of wide grid interference in the
hybrid architecture is technical as well as an economical issue [56]. The hybrid structure of the
microgrid generally commits a very cheap unit price with respect to the wide grid. Therefore,
the period of wide grid interference in the hybrid microgrid should be minimum to bear the unit
commitment. The amount of utility interference is a challenge in the field of optimization.
Distributed micro-generators are integrated into the network through some power
electronic converters. The interfacing converter can be simply either a dc/dc type or the dc/ac
according to the topological demand. The price per watt of the switching elements of converters
like MOSFETs and IGBTs is high. Therefore, it is always preferred to operate an interfacing
converter at the maximum loading condition without keeping the provision for the peak
demands [57]. Therefore, the total overrating capacity of the microgrid is sacrificed which
eventually affects the transient stability. Inertia plays a big role in the power system. For a wide
grid network, the inertia is infinite. As a result, the short circuit capacity of the wide grid
network remains above twenty times of the nominal rating which indirectly offers a larger
transient stability region. Due to the presents of power electronic switches, the available
rotational inertia from micro sources is not strongly coupled with the electrical network.
Therefore, the fast frequency response of the microgrid is always sacrificed. Besides the
stability, the low electrical inertia of the microgrid directly affects the protection scheme in the
microgrid. Improvement of the inertia followed by the high short circuit capacity is a challenge
for the microgrid framework.

Introduction
9
The electric vehicle is the modern trend in the transportation system. It has gained the
attention of the environmentally-conscious customers in the recent decade. Manufacturing
industries of the automobile sector are also participating to develop their model. With the
technological improvement in the battery industry, the cost for the lithium-ion batteries is
decreasing day by day. The improvement of the energy density in the lithium-ion batteries over
the decade is significant. Therefore, huge growth in this field is expected by the next twenty
years [58]. The huge number of plug-in electric vehicles will be a potential threat for the
microgrid. The plug-in EVs are the most scattered load in the network. Therefore, the active
load management for this type of scattered load is quite impractical. However, dramatically it
will reduce the stability of the microgrid due to the scattered nature of the demand point [59].
Therefore, some kind of topological modification is required in the electric vehicle charger to
offer ancillary services for the microgrid. The ancillary service can be reactive power
compensation, load shifting, peak demand management, virtual inertia, etc [60]. The designing
of the EV chargers particularly for the environment of the renewable penetrated microgrid is a
challenge.
1.6. The motivation
The motivation for the study has been derived by exploring the challenges and
technically analyzing the issues to ensure a complete solution for the microgrid from the
perspective of the topology and the controllability. Broadly relating the challenges like power-
sharing in dc sub-grid, coordination in the hybrid microgrid, wide grid interference, seamless
transition between grid forming and grid following mode, decaying inertia and the stability
issues have the single root of origin. The origin is the distributed generators which do not
behave like the conventional synchronous machine. The conventional synchronous machine
has the two major characteristics, natural drooping and the rotational inertia. With the natural
governor drooping as in synchronous machine, communication less DG integration is possible.
With the suitable inertia in the network, issues like transient stability, fast frequency response,
protection mishap and load-shading management disappear. With the large short circuit current,
problems in islanding detection and re-synchronization of the microgrid turn out to be simple.
The issue related to the power qualities in the microgrid partially fades away while the network
is critically damped.
If we consider the electronic drooping in the microgrid, the power-frequency drooping
is already an established technique and even for the low reactive line, the power-frequency
droop in the ac system works perfectly with an auxiliary loop of virtual resistance in the
network. However, in the dc sub-grids, the power-voltage drooping is not a reliable technique
to be adopted due to the unbalanced line resistance in the network. The study has put an effort
to initially develop a drooping technique particularly for the dc sub-grids where instead of
taking the voltage, which is a local reference, a synthetic signal has been computed which can
be used as the global reference to solve the issue. Further, the technique has been modified to
establish robust coordination between the ac and dc sub-grids of a hybrid microgrid. The issues
like circulating current, thermal stress and stability have been taken into consideration for the
analysis.

P. Bhowmik
10
Inertia is a vital factor in the microgrid. The inertia of a network defines the short circuit
capacity of the network which eventually predicts the transient stability limit. In a network, if
the instantaneous power mismatch can be minimized through some power injection scheme,
the short circuit capacity of the system can be improved which incidentally expands the
transient stability limit. To keep the instantaneous power mismatch in a check, the study has
put an effort to develop some novel schemes for the microgrid accomplishing the energy storage
systems. The power density of the energy storage system is one of the most important factors
while the virtual is concerned. Therefore, the study has analysed the impact of storage types on
the network. The benefits of cascading and hybridization of the storage types have been studied
systematically. The battery energy storage, compressed air energy storage, supercapacitor,
flywheel and the super magnetic energy storage have been taken into consideration in the
designing and hybridization stage. Besides the importance and functionality of the state of
charge management for the energy-dense storages, a novel scheme has been proposed to keep
the energy equalization factor high between the battery and the compressed air. Finally, the
concept of direction sensitive virtual inertia management scheme has been developed in the
study.
Lastly, the study has explored the potential types of load demands in the hybrid
microgrid. The electric vehicle is one of the most growing and emerging area which has a nature
of highly scattered demand points in the small network. The study has considered plug-in
electric vehicles in the network to analyse the stability issues. The study has explored the
opportunity and the provision of ancillary services through PEVs to improve the transient
stability limit of the microgrid.
1.7. Layout and the synopsis of the study
A complete layout and the synopsis of the whole study has been showcased in this
section. The layout of the study has been deliberated in synchronization with the challenges and
motivation. Issues like designing of the storage devices, hybridization of the storage, state of
charge management, Filterless power allocation and regulation scheme for the dc microgrid,
frequency superimposed energy bifurcation technology for dc microgrid, robust coordinated
control between dc and ac sub-grids, the introductory concept of the auxiliary damping loop for
the ac sub-grids, a non-directional synthetic inertial scheme for the hybrid islanded microgrid,
direction sensitive synthetic inertial scheme for the hybrid microgrid, designing of the electric
vehicle as a potential distributed load in a hybrid microgrid, and single-phase virtual inertia
emulation technique for a plug-in electric vehicle in hybrid microgrid has been considered and
contemptuously analysed in the study.
1.7.1. Energy storage devices in microgrids
The energy storage system in the microgrid plays a big role in the transient and steady-
state stability. The first and foremost responsibility of the storage system is to offer and ensure
uninterrupted service to the consumers. The primary role of the storage devices in the microgrid
is to build-up a proper backup system which can satisfy the total power demand for several
hours a day. The storage devices have a secondary role either to minimize the instantaneous

Introduction
11
power mismatch in the network during the contingency. The contingency in the network where
a large transient mismatch of power is observed which persist for a very short period. It may
either be introduced from the demand end or the sources side. The change in solar irradiation,
wind speed are the few causes of source end contingency in the network. Load switching, faults
in the distribution line, charging current, islanding are the few examples of demand-side
contingency. A microgrid should be capable to withstand the period of contingency or simply
it should be capable to handle the transients. To satisfy the primary objective to back-up the
total load demand, high energy-dense storage systems like battery and compressed air are
preferred. While the short term contingency which requires a large amount of power to
compensate cannot be handled by this type of storage system. To compensate the transient
mismatches in the network, power-dense storage systems like supercapacitor, flywheel and
super magnetic storage elements are required. The storage components in the microgrid, which
is later referred for several topological studies, have been mathematically designed and the
state-space models have been developed in Chapter 2.
1.7.2. State of charge and state of power management in dc microgrids
Storage elements which contains a large amount of energy and dissipates the energy
through a longer period and act as a backup system are specified as the energy-dense storage
system. To satisfy the power demand and to withstand several hours a day, single unit storage
systems are not sufficient. Battery energy storage system (BESS) and the compressed air energy
storage systems (CAES) categorically fall under the energy-dense system. In practice, to build
up a backup system, several units of storage systems are used in the microgrid. These storage
units are coupled to the network in a very scattered way, preferably closer to the demand points.
If the energy drawn from the storage units are not proportionally balanced, few of the units in
the network may get exhausted while the others may have a sufficient amount of charge
remaining. This is not a preferable situation where deep discharge is often expected. Repeated
deep discharge hampers the storage life particularly for the system which electrochemically
converts the energy as in a battery. Certainly, drawing the equal power from the unit is not the
solution for this issue, because units are often unequal in storage capacity. Therefore, the state
of charge management is considered as a vital factor in the microgrid. Unlike the energy-dense
storage element, power-dense storage systems are responsible for the compensation of the
instantaneous mismatch. Supercapacitor, flywheel, and super magnetic energy storage system
are often referred to as the transient storage system. In a hybrid framework, it is always
preferred that the individual transient unit should be stressed in proportion to their nominal
capacity. It signifies that the state of power among the power-dense storage units should be
equal. The state of power management is quite difficult as it only deals with the transients. The
provision for the improvement in the state of charge and state of power management has been
explored in Chapter 3.
1.7.3. Filter less power allocation and regulation scheme for the dc microgrid
As it has been already discussed that a microgrid is incomplete without the storage
system. The hybridization in the storage system is a trend in this area to ensure the backup as
well as the stability. The backup time is ensured by the energy-dense system and the stability

P. Bhowmik
12
is by the power-dense storage units. The demand is very complex in nature which certainly
contains both steady-state and transient state. Taking an example of the load switching in the
network, the statement can be clarified further. At the instant of the switching, there is a huge
demand for power which pursues for few milliseconds is referred to as the transient power
demand. After the accomplishment of the switching event, while the system settles back to the
steady-state, continuously there is an extra demand of power to feed the new load switched.
This steady-state demand should be satisfied by the energy-dense storage systems present in
the network. To decompose the demand into the steady-state and transient state, conventionally
LC filters are used. This type LC filter which decomposes the demand is sometimes referred to
as the power filter. The power filter is designed once and therefore it has a constant cut-off
frequency. The cut-off frequency plays a major role in the power decomposition. The
performance and the stability of the microgrid in the transient period is largely dependent on
this cut-off frequency. The compensation capability and the response time of the supercapacitor,
flywheel and super magnetic energy storage systems are highly proportional to the state of
power. Taking the flywheel as an example, it can be further clarified. While the flywheel is on
its full spin, the transient response from the storage type is the maximum and the response time
decreases in proportion to the squire of the angular velocity. The transient instant may come
into the scenario at any instant of time at any angular velocity of the flywheel. Therefore, the
constant cut-off frequency-based power decomposition technique is not a very effective
approach to this problem. Eventually, a technique will be more appropriate where the cut-off
frequency is not constant and it automatically adjusts according to the operational scenario. The
provision of the optimal cut-off frequency in a filterless power decomposition technique has
been explored in Chapter 4.
1.7.4. Frequency superimposed energy bifurcation technology for dc microgrid
It has been already discussed why a communication less power-sharing technique is
always preferred in the microgrid. The communication less power-sharing techniques are all
droop based scheme. There is a problem in the droop control is that it is highly sensitive and
with improperly tuned gain it often goes into the instability zone. In the dc microgrid, the
problem becomes even severe. In dc microgrid, the power which is in obvious the active power
is dependent on the voltage. The voltage is a parameter which cannot be treated as a global
reference. Due to the resistance in the system, the reference (i.e. voltage) varies based on the
point of measurement. With a local reference, while the dc droop techniques are designed it
becomes unreliable. There is another issue. The concept of the electronic droop technique was
developed to promote the plug-and-play feature in the microgrid. To design a voltage-power
based drooping technique for the dc microgrid, one must have the knowledge of line resistances
of each of the branches which practically violates the concept of the plug-and-play. Therefore,
the opportunity of the frequency superimposed droop based power-sharing technique for the dc
microgrid has been explored in Chapter 5.
1.7.5. Robust coordinated control between dc and ac sub-grids
In the hybrid microgrid, robust coordination among the sub-grids is always expected.
These sub-grids are topologically two types in nature, dc sub-grid and the ac sub-grid. There

Introduction
13
are three types of coordination required which are the coordination inside the ac sub-grid,
coordination inside the dc sub-grid, and the coordination between the dc and ac sub-grids. The
coordination inside the ac sub-grid through the frequency-drooping technique is a standardized
practice. Maintaining the coordination inside the dc sub-grid is little difficult through the
conventional voltage-power droop. In Section 1.7.4, the possibilities of the frequency
superimposed drooping technique in the dc sub-grids have been discussed. To build up robust
coordination between the dc and ac sub-grids is the most difficult problem in a hybrid
framework. Enforcing some extra conditions in the form of an auxiliary control loop, the
frequency superimposition based power bifurcation technique can be implemented for the
purpose of building up robust coordination between the dc and ac sub-grids. The possibilities
of the master-slave based conditional drooping scheme for the robust coordination between the
dc and ac sub-grids have been explored in Chapter 6.
1.7.6. Introductory concept of the auxiliary damping loop for the ac sub-grids
Frequency in an unstable ac network fluctuates. The peak frequency drop which is
sometimes referred to as the frequency nadir is inversely proportional to the damping of the
system. Persistence of the transient period is highly relative to the amount of damping enforced
in the network. In the DG penetrated the small network, the concept of natural damping does
not exist. While, in the wide grid network, due to the availability of large short circuit current,
the natural damping in the network is always close to the critical damping value. Ensuring the
critical damping in the ac sub-grids is very important. The response time of an over-damped
system is sluggish in nature. Therefore the frequency restraining period in an over-damped
system is often more than the expectation. While in an under-damped system, once the
frequency is perturbed, the oscillation persists for a very long period. Therefore, the possibilities
of the auxiliary dynamic damping loop to ensure critical damping for the ac sub-grid has been
explored in Chapter 7.
1.7.7. Non-directional synthetic inertial scheme for the hybrid islanded
microgrid
Renewable energy is a blessing for society. The harnessing of renewable energy should
always be given the highest priority. Due to the interfacing converters involved in the process,
the overall inertia of the hybrid microgrid is highly sacrificed. The impact of the system inertia
on the stability of the hybrid microgrid is huge. The severity of the issue is raised further while
the hybrid microgrid operates in the islanded mode. In the grid following mode of operation,
the wide grid network compensates the lack of inertia in the microgrid. To improve the stability,
improvement in the inertial response of the system is essential. The perspective of the virtual
inertia through a fuzzy tuned control loop has been explored in Chapter 8.
1.7.8. Direction sensitive synthetic inertial scheme for the hybrid microgrid
Frequency regulation is an important part of the stability assessment in the hybrid
microgrid. A transient event in the network perturbs the frequency and initiate the frequency
oscillation. An oscillation has fundamentally two parts which are the deflection and the

P. Bhowmik
14
restoration. Taking an example of the single-cycle oscillation, it can be stated that the total
period of oscillation is the sum of the deflection period and the restraining period. A high value
of inertia often suppresses the deflection time which results in the shorten oscillation period.
However, a high value of the inertia prolongs the natural restraining time of the system which
eventually stretches the oscillation period. The suppression in the frequency deflection time is
always more than the prolongation in the restraining time. Therefore, apparently, it is true that
a high value of inertia always shortens the oscillation period. If an optimal virtual inertia
emulation scheme can be developed where the high value of inertia will be enforced during the
frequency deflection period and the low-value inertia will be enforced during the frequency
restraining period, the total oscillation period can be suppressed dramatically. Therefore, the
scope and the perspective of the vector measurement-based direction sensitive virtual inertia
emulation scheme has been explored in Chapter 9.
1.7.9. Electric vehicle as a potential distributed load in hybrid microgrid
There is a huge growth is observed in the field of electric vehicle in the last decade.
Many automobile companies are gradually shifting their focus to the electric vehicle. Even a
decade ago, at the initial stage of the electric vehicle, the lead-acid battery was the choice. The
distance covered in a single charge was not satisfactory at that stage and customer had a fear to
prefer the electric vehicle as an alternative for a long-distance journey. But, the present scenario
is completely different. Advance lithium-ion cells are preferred these days in the electric vehicle
which ensures a long distance on a single charge. However, there is inequality observed in the
market share while compared to the combustion engine based utility vehicle. The real-life
performance is one major factor which is probably suppressing the growth rate of the electric
vehicle in comparison to the fossil fuel-driven vehicle. A small development in the acceleration
profile, cruise control ability, and aerodynamics can have a good impact and a large percentage
of the potential buyers may show their interest in an electric vehicle. The precision in the
regulation of the electromagnetic torque in the drivetrain is reflected in the acceleration profile
and the dynamics of the vehicle. However, due to the presence of nonlinearities, computation
of the optimal amount of drive-train torque in the real-time is a crucial issue and the
conventional deterministic approaches do not perform excellently in this case. Therefore, the
perspective of the dual-layer cascaded torque control mechanism for the electric vehicle has
been explored in Chapter 10.
1.7.10. Single phase virtual inertia emulation technique for hybrid microgrid
through the plug-in electric vehicle
The short term frequency stability limit is one of the major concern which can disrupt
the bidirectional protection schemes in the distribution level significantly. However, certain
kind of vehicle-to-grid services can massively improve the transient stability limit and
neutralize the potential threat from the high penetration rate of the PEVs in the distribution
network. With the adaptation of the bidirectional converter topologies, many ancillary
elementary services like reactive power compensation, voltage regulation and demand shifting
can be ensured. Beyond the elementary services, through the precise regulation of the active
power compensation, PEVs can be deployed for the emulation of the virtual inertia to improve

Introduction
15
the transient stability limit in the hybrid microgrid. Inertia emulation schemes are typically
designed for the three-phase topology, while the domestic charging arrangement in EVs is for
the single phase. Therefore, these three-phase based schemes have limitations in ancillary V2G
services. Due to the mismatch of the instantaneous power, the hybrid microgrid may undergo
the frequency oscillations in such circumstances. To ride through the tendency of the frequency
excursion in the single-phase topology, the perspective of the virtual two phase space vector
based inertia emulation topology has been explored in Chapter 11.

ENERGY STORAGE
DEVICES IN MICROGRID
Chapter 2
Topologies and Controls for Optimal Energy Bifurcation in an AC, DC and Hybrid
Microgrid
Pritam Bhowmik

Chapter 2
Energy storage devices in microgrids
2.1. Introduction
There is a synergistic relationship between nature and activities of mankind. Therefore,
human activities which have a negative impact on the environment are being globally
considered as a major issue. Appreciating Kyoto protocol [61], many countries have agreed to
reduce the greenhouse gas emission in every potential area. In the area of the power system, it
can be reduced by diminishing loss factors associated to generation, transmission, distribution
and consumption of energy. On the other hand, the overall efficiency can be increased to a
greater extend by adopting the concept of distributed generation system. Thus, resulting in
minimized loss factor and environmental effects [62]-[63]. An effort to offer clean energy to
the society is observed from the last few years. It is reflected as a high rate of penetration of
renewable power in the established electrical network. The interfacing power electronic
converter synchronizes diverse renewable power generators but fails to integrate the inertia of
any rotating mass, if available. As a consequence, even with rapidly growing wind farms in
conjunction with solar farms, system inertia remains an ever decaying function. However,
system inertia buffers many frequency events in a power network by firmly coupling the
potential electrical energy with the kinetic energy. Large system inertia also helps minimizing
cascaded blackout events by preventing the malfunction of protection relays.
Reported research articles in this domain have revealed many prospective
interpretations about this continually decaying inertia. Since stored kinetic energy in the
spinning mass naturally supplies the inertia to a system, partially loaded distributed scaled-
down synchronous generators (SGs) can cumulatively build up system inertia even in the
renewable power dominated environment [64]. However, the simplest solution reported will
invariably enlist higher plant installation cost. Therefore, as a substitute, utilization of energy
storage devices are promoted for the improvement of dynamic stability in microgrids. In this
chapter the detailed mathematical modeling and the state space analysis of multiple energy
storage devices have been developed.
2.2. Modelling of energy storage devices
This section highlights the mathematical modelling portion of the energy dense and
power dense energy storage system which have been later considered in the topological study
of the microgrid.

Energy Storage Devices in Microgrids
17
2.2.1. Battery Energy Storage
The lead acid battery was first introduced in 1859 by Gaston Plante. The lead-acid
battery is potentially capable to handle large power for the longer period of time due to its low
internal resistance. So, a lead-acid battery is considered as a primary source in the designed dc
microgrid system. The mathematical modelling of the storage device is detailed in this section.
An integrated dc-dc converter with a lead-acid battery can be schematically represented as
shown in Fig. 2.1.
The average mathematical modelling of the dc-dc converter can be equated and presented as:
‫ܮ‬௖௢௡
௕௘௦ ௗ௜
್೐ೞ
ௗ௧
+ ܴ௖௢௡
௕௘௦
݅
௕௘௦ = ܸ௕௘௦ − ݉ ௕௘௦ܸ௕௨௦ (2.1)
In article [65] a state space modelling of the lead acid battery is derived. Integrating the derived
state space model from [65] with the equation 2.1, RC model can be represented as:
‫ݔ‬ᇱ
௕௘௦ = ‫ܣ‬௕௘௦‫ݔ‬௕௘௦ + ‫ܤ‬௕௘௦݉ ௕௘௦ (2.2)
‫ݕ‬௕௘௦ = ‫ܥ‬௕௘௦‫ݔ‬௕௘௦ (2.3)
where
‫ݔ‬௕௘௦ = ൣ
ܸ௦௨௕ ܸ
௙௔௖௜
௔௟ ܸ௕௘௦ ݅
௕௘௦൧
்
(2.4)
‫ݕ‬௕௘௦ = [‫ܥ‬௕௘௦ ‫ݔ‬௕௘௦]்
(2.5)
‫ܣ‬௕௘௦ =
⎣
⎢
⎢
⎢
⎡
ܽଵଵ ܽଵଶ 0 ܾଵଵ
ܽଶଵ ܽଶଶ 0 ܾଶଵ
ܽଷଵ 0 ܽଷଷ ܾଷଵ
0 0
ଵ
௅೎೚೙
್೐ೞ
ିோ೎೚೙
್೐ೞ
௅೎೚೙
್೐ೞ ⎦
⎥
⎥
⎥
⎤
(2.6)
‫ܤ‬௕௘௦ = ቂ
0 0 0
ି௏್ೠೞ
௅೎೚೙
್೐ೞ ቃ
்
(2.7)
int
R
sub
V
sub
C
bound
R
facial
R
facial
V
facial
C
bes
i
bes
V bus
besV
m
bes
con
L bes
con
R
Fig. 2.1. Conceptualized schematic representation of the lead-acid battery

P. Bhowmik
18
‫ܥ‬௕௘௦ = ൦
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
൪ (2.8)
where
ܽଵଵ =
ିଵ
஼ೞೠ್(ோ೔
೙೟ାோ೑ೌ೎೔
ೌ೗
)
ܽଵଶ =
ଵ
஼ೞೠ್(ோ೔
೙೟ାோ೑ೌ೎೔
ೌ೗
)
ܽଶଵ =
ଵ
஼೑ೌ೎೔
ೌ೗
(ோ೔
೙೟ାோ೑ೌ೎೔
ೌ೗
)
;
ܽଶଶ =
ିଵ
஼೑ೌ೎೔
ೌ೗
(ோ೔
೙೟ାோ೑ೌ೎೔
ೌ೗
)
ܽଷଵ =
ோ೔
೙೟ାோ೑ೌ೎೔
ೌ೗
஼೑ೌ೎೔
ೌ೗
(ோ೔
೙೟ାோ೑ೌ೎೎೔
ೌ೗
)మ
−
ோ೔
೙೟ோ೑ೌ೎೔
ೌ೗
ାோమ
೑ೌ೎೔
ೌ೗
஼೑ೌ೎೔
ೌ೗
(ோ೔
೙೟ାோ೑ೌ೎೔
ೌ೗
)మ
;
ܽଷଷ =
ோ೑ೌ೎೔
ೌ೗
ோ೔
೙೟஼ೞೠ್(ோ೔
೙೟ାோ೑ೌ೎೔
ೌ೗
)
−
ଵ
஼೑ೌ೎೔
ೌ೗
(ோ೔
೙೟ାோ೑ೌ೎೔
ೌ೗
)
ܾଵଵ =
ିோ೑ೌ೎೔
ೌ೗
஼ೞೠ್(ோ೔
೙೟ାோ೑ೌ೎೔
ೌ೗
)
ܾଶଵ =
ିோ೔
೙೟
஼೑ೌ೎೔
ೌ೗
(ோ೔
೙೟ାோ೑ೌ೎೔
ೌ೗
)
ܾଷଵ =
ோ್೚ೠ೙೏ோ೑ೌ೎೔
ೌ೗
ோ೔
೙೟஼ೞೠ್(ோ೔
೙೟ାோ೑ೌ೎೔
ೌ೗
)
−
ோ್೚ೠ೙೏
஼೑ೌ೎೔
ೌ೗
൫
ோ೔
೙೟ାோ೑ೌ೎೔
ೌ೗
൯
−
ோ೔
೙೟ோ೑ೌ೎೔
ೌ೗
ାோ೔
೙೟
మ
஼೑ೌ೎೔
ೌ೗൫
ோ೔
೙೟ାோ೑ೌ೎೔
ೌ೗
൯
మ;
where ‫ܥ‬௦௨௕ signifies the stored charge in the battery, ‫ܥ‬௙௔௖௜
௔௟specifies the diffusion effect, ܴ௜
௡௧
represents the internal resistance of the cell, ܴ௙௔௖௜
௔௟symbolises the facial or surface resistance,
and ܴ௕௢௨௡ௗ signifies the boundary resistance. As in Fig. 2.1, RC battery model is demonstrated
by the two storage element ‫ܥ‬௦௨௕ and ‫ܥ‬௙௔௖௜
௔௟
. For that reason, state space model of the system
can be expressed only by the ܸ௦௨௕ and ܸ
௙௔௖௜
௔௟
.
2.2.2. Compressed Air Energy Storage
Since the first commissioning, many researchers have taken keen effort to analyse its
thermodynamics [66]-[68]. Through compressing the air, a large amount of electrical energy
can be transformed to the form of pressure. As a result, a large amount of energy can be stored
in a small volume. In order to maintain the system specific energy high the CAES is considered
as one of the prime element in this study.
The only variation in the thermodynamic cycle of a CAES system compared to the
conventional is on the basis of automated pressure control system. The working cycle is
illustrated in Fig. 2.2. In this study, it has been assumed that the automated pressure control
system maintains the entropy of the system constant. It signifies that the compression and
expansion process follow the characteristics of an isothermal process. Therefore, the volume of
fluid which passes per unit time during the compression process can be expressed as [69]:

19
machine-driven
power source
)
(t
Pin
compressor
)
(
'
t
Q in
)
(
'
t
Q out
gas turbine set
storage tank
)
(t
Pout
ac grid
Fig. 2.2. Operational layout of compressed air energy storage system
ܳ௖௛௔௥௚௘
ᇱ
=
௉೎೓ೌೝ೒೐
஼೛೎೓ೌೝ೒೐
்೎೓ೌೝ೒೐቎
ቆ
ುೝ೏೔
ೞ೎೓ೌೝ೒೐
ುೝ೎೓ೌೝ೒೐
ቇ
ംషభ
ം
ିଵ቏
(2.9)
where the poison constant ߛrepresenting the isothermal index is presented as follows:
ߛ =
஼೛೎೓ೌೝ೒೐
஼ೡ೏೔
(2.10)
where the suffix ܿℎܽ‫݁݃ݎ‬ and ݀݅
‫ܿݏ‬ℎܽ‫݁݃ݎ‬ in the equations represent the individual process of
compression and expansion of fluid respectively. The terms ܲ, ܲ
௥ and ܶ signify the power,
pressure and temperature of the compressor. The term ‫ܥ‬௣ and ‫ܥ‬௩ represent specific heat.
Similarly, the volume of fluid which passes per unit time is stated as [70]:
ܳௗ௜
௦௖௛௔௥௚௘
ᇱ
=
൬
௉೏೔
ఎ
ൗ ൰
ఎ೘ ఎ೒஼೛೏೔
்ಽುቆଵା
ೂ೏೔
ೂ೑ೠ೐೗
ቇቌ
಴೛೏೔
೅ಹ ು
಴೛೏೔
೅ಽು
቎
ଵି൬
ುೝಹ ು
ುೝಽು
൰
ೖభషభ
ೖభ
቏
ାଵି൬
ುೝೌ೟೘
ುೝಹ ು
൰
ೖభషభ
ೖభ
ቍ
(2.11)
where the suffix ‫ܲܮ‬ and ‫ܲܪ‬ indicate the low pressure and high pressure respectively at the inlet
of a turbine. The term ܳ and ܳᇱ
represent the mass and the rate of discharge respectively. The
system efficiency at different stages (i.e. overall, mechanical and electrical) are presented using
the notations ߟ, ߟ௠ and ߟ௚.
The mass and pressure inside the reservoir of a CAES system can be derived as [71]:

P. Bhowmik
20
ܳ = ∫ ܳ௖௛௔௥௚௘݀‫ݐ‬
௧
ଶ
௧
ଵ
− ∫ ܳௗ௜
௦௖௛௔௥௚௘݀‫ݐ‬
௧
ସ
௧
ଷ
(2.12)
ܲ‫ݎ‬=
ோ
௏
ቀ∫ ܳ௖௛௔௥௚௘ܶ௜
௡௧݀‫ݐ‬
௧
ଶ
௧
ଵ
− ∫ ܳௗ௜
௦௖௛௔௥௚௘ܶ
௙௜
௡݀‫ݐ‬
௧
ସ
௧
ଷ
ቁ (2.13)
The suffix ݅
݊‫ݐ‬and ݂݅
݊ signifies the initial and final value respectively. ܴ signifies Boltzmann
constant. ܸ represents the capacity of the reservoir.
The derived system equation are used to design the state variables of the CAES system
as follows:
ቈ
ܳ௖௛௔௥௚௘(‫ݐ‬
)
ܳௗ௜
௦௖௛௔௥௚௘(‫ݐ‬
)
቉= ቂ
1 0
0 1
ቃቈ
ܳ௖௛௔௥௚௘(‫ݐ‬− 1)
ܳௗ௜
௦௖௛௔௥௚௘(‫ݐ‬− 1)
቉+
቎
1
‫ܭ‬௖௛௔௥௚௘
ൗ 0
0 1
‫ܭ‬ௗ௜
௦௖௛௔௥௚௘
ൗ
቏ቈ
ܲ௖௛௔௥௚௘(‫ݐ‬− 1)
ܲௗ௜
௦௖௛௔௥௚௘(‫ݐ‬− 1)
቉ (2.14)
൤
ܳ(‫ݐ‬
)
ܲ‫ݐ(ݎ‬
)
൨= ൤
1 −1
൫
ܴ
ܸ
ൗ ∗ ܶ௜
௡௧൯ −൫
ܴ
ܸ
ൗ ∗ ܶ
௙௜
௡൯
൨ቈ
ܳ௖௛௔௥௚௘(‫ݐ‬− 1)
ܳௗ௜
௦௖௛௔௥௚௘(‫ݐ‬− 1)
቉ (2.15)
where ‫ܭ‬ signifies the equation denominators.
Thus the complete thermodynamic cycle of the operating CAES is expressed using the system
constraints (i.e. mass and pressure). From the variables ܳ(‫ݐ‬
) and ܲ‫ݐ(ݎ‬
), the regulating
parameters can be enabled. These controllable parameters can be regulated through any linear
or nonlinear controller.
2.2.3. Flywheel Energy Storage
The concept of the fast responding mechanical storage is simulated by incorporating a
large inertia as a rotating element [72]. The angular velocity of the added inertia is regulated
through a permanent magnet machine. The principal operational layout of the undertaken
flywheel is shown in Fig. 2.3.
The instantaneous current equations in the ݀ − ‫ݍ‬ frame, where the ݀ − ܽ‫݅ݔ‬
‫ݏ‬leads the
‫ݍ‬− ܽ‫݅ݔ‬
‫ݏ‬by 90° are represented as:
fes
I
rc
V
Fig. 2.3. Structural layout of the flywheel storage system

21
ଵ
ఠ ್
‫ܮ‬ௗ
ௗ௜
೏
ௗ௧
= ‫ݒ‬ௗ − ‫ݎ‬
௦݅
ௗ + ߱௥‫ܮ‬௤݅
௤ (2.16)
ଵ
ఠ ್
‫ܮ‬௤
ௗ௜
೜
ௗ௧
= ‫ݒ‬௤ − ‫ݎ‬
௦݅
௤ − ߱௥൫
‫ܮ‬ௗ݅
ௗ + ߮௙൯ (2.17)
2‫ܪ‬
ௗఠ ೝ
ௗ௧
= ܶ௠ − ܶ௘ (2.18)
where
‫ܪ‬ =
ଵ
ଶ
‫ܬ‬
௙௘௦߱଴
ଶ
(2.19)
ܶ௘ = ߮௙݅
௤ (2.20)
where r, L and J represents resistance, inductance and system inertia respectively. ߮௙ and ߱௕
signify the field flux and angular velocity respectively. The torque of the rotating body in terms
of mechanical and electrical is symbolized using ܶ௠ and ܶ௘ respectively.
In order to derive the ܲ
௙௘௦ with respect to ߱௥ and ܶ௘, it can be written as:
݅
௙௘௦ =
ఠ ೝ்೐
௩ೝ೎
− ܴ‫ܥ‬
ௗ௩ೝ೎
ௗ௧
(2.21)
ܲ
௙௘௦ = ‫ݒ‬௥௖݅
௙௘௦ (2.22)
During the designing process the friction due to the mechanical rotation has been assumed to
be zero. Subsequently the mechanical torque on the rotor shaft tends to be zero. Further, ‫ݎ‬
௦ of
the designed system is assumed to be negligible [73].
It should be noted that the considered large inertia in the system makes the deceleration of the
angular velocity insignificant. Therefore, the designed system maintains the angular momentum
tends to constant i.e. ቂ
௅೏
ఠ ್
≪ {ܴ‫ܥ‬, 2‫ܪ‬}ቃand ቂ
௅೜
ఠ ್
≪ {ܴ‫ܥ‬, 2‫ܪ‬}ቃ
. On equating to zero, the equations
(2.16) and (2.17) can be expressed as:
‫ݒ‬ௗ − ‫ݎ‬
௦݅
ௗ + ߱௥‫ܮ‬௤݅
௤ = 0 (2.23)
‫ݒ‬௤ − ‫ݎ‬
௦݅
௤ − ߱௥൫
‫ܮ‬ௗ݅
ௗ + ߮௙൯= 0 (2.24)
Considering ‫ݎ‬
௦ = 0 and ݅
ௗ = 0, equation (2.23) and (2.24) can be expressed as:
‫ݒ‬ௗ = −߱௥‫ܮ‬௤݅
௤ (2.25)
‫ݒ‬௤ = −߱௥߮௙ (2.26)
The above stated equation signifies that the term ‫ݒ‬௤ is a dependent factor of ߱௥. Thus the
generated power from the mismatch of angular velocity can be stated as:
ܲ
௙௘௦ = ߱௥ܶ௘ = ߱௥߮௙݅
௤ = ‫ݒ‬௤݅
௤ (2.27)

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