Essay: VARIABLE STRUCTURE CONTROL OF A WIND / PHOTOVOLTAIC HYBRID GENERATION SYSTEM

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Control Engineering

Prepared by
Hxxxx Fxxxx Mxxxxx


Summary
The need for power generation from renewable sources is rapidly increasing worldwide because they are more environment-friendly and because fossil fuels reserves are decreasing over time. The potential for renewable energy resources is enormous because they can, in principle, exceed the world’s energy demand in addition to reducing greenhouse gases emission. Therefore, these types of resources will have a significant share in the future global energy share. Accordingly, this research presents how renewable energy resources are currently being used; focusing on maximum power extraction from solar and wind energy conversion systems. Complete grid-connected systems are simulated for dispatching generated power to the utility grid. This clearly shows the impact of power electronics and robust control technologies to enable the share of renewable energy resources.
The proposed controlled renewable energy system includes DC-DC power converters, DC link capacitance, voltage source inverter, and grid filter. Variable structure control with sliding mode is used on the power converter for maximum power tracking. For DC-link, voltage control is energy based. For the inverter, space vector pulse width modulation with current control in dq rotating frame is implemented. Simulation results prove the robustness of the controllers. Furthermore, practical experiments on a real solar module are performed including measuring, power, and interface circuits. Several experiments are done to ensure the validity of the control scheme. The results prove the potency of the variable structure controller.
This thesis demonstrates facts about renewable sources energy global share, historical background showing previous work related to this work, thesis objectives, and thesis layout. Next, a proposed solar energy conversion system is described. This discusses photovoltaic cells and their modeling, DC-DC converter, voltage source inverter, and grid-tie filter. Then, the detailed control and simulation of the photovoltaic system is described. Variable structure control and sliding mode are explained, Control methods of system components are proposed, the system is simulated and simulation results are shown and findings are explained. In the same manner, a complete wind turbine energy conversion system is described, modeled, and simulated showing results indicating the robustness of the proposed control. Following that, a more complex system is simulated. The system is a grid-connected hybrid wind/solar generation system. Simulation results are shown and superiority of control is ensured. For more confidence, practical experimentation is introduced; Showing practical setup and control of experimental system with real photovoltaic panel and power circuit plus interfacing the system to a personal computer. Experimental results are shown. The proposed design is subjected to various experimental tests to ensure its validity. The thesis is then concluded in addition to recommendations for future work.

Abstract

‘VARIABLE STRUCTURE CONTROL OF A WIND / PHOTOVOLTAIC HYBRID GENERATION SYSTEM’
The contribution of renewable energy sources in power generation globally increases rapidly over time. Research concerning maximum power extraction of these sources attracts scholars worldwide. This thesis presents digital control of grid-connected wind and solar generation systems. The technique used for maximum power point tracking of wind and photovoltaic power is variable structure control with sliding mode. Complete theoretical foundation needed for system simulation is presented. Simulation is performed and results proved robustness of the control. Practical experiments on a photovoltaic system are executed and simulation results are verified.

Key Words: Variable structure control, Sliding mode control, DC-DC power converters, Wind power generation, solar energy, Computer simulation, Digital control, Space vector pulse width modulation.
Acknowledgement

TABLE OF CONTENTS
Summary IV
Abstract VI
Acknowledgement VII
Chapter 1 – Introduction 1
1.1. Review Of Previous Literature 5
1.2. Thesis Objectives 7
1.3. Thesis Outline 8
Chapter 2 – Photovoltaic Generation System And Grid Connection 11
2.1. Introduction 11
2.2. PV System Components 13
2.2.1. Photovoltaic Array Model 13
2.2.2. DC-DC Power Converter 18
2.2.3. Voltage Source Inverter 22
2.2.4. LC Filter For Grid Connection 24
2.3. Conclusion 24
Chapter 3 – Photovoltaic Generation System Control And Simulation 27
3.1. Introduction 27
3.2. System Control 28
3.2.1. Photovoltaic Array Maximum Power Point Tracking 28
3.2.2. Variable Structure Control With Sliding Mode 29
3.2.2.1. Sliding Mode Controller Design For The DC-DC Converter 35
3.2.3. Energy Based DC Link Voltage Control 38
3.2.4. Current Control Of Voltage Source Inverter 39
3.2.5. Space Vector Pulse Width Modulation 43
3.2.5.1. Computation Of Reference Voltage And Angle 46
3.2.5.2. Determination Of Sector Number 46
3.2.5.3. Determination Of Switching Time Intervals 46
3.2.5.4. Generating Transistors Switching Signals 48
3.3. Simulation Of Pv Generation System 50
3.3.1. Simulation Parameters 50
3.3.2. Simulation Results 51
3.4. Conclusion 64
Chapter 4 – Grid-Tied Wind Turbine Energy Conversion System 65
4.1. Introduction 65
4.2. Wind Turbines 66
4.3. DC Machine 72
4.3.1. Advantages Of DC Generator 75
4.4. Single Mass Model Of Turbine Plus Generator 75
4.5. Wind Generation System 76
4.6. Simulation Of Grid-Tied Wind Energy Conversion System 76
4.6.1. Simulation Parameters 77
4.6.2. Simulation Results 78
4.7. Comparison With Perturb And Observe MPPT Algorithm 85
4.8. Conclusion 96
Chapter 5 – Hybrid Wind / Photovoltaic Generation System With Variable Structure Control 97
5.1. Introduction 97
5.2. Hybrid Wind / Pv Generation System 100
5.3. Simulation Of The Hybrid Grid-Connected Generation System 103
5.4. Conclusion 111
Chapter 6 – Experimental Setup And Results Of Solar Energy Conversion System 113
6.1. Introduction 113
6.2. Interfacing Module 114
6.3. Measuring Module Of Solar Panel 115
6.3.1. Solar Panel Voltage Measuring 116
6.3.2. Solar Panel Current Measuring 116
6.4. DC-DC Converter 117
6.5. Software And Programming 118
6.6. Experimental Results Of Solar Energy Conversion Unit 120
6.7. Conclusion 133
Chapter 7 – Conclusions 135
7.1. Discussion And Conclusions 135
7.2. Suggestions For Future Work 137
References 139
Appendix I 147
Published Paper 153


TABLE OF FIGURES

Fig. ‘1.1: World electricity production from all energy sources in 2014 (TW.h) 2
Fig. ‘1.2: Solar PV global capacity, 2005-2015 3
Fig. ‘1.3: Wind power global capacity, 2005-2015 4
Fig. ‘1.4: Estimated Renewable energy share of global electricity production, End-2015 5
Fig. ‘2.1: Block diagram of the photovoltaic generation system 13
Fig. ‘2.2: Photovoltaic cell, module and array 14
Fig. ‘2.3: PV array power curve 14
Fig. ‘2.4: Circuit diagram of the PV module model 15
Fig. ‘2.5: Circuit diagram of the PV module model 17
Fig. ‘2.6: PLECS implementation of PV module 17
Fig. ‘2.7: PLECS circuit diagram of DC-DC converter 18
Fig. ‘2.8: Basic principle of the buck’boost converter. 19
Fig. ‘2.9: PLECS circuit diagram of VSI 23
Fig. ‘2.10: example of inverter output: (a) phase to neutral voltage. (b) phase to phase voltage. 23
Fig. ‘2.11: PLECS circuit diagram of LC filter 25
Fig. ‘2.12: Complete PV power circuit 25
Fig. ‘3.1: Block diagram of the photovoltaic generation system. 27
Fig. ‘3.2: System model of a simple VSC example 30
Fig. ‘3.3: Regions defined by the switching logic 31
Fig. ‘3.4: Phase portraits: (a) Unstable system I. (b) Unstable system II. 32
Fig. ‘3.5: Phase portrait of the composed system. 33
Fig. ‘3.6: System modes during SMC. 34
Fig. ‘3.7: System model of PV sliding mode control 36
Fig. ‘3.8: PLECS subsystem block for estimation of function u 37
Fig. ‘3.9: DC-link voltage controller 39
Fig. ‘3.10: PLECS subsystem block of a PLL system 41
Fig. ‘3.11: Grid current control including cross-coupling terms 43
Fig. ‘3.12: Eight Switching Configuration of a Three-Phase Inverter 44
Fig. ‘3.13: Voltage Space Vectors in SVPWM 45
Fig. ‘3.14: PLECS subsystem block for sector identification 47
Fig. ‘3.15: Switching intervals Ta, Tb, Tc 48
Fig. ‘3.16: Triangular wave parameters 49
Fig. ‘3.17: Transistors switching signals generation 50
Fig. ‘3.18: Simulation Result of the PV Generation System: (a) Irradiation step input. (b) Current output at phase a. (c) PV Power. 52
Fig. ‘3.19: Simulation Result of the PV Generation System: (a) Irradiation step input. (b) Current output at phase a. (c) PV Power. 53
Fig. ‘3.20: Simulation Result of the PV Generation System: (a) Irradiation step input. (b) Current output at phase a. (c) PV Power. 54
Fig. ‘3.21: Simulation Result of the PV Generation System: (a) Irradiation step input. (b) Current output at phase a. (c) PV Power. 55
Fig. ‘3.22: Simulation Result of the PV Generation System: (a) Irradiation step input. (b) Current output at phase a. (c) PV Power. 56
Fig. ‘3.23: Simulation Result of the PV Generation System: (a) Irradiation ramp input. (b) Current output at phase a. (c) PV Power. 57
Fig. ‘3.24: Simulation Result of the PV Generation System: (a) Irradiation triangle input. (b) Current output at phase a. (c) PV Power. 58
Fig. ‘3.25: Simulation Result of the PV Generation System: (a) Irradiation input varying between 1 and 0. (b) Current output at phase a. (c) PV Power. 59
Fig. ‘3.26: Simulation Result of the PV Generation System: (a) Irradiation input varying between 5 levels. (b) Current output at phase a. (c) PV Power. 60
Fig. ‘3.27: Simulation Result of controlled and uncontrolled systems: (a) Irradiation input. (b) PV voltage. (c) PV current. (c) PV power. SM in black, Uncontrolled in gray. 61
Fig. ‘3.28: Simulation Result of controlled and uncontrolled systems: (a) Irradiation input. (b) PV voltage. (c) PV current. (c) PV power. SM in black, Uncontrolled in gray. 62
Fig. ‘3.29: Simulation Result of controlled and uncontrolled systems: (a) Irradiation input. (b) PV voltage. (c) PV current. (c) PV power. SM in black, Uncontrolled in gray. 63
Fig. ‘4.1: Block diagram of the wind generation system. 66
Fig. ‘4.2: An air parcel moving towards a wind turbine 67
Fig. ‘4.3: Power coefficient as a function of TSR and pitch angle 69
Fig. ‘4.4: Turbine mechanical power as a function of rotor speed for various wind speeds. 70
Fig. ‘4.5: Wind turbine power output with wind speed 71
Fig. ‘4.6: Wind turbine model 71
Fig. ‘4.7: DC Machine equivalent circuit 72
Fig. ‘4.8: System of DCM model 74
Fig. ‘4.9: Wind turbine Power circuit 76
Fig. ‘4.10: DC machine block parameters 78
Fig. ‘4.11: Simulation Result of the Wind Generation System: (a) Wind speed step input. (b) Generator rotor speed. (c) Current output at phase a. (d) DCM Power. 79
Fig. ‘4.12: Simulation Result of the Wind Generation System: (a) Wind speed step input. (b) Generator rotor speed. (c) Current output at phase a. (d) DCM Power. 80
Fig. ‘4.13: Simulation Result of the Wind Generation System: (a) Wind speed step input. (b) Generator rotor speed. (c) Current output at phase a. (d) DCM Power. 81
Fig. ‘4.14: Simulation Result of the Wind Generation System: (a) Wind speed input varying between 10 and 5. (b) Generator rotor speed. (c) Current output at phase a. (d) DCM Power. 82
Fig. ‘4.15: Simulation Result of the Wind Generation System: (a) Wind speed input varying between 10 and 5. (b) Generator rotor speed. (c) Current output at phase a. (d) DCM Power. 83
Fig. ‘4.16: Simulation Result of the Wind Generation System: (a) Wind speed input varying between 10 and 5. (b) Generator rotor speed. (c) Current output at phase a. (d) DCM Power. 84
Fig. ‘4.17: Flow chart of the Perturb and Observe algorithm. 86
Fig. ‘4.18: PLECS simulation of the Perturb and Observe algorithm . 86
Fig. ‘4.19: Simulation Result of Wind Generation System with P&O controller: (a) Wind speed input. (b) Generator rotor speed. (c) DCM Power. 87
Fig. ‘4.20: Simulation Result of the Wind Generation System: (a) Wind speed input. (b) Generator rotor speed. (c) DCM Power. SM in black, P&O in gray 88
Fig. ‘4.21: Simulation Result of the Wind Generation System: (a) Wind speed input. (b) Generator rotor speed. (c) DCM Power. SM in black, P&O in gray. 89
Fig. ‘4.22: Simulation Result of the Wind Generation System: (a) Wind speed input. (b) Generator rotor speed. (c) DCM Power. SM in black, P&O in gray. 90
Fig. ‘4.23: Simulation Result of the Wind Generation System: (a) Wind speed input. (b) Generator rotor speed. (c) DCM Power. SM in black, P&O in gray. 91
Fig. ‘4.24: Simulation Result of the Wind Generation System: (a) Wind speed input. (b) Generator rotor speed. (c) DCM Power. SM in black, P&O in gray. 92
Fig. ‘4.25: Simulation Result of the Wind Generation System: (a) Wind speed input. (b) Generator rotor speed. (c) DCM Power. SM in black, P&O in gray. 93
Fig. ‘4.26: Simulation Result of the Wind Generation System: (a) Wind speed input. (b) Generator rotor speed. (c) DCM Power. SM in black, P&O in gray. 94
Fig. ‘4.27: Simulation Result of the Wind Generation System: (a) Wind speed input. (b) Generator rotor speed. (c) DCM Power. SM in black, P&O in gray. 95
Fig. ‘5.1: Possible system configuration in designing the WTG/PV hybrid system: (a) The stand-alone system. (b) The grid-supported stand-alone system configuration. (c) The grid’tie hybrid system configuration. (d) The combined stand-alone and grid’tie configuration. (e) The combined UPS and grid’tie configuration 99
Fig. ‘5.2: Block diagram of the proposed Hybrid generation system. 101
Fig. ‘5.3: Hybrid Wind/Solar generation system circuit 102
Fig. ‘5.4: Simulation Result of the Hybrid Generation System: (a) Irradiation input. (b) Wind speed input. (c) Current output at phase a. (d) Power output to grid. 104
Fig. ‘5.5: Simulation Result of the Hybrid Generation System: (a) Irradiation input. (b) Wind speed input. (c) Current output at phase a. (d) Power output to grid. 105
Fig. ‘5.6: Simulation Result of the Hybrid Generation System: (a) Irradiation input. (b) Wind speed input. (c) Current output at phase a. (d) Power output to grid. 106
Fig. ‘5.7: Simulation Result of the Hybrid Generation System: (a) Irradiation input. (b) Wind speed input. (c) Current output at phase a. (d) Power output to grid. 107
Fig. ‘5.8: Simulation Result of the Hybrid Generation System: (a) Irradiation input. (b) Wind speed input. (c) Current output at phase a. (d) Power output to grid. 108
Fig. ‘5.9: Simulation Result of the Hybrid Generation System: (a) Irradiation input. (b) Wind speed input. (c) Current output at phase a. (d) Power output to grid. 109
Fig. ‘5.10: Simulation Result of the Hybrid Generation System: (a) Irradiation input. (b) Wind speed input. (c) Current output at phase a. (d) Power output to grid. 110
Fig. ‘6.1: Block diagram of typical PV conversion system. 113
Fig. ‘6.2: Block diagram of the photovoltaic system experimental setup. 115
Fig. ‘6.3: Solar panel voltage measuring circuit. 116
Fig. ‘6.4: Solar panel current measuring circuit. 116
Fig. ‘6.5: Practical DC-DC converter. 117
Fig. ‘6.6: PV system circuit diagram. 117
Fig. ‘6.7: Photograph of experimental setup. 118
Fig. ‘6.8: LabVIEW While loop. 119
Fig. ‘6.9: Flow chart of MATLAB script. 121
Fig. ‘6.10: Experimental Result of the PV Generation System: (a) PV Panel voltage. (b) PV Panel Current. (c) PV Panel Power. (d) ”P/”V. (e) Control Output. 122
Fig. ‘6.11: Experimental Result of the PV Generation System: (a) PV Panel voltage. (b) PV Panel Current. (c) PV Panel Power. (d) ”P/”V. (e) Control Output. 123
Fig. ‘6.12: Experimental Result of the PV Generation System: (a) PV Panel voltage. (b) PV Panel Current. (c) PV Panel Power. (d) ”P/”V. (e) Control Output. 124
Fig. ‘6.13: Experimental Result of the PV Generation System: (a) PV Panel voltage. (b) PV Panel Current. (c) PV Panel Power. (d) ”P/”V. (e) Control Output. 125
Fig. ‘6.14: Experimental Result of the PV Generation System: (a) PV Panel voltage. (b) PV Panel Current. (c) PV Panel Power. (d) ”P/”V. (e) Control Output. 126
Fig. ‘6.15: Experimental Result of the PV Generation System: (a) PV Panel voltage. (b) PV Panel Current. (c) PV Panel Power. (d) ”P/”V. (e) Control Output. 127
Fig. ‘6.16: Experimental Result of the PV Generation System: (a) PV Panel voltage. (b) PV Panel Current. (c) PV Panel Power. (d) ”P/”V. (e) Control Output. 128
Fig. ‘6.17: Experimental Result of the PV Generation System: (a) PV Panel voltage. (b) PV Panel Current. (c) PV Panel Power. (d) ”P/”V. (e) Control Output. 129
Fig. ‘6.18: Experimental Result of the PV Generation System: (a) PV Panel voltage. (b) PV Panel Current. (c) PV Panel Power. (d) ”P/”V. (e) Control Output. 130
Fig. ‘6.19: Experimental Result of the PV Generation System: (a) PV Panel voltage. (b) PV Panel Current. (c) PV Panel Power. (d) ”P/”V. (e) Control Output. 131
Fig. ‘6.20: Experimental Result of the PV Generation System: (a) PV Panel voltage. (b) PV Panel Current. (c) PV Panel Power. (d) ”P/”V. (e) Control Output. 132

LIST OF TABLES

Table ‘3.1: Major characteristics of MPPT techniques 28
Table ‘3.2: Voltage Space Vectors and switching states 44
Table ‘3.3: Switching Pattern Lookup Table 49
Table ‘3.4: Function Blocks Expressions 49
Table ‘3.5: PV System Simulation Parameters 50
Table ‘4.1: Wind System Simulation Parameters 77
Table ‘6.1: Converter Components Values 118


LIST OF SYMBOLS

Symbol Description
Id Photovoltaic diode current
Isat PV array reverse saturation current
q Electron charge
A P-N junction ideality constant
K Boltzmann’s constant
T PV array temperature
Upv Applied voltage across the terminals of the diode
Ig Current generated by the incident light
Rs Series resistance of PV cell model
CDC DC-link capacitor value
X System power rating
Vm System peak voltage
Lf Inductance of the LC filter
Cf Capacitance of the LC filter
”c Filter damping factor
Rf Inductance branch resistance
R Output branch resistance
Ppv PV array output power

Upv PV array output Voltage
Ipv PV array output current
u Converter switch control signal
S Switching function
VDCref DC voltage required at inverter input
Vrms phase-to-neutral grid voltage rms value
CDC DC-link capacitor value
WDC Energy required from the DC-link capacitor
VDC Actual voltage of the DC-link capacitor
VDCref the reference value of the DC-link capacitor
P’DC The DC power required from the capacitor
Tc ripple period of the DC-link capacitor
Pref reference DC power

Kpe, Kie Proportional and integral gains DC-link voltage controller
” the rotating dq frame angle
Va,b,c Grid voltages
Vd, Vq d and q components of three phase voltages

Ia,b,c Grid Currents
Id, Iq d and q components of three phase currents
ed* PLL reference d component voltage
”ref Reference voltage vector
Uref Magnitude of vector ”ref
”ref Angle of vector ”ref
Udref, Uqref d and q reference voltage at inverter output
U”, U” Inverter Voltage mapped to the complex orthogonal (”) plane
m The modulation index
”m angle in the range (0 ‘ 60”) inside the sector
T1, T2, T0 The switching time intervals
Tsw Switching interval for one leg of inverter transistors
fsw Switching frequency
Ta, Tb, Tc ON intervals of the three phases
S1 to S6 Inverter transistors switching signals
P Mechanical output power of wind turbine
Cp Performance coefficient of wind turbine
” Air density
V Wind speed
” Tip speed ratio
” Blade pitch angle
Jg Generator rotational inertia
Jwt Turbine rotational inertia [kg.m2]
r Ripple factor


LIST OF ABBREVIATIONS

Abbreviation Full Name
CSP Concentrating Solar Power
PV Photovoltaic
PWM Pulse Width Modulation
SVPWM Space Vector Pulse Width Modulation
VSI Voltage Source Inverter
IGBT Insulated Gate Bipolar Transistor
PLL Phase Locked Loop
SM Sliding Mode
SMC Sliding Mode Control
VSC Variable Structure Control
MPPT Maximum Power Point Tracking
MPP Maximum Power Point
DCM DC Machine
P&O Perturb and Observe
WTG Wind Turbine Generator
PLECS” Piece-wise Linear Electrical Circuit Simulation

INTRODUCTION
The need for power generation from renewable energy sources is rapidly increasing worldwide because they are more environment-friendly and because fossil fuels reserves are decreasing over time. Today, global energy system is based on extracting highly concentrated forms of energy found existing in nature, such as fossil fuels, large rivers and waterfalls, burning trees and splitting uranium. The environmental impacts of energy supply are growing and already dominant contributors to local, regional, and global environmental problems (including air, water, and ocean pollutions and climate change). Unfortunately, existing energy system could become dysfunctional because highly concentrated forms of energy are both in short supply and play critical roles in the ecosystem.
The world consumes more than 22000 TW.h of electric energy per year and increasing. About 66% of this energy is produced by burning coal, gas, and oil. World electricity production from all energy sources is shown in Fig. ‘1.1. The high cost and limited sources of fossil fuels, in addition to the need to reduce greenhouse gases emission, have made renewable resources attractive in world energy based economies. Renewable energies are energy sources that are continually replenished by nature. Some of these energy types are derived directly from the sun (such as thermal, photo-chemical, and photo-electric). Other sources are indirectly derived from the sun (such as wind, hydropower, and photosynthetic energy stored in biomass), or from other natural movements and mechanisms of the environment (such as geothermal and tidal energy). Renewable energy does not include energy resources derived from fossil fuels, waste products from fossil sources, or waste products from inorganic sources [1, 2, 3].

Fig. ‘1.1: World electricity production from all energy sources in 2014 (TW.h)
The power emission from the sun is 1.37 kW/m2 on the surface of the earth continuously. The power hits the cross-section of earth facing the sun; a circular disc with an area of 1.27 x 1014 m2. The total power emitted to the earth is thus 1.74 x 1017 W. About 1-2 % of the energy coming from the sun is converted into wind energy [4].
Renewables contributed 23.7% to humans’ global generation of electricity in 2015. The solar PV market was up 25% over 2014 to a record of 50 GW, lifting the global total to 227 GW. The annual market in 2015 was nearly 10 times the world’s cumulative solar PV capacity of a decade earlier. China, Japan and the United States again accounted for the majority of capacity added, but emerging markets on all continents contributed significantly to global growth, driven largely by the increasing cost-competitiveness of solar photovoltaics. An estimated 22 countries had enough capacity at end-2015 to meet more than 1% of their electricity demand, with far higher shares in some countries (e.g., Italy 7.8%, Greece 6.5% and Germany 6.4%). Solar PV global capacity and annual additions is shown in Fig. ‘1.2.

Fig. ‘1.2: Solar PV global capacity, 2005-2015
Wind power was the leading source of new power generating capacity in Europe and the United States in 2015, and the second largest in China. Globally, a record 63 GW was added for a total of about 433 GW. Wind power is playing a major role in meeting electricity demand in an increasing number of countries, including Denmark (42% of demand in 2015), Germany (more than 60% in four states) and Uruguay (15.5%). Wind power global capacity and annual additions is shown in Fig. ‘1.3.
As shown in Fig. ‘1.4, the estimated renewable energy share of global electricity production end’2015 is 23.7% distributed as 16.6% Hydropower, 3.7% wind power, 2.0% bio-power, 1.2% solar power, and 0.4% geothermal, CSP (concentrating solar thermal power) and ocean power [5, 6].

Fig. ‘1.3: Wind power global capacity, 2005-2015
Wind and PV power plants are connected to the grid through grid converters which, besides capturing maximum available amount of power and transferring the generated DC power to the AC grid, should be able to exhibit advanced functions. These functions include dynamic control of active and reactive power, stationary operation within a range of voltage and frequency, reactive current injection during faults, participation in a grid balancing act like primary frequency control, etc.
Wind and solar energy are variable renewables, together with wave and tidal energy, are based on sources that fluctuate during the course of any given day or season. That’s why the research of the Maximum Power Point Tracking (MPPT) control methods has been paid extensive attention by many researchers.

Fig. ‘1.4: Estimated Renewable energy share of global electricity production, End-2015
REVIEW OF PREVIOUS LITERATURE
Zhang et al. [7] developed a maximum power point tracking system based on slide technology consisting of a Buck-type DC-DC converter, which is controlled by a micro-controller-based unit. The experimental work used a DC source and a resistance to simulate the solar array instead of a real photovoltaic panel. This work showed the method is feasible.
Guldemir [8] worked on the modeling of a sliding mode controlled DC-DC buck-boost converter fed by a battery and feeding a resistive load. Matlab/Simulink was used for the simulation with no practical experiments. No renewable source, inverter, or grid connection introduced.
Kora’s work [9] was about a Fuzzy logic DC-Link voltage controller for three-phase DSTATCOM to compensate AC and DC loads. This included DC-link capacitor selection and voltage control.
Sch”nberger [10] of Plexim GmbH presented an accurate PV string model that can be included in power electronic simulations. The PV model accounts for the nonlinear V-I characteristic of a module, temperature and sun strength.
Rathnakumar et al. [11] proposed a new software implementation for Two Level Inverter using Space Vector Modulation technique. The software implementation was performed by combining Matlab and Psim software packages. He stated the advantages of Space Vector Pulse Width Modulation technique for three phase Voltage Source Inverters but did not work on renewable energy, maximum power, or complete power generation systems.
Malesani et al. [12] gave a survey of available current control techniques of the voltage source inverters with their advantages and limitations but did not work on renewable energy sources or energy control.
Fuchs et al. [13] worked on discrete sliding mode current control of grid-connected three-phase PWM converter supplying an induction motor with load. In their work, they described sliding mode control as part of variable structure control. Their work did not contain power generation from renewable sources.
Esram et al. [14] compared nineteen different techniques for maximum power point tracking of photovoltaic arrays and stated the major characteristics of sliding mode control. This work was only a review of previous literature.
Abdalrahman et al. [15] presented simulation of a three-phase grid-connected inverter with space vector pulse width modulation. In the simulation, the inverter was fed by a battery. No renewable source was simulated and maximum power was not considered.
Kim’s work [16] included control of active and reactive power delivered to the grid in synchronous dq rotating frame.
Milosevic [17] explained decoupled current control of three-phase pulse width modulated voltage source inverter in the rotating dq reference frame but without simulation and no renewable energy connection.
Krishnan et al. [18] used a brushless DC generator in their work of modeling, simulation, and analysis of variable-speed constant frequency power conversion scheme and stated the advantages of DC generator. Wind energy, maximum power, energy control, and space vector pulse width modulation were not part of their work.
Ma et al. [19] verified the feasibility and advantages of DC generator based wind power generation system. They studied variable pitch wind turbine generator and used simulative laboratory experiments not real wind
THESIS OBJECTIVES
In this thesis, wind and solar generation systems including maximum power point tracking controllers for power converters are studied. The study goes through solar alone, wind alone, and hybrid solar/wind configurations. Work also includes controlling energy extraction from the DC-link capacitor between power converter and power inverter, inverter current control in dq synchronous frame, using space vector pulse width simulation plus grid connection. Systems simulated and subjected to various different inputs and output to the grid. It is to be proven that the power captured from PV modules and wind generator systems and delivered to the grid tracks variations of inputs with favorable fast response.
The main objective of this research in summary is to track maximum power points for solar panels, wind turbines and deliver that power to electric grid by controlling power systems components. To achieve this goal, several research steps will be followed. A solar generation system connected to power grid will be suggested. Control and simulation of the power system will be done. Variable structure control with sliding mode will be used for maximum power tracking. Validity of the suggested control scheme will be tested by simulation. Research will be further extended to wind turbine power system connected to the grid. Simulation of the wind system will also test the control scheme. Then, a hybrid wind/solar generation system will be considered, simulated, and validated. After that, practical experiments for maximum power extraction from a real solar panel will be executed including measurements, data acquisition, computer interface, digital control to ensure the robustness of the proposed control.
Software used include PLECS Standalone Simulation Platform, LabVIEW System Design Software, and MATLAB. PLECS Simulation Platform was chosen because it offers high-speed simulations of power electronic systems compared to similar software like Simulink.
At every stage, every system will be subjected to a wide range of inputs and disturbances concerning solar irradiation and/or wind speed. Simulation results will be recorded as PLECS plots. Results of the experiments will be recorded as MATLAB figure files.
THESIS OUTLINE
Including this first introductory chapter, this thesis is composed of seven chapters.
Chapter 2 describes solar cells and components of grid-connected photovoltaic power generation system. System includes photovoltaic modules, DC-DC converter, Three-phase voltage source inverter, and an LC filter. Calculations of DC-link and LC filter parameters are explained.
In Chapter 3, the control of the solar energy conversion system is proposed. Variable structure control with sliding mode will be used for maximum power tracking. DC-link voltage control will be energy based. For the inverter, space vector pulse width modulation will be used with current control in dq rotating frame. A 6 kilowatts system is simulated using PLECS software package to validate the proposed system design. Photovoltaic power extracted using variable structure control with sliding mode is compared to uncontrolled scheme.
In Chapter 4, Wind energy is discussed. The design and control of a complete wind energy conversion system is shown. A 4 kilowatts system is simulated and tested. Variable structure control with sliding mode is compared to a conventional control method.
In Chapter 5, a hybrid wind/solar grid-tied system is studied using two converters and two separate maximum power tracking controllers but with one common inverter. The whole system was simulated and subjected to various different inputs of wind and irradiation inputs.
In Chapter 6, Practical experiments for a solar power system are shown with real solar module subjected to sun light, measurements taken, data acquisition, control program run on a personal computer, and results plotted.
In chapter 7, the conclusions are presented with recommendations for future work.

Photovoltaic Generation System and Grid Connection
INTRODUCTION
Solar energy generation involves the use of the sun’s energy to provide hot water via solar thermal systems or electricity via solar photovoltaic (PV) panels or concentrating solar power (CSP) systems. These technologies are technically well proven with numerous systems installed around the world over the last few decades. Solar PV panels have two advantages. On one hand, module manufacturing can be done in large plants, which allows for economies of mass production. On the other hand, PV is a very modular technology (modules can be independently created and then used in different systems).
Photovoltaic systems are classified into two major types: off-grid and grid-connected applications. Off-grid PV systems have a significant opportunity for economic application in the un-electrified areas of developing countries, and off-grid centralized PV mini-grid systems have become a reliable alternative for village electrification over the last few years. Centralized systems for local power supply have different technical advantages concerning electrical performance, reduction of storage needs, availability of energy, and dynamic behavior. Centralized PV mini-grid systems could be the most cost efficient for a given level of service, and they may have a diesel generator set as an optional balancing system or operate as a hybrid PV-wind-diesel system. These kinds of systems are relevant for reducing and avoiding diesel generator use in remote areas.
Grid tied PV systems use an inverter to convert electricity from direct current to alternating current, and then supply the generated electricity to the electric grid. Compared to an off-grid installation, system costs are lower because energy storage is not required. Grid-connected PV systems are classified into two types of applications: distributed and centralized. Grid-connected distributed PV systems are installed to provide power to a grid-connected customer or directly to the electric network. These systems have a number of advantages: 1) distribution losses in the electric network are reduced because the system is installed at the point of use, 2) extra land is not required for the PV system, 3) costs for mounting the systems can be reduced if the system is mounted on an existing structure, and 4) the PV array itself can be used as a cladding or roofing material as in building-integrated PV. Typical sizes are 1 to 4 kW for residential systems, and 10 kW to several MW for roof tops on public and industrial buildings.
Grid-connected centralized PV systems perform the functions of centralized power stations. The power supplied by such a system is not associated with a particular electricity customer, and the system is not located to specifically perform functions on the electricity network other than to supply bulk power. Typically, centralized systems are mounted on the ground, and they are larger than 1MW. The economic advantages of these systems are the optimization of installation and operating costs by bulk buying and the cost effectiveness of the PV components and balance of systems on a large scale. In addition, there liability of centralized PV systems can be greater than distributed PV systems because they can have maintenance systems with monitoring equipment, which can be a smaller part of the total system cost [2].
This chapter describes a grid-connected Photovoltaic (PV) generation system. A PV array is connected to a DC-DC converter. The capacitor at converter output was used as the DC-link to a grid side inverter. The inverter is connected to the grid via an LC filter to reduce the harmonics caused by switching. Block diagram of the proposed system is shown in Fig. ‘2.1. System modeling for simulation purposes is described.

Fig. ‘2.1: Block diagram of the photovoltaic generation system
PV SYSTEM COMPONENTS
Photovoltaic Array Model
The photovoltaic effect is the creation of electric voltage or current in a material upon exposure to light and is a physical and chemical phenomenon. A photovoltaic (PV) cell is a simple semiconductor device that converts light into electric energy. The conversion is accomplished by absorbing light and ionizing semiconductor atoms. PV cells are electrically connected to form PV modules (panels). PV modules are the fundamental building blocks of PV systems. To form a power generating unit, modules are arranged in an array and subjected to sunlight. Photovoltaic cell, module and array are illustrated in Fig. ‘2.2. PV power output is related to solar irradiation and cells temperature. At each condition, there is a voltage level at PV array terminals that gives maximum power as shown in Fig. ‘2.3.

Fig. ‘2.2: Photovoltaic cell, module and array

Fig. ‘2.3: PV array power curve
The largest confirmed solar module efficiency measured under the global spectrum (1000W/m2) at a cell temperature of 25 ”C is 24.1% ” 1.0. This module was fabricated by Alta Devices – USA. Alta Devices has fabricated a thin-film single junction Gallium Arsenide (GaAs) module with total area of 856.8 cm2 with an independently confirmed solar energy conversion efficiency of 23.5%, under the global AM1.5 spectrum at one sun intensity. More common efficiencies are in the range of 13-18% [20, 21].
In this work, a PV module model with moderate complexity is used. Model circuit includes a current source, a diode as shown in Fig. ‘2.4. The current source output Ig is directly proportional to the light G falling on cells and dependent on temperature T and voltage Upv [22].

Fig. ‘2.4: Circuit diagram of the PV module model
From the theory of semiconductors, the current Id shunted through the diode is
(2.1)
Where
Isat: PV array reverse saturation current (of the diode)
q: Electron charge
A: P-N junction ideality constant
K: Boltzmann’s constant
T: PV array temperature
Upv: applied voltage across the terminals of the diode (PV array output voltage)
Ig: current generated by the incident light (it is directly proportional to the Sun irradiation)
From Kirchhoff’s law, we have
(2.2)
So, the Ideal model of the solar cell could be expressed as
(2.3)
To obtain a better representation of the electrical behavior of the cell of the ideal model, the model takes account of material resistivity and the ohmic losses due to levels of contact. These losses are represented by the series resistance Rs as shown in Fig. ‘2.5. The current voltage equation of the model of the solar cell is given as
(2.4)
As mentioned before, PV cells are electrically connected to form PV modules (panels). A number of series connected modules form a string. Increasing the number of modules in a string increases the total output voltage. Strings are connected in parallel to increase the total power output and form a PV array. All of the constants in the above equations can be determined by examining the manufacturer’s ratings of the PV module, and then the published or measured I-V curves of the module [22].

Fig. ‘2.5: Circuit diagram of the PV module model
The calculated current characteristic of the PV module is implemented in PLECS Simulation Platform for Power Electronic Systems version 3.2.7 using a 3-D lookup table [10]. Table outputs a 3-D function using interpolation or extrapolation.
To model a string, the voltage input to the lookup table is formed by dividing the output voltage by the number of modules (num_panels) in the string as shown in Fig. ‘2.6. To model an array, the current output of the lookup table is multiplied by the number of strings in parallel.

Fig. ‘2.6: PLECS implementation of PV module
DC-DC Power Converter
In order to cope with the continuously varying solar irradiation intensity, a buck-boost type DC-DC converter topology is used to transfer power from PV array as shown in Fig. ‘2.7. The buck’boost converter is a type of DC-to-DC converter that has an output voltage magnitude that is either greater than or less than the input voltage magnitude. Here, the inverting topology is used where the polarity of output voltage is opposite to that of the input.

Fig. ‘2.7: PLECS circuit diagram of DC-DC converter
The basic principle of the buck’boost converter could be explained as follows: When the switch is turned on, the input voltage source supplies current to the inductor L, and the capacitor CDC supplies current to the output load. When the switch is opened, the inductor L is connected to the output load and capacitor, so energy is transferred from L to CDC and output load. The basic principle of the buck’boost converter is shown in Fig. ‘2.8.
u represents the switch function of the power switch device. When u = 1, switch SW is close; while u = 0, means SW is open. This configuration allows the control to switch between two system structures: first; structure where the switch is open, second; structure where the switch is closed [7].

Fig. ‘2.8: Basic principle of the buck’boost converter.
The operation of the buck-boost is best understood in terms of the inductor’s “reluctance” to allow rapid change in current. From the initial state in which nothing is charged and the switch is open, the current through the inductor is zero. When the switch is first closed, the blocking diode prevents current from flowing into the right hand side of the circuit, so it must all flow through the inductor. However, since the inductor doesn’t like rapid current change, it will initially keep the current low by dropping most of the voltage provided by the source. Over time, the inductor will allow the current to slowly increase by decreasing its voltage drop. Also during this time, the inductor will store energy in the form of a magnetic field.
If the current through the inductor L never falls to zero during a commutation cycle, the converter is said to operate in continuous mode.
From t=0 to t=DT, the converter is in On-State, so the switch SW is closed. The rate of change in the inductor current (IL) is therefore given by
(dI_L)/dt= V_in/L (2.5)
At the end of the On-state, the increase of IL is therefore:
‘I_(L_on )= ‘_0^DT’d I_L=’_0^DT”V_in/L dt=(V_in DT)/L’ (2.6)
Where D is the duty cycle. It represents the fraction of the commutation period T during which the switch is on. Therefore D ranges between 0 (SW is never on) and 1 (SW is always on).
During the Off-state, the switch S is open, so the inductor current flows through the load. If we assume zero voltage drop in the diode, and a capacitor large enough for its voltage to remain constant, the evolution of IL is
(dI_L)/dt= V_out/L (2.7)
Therefore, the variation of IL during the Off-period is
‘I_(L_off )= ‘_0^((1-D)T)’d I_L=’_0^((1-D)T)”V_out/L dt=(V_out (1-D)T)/L’ (2.8)
As we consider that the converter operates in steady-state conditions, the amount of energy stored in each of its components has to be the same at the beginning and at the end of a commutation cycle. As the energy in an inductor is given by
E=1/2 L’ I’_L^2 (2.9)
Because the value of IL at the end of the off state must be the same with the value of IL at the beginning of the on-state, i.e. the sum of the variations of IL during the on and the off states must be zero
‘I_(L_on )+ ‘I_(L_off )= 0 (2.10)
(V_in DT)/L+ (V_out (1-D)T)/L=0 (2.11)
This can be written as
V_out/V_in = (-D)/(1-D) (2.12)
This in return yields that
D=V_out/(V_out- V_in ) (2.13)
From the above expression it can be seen that the polarity of the output voltage is always negative (because the duty cycle goes from 0 to 1), and that its absolute value increases with D, theoretically up to minus infinity when D approaches 1. Apart from the polarity, this converter is either step-up (a boost converter) or step-down (a buck converter). Thus it is named a buck’boost converter.
The DC-link capacitor at DC-DC converter output is considered as the energy source for the inverter. The value of the DC-link capacitor can be selected based on its ability to regulate the voltage under transient conditions. Let us assume a system with the rating of X kilovolt amperes. The energy of the system is given by 1000 X J/s. Let us further assume that the system deals with half (i.e., X /2) and twice (i.e., 2 X) capacity under the transient conditions for cycles with the system voltage period of T seconds. Then, the change in energy to be dealt with by the DC capacitor is given as
‘E=(2X- X/2 )T=(3X/2 )T (2.14)
This change in energy should be supported by the energy stored in the DC capacitor. Let us allow the DC capacitor to change its total DC-link voltage from 1.4Vm to 1.8Vm during the transient conditions where Vm is the peak value of phase voltage. Hence, we can write
1/2 C_DC [(1.8V_m )^2-(1.4V_m )^2 ]=(3X/2 )T (2.15)
For T equals the time of half of a 50 Hz AC cycle (0.01 Sec), the value of the DC-link capacitor CDC is selected as [9]
C_DC= (0.03 X)/(‘(1.8V_m)’^2-‘(1.4V_m)’^2 ) (2.16)
Where, X is the system power rating and Vm is the system peak voltage
Voltage Source Inverter
The inverter is the power electronic circuit, which converts the DC voltage into AC voltage with required voltage and frequency. The main function is to convert the DC power generated by PV panels into grid-synchronized AC power. The output voltage can be controlled with the help of drives of the switches. The pulse width modulation (PWM) techniques are most commonly used to control the output voltage of inverters. Such inverters are called PWM inverters. The output voltage of the inverter contains harmonics whenever it is not sinusoidal. In this work, a three-phase, two-level voltage source inverter (VSI) is used.
The three-phase Voltage Source Inverter generates at each output phase i (i = a,b,c) a voltage Vi with two-level rectangular waveform. Phase switching sequence is controlled by modulation according to a given reference Vi*, so that the phase voltage low-order harmonics result in a voltage Vi (mean average) whose waveform should follow Vi* as close as possible. Modulation also generates high order harmonics around the switching frequency [12]. Fig. ‘2.9 shows PLECS circuit diagram of a VSI consisting of six Insulated Gate Bipolar Transistors (IGBT) having integrated anti-parallel diodes. Fig. ‘2.10 shows an example of inverter output voltage. Fig. ‘2.10 (a) shows phase to neutral voltage at inverter output, and Fig. ‘2.10 (b) shows phase to phase voltage at inverter output.

Fig. ‘2.9: PLECS circuit diagram of VSI

Fig. ‘2.10: example of inverter output: (a) phase to neutral voltage. (b) phase to phase voltage.
LC Filter for Grid Connection
In order to reduce high order harmonics caused by switching, a low pass filter at inverter terminals is needed to fulfill power quality requirements. A LC-filter is commonly used for that purpose [23]. Design procedure for the filter is explained as follows [24];
Calculate Rbase for rated power P and nominal voltage V
R_base= V^2/P (2.17)
f_c= 1/10 f_sw (2.18)
LC=(1/(2”f_c ) )^2 (2.19)
Calculate Lf and Cf of the LC filter
L_f= R_base/(2”f_c ”_c ) (2.20)
C_f=”_c/(2”f_c R_base ) (2.21)
Where, ”c is the filter damping factor. Fig. ‘2.11 shows circuit diagram of LC filter. Where, Rf is the inductance branch resistance, R is the output branch resistance. Fig. ‘2.12 shows complete PV power circuit diagram.
CONCLUSION
In this chapter, a grid-connected PV generation system was introduced. A photovoltaic array model was presented, a buck-boost DC-DC power converter, a voltage source inverter, and a suitable LC grid filter. Calculations for the choice of DC-link capacitor and LC filter components values were explained.

Fig. ‘2.11: PLECS circuit diagram of LC filter

Fig. ‘2.12: Complete PV power circuit

Photovoltaic Generation System Control and Simulation
INTRODUCTION
This chapter describes simulation and control procedure for a grid-connected Photovoltaic (PV) generation system. The DC-DC converter is controlled by a variable structure controller with sliding mode. The capacitor at converter output is used as the DC-link to the grid side inverter. A controller for DC link voltage and energy extraction was designed. Power, voltage and current calculations and control were performed in dq synchronous frame. A phase locked loop (PLL) technique was implemented to synchronize the rotating frame with grid voltages. SVPWM technique synthesizes switching signals for inverter transistors given reference voltage and phase angle. Validity of proposed controllers is verified by simulation. Fig. ‘3.1 shows block diagram of the system.

Fig. ‘3.1: Block diagram of the photovoltaic generation system.
SYSTEM CONTROL
Photovoltaic Array Maximum Power Point Tracking
The MPPT function is a key point of any photovoltaic power processing system [25]. To achieve maximum power point tracking (MPPT), Variable structure control with sliding mode for the buck-boost converter is used in this work. Variable structure control with sliding mode (or shortly sliding mode control) is a nonlinear control approach suitable for DC-DC converters achieving both robustness and stability [8]. Sliding mode control is very adequate for controlling switched mode converters and is well known for its robustness. Its most important feature is the invariance, giving independence of model uncertainties and strong disturbance rejection. Sliding mode control (SMC) is the dominant part of variable structure control types that switches between system structures [13], [26]. Compared to several other MPPT techniques for PV arrays, SMC is characterized by not being PV array dependent, needs no periodic tuning, has fast convergence speed, has medium implementation complexity, and does not need irradiation measurement as shown in Table ‘3.1 [14].
Table ‘3.1: Major characteristics of MPPT techniques
Sensed
Parameters Implementation Complexity Convergence Speed Periodic Tuning? Analog or Digital? True MPPT? PV Array Dependent? MPPT Technique
Voltage, Current Low Varies No Both Yes No Hill-climbing/P&O
Voltage, Current Medium Varies No Digital Yes No Incremental Conductance
Voltage Low Medium Yes Both No Yes Fractional VOC
Current Medium Medium Yes Both No Yes Fractional ISC
Varies High Fast Yes Digital Yes Yes Fuzzy Logic Control
Varies High Fast Yes Digital Yes Yes Neural Network
Voltage, Current Low Fast No Analog Yes No Ripple Correlation Control
Voltage, Current High Slow Yes Digital Yes Yes Current Sweep
Voltage Low Medium No Both No No DC Link Capacitor Droop Control
Voltage, Current Low Fast No Analog No No Load I or V Maximization
Voltage, Current Medium Fast No Digital Yes No dP/dV or dP/dI Feedback Control
Voltage, Current High Slow Yes Digital No Yes Array Reconfiguration
Irradiance Medium Fast Yes Digital No Yes Linear Current Control
Irradiance,
Temperature Medium N/A Yes Digital Yes Yes IMPP & VMPP Computation
Voltage, Current High Fast Yes Both Yes Yes State-based MPPT
Current Medium Fast Yes Both No Yes One Cycle Control
None Low N/A Yes Both No Yes Best Fixed Voltage
Voltage, Current High N/A No Digital No Yes linear reoriented Coordinates Method
Voltage, Current Medium Fast No Digital Yes No Slide Control
Variable Structure Control with Sliding mode
Variable structure control (VSC) was first proposed and elaborated in the early 1950’s in the Soviet Union. In the pioneer works, the plant considered was a linear second-order system. Since then, VSC has developed into a general design method being examined for a wide spectrum of system types including nonlinear systems, multi-input/multi-output systems, discrete-time models, large-scale and infinite-dimensional systems, and stochastic systems. In addition, the objectives of VSC have been greatly extended from stabilization to other control functions. The most distinguished feature of VSC is its ability to result in very robust control systems that are completely insensitive to parametric uncertainty and external disturbances. The advances in computer technology and high-speed switching circuitry have made the practical implementation of VSC a reality and of increasing interest to control engineers. Variable structure control with sliding mode utilizes a high-speed switching control law to drive the nonlinear plant’s state trajectory onto a specified and user-chosen surface in the state space (called the sliding or switching surface), and to maintain the plant’s state trajectory on this surface for all subsequent time. By proper design of the sliding surface, VSC attains the conventional goals of control such as stabilization, tracking, regulation, etc [27].
The basic idea of VSC was originally illustrated by a second-order system similar to
(x_1 ) ”=x_2=y
x ”_2=ax_1+bx_2+u
u= – ”x_1
Where ” = ” when S > 0, ” = ” when S < 0 And S= x1'' And '' = cx1+x2 A block diagram of the system is shown in Fig. '3.2. The functions x1=0 and cx1+x2=0 describe lines dividing the phase plane (xy plane) into regions where S has different sign as shown in Fig. '3.3. These lines that define the set of points in the phase plane where S=0 are called switching lines and sometimes called known as the switching surface; and S is called a switching function. Fig. '3.2: System model of a simple VSC example The feedback gain '' is switched according to the sign of S. Therefore, the system is analytically defined in two regions of the phase plane by two different mathematical models: In region I where S > 0, model is
(x_1 ) ”=x_2=y
x ”_2=ax_1+bx_2+u
x ”_2=ax_1+bx_2-”x_1
x ”_2=(a-”)x_1+bx_2
In region II where S < 0, model is (x_1 ) ''=x_2=y x ''_2=ax_1+bx_2+u x ''_2=ax_1+bx_2-''x_1 x ''_2=(a-'')x_1+bx_2 The phase plane trajectories for the two models are shown in Fig. '3.4 for a=-1, b=2, c=0.5, ''=4, ''=-4. Fig. '3.3: Regions defined by the switching logic (a) (b) Fig. '3.4: Phase portraits: (a) Unstable system I. (b) Unstable system II. The equilibrium point of the first model is an unstable focus at the origin (i.e. the real part of the system eigen values is positive and states diverge to infinity) and the equilibrium point of the second model is a saddle at the origin (i.e. the real part of one of the system eigen values is positive, almost all of the system trajectories diverge to infinity) which is also unstable. The two unstable structures have certain regions of stability. To have the desired regions of the two structures in a resultant system, the phase portrait for the system in Fig. '3.5 is formed by composing a desired trajectory from the parts of stable trajectories of different structures. To obtain the complete phase portrait, the trajectory of the system on the set S=0 must be described. On the line x=0, the phase trajectories of regions I and II are now joined together. The line '' = cx1+x2 = 0, which itself is a dynamical equation, contains endpoints of trajectories coming from both sides of the line and the phase portrait is a trajectory along the line '' = 0 that asymptotically tends to the origin of the phase plane representing motion called a sliding mode as shown in Fig. '3.5. Fig. '3.5: Phase portrait of the composed system. Thus, a phase trajectory of this system generally consists of two parts, representing two modes of the system. The first part is the reaching mode, also called non-sliding mode, in which the trajectory starting from anywhere on the phase plane moves toward a switching line and reaches the line in finite time. The second part is the sliding mode, in which the trajectory asymptotically tends to the origin of the phase plane as shown in Fig. '3.6. During the control process, the structure of the control system varies from one structure to another, thus earning the name variable structure control. It should be noted that a variable structure control system can be devised without a sliding mode, but such a system does not possess the associated merits. VSC is an attractive method of control only when a sliding mode (or sliding regime) is defined. It should also be noted that during the sliding mode, trajectory dynamics are of a lower order than the original model. The main arguments in favor of sliding-mode control are order reduction, decoupling design procedure, disturbance rejection, insensitivity to parameter variations, and simple implementation by means of power converters. In practical applications of sliding mode control, systems may experience undesirable oscillations having finite frequency and amplitude, which is known as 'chattering'. Chattering leads to lower control accuracy. At the first stage of sliding mode control theory development, the chattering was the main obstacle for its implementation. Due to advances in microprocessors and microcontrollers speed, chattering could be suppressed by increasing the sampling rate and computational speed of controllers. Fig. '3.6: System modes during SMC. The design of the sliding mode control law can be divided in two phases: 1. Phase 1 consists of the construction of a suitable sliding surface so that the dynamics of the system directed to the sliding manifold produce a desired behavior. Usually, the sliding surface is constructed by the linear combination of state variable errors which are defined as the differences between the state variables and their references 2. Phase 2 entails the design of a discontinuous control law which forces the system trajectory to the sliding surface and maintains it there. So, the main idea of sliding mode control is to design a controller rendering the trajectory of states trapped on a predetermined sliding surface and remained on it thereafter. Sliding mode control utilizes a high-speed switching control law to drive the state trajectory staying on this sliding surface for all subsequence time such that the robust stability of the system is assured. In the present, sliding mode control is a highly active area of research. Some known applications of variable structure control with sliding mode include robots, aircrafts, spacecrafts, load frequency control of power systems, servomechanisms, guidance, process control, phase-locked loop, power converters, and remote vehicle control [13, 27, 28, 29, 30]. Sliding Mode Controller Design for the DC-DC Converter Considering PV array voltage UPV and current iPV, the output power is Ppv = Upv . ipv (3.1) When the solar array is operating in its maximum output power (3.2) (3.3) the switching function S is chosen as (3.4) PV array power curve shown in Fig. '2.3 shows that dP/dV > 0 (state 1) on the left of the maximum power point and dP/dV < 0 (state 2) on the right. On the basis of these two states, converter switch control signal u is expressed as [7], [14] u={'(1,&S<[email protected],&S'0)' (3.5) The resulting system model is shown in Fig. '3.7. A PLECS subsystem block was designed to calculate function u from PV voltage and current as shown in Fig. '3.8. To work in discrete-time, PV voltage and current are sampled at an interval T. Fig. '3.7: System model of PV sliding mode control A five point quadratic smoothing function is used for each signal to reduce noise in sampled data as described in [31]. Smoothing function could be written in the z-domain as (Y(z))/(U(z))=(31z^4+ 9z^3- 3z^2- 5z+ 3)/(35z^4 ) (3.6) Then, dI/dV is estimated using discrete transfer function for voltage and current difference over time function F(Z) difference for each sampling interval T as follows ('I(z))/('F(z))=(z- 1)/(T z) (3.7) ('V(z))/('F(z))=(z- 1)/(T z) (3.8) ('I(z))/('V(z))=('I(z))/('F(z))/('V(z))/('F(z)) (3.9) After calculation of function S from equation (3.4), u is obtained from equation (3.5) using PLECS relay block. Fig. '3.8: PLECS subsystem block for estimation of function u Ensuring that the sliding mode is attained in finite time is called 'Reachability'. The condition for Reachability is that the chosen switching function S guarantees that SS ''<0 at all time. System stability during simulation acknowledges that this condition was fulfilled. Energy Based DC Link Voltage Control The DC-link capacitor at DC-DC converter output is considered as the energy source for the VSI. DC voltage Vdcref required at inverter input is calculated from phase-to-neutral grid voltage rms value Vrms as follows V_dcref= (3'3)/'' V_peak (3.10) Where, V_peak= '2 V_rms (3.11) The energy WDC required from the DC-link capacitor CDC to discharge from actual voltage VDC to the reference value Vdcref is given as [9] W_DC= 1/2 C_DC ('V_DC'^2- 'V_dcref'^2 ) (3.12) Because the DC-link capacitor voltage has ripples with frequency double that of the supply frequency, The DC power P'DC required from the capacitor is given as 'P''_DC= W_DC/T_c (3.13) Where, Tc is the ripple period of the DC-link capacitor voltage and equals half the period of one AC cycle. Steady-state error is eliminated by adding an integral term. This controller is shown in Fig. '3.9 and the reference DC power Pref is computed as P_ref= K_pe ('V_DC'^2- 'V_dcref'^2 )+ K_ie ''('V_DC'^2- 'V_dcref'^2 ) dt (3.14) Fig. '3.9: DC-link voltage controller Proportional and integral gains Kpe and Kie of the controller could be given as [9] K_pe= C_DC/(2T_c ) (3.15) K_ie= K_pe/2 (3.16) The discrete transfer function of integral is estimated as (Y(z))/(F(z))=(Tz+T)/(2z-2) (3.17) Current Control of Voltage Source Inverter Modulation techniques are used to obtain variable output from inverters having a maximum fundamental component plus harmonics. Among these techniques, space vector pulse width modulation (SVPWM) is popular because it has various excellent features [11]. The grid connected system aims to transfer maximum solar array energy into grid with a unity power factor. So, the system has to control active power P and reactive power Q. For that purpose, dq transformation of voltage and current are performed. Direct'quadrature or dq transformation is a mathematical transformation that rotates the reference frame of three-phase systems in an effort to simplify the analysis of three-phase circuits. The dq transformation can be thought of in geometric terms as the projection of the three separate sinusoidal phase quantities that are equal in magnitude and are separated from one another by 120 electrical degrees onto two axes rotating with the same angular velocity '' as the sinusoidal phase quantities. The two axes are called the direct or d axis; and the quadrature or q axis with the q-axis being at an angle of 90 degrees from the direct axis. The d axis makes an angle ''=''t with the a phase quantity chosen as the reference. The transformation matrix K is given as K = 2/3 ('(cos'''&cos''(''-'120'^0)'&cos''(''+'120'^0)'@sin'''&sin''(''-'120'^0)'&sin''(''+'120'^0)' )) (3.18) Where, '' is the rotating dq frame angle. '' is synchronized with the phase angle of grid voltage giving d component of grid voltage equal to zero. d and q components of three phase voltages and currents are given as follows (V_d''V_q ) = K ('([email protected][email protected]_c )) (3.19) (I_d''I_q ) = K ('([email protected][email protected]_c )) (3.20) To extract the phase angle '' of grid voltage, a phase locked loop (PLL) technique was implemented as shown in Fig. '3.10. Grid voltages Va,b,c are first transformed into dq components. PLL is locked by setting reference d component voltage ed* to zero. A PI controller is used to control Vd and bring it to zero. Grid nominal frequency is then added to the output of the controller. The resulting frequency is then integrated to give the grid locked angle '' [15]. PLECS math function mod is added at the output to bring the output back to zero after each time the value 2'' is reached. Proportional and integral gains were to chosen by trial and error in simulation. The chosen values of 10 and 1000 respectively caused the output to stabilize in less than 5 mSec. Fig. '3.10: PLECS subsystem block of a PLL system The instantaneous power S delivered to the grid is given as [16], [32] S = P+jQ (3.21) Where P = 3/2 (V_d I_d+ V_q I_q ) (3.22) Q = 3/2 (V_q I_d- V_d I_q ) (3.23) In synchronous dq rotating frame, Vd = 0. Therefore P = 3/2 (V_q I_q ) (3.24) Q = 3/2 (V_q I_d ) (3.25) The active power P and reactive power Q are controlled by Iq current and Id current respectively [16]. To transfer DC link power Pref to the grid with zero reactive power we have the following reference currents I_qref = 2/3 P_ref/V_q (3.26) I_dref =0 (3.27) For a grid-connected inverter, if L is the inductance between the grid-connected inverter and the grid, R is the resistance between the grid-connected inverter and the grid then, the output voltages in the dq frame are given by [33] (U_d''U_q ) = L d/dt (I_d''I_q )+R(I_d''I_q )+''L('-I'_q''I_d )+(V_d''V_q ) (3.28) To calculate reference voltage at inverter output, considering the RL components of the grid filter circuit of Fig. '2.11, we have U_dref=(d'(I'_dref-I_d))/dt L_f+'(I'_dref-I_d)R_f+V_d-''L_f I_q (3.29) U_qref=(d'(I'_qref-I_q))/dt L_f+'(I'_qref-I_q)R_f+V_q+''L_f I_d (3.30) So, the differences between measured inverter output currents (Id, Iq) and desired reference currents are input to PD controllers. Proportional and derivative gains for the controllers are Rf and Lf respectively. This actually means the required voltage at inverter output is higher than the grid voltage with the value that causes the required current to flow from the inverter to the grid through the filter with cross-coupling between the d and q components. The discrete Transfer function of derivative is estimated as (''I(z))/(''F(z))=(z- 1)/(T z) (3.31) Complete current control loop is shown in Fig. '3.11 [17], [34]. Fig. '3.11: Grid current control including cross-coupling terms Space Vector Pulse Width Modulation Space vector pulse width modulation (SVPWM) is a popular modulation technique for PWM inverter with various advantages including not having to store lookup table containing sine values. The space-vector PWM technique is used to produce the switching control signals to be applied to the three-phase inverter. The SVPWM inverter has constant switching frequency, higher DC link voltage utilization, and low output harmonic distortions compared with the conventional sinusoidal PWM inverter. The control strategy of the SVPWM inverter is the voltage/frequency control method which is based on the space-vector modulation technique. In SVPWM, there are eight possible unique switching states shown in Fig. '3.12, each of which determines a voltage space vector. As shown in Fig. '3.13, six active voltage space vectors U1, U2, U3, U4, U5, U6 shape the axis of a hexagon and divide the whole space into six sectors from 1 to 6. In addition, there are two zero vectors, U0 and U7 which lie at the origin associated with having all three of the lower switches on or all three of the upper switches on. Therefore, SVPWM is a digital modulating technique with eight state operation whose objective is giving appropriate combination of these eight vectors to approximate a given reference voltage. Considering the voltage source inverter shown in Fig. '2.9 with six switches SW1 to SW6 and input voltage VDC and three output voltages Va, Vb, Vc gives the switching states described in Table '3.2. To implement space vector modulation, a reference signal Uref is sampled with a frequency fsw and Tsw = 1 / fsw is the switching time interval for one active voltage space vector. SVPWM is implemented as follows [15]. Fig. '3.12: Eight Switching Configuration of a Three-Phase Inverter Table '3.2: Voltage Space Vectors and switching states Vector ('','') SW1 SW3 SW5 SW2 SW4 SW6 Vab Vbc Vca U0 = (000) (0,0) OFF OFF OFF ON ON ON 0 0 0 U1 = (100) (2/3,0) ON OFF OFF OFF ON ON +VDC 0 'VDC U2 = (110) (1/3,1/'3) ON ON OFF OFF OFF ON 0 +VDC 'VDC U3 = (010) (-1/3,1/'3) OFF ON OFF ON OFF ON 'VDC +VDC 0 U4 = (011) (-2/3,0) OFF ON ON ON OFF OFF 'VDC 0 +VDC U5 = (001) (-1/3,-1/'3) OFF OFF ON ON ON OFF 0 'VDC +VDC U6 = (101) (1/3,-1/'3) ON OFF ON OFF ON OFF +VDC 'VDC 0 U7 = (111) (0,0) ON ON ON OFF OFF OFF 0 0 0 Fig. '3.13: Voltage Space Vectors in SVPWM Computation of Reference Voltage and Angle ''ref is the required reference voltage vector. Current control outputs were Udref and Uqref as shown in Fig. '3.11. Magnitude Uref and angle ''ref of vector ''ref are obtained as follows: First, Udref and Uqref are mapped to the complex orthogonal ('') plane using the following transformation (U_''U_'' ) = ('(cos'''&-sin'''@sin'''&cos''' )) ('([email protected]_q )) (3.32) Where, '' is the angle between the rotating and stationary frame calculated by the PLL system. Next, Uref and angle ''ref are calculated as U_ref ='(U_''^2+U_''^2 ) (3.33) ''_ref = tan^(-1)''U_''/U_'' ' (3.34) Determination of Sector Number Angle ''ref is compared to angles range of sectors 1 to 6 so as to determine the sector in which ''ref lies. A PLECS subsystem block is designed and used for sector determination as shown in Fig. '3.14. The angle ''m in the range (0 ' 60'') inside the sector is calculated as ''_m =''_ref-''/3 (Sector-1) (3.35) Determination of Switching Time Intervals At the input of the voltage source inverter, DC-link capacitor voltage VDC is the actual DC voltage and Uref is the magnitude of required voltage. The modulation index m is calculated as m = U_ref/(V_DC/2) (3.36) Using vectors calculation, the switching time shares T1, T2 of two adjacent active vectors are calculated as T_1 = '3/2 T_sw m sin'(''/3-''_m ) (3.37) T_2 = '3/2 T_sw m sin'(''_m ) (3.38) And T0 is the period in one switching period for null vectors to fill T_0 =T_sw-T_1-T_2 (3.39)

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