Introduction Renewable Energy Energy is the crucial necessity for the mankind and is the motive power that keeps the industry moving and other things live and dynamic

Renewable Energy
Energy is the crucial necessity for the mankind and is the motive power that keeps the industry moving and other things live and dynamic. With the advancement of the civilization, there is ever increasing demand of energy in every walk of human life. The conventional energy sources (fossil fuels) will not be sufficient to meet our ever-increasing demand of energy as they are limited in quantity and will get exhausted soon. The increased usage of fossil fuels increases carbon emissions and catalyzes global climate change, which causes global warming, air pollution, depletion of forests and many other ecological problems. The carbon dioxide emission in developing countries has jumped by significant amount in recent years. Therefore, there is an urgent need to discourage the use of traditional sources of energy and promote the use of renewable sources of energy like solar, wind, tidal waves, biogas etc. There is a vast scope and many opportunities in this sector of power-generation. In the recent years, the world has observed an exponential growth of renewable power capacity. Fig.1.1 shows the total capacity of renewable across the globe in 2015 and 2016. 1

Fig-1.1: Global Summary of Renewable Power Installations in 2015 and 2016
Unlike the conventional energy sources, which are concentrated in a particular region, renewable resources are spread over wide geographical areas. Rapid deployment of renewable energy and energy efficiency is resulting in significant energy security, climate change mitigation, and economic benefits. The main advantages of renewable energy are:
Reduction in Green House Gases (GHGs)
Reducing Energy Dependency
Increasingly Competitive
Wind Energy & Wind Turbines
Wind is one of the sustainable forms of energy source as it is renewable, widely distributed, and plentiful in quantity. Motion energy of the wind flow is used by humans for many purposes such as water pumping, electricity generation, grain milling, etc., through windmills for centuries. Windmills that are used for electricity generation are called wind turbines in order to distinguish them from the traditional mechanical wind power applications. The kinetic energy of winds rotates the blades of a wind turbine which are connected to a shaft. This shaft is coupled to an electric generator, which converts the mechanical power into electrical power. Even though, the philosophy of converting the kinetic energy from the wind into electrical energy sounds simple, there are many complications involved in interconnection of wind turbines to the grid, energy generation and maintaining the power quality of the generated energy, owing to the fact that there are frequent variations in the characteristics of the wind resources.

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During the early years, the wind turbine is coupled with squirrel cage induction motor, where the range of operational speed and control of power outputs is very less. These turbines are categorized as Type-1. For any given wind speed, the operational speed under steady state conditions and torque are linearly related. The mechanical inertia of the system limits the rate of change of output power for sudden changes in wind speed. To overcome this disadvantage, wound rotor machines are used where the variable resistors are connected to the rotor circuit through power-electronic devices (Type-2 wind turbines). These resistors control the rotor currents very rapidly and keep constant power even during wind gusts and can improve the dynamic response of the machine during disturbances from the grid. The type-2 turbines were taken to next level by adding variable AC excitation to the rotor circuit instead of resistors. This type-3 wind turbine and commonly known as Doubly Fed Induction Generator (DFIG). The rotor excitation is supplied by a current controlled, voltage source converter which can adjust the magnitude and phase of the rotor currents instantaneously. This converter is connected back-to-back with another converter which is connected directly to the grid. With the advancement of power electronics technologies, the back-to-back converters connected to rotor were brought directly between the stator terminals and grid (Type-4 turbines). With further advancement of technology, the induction generator is replaced with synchronous generator (Type-5 turbine). However, there are certain advantages of Type-3 turbines over the latter. The converters employed in the DFIG are rated at 30% of the machines rated power which reduces the cost for power electronic devices. The machine is also capable of working in sub-synchronous generation and super-synchronous motoring modes. Hence, our topic of interest for this thesis will be Type-3 Wind turbine or DFIG.

Literature Review
Harmonic Resonance
Resonance is a phenomenon in electrical circuits, when the impedance is minimum in series circuits or maximum in parallel circuits. In other words, it is when the transfer function is at maximum. With the technological advancement in power electronics, harmonics became more prevalent in electrical systems, where the voltages and currents in the system will be having components with frequencies in multiples of the fundamental frequency. The operations of non-linear loads and power electronic devices in an electrical system create harmonic currents throughout the system. With the increase in the frequency, the inductive reactance increases and the capacitive reactance decreases. At a particular frequency, there comes a cross-over point where the inductive reactance and capacitive reactance will match creating resonance in the system. This phenomenon is called as harmonic resonance. This results in very high harmonic currents and voltages in the system. It is unlikely that both the capacitive and inductive impedance match, but even the near resonance also can cause damage to the system. The harmonic resonance is caused by non-linear loads and power electronic devices such as AC/Dc drives, VFDs, induction heaters, switch mode power supplies, rectifiers, converters, inverters etc.

Impedance Based Nyquist Stability Criterion
The recently developed interest in renewable energy installation across the globe has brought a downside along with it. These renewable energy sources are connected to the grid via power electronic converters/inverters, which are the major source of harmonics in the system. The impedance interaction between the inverter and the grid creates harmonic resonance and in some case may lead to instability. Impedance based small signal analysis can be applied on the converters to further understand the harmonic resonance in any system and its effects.

Consider a system with source impedance and load impedance as shown in the above figure. The current through the system can be found by
Is=V(s)Zss+Zl(s)=V(s)Zl(s)?11+Zs(s)Zl(s)Assuming the voltage source and load are stable, then for the system to be stable the 1+ZssZls should have all the zeros in left half plane (LHP). According to Nyquist stability criterion, the system is stable if the number of anti-clockwise encirclement around (-1,0) are equal to the number of RHP poles of ZssZls. If there are not RHP poles, the Nyquist map of ZssZls should not encircle (-1,0).

Harmonic Impedance Modeling of DFIG
For developing the impedance model of the induction machine, the popular DQ0-model is used. The d-q axis circuit of the DFIG is as shown in the below figure.

The relationship between the stator voltages, currents and flux linkages can be expressed as

Where ā€˜pā€™ is the differential operator d/dt.The relation between rotor voltages, currents and flux linkages can be represented as

Two complex vector can be defined as
Vqds=vq-jvd and Iqds=iq-jidA space vector for a voltage can be defined using the following equation
V=va+?vb+?2vc and ?=ej2?3
Using the complex vector notation and transforming the rotor voltages into Laplace domain

Using the above equation in the stator voltage expression

Applying Lapalce transform to the voltage space vector
Vs=Vqdss-j?So, the space vector for stator voltage can be expressed as

If LM is very large compared to the other components, then the impedance from the above equation can be simplified as

The slip for the machine can be expressed as
slips=s-j?msHence the impedance of the DFIG as seen from its terminals can be written as

The above impedance model is derived by ignoring the RSC and GSC.

Harmonic Impedance Modeling of Converter
Typically the converter will be controlled using two control loops. The outer loop will control the voltages or power which is slow and have a band width of few Hz. The inner current control loop is having fast dynamics and is having bandwidth around 100 Hz. For small signal analysis, the behavior of the fast acting inner current loop is of our interest and the effects of the outer loop are ignored.

The current control scheme for the converter in dq-model can be represented as shown in the below figure.

The relationship between the voltage and current of the converter in dq-axis is represented as

Expressing the above two equations in the complex vector form leads to

The above equation using the space vector can be rewritten as

For a GSC, it can be represented by voltage source Ig*Hgs-j? behind the impedance Zgsc=Hgs-j?-jKdgSimilarly for RSC, the voltage source Ir*Hrs-j? behind the impedance Zrsc=Hrs-j?-jKdrThe equations and figures in the above section are only tentative. Will be corrected accordingly to the simulation equations.Aims and Objectives
Will be done after completion of the project and obtaining the final results
Methodology/ Contributions
Will be done after completion of the project and obtaining the final results
Thesis outline
After completion of all the chapters.