SYNOPSIS OF THE THESIS

“ROBUST SECOND-ORDER SLIDING MODE

CONTROLLER FOR GRID-CONNECTED DFIG

SYSTEM”

to be submitted for partial fulfillment of the requirement

for the degree of

Doctor of Philosophy

SHAH ANKIT PINAKINKUMAR

(Enrollment No. 119997109008)

under the guidance of

Dr. Axaykumar J. Mehta

Electrical Engineering

GUJARAT TECHNOLOGICAL UNIVERSITY

Ahmedabad, Gujarat, India

1. Abstract

Harnessing wind energy for electric power generation is an important area of research

and there is more emphasis on effective extraction of wind energy along with the quality

and reliability of power in the electricity market. In Wind Energy Conversion System

(WECS), grid-connected Doubly-Fed Induction Generators (DFIGs) driven by Variable

Speed Wind Turbines (VSWTs) are extensively used in modern power system as com-

pared to Fixed-Speed Induction Generators (FSIGs) or Synchronous Generators (SGs).

The prime advantages of DFIGs are that adaptability of their shaft speed when the wind

speed changes, active and reactive power capability in four quadrant, reduced cost of

Power Electronics (PE) converters due to reduced size and low amount of losses. The size

of the PE converters in DFIG-based VSWT is 20− 30% of the generator rating.

Typically, VSWT based power generation system employs aerodynamic control in com-

bination with the PE converters to vary speed of wind turbine by regulating torque or

active power. The main aim to vary the speed of the wind turbine is to maximize wind

power extraction when the wind speed changes. Aerodynamic control systems are gener-

ally variable pitch mechanism systems which are expensive and complex, especially when

turbines are larger. This situation leads to finding alternative control strategies.

Grid-connected DFIG run by VSWT exhibits highly nonlinear behavior due to parametric

uncertainties, wind fluctuation as well as variation in grid voltage and frequency due to

power system dynamics. These nonlinearities and disturbances pose serious threat to the

performance of control system and degrades the power quality and life of the mechanical

parts of the WECS structure. So development of a robust control scheme for a DFIG in

such a highly perturbed environment is necessary.

The classical approach for the control of DFIG is to use Vector Control (VC) strate-

gies either Stator Flux Oriented (SFO) or Stator Voltage Oriented (SVO). These vector

control strategies are complex in nature as they involve synchronous coordinate transfor-

mation and DFIG rotor current decoupling in d-axis and q-axis in synchronously rotating

reference frame to provide decoupled and indirect control of torque or active power and

reactive power. The effectiveness of these control strategies depend on the accuracy of

plant parameters. These machine parameters vary over a period of time due to ageing,

temperature etc. These parametric uncertainties along with unmodeled dynamics of the

plant cause poor dynamic performance of the control scheme, thus losing the robust-

1

ness to external and internal perturbations. Many schemes besides VC such as Direct

Torque/Power Control (DTC/DPC), Model Predictive Control (MPC), optimal control,

Sliding Mode Control (SMC) are proposed for the control of grid-connected DFIG for the

wind energy conversion. Among them, SMC is a robust controller for nonlinear systems

working in such a highly disturbed environment.

This thesis presents robust Second-Order Sliding Mode (SOSM) scheme based on Super-

Twisting Algorithm (STA) for direct control of stator active and reactive power of DFIG

in stationary reference frame with two-fold objectives. The stator active power is con-

trolled for optimization of extracted wind power by varying the speed of DFIG (and thus

the speed of wind turbine) between the minimum and rated wind speed of wind turbine.

The stator reactive power of the DFIG is controlled as per the grid demand. SOSM

control inherits all advantages of SMC and effective in attenuating chattering without

compromising the robustness to disturbances. The proposed controller scheme is simple

in implementation as complex synchronous coordinate transformation is not required.

2. Introduction

Renewable energy resources have been attracting great attention during the last 20 years

due to increased cost, limited reserves, and adverse environmental impacts of fossil fuels.

Also due to technological advancements, cost reduction and governmental incentives, re-

newable energy resources have become more competitive in the recent market. Among

all renewable energy resources, wind energy has received the strongest impulses in recent

years. Conceptually wind turbines capture the wind power by means of aerodynamically

designed wind turbine blades and convert it to the mechanical power. This mechanical

power is again converted to the electrical power by the electrical generator. The gen-

erator is either connected through gearbox or connected directly to the wind turbine in

case of multi-pole generator. Gearbox converts low-speed, high torque mechanical power

into high-speed, low torque mechanical power. This power is transmitted to the electrical

grid through a transformer and transmission lines [1]. The electrical power produced by

the generator is fed to the grid through power electronics converters and transformers.

The early technology used in the Wind Energy Conversion System (WECS) was based

on Squirrel Cage Induction Generator (SCIG) running at an almost constant speed and

directly connected to the grid. However due to fixed speed and direct connection to the

2

grid, power pulsations in the wind are directly transferred to the electrical grid. Addi-

tionally, there is no control over active and reactive power which are typically important

control parameters to regulate the frequency and voltage. Further, controllability of wind

turbine has become more and more important as the power level of wind turbine in-

creases. Recent advances in the WECS employ variable speed wind turbines along with

the power electronics converters to improve the overall extraction efficiency, smoothen the

power pulsations and enhance the life of the wind turbine tower structure. The power

electronics converters are efficient interface between the grid and wind turbine system.

They are used to match the characteristics of wind turbines with the grid requirements

such as frequency, voltage, control of active and reactive power and harmonics injected

in the grid [2].

Due to obvious disadvantages of directly grid-connected SCIG which is a Fixed-Speed

Induction Generator (FSIG), the technology has developed towards variable speed oper-

ation of wind turbine. Among several configurations of variable-speed WECS topologies,

wind turbine connected to Wound-Rotor Induction Generator (WRIG) with power elec-

tronics converters in the rotor circuit are extensively used due to variable speed operation

with small power rating of converters and four quadrant controllability of active/reactive

power. This type of system is an economical way to supply reactive power and obtain

variable speed for increased energy yield at wind speed below the rated speed [3]. In

this configuration, the stator windings are directly connected to the grid whereas, rotor

windings are connected to the grid through slip rings and back-to-back connected Power

Electronics (PE) converters. As both the stator and rotor windings are connected to the

supply, this type of generator is often called Doubly-fed Induction Generator (DFIG).

The schematic diagram of the DFIG based wind energy generation system is shown in

Fig. 1. As shown in Fig. 1, two bidirectional Insulated Gate Bipolar Junction Transistor

(IGBT)-based switching converters sharing a common dc link (Capacitor C) are normally

used in the rotor circuit. They have the capability to control both active and reactive

power delivered to the grid. The converter which is connected to the rotor terminals

of DFIG is known as Rotor Side Converter (RSC) whereas, which is connected to the

grid is known as Grid Side Converter (GSC). The DFIG can feed the power to the grid

at both super-synchronous and sub-synchronous speed. The slip of the DFIG is varied

by controlling the RSC. Since the rotor power in DFIG is 20 − 30% of the mechanical

power, the converter has to handle only part of the power produced. The nominal power

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Figure 1: Schematic diagram of DFIG-based wind generation system.

rating of the converter may be about 30% of the wind turbine power enabling a rotor

speed variation in a range about ±30% of the nominal speed. This results in reduced

cost of power electronics converter and low amount of losses. Typically, Variable-Speed

Wind Turbine (VSWT) based power generation system employs aerodynamic control in

combination with the PE converters to vary speed of wind turbine by regulating torque

or active power. The main aim to vary the speed of the wind turbine is to maximize wind

power extraction when the wind speed changes. Aerodynamic control systems are gener-

ally variable pitch mechanism which are expensive and complex, especially when turbines

are larger. This situation leads to finding alternative control strategies. The WECS can

be considered as an extremely nonlinear plant with uncertainty of parameter variation

and unmodelled dynamics. These nonlinearities are present in the characteristics of each

component of WECS (wind turbine, drive train, DFIG, Grid). Apart from characteris-

tics, the machine parameters of the system are continuously affected by environmental

conditions such as temperature, moisture, ageing etc. Besides, the wind signal itself is a

stochastic in nature and depends on climatic characteristics, geographic location, height

above the ground, surface topography. For these reasons, accurate modeling of the wind

signal is complex. Hence, grid-connected DFIG run by VSWT exhibits highly nonlinear

behavior due to parametric uncertainties, wind fluctuation as well as variation in grid

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voltage and frequency due to power system dynamics. These nonlinearities and distur-

bances severely affect the performance of the control system. These uncertainties produce

large ripple in the drive train torque as well as in the active power produced by the DFIG

which may lead to damage of mechanical components, causes flicker in the weak grid as

well as weakens the quality of power supplied at the user end. So development of a robust

control scheme for a DFIG is a challenging task.

Various researchers have extensively worked for the development for the efficient control

of induction machines since 70s, when the concept of field orientation was proposed by

Hasse in 1969 and Blaschke in 1972 [4]. Field Oriented Control (FOC) was important

paradigm in the theory and practice of control of induction motors. In essence, the objec-

tive of the field orientation is to make the induction motor emulate the separately excited

dc machine as a source of adjustable torque. Majorally, it can be classified into direct field

oriented and indirect field oriented control schemes. Broadly these control strategies are

known as Vector Control (VC) schemes. Since the development of FOC scheme for the

induction machine, several researchers have laid their sincere efforts for improvement in

the dynamic performance of control scheme at low speed, parameters estimation for sen-

sorless operation of the control scheme and for getting robustness to parameter variation.

A continuous online tuning of rotor flux feed forward was proposed for FOC of induction

machine in [5]. Electromagnetic torque was estimated independently from the rotor flux

FOC. But the performance of the scheme deteriorated at low speeds due to increasing

dependency of stator voltage on stator resistance. In [6], a self-tuning stator-flux oriented

VC scheme was developed for induction machine drives in electric vehicles. The control

scheme estimates the stator flux at high and low speed of the motor resulting in periodi-

cal update of stator and rotor resistances. The torque and stator flux are controlled in a

deadbeat fashion. Adequate dynamic performance over a wide speed range was achieved.

But the adaptive technique employed by [6] increases the complexity of control and re-

quires a high computation time. A digital scheme based on deadbeat control theory for

field-oriented induction motor drives without speed and voltage sensors was proposed in

[7]. The speed of induction motor and rotor flux are estimated using predictive observer

from the measurement of stator currents only. Reduction of ripples in stator currents

and torques are observed due to estimated speed and rotor flux with very low sensitivity

to parameter variations. In [8], both the rotor resistance and rotor speed are estimated

simultaneously to reduce effect of variation of rotor resistance on estimation of rotor speed

5

of the induction motor. To improve the accuracy of flux estimation in sensorless speed

and flux control at nearly zero speed operation, a programmable cascaded low-pass fil-

ter method of flux estimation was verified and implemented on 100 kW drive in [9]. In

[10], computation based on accurate applied-voltage was proposed under considerations

of various compensations for the quantization error in the digital controller, the forward

voltage drop of switching devices, and the dead time of the inverter to improve low-speed

drive characteristics. In [11], two Artificial Neural Networks (ANNs) were introduced for

decoupling control as an alternative to conventional field-oriented decoupling control of

induction motors. But it requires several online computations and the method is com-

plex in nature. A minimum-time minimum-loss algorithm was developed under the FOC

of induction motor in [12] to get high dynamic response during transient stage and to

improve the efficiency during the steady state.

Further, the principle of the FOC was applied for the control of DFIG in wind energy

generation system. The classical design of the control scheme for the DFIG-based WECS

is based on rotor current vector control with decoupling in d − q axis [13], [14], [15].

The control system is usually defined in the synchronous d − q reference frame fixed to

either stator voltage [13] or the stator flux [14], [15]. It has nested power and rotor

current controllers. It involves complex transformation of currents, voltage and control

outputs among stationary, rotor and synchronous reference frames. Similar to the control

of induction motors, several researchers adopted the VC schemes for the sensorless con-

trol of DFIG. A rotor position sensorless scheme using rotor side variables as measured

signals was proposed in [16] to realize decoupled control of torque and stator reactive

power of DFIG. d-axis of synchronously rotating reference frame is aligned with the air-

gap flux linkage vector and torque angle (angle between air-gap flux linkage vector and

rotor current vector) is estimated and controlled. The torque estimation algorithm was

tested over a wide speed range covering both sub-synchronous and super-synchronous

speed. However the estimation accuracy degrades when the DFIG rotor speed crosses

the synchronous speed. Sensor-less control schemes which do not require rotor or shaft

position sensor based on stator flux orientation were proposed to regulate (rotor speed /

stator active power, stator reactive power) in [17] and (stator active, reactive power) in

[18] respectively. The drawback of the control scheme in [17] is that the reference d-axis

component of rotor current has to be set at minimum value for proper functioning of

the control scheme. Stator Flux Oriented (SFO) or Stator Voltage Oriented (SVO) VC

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schemes are extensively used for modelling and decoupled control of stator active and

reactive powers for DFIG-based WECS for real-time simulation [19], [20], to validate the

WECS models and control schemes [21], for power system stability studies [22], [23], [24]

and small signal stability analysis [25] for integration of wind energy systems with the

power grid. The major drawback of VC schemes is that their performance relies heav-

ily on accuracy of machine parameters such as stator, rotor resistances and inductances.

Thus when actual parameters changes due to ageing, temperature as well as wear and

tear, performance of the control scheme degrades.

As a substitute for VC schemes of induction machines, Direct Torque Control (DTC)

schemes for the control of induction motors in [26], [27], Direct Power Control (DPC)

schemes for three-phase Pulse-Width Modulated (PWM) rectifiers in [28], [29] and for

the control of DFIG in [30], [31] were proposed. In these techniques, current control loop

is eliminated and the control signal or the output voltage is directly selected from look-up

table to control combination of torque and flux in DTC schemes and combination of ac-

tive and reactive power in DPC schemes during the sample time. The main advantages of

DTC/DPC methods are minimal use of machine parameters, enhanced transient response

and simple control structure. Nevertheless, there is always significant torque/power ripple

due to the high bandwidth of the controller and converter switching frequency changes

depending upon the operating conditions of the machine. Besides, the controller perfor-

mance may deteriorate during machine starting and low-speed operations. In order to

achieve constant switching frequency of the converter, several modifications were proposed

by various authors in [32], [33], [34], [35], [36], [37], [38], but at cost of compromising the

simplicity and robustness of the basic DPC schemes.

As discussed, wind turbines inherently exhibit nonlinear dynamics and are exposed to

large cyclic disturbances that may excite the poorly damped vibration modes of drive-

train and tower. Furthermore, accurate mathematical models describing their dynamic

behaviour are difficult to obtain because of the particular operating conditions. In view of

this, many researchers have paid much attention on designing nonlinear control schemes

which are simple in nature and robust enough to plant parameter uncertainties and ex-

ternal disturbances. Variable Structure Control (VSC) or Sliding Mode Control (SMC)

strategy is an effective and high-frequency switching control for nonlinear systems with

uncertainties [39]. The well-known property of VSC is that the discontinuous feedback

control switches on one or more manifolds in the state space. Thus the structure of the

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feedback system is altered or switched as the state crosses the discontinuous surface [40].

It features good robustness and operates effectively over a specified magnitude range of

system parameter variations and disturbances without any on-line identification of the

system parameters as in the case of adaptive control [41]. The design principle of SMC

and its applications to electrical drive systems were initially proposed by [42]. DTC

scheme based on SMC theory for induction machine was proposed by [43] and [44]. In

order to take advantage of SMC’s invariant property to disturbances, researchers have

laid sincere efforts to develop control strategies based on SMC and its variant for grid-

connected DFIG in WECS. A dynamical SMC based approaches were proposed by [45]

and [46] to regulate power of Double Output Induction Generator (DOIG) driven by

VSWT similar to classical static Kramer drive in two regions; normal and stall regions.

Wind energy systems produce the transient aerodynamic loads and thus the stresses on

the drive train, tower structure due to highly perturbed environment of stochastic wind

signal. A SMC approach based on integral compensation to reduce chattering was pro-

posed by [47] to provide tradeoff between power maximization and torque smoothing for

control of variable speed DOIG. Similarly, various researchers in [48], [49] and [50] used

sliding mode VC strategies for controlling rotor current components of the DFIG run by

VSWT to regulate torque and DFIG rotor speed for optimum wind power extraction. In

[48], sliding surface was designed according to imposed tradeoff between torque ripple and

tracking of optimal power.

A cascaded nonlinear SMC system for optimal extraction of wind power was proposed

in [51] to control torque and rotor flux of DFIG equipped by VSWT. In order to reduce

chattering, the signum function in the sliding mode control law was replaced by smooth

approximation using hyperbolic tangent sigmoid function. In presence of rotor and stator

resistances uncertainties, SMC scheme in [51] achieve a good tracking performance of rotor

flux and torque. However, variation in mutual induction of DFIG was not considered in

addition to variation in resistances to prove the robustness of the SMC scheme. Similarly,

combining the advantages of basic DPC scheme, SVM and SMC, DPC based on First-

Order Sliding Mode (FOSM) control scheme was proposed by [52] in stator stationary

reference frame to get ride of the complexity of vector orientation similar to VC schemes.

Simple sliding surfaces were adopted based on the differences between reference and actual

stator active and reactive powers. The basic problem associated with the FOSM control

or SMC scheme is that the controlled quantity may exhibit undesired chattering. The

8

chattering may excite unmodeled high-frequency system transients and even result in

unforeseen instability. To eliminate chattering due to fast switching, a boundary layer

around the sliding surface was introduced in [52]. Any effort to reduce chattering either

by smoothing the control function or using boundary layer around sliding surface will

reduce chattering but at a cost of robustness and accuracy [53]. Moreover, the smooth

control function cannot provide finite-time convergence of sliding variable to zero in the

presence of external disturbance [54], [55].

The inherent difficulties of FOSM control can be attenuated by Second-Order Sliding

Mode (SOSM) controllers. SOSM controllers drive the sliding variable and its first time

derivative to zero. SOSM approach suggests treating the chattering effect using a time

derivative of control as a new control [54]. Thus, high frequency control switching is hidden

in the higher derivative of the sliding variable [54]. Based on the this idea, a few SOSM

control approaches have been introduced for the control of wind turbine in [56], [57], for the

control of power converters in [58] for DFIG-based VSWT and for variable-speed WECS

based on Brushless Doubly-Fed Reluctance Machine (BDFRM) in [59]. SOSM control

schemes were proposed to regulate the d-axis and q-axis rotor currents or d-axis rotor

current and electromagnetic torque in Stator Flux Oriented (SFO) synchronous reference

frame for the RSC of DFIG driven by marine current turbine in [60] and wind turbine

in [58], [59]. Super-Twisting Algorithm (STA) based on SOSM was used to derive the

control law in [37] and [58] to regulate the rotor current components. The information

required for implementing the SOSM control algorithm is knowledge of sliding surface

and its first-time derivative [58]. The exception is Super-twisting Algorithm (STA) which

only needs information of sliding surface. STA is a continuous controller which attenuates

the chattering and ensures all the main properties of FOSM control for the system with

smooth matched bounded uncertainties/disturbances with bounded gradients.

These converters’ control strategies proposed by [48], [49], [50], [58], [60] and [59] require

synchronous coordinate transformation associated with the angular information of stator

flux or voltage similar to VC [14], [15] and predictive DPC [36], [37] schemes. Additionally

similar to VC schemes, outer control loop for active and reactive powers is required to

generate the reference values of d-axis and q-axis rotor currents.

In [61], Variable Gain Super-Twisting (VGST) algorithm designed by Lyapunov function

based on SOSM strategy is used to control the speed of grid-connected DOIG driven by

VSWT. Reduced order model of the WECS is used and GSC is controlled to vary the

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speed of the generator with slip power recovery to extract optimum power from the wind

turbine and transfer it to the grid. In continuation with the work in [61], VGST algorithm

was proposed to regulate stator active power in both zones of operation of WECS (i.e. in

partial load and full load zones) and stator reactive power as per the grid demand in [62].

Similarly, VGST algorithm based SOSM control is applied to regulate d-axis and q-axis

stator current components as well as rotor speed in [63] for VSWT driven by permanent

magnet synchronous generator. The advantage of the VGST algorithm as compared to

Fixed-Gain ST (FGST) algorithm is reduced control effort associated with the adaptive

characteristics of the variable gains of the controller with similar simplicity in implemen-

tation and operation of the controller. But the proposed controller in [62] requires rotor

current decoupling in d-axis and q-axis in order to regulate stator active and reactive

power in SFO synchronous reference frame similar to VC schemes which are complex in

nature. Similarly, stator current decoupling along d-axis and q-axis is required to regulate

d-axis stator current component and generator torque in [63].

3. Motivation, Objective and Scope

Control of grid-connected DFIG system in wind energy conversion system is a challenging

task as the system is nonlinear having a highly perturbed environment. Higher annual

energy generation, damping of aerodynamic loads and stresses as well as improved power

quality delivered to the grid are certain advantages of variable speed configuration of wind

turbine in comparison with the fixed speed wind turbine configuration. Control of speed

of wind turbine is essential to fully achieve the advantages of variable speed wind turbine

topology. It is worth to mention here that control scheme for the DFIG must be simple

in implementation. Due to nonlinearities, parametric uncertainties involved in the plant,

apparent grid and environmental disturbances, SMC emerged to be promising solution

due to its invariance properties to disturbances and parametric uncertainties. SOSM con-

trol, inheriting all the advantages of first-order sliding mode further reduces chattering

without compromising the robustness. SOSM approaches for the control of rotor current

components (along d- and q-axis) in synchronously rotating reference frame have been

extensively used for indirect regulation of stator active power (or torque of DFIG) and

stator reactive power similar to complex VC schemes. On the contrary and as per the

authors best knowledge, development of a direct power control scheme to regulate stator

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active and reactive powers independently in stationary reference frame using SOSM ap-

proach remained to be an open issue to be investigated. Modeling of DFIG based wind

generation system and application of control strategy in stationary reference frame elim-

inate the complexities of VC schemes. This motivates the authors to carry out DFIG

modeling and presenting its control scheme in stationary reference frame to regulate the

stator powers in wind energy conversion system employing VSWT topology to realize the

objectives.

This thesis presents robust Second-Order Sliding Mode (SOSM) scheme based on recently

developed Super-Twisting Algorithm (STA) for direct control of stator active and reactive

power of grid-connected DFIG in stationary reference frame with two-fold objectives. The

stator active power is controlled for optimization of extracted wind power by varying the

speed of DFIG (and thus the speed of wind turbine) between the minimum and rated

wind speed of wind turbine. The stator reactive power of the DFIG is controlled as per

the grid demand.

The proposed control scheme can be further used to deal with the power system issues

related to grid integration of DFIG-based VSWT topology, Low Voltage Ride Through

(LVRT) performance and follow the country specific grid codes for frequency and voltage

support since the rising integration of wind power in the utility grid demands more con-

straining requirements of connection.

4. Summary of the Research Work

This thesis contributes mainly following:

� Mathematical model of an entire WECS incorporating 5 kW VSWT, drive train,

DFIG, PE converters and grid is developed in MATLAB/Simulink environment.

Out of the two PE converters, Grid Side Converter (GSC) is controlled by Grid

Voltage Oriented Vector Control (GVOVC) scheme.

� The main control of the DFIG is through the rotor which is connected to the PE

converter known as Rotor Side Converter (RSC). The stator active and reactive

powers of the DFIG are controlled by the Look-up Table (LUT)-based DPC and

First-Order Sliding Mode (FOSM)-based DPC schemes in stationary reference frame

of the DFIG to maximize the wind power extraction when the wind speed changes.

11

In LUT-based DPC scheme, inverter switching vectors are selected from the optimal

look-up table using rotor flux position and errors of stator active and reactive powers.

In FOSM-based DPC scheme, the condition for the stability of the closed loop system

using control law is derived using Lyapunov approach. Boundary layer around the

sliding surface is used to reduce chattering. Simulation results by both the control

schemes are compared for possible reduction in chattering in the controlled quantities

by FOSM-DPC scheme and rotor current harmonic spectra.

� The above FOSM controller is using boundary layer around the sliding surface to

reduce chattering. But the chattering is reduced at the cost of compromise of ro-

bustness of the controller scheme to uncertainties and disturbances. To maintain

invariance properties of FOSM control and attenuate chattering in the controlled

quantity, SOSM-DPC scheme using STA is proposed to regulate DFIG’s stator ac-

tive and reactive powers directly in stationary reference frame. Again, the closed loop

stability is proved using Lyapunov function. The efficacy and dynamic performance

of the proposed controller are proved by simulation results which are compared with

those gained by LUT-based DPC and FOSM-based DPC schemes. The robustness

of the STA-based SOSM-DPC scheme is endorsed by simulation results showing

the dynamic performance of the control scheme during ramp change in DFIG rotor

speed as an external perturbation and for different combinations of DFIG parameter

variations by giving step variation in stator active and reactive powers.

� The proposed STA-based SOSM-DPC scheme is having fixed controller gains. Ex-

tending this work, Variable Gain STA (VGSTA)-based SOSM-DPC scheme is pro-

posed to regulate stator active power for optimization of extracted wind power and

stator reactive power following the grid requirements. Adaptive characteristics of

the gains of the controller together with the inherited robustness property of SMC

are used together to attenuate chattering in controlled quantities and to provide ro-

bust controller for such a highly disturbed environment of WECS. The closed loop

stability of the systems controlled by proposed scheme using VGST algorithm is

proved using Lyapunov approach. The efficacy and the dynamic performance of the

proposed control scheme are endorsed by comparing simulation results with those

obtained by FOSM-DPC scheme in the absence as well as in the presence of grid

voltage unbalance and DFIG parametric uncertainties. Robustness of the proposed

control scheme is evaluated during ramp change in the DFIG rotor speed as an ex-

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ternal perturbation and for different combinations of DFIG parameter variations by

giving step variation in stator active and reactive powers.

� Further, Extended State Observer (ESO)-based FOSM-DPC scheme is proposed to

attenuate the effect of disturbances on the control system. ESO estimates the state

variables and lumped disturbances in the system. These estimated state variables

which are free from disturbances are fed back for the design of control algorithm.

This approach attenuates the effect of disturbances on the control system. The ef-

ficacy of the ESO-based FOSM-DPC strategy is demonstrated by comprehensive

simulations for optimum wind power extraction during step variations of wind speed

and reactive power. These results are compared with FOSM-DPC scheme without

ESO in the absence and presence of disturbances and uncertainties.

5. Proposed Contents of the Thesis

The outline of the thesis is as follows:

� Chapter − 1 briefs about the main components of grid-connected WECS and

presents a survey on past work on control schemes for grid-connected DFIG sys-

tem. The survey is essentially on a literature concerned with the aspects of control

schemes for induction motor and grid-connected DFIG.

� Chapter − 2 discusses and compares the briefly fixed-speed and variable-speed

WECS topologies and their components. This chapter describes the modeling of the

grid-connected DFIG based WECS in MATLAB/Simulink environmentr. GVOVC

scheme used to control GSC is outlined and discussed in this chapter.

� Super-Twisting Algorithm (STA)-based Second-Order Sliding Mode (SOSM)-Direct

Power Control (DPC) scheme in stationary reference is proposed in Chapter − 3

for the regulation of stator active and reactive power in grid-connected DFIG. The

stator active power is controlled for optimization of extracted wind power by varying

the speed of DFIG (and thus the speed of wind turbine) below the rated wind speed

of wind turbine. The stator reactive power of the DFIG is controlled as per the

grid demand. The stability of the closed-loop system using proposed SOSM control

law is proved using quadratic Lyapunov function which ensures finite convergence

of the system states within the specified band. Comprehensive simulation results

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are presented on 5 kW DFIG system and the performance of the control scheme

is compared with Look-up Table (LUT)-based DPC scheme, First-Order Sliding

Mode (FOSM)-based DPC scheme in stationary reference frame. The results are

compared for dynamic performance during the step regulation of stator active and

reactive power in constant speed mode, amount of chattering in controlled quantity

and rotor current harmonic spectra. Further, robustness of the proposed control

scheme is shown in this chapter during simultaneous ramp change in DFIG rotor

speed from sub-synchronous to super-synchronous, active and reactive power steps

and DFIG parametric uncertainties. Moreover, the efficacy of the proposed controller

in tracking Maximum Power Point (MPP) for an entire WECS is tested for step

change in wind speed for extraction of optimum wind power.

� Chapter− 4 concerns about extending work presented in Chapter− 3 by employ-

ing variable-gain alternative of fixed-gain STA due to its adaptive characteristics in

reducing the chattering in controlled quantity. It is essentially related to the imple-

mentation of Variable Gain STA (VGSTA)-based SOSM-DPC scheme in stationary

reference frame for grid-connected DFIG. The proposed VGSTA-based controller

scheme is designed using Lyapunov function. At first, the chattering reduction and

faster dynamic response by the proposed controller scheme in regulation of stator

active and reactive power of DFIG is demonstrated and compared with those by

FOSM-DPC scheme during balanced grid voltage and absence of DFIG parametric

uncertainties. Later, similar performance is tested in the presence of DFIG paramet-

ric uncertainties and unbalance in grid voltage. Additionally, simulation results are

carried out to prove the robustness of the proposed controller scheme in the presence

of ramp change in DFIG rotor speed from sub-synchronous to super-synchronous,

active and reactive power steps, different combination of unbalance in grid voltage

and DFIG parametric uncertainties.

� Chapter−5 describes the design of Extended State Observer(ESO)-based on FOSM-

DPC scheme for the grid-connected DFIG system. In this chapter, ESO is proposed

to estimate the state variables and lumped disturbances in a system. These estimated

state variables which are free from the disturbances are fed back for the design of

FOSM-DPC scheme. The Lyapunov approach is used to demonstrate the stability of

closed-loop system. Simulation results are carried out on 5 kW DFIG system in the

presence of unbalance in grid voltage variation and DFIG parametric uncertainties to

14

prove the efficacy of the proposed ESO in attenuating the effect of the disturbances,

thus improving the dynamic performance of the FOSM-DPC scheme.

� Finally, Chapter − 6 serves as a conclusion. It contains a summary of the thesis

and final comments on the work proposed. It tries to point out the possible course

of future work on implementation of the SOSM-DPC scheme in stationary reference

frame for the operation of grid-connected DFIG system dealing with various power

system issues which still remain unsolved.

6. Conclusion

This thesis is concerned with the control of electrical power generation supplied to the

grid or network in wind energy conversion system. We summarize here the principal con-

clusions and some of the key contributions of this work. As stated previously, the aim

of the work is to present robust SOSM scheme based on STA for direct control of sta-

tor active and reactive power of grid-connected DFIG in stationary reference frame with

two-fold objectives. The stator active power is controlled to operate the DFIG such that

wind turbine runs on its MPP curve to extract the optimum power from the wind and

transfer it to the grid. The stator reactive power is controlled as per the grid demand.

On the basis of the work presented in this thesis, following can be concluded.

� There is a definite trend towards the use of Variable Speed Wind Turbine (VSWT)

topology as compared to its fixed-speed counterpart in wind power generation due to

more annual energy capture, increased life of the structure due to less aerodynamic

loads and stresses in drive-train as well as in the structures.

� DFIG due to its limited but variable speed operation is better suited for VSWT

topology due to reduced size of PE converters (20% to 30% of the size of wind

turbine), four quadrant active and reactive power capability. Controllability of active

and reactive power enables the overall system work as an active source of energy

giving wind turbine a conventional power plant like characteristics.

� VC schemes are still prevailing having decoupled control of torque and reactive power

or stator active/reactive power of DFIG. But these are indirect control schemes

and involve rotor current decoupling in d-axis and q-axis in synchronously rotating

15

reference frame. These schemes are complex in nature due to involvement of complex

synchronous coordinate transformation.

� Prime control of the DFIG in this thesis for the stated objectives is attained through

control of PE converter which is connected to the rotor terminals of the DFIG, which

is known as Rotor Side Converter (RSC). Initially, RSC is controlled by three control

schemes. The simulation results are compared for dynamic performance during step

regulation of stator active and reactive power in constant speed mode, rotor current

harmonic spectra.

– Look-Up Table (LUT)-based DPC scheme using rotor flux vector position.

– FOSM-DPC scheme in stationary reference frame.

– SOSM-DPC scheme using STA in stationary reference frame.

It is concluded that,

� SOSM-DPC scheme provides enhanced transient performance similar to LUT-based

DPC scheme.

� The implementation of proposed SOSM-DPC is simple as it is formulated in station-

ary reference frame. It does not involve rotor current decoupled control, synchronous

coordinate transformation similar to VC schemes. Among the several SOSM algo-

rithms, super-twisting algorithm (STA) is used as it needs only the information of

sliding manifold or switching surface. This further eases the design of controller

strategy.

� The SOSM approach attenuates chattering in the stator active and reactive powers

as compared to LUT-DPC. The general approach to reduce chattering in SMC is to

use saturation function or boundary layer around the sliding surface. To attenuate

the chattering in stator active power and reactive power, boundary layer is used in

FOSM-DPC scheme. But literature suggests that this approach reduces chattering

in the controlled quantity at a cost of robustness to small disturbances as system

states are no longer confined to switching surface but in a small vicinity around it.

It is shown in the simulation results that SOSM-DPC scheme attenuates chatter-

ing in stator active and reactive power without using boundary layer maintaining

robustness to parametric uncertainties.

� In contrast to decoupled and indirect control of stator active and reactive powers

found in VC schemes, control of both the stator powers are not decoupled to par-

16

ticular components of rotor voltage (along α-axis or β-axis). Nevertheless, effect of

change in stator active or reactive power has a negligible effect on the other.

� To prove the robustness of the proposed scheme, different combination of DFIG

parameter variations are taken into consideration. Simulation results corroborate

the robust performance of proposed STA based SOSM-DPC scheme which effectively

tracks step variation of active and reactive power even during ramp change in DFIG

rotor speed and having such large DFIG parametric variations.

� Maximum power point (MPP) tracking performance during step change in wind

speed by the proposed controller scheme is satisfactory. Simulation results show

that there is almost negligible effect of change in stator active power (due to change

in wind speed) on the regulation of stator reactive power and vice a versa.

� Besides, proposed SOSM-DPC scheme generates pulses for RSC by Sinusoidal Pulse-

Width Modulation (SPWM) technique. It can be seen that harmonic spectra in rotor

current remain centered around the switching frequency (1 kHz) of the converter and

its multiples similar to FOSM-DPC scheme. Whereas, broadband harmonics can be

seen in rotor current harmonic spectra generated by LUT-DPC as the switching

frequency is variable and depends upon operating conditions.

The above approach is based on STA having fixed gain. Variable gain alternative of the

proposed STA-based SOSM-DPC scheme is proposed as variable gains render the sliding

surface insensitive to perturbations growing with bounds by known functions. Moreover

the adaptive characteristics of the proposed Variable Gain STA (VGSTA) based SOSM-

DPC scheme reduces chattering in the controlled quantity. The efficacy of VGSTA based

SOSM-DPC scheme is proved by comparing the simulation results with those obtained

by FOSM-DPC scheme having similar sliding manifold. The closed loop stability of

the systems controlled by both VGSTA based SOSM-DPC and FOSM-DPC schemes

are proved using Lyapunov approach and both the controller schemes are formulated in

stationary reference frame to maintain the simplicity in implementation. It is found that,

� VGSTA based SOSM-DPC scheme effectively controls stator active power in re-

sponse to change in wind speed by varying the speed of DFIG for optimum extraction

of wind power.

� Similarly, tracking of stator reactive power by the proposed control strategy is quite

satisfactory.

17

� Even in the absence of disturbances and parametric uncertainties, the proposed con-

troller scheme reduces chattering in stator active power and DFIG electromagnetic

torque as compared to those obtained by FOSM-DPC scheme. Faster tracking per-

formance can be seen during step regulation of stator reactive power as compared to

that obtained by FOSM-DPC scheme.

� During unbalance in grid voltage and DFIG parametric uncertainties, the poor dy-

namic performance and increased amount of chattering can be seen in the stator

active power controlled by FOSM-DPC scheme. The same is reflected in electromag-

netic torque of DFIG. Due to variability of controller gains, the proposed VGSTA

based SOSM-DPC scheme attenuates chattering, improves the tracking behaviour

which shows robust performance to external perturbations and model parameter

variations.

Apart from SOSM control approach to attenuate the chattering or to reduce the main

drawback of FOSM control, Extended State Observer (ESO) based approach is utilized

to enhance the performance of FOSM controller, particularly during imbalances in grid

voltage and parametric uncertainties. The simulation results are carried out and it is seen

that,

� ESO observes the states very effectively and works as a patch to existing FOSM-DPC

scheme which do not require considerable changes in the design.

� Even in the case of balanced grid voltages and no parametric uncertainties, ESO

based FOSM-DPC scheme attenuates the chattering in stator active power as com-

pared to FOSM-DPC scheme without ESO.

� In the presence of imbalances in grid voltages and parametric uncertainties, the dy-

namic performance of ESO based FOSM-DPC scheme is satisfactory. High frequency

chattering in stator active power and DFIG torque are almost reduced by 73% as

compared to FOSM-DPC scheme.

18

Patent, Publications and Acknowledgements

� Indian Patent

1. A J Mehta, A P Shah, H A Mehta, Direct Power Control of Grid-Connected DFIG

Using Variable Gain Super-Twisting Sliding Mode Controller for Wind Energy Optimiza-

tion, Application No. 201721015487, May, 2017.

� Papers in Referred Journals

1. A P Shah and A J Mehta, Extended State Observer Based Sliding Mode Direct Power

Control of Grid-Connected DFIG, Asian Journal of Control, Wiley Interscience, Under

Review.

� Presentations in Conferences

1. A P Shah and A J Mehta, Direct Power Control of DFIG Using Super-twisting Algo-

rithm Based on Second-order Sliding Mode Control, 14th IEEE International Workshop

on Variable Structure Systems (VSS 2016), Nanjing, China. (ISBN-978-1-4673-9787-2),

pp. 136-141, Jun. 1-4, 2016.

2. A P Shah and A J Mehta, Direct Power Control of Grid-Connected DFIG Using

Variable Gain Super-twisting Sliding Mode Controller for Wind Energy Optimization,

43rd Annual Conference of the IEEE Industrial Electronics Society, (IECON 2017),

Beijing, China, Oct. 29−Nov. 1 2017.

� Acknowledgements

1. Received International Travel Support from Science and Engineering Research Board

(SERB), New Delhi of Rs. 62,586/- (Application No.: ITS/815/2016-17) to present the

research paper in 14th IEEE International Workshop on Variable Structure Systems (VSS

2016), Nanjing, China, June 2016.

19

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