Modeling of Wind Farms in the Load Flow Analysis

Modeling of Wind Farms in the Load Flow Analysis

Project report

Submitted in partial fulfillment of the

Requirements for the award of the degree

of

Bachelor of Technology

In

Electrical Engineering

by

1. Rahul Syal (20108011)

2. Vivek Sisaudia (20108017)

3. Vikalp Dhiman (20102005)

4. Pranjal Mishra (20108090)

5. Prashant Srivastava(20102076)

Guided

by

Dr. Asheesh Kumar Singh

DEPARTMENT OF ELECTRICAL ENGINEERING

MOTILAL NEHRU NATIONAL INSTITUTE OF TECHNOLOGY-ALLAHABAD

1

MOTILAL NEHRU NATIONAL INSTITUTE OF TECHNOLOGY

ALLAHABAD

DEPARTMENT OF ELECTRICAL ENGINEERING

CERTIFICATE

We hereby certify that the work which is being presented in this project report

Modeling of Wind Farms in the Load Flow Analysis in partial fulfillment of the requirements

for the award of the Degree of Bachelor of Technology in Electrical Engineering and submitted

in the Department of Electrical Engineering of Motilal Nehru National Institute of Technology

Allahabad is an authentic record of our own work carried out during a period from July 2013 to

May 2014 under the guidance of Dr. Asheesh K.Singh.The matter presented in this project

report has not been submitted by us for the award of any other degree of this or any other

institution.

Submitted by:

1. Rahul Syal (20108011)

2. Vivek Sisaudia (20108017)

3. Vikalp Dhiman (20102005)

4. Pranjal Mishra (20108090)

5. Prashant Srivastava

(20102076)

Project Guide :

Dr. Asheesh K.Singh

2

Associate Professor

Electrical Engineering

Department

Acknowledgement

We would like to articulate our deep gratitude to our project guide Dr. Asheesh K.

Singh, Associate Professor, Electrical Engineering Department who has always been source

of motivation and firm support for carrying out the project. We express our gratitude to Dr.

Asheesh K. Singh, Associate Professor,Electrical Engineering Department for his invaluable

suggestion and constant encouragement all through the thesis work. We would also like to

convey our sincerest gratitude and indebtedness to all other faculty members and staff of

Department of Electrical Engineering, MNNIT, Allahabad who bestowed their great effort

and guidance at appropriate times without which it would have been very difficult on our

project work. An assemblage of this nature could never have been attempted with our

reference to and inspiration from the works of others whose details are mentioned in

references section. We acknowledge our indebtedness to all of them. Further, we would like

to express our feeling towards our parents and God who directly or indirectly encouraged and

motivated us during this dissertation.

3

Abstract

The purpose of this project is to Modeling of Wind Farms in the Load Flow Analysis. Two

methods are proposed, for the simulation of wind farms with asynchronous generators in the

load flow analysis. Both methods are based on the steady-state model of the induction

machine. The first involves improving the conventional PQ bus, and the second involves

modeling the generators in steady-state in the bus where the wind farm is located. The two

sets of results are then compared.

When the conventional PQ bus model is used, the real and reactive powers have constant

values, although some authors propose methods for modifying these values in order to

represent loads depending either on the voltage or on the frequency. When the PX bus model

is used, the real power is known and the reactive power is calculated as a function of the

magnetizing reactance of the generators.

Both methods suppose prior knowledge of the WT features. The turbine’s power curve is

generally supplied by the manufacturer. When the induction generator parameters are not

known, they must be estimated. One of the problems that wind energy will create in electrical

power systems is the dependence of the injected power on the wind speed. The wind speed

cannot he predicted, but the probability of a particular wind speed occurring can be estimated.

This can be done if the probability distribution is known by assuming it to be a Wei-bull

distribution.

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Certificate of Non plagiarism

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and am aware that there is further information available in the form of the Student Plagiarism

and Academic Misconduct: Coursework Policy, the document Avoiding Plagiarism and

Academic Misconduct the relevant sections on plagiarism provided in the Referencing Guide

To the best of my knowledge and belief, this assessment task is my own work, all sources have

been properly acknowledged, and the assessment task contains no plagiarism.

I have not previously submitted this work or any version of it for assessment in any other unit

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Date of signing: _______________________________________________________

5

Table of Content

Title 1

Certificate 2

Acknowledgement 3

Abstract 4

Certificate of Non plagiarism 5

Table of content 6

Chapter 1: WIND ENERGY- AN OVERVIEW 8

1.1 Wind energy in India 8

1.2 Economy of wind energy in India 9

1.3 Wind farms in India 10

Chapter 2: FUNDAMENTALS OF WIND TURBINES. 12

2.1 Power contained in the wind 12

2.2 Power Speed Characteristics 13

2.3 WEI-BULL Distribution 15

Chapter 3: WIND TURBINE CONTROL SYSTEMS 17

3.1 Pitch Angle Control 17

3.2 Stall Control 18

3.3 Power Electronic Control 18

3.4 Yaw Control 19

3.5 Control Strategy 20

6

Chapter 4: GRID CONNECTED AND ASYNCHRONOUS GENERATOR (DFIG)

FOR WIND TURBINES

4.1 Model of Wind Turbine 25

4.2 Generator Model 26

4.3 Requirement of the load flow analysis 28

4.4Loadflow models considered (with flow charts) 31

4.5 AC load flows and their drawbacks 36

4.6 Genetic Algorithm Approach for Solving AC DC Optimal Power

Flow

42

4.7 AC/DC load flow

43

Chapter 5: MODELS OF ASYNCHRONOUS WIND TURBINES

5.1 INTRODUCTION 46

5.2 VARIOUS TYPES OF WTGUs

50

Chapter 6: SIMULATION AND RESULT

6.1 MODELING OF THE POWER IN THE WIND POWER SYSTEM

6.2 SIMULATION 61

6.3 RESULT 63

DISCUSSION

CONCLUSION

REFERENCES

7

CHAPTER 1

WIND ENERGY- AN OVERVIEW

INTRODUCTION

The conventional energy sources are limited and pollute the environment. So more attention

and Interest have been paid to the utilization of renewable energy source such as Wind

Energy, Fuel-cell, Solar Energy etc., Wind Energy is the fastest growing and most

promising renewable Energy source among them as it is economically viable.

1.1 WIND ENERGY IN INDIA

In 2008, India was the country that brought online the third largest amount of wind energy,

after the US and China, and it now ranks fifth in total installed capacity with 9,645 MW

of wind power installed at the end of 2008. A strong domestic manufacturing base has

underpinned the growth of the Indian wind energy market. The Indian wind turbine

manufacturer Suzlon is now a recognized player on the global market and many international

companies are established in India. India has a great untapped potential for wind energy. A

strong domestic manufacturing base has underpinned the growth of the Indian wind energy

market. India has a great untapped potential for wind energy. According to official estimates,

the Country's total wind energy resource amounts to 48 GW of installed capacity, but some

experts think that this figure is on the conservative side, and that technological

improvements could significantly increase this potential. The positive development of wind

energy in India has mainly been driven by progressive state level legislation, including policy

measures such as renewable portfolio standards and feed -in-tariffs. At the moment, there is

no coherent national renewable energy policy to drive the development of wind energy.

This is urgently needed to realize the country’s full potential and reap the benefits for both the

environment and the economy. The Government of India is currently considering the

8

introduction of a national renewable energy policy, so this report comes as a timely

reminder of how important a role wind energy could play in securing India’s energy

security, curbing its CO2 emissions, providing new employment and boosting economic

development. This also realizes how important a role wind energy could play in

securing India's energy security, curbing its CO2 emissions, providing new employment

and boosting economic development. As can be seen by the Indian Wind Energy

Outlook, the wind industry, both domestic and international, stands ready to do its part in

achieving an energy revolution in India.

1.2 ECONOMY OF WIND ENERGY IN INDIA

In the early 1980s, the Indian government established the Ministry of Non-Conventional

Energy Sources (MNES) to encourage diversification of the country's energy supply, and

satisfy the increasing energy demand of a rapidly growing economy. In 2006, this ministry

was renamed the Ministry of New and Renewable Energy (MNRE). Renewable energy is

growing rapidly in India. With an installed capacity of 13.2 GW, renewable energy sources

(excluding large hydro) currently account for 9% of India's overall power generation capacity.

By 2012, the Government of India is planning to add an extra 14 GW of renewable resources in

its 10th Five Year Plan. The Government of India had set itself a target of adding 3.5 GW of

renewable energy sources to the generation mix. In reality, however, nearly double that figure

was achieved. In this period, more than 5.4 GW of wind energy was added to the

generation mix, as well as 1.3 GW from other Resources.

The Indian Ministry of New and Renewable Energy (MNRE) estimates that there is a potential

of around 90,000 MW for the country, including 48,561 MW of wind power, 14,294

MW of small hydro power and 26,367 MW of biomass In addition, the potential for

solar energy is estimated for most parts of the country at around 20 MW per square

kilometer of open, shadow free area covered with 657 GW of installed capacity.

1.3 WIND POTENTIAL

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The total potential for wind power in India was first estimated by the Centre for Wind Energy

Technology (C-WET) at around 45 GW, and was recently increased to 48.5 GW. This figure was

also adopted by the government as the official estimate. The C-WET study was based on a

comprehensive wind mapping exercise initiated by MNRE, which established a country-wide

network of 105O wind monitoring and wind mapping stations in 25 Indian States. This effort

made it possible to assess the national wind potential and identify suitable areas for

harnessing wind power for commercial use, and 216 suitable sites have been identified.

However, the wind measurements were carried out at lower hub heights and did not take into

account technological innovation and improvements and repowering of old turbines to replace

them with bigger ones at heights of 55-65 meters, to replace them with Bigger ones. At heights

of 55-65 meters, the Indian Wind Turbine Manufacturers Isolation (IWTMA) estimates that the

12 potential for wind development in India is around 65-70 GW. The World Institute for

Sustainable Energy, India (WISE) considers that with larger turbines, greater land

availability and expanded resource exploration, the potential could be as big as 100 GW.

Wind power in India has been concentrated in a few regions, especially the Southern state of

Tamil Nadu, which maintains its position as the state with the most wind power, with 4.1 GW

installed at the end of 2008, representing 44% of India’s total wind capacity.

1.4 WIND FARMS IN INDIA

1. Muppandal–Perungudi (Tamil Nadu) With an aggregate wind power capacity of 450

MW, the Muppandal–Perungudi region near Kanyakumari in Tamil Nadu has the

distinction of having one of the largest clusters of wind turbines. About Rs 2500 crores has

been invested in wind power in this region.

2. KavdyaDonger, Supa (Maharashtra)

A wind farm project has been developed at Kavdya Donger at Supa, off the Pune–Ahmednagar

highway, about 100 km from Pune. This wind farm has 57 machines of 1-MW capacity each.

Annual utilization capacity of up to 22% has been reported from this site. The farm is

10

connected through V-SAT to project developers as well as promoters for online performance

monitoring.

3. Satara district (Maharashtra) Encouraging policy for private investment in wind power

projects has resulted in significant wind power development in Maharashtra, particularly in

the Satara district. Wind power capacity of about 340 MW has been established at

Vankusawade, Thosegarh, and Chalkewadi in Satara district, with an investment of about

Rs.1500 crores.

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CHAPTER 2:

FUNDAMENTALS OF WIND TURBINES

2.1 Power in the wind.

Wind energy is not a constant source of energy. It varies continuously and gives energy in

sudden bursts. About 50% of the entire energy is given out in just 15% of the operating time.

Wind strengths vary and thus cannot guarantee continuous power. It is best used in the

context of a system that has significant reserve capacity such as hydro, or reserve load,

such as a desalination plant, to mitigate the economic effects of resource variability. The total

capacity of wind power on this earth that can be harnessed is about 72 TW. There are now

many thousands of wind turbines operating in various parts of the world, with utility

companies having a total capacity of 59,322 MW. The power generation by wind energy was

about 94.1GW in 2007 which makes up nearly 1% of the total power generated in the world.

Globally, the long-term technical potential of wind energy is believed to be 5 times

current global energy consumption or 40 times current electricity demand. This would require

covering 12.7% of all land area with wind turbines. This land would have to be covered with 6

large wind turbines per square kilometer. The power extracted from the wind can be

calculated by the given formula:

P=0.5× ρ×A×V 3×CP (1)

P= extracted power from the wind,

ρ = air density, (approximately 1.225 kg/m3at 20₀C at sea level)

V= wind velocity (m/s) (velocity can be controlled between 3 to 30 m/s)

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CP =the power coefficient which is a function of both tip speed ratio, and blade pitch angle,

Power coefficient (CP ) is defined as the ratio of the output power produced to the power

available in the wind.

Betz Limit:

No wind turbine could convert more than 59.3% of the kinetic energy of the wind into

Mechanical energy turning a rotor. This is known as the Betz Limit, and is the

theoretical Maximum coefficient of power for any wind turbine. The maximum value of CP

according to Betz limit is 59.3%. For good turbines it is in the range of 35-45%.

2.2. Types of Wind energy Conversion Devices.

A wind turbine is a rotating machine which converts the kinetic energy in wind into mechanical

energy. If the mechanical energy is then converted to electricity, the machine is called a wind

generator, wind turbine, wind power unit (WPU), wind energy converter (WEC), or aero

generator. Wind turbines can be separated into two types based by the axis in which the

turbine rotates. Turbines that rotate around a horizontal axis are more common. Vertical-axis

turbines are less frequently used.

1. Horizontal axis wind turbine

a) “Dutch-type” grain grinding windmills.

b) Multi-blade water-pumping windmills.

c) High speed propeller type windmills

2. Vertical axis wind turbine

a) The Savonius rotor.

b) The Darrieus rotor.

2.3 Power speed characteristics:

The wind turbine power curves shown in figure illustrate how the mechanical power that can

be extracted from the wind depends on the rotor speed. For each wind speed there is an

optimum turbine speed at which the extracted wind power at the shaft reaches its maximum.

Such families of Wind turbine power curves can be represented by a single dimensionless

13

characteristic curve namely the CP - curve, as in the figure, where the power coefficient is

plotted against the TSR. For a given turbine, the power coefficient depends not only on the TSR

but also on the blade pitch angle. Figure shows the typical variation of the power coefficient

with respect to the TSR 𝛌 with the blade pitch control. The mechanical power transmitted to

the shaft is—

P=0.5× ρ×A×V 3×CP(2)

Where is the function of TSR 𝛌 and the pitch angle α. For a wind turbine with radius R, it can

be expressed

λ=ω×RV

(3)

The maximum value of the shaft mechanical power for any wind speed can be expressed as

P=0.5×CP×π×(R5

λ3)×ω3

(4)

Thus the maximum mechanical power that can be extracted from the wind is proportional to

the cube of the rotor speed.

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2.4 Wei-bull Distribution-

Wind speed keeps changing hence to define constant power there is a need of probability speed distribution. It is done by Wei-bull or Rayleigh Distribution.

Fig- Probability density function variation with wind speed

Due to the non-linear variation of power with steady wind speed, the mean power obtained over time in a variable wind with a mean velocity Um is not the same as the power obtained in a steady wind of the same speed.

Fig- Power output variation in steady and variable wind

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Fig- Steady wind power curve and wind speed probability density.

The final mean power at a mean wind speed Um is the steady power W(u) multiplied by the

probability density distribution P(u) and summed (i.e. integrated) over all the range of wind

speeds. Thus, the mean power Pm at a mean speed U is given by:

Pm=∫0

∞

P (u ) .W (u) .du

CHAPTER 3

Wind Turbine Control Systems

16

Wind turbines require certain control systems. Horizontal-axis turbines have to be oriented to

face the wind. In high winds, it is desirable to reduce the drive train loads and protect the

generator and the power electronic equipment for overloading, by limiting the turbine power

to the rated value up to the furling speed. At gust speeds, the machine has to be stalled. At

low and moderate wind speeds, the aim should be to capture power as efficiently as possible.

Along with many operating characteristics, the technical data sheet of a turbine mentions its

output at a particular wind speed. This is the minimum wind speed at which the turbine

produces its designated output power. For most turbines, this speed is normally between 9

and 16 m/s. The choice of the rated wind speed depends on the factors related to the wind

characteristics of a given site. The generator rating is best chosen so as to best utilize the

mechanical output of the turbine at the rated wind speed. Wind turbines can have four

different types of control mechanisms, as discussed below:

3.1 Pitch Angle Control:

The system changes the pitch angle of the blades according to the variation of wind speed. As

discussed earlier, with pitch control, it is possible to achieve a high efficiency by continuously

aligning the blade in the direction of the relative wind. On a pitch controlled machine, as the

wind speed exceeds its rated speed, the blades are gradually turned about the longitudinal

axis and out of the wind to increase the pitch angle. This reduces the aerodynamic efficiency of

the rotor, and the rotor output power decreases. When the wind speed exceeds the safe limit

for the system, the pitch angle is so changed that the power output reduces to zero and the

machine shifts to the stall mode. After the gust passes, the pitch angle is reset to the normal

position and the turbine is restarted. At normal wind speeds, the blade pitch angle should

ideally settle to a value at which the output power equals the rated power. The input variable

to the pitch controller is the error signal arising from the difference between the output

electrical power and the reference power. The pitch controller operates the blade actuator to

alter the pitch angle. During operation below the rated speed, the control system endeavors to

the pitch the blade at an angle that maximizes the rotor efficiency. The generator must be able

to absorb the mechanical power output and deliver to the load. Hence, the generator output

power needs to be simultaneously adjusted.

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3.2 Stall Control:

(a) Passive stall control:

This stall control to limit the power output at high winds is applied to constant-pitch

turbines driving induction generators connected to the network. The rotor speed is fixed by

the network, allowing only 1-4% variation. As the wind speed increases, the angle of attack

also increases for a blade running at a near constant speed. Beyond a particular angle of

attack, the lift force decreases, causing the rotor efficiency to drop. This lift force can be

further reduced to restrict the power output at high winds by properly shaping the rotor blade

profile to create turbulence on the rotor blade side not facing the wind.

(b) Active stall control:

In this method of control, at high wind speeds, the blade is rotated by a few degrees

in the direction opposite to that in a pitch controlled machine. This increases the angle of

attack, which can be controlled to keep the output power at its rated value at all high wind

speeds below the furling speed.

A passive controlled machine shows a drop in power at high winds. The action of active stall

control is sometimes called deep stall. Owing to economic reasons, active pitch control is

generally used only with high capacity machines.

3.3 Power Electronic Control:

In a system incorporating a power electronic interface between the generator and load (or the

grid), the electrical power delivered by the generated to the load can be dynamically

controlled. The instantaneous difference between mechanical power and electrical power

changes the rotor speed following the equation

J .dωdt

=Pm−Peω

(6)

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Where J is the polar moment of inertia of the rotor, ω is the angular speed of the

rotor, is the mechanical power produced by the turbine, and is the electrical power delivered

to the load. Integrating, we the above equation, we get:

0 .5×J×(ω22−ω12 )=∫

t1

t2

(Pm−Pe) .dt

(7)

3.4 Yaw Control:

Turbine is continuously oriented along the direction of the wind flow. This is achieved with a

tail-vane in small turbines, using motorized control systems activated either by fan-tail, in case

of wind farms, by a centralized instrument for the detection of the wind direction. It is also

possible to achieve yaw control without any additional mechanism, simply by mounting

the turbine downwind so that the thrust force automatically pushes the turbine in the

direction of the wind.

Speed of the rotor can also be controlled using the yaw control mechanism. The rotor is made

to face away from the wind direction at high wind speeds, thereby reducing the mechanical

power. Yawing often produces loud noise, and it is restriction of the yawing rate in large

machines to reduce noise is required.

3.5 Control Strategy:

Different speed control strategies are required for the five different ranges of wind speed.

a) Power is not generated by the machine below a cut-in speed. Rotation of the machine

may start in this speed range if there is sufficient starting torque. But no power is

generated and rotor rotates freely.

b) Maximum power is extracted from the wind at normal wind speeds. This is

achieved at a particular TSR value. Hence, for tracking maximum power point,

rotational speed is changed continuously proportional to the wind speed.

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c) At high wind speeds, rotor speed is limited to a maximum value which depends on the

design of the mechanical components. Here Cp is lower than the maximum value.

Power output is not proportional to the cube of the wind speed.

d) At even higher wind speeds, output power is kept constant at the maximum value

allowed by the electrical components.

CHAPTER 4

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GRID CONNECTED AND ASYNCHRONOUS GENERATOR FOR WIND

TURBINES

In terms of the generators for wind-power application, there are different concepts in use

today. The major distinction among them is made between fixed speed and variable speed

wind turbine generator concepts. In the early stage of wind power development, fixed-speed

wind turbines and induction generators were often used in wind farms. But the limitations of

such generators, e.g. low efficiency and poor power quality, adversely influence their further

application. With large-scale exploration and integration of wind sources, variable speed wind

turbine generators, such as doubly fed induction generators (DFIGs) and permanent magnetic

synchronous generators (PMSGs) are emerging as the preferred technology. In contrast to

their fixed-speed counterparts, the variable speed generators allow operating wind turbines at

the optimum tip-speed ratio and hence at the optimum power efficient for a wide wind speed

range. As the penetration of wind power increases, integrating large wind farms to power grids

and the relevant influences on the host grids needs to be carefully investigated. So, accurate

and reliable model of variable speed wind turbine generators are urgently needed for power

system simulation analysis. The paper is dedicated to analyzing the complete model of a

variable speed wind turbine with permanent magnet synchronous generator and developing

control schemes for the wind turbine generator. The modeled system consists of a PMSG

model, a pitch-angled controlled wind turbine model and a drive train model.

4.1 Aerodynamic Model

The wind turbine extracts power from wind and then converters it into mechanical power. The

amount of aerodynamic torque is related to the wind speed. The drive train of PMSG consists

of five parts, namely, rotor, low speed shaft, gearbox, high-speed shaft and generator. In the

analysis, other parts of wind turbines, e.g. tower and flap bending modes can be reasonably

neglected. When the interest of study varies the complexity of the drive train differs. For

example, when the problems such as torsional fatigue are studied, dynamics from both sides

of gearbox have to be considered. So, two-lumped mass or more sophisticated models are

required. But when the study focuses on the interaction between wind farms and AC grids the

21

drive train can be treated as one-lumped mass model for the sake of time efficiency and

acceptable precision. So, the drive train takes the form of the latter one in the paper and is

displayed in figure in which the parameters have been referred to the generator side.

4.2 Generator Model

Doubly fed electric machines are electric motors or electric generators that have windings on

both stationary and rotating parts, where both windings transfer significant power between

shaft and electrical system. Usually the stator winding is directly connected to the three-phase

grid and the three-phase rotor winding is fed from the grid through a rotating or static

frequency converter.

Although the multiphase slip ring assembly reduces reliability and requires regular

maintenance, it allows easy control of the rotor (moving) winding set so both multiphase

winding sets actively participate in the energy conversion process with the electronic

controller controlling half (or less) of the power capacity of the electric machine for full control

of the machine.

This is especially important when operating at synchronous speed, because then the rotor

current will be DC current. Without slip rings the production of DC current in the rotor winding

is only possible when the frequency converter is at least partly located in the rotor and

rotating with it. This kind of rotor converter naturally requires its own winding system

22

http://en.wikipedia.org/wiki/Electric_generator

http://en.wikipedia.org/wiki/Electric_motor

(preferably using high frequency in the 10 kHz range for compact size) for power transfer out

of or into the rotor. Furthermore, there are thermal and mechanical constraints (for example

centrifugal forces) of the power electronic assembly in the rotor. However, high speed

alternators have had electronics incorporated on the rotor for many years. Furthermore, high

frequency wireless power transfer is used in many applications because of improvements in

efficiency and cost over low frequency alternatives.

4.3 Requirement of the load flow analysis (both AC and AC/DC) for the power system

DC power flow is a simplification, and linearization of a full AC power flow. DC power flow

looks only at active power flows, neglecting voltage support, reactive power management and

transmission losses. Thanks to its simplicity and linearity it is very often used for contingency

analysis [5] and techno economic studies of power systems for assessing the influence of

commercial energy exchanges on active power flows in the transmission network. The method

as such is well-known and its fundamentals have been discussed extensively.

The classic power flow problem consists of active and reactive power flow and can be

formulated using four variables per node – voltage angle, voltage magnitude, active and

reactive power injections. Active power losses are not known in advance as they depend on

the active power injection pattern and voltage profile. Other variables are also

interdependent, making the problem non-linear. This is why it is often linearized and the

solution is obtained using successively linearized steps iteratively. The losses are re-estimated

at each iteration based on all other variables. Modern power system analysis tools use as a

basis the Newton-Raphson algorithm. Assumptions of DC power flow:

Voltage angle differences are small

Flat voltage profile

Line resistance is negligible

23

4.4 Load flow models considered

Newton Raphson Method

In numerical analysis, Newton's method (also known as the Newton–Raphson method),

named after Isaac Newton and Joseph Raphson, is a method for finding successively

better approximations to the roots (or zeroes) of a real-valued function. Limitations of

Newton Raphson Method are:

i. Finding the f’(x) i.e. the first derivative of f(x) can be difficult in cases where f(x) is

complicated.

ii. Infinite oscillation resulting in slow convergence near local maxima or minima. If the

initial guess is far from desired root, then the method may converge to some other

root

Gauss-Seidel Method

In an n -bus power system, let the number of P-Q buses be np and the number of P-V

(generator) buses be ng such that n = np + ng + 1. Both voltage magnitudes and angles of the P-

Q buses and voltage angles of the P-V buses are unknown making a total number of

2np + ng quantities to be determined. Amongst the known quantities are 2np numbers of real

and reactive powers of the P-Q buses, 2ng numbers of real powers and voltage magnitudes of

24

http://en.wikipedia.org/wiki/Function_(mathematics)

http://en.wikipedia.org/wiki/Real_number

http://en.wikipedia.org/wiki/Root_of_a_function

http://en.wikipedia.org/wiki/Joseph_Raphson

http://en.wikipedia.org/wiki/Isaac_Newton

http://en.wikipedia.org/wiki/Numerical_analysis

the P-V buses and voltage magnitude and angle of the slack bus . Therefore there are sufficient

numbers of known quantities to obtain a solution of the load flow problem.

Flow chart for Gauss Siedel Method

Fast Decoupled Method

In the operations of a power system, it is important for personnel to have a high level of

contingent information. The reason is that personnel need to know what power-flow changes

will occur due to generator outages. The contingent information can also be used to anticipate

future power disruptions in the power network. In this case fast decoupled load flow method

is used as a common method to retrieve contingent information conveniently.

25

Flow chart for Fast Decoupled Method

4.5 AC load flows and their drawbacks

The classic power flow problem consists of active and reactive power flow and can be

formulated using four variables per node – voltage angle, voltage magnitude, active and

reactive power injections. Active power losses are not known in advance as they depend on

the active power injection pattern and voltage profile. Other variables are also

interdependent, making the problem non-linear. This is why it is often linearized and the

solution is obtained using successively linearized steps iteratively. The losses are re-estimated

at each iteration based on all other variables. DC power flow is a commonly used tool for

contingency analysis. Recently, due to its simplicity and robustness, it also becomes

increasingly used for the real-time dispatch and techno economic analysis of power systems. It

is a simplification of a full power flow looking only at active power. Aspects such as voltage

support and reactive power management are possible to analyze. However, such

simplifications cannot always be justified and sometimes lead to unrealistic results. Especially

the implementation of power flow controlling devices is not trivial since standard DC power

flow fundamentally neglects their effects. Until recently, this was not an issue as the

26

application of power flow controlling devices in the European grid was limited. Therefore, it is

important to fundamentally re-validate the fast, but less accurate, DC power flow method.

4.6 AC/DC load flow

Sequential Power Flow

Simultaneous Power Flow

The advantage of sequential load flow algorithm is the easy integration of dc side equations

into ac load flow framework without making any changes to the existing framework. Figure

shows flow chart of sequential load flow algorithm-

It is worth mentioning that the dc network as well as the ac network power flows has to be

solved iteratively. Once the dc slack bus power injection is updated, the ac power flow solution

changes. So, apart from these internal iterations for dc and ac power flow solutions, an

external iteration loop is required to ensure the overall convergence of the algorithm. In the

initial dc slack bus power is estimated as the algebraic sum of all other converters, which can

increase the total number of iterations.

In Sequential Power Flow method, both ac and dc sides are considered together as a unified

ac-dc grid for solving the power flow. Since ac and dc equations are solved simultaneously, an

27

external iteration loop is not required here. However, in this algorithm, the slack station losses

are considered as a separate variable XS. Apart from ac and dc mismatch equations, an

additional mismatch equation is therefore included to account for slack converter losses.

With sequential algorithm, power flow convergence in two external iterations when a flat start

is considered. In the first external iteration, ac side requires five and dc side requires two

internal iterations for convergence.

28

CHAPTER 5

MODELS OF ASYNCHRONOUS WIND TURBINES

5.1 INTRODUCTION

Wind energy is one of the important renewable energy sources. As opposed to the currently

existing carbon-based energy sources such as coal, petroleum, and natural gas, wind energy

has the advantages that it is clean, unpolluted, inexhaustible, and free in term of its

natural existence . Current trend shows that wind energy is getting popular to replace

the traditional energy sources due to the expectable depletion of traditional energy

resource and the humankind’s effort in reduction of carbon dioxide emission but not

affecting the usable energy production for the continuous developments. Wind energy,

although with the advantages mentioned, is still developed at preliminary stage of power

generation. Generally, wind energy is converted into kinetic energy before the Conversion

to the usable electrical energy. Wind energy is converted to low speed rotational energy

via blades and through the gear box, the rotational energy is used to drive the generator for

electric power generation. Wind energy is an abundant resource with free cost but it is

important to study the way to maximize the power generation by wind energy. Several control

methods of wind energy conversion system has been proposed by researchers to maximize

the wind energy harvest. However, most of the proposed methods have rather low

efficiency to extract power. Besides, the extracted energy is the very unstable since the nature

of wind flow is spontaneous which this situation will lower the power extraction and

subsequently reduce the efficiency of power generation.

Wind Turbine with Variable Speed Generator The wind turbine model is used to generate

mechanical torque. The negative value of output torque means the wind turbine is providing

torque. Result shows the output torque is positive for wind speed smaller than 7 m/s,

which represent that the wind turbine is not providing power, but consuming power

from the load. Hence, the value of wind speed at 7 m/s could be possibly as the cut-in speed

of the wind turbine model and the result of output mechanical torque. For a range of wind

speed is shown in Figure, the effect of both varying generator speed and wind speed on

the output torque is investigated in simulation and the results are shown in Figure. It can be

29

noticed that higher wind speed can provide larger torque and hence larger power to the load.

For instance, at Ω 1.5 m/s, the turbine output torque by wind speed 12 m/s is about -0.38 W,

but the turbine output torque by wind speed 18 m/s is about -1.35 W. wind turbine at higher

output torque can provide larger output power, hence improving the power efficiency of

the power generation.

5.2 Various types of WTGUs:

1 Fixed speed WTGU: This type of WTGU has a squirrel cage induction generator which is

driven by a wind turbine either having a fixed turbine blade angle (stall regulated fixed

speed WTGU) or having a pitch controller to regulate the blade angle (pitch regulated fixed

speed WTGU). In both these types of WTGU, the induction generator is directly connected

to the grid. In the operating range the rotor speed varies within a very small range (around

5% of the nominal value) and hence, these are reckoned as fixed speed WTGU. Normally in

these WTGU a fixed shunt capacitor is used to provide reactive power compensation.

(a) Stall regulated fixed speed WTGU: The power output of this class of WTGU depends

on the turbine and generator characteristics, wind speed, rotor speed and the terminal

voltage. For a given turbine and generator characteristics, wind speed alone is the

independent variable while the rotor speed and terminal voltage are interdependent

and vary with wind speed as well as the network conditions. In some of the existing

models for this WTGU, either the turbine characteristics is neglected (constant

mechanical input) or the WTGU power output is considered to be independent of the

terminal voltage variation. The method suggested here facilitates the computation of

the power output of the WTGU without making these simplifying assumptions. In order

to take this interdependency of rotor speed and voltage into account, the power

output is calculated iteratively. For a given wind speed, the power output is computed

for an assumed terminal voltage. The calculation is repeated if the computed power

output results in a change in the terminal voltage. The power output calculation

requires finding the rotor speed common to both the turbine and the generator. This

rotor speed corresponds to the intersection of the turbine and the generator

30

characteristics. Since the two characteristics are non-linear, an iterative method has

been developed here for computing the rotor speed.

(b) Pitch regulated fixed speed WTGU: In this class of WTGU, the pitch angle controller

regulates the wind turbine blade angle (ν) according to the wind speed variations.

Hence, the power output of this class of WTGU depends on the characteristics of the

pitch controller in addition to the turbine and generator characteristics. Since the

interest here is in steady state behavior, rather than the actual control process the

effect of the control process is important. This control guarantees that the power

output of the WTGU for any wind speed will be equal to the designed value for that

speed (irrespective of the voltage). This designed power output Pe of the WTGU with

wind speed is provided by the manufacturer in the form of a power curve. Hence, for a

given wind speed Pe can be obtained from the power curve of the WTGU, but Qe

needs to be computed. With Pe known and an assumed voltage, the induction

generator Pe expression can be recast as a quadratic equation in slip (rotor speed). This

equation is solved to get the slip value. With the slip known, the reactive power output

Qe is calculated from the induction generator equivalent circuit. Any change in voltage

due to these output changes is computed and the above process is repeated till

convergence.

2. Semi variable speed WTGU: This class of WTGU consists of a pitch controlled wind turbine

and a wound rotor induction generator. The rotor circuit of the generator is connected to an

external variable resistance. Power electronic devices are used to vary the rotor resistance.

In these WTGU, the reactive power compensation is normally provided by a fixed shunt

capacitor. There are two controllers, a pitch controller and rotor resistance controller. These

two controllers are designed to operate in a coordinated manner. This design guarantees that

the active power output is equal to the maximum power at wind speeds below nominal and

equal to rated power above nominal wind speeds. For this class of WTGU also, the

manufacturer provides the designed real power output versus wind speed characteristics.

3. Variable speed WTGU: WTGU having double fed induction generator (DFIG): The DFIG

consists of a pitch controlled wind turbine and an induction generator whose stator winding is

directly connected to the grid but the rotor circuit is connected to the grid through a back to

31

back voltage source converter. The voltage source converter (connected to the rotor) applies

voltage across the rotor which is regulated by two rotor current controllers. WTGU having

generator (synchronous/induction) with front end converter (GFEC): The GFEC consists of a

pitch controlled wind turbine and a variable frequency synchronous or induction generator

connected to the grid through a power electronic converter (back to back voltage source

converter). In this case, the voltage source converter output applied to the stator is varied by

the control signals obtained from the current controllers.

PQ MODEL OF AN ASYNCHRONOUS WIND TURBINE

A way to model a wind farm as a PQ bus is to assume a generated real power and a given power factor,

with which the consumed reactive power is calculated. Some improvements can be achieved if the

steady-state model of the induction machine is taken into account. The model shown in Fig is assumed.

In this model, applying the conservation of complex power theorem (Boucherot’s theorem) allows the

following expression to be written for the reactive power consumed by the machine:

Fig. Reactive Power consumed variation with wind speed

The reactive power curve as a function of wind speed can be seen in Fig. Q=−Q0−Q1P−Q2P

2

(8)

Where above mentioned constants are experimentally obtained. If the wind speed is desired to be the

input datum for the problem, the real power can be obtained as a function of it:

P=0.5×ρ×A×V 3×CP (9)

All parameters have been mentioned already.

PQ MODEL OF AN ASYNCHRONOUS WIND TURBINE

32

The other method proposed here consists of modeling the machine as an RX bus, following the

next three steps-

(a) Calculate the power that each WT can extract from the wind for a given wind speed and a

given rotor speed, according to its power coefficient curve.

(b) Calculate the power that each WT can generate, according to the results of the load flow

analysis, and to the rotor speed given in step (a).

Fig- Curves for the generator and turbine

(c) Compare both powers and look for the value of the slip, for which the electrical and the

mechanical powers coincide, for the wind speed given.

33

CHAPTER 6SIMULATION AND RESULTS

Load Flow Analysis of 33 Bus System Using Wei bull Distribution using paper[1] & [2]

Input bus data:

Br. No. Rc. Nd. Sn Nd. Branch R (OHM) X (OHM) SENDING PL (KW) NODE QL (KVAR)1 1 2 0.0922 0.047 100 602 2 3 0.493 0.2511 90 403 3 4 0.366 0.1864 120 804 4 5 0.3811 0.1941 60 305 5 6 0.819 0.177 60 206 6 7 0.1872 0.6188 200 1007 7 8 0.7114 0.2351 200 1008 8 9 1.03 0.74 60 209 9 10 1.044 0.74 60 20

10 10 11 0.1966 0.065 45 3011 11 12 0.3744 0.1238 60 3512 12 13 1.468 1.155 60 3513 13 14 0.5416 0.7129 120 8014 14 15 0.591 0.526 60 1015 15 16 0.7463 0.545 60 2016 16 17 1.289 1.721 60 2017 17 18 0.732 0.574 90 4018 18 19 0.164 0.1565 90 4019 19 20 1.5042 1.3554 90 4020 20 21 0.4095 0.4784 90 4021 21 22 0.7089 0.9373 90 4022 22 23 0.4512 0.3083 90 5023 23 24 0.898 0.7091 420 20024 24 25 0.896 0.7011 420 20025 25 26 0.203 0.1034 60 2526 26 27 0.2842 0.1447 60 2527 27 28 1.059 0.9337 60 2028 28 29 0.8042 0.7006 120 7029 29 30 0.5075 0.2585 1200 60030 30 31 0.9744 0.963 1500 7031 31 32 0.3105 0.3619 210 10032 32 33 0.341 0.5302 60 40

34

Pe : Active Power in MW Qe : Reactive Power in MVAR|V| : Terminal Voltage in P.U.

CASE BUS NO. TYPE of WTGU Wind

Speed

Pe(MW) Qe(MVAR) |V| (pu)

1 33 Stall Regulated Fixed

Speed

- 0.000000 0.000000 0.850821

6 Semi Variable Speed - 0.000000 0.000000 0.886101

18 DFIG - 0.000000 0.000000 0.867649

25 GFEC - 0.000000 0.000000 0.933572


Speed

11 0.710965 0.138621 0.894289

6 Semi Variable Speed 8 0.367190 0.047734 0.928876

18 DFIG 9.5 0.599402 0.000000 0.931083

25 GFEC 9 0.560438 0.000000 0.962401


Speed

13 0.867095 0.240592 0.915962


18 DFIG 11 0.908436 0.000000 0.971893

25 GFEC 10.5 0.851965 0.000000 0.971908


Speed

13 0.870471 0.191872 0.985108


18 DFIG 11 0.908436 0.000000 0.991258

25 GFEC 10.5 0.851965 0.000000 0.984167

35

PERFORMING LOAD FLOW ANALYSIS ON DIFFERENT TYPES OF WTGUs using paper [1]

ACTUAL RESULT:


Speed

( Uw )


1 33 Stall Regulated Fixed Speed - 0.000000 0.000000 0.878486


18 DFIG - 0.000000 0.000000 0.895878

25 GFEC - 0.000000 0.000000 0.964824

2 33 Stall Regulated Fixed Speed 11 0.748595 0.157656 0.919991


18 DFIG 9.5 0.619500 0.000000 0.958991

25 GFEC 9 0.586000 0.000000 0.982107



18 DFIG 11 0.929250 0.000000 0.991195

25 GFEC 10.5 0.879000 0.000000 0.991210



18 DFIG 11 0.929250 0.000000 1.051119

25 GFEC 10.5 0.879000 0.000000 1.013085

36

USING NEWTON RAPHSON METHOD:


Speed

( Uw )




18 DFIG - 0.0000 0.0000 0.8422

25 GFEC - 0.0000 0.0000 0.9150



18 DFIG 9.5 0.4728 0.0000 0.9167

25 GFEC 9 0.4113 0.0000 0.9349



18 DFIG 11 0.7561 0.0000 0.9532

25 GFEC 10.5 0.6281 0.0000 0.9976



18 DFIG 11 0.7561 0.0000 0.9968

25 GFEC 10.5 0.6281 0.0000 0.9902

37

USING GAUSS SEIDEL METHOD:


Speed

( Uw )



Speed

- 0.0000 0.0000 0.8165


18 DFIG - 0.0000 0.0000 0.8396

25 GFEC - 0.0000 0.0000 0.9076


Speed

11 0.5063 0.1210 0.8814


18 DFIG 9.5 0.4713 0.0000 0.9102

25 GFEC 9 0.4099 0.0000 0.9322


Speed

13 0.6944 0.1889 0.9018


18 DFIG 11 0.7548 0.0000 0.9513

25 GFEC 10.5 0.6219 0.0000 0.9941


Speed

13 0.6944 0.1799 0.9779


18 DFIG 11 0.7548 0.0000 0.9912

25 GFEC 10.5 0.6219 0.0000 0.9837

38

USING FAST DECOUPLED METHOD:


Speed

( Uw )

Pe(MW) Qe(MVAR) |V|

(pu)



18 DFIG - 0.0000 0.0000 0.8387

25 GFEC - 0.0000 0.0000 0.9065



18 DFIG 9.5 0.4702 0.0000 0.9095

25 GFEC 9 0.4089 0.0000 0.9301



18 DFIG 11 0.7541 0.0000 0.9498

25 GFEC 10.5 0.6207 0.0000 0.9926



18 DFIG 11 0.7541 0.0000 0.9901

25 GFEC 10.5 0.6207 0.0000 0.9815

39

COMPARISION OF PERFORMANCE OF VARIABLE SPEED WIND TURBINE AT A

PARTICULAR SPEED AND USING WEIBULL DISTRIBUTION

AT A PARTICULAR SPEED:


Speed

( Uw )

Pe(MW) Qe(MVAR) |V|

(pu)



18 DFIG - 0.0000 0.0000 0.8422

25 GFEC - 0.0000 0.0000 0.9150



18 DFIG 9.5 0.4728 0.0000 0.9167

25 GFEC 9 0.4113 0.0000 0.9349



18 DFIG 11 0.7561 0.0000 0.9532

25 GFEC 10.5 0.6281 0.0000 0.9976



18 DFIG 11 0.7561 0.0000 0.9968

25 GFEC 10.5 0.6281 0.0000 0.9902

USING WEIBULL DISTRIBUTION:

40


Speed

( Uw )


1 33 Stall Regulated

Fixed Speed

- 0.000000 0.000000 0.850821

6 Semi Variable

Speed

- 0.000000 0.000000 0.886101

18 DFIG - 0.000000 0.000000 0.867649

25 GFEC - 0.000000 0.000000 0.933572


Fixed Speed

11 0.710965 0.138621 0.894289

6 Semi Variable

Speed

8 0.367190 0.047734 0.928876

18 DFIG 9.5 0.599402 0.000000 0.931083

25 GFEC 9 0.560438 0.000000 0.962401


Fixed Speed

13 0.867095 0.240592 0.915962

6 Semi Variable

Speed

10 0.565784 0.095813 0.947733

18 DFIG 11 0.908436 0.000000 0.971893

25 GFEC 10.5 0.851965 0.000000 0.971908


Fixed Speed

13 0.870471 0.191872 0.985108

6 Semi Variable

Speed

10 0.565784 0.097548 0.983276

18 DFIG 11 0.908436 0.000000 0.991258

25 GFEC 10.5 0.851965 0.000000 0.984167

41

Performing Load Flow Analysis on all types of WTGU Model on a

different Set of Bus using paper [1]

Pe : Active Power Generation

Qe : Reactive Power Generation

V : Terminal Voltage

Uw : Wind Speed


Speed

( Uw )




14 DFIG - 0.000000 0.000000 0.867649

22 GFEC - 0.000000 0.000000 0.933572



14 DFIG 9.5 0.599402 0.000000 0.931083

22 GFEC 9 0.560438 0.000000 0.962401



14 DFIG 11 0.908436 0.000000 0.971893

22 GFEC 10.5 0.851965 0.000000 0.971908



14 DFIG 11 0.908436 0.000000 0.991258

22 GFEC 10.5 0.851965 0.000000 0.984167

42

Comparison of Various Wind Turbine Models using paper [1]

Variable Speed Wind Turbines:

1. DFIG (Doubly Fed induction Generator)

Case No. Bus No. Wind Speed

(Uw) in m/s

Pe(MW) Qe(MW) |V| (pu)

1. 18 - 0.0000 0.0000 0.8422

14 - 0.0000 0.0000 0.8676

2. 18 9.5 0.4728 0.0000 0.9167

14 9.5 0.5994 0.0000 0.9310

3. 18 11 0.7561 0.0000 0.9532

14 11 0.9084 0.0000 0.9718

4. 18 11 0.7561 0.0000 0.9968

14 11 0.9084 0.0000 0.9912

2. GFEC (Generator with Front End Converter)


(Uw) in m/s


1. 25 - 0.0000 0.0000 0.9150

22 - 0.0000 0.0000 0.9335

2. 25 9 0.4113 0.0000 0.9349

22 9 0.5604 0.0000 0.9624

3. 25 10.5 0.6281 0.0000 0.9976

43

22 10.5 0.8519 0.0000 0.9719

4. 25 10.5 0.6281 0.0000 0.9902

22 10.5 0.8519 0.0000 0.9841

Fixed Speed Wind Turbines:

Stall Regulated Fixed Speed


(Uw) in m/s


1. 33 - 0.0000 0.0000 0.8172

31 - 0.0000 0.0000 0.8508

2. 33 11 0.5102 0.1235 0.8876

31 11 0.7109 0.1386 0.8942

3. 33 13 0.7010 0.1909 0.9089

31 13 0.8670 0.2405 0.9159

4. 33 13 0.7010 0.1823 0.9812

31 13 0.8704 0.1918 0.9851

Semi Variable Speed Wind Turbines:


(Uw) in m/s


1. 6 - 0.0000 0.0000 0.8921

9 - 0.0000 0.0000 0.8861

2. 6 8 0.2634 0.0374 0.9162

44

9 8 0.3671 0.0477 0.9288

3. 6 10 0.5016 0.0981 0.9293

9 10 0.5657 0.0958 0.9477

4. 6 10 0.5016 0.0873 0.9801

9 10 0.5657 0.0942 0.9832

In above tables:

Pe: Active power in MW.

Qe: Reactive Power In MW.

|V|: Bus voltage in pu.

Note: In all the above tables four different cases have been tabulated. These cases are

1. WTGU operating below cut-in wind speed (which is equivalent to the system without

WTGU) and system loads corresponds to the base load.

2. WTGU operating at low wind speeds with all the variable speed WTGU operating with

specified Q and system loads corresponds to the base load.

3. WTGU operating at higher wind speeds than case 2 with GFEC and DGIG operating with

settable Q and system loads corresponds to the base load.

4. WTGU operating at wind speeds corresponding to case 3 with GFEC and DFIG operating

with settable Q and system load corresponds to 30 % of the base load.

The feeder voltage is 12.66 kV (base voltage). The base case total load is 4.715 MW and

2.3 MVAR.

AC/DC Combined Power Flow Solution using paper [3]

45

Data: Under nominal condition each of G1, G2, G3, G4, G5, and G6 generates 700 MW

whereas G3 left slack. The converters connected to DC buses DC1, DC2 and DC3 control the DC

power at 600 MW, 300 MW and 300 MW respectively. The converter connected to DC4 is slack

converter keeps the DC link constant at 320KV.The base power for the DC side is 600 MW

however the base MVA for the AC side is 100 MVA.

Note: Each generating source comprises of stall regulated wind turbines in wind farm, where

the generators are induction machine with following parameters:

Stator resistance Rs = 0.01352 ohms

Stator reactance Xs = 0.5380 ohms

Rotor resistance Rr = 0.01290 ohms

Rotor reactance Xr = 0.21289 ohms

Magnetizing reactance Xm = 3.42979 ohms

Area swept by the blades of wind turbine is 961 meter2.

Wind speed varies from 13 m/sec to 29 m/sec.

Case 1: All Converters are in PQ model with zero reactive power injection and with rated active

power.

46

Sequential Algorithm Simultaneous Algorithm

AC Bus Voltage(p.u.) Angle(rad) Pinj (p.u.) Voltage(p.u.) Angle(rad) Pinj (p.u.)

1 1.0219 0.2918 7.000 1.0219 0.2918 7.000

2 1.0018 0.1256 7.000 1.0018 0.1256 7.000

3 1.0219 -0.1079 7.000 1.0219 -0.1079 7.000

4 1.0018 -0.2785 7.051 1.0018 -0.2785 7.0509

5 0.9926 0.1828 0 0.9926 0.1828 0

6 0.9759 0.0086 0 0.9759 0.0086 0

7 0.9616 -0.1317 0 0.9616 -0.1317 0

8 0.9616 -0.3372 0 0.9616 -0.3372 0

9 0.9764 -0.5374 0 0.9764 -0.5374 0

10 0.9842 -0.3950 0 0.9842 -0.3950 0

11 1.0081 -0.2201 0 1.0081 -0.2201 0

12 0.9923 -0.3387 0 0.9923 -0.3387 0

13 0.9771 -0.5850 0 0.9771 -0.5850 0

14 1.0018 -0.2236 7.000 1.0018 -0.2236 7.000

15 1.0018 -0.4680 7.000 1.0018 -0.4680 7.000

DC Bus Voltage(p.u.) Angle(rad) Pinj (p.u.) Voltage(p.u.) Angle(rad) Pinj (p.u.)

1 0.9986 - -1.0000 0.9986 - -1.0000

2 0.9893 - 0.5000 0.9893 - 0.5000

3 0.9953 - -0.5000 0.9953 - -0.5000

4 1.0000 - 0.97706 1.0000 - 0.97706

Case 2: All the converters are in PV mode maintaining the PCC voltage to 1.0 p.u.

Sequential Algorithm Simultaneous Algorithm

47

AC Bus Voltage(p.u.) Angle(rad) Pinj (p.u.) Voltage(p.u.) Angle(rad) Pinj (p.u.)

1 1.0219 0.2743 7.000 1.0219 0.2743 7.000

2 1.0018 0.1062 7.000 1.0018 0.1062 7.000

3 1.0219 -0.1074 7.000 1.0219 -0.1074 7.000

4 1.0018 -0.2767 7.0291 1.0018 -0.2767 7.02958

5 1.0078 0.1623 0 1.0078 0.1623 0

6 0.9911 -0.0050 0 0.9911 -0.0050 0

7 0.9926 -0.1445 0 0.9926 -0.1445 0

8 0.9861 -0.3403 0 0.9861 -0.3403 0

9 0.9926 -0.5327 0 0.9926 -0.5327 0

10 0.9911 -0.3928 0 0.9911 -0.3928 0

11 1.0078 -0.2200 0 1.0078 -0.2200 0

12 0.9926 -0.3338 0 0.9926 -0.3338 0

13 0.9926 -0.5782 0 0.9926 -0.5782 0

14 1.0018 -0.2179 7.000 1.0018 -0.2179 7.000

15 1.0018 -0.4621 7.000 1.0018 -0.4621 7.000

DC Bus Voltage(p.u.) Angle(rad) Pinj (p.u.) Voltage(p.u.) Angle(rad) Pinj (p.u.)

1 0.9986 - -1.0000 0.9986 - -1.0000

2 0.9893 - 0.5000 0.9893 - 0.5000

3 0.9953 - -0.5000 0.9953 - -0.5000

4 1.0000 - 0.97706 1.0000 - 0.97706

Comparison of Genetic Algorithm and Newton Raphson Approach for

Solving AC DC Optimal Power Flow Problem

48

For IEEE-14 Bus System:

Bus Data:

Problem Statement: The problem here is to minimize the overall cost function. The overall

cost function fi(PGi) is given by:

49

Note: The problem was solved using two methods (Genetic Algorithm and Newton Raphson)

and there results were tabulated. A DC link is connected between bus 1 and bus 14.The

voltage values of all buses have been bounded between 0.95 and 1.05.

Also for Genetic Algorithm:

Number of Iterations: 100

Number of runs: 9

For Newton Raphson:


Number of runs: 1

Result:

Actual Result:

50

Bus No. Voltage (pu) Generator Cost ($/MWh)

GAOPF Newton OPF GAOPF Newton

OPF

Best Worst Best Worst

1 0.98 1.02 0.99

2 0.99 1.00 0.98 68.47 120.01 90.94

3 1.01 0.97 0.97 60.34 180.20 90.46

4 0.96 0.96 0.96

5 0.97 0.99 0.96

6 0.99 0.99 1.02 102.6 85.51 89.87

7 1.02 0.98 0.97

8 0.99 1.01 1.02 118.6 120.91 88.40

9 0.98 0.98 0.95

10 0.97 0.95 0.96

11 1.01 1.01 0.99

12 0.98 0.95 1.00

13 1.03 0.99 0.99

14 0.97 1.02 0.95

Obtained Result:

51

Bus

No.

Voltage (pu) Generator Cost ($/MWh)

GAOPF Newton

OPF

GAOPF Newton

OPF


1 0.976 1.013 0.987

2 0.989 0.998 0.974 68.453 119.157 90.652

3 1.005 0.967 0.968 60.332 179.861 90.381

4 0.958 0.958 0.952

5 0.967 0.989 0.952

6 0.989 0.989 1.011 102.514 85.480 89.613

7 1.013 0.976 0.968

8 0.989 1.005 1.011 118.538 120.864 88.228

9 0.976 0.976 0.941

10 0.967 0.944 0.952

11 1.005 1.005 0.987

12 0.976 0.944 0.997

13 1.023 0.989 0.987

14 0.967 1.013 0.941

Genetic Algorithm Approach for Solving AC DC Optimal Power Flow

Problem

For IEEE-30 Bus System:

52

Bus Data:

53

Given bus data

Problem Statement: The problem here is to minimize the overall cost function. The overall

cost function fi(PGi) is given by:

54

Note: The problem was solved using two methods (Genetic Algorithm and Newton Raphson)

and there results were tabulated. A DC link is connected between bus 1 and bus 28. The rating

of converter at bus 1 and 28 is 1.00 pu. The voltage values of all buses have been bounded

between 0.95 and 1.05.

Also for Genetic Algorithm:


Number of runs: 14

For Newton Raphson:


Number of runs: 1

Result:

55

Actual Result:

Bus

No.

Voltage (pu) Generator Cost

($/MWh)

GAOPF Newton

OPF

GAOPF Newton

OPF

Best Worst Best Wors

t

1 1.00 0.99 1.00 9.77 11.67 10.55

2 0.99 1.00 0.99 7.97 11.06 6.53

3 0.96 0.98 0.99

4 0.98 0.96 0.98

5 1.01 1.02 0.99 8.13 11.40 6.52

6 0.99 1.00 0.97

7 0.98 0.95 0.98

8 0.96 0.99 1.03 8.15 10.57 6.93

9 0.96 1.01 0.99

10 1.01 1.02 1.02

11 0.99 1.00 1.01 8.40 10.54 11.87

12 1.01 0.95 1.00

13 0.99 1.01 1.01 6.12 10.56 6.90

14 0.97 0.96 0.99

15 1.00 1.00 0.99

16 0.98 0.97 1.00

17 0.99 0.96 1.00

18 0.99 1.01 0.99

19 1.01 0.98 0.99

20 0.97 1.01 1.03

21 0.98 0.97 0.99

22 0.99 0.99 0.98

56

23 0.99 1.01 0.99

24 1.01 1.01 1.02

25 0.98 0.97 1.03

26 0.99 1.01 1.02

27 0.98 0.97 1.05

28 0.99 0.95 0.99

29 1.01 0.98 1.05

30 0.99 0.98 1.05

Obtained Result:

57

Bus

No.

Voltage (pu) Generator Cost

($/MWh)

GAOPF Newton

OPF

GAOPF Newton

OPF


1 0.997 0.988 0.997 9.53 11.42 10.32

2 0.988 0.997 0.988 7.72 10.75 6.29

3 0.959 0.976 0.988

4 0.976 0.959 0.976

5 1.005 1.014 0.988 7.83 11.19 6.31

6 0.988 0.997 0.967

7 0.976 0.949 0.976

8 0.959 0.988 1.028 7.79 10.35 6.74

9 0.959 1.005 0.988

10 1.0005 1.014 1.014

11 0.988 0.997 1.005 8.22 10.39 11.69

12 1.005 0.949 0.997

13 0.988 1.005 1.005 5.89 10.34 6.78

14 0.967 0.959 0.988

15 0.997 0.997 0.988

16 0.976 0.967 0.997

17 0.988 0.959 0.997

18 0.988 1.005 0.988

19 1.005 0.976 0.988

20 0.967 1.005 1.028

21 0.976 0.967 0.988

22 0.988 0.988 0.976

23 0.988 1.005 0.988

24 1.005 1.005 1.014

25 0.976 0.967 1.028

26 0.988 1.005 1.014

27 0.976 0.967 1.046

28 0.988 0.949 0.988

29 1.005 0.976 1.046

30 0.988 0.976 1.046

58

Simulation of IEEE-14 and IEEE-30 Bus system using modified Newton

Raphson Method for AC/DC Circuits.

Actual Result: (obtained using genetic algorithm)

1. for IEEE-14 Bus System

Bus No. Voltage(p.u.) Generator Cost ($/MWh)

GAOPF GAOPF


1 0.976 1.013

2 0.989 0.998 68.453 119.157

3 1.005 0.967 60.332 179.861

4 0.958 0.958

5 0.967 0.989

6 0.989 0.989 102.514 85.480

7 1.013 0.976

8 0.989 1.005 118.538 120.864

9 0.976 0.976

10 0.967 0.944

11 1.005 1.005

12 0.976 0.944

13 1.023 0.989

14 0.967 1.013

For IEEE-30 Bus System

59

60

Bus No. Voltage(p.u.) Generator Cost

($/MWh)

GAOPF GAOPF


1 1.00 0.99 9.77 11.67

2 0.99 1.00 7.97 11.06

3 0.96 0.98

4 0.98 0.96

5 1.01 1.02 8.13 11.40

6 0.99 1.00

7 0.98 0.95

8 0.96 0.99 8.15 10.57

9 0.96 1.01

10 1.01 1.02

11 0.99 1.00 8.40 10.54

12 1.01 0.95

13 0.99 1.01 6.12 10.56

14 0.97 0.96

15 1.00 1.00

16 0.98 0.97

17 0.99 0.96

18 0.99 1.01

19 1.01 0.98

20 0.97 1.01

21 0.98 0.97

22 0.99 0.99

23 0.99 1.01

24 1.01 1.01

25 0.98 0.97

26 0.99 1.01

27 0.98 0.97

28 0.99 0.95

29 1.01 0.98

30 0.99 0.98

Obtained Result: (Using Modified Newton Raphson)



Advanced Newton Raphson

Method

Advanced Newton Raphson

Method

1 0.985

2 0.971 90.471

3 0.963 90.194

4 0.949

5 0.951

6 1.007 89.472

7 0.965

8 1.007 88.095

9 0.936

10 0.951

11 0.985

12 0.993

13 0.985

14 0.936


61


Advanced Newton

Raphson Method

Advanced Newton

Raphson Method

1 0.998 10.38

2 0.986 6.34

3 0.986

4 0.979

5 0.986 6.41

6 0.967

7 0.979

8 1.026 6.74

9 0.986

10 1.019

11 1.005 11.69

12 0.998

13 1.005 6.71

14 0.986

15 0.986

16 0.998

17 0.998

18 0.986

19 0.986

20 1.026

21 0.986

22 0.979

23 0.986

24 1.019

25 1.026

26 1.019

62

27 1.048

28 0.986

29 1.048

30 1.048

Discussion

63

1. With its abundant, inexhaustible potential, its increasingly competitive cost, and

environmental advantage, wind energy is one the best technologies available today to

provide a sustainable supply to the world development. In depth understanding and

investigation of wind power generators, wind farm integration, grid core and etc. is

very meaningful.

2. In terms of generators for wind power application, there are different concepts in use

today. The major distinction among them is made between fixed speed and variable

speed wind turbine generator concepts. In the early stage of the power development,

fixed speed wind turbines and induction generators were often used in wind farms. But

the limitations of such generators like low efficiency and poor power quality adversely

influences their further application. With large scale exploration and integration of

wind sources, variable speed wind turbines generators, such as doubly fed induction

generator (DFIG) and permanent magnet synchronous generators are emerging as

preferred technology. In contrast to their fixed speed counterparts, the variable speed

induction generators allow operating wind turbines at the optimum speed tip speed

ratio and hence at the optimum power efficient for a wide wind speed range.

3. As the penetration of wind power increases, integrating large wind farms to power

grids and the relevant influences on the host grids needs to be carefully investigated.

So, accurate and reliable model of the variable speed wind turbine generators and

urgently needed for power simulation analysis. Two models were propose namely PQ

and RX model. It was found that RX model was better as it obtained a single working

point for each wind speed,. However the conventional PQ model has its advantage of

being simpler and easy to implement.

4. One of the greatest problem facing wind farms is that the electrical power generated

depends on variable characteristics of the wind. To become competitive in liberalized

market, the reliability of wind energy must be guaranteed. Good local wind forecast

are therefore essential for accurate prediction of generation levels for each moment of

the day.

64

5. From above tables of individual wind turbines following can be deduced:

a) The power output of DFIG is greater than that of GFEC for a given wind speed.

b) GFEC has better voltage profile than that DFIG for wind speed up to cut off speed.

In fact DFIG has best voltage profile amongst all generator models.

c) Voltage profile of Variable Speed Wind Turbine is far better as compared to Semi

Variable and Fixed Speed Turbines.

d) At speed considerably below cut off speed the output of fixed speed Wind Turbine

is greatest.

e) Semi Variable Wind Turbines are used to employ benefits of both Fixed and

Variable speed Generators. Although their performance is inferior than that of

Fixed Speed at low wind speed and Variable Speed at higher wind speeds.

f) The major advantage of Variable Speed Wind Turbines is that reactive power

compensation can be employed.

Conclusion

1. This study brings out some interesting features about the WTGU performance and

their impact when used as DG sources. The real power output of all the types of

65

WTGU (considered here) at any given wind speed does not change perceptibly

even with significant changes in terminal voltage.

2. The Q demand of the fixed and semi-variable speed WTGU is sensitive to terminal

voltage variations. However, in the case of variable speed WTGU the terminal

voltage variation (normal range) has no impact on their Q demand.

3. From load flow analysis of different wind turbines models using different methods

it was concluded that Newton Raphson method was best for performing load flow

analysis as it is more accurate.

4. It was also found that load flow results obtained using Weibull distribution were

far accurate than those obtained at particular speed.

5. After plotting load flow results of different wind turbines on two sets of bus it was

found that choice for a given wind turbine really exists between DFIG and GFEC.

6. However DFIG has greater power output as compared to its counterpart it is the most

preferable choice. Also GFEC is more expensive because of power electronics associated

with it.

7. From the results one could conclude that result obtained by GAOPF best solution

has shown improvement as compared to Newton OPF solution. Also the overall

cost of generation obtained by GAOPF best solution is less.

8. But GAOPF required 100 iterations and 9 runs compared to 20 iterations and 1 run

required by Newton OPF method. Thus Newton OPF method is faster as compared

to GAOPF method.

9. From the results one could conclude that result obtained by GAOPF best solution

has shown improvement as compared to Newton OPF solution. Also the overall

cost of generation obtained by GAOPF best solution is less.

10. But GAOPF required 100 iterations and 14 runs compared to 30 iterations and 1

run required by Newton OPF method. Thus Newton OPF method is faster as

compared to GAOPF method.

References

66

[1] K.C. Divya, P.S. Nagendra Rao “Models for wind turbine generating systems and

their application in load flow studies”, Department of Electrical Engineering,

Indian Institute of Science, Bangalore 560012, India.

[2] Heras,Escriva,Ortega “Wind farm electrical power production model for load flow

analysis”.

[3] Nakul Narayanan K & Pinaki Mitra “A comparative study of sequential and

simultaneous AC/DC power flow algorithm”.

[4] Feijoo and Cidras “Modeling of wind farms in the load flow analysis”.

[5] A. Panosyan, B. R. Oswald “Modified Newton Raphson Load Flow Analysis for

Integrated AC/DC Power Systems” in Institute of Electric Power Systems,

University of Hannover, Germany.

[6] Warkad,Khedkar,Dhole “A Genetic algorithm approach for solving AC-DC optimal

power flow problem” in Department of Electrical Engineering, Visvesvaraya

National Institute of Technology, Nagpur, India.

[7] Slootweg,Haan,H.Polinder “General Model for Representing Variable SpeedWind

Turbines in Power System Dynamics Simulations” in IEEE Porto Power Tech,

Porto, Potugal.

[8] E. Simiu and R. H. Scanlan, “Wind Effects on Structures, an Introduction to Wind

Engineering”, 2nd Ed. New York: Wiley, 1986.

[9] R. Pena, J. C. Clare, and G. M. Asher, “Doubly fed induction generator using back-

to-back PWM converters and its application to variable- speed wind–energy

conversion,” Proc. Inst. Elect. Eng., vol. 143.

[10] S. Heier, “Grid Integration of Wind Energy Conversion Systems”. Chicester, U.K.:

Wiley, 1998.

[11] O. Wasynczuk, D. T. Man, and J. P. Sullivan, “Dynamic behavior of a class of wind

turbine generators during random wind fluctuations,” IEEE Trans. Power App.

Syst., vol. 100, pp. 2837–2845, June 1981.

[12] M. Fujimitsu, T. Komatsu, K. Koyanagi, K. Hu, and R. Yokoyama, “Modeling of

doubly-fed adjustable-speed machine for analytical studies on long-term

dynamics of power system” in Proc. PowerCon, Dec. 2000.

67

[13] Ming Yin, Student Member, IEEE, Gengyin Li, Member,” Modeling of the Wind

Turbine with a PermanentMagnet Synchronous Generator for Integration” in IEEE

Power Engineering Society General Meeting, Jun. 2006, Montreal, Canada.

[14] S. Hier, “Grid Integration of Wind Energy Conversion Systems”, John Wiley and

sons, 1998.

[15] Y. D. Song, B. Dhinakaran, and X. Y. Bao, “Variable speed control of wind

turbines using nonlinear and adaptive algorithms,” Journal of Wind Engineering

and Industrial Aerodynamics, vol. 85, pp. 293-308.

[16] S. K. Chung, “Phase-locked loop for grid-connected three-phase power conversion

systems”, IEE Proc. Electr. Power Appl., vol. 147.

[17] T. Sun, Z. Chen, and F. Blaabjerg, “Voltage recovery of grid-connected wind

turbines after a short-circuit fault,” in Proc. The 29th Annual Conf. Of IEEE Ind.

Electron. Soc., IECON’03, Roanoke, VA, USA.

68

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Modeling of Wind Farms in the Load Flow Analysis

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