Modeling of Bi-directional Converter for Wind Power Generation
THESIS
Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in
the Graduate School of The Ohio State University
By
Muthanna Saleh Abu-hamdeh
Graduate Program in Electrical and Computer Science
The Ohio State University
2009
Master's Examination Committee:
Professor Ali Keyhani, Adviser
Professor Donald G. Kasten
Copyright by
Muthanna Saleh Abu-hamdeh
2009
Abstract
The global electrical power demand is steadily increasing. The absolute
dependence of conventional energy resources such as oil, coal or natural gas to
meet this demand is problematic for many reasons: its environmental impacts
such as pollution and global warming caused by greenhouse emissions, the rising
and unstable prices for fossil fuels and for some nations energy security is
considered as indispensable part of the national security.
Therefore, renewable energy technologies have been playing a key role in the
worldwide electrical power production. The advancement of power electronics in
terms of efficiency and functionality along with their declining cost all have
increased the contribution of renewable energy systems in the electricity
generation and solved significant problems in integrating those technologies with
existing power systems . Among renewable wind energy is the fastest growing,
however world has abundant amount of usable wind energy which has not been
utilized.
This thesis firstly discusses the contributions of some conventional energy sources
in electricity generation , then it covers essential topics about wind turbine
systems such as the power content of wind , the components and operation of
ii
wind turbine system , power and speed control methods implemented in modern
turbine systems and the electrical systems for wind turbines with focus on
generators and power converters used.
Finally, it deals with the core topic which is the bi-directional three-phase power
converter using pulse width modulation (PWM). PWM techniques in power
converters are gaining importance especially for harmonics control. The thesis
presents the mathematical modeling of the converter and a computer simulation
for its operation using Matlab/Simulink , then the analysis of the input/output
characteristics is presented.
iii
Dedication
This thesis is dedicated to my family.
iv
Acknowledgments
I wish first to thank my parents for their unlimited support and care. I am indebted
to my professors in the Electrical and Computer Engineering at The Ohio State
University for their help and guidance throughout my study. Special thanks to my
advisor Professor Ali Keyhani for his information and advices that helped me in
my graduate study and will help me in my profession. I wish also to thank
Professor Donald Kasten for his advices and for the great deal of knowledge I
learned from him in the classes he instructed or during his office hours.
v
Vita
January 1981 ..................................................……………………..Born in Kuwait
2003 ............................................................... …..B.Sc. Electrical Engineering, The
University of Jordan
2003-2007 ...................................................... Electrical Engineer for electric utility
companies in Jordan and for Gulf Consult in Kuwait
Fields of Study
Major Field: Electrical and Computer Engineering
vi
Table of Contents
Abstract ................................................................................................................... ii
Dedication .............................................................................................................. iv
Acknowledgments................................................................................................... v
Vita......................................................................................................................... vi
List of Figures ......................................................................................................... x
Chapter 1: World Energy Scene and Prospective ................................................... 1
1.1 Introduction ................................................................................................... 1
1.2 Fossil Fuel Power Generation ....................................................................... 7
1.3 Nuclear Power ............................................................................................. 11
1.4 Hydro-electric power .................................................................................. 15
1.4.1 Nomenclature ................................................................................................... 15
1.4.2 Notation ........................................................................................................... 16
1.4.3 Introduction ...................................................................................................... 17
1.4.4 Electric Power Output of Hydropower Plant ................................................... 18
1.4.5 Types of Hydro-turbines .................................................................................. 18
1.4.6 Types of Hydro-electric Generators ................................................................. 19
vii
1.4.7 Speed of Hydro-electric Generators ................................................................. 20
1.4.8 Hydro-electric Power World Utilization .......................................................... 21
Chapter 2: Wind energy ........................................................................................ 24
2.1 Nomenclature .............................................................................................. 24
2.2 Notation....................................................................................................... 24
2.3 Introduction ................................................................................................. 27
2.4 The Wind resource ...................................................................................... 28
2.5 Power Production ........................................................................................ 34
2.6 Estimating Annual Energy Production ....................................................... 37
2.6.1 Example ........................................................................................................... 39
2.6.2 Effect of height and surroundings .................................................................... 40
2.7 Horizontal-axis Wind Turbine Components and Operation ....................... 44
2.8 Speed and Power Control of Wind Turbines .............................................. 47
2.9 Wind Speed Range...................................................................................... 53
Chapter 3: Electrical System of a Wind Turbine ................................................. 58
3.1 Nomenclature .............................................................................................. 58
3.2 Notation....................................................................................................... 58
3.3 Introduction ................................................................................................. 60
3.4 Induction (Asynchronous) Generator Directly Coupled to the Grid .......... 63
3.5 Synchronous Generator with DC- link Converter ...................................... 69
3.6 Selection of Converter ................................................................................ 72
viii
Chapter 4: Power Electronics for Renewable Energy Systems ............................ 78
4.1 Notation....................................................................................................... 78
4.2 Introduction ................................................................................................. 80
4.3 Power Electronic Switch-mode Inverter ..................................................... 83
4.4 The Single-Phase Full Bridge Voltage Source Inverter.............................. 85
4.5 Principles of PWM ...................................................................................... 91
4.6 The Six-Step Three Phase Voltage Source Inverter ................................... 93
4.7 Three Phase Voltage Source Inverter Utilizing Space Vector PWM
Switching .......................................................................................................... 96
4.8 Three Phase Voltage Source Inverter Utilizing Sinusoidal PWM Switching
......................................................................................................................... 102
4.9 Three Phase Voltage Source Rectifier Utilizing Sinusoidal PWM Switching
......................................................................................................................... 108
4.10 Summary of Inverter Operation Range ................................................... 114
4.11 Summary of Rectifier Operation Range ................................................. 116
4.12 Conclusion .............................................................................................. 118
Bibliography ....................................................................................................... 119
Appendix ............................................................................................................. 121
ix
List of Figures
Figure 1 World net electric power generation in trillion (1012) killowatthours ..... 2
Figure 2 Growth of world net electric power generation and total energy
consumption. Year 1990 taken as reference. ......................................................... 3
Figure 3 World electricity generation by energy source in 2006 .......................... 4
Figure 4 World electricity generation by energy source in 2006 and projections
for 2010-2030 in trillion (1012) killowatthours ...................................................... 4
Figure 5 Renewable electricity generation in the US ........................................... 5
Figure 6 Diagram showing the components of a coal-fired power plant ............... 7
Figure 7 Diagram of the components of a gas turbine-based power plant ............ 8
Figure 8
CO2 sequestration process. CO2 emissions are captured then
sequestrated ........................................................................................................... 10
Figure 9 Diagram of Boiling-Water nuclear Reactor (BWR) components and
operation ............................................................................................................... 12
Figure 10 Diagram of Pressurized-Water nuclear Reactor (PWR) components and
operation . ............................................................................................................. 12
Figure 11 Top net electricity generation by nuclear power countries in 2007 . ... 15
Figure 12 Diagram of hydro-electric power plant . .............................................. 17
x
Figure 13 Contribution of hydroelectricity in the net electricity generation for
selected countries in 2007 .................................................................................... 21
Figure 14 Years 2000-2008 worldwide electricity generation for wind, biomass,
geothermal and solar resources . .......................................................................... 28
Figure 15 Rayleigh distribution functions for three different mean wind speeds. 31
Figure 16 Rayleigh wind speed frequency distribution functions for two sites each
having the same average wind speeds .................................................................. 32
Figure 17 Contiguous United States wind resource map ..................................... 33
Figure 18 Change of wind speed at a wind turbine ............................................. 35
Figure 19 Wind speed data for the case study ...................................................... 39
Figure 20 Effect of obstacles on wind speed, numbers shown are for wind speed
as a percent of speed if no obstacle is there ......................................................... 43
Figure 21 Wind turbine main components .......................................................... 44
Figure 22 Wind turbine rotor motion and blade cross-section ........................... 48
Figure 23 Wind forces on rotor blade .................................................................. 48
Figure 24 Distribution of aerodynamic forces over the blade length .................. 50
Figure 25 Rotor power coefficient of different rotor types .................................. 51
Figure 26 Turbine output power vs. wind speed curve ...................................... 55
Figure 27 Technical specifications for Vestas 2-MW wind turbine . ................... 57
Figure 28 Electrical system for wind turbine with synchronous generator and DClink converter ....................................................................................................... 61
Figure 29 Induction machine speed-torque characteristics .................................. 64
xi
Figure 30 Induction generator directly coupled to the grid ................................. 65
Figure 31 Fixed speed induction generator speed-power curves for a range of
wind speed . .......................................................................................................... 66
Figure 32 Induction generator system with rotor resistance converter for slip
control .................................................................................................................. 67
Figure 33 Sample technical specifications sheet for 1-MW/61.4-m fixed-speed
wind turbine with induction generator by Mitsubishi. .......................................... 68
Figure 34 Multi-pole synchronous generator with DC-link converter ................ 69
Figure 35 Power limiting at high wind speeds for variable-speed wind generator.
............................................................................................................................... 70
Figure 36 Sample technical specifications sheet for 0.9-MW/44-m variable-speed
wind turbine with synchronous generator and inverter by Enercon. .................... 71
Figure 37 Wind turbine system with AC/DC and DC/AC converters. ................. 72
Figure 38 Power conversion applications for renewable energy systems. ........... 81
Figure 39 Switch mode converter application for motor drive. The direction of
power flow is shown for motoring action. The opposite direction is for
regenerative or braking action when power is injected to the AC grid. ............... 84
Figure 40 Wind turbine system with bi-directional converter using batteries for
energy storage. ...................................................................................................... 85
Figure 41 Single phase inverter circuit. ................................................................ 86
Figure 42 Output voltage of full bridge inverter................................................... 88
Figure 43 Output voltage and current with blanking time. .................................. 90
xii
Figure 44 Magnitude spectrum. ........................................................................... 91
Figure 45 Three-phase inverter. ............................................................................ 93
Figure 46 Switching functions .. ......................................................................... 94
Figure 47 Output voltage of six-step inverter. ...................................................... 95
Figure 48 Phase voltage normalized spectrum. .................................................... 95
Figure 49 Three phase inverter output voltage space vectors .............................. 96
Figure 50 Allocation of switching periods for sector (I) to achieve minimal
switching losses. ................................................................................................... 99
Figure 51 Switched pulses generation for sine-triangle PWM. .......................... 103
Figure 52 Line and phase output voltages. ......................................................... 106
Figure 53 Phase voltage normalized frequency spectrum (Ma=0.566, Mf=15). 108
Figure 54 One-leg model of three-phase PWM rectifier. ................................... 110
Figure 55 Per-phase equivalent circuit at steady-state for fundamental frequency
voltage and ignoring line resistance. ................................................................... 110
Figure 56 Phase diagram for rectifier mode (fundamental frequency only). ...... 111
Figure 57 Rectifier mode at unity input power factor (fundamental frequency
only). ................................................................................................................... 111
Figure 58 AC side input voltage and current waveforms .................................. 112
Figure 59 DC output voltage.............................................................................. 112
Figure 60 Bridge leg to neutral PWM’ed voltage (VPWM,a) ................................ 113
Figure 61 AC input current spectrum ................................................................. 113
xiii
Figure 62 DC output variation with amplitude modulation index for PWM
rectifier at constant δ=20o(values in boxes are for AC input power factor at
operating point) ................................................................................................... 117
Figure 63 DC output variation with power angle for PWM rectifier at constant
Ma=0.7................................................................................................................. 117
Figure 64 Simulink model of switching pulses generation for 6-step inverter ... 123
Figure 65 Simulink model of switching pulses generation for sine-triangle PWM
............................................................................................................................. 124
Figure 66 Simulink model of three-phase voltage source full bridge inverter ... 125
Figure 67 Simulink model of three-phase voltage source full bridge rectifier ... 126
xiv
Chapter 1: World Energy Scene and Prospective
1.1 Introduction
The increasing interest in developing alternative energy sources is the product of
several factors. First, the rapid growth in electrical power demand. According to
the US Energy Information Administration (EIA) world electricity generation is
projected to increase by 44 percent from 2006 to 2020 as shown in Figure 1 . In
2006, world’s net electricity generation was 18 trillion kilowatthours and will
reach 26.02 trillion kilowatthours in 2020. The rising demand associated with
high and unstable fossil fuel prices apparently fosters the development efforts
towards alternative energy.
1
Figure 1 World net electric power generation in trillion (1012) killowatthours
(Data source: EIA,2009)
Second, the consumption of fossil fuels is associated with polluting emissions
such as COx and other gases causing global warming due to greenhouse effect,
besides their harmful effects on the living kinds. As a result, governments make
efforts to limit emissions by legislations and incentives to support the use and
development of renewable energy sources.
Furthermore, annual growth in world net electricity generation since 1990 has
outpaced the annual growth in world total energy consumption by 1 per cent, and
the growth in demand for electricity is projected to continue to outpace growth in
total energy as shown in Figure 2[1].
2
Figure 2 Growth of world net electric power generation and total energy
consumption. Year 1990 taken as reference. (Data source: EIA, 2009)
According to EIA, natural gas and coal are the second and third fastest-growing
sources of energy for electricity generation after renewable sources as it is
illustrated in Figure 4. However, the projections for coal could be changed if more
legislations are introduced to limit the emission of greenhouse gases.
In the 1960s, nuclear energy started to take a place as an energy source but the
share of nuclear electricity of today’s primary energy demand is still relatively
low[2]. In 2006, the fossil energy sources (coal, crude oil and natural gas)
generated more than 65 per cent of the world electricity as shown in Figure 3.
3
5%
15%
Liquids
41%
Nuclear
Renewables
Natural Gas
19%
Coal
20%
Figure 3 World electricity generation by energy source in 2006 (Data source:
EIA, 2009)
14.000
12.000
10.000
Liquids
8.000
Nuclear
6.000
Renewables
4.000
Natural Gas
2.000
Coal
0.000
2006
2010
2015
2020
2025
2030
Figure 4 World electricity generation by energy source in 2006 and projections
for 2010-2030 in trillion (1012) killowatthours (Data source: EIA, 2009)
EIA anticipates that the current world economic recession will not have any effect
on the electricity demand after 2010. Moreover, the recession mainly affects the
industrial sector compared to the residential sector since the latter continue to use
electrical power for home appliances, heating and cooling.
4
To sum up, the global energy demand will continue to increase in the foreseeable
future which demonstrates the need to secure energy supplies in an environmental
friendly way. Therefore, exploitation of renewable energies forms the key
solution for humanity.
As seen in Figure 5 ,although renewable electricity in 2008 represented less than
10% of overall electricity generation in the United States, a high level of
penetration for renewable energy sources in electricity generation is projected to
be seen especially with the low price per kWh they offer and their high efficiency.
Figure 5 Renewable electricity generation in the US [1]
5
Indications of the growing contribution in the US electricity supply include [3]:
•
Renewable electricity installations in the United States (excluding
hydropower) have nearly tripled since 2000. In 2008, it represented 41.9
GW of installed capacity. Wind energy installed capacity in 2008 (25 GW)
is almost ten times that of 2000 (2.6 GW).
•
Wind energy and solar PV cumulative capacity grew 51% and 44%,
respectively from 2007 to 2008.
6
1.2 Fossil Fuel Power Generation
Fossil fuel-based electrical power plants consist of three main components [4]:
1. Combustion chamber or boiler: to convert fuel to heat. Combustion
chamber is used in gas-fired systems whereas boilers heat water in coal
plants.
2. Turbine: converts thermal energy to mechanical energy. In coal fired
plants high pressure steam spins the turbine which spins the generator. The
steam is condensed into water after cooling and pumped back to boiler.
3. Generator (alternator): converts mechanical energy to electrical.
Figure 6 Diagram showing the components of a coal-fired power plant [5]
7
Figure 6 shows the components of a typical coal-fired electricity generating plant.
Coal plants are normally operated to meet the base load requirements. The
efficiency of a conventional coal plant is not more than 40% [6].
As an example, boilers at a 1.7-GW coal-burning power plant heat water to about
540oC to generate steam. The steam at a pressure of about 130 kg/cm2 is piped to
the turbine which spins the generator at 3600 rpm to generate voltage at 60 Hz, 20
kV. The plant generates annually about 10 billion kWh and burns daily about
14000 tons of coal [5].
Peak loads appear generally for short period and they are met by gas turbines
which start quickly. Open cycle Gas turbines capital cost is lower relative to coal
plants but the operation cost for the former is higher. Figure 7 shows the
components of gas turbine power plant.
Figure 7 Diagram of the components of a gas turbine-based power plant [5]
8
The current developments on fossil fuel power plants aim to achieve the following
objectives [4]:
1.
Reduce CO2 emissions mainly by replacing existing turbines with
poor efficiency with the new generation of turbines. Currently,
development
of combined cycle gas turbines (CCGT) led to
efficiencies of about 50% [6].In these turbines the natural gas is
burnt at temperatures of about 1000 °C to spin a turbine and the
exhaust gases are subsequently used to produce steam for a
traditional steam turbine. Both turbines drive separate generators
feeding power to the grid. Despite the international interest and plans
to shift towards renewable energy systems, difficulties such as high
capital costs and limited renewable energy systems manufactures’
production capacity obstructs the shift and results in that small
contribution of renewable energy systems in the total electricity
generation as illustrated in the statistics previously. On the other
hand, it takes less time to manufacture the new combustion turbines
compared to the time required to manufacture an equivalent system
of wind or solar power.
2.
Utilization of biofuels in electricity generation either by including
them in the fuel mix of existing plants or by building new stations
biofuel based stations. Biofuels are produced from crops and forest
products. The difference between fossil fuels and biofuels is the fact
9
that the carbon in boifuels comes from the atmosphere, therefore,
combustion of biofuels causes no net CO2 emission to the
atmosphere. The growth of utilizing this recourse is limited by the
world needs to foodstocks to feed people.
3.
CO2 sequestration : in this process CO2 generated from combustion is
separated and transferred in to a sequestration facility .Modifying the
existing fossil fuel power plants with such technology would
increase their viability in the long run. Figure 8 illustrates the
process of sequestration.
Figure 8 CO2 sequestration process. CO2 emissions are captured then
sequestrated [4].
10
1.3 Nuclear Power
There are two types of nuclear reactions, fusion and fission. Fissioning of
Uranium-235 atoms have been used to generate a significant percentage of
worldwide electrical power (uranium is the most commonly used nuclear fuel).
Fission takes place in the reactor core which comprises metal tubes “fuel rods”
containing fissionable material (slightly enriched uranium dioxide). The reactor
core is contained within a pressure vessel safety shield. To regulate the chain
reaction, water or graphite moderators slow down the neutrons and control rods
are inserted into the core to absorb neutrons. Control rods are made of a material
such as boron. In Boiling-water Reactors (BWR) water or gas passes through the
reactor to absorb heat then it is carried away from the core as steam(see Figure 9).
Similar to coal fired station, steam turbine then drives electrical generator [6].
A variation of BWR is implemented in Pressurized-Water Reactors (PWR) shown
in Figure 10 where the superheated water in the primary cooling loop flows
through heat exchanger “steam generator” that is used to boil water and create
steam in a secondary loop that feeds the turbo-generator. The two loop design of a
PWR keeps the radioactivity isolated and only clean steam is circulated through
the turbine. This helps to minimize maintenance costs and radiation exposures to
the plant personnel [1].
11
Figure 9 Diagram of Boiling-Water nuclear Reactor (BWR) components and
operation [5].
Figure 10 Diagram of Pressurized-Water nuclear Reactor (PWR) components and
operation [5].
The main advantages of nuclear reactors in electricity generation are:
1. They deliver huge amount of power per mass of fuel consumed.
12
2. Low fuel and operational costs hence they are normally used to supply
base loads
3. High load factor.
4. Relatively small footprint for the amount of power generated.
5. No air pollutants emissions from the consumption of nuclear fuel.
The environmental advantages of nuclear power are well publicized, even if they
are not often paired with the relative disadvantages of spent fuel management and
plant decommissioning costs [7]. Following are the main limitations and
disadvantages of electricity generation by nuclear reactors:
1. Inflexible and undispatchable.
2. Issues related to plant safety.
3. Hazard and high cost associated with handling radioactive by-products
during nuclear fuel extraction, consumption and at the disposal stage.
4. High cost to decommission the nuclear plant and its site and the end of its
lifetime. Official estimates in the US projects decommissioning cost of
$300 to $500 million per nuclear plant [7].
5. As coal-fired power plants, nuclear reactors require large amount of water
for cooling.
6. Earth has limited reserve of uranium, therefore if all fossil fuel based
stations are replaced by nuclear sources then uranium will deplete.
7. Significant indirect CO2 emissions (during construction stage, uranium
mining, transport and disposal).
13
8. Final storage of radioactive waste is also very problematic, because this
waste will retain its lethal properties over thousands of years [2].
Despite the fact that nuclear power is one of the most readily available sources of
energy independence for any country , any decision to utilize the advantages of
nuclear power in mitigating greenhouse emissions will arise from a combination
of political and economic considerations. The economic component of this
decision presently is not encouraging since new nuclear power plants presently
cost more to build than do fossil fuel plants whether these plants are coal fired or
natural gas-fired [7].
To demonstrate how nuclear power utilization varies from country to another
(Figure 11), one could consider France in which nuclear power supplies most of
its electricity needs, whereas industrial nations such as Australia, Austria,
Denmark, Norway or Portugal do not operate any nuclear power stations at all.
After the Chernobyl, disaster Italy decided to abandon nuclear power
utilization[2].
14
Figure 11 Top net electricity generation by nuclear power countries in 2007 [1].
1.4 Hydro-electric power
1.4.1 Nomenclature
The following terms are used throughout this section:
Head: The difference in elevation between two specified points, for example, the
vertical height of water in a reservoir above the turbine.[8]
Low-head plant: A power plant with a head less than 100 ft (30.5 meter) [8].
Reservoir: A body of water impounded in an artificial lake behind a dam [8].
Turbine runner: The rotor-blade assembly portion of the hydraulic turbine where
moving water acts on the blades to spin them and impart energy to the rotor [8].
15
1.4.2 Notation
The following notations are used throughout this section:
fe : Electrical frequency , Hz
g : Standard gravitational acceleration , m/s2
H : Total net head (water height), m
Hz : Hertz
nr : Rotational speed of the rotor , r.p.m
p : Number of magnetic poles in the machine
P : Power, Watt (W)
Q : Volumetric flow rate, m3/s
r.p.m : Revolution per minute
ηg : Generator power efficiency
ηt : Hydro-turbine power efficiency
ρ : Density of water, kg/m3
16
1.4.3 Introduction
Large scale hydro makes use of large reservoirs of earth surface water , usually
created by damming rivers. Water is allowed to flow out of the reservoir in a
controlled manner, turning turbines that drive electrical generators.
As illustrated in Figure 12, a weir creates a height or potential difference between
the water before and after the weir. The potential difference forces water to flow
through a turbine, which transforms the potential energy into mechanical energy.
The turbine drives an electric generator which converts mechanical power into
electricity. A power transformer converts the generator voltage to the grid
voltage.
Head (H)
Flow rate Q
(in m3/s)
Figure 12 Diagram of hydro-electric power plant [5].
17
1.4.4 Electric Power Output of Hydropower Plant
The electric power output of the hydropower plant can be calculated from the
efficiency of the generator (ηg) and the turbine (ηt), the density of the water, the
effective head H (in meters) which includes the effect of friction, the gravitation
constant and the flow rate Q (in m3/s).
P = ηg × ηt × ρ ×g×Q× H
(in Watts) [2]
Where water density ρ = 1000 kg/m3 and g = 9.81 m/s2
1.4.5 Types of Hydro-turbines
Hydro-turbines are classified according to the relative proportions of power
transferred by a change of static pressure and by a change in velocity for water.
The term “reaction” is defined as the ratio of this transfer by means of a change in
static pressure to the total change in the runner, sometimes “reaction” is called the
“degree of reaction”. Based on this concept a hydro-turbine is a reaction turbine if
there is any significant pressure change in the runner of a turbine. On the other
hand, if there is no change in pressure, only in velocity, the turbine is called
“impulse’’ hydraulic turbine [8].
Hydro-turbines are classified further in two separate ways; by the type of runner
and by the configuration of the water passages. For reaction turbines, there are
different classifications of runners - axial, radial, and mixed depending on
18
whether the flow enters the runner parallel or perpendicular to the shaft, or at
some angle in between. In modern reaction turbines, the flow leaves the runner
axially. Depending on the head height and flow rate, different turbines are used.
Common turbines are the Pelton, Francis or Kaplan turbines. For the lowest head
applications, reaction turbines with propeller type runners are utilized [8].
1.4.6 Types of Hydro-electric Generators
The majority of hydro-electric generators are synchronous machines with
stationary armatures and salient pole rotor.
A three-phase set of windings is embedded in the stator (armature) slots .The
stator is made of a steel core encircled by a frame that is mounted to the power
plant foundation. Three phase voltages are generated in the stator windings threephase armature winding, in which the alternating current is generated. The stators
of hydro-electric generators normally have large diameter compared to other types
of generators, and can exceed 60 ft [8].
The rotor is mechanically coupled to the turbine and it produces a rotating
magnetic flux. The rotor windings are connected to external DC source using
brushes and slip rings to generate the magnetic field. For some generators an
amortisseur (damper) winding is mounted on the rotor poles to reduce mechanical
oscillations that may occur during abnormal conditions.
19
The capacity of hydroelectric generators may range from a fraction of an MVA to
more than 800 MVA. Hydroelectric generators are typically air cooled, for
highest capacity generators the stator windings are directly water cooled [8].
1.4.7 Speed of Hydro-electric Generators
The rotational speeds of the generator and turbine are usually the same because
their shafts are directly connected. However, in some cases a speed increaser
(gearbox) is used to enable the generator to operate at a higher speed than that of
the turbine, thus permitting a smaller and less expensive generator to be used.
Hydro-generators are relatively low-speed machines, typically ranging from 50 to
600 rpm with large number of poles in the stator. Large diameter units with a
lower hydraulic head operate at slower speeds, whereas physically smaller units
with high hydraulic head operate at higher speeds. The best speed for each type of
turbine is first established, and a generator is then designed that will produce 60
cycle alternating current at that speed [8].
For synchronous generator operating at 60 Hz, the rotational speed of the rotor
(nr) in rpm is related to the number of field poles (p) in the rotor as follows.
Hence,
𝑓𝑓𝑒𝑒 = 60 = 𝑛𝑛𝑟𝑟 × 𝑝𝑝 /120
𝑛𝑛𝑟𝑟 × 𝑝𝑝 = 7200
20
In other words, the higher the number of magnetic poles in the machine the lower
the rotor speed will be and vice versa.
1.4.8 Hydro-electric Power World Utilization
A significant portion or world energy demand is supplied by hydro-electric
power. According to EIA the share was about 15% in 2007. Figure 13 shows the
contribution of hydro-electric power in the net electricity generation for selected
countries. It is clear that the utilization depends of the availability of the hydro
resource (mainly rivers) in the first place.
100
90
Percent share
80
70
60
50
40
30
20
10
United Kingdom
Germany
United States
France
Egypt
India
Sweden
Canada
Iceland
Brazil
Norway
Paraguay
0
Figure 13 Contribution of hydroelectricity in the net electricity generation for
selected countries in 2007 [1].
21
There are several advantages of hydroelectric power plants:
1. Hydroelectric power plant projects provide multidiscipline development
for the targeted are such as flood control, irrigation and water supply.
2. High efficiency of power conversion.
3. Provides abundant amount of electricity at very low cost. According to US
department of Energy, the price of hydro-generated electricity in 2008
ranged from 2-5 cents per kWh which is effectively the lowest among all
other renewable technologies.
4. No greenhouse gas emission.
5. No fuel required to generate electricity.
6. Flexible and provides the best solution to meet peaking load demands at
low operational cost relative to gas turbines for example.
7. Hydro generators are effective in providing critical services to maintain
reliable operation of power systems. These include[8]:
a) Reactive Supply and Voltage Control: by operating hydro
generator in synchronous condense mode they are capable of
providing voltage control to the system.
b) Regulation: by providing the amount of real power required to
balance generation and loads in the system on minute-by-minute
basis.
22
c) Spinning reserve: hydro generators can act as stand by generating
capacity able to respond immediately in case of system
contingency, this capacity is fully available in ten minutes.
A side from high capital cost, the disadvantages of hydroelectric plants are mainly
related to environmental impacts of these plants and sometimes the need to
relocate people.
Table 1 shows features of different generators for selected conventional and
renewable sources.
Table 1 [6]
Energy source
Gas (Closed
Cycle Gas
Turbine)
Gas (Open Cycle
Gas Turbine)
Coal
Nuclear
Hydro with
reservoir
Wind
Photovoltaic
Typical unit
size
Output
varies with
time?
No
Predictable
Dispatchable
Yes
Yes
100 MW
No
Yes
Yes
500 MW
500 MW
Up to 500
MW
Up to 5 MW
1 kW,
domestic
No
No
No
Yes
Yes
Yes
Yes
No
Yes
Yes
Yes
Not accurately
Not
accurately
No
No
Up to 500
MW
up to 100 kW
commercial
23
Chapter 2: Wind energy
2.1 Nomenclature
The following terms are used throughout this chapter:
Blade pitching : Adjusting (turning) the turbine blades to vary rotor’s speed.
Nacelle: Weather-proof streamlined enclosure for housing shafts, generator,
controller and rotor brakes.
TSR (tip speed ratio) : The ratio between the rotor’s blade outermost tip speed
and the wind speed.
Weibull and Rayleigh Distribution Functions: probability distribution functions
used to describe random quantities such as wind speed.
2.2 Notation
The following notations are used throughout this chapter:
A: Area or rotor blades swept area , m2.
a: Scale parameter of the distribution function.
24
cP: Rotor’s power coefficient or efficiency.
F: Force , Newton.
f: Relative probability of wind speed being v during any time interval .
h : Height , m.
k: Shape parameter of the distribution function .
mph: Mile per hour
nr : Rotor’s rotational speed , r.p.m.
P : Power , Watt.
PT: Power captured by the turbine, Watt.
r : Radius of the turbine’s rotor, m.
r.p.m: Revolution per minute.
u: Linear speed of the blade’s outermost tip , m/s.
v: Wind speed, m/s.
va : Apparent wind speed , m/s.
vD : Design wind speed for a turbine , m/s.
25
VRMC : Root mean cube of the wind speed, m/s.
vw : Upstream wind speed , m/s.
𝑣𝑣̅ : Average wind speed, m/s.
α : Blade pitch angle , degrees.
α : Friction coefficient of the ground surface .
β : Blade’s attack angle, degrees.
ρ : air density, kg/m3.
ω : Rotor’s angular rotational speed , rad/s.
𝜂𝜂 : Power efficiency.
𝜆𝜆 : Tip speed ratio.
26
2.3 Introduction
Historians estimate that wind energy has been utilized to sail ships about 5000
years ago. Besides transpiration, old applications include grains milling and water
pumping.
The first wind turbine for electricity generation was in Denmark in 1891. In the
modern history, the 1973 oil crisis initiated broad development efforts in western
industrialized countries to reduce dependence on imported oil. Since that year,
Denmark has been the leading country in utilizing small wind turbines in
electrical power generation.
Nowadays, wind energy is the fastest growing renewable energy technology
worldwide as shown in Figure 14.
Improved turbine and power converters
designs caused a significant drop in wind energy generation cost making it the
least expensive source of electricity (from 37 cents/kWh in 1980 down to 4
cents/kWh in 2008).
In 2008, wind energy systems worldwide generated 331,500 million kWh which
is 1.6% of total electricity generation placing it in the second rank after hydroelectric power (16.6%). Photovoltaic (PV) technology contribution was 0.1% only
[1].
27
Figure 14 Years 2000-2008 worldwide electricity generation for wind, biomass,
geothermal and solar resources [1] .
World have abundant wind resources. Consider, for example, the United States
which possesses more than 8,000 GW of land-based wind resources suitable for
harness and an extra 2,000 GW of shallow offshore resources (for the purpose of
comparison , US total electricity generating capacity was 1,109 GW in 2008).
2.4 The Wind resource
The main consideration for sitting a wind project in a certain site is the wind
resource. Other considerations include site accessibility, terrain, land use and
proximity to transmission grid for grid-connected wind farms.
28
The main sources of the global wind movements are the earth rotation, regional
and seasonal variations of sun irradiance and heating. Local effects on wind
include differential heating of the land and the sea (land heats up faster),
topographical nature such as mountains and valleys, existence of trees and
artificial obstacle such as buildings.
At any location wind is described by its speed and direction. The speed of the
wind is measured by anemometer in which the angular speed of rotation is
translated into a corresponding linear wind speed (in meters per second or miles
per hour). A Standard anemometer averages wind speed every 10 minutes. Wind
direction is determined by weather vane.
Average (mean) wind speed is the key in determining the wind energy potential in
a particular site. Although long-term (over 10 years) speed averages are the most
reliable data for wind recourse assessment, this type of data is not available for all
locations. Therefore, another technique based on measurement, correlation and
perdition is used. Wind speed measurements are recorded for a 1-year period and
then compared to a nearby site with available long-term data to forecast wind
speed for the location under study.
The annual available wind energy is obtained by studying wind speed distribution.
Weibull [2] probability or frequency distribution function is used to describe the
variation in wind speed and it is given by [2]
29
𝑓𝑓(𝑣𝑣) =
Where
𝑘𝑘 𝑣𝑣 𝑘𝑘−1 −(𝑣𝑣 )𝑘𝑘
� �
. 𝑒𝑒 𝑎𝑎
𝑎𝑎 𝑎𝑎
f is the relative probability of wind speed being v during any time interval ,
v is the wind speed,
k is the shape parameter of the distribution function, and
a is the scale parameter of the distribution function.
At most sites, wind speed has the Rayleigh distribution which is a special case of
Weibull distribution with k = 2.This makes Rayleigh distribution a simple and
fairly accurate representation for wind speed with only the scale parameter (a).
The frequency of a particular wind speed band over a period of one year is found
from wind speed data by[9]
𝑓𝑓 =
𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 𝑜𝑜𝑜𝑜 ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 𝑝𝑝𝑝𝑝𝑝𝑝 𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦 𝑡𝑡ℎ𝑒𝑒 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 𝑖𝑖𝑖𝑖 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑣𝑣 𝑎𝑎𝑎𝑎𝑎𝑎 𝑣𝑣 + ∆𝑣𝑣
∆𝑣𝑣
Mean wind speed over the period of time is defined as the total area under the f–v
curve integrated from v = 0 to ∞ and divided by the total number of hours in the
period (365×24=8760 if the period is one year). The approximate annual mean
speed is given by [9]
𝑣𝑣̅ = 0.9 𝑎𝑎
30
Hence,
given
the
mean
wind
speed
for
a
site
and
assuming
𝑎𝑎 = 𝑣𝑣̅ , the Rayleigh distribution would be [9]
𝑓𝑓(𝑣𝑣) =
2𝑣𝑣 −(𝑣𝑣 )2
. 𝑒𝑒 𝑣𝑣�
𝑣𝑣̅ 2
The Rayleigh distribution functions for different mean wind speeds is shown in
Figure 15. It is noted that the curve moves to the right for greater mean wind
speeds (also greater value of shape parameter a) which means more days have
high winds and hence a better potential wind energy revenue.
Figure 15 Rayleigh distribution functions for three different mean wind speeds.
31
Figure 16 Rayleigh wind speed frequency distribution functions for two sites each
having the same average wind speeds [10].
The wind speed frequency distributions shown in Figure 16 are obtained from
wind speed data for a year of 10-minute means for two sites with similar average
wind speed. The site on the left experiences prevailing winds while receives most
of its wind during high-wind storms.
32
Figure 17 Contiguous United States wind resource map [11]
Wind energy resource map for contiguous United States is shown in Figure 17.
This wind map provides information about annual average wind speed and wind
power density (in W/m2) at 50-meter (164-ft) tower height and it can be used for
initial site assessment. It noted that coastal areas have high wind energy potential.
However, about 90% of the usable wind resource in the US lies in the wind belt
spanning the eleven Great Plain states [9].This map is prepared by The National
Renewable Energy Laboratory (NREL) which periodically classifies the US wind
resources by wind speed. Areas of wind power class of 4 or higher are favorable
locations for wind generation projects.
33
As mentioned previously, even if an area has good wind conditions, other
important factors should be considered for sitting wind farm project such as
geographical, terrain and meteorological data. Therefore, estimates of the
electricity that could potentially be generated by wind power are based on wind
resource data and exclude windy lands that are not suitable for development as a
result of environmental and land-use considerations [9].
2.5 Power Production
The mechanical power of the wind passing an area of A with speed v is
𝑃𝑃 =
1
𝜌𝜌. 𝐴𝐴. 𝑣𝑣 3
2
Where ρ is the density of air. The density of air varies with the air temperature
and pressure. For the wind turbine rotor shown in Figure 18 , the area swept by
the rotor blades is A and the turbine slows the wind from speed v1 (wind speed at
the entrance of the rotor blades)to v2 (wind speed at the exit of the rotor
blades).Since A2 > A1 then v1 > v2.
It can be noted from the previous equation that the power of the wind varies
linearly with the air area swept by rotor blades and with the cube of wind speed.
34
Figure 18 Change of wind speed at a wind turbine [2]
Assuming constant pressure and hence constant air density , the mass air flow is
the same after and before the turbine [2]
𝑑𝑑𝑑𝑑
𝑑𝑑𝑑𝑑
𝑑𝑑
= (𝜌𝜌 . 𝑉𝑉) = 𝜌𝜌.
= 𝜌𝜌. 𝐴𝐴. 𝑣𝑣 = 𝜌𝜌. 𝐴𝐴2 . 𝑣𝑣2
𝑑𝑑𝑑𝑑
𝑑𝑑𝑑𝑑
𝑑𝑑𝑑𝑑
Where V is the air volume and v is the wind speed at the height of the turbine
rotor. Moreover, v is the average of winds speeds v1 and v2.
That is,
𝑣𝑣 =
𝑣𝑣1 + 𝑣𝑣2
2
And the mechanical power taken from or extracted the wind after passing through
the turbine[2],
35
𝑃𝑃𝑇𝑇 =
1
𝜌𝜌. 𝐴𝐴. (𝑣𝑣1 2 − 𝑣𝑣2 2 ). (𝑣𝑣1 + 𝑣𝑣2 )
2
The power content of wind passing through the area A in the absence of the
turbine is [2]
𝑃𝑃 =
1
𝜌𝜌. 𝐴𝐴. 𝑣𝑣 3
2
Hence, the power coefficient cp or rotor coefficient which is the ratio between PT
and P is found[2].
1
𝑣𝑣2 2
𝑣𝑣2
𝑐𝑐𝑝𝑝 = 𝑃𝑃𝑇𝑇 /𝑃𝑃 = �1 − 2 � . �1 + �
𝑣𝑣1
𝑣𝑣1
2
That represents the fraction of the upstream wind power that is extracted by the
rotor blades .It can be shown that cp is at its maximum when
𝑣𝑣2 1
=
𝑣𝑣1 3
Which is the ideal wind speed ratio, the maximum power coefficient will be[2]
𝑐𝑐𝑝𝑝,𝑚𝑚𝑚𝑚𝑚𝑚 ≈ 0.593
This is often called Betz Power Coefficient and it means that theoretically about
60% of the wind power is taken by the turbine if it slows the air to one-third of its
original speed. However, practical wind turbines have power coefficient values
ranging from 0.4 to 0.5 for modern high-speed turbines and between 0.2 to 0.4 for
36
low speed turbines with more blades [9]. The efficiency of the wind turbine
would then be the ratio of the power taken to the ideal usable power
𝜂𝜂 =
𝑃𝑃𝑇𝑇
𝑐𝑐𝑝𝑝,𝑚𝑚𝑚𝑚𝑚𝑚 . 𝑃𝑃
=
𝑐𝑐𝑝𝑝 . 𝑃𝑃
𝑐𝑐𝑝𝑝
=
𝑐𝑐𝑝𝑝,𝑚𝑚𝑎𝑎𝑎𝑎 . 𝑃𝑃 𝑐𝑐𝑝𝑝,𝑚𝑚𝑚𝑚𝑚𝑚
In summary, the maximum power output of the turbine per square meter of rotor
swept area is (assume rotor coefficient equal to ½ )
𝑃𝑃𝑇𝑇,𝑚𝑚𝑚𝑚𝑚𝑚
11
. 𝜌𝜌. 𝐴𝐴. 𝑣𝑣 3 1
2
2
=
= 𝜌𝜌. 𝑣𝑣 3
𝐴𝐴
4
2.6 Estimating Annual Energy Production
It has been shown that the power extracted by the rotor is proportional to the cube
of wind speed , therefore it is useful to define a new value called room mean cube
(RMC) of the wind speed which gives better representation
to the energy
collected over a year
𝑉𝑉𝑅𝑅𝑅𝑅𝑅𝑅
∞
∫ 𝑓𝑓(𝑣𝑣). 𝑣𝑣 3 . 𝑑𝑑𝑑𝑑
=�0
365 × 24
3
Where the f(v) is the frequency distribution function for wind speed at that
location (as mentioned previously a Rayleigh function with corresponding scale
parameter a best fits wind speed frequency data for most sites).
37
Therefore, the annual average power generation (in watts per square meters of
rotor blades swept area) is
𝑃𝑃𝑇𝑇,𝑚𝑚𝑚𝑚𝑚𝑚 =
1
𝜌𝜌. 𝑉𝑉𝑅𝑅𝑅𝑅𝑅𝑅 3
4
And the annual energy production is found as
𝐸𝐸 =
1
𝜌𝜌. 𝑉𝑉𝑅𝑅𝑅𝑅𝑅𝑅 3 × 365 × 24
4
The wind resource map shown in Figure 17 indicates both average wind speed
and annual average power density. However, there is no unique correspondence
between the two quantities. This is illustrated by the example shown in Table 2
below which shows three wind farm sites with the same average wind speed but
different annual power density and hence different energy yield.
Table 2 [9]
Site
Annual Average Wind
Speed (m/s)
Annual Power Density
(W/m2)
Culebra,PR
6.3
220
Tinna Beach,NY
6.3
285
San Gorgonio,CA
6.3
365
38
2.6.1 Example
Assuming the annual wind speed data for a site are shown in Figure 19 with
annual mean speed of 𝑣𝑣̅ = 13.29 𝑚𝑚/𝑠𝑠 , it is required to estimate the average
annual power and energy density for that site .
Figure 19 Wind speed data for the example
Solution : In order to find the average annual power and energy density, the RMC
speed need to be calculated .The annual average wind speed is given as
𝑣𝑣̅ = 13.29 𝑚𝑚/𝑠𝑠
Assuming Rayleigh distribution with shape parameter a equal to
𝑎𝑎 =
𝑣𝑣̅
= 14.77
0.9
Therefore, the Rayleigh distribution function which fits wind data is
39
𝑓𝑓(𝑣𝑣) =
𝑣𝑣 2
2 𝑣𝑣
. 𝑒𝑒 −(14.77 )
14.77
Where f is expressed in relative frequency, then the RMC wind speed is found by
evaluating the following integral using trapezoidal numerical integration
3
∞
𝑉𝑉𝑅𝑅𝑅𝑅𝑅𝑅 = �� 𝑓𝑓(𝑣𝑣). 𝑣𝑣 3 . 𝑑𝑑𝑑𝑑
0
Hence,
𝑉𝑉𝑅𝑅𝑅𝑅𝑅𝑅 = 16.24 𝑚𝑚/𝑠𝑠
The wind power density which can be captured by the wind turbine assuming
maximum theoretical rotor power coefficient cp=0.5 and air density ρ=1.225
kg/m3
𝑃𝑃𝑇𝑇,𝑚𝑚𝑚𝑚𝑚𝑚 =
1
𝜌𝜌. 𝑉𝑉𝑅𝑅𝑅𝑅𝑅𝑅 3 = 1311 W/m2
4
And the site estimated annual energy yield per square meter of the turbine rotor
swept area is
E = 1311 × 365 × 24 = 11500
2.6.2 Effect of height and surroundings
kWh
/yr
m2
Wind speed increases with height up to 450 m from ground level then it
decreases. This is an important fact to utilize in the design of modern wind turbine
40
towers by increasing the tower height and consequently increasing the wind
power density.
To estimate wind speed at a certain height from available measurements at
another height the following relationship
Where
𝑣𝑣(ℎ2 ) = 𝑣𝑣(ℎ1 ). (ℎ2 /ℎ1 )𝛼𝛼
h1 is the reference height ,
v1 wind speed at the reference height ,
h2 the height at which wind speed v2 need to be estimated and
α is the friction coefficient of the ground surface .
The ground surface friction coefficient is dependent on the terrain type. Friction
coefficient α for different terrains is shown in Table 3 .
Trees, hills, buildings and other obstacles slow wind speed and cause wind
turbulence. Wind turbulence reduces usable wind energy by the so called wind
shading -wind speed reduction especially behind the obstacle if it is in the side of
upstream prevailing wind-and increases the stress and wear of that turbine which
affects its lifetime.
41
Therefore, for sitting the wind turbine in a particular site with obstacles it is
important to keep ample clearance between the tower and the obstacle.
Furthermore, the bottom of the rotor blade should be three times higher than the
obstacle [2]. Co-location of wind turbines can also cause disturbance between
them. A noteworthy advantage for offshore wind that wind speed is less
dependent on the altitude because of the smooth surface of the water, therefore
lower hub height and smaller rotor diameter turbines cab be used .
Table 3 [9]
Terrain Type
Friction Coefficient
Lake, ocean smooth hard ground
0.1
Foot-high grass on level ground
0.15
Tall crops, hedges, and shrubs
0.2
Wooded country with many trees
0.25
Small town with some trees and shrubs
0.3
City area with tall buildings
0.4
42
Figure 20 Effect of obstacles on wind speed, numbers shown are for wind speed
as a percent of speed if no obstacle is there [12]
The effect of wind shading is delineated in Figure 20. A 20-m tall obstacle
(shown with dark grey color on the left) is located 300 meter way from a 50-m tall
turbine tower. It is noted that wind speed at the hub height is 97% of the speed
without obstacle, the corresponding wind power is 0.973=91% and that means a
loss of about 10% in wind power.
43
2.7 Horizontal-axis Wind Turbine Components and Operation
Figure 21 Wind turbine main components [3]
Horizontal-axis wind turbine is made of the following components:
1. Blades: two or three blades are attached to the hub; they are made of high
density wood or epoxy and fibreglass composites. Wind exerts drag
(perpendicular to the blades) and lift forces on the blades. Since lift forces
cause the rotor to turn, blades cross section is designed to minimize drag
forces and boost lift forces to increase turbine output power at various
44
speeds. Some aerodynamic blade designs make use of the stall effect to
limit the rotor speed at high wind speeds.
2. Rotor.
3. Pitch control (optional) :an electric motor or hydraulic mechanism is used
to turn (or pitch) the blades to maximize the power capture of the turbine
or to reduce rotor’s rotational speed in high winds.
4. Rotor brake could be disk type to stop the rotor for maintenance or in
emergencies. Some modern turbines are provided with hydraulic brakes.
Turbines’ manufactures specify the cut-in and the cut-out wind speeds for
their turbines and the rotor brakes stop the wind turbine when its power
output is either too low or too high.
5. Low-speed shaft transfers mechanical power of the rotor at a speed of 3060 rpm [9] to the gearbox.
6. Gearbox couples low-speed and high-speed shafts and steps-up the
rotational speed to 1200-1600 rpm [9] suitable for electric generators.
Some turbine designs contain no gearbox due to many disadvantages such
as noise, high cost, frictional losses and maintenance requirements.
7. Generator to convert mechanical power to electrical power. Mostly
induction generators are used for wind turbines. For gearless or directdriven turbines, the generator must have large number of magnetic poles
which means higher cost.
45
8. Controller receives signals from sensors (e.g. anemometer, tail vain) to
regulate and control the turbine’s electrical and mechanical operation.
9. Anemometer: measures the wind speed and sends the measurements to the
controller.
10. Wind vane to measure wind direction and sends it to the controller which
in turn commands the yaw drive to aim the turbine nose cone in the proper
orientation as the wind direction changes.
11. Nacelle: a weather-proof streamlined enclosure for housing shafts,
generator, controller and rotor brakes.
12. High-speed shaft which mechanically couples the gearbox and rotor of the
electric generator.
13. Yaw drive to orient the nacelle and the rotor using the yaw motor or
hydraulic mechanism. Yawing is required only for upwind turbines
because the wind automatically orients downwind turbines.
14. Yaw motor moves the nacelle with its components.
15. Tower made of steel or concrete which holds the rotor blades and the
nacelle. Modern turbines towers are tubular with heights of approximately
equal to the rotor diameter, however minimum height is 25 meters [9] to
avoid turbulence caused by obstacle. The large masses of the rotor and the
nacelle, strong vibrations and wind shear forces acting on the tower all
make high tower designs and construction an increasingly serious
challenge.
For
instance,
the
46
top
head
mass
(THM)
of
Vistas 80-2 MW /80–meter three-blades turbine is 107 metric tons , this
includes the weight of nacelle, hub and blades.
2.8 Speed and Power Control of Wind Turbines
Wind acts on rotor blade by two types of forces. The first is the drag force, which
ties to move the blade in the same direction as the wind; this force causes the cup
anemometer to rotate, for a wind turbine rotor this force act perpendicularly to the
blades and hence it slows the rotor down . The second and the desirable force for
a wind turbine is the lift force which a buoyancy force according to Bernoulli
principle in fluid dynamics, this force causes the blades to rotate about the hub.
As seen in Figure 22 the blade section has unsymmetrical sides for aerodynamic
purpose, when wind flows (vw) the upper surface of the section experiences high
speed flow (underpressure) and the lower experiences low speed flow
(underpressure). The pressure difference produces lift force which moves the
blade and rotates the rotor with velocity u (linear speed of the blade’s outermost
tip).
47
Figure 22 Wind turbine rotor motion and blade cross-section [2]
The apparent wind velocity (vA) is produced from real wind speed (vw) and rotor
blade tip speed (u), that is
|𝑣𝑣𝐴𝐴 | = �|𝑢𝑢|2 + |𝑣𝑣𝑊𝑊 |2
An important ratio is called the Tip Speed Ratio (TSR) λ
𝜆𝜆 = 𝑢𝑢/𝑣𝑣𝑊𝑊
Figure 23 Wind forces on rotor blade [2]
48
As illustrated in Figure 23, lift force (FL) and drag force (FD) provide a resultant
force (FR). The resultant force can be decomposed into tangential component (FT)
which produces rotational torque and the axial component (FA) pushing the blade
backward.
For the blade shown, the aerodynamic drag force is [2]
𝐹𝐹𝐷𝐷 =
1
𝜌𝜌. 𝐴𝐴𝑝𝑝 . 𝑣𝑣𝐴𝐴 2 . 𝑐𝑐𝐷𝐷
2
The drag coefficient cD depends on the blade shape. Ap is the projected body area,
for a blade with chord (t) and span equal to rotor radius Ap=r.t .
The aerodynamic lift force is found in similar way
𝐹𝐹𝐿𝐿 =
1
𝜌𝜌. 𝐴𝐴𝑝𝑝 . 𝑣𝑣𝐴𝐴 2 . 𝑐𝑐𝐿𝐿
2
Where cL is the lift confident and depends on the blade shape. In Rotor designs it
is an objective to maximize the so called lift force to drag force (L/D) ratio. Ratios
up to 400 [2] can be achieved. Figure 24 shows how blowing wind produces the
driving torque for the rotor, tangential components of the wind force produces
mechanical thrust on the rotor structure.
49
Figure 24 Distribution of aerodynamic forces over the blade length [13]
Rotor speed control in pitch-controlled turbines utilizes the fact that changing the
blade pitch angle (α) with respect to rotor plane changes the wind angle of attack
(β) and the resultant wind force on the blade, and that changes the tip speed (u) at
a given wind speed (vW). This consequently alters the tip speed ratio. The tip
speed ratio affects the rotor power coefficient and therefore varies the power
captured by the turbine.
50
Figure 25 shows the differences in the rotor power coefficients (the envelope of
the family of power characteristics in the case of adjustable-pitch rotors) vs. tip
speed ratio for rotors of various designs. While the historical wind wheels, which
essentially only operated with aerodynamic drag, only achieved power
coefficients of about 0.3 at the most, modern rotors achieve power coefficients of
almost 0.5 which clearly demonstrate the superiority of the principle of using
aerodynamic lift [13].
Figure 25 Rotor power coefficient of different rotor types [13]
Moreover, it is noteworthy here that the blade tip speed is related to the rotor
angular speed as follows
𝜔𝜔 =
51
𝑢𝑢
𝑟𝑟
Where (r) is the rotor radius . The rotor speed in revolutions per minute is
𝑛𝑛𝑟𝑟 =
𝜔𝜔
30. 𝑢𝑢
. 60 =
2𝜋𝜋
𝜋𝜋𝜋𝜋
This clearly shows that rotor rotational speed is an indicator of blade tip speed.
For example, a 900-kW turbine with 44-m rotor diameter has a maximum
rotational speed of 34 rpm so its maximum blade-tip speed is 78.3 m/s (175
mph).The rotational speed decreases as the rotor diameter increases.
As depicted in Figure 25 , the maximum rotor efficiency for the turbine occurs at
a tip speed ratio of about 8, therefore to maximize power extraction for this
turbine TSR need to be maintained at its optimal value and that is achieved by
controlling the pitch-angle. Therefore, the rotor needs to spin faster at high wind
speeds so that TSR remains constant.
In pitch-controlled rotors, to start-up the turbine (low tip speed ratio) high pitch
angles are chosen to increase the rotor speed. On the other hand, at higher wind
speeds lower angle of attack is chosen by increasing pitch angle to decrease the
power captured by the blades. Pitch control is also helpful in storm condition
when wind generator is shut down for protection. This is achieved by adjusting
the blades in the feathered position which effectively decreases the mechanical
power input of the turbine.
For small wind turbines with no pitch control, passive or self-regulatory speed
control method at high wind speeds is implemented and that is the stall control
.Rotor blades are aerodynamically designed such that in storms above a certain
wind speed lift or buoyancy force is destroyed by flow separation which limits the
52
mechanical power extracted from the flowing wind stream, without adjusting
rotor pitch angle. The rotor’s rotational speed (or tip speed) remains constant but
tip speed ratio drops at high wind speeds for stall-controlled wind turbines.
To summarize the above, rotor speed control must be implemented in wind
turbines for the following objectives:
1. To maximize power extracted from wind.
2. To protect the turbine components from overload due to over-speed wind.
3. When the turbine is not loaded (generator is disconnected for some
reason), the rotor must to be protected from over speeding which can
destroy it.
2.9 Wind Speed Range
For fixed-speed wind turbines, the so called design wind speed vD is found as [2]
𝑣𝑣𝐷𝐷 =
Where
𝑢𝑢
2𝜋𝜋𝜋𝜋. 𝑛𝑛/60
=
𝜆𝜆𝑜𝑜𝑜𝑜𝑜𝑜
𝜆𝜆𝑜𝑜𝑜𝑜𝑜𝑜
λopt is the optimum tip speed ratio at which rotor power efficiency is maximum ,
it ranges between 7-8 for three bladed rotors [13] ,
n is the rotor rotational speed in rpm and
r is the rotor radius.
However, variable speed turbines can achieve maximum power capture at a range
of wind speeds, therefore manufactures specify a range of wind speeds at which
53
turbine can operate. Table 4 lists the advantages of fixed-speed and variable speed
turbines.
Table 4 [9]
Fixed-speed turbine
Variable-speed turbine
Fewer parts and higher reliability
Higher annual energy capture due to higher
rotor efficiency
Simple and low cost electrical system
Low cost gearbox due to fewer gear steps
Lower risk of mechanical resonance of the
structure
Mechanical damping system not needed,
electrical system could provide damping
(if required)
No frequency conversion , no current
harmonics
No synchronization problems with the grid
Lower capital cost
Power electronics could reduce voltage
sags
54
Figure 26 Turbine output power vs. wind speed curve [9]
Wind turbine systems have five regions of operation depending on the wind speed
[9] as shown in Figure 26:
1. The cut-in or starting wind speed at which the turbine starts generating
power. Below the cut-in speed the brake should stop the rotor since it is
not efficient to turn the turbine on; otherwise with very little power
generated the turbine system may act as a load rather than a generator.
2. The constant rotor efficiency cp region where the rotor speed varies with
the wind speed variation to operate at the constant TSR corresponding to
the maximum cp value.
3. During high winds, the rotor speed is limited to an upper constant limit
based on the design limit of the system components. Since the rotor speed
is held constant, the rotor efficiency drops which makes the power output
constant at the rated value even if wind speed increased further.
55
4. At still higher wind speeds, such as during a gust, the machine is operated
at a controlled constant power to protect the generator and power
electronics from overloading. This can be achieved by lowering the rotor
speed by the rotor brake.
5. The cutout speed, at which the rotor is shut off by the rotor brake (and if
possible turned away from the wind direction) to protect the blades, the
electrical generator, and other components of the system beyond a certain
wind speed.
Typically, these wind speeds have the following ranges [2]:
a) Cut-in speed = 2.5–4.5 m/s
b) Design speed = 6–10 m/s
c) Nominal speed = 10–16 m/s
d) Cut-out speed = 20–30 m/s
e) Survival speed = 50–70 m/s.
Figure 27 shows specification data sheet for 2 MW/ 80-meter variable speed wind
turbine manufactured by the leading Danish company Vestas . It is noted from the
wind speed-output power curve that for wind speeds above the rated the output
power is limited.
56
Figure
27
Technical
specifications
(www.vestas.com).
57
for
Vestas
2-MW
wind
turbine
Chapter 3: Electrical System of a Wind Turbine
3.1 Nomenclature
The following terms are used throughout this chapter:
Nacelle: Weather-proof streamlined enclosure for housing shafts, generator,
controller and rotor brakes.
3.2 Notation
The following notations are used throughout this chapter:
f1 : Grid’s electrical frequency, Hz.
λotp : Optimal tip-speed ratio of a wind turbine (to achieve maximum power
capture).
LC filter : Electrical filter consisting of inductor (L) and capacitor (C).
L-N : Line to neutral or phase-voltage .
Ma : Amplitude modulation index.
MB : Breakdown torque of an induction machine.
58
Mf : Frequency modulation index.
nr or n: Rotational speed of the rotor in a machine, r.p.m.
nsync: Synchronous speed of the generator, Hz or r.p.m.
p: Number of magnetic poles in the electric machine.
r.p.m: Revolution per minute.
r.p.s: Revelation per second.
rms : Root mean square value.
s : Slip speed of an induction machine.
sB : Breakdown slip of an induction machine.
v: Wind speed, m/s.
59
3.3 Introduction
The complexity of the electrical system of a wind turbine depends mainly on the
generator system used. For instance, a fixed-speed grid-connected induction
generator requires less complicated electrical system than a variable-speed
synchronous generator with DC link converter (both types are discussed in details
later in this chapter). The components of electrical system for a large wind turbine
with a generator from the second category are shown in Figure 28. The nacelle
holds the generator and the rectifier, whereas the inverter is installed at the base of
the tower or in a weather proof enclosure near the tower.
Control and supervisory system is provided to control power and speed and to
monitor operation. DC supply and distribution system provides DC to
instrumentation and control system, ac voltage often is used for generator control
system , cooling pumps, fans , actuators, heaters and lights. The generator output
voltage is usually 690V and most modern commercial wind turbines have a
transformer to step-up the voltage to MV level (e.g. 20 kV). For induction
generators, reactive power compensators (capacitor bank or synchronous
generator in condensing mode) are used to supply the reactive consumed by the
generator. For grid-connected turbines the reactive power needed is proportional
to the real power output, therefore for fixed-capacitor systems any additional
reactive power is supplied by the grid. Other compensation systems involve
continuous switching of capacitor banks following the output power.
60
The
inverter produces harmonics that must be filtered out using LC filters. The turbine
tower is also equipped with lighting protection system and some towers have
aviation warning lights.
Figure 28 Electrical system for wind turbine with synchronous generator and DClink converter [13]
Several generator systems have been developed for wind turbines. Two systems
61
are presented here , one uses induction generator and the other uses synchronous
generator with DC/AC and AC/DC power electronic converters .
Table 5 compares various generator systems implemented in wind turbines in
terms of rotor speed range, maximum electrical efficiency and relative cost .The
comparison is based on rated power of 1 MW .
Table 5 [13]
System
Induction generator (squirrelcage rotor) with static reactivepower compensation
Pole-changing two-speed
induction generator
Induction generator with
oversynchronous cascade with
harmonic frequency filter and
reactive-power compensation
Double-fed induction generator
with static inverter (AC-DCAC) with harmonic frequency
filter and reactive-power
compensation
Synchronous generator with
static inverter (AC-DCAC)with harmonic frequency
filter
Direct-drive synchronous
generator with static inverter
(AC-DC-AC) and harmonics
filter
Direct-drive synchronous
generator (permanent magnet
excitation) static inverter (ACDC-AC) with harmonics filter
and reactive-power
compensation
Speed range
Efficiency of
generator with
inverter
100 ± 0.5%
0.955
100 ± 0.5%
66 2/3 ± 0.5%
0.945
110%
100 + 30%
0.935
150%
100 ± 50 %
0.94
160%
100 ± 50 %
0.94
180%
100 ± 50 %
0.94
350%
100 ± 50 %
0.94
450%
62
Approximate
cost ratio
100%
3.4 Induction (Asynchronous) Generator Directly Coupled to the Grid
The rotor of the induction generator rotates at a higher speed than the
synchronous speed . The synchronous speed depend on the number of magnetic
poles (p) in the machine and the grid frequency (f1)
𝑛𝑛𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 =
𝑓𝑓1
𝑝𝑝/2
Which is the rotational speed of the stator-produced magnetic field. For example,
a 4-pole 60-Hz machine has a synchronous speed of 1800 r.p.m (30 r.p.s. or Hz).
For induction generator, the rotor rotates at slightly higher speed (nr) than the
synch speed, the difference is expressed in terms of slip
𝑠𝑠 =
𝑛𝑛𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 − 𝑛𝑛𝑟𝑟
𝑛𝑛𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
Therefore, the rotor speed is dependent on the mains frequency and the slip as
follows
𝑓𝑓
𝑛𝑛𝑟𝑟 (𝑟𝑟𝑟𝑟𝑟𝑟) = (1 − 𝑠𝑠) × 120 × 1�𝑝𝑝
Note that slip is negative for generator mode .Induction generators required
reactive power for magnetizing the rotor, and this power is supplied by different
ways: from the grid for grid-connected turbines, by power electronic circuits, by a
capacitor bank, by a small synchronous generator with field current adjusted to
operate in condensing mode or by a combination of these methods.
63
Induction generators start from standstill (nr=0) at unity slip as shown in Figure
29. After rotor speed passes the synchronous speed (s=0) the machine operates at
the normal range (slip range from 0 to -sB) and for mechanical torque less than the
breakdown torque (MB). If in gust-wind the rotor torque exceeded breakdown
torque , rotor speed increases rapidly (high slip values in the critical range) which
could cause mechanical damage .Therefore, the generator system shown in Figure
30 must be provided with pitch ,stall or active stall control to limit power at high
wind speeds.
Figure 29 Induction machine speed-torque characteristics [2]
64
Figure 30 Induction generator directly coupled to the grid [19]
A power electronic soft starter is required to smooth the connection and
disconnection of the generator to the grid by limiting the unwanted inrush current
to about 1.5 times the nominal current.
Soft starters also protect the mechanical parts of the turbines (such as gearbox and
shaft) against high forces. Using controllable thyristors the generator is soft
started and after two seconds the soft starter is bypassed by contactor and coupled
directly to the grid.
The speed of the rotor for fixed speed generators is almost constant for different
wind speeds as shown in Figure 31. This means that the turbine does not work at
optimal power point (at optimal tip-speed ratio λotp). For this case no power can
be extracted from the wind for wind speeds below 4 m/s and for wind speed of 8
m/s optimal power efficiency is achieved.
65
Figure 31 Fixed speed induction generator speed-power curves for a range of
wind speed [2].
Variable rotor speed (consequently variable slip) provides the capability to
increase the power captured from the wind at different wind speeds. This can be
achieved by changing the slip via external resistors connected to the wound rotor
of the generator (Figure 32). The external resistors will only be connected in order
to produce the desired slip when the load on the wind turbine becomes high [13].
66
Figure 32 Induction generator system with rotor resistance converter for slip
control [13]
Sample technical data sheet for a wind turbine with induction generator system is
shown in Figure 33.
67
Figure 33 Sample technical specifications sheet for 1-MW/61.4-m fixed-speed
wind turbine with induction generator by Mitsubishi.
68
3.5 Synchronous Generator with DC- link Converter
The rotor of the synchronous generator rotates at synchronous speed (that is ,
nr=nsync ) , the frequency of the voltage induced in the stator windings is
𝑓𝑓1 = 𝑛𝑛𝑟𝑟 . 𝑝𝑝/2
As shown in Figure 34 , this variable-speed turbine is gearless (often called directdrive) therefore the speed of the rotor for the synchronous generator is the same as
that for the blades rotor (low r.p.m.).Although gearless systems require much less
maintenance, such generators have high number of poles (80 or more) [2] and
large-diameter stator and that generator is very heavy and hard to cool .Technical
specification data sheet for a sample turbine of this type is shown in
The DC excitation in the rotor is produced by a small rectifier which makes it
possible to control the generators’ power factor and terminal voltage.
1
2
Figure 34 Multi-pole synchronous generator with DC-link converter [19]
69
Power electronic converters used in this system of course put extra power losses,
however they improve the performance of the system especially from the speed
range point of view (see Table 5). Moreover, active and reactive power flows both
are controllable which makes wind turbine systems resemble complete power
plants expect in the fact that wind power is not always available. Also, power
electronic converters made it possible to employ wind turbine systems as reactive
power source for the power system whenever needed.
Converter (1) shown in Figure 34 changes the generator frequency and
consequently varies the rotor speed when wind speed changes to operate at the
optimum speed for maximum power efficiency. This is valid for low and medium
wind speeds. To limit the power for gust-winds various approaches are used: stall
control system, blades-pitch control system, the converter can keep rotor speed
constant or inverter (2) can keep the output power constant (see Figure 35 , fixed
rotor speed technique is marked 1 whereas fixed power technique is marked 2).
Figure 35 Power limiting at high wind speeds for variable-speed wind generator.
70
Figure 36 Sample technical specifications sheet for 0.9-MW/44-m variable-speed
wind
turbine
with
synchronous
generator
(www.enercon.de).
71
and
inverter
by
Enercon
3.6 Selection of Converter
This section provides problems and solutions for sizing AC/DC converter and
DC/AC inverter used in the wind turbine system shown in Figure 37.
AC bus
Rectifier
Inverter
Step-up
Transfomer
DC bus
G
DC
AC
AC
c
DC
Power System
PM Three-phase
synch Gen.
Local Loads
Figure 37 Wind turbine system with AC/DC and DC/AC converters.
Assuming the following data for the wind turbine system:
1. Wind turbine characteristics: 500 kW, Rotor speed 16 – 15.4 r.p.m.
2. Generator characteristics:
PM synchronous generator, rated rms line-
neutral voltage 120 V, 140 poles, speed 16 – 15.4 r.p.m.
3. DC-bus characteristics: 600 V nominal.
It is required to size the AC/DC and DC/AC converters for the system.
72
Solution:
Sizing the AC/DC Converter
For a given rotor speed in r.p.m the frequency of the generator output voltage in
Hz is
𝑓𝑓𝑒𝑒 = 𝑛𝑛𝑟𝑟 . 𝑝𝑝/120
Where p is the number of poles (140)
Rotor speed varies from 16 – 15.4 r.p.m., therefore the frequency of the generator
output voltage ranges from 18.7 – 60 Hz and the output voltage of the generator
varies from 37.4 –120 V (L-N).
@ 18.7 Hz and 37.4 V the amplitude modulation index of the AC/DC converter is
(𝑉𝑉𝑎𝑎𝑎𝑎 )peak = 𝑀𝑀𝑎𝑎 𝑉𝑉𝑑𝑑𝑑𝑑 /2
𝑉𝑉𝑑𝑑𝑑𝑑 = 600 V
Therefore,
𝑀𝑀𝑎𝑎 = 2 × √2 ×
37.4
= 0.18
600
@ 30 Hz and 60 V the amplitude modulation index of the AC/DC converter is
(𝑉𝑉𝑎𝑎𝑎𝑎 )peak = 𝑀𝑀𝑎𝑎 𝑉𝑉𝑑𝑑𝑑𝑑 /2
73
𝑉𝑉𝑑𝑑𝑑𝑑 = 600 V
Therefore,
𝑀𝑀𝑎𝑎 = 2 × √2 ×
60
= 0.28
600
@ 40 Hz and 80 V the amplitude modulation index of the AC/DC converter is
(𝑉𝑉𝑎𝑎𝑎𝑎 )peak = 𝑀𝑀𝑎𝑎 𝑉𝑉𝑑𝑑𝑑𝑑 /2
𝑉𝑉𝑑𝑑𝑑𝑑 = 600 V
Therefore,
𝑀𝑀𝑎𝑎 = 2 × √2 ×
80
= 0.38
600
@ 50 Hz and 100 V the amplitude modulation index of the AC/DC converter is
(𝑉𝑉𝑎𝑎𝑎𝑎 )peak = 𝑀𝑀𝑎𝑎 𝑉𝑉𝑑𝑑𝑑𝑑 /2
𝑉𝑉𝑑𝑑𝑑𝑑 = 600 V
Therefore,
𝑀𝑀𝑎𝑎 = 2 × √2 ×
100
= 0.47
600
@ 60 Hz and 120 V the amplitude modulation index of the AC/DC converter is
(𝑉𝑉𝑎𝑎𝑎𝑎 )peak = 𝑀𝑀𝑎𝑎 𝑉𝑉𝑑𝑑𝑑𝑑 /2
74
𝑉𝑉𝑑𝑑𝑑𝑑 = 600 V
Therefore,
𝑀𝑀𝑎𝑎 = 2 × √2 ×
120
= 0.57
600
The following chart can be used for sizing the AC/DC converter.
Vac L-N rms (V)
f (Hz)
Vdc (V)
Ma
37.4
18.7
600
0.18
60
30
600
0.28
80
40
600
0.38
100
50
600
0.47
120
60
600
0.57
Sizing the DC/AC Converter
The inverter can be used for AC bus voltage (Vac bus ) of 120 V ± 5 % by adjusting
the amplitude modulation index .
Assuming that DC bus voltage is 600 V and AC bus voltage is 114 V (rms L-N)
𝑀𝑀𝑎𝑎 = 2 × √2 ×
75
114
= 0.54
600
Assuming that DC bus voltage is 600 V and AC bus voltage is 120 V (rms L-N)
𝑀𝑀𝑎𝑎 = 2 × √2 ×
120
= 0.57
600
Assuming that DC bus voltage is 600 V and AC bus voltage is 126 V (rms L-N)
𝑀𝑀𝑎𝑎 = 2 × √2 ×
126
= 0.59
600
The following charts can be used for sizing the DC/AC inverter.
Vac L-N rms
(V)
Vdc (V)
Ma
114
600
0.54
120
600
0.57
126
600
0.58
Minimum
Maximum
DC input voltage (V)
325.7
660
AC output voltage L-N rms (V)
114
126
Amplitude modulation index
0.49
0.99
No restriction, and determined
only by the inverter switching
frequency as specified by the
manufacturer.
Frequency modulation index
76
Output voltage as Amplitude Modulation Index (Ma) varies
AC output voltage
Ma
L-N rms (V)
0.3
90
0.6
180
0.9
270
Output voltage as Frequency Modulation Index (Mf ) varies for
Ma=0.566
fs
AC output voltage
(Hz)
L-N rms (V)
15
900
120
20
1200
120
25
1500
120
Mf
77
Chapter 4: Power Electronics for Renewable Energy Systems
4.1 Notation
The following notations are used throughout this chapter:
a or Ma: Amplitude modulation index .
f1 or fo: Fundamental frequency, Hz.
fs : Switching frequency, Hz.
GW: Giga watts.
I or i : Current , Amps.
L: Inductance, Henries.
Mf: Frequency modulation index.
PWM: Pulse width modulation.
R: Resistance, Ohms.
r.m.s: Root mean square value.
78
SW or S: Power-electronic switching device.
Tz: Switching time period, sec.
Vdc : DC bus or battery voltage, Volts.
VL: Load voltage, Volts.
ω : Angular frequency , rad/sec.
X : Reactance, Ohms.
79
4.2 Introduction
The term ‘power electronics’ refers to electronic devices with power rating from
less than few watts to more than 2 GW [14].
The need for power electronic converters arises from the fact that renewable
energy sources such as sun, wind and tidal power are of variable nature seasonally
and even daily and the output power they generate is variable. Hence, power
converters provides the control and power conditioning required to make
renewable energy suitable for existing electrical systems and to store the excess
energy as well.
Different conversions of electric power are used to interface renewable energy
sources: DC/DC, DC/AC, AC/DC and AC/AC as shown in Figure 38 where
renewable energy systems and storage systems are classified as follows [14]:
•
Static renewable energy systems include fuel cells and photovoltaic arrays.
These systems require unidirectional power flow ( silent since they have
no moving parts and no vibration)
•
Rotating renewable systems which employ AC generators to convert
mechanical power into electrical in gas turbines, wind and hydropower
systems. These systems require bidirectional power flow (rotating parts
generate noise , volume and weight , inrush/starting currents)
80
•
Static storage systems such as batteries and super capacitors (bidirectional
conversion is required for charging and discharging).
•
Rotating storage systems such as flywheels( bidirectional conversion is
necessary)
Rotating
Storage System
AC
Static
Renewable
Energy system
DC
Rotating
Renewable
Energy system
AC
Static
Storage System
DC
Figure 38 Power conversion applications for renewable energy systems.
81
According their function, power electronic circuits for renewable energy systems
are classified as follows [14]
1. Regulators or battery charge controllers are used to protect battery from
overcharging and discharging.
1.1
Shunt regulators commonly used for wind turbine systems, the
power from the wind turbine is dissipated in a shunt-connected dump load
when the batteries are fully charged.
1.2
Series regulators .They Switch off the power from the renewable
energy source when the batteries are fully charged.
1.3
Chopper regulators: a high frequency switching is used to control
the level of charging required according to the battery state.
2. Inverters : most renewable energy sources provide DC power .Inverters
convert DC power to AC suitable for appliances and injection in the main
power grid. If they interface with the main grid, they need to comply with
harmonic distortion standards. However, they can be part of a stand-alone
system. Inverter systems incorporate circuits for load management and battery
charging control.
3. Protection and monitoring units: system controllers receive signals indicating
the status and measurements of loads and devices in the system . A
82
microprocessor sends commands to make changes in the system operation if
necessary. They perform functions which include:
3.1
Disconnecting and reconnecting renewable energy sources and loads.
3.2
Load management
3.3
Synchronizing AC power sources such as inverters , diesel generators
and gas turbines
3.4
Shutting systems off in overload condition
3.5
Monitoring and recording main system parameter
This chapter discusses the principle of power electronic inverters , then it
illustrates two pulse width modulation that are widely used and finally presents a
computer simulation using Matlab/Simulink for three-phase voltage source
bidirectional converter utilizing PWM switching .
4.3 Power Electronic Switch-mode Inverter
The objective of switch mode inverters is to produce a sinusoidal AC output with
controllable magnitude and frequency .Typical applications are AC motor drives
and uninterruptible power supplies (UPS) [15].
The power flow in switch-mode inverter is revisable. For the circuit shown in
Figure 39 , most of the time the AC grid supplies power to the DC bus and then
the DC is inverted to drive the AC motor. However, it is sometimes required for
this converter to allow bidirectional operation as in braking (slowing down) of the
83
motor when the kinetic energy of the motor is dissipated by operating as a
generator and feeding the power back to the DC bus.
P
P
Vdc +
AC voltage
Ac Motor
Switchmode
converter
Switchmode
converter
Figure 39 Switch mode converter application for motor drive. The direction of
power flow is shown for motoring action. The opposite direction is for
regenerative or braking action when power is injected to the AC grid.
A second application of interest is energy storage for renewable energy systems as
shown in Figure 40 where the wind turbine generated voltage is rectified and then
inverted to a 60 Hz ac voltage suitable to be fed to the grid. The battery storage
system is charged when there is surplus amount of energy generated by the wind
turbine and during the time of day when energy purchased from the utility is at
low rate. The reverse operating takes place when it is desired to extract the stored
energy from the battery and convert it to AC voltage to feed local loads and/or the
utility.
84
Rectifier
G
Step-up
Transfomer
AC
DC
AC
PM Three-phase
synch Gen.
PWM Inverter
Power System
DC
Bi-directional
Converter DC
AC
Local Loads
Deep
Cycle
Battery
System
Figure 40 Wind turbine system with bi-directional converter using batteries for
energy storage.
4.4 The Single-Phase Full Bridge Voltage Source Inverter
A voltage source “VS” inverter is and inverter with a prescribed voltage at its
input irrespective of the magnitude or direction of current flowing through the
source. The counterpart is the current source “CS” inverter with a prescribed
current at its input regardless of the magnitude or polarity of the voltage applied
to its input terminals. Table 6 below summarizes a comparison between the two
types .
85
Table 6 [14]
VSI
Output voltage is constrained
DC bus is dominated by shunt capacitor
(voltage stiff element)
DC bus current proportional to
motor/generator power and therefore it is
dependent on motor/generator power factor
Output voltage contains harmonics varying
inversely as harmonic order
Can handle motor/generator smaller than
inverter rating
DC bus current reverses in regeneration
mode
Immune to open circuit
CSI
Output current is constrained
DC bus is dominated by series inductor
(current stiff element)
DC bus voltage proportional to
motor/generator power and therefore it is
dependent on motor/generator power factor
Output current contains harmonics varying
inversely as harmonic order
Can handle motor/generator larger than
inverter rating
DC bus voltage reverses in regeneration
mode
Immune to short circuit
The full bridge inverter shown in Figure 41 consists of four switches and four
anti-parallel protective diodes to provide path for the inductive current to flow
when the switches are open and this will protect the switch from the large
voltages caused by interrupting the inductive current (high di/dt).
SW1
SW2
-
VL +
Vdc
SW4
SW3
Figure 41 Single phase inverter circuit.
86
The load of the inverter is normally a single-phase AC motor or primary winding
of a step-up transformer feeding an AC load. By following a switching scheme
such that SW1 and SW3 are closed for half of the switching cycle, and for the
second half SW2 and SW4 are closed, the load voltage would be:
𝑉𝑉 , 𝑓𝑓𝑓𝑓𝑓𝑓 0 < 𝜑𝜑 < 𝜋𝜋
𝑉𝑉𝐿𝐿 = � 𝑑𝑑𝑑𝑑
−𝑉𝑉𝑑𝑑𝑑𝑑 , 𝑓𝑓𝑓𝑓𝑓𝑓 0 < 𝜑𝜑 < 2𝜋𝜋
The resulting output voltage shown in Figure 42 is clearly alternating and its timeaverage is zero, hence it is called an AC voltage. Obviously, the sharp transition
in voltage indicates the high frequency harmonics associated with the desired
sinusoidal voltage (i.e. the 60- Hz voltage), these harmonics produce current
harmonics causing variation in torque output in AC motors .Harmonics can be
filtered by special filters or controlled by implementing PWM techniques.
SW1 and SW4 shall not be closed simultaneously since that will short-circuit the
DC bus, same statement is applicable for SW2 and SW3.
87
Figure 42 Output voltage of full bridge inverter.
For a load modeled by resistance and inductance (RL load) the system differential
equation is
𝑉𝑉𝑑𝑑𝑑𝑑 = 𝐿𝐿
𝑑𝑑𝑑𝑑
𝑑𝑑𝑑𝑑
+ 𝑅𝑅𝑅𝑅
The solution of this dynamic equation gives the instantaneous inductive load
current [16]
−𝜑𝜑𝜑𝜑
𝑉𝑉𝑑𝑑𝑑𝑑 𝑉𝑉𝑑𝑑𝑑𝑑
𝜋𝜋𝜋𝜋
−
)� 𝑒𝑒 𝜔𝜔𝜔𝜔 , 𝑓𝑓𝑓𝑓𝑓𝑓 0 < 𝜑𝜑 < 𝜋𝜋
�1 + tanh(
𝑅𝑅
𝑅𝑅
2𝜔𝜔𝜔𝜔
𝑖𝑖𝐿𝐿 (𝜑𝜑) = �
−(𝜑𝜑−𝜋𝜋)𝑅𝑅
−𝑉𝑉𝑑𝑑𝑑𝑑 𝑉𝑉𝑑𝑑𝑑𝑑
𝜋𝜋𝜋𝜋
+
)� 𝑒𝑒 𝜔𝜔𝜔𝜔 , 𝑓𝑓𝑓𝑓𝑓𝑓 0 < 𝜑𝜑 < 2𝜋𝜋
�1 + tanh(
𝑅𝑅
𝑅𝑅
2𝜔𝜔𝜔𝜔
The switching method described above is, however, modified in practical circuits
due to the finite switching times (or turn-on and turn-off times) associated with
switches. A blanking time is introduced in the switching cycle to avoid a short
88
circuit across the DC bus. This short circuit could take place if SW1 and SW4 in
Figure 40 happened to be ON simultaneously due to the time delay associated
with the process of turning the switch OFF. During the blanking, time both SW1
and SW2 or SW2 and SW3 will be closed and hence the output voltage will be
zero, this introduces low order harmonics in the output voltage. Low order
harmonics are the vicinity of the fundamental frequency are hard to filter out.
Table 7 shows a switching sequence used to provide blanking time.
Table 7
Switching State
1
2
3
4
SW1
ON
ON
OFF
OFF
SW2
OFF
ON
ON
OFF
SW3
ON
OFF
OFF
ON
SW4
OFF
OFF
ON
ON
Magnitude of VL
Vdc
0
-Vdc
0
Blanking Time
Blanking Time
Applying the switching scheme described above results in load voltage and
current waveforms as depicted in Figure 43. Typically, the blanking time is a few
milliseconds for fast switches like MOSFETs [15].
89
Figure 43 Output voltage and current with blanking time.
The magnitude of the n-th harmonic in the voltage shown above can be found
using conventional Fourier analysis [16] ,
𝑉𝑉𝑛𝑛 = 4 𝑉𝑉𝑑𝑑𝑑𝑑
cos(𝑛𝑛𝑛𝑛)
; n = 1,2,3 …
𝑛𝑛𝑛𝑛
Therefore, the magnitude of each harmonic is dependent on the blanking time (α).
By choosing the blanking time such that
𝛼𝛼 =
π
2𝑛𝑛
Therefore, the nth harmonic is eliminated. However, this will vary the magnitude
of the fundamental component of the output voltage as well which makes the
harmonic control and voltage regulation dependent on each other.
90
Figure 44 shows the normalized magnitude spectrum of the output voltage when
blanking time α=10o , note that the ninth harmonic has been eliminated.
Figure 44 Magnitude spectrum.
The PWM techniques, which will be described later, provide the tool to control
harmonics and the fundamental output voltage independently, in addition to
eliminating the need to output filter since the harmonics are at high frequencies.
4.5 Principles of PWM
The fundamental concept Pulse Width Modulation (PWM) is varying the duty
cycle of the converter switches at high frequency to achieve as a primary
objective the desired low frequency (60 or 50 Hz) output voltage or current . A
secondary objective is to find out the most effective way of arranging the
91
switching processes to minimize unwanted specific performance parameter such
as harmonic distortion or switching losses .Three major alternatives are
implemented to achieve PWM switching signals [17]:
•
Naturally sampled PWM: switching at the intersection of a target
reference waveform and a high frequency carrier .
•
Regular sampled PWM: switching at the intersection between a
regularly sampled target reference waveform and a high frequency
carrier. The well-known space vector modulation technique is only
a variation of this technique.
•
Direct PWM: Switching so that the integrated area of the target
reference waveform over the carrier interval is equal to the
integrated area of the converter switched output.
Three main factors form the basis for fixed –frequency PWM strategies
•
Determination of the pulse width.
•
Pulse position within a carrier interval.
•
Pulse sequence within and across carrier intervals.
These factors affect the harmonic performance that is determined both by the
harmonics generated by each phase leg and the potential harmonic cancellation
that may occur between the converter phase legs.
92
4.6 The Six-Step Three Phase Voltage Source Inverter
The circuit shown in Figure 45 is quite similar to the full bridge inverter discussed
before. With a fixed DC link voltage and the conventional six-step operation it is
not possible to have output voltage control. However, as mentioned before with
PWM techniques the same circuit can produce ac voltage with controllable
magnitude and frequency.
+
+
SW1
SW3
SW5
SW4
SW6
SW2
½ Vdc
z
+
½ Vdc
Vdc
o
a
b
c
Figure 45 Three-phase inverter.
Figure 45 Illustrates the switched pulses applied to produce a symmetrical three
phase ac voltage on the legs a, b and c. Switch pairs (SW1, SW4) , (SW3, SW6)
and (SW5, SW2) should be switched ON for equal duration. SW1 is closed for
180° (half cycle of the fundamental frequency) then SW4 is closed for the next
half cycle. Switching signals for any two legs are displaced 120°. It can be
noticed that for each one-sixth of the cycle (60°) one and only one switch in each
leg will be ON. The resulting output voltage shown in Figure 46 is obtained for
93
DC bus voltage of 600V and switching frequency equal to the desired ac output
frequency (i.e. 60 Hz).It is obvious from Figure 48 that harmonics of significant
magnitude are close to the fundamental frequency.
Figure 46 Switching functions .The switching ON sequence for 60° period shall
be SW1 SW6 SW5 ,then SW1 SW6 SW2 ,then SW1 SW3 SW2 ,then SW4 SW3
SW2 ,then SW4 SW3 SW5 ,then SW4 SW6 SW5.
It is useful to recognize that the fundamental- frequency component in the output
voltage is fixed once the DC bus voltage is selected
(𝑉𝑉𝑎𝑎𝑎𝑎 )1,𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 = 1.278 𝑉𝑉𝑑𝑑𝑑𝑑 /2
94
Figure 47 Output voltage of six-step inverter.
Figure 48 Phase voltage normalized spectrum.
95
The following list depicts the simulation settings and output measurements
Vdc
f1
fs
Van, fundamental
Vab, fundamental
600 V
60 Hz
60 Hz
271 V rms
470 V rms
4.7 Three Phase Voltage Source Inverter Utilizing Space Vector PWM
Switching
The three phase output voltages in the full bridge inverter at any instant of time
can be represented by a set of eight base space vectors according to eight
switching positions of the inverter.
Figure 49 shows these base vectors V1 through V6 and the two zero vectors
which correspond to switching positions resulting in zero output voltage.
Figure 49 Three phase inverter output voltage space vectors
96
One cycle of the output voltage can be represented by six sectors (60o each) . For
instance, a rotating reference voltage such as V shown in Figure 48 can be
decomposed into three base vectors or states V1,V2 and V7 or V8 since it lies in
the first sector ;
𝑇𝑇𝑧𝑧 ∙ 𝑉𝑉 = 𝑇𝑇1 ∙ 𝑉𝑉1 + 𝑇𝑇2 ∙ 𝑉𝑉2 + 𝑇𝑇𝑜𝑜 ∙ 𝑉𝑉7
𝑇𝑇𝑧𝑧 = 𝑇𝑇1 + 𝑇𝑇2 + 𝑇𝑇𝑜𝑜
Where T0 , T1 and T2 are the time weights for V8,V1,V2 respectively . Noting that
0 ≤ 𝛼𝛼 ≤ 𝜋𝜋⁄3
which is the angle between V and V1 ,the above formula can
described in rectangular coordinates
2
cos 𝛼𝛼
cos 𝜋𝜋⁄3
2
2
1
� = 𝑇𝑇1 ∙ 𝑉𝑉𝑑𝑑𝑑𝑑 � � + 𝑇𝑇2 ∙ 𝑉𝑉𝑑𝑑𝑑𝑑 �
�
3
3
sin 𝛼𝛼
sin 𝜋𝜋⁄3
0
𝑇𝑇𝑧𝑧 ∙ 𝑉𝑉𝑑𝑑𝑑𝑑 ∙ 𝑎𝑎 ∙ �
3
Where
2
𝑉𝑉 = . 𝑎𝑎. 𝑉𝑉𝑑𝑑𝑑𝑑
3
And a is the modulation index.
Therefore, T0, T1 and T2 can be determined and the switching sequence
corresponding to the appropriate base vector is applied to the inverter switches for
the specified amount of time.
97
In our example, switching sequence S1S3S5S4S6S2=100011 will be applied for T1
duration and switching sequence 110001 for T2 duration and a zero vector
sequence for the remaining time slot within Tz. The following table shows the
switching states for each base vector.
Table 8
Base
Switch Status
Vectors
Upper Leg
Lower Leg
S1
S3
S5
S4
S6
S2
𝑽𝑽𝟏𝟏
1
0
0
0
1
1
𝑽𝑽𝟐𝟐
1
1
0
0
0
1
𝑽𝑽𝟑𝟑
0
1
0
1
0
1
𝑽𝑽𝟒𝟒
0
1
1
1
0
0
𝑽𝑽𝟓𝟓
0
0
1
1
1
0
𝑽𝑽𝟔𝟔
1
0
1
0
1
0
𝑽𝑽𝟕𝟕
1
1
1
0
0
0
𝑽𝑽𝟖𝟖 𝒐𝒐𝒐𝒐 𝑽𝑽𝟎𝟎
0
0
0
1
1
1
In order to obtain an optimum PWM only the three switching states adjacent to
the reference vector are used, and the cycle wherein the average voltage vector
becomes equal to the reference vector consists of three successive switching states
only.
98
It can be shown that at any sector n the switching time duration T1 and T2 are
𝑇𝑇1 =
𝑇𝑇2 =
2√3𝑎𝑎
𝑛𝑛𝑛𝑛
𝑇𝑇𝑧𝑧 × 𝑠𝑠𝑠𝑠𝑠𝑠 � − 𝛼𝛼�
3
3
2√3𝑎𝑎
𝑛𝑛 − 1
𝑇𝑇𝑧𝑧 × �𝑠𝑠𝑠𝑠𝑠𝑠 �𝛼𝛼 +
𝜋𝜋��
3
3
Where n=1 through 6.
In order to reduce the number of swithcing within each Tz . An algorithm devides
Tz in the first sector in the fasion shown in Figure 50. Similar approach is adopted
for sectors III and V . However, for sectors II,IV and VI the time periods T1/2 and
T2/2 are interchanged. This approach provides the advantage of lower number of
inverter state changes in addition to a possible higher modulation index compared
to the three phase sinusoidal PWM method which has the problem of pulse drop
out at high modulation index.
Figure 50 Allocation of switching periods for sector (I) to achieve minimal
switching losses.
99
Example:
Assuming the following data for a space vector PWM inverter:
Vdc=400 V , a : 0.1 - 0.9 , Three-phase load Y connected R=0.5 Ω and L=14 mH.
Find the range of fundamental-frequency AC output voltage and current.
Solution:
The peak of the fundamental –frequency (60-Hz) output phase voltage is given by
Vac= 2/3 × a × Vdc
For a=0.1 ,
Vac= 2/3 × 0.1× 400 =26.7 V peak = 18.9 V rms
For a=0.9 ,
Vac= 2/3 × 0.9× 400 =240 V peak = 169.7 V rms
Therefore the range of output voltage (L-N rms) is,
Vac : 18.9 – 169.7 V
To find the 60-Hz component of the current , the per-phase load impedance is
calculated
100
ZL=RL+ 2π ×f ×LL i = 0.5+2π ×60×0.014 i = 0.5 + 5.28 i Ω
| ZL|=5.3 Ω
IL= Vac/ZL
Therefore , the rms value of the load current varies as follows
@ a=0.1, the output voltage is 18.9 V and | IL |=18.9/5.3=3.6 A
@ a=0.9, the output voltage is 169.7 V and | IL |=169.7/5.3=32.1 A
Summarizing the above,
a :0.1 – 0.9
Vac (60 Hz): 18.9 – 169.7 V rms
Iac (60 Hz): 3.6 – 32.1 V rms
101
4.8 Three Phase Voltage Source Inverter Utilizing Sinusoidal PWM
Switching
In sine-triangle three phase PWM inverter three sinusoidal reference voltage
waveforms that are 120o apart are compared to the same triangular carrier as
shown in Figure 51 .For example , switch SW1 is ON when vtri < va,ref and SW4 is
OFF which makes the voltage vao=Vdc .
𝑣𝑣𝑎𝑎,𝑟𝑟𝑟𝑟𝑟𝑟 = Vref sin(2πfo × t)
𝑣𝑣𝑏𝑏,𝑟𝑟𝑟𝑟𝑟𝑟 = Vref sin(2πfo × t − 2π/3)
𝑣𝑣𝑐𝑐,𝑟𝑟𝑟𝑟𝑟𝑟 = Vref sin(2πfo × t + 2π/3)
Leg a ∶ �
Leg b ∶ �
Leg c ∶ �
connected to Vdc when va,ref > vtria → Close SW1
otherwise, connected to the lower leg of Vdc → Close SW4
connected to Vdc when vb,ref > vtria → Close SW3
otherwise, connected to the lower leg of Vdc → Close SW6
connected to Vdc when vc,ref > vtria → Close SW5
otherwise, connected to the lower leg of Vdc → Close SW2
102
10
vtria
va, ref
5
vb, ref
0
vc, ref
-5
-10
0.032
0.034
0.036
0.038
0.04
0.042
0.044
0.046
0.048
0.05
0.034
0.036
0.038
0.04
0.042
0.044
0.046
0.048
0.05
1000
Vdc
v
ao
500
0
-500
-1000
0.032
time (sec)
Figure 51 Switched pulses generation for sine-triangle PWM.
Two important terms are the amplitude modulation ratio (or index) Ma and the
frequency modulation ratio (Mf). The amplitude modulation index is
𝑀𝑀𝑎𝑎 =
𝑉𝑉𝑡𝑡𝑡𝑡𝑡𝑡
𝑉𝑉𝑟𝑟𝑟𝑟𝑟𝑟
Where Vtri is the peak amplitude of the triangular carrier signal and Vref is the
peak amplitude of the sinusoidal reference signal.
103
The triangular signal is at the frequency fs, which establishes the frequency at
which the inverter switches are operated. The frequency of the reference
sinusoidal voltage is f1, which is the frequency of the desired fundamental inverter
𝑀𝑀𝑓𝑓 =
output voltage. The frequency modulation index is
𝑓𝑓𝑠𝑠
𝑓𝑓1
The Simulink/Matlab simulation waveforms are shown in Figure 51 and Figure
52 with to the following inverter settings:
Vdc
Vtria
Vref
f1
fs
Ma
Mf
600 V
10 V
5.66 V
60 Hz
900 Hz
0.566
15
Since the frequency of the sinusoidal reference is much less than the switching
frequency, it can be assumed that the instantaneous average of the output voltage
over one switching cycle is the same as the fundamental frequency component of
the output voltage. Based on that,
(𝑉𝑉𝑎𝑎𝑎𝑎 )1 = 𝑀𝑀𝑎𝑎 𝑉𝑉𝑑𝑑𝑑𝑑 /2 , 0 ≤ Ma ≤ 1
Which is the peak amplitude of the fundamental frequency component in the
phase output voltage (in linear modulation mode when Ma≤1).In the linear region
this circuit works as Buck converter, whereas under rectifier operation it works as
Boost converter [18].
104
The line to neutral fundamental-frequency output voltages of the inverter
𝑣𝑣𝑎𝑎𝑎𝑎 ,1 =
𝑣𝑣𝑏𝑏𝑏𝑏 ,1 =
𝑣𝑣𝑐𝑐𝑐𝑐 ,1 =
𝑀𝑀𝑎𝑎 𝑉𝑉𝑑𝑑𝑑𝑑
sin(2πfo × t)
2
𝑀𝑀𝑎𝑎 𝑉𝑉𝑑𝑑𝑑𝑑
sin(2πfo × t − 2π/3)
2
𝑀𝑀𝑎𝑎 𝑉𝑉𝑑𝑑𝑑𝑑
sin(2πfo × t + 2π/3)
2
The line-to-line voltage RMS value at the fundamental frequency is found by
multiplying the value obtained from the previous formula by √3/√2.
Several factors affect the selection of switching frequency; it is desirable to use
high switching frequency due to the relative ease of filtering harmonic voltages.
However, switching losses increase in proportion to the switching frequency.
Hence, for most applications the switching frequency is selected to be out of the
audible frequency range (i.e. either below 6 kHz or above 20 kHz) [15].
105
Figure 52 Line and phase output voltages.
The inverter has been simulated using Simulink/Matlab and the output voltage
specifications are found to meet the desired requirements for inverter operation :
Van, fundamental
Vab, fundamental
ffundamental
120 V rms
208 V rms
60 Hz
106
Amplitude modulation ratios over 1 correspond to the non-linear region of
operation in which the fundamental frequency component does not vary linearly
with Ma. This mode of operation is called overmodulation and it is useful when it
is desired to increase the fundamental frequency component above (Vdc/2).
However, overmodulation causes the output voltage to have more harmonics in
frequencies close to the fundamental frequency. The upper limit of
overmodulation is when output voltage waveform looks quite similar to the sixstep shape with few notches; therefore, the maximum output voltage would be
(1.278 Vdc/2).
The sine-triangle PWM voltage spectrum shown in Figure 53 depicts the
improvements achieved in the inverter performance in terms of harmonics order
in comparison to the six-step operation discussed previously. The harmonics are
located at high frequency in the side-bands of the switching-frequency integer
multiples.
The next section discusses the operation of the previous circuit as a rectifier.
107
1
0.9
0.8
Normalized magnitude
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 1
11 1213 1415 1617 1819
2627 2829 3031 3233 3435
39 4041 4243 4445 4647 4849 50
5455 5657 5859 6061 6263 64
Harmonic order
Figure 53 Phase voltage normalized frequency spectrum (Ma=0.566, Mf=15).
4.9 Three Phase Voltage Source Rectifier Utilizing Sinusoidal PWM
Switching
The analysis of the rectifier mode of operation is discussed on per-phase basis
(i.e. for only one leg of the converter) and considering only the fundamental
frequency component of VPWM,a shown in Figure 54 . The circuit works in
rectifier mode when if the converter voltage VPWM,a is made to lag the supply
voltage VAN by an angle of (δ) , this causes the power to flow from the ac side to
108
the dc side , as shown in the simplified equivalent circuit in Figure 54 which
allows the use of simple ac power transfer formula
𝑃𝑃 =
𝑉𝑉𝐴𝐴𝐴𝐴 𝑉𝑉𝑃𝑃𝑃𝑃𝑃𝑃 ,𝑎𝑎
sin 𝛿𝛿
𝑋𝑋
Where the symbol V denotes the RMS value of the fundamental-frequency
voltage. The control of power angle δ is achieved by controlling the phase
displacement of the command (reference) sinusoidal waveforms. For example,
when Va,ref shown in Figure 51 is set to lag the ac source voltage by say 20o then
the fundamental component of VPWM,a will lag the source voltage by the same
angle, consequently power will be delivered to the dc bus. Moreover, the
magnitude of VPWM,a is controllable by the means of controlling the amplitude
modulation index which gives another tool to control current and power as well.
Phasor-diagram shown in Figure 56 illustrates rectifier mode of operation .It is
also possible to control the input power factor angle θ of the rectifier by
controlling the angle δ ; therefore, to achieve unity power factor the angle δ
should be set such that Ia will be in-phase with the input voltage VAN as shown in
Figure 57.
109
SW1
- VAN +
- VBN +
+
½ Vdc
ia
-
RLine
VPWM,a
LLine
z
+
SW4
-VCN +
-
½ Vdc
Figure 54 One-leg model of three-phase PWM rectifier.
ia
+
LLine
+
VPWM,a
VAN
-
-
Figure 55 Per-phase equivalent circuit at steady-state for fundamental frequency
voltage and ignoring line resistance.
110
θ
Ia
VAN
δ
Ia jωL
Ia
VPWM,a
Figure 56 Phase diagram for rectifier mode (fundamental frequency only).
Ia
VAN
δ
Ia jωL
VPWM,a
Figure 57 Rectifier mode at unity input power factor (fundamental frequency
only).
Rectifier operation of the circuit has been simulated using Simulink/Matlab using
the following settings
VAN
f1
fs
Ma
Mf
δ
120 V rms
60 Hz
900 Hz
0.8
15
21.24o
111
200
VAN
150
ia
100
50
0
-50
-100
-150
-200
0.8
0.82
0.84
0.86
0.88
0.9
time (sec)
0.92
0.94
0.96
0.98
1
Figure 58 AC side input voltage and current waveforms
700
600
500
Vdc
400
300
200
100
0
0
0.2
0.4
0.6
0.8
1
time (sec)
Figure 59 DC output voltage
112
1.2
1.4
1.6
1.8
2
500
400
300
200
V
100
0
-100
-200
-300
-400
-500
1.95
1.955
1.96
1.965
1.97
1.975
time (sec)
1.98
1.985
1.99
1.995
Figure 60 Bridge leg to neutral PWM’ed voltage (VPWM,a)
1
0.9
0.8
Normalized magnitude
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
Harmonic order
Figure 61 AC input current spectrum
113
2
It is noted from Figure 58 that input current leads the input voltage by a small
angle which illustrates the capability of the rectifier to operate at power factor
close to unity. The input current spectrum in Figure 61 shows that the current is
almost a pure sinusoid and this forms an advantage since no high harmonic
currents will flow in the AC supply (grid).
The following list contains summary of the simulation results
Vdc
VPWM,a,1
AC input p.f.
600 V
128.2 V rms
0.88
4.10 Summary of Inverter Operation Range
During inverter mode of operation, the bidirectional converter shown previously
in Figure 40 delivers AC voltage (with harmonics) to the AC bus. The magnitude,
phase and frequency of the inverter fundamental frequency output voltage should
be equal to that for the grid voltage (i.e. synchronized).
As stated before for sinusoidal-triangle PWM, in order to control the magnitude
of the output voltage the amplitude modulation index can be adjusted. The
following table illustrates the variation of amplitude modulation index required to
generate a fixed-amplitude AC voltage when the DC bus voltage (i.e. battery
storage system) varies between overcharged and discharged states.
114
Table 9
Vdc Minimum = 339 V
Vdc Maximum =660V
1
0.51
Ma required to maintain fixed
AC output
*Assume Vdc nominal =600 V , Vout,fund nominal =120 V rms (L-N)=208 V rms
(L-L)
The minimum allowable DC voltage to maintain linear PWM is found by
selecting Ma to equal 1, which is the boundary between linear modulation, and
overmodulation , therefore
(𝑉𝑉𝑎𝑎𝑎𝑎 )1 = 𝑀𝑀𝑎𝑎 𝑉𝑉𝑑𝑑𝑑𝑑 /2
(𝑉𝑉𝑑𝑑𝑑𝑑 )𝑚𝑚𝑚𝑚𝑚𝑚 =
2 × 120 × √2
= 339 𝑉𝑉
1
The maximum DC voltage corresponds to the overcharged battery system state
and it is assumed to be 10% above the nominal
𝑀𝑀𝑎𝑎 =
2 × 120 × √2
= 0.51
110% × 600
The table below shows different operational scenarios for the inverter when the
AC output is allowed to vary within ±5% of nominal value.
115
Table 10
(𝑽𝑽𝒂𝒂𝒂𝒂 )𝟏𝟏,𝒓𝒓𝒓𝒓𝒓𝒓 min.
(5% below nominal)
(5% above nominal)
=114 V
322 V
=126 V
356 V
0.490
0.540
Vdc Minimum allowable
(at Ma=1)
Ma at 10% DC bus
overcharge
(𝑽𝑽𝒂𝒂𝒂𝒂 )𝟏𝟏,𝒓𝒓𝒓𝒓𝒓𝒓 max.
*Assume Vdc nominal =600 V , Vout,fund nominal =120 V rms (L-N)=208 V rms (L-L)
4.11 Summary of Rectifier Operation Range
The DC output voltage of the three-phase sine-triangle PWM rectifier is
determined not only by amplitude modulation index , but also the power angle
( δ ) shown in Figure 56 .
However, the basic formula (𝑉𝑉𝑎𝑎𝑎𝑎 )1 = 𝑀𝑀𝑎𝑎
well.
𝑉𝑉𝑑𝑑𝑑𝑑
2
holds valid for rectifier mode as
The interaction between VAN and VPWM,a shown in Figure 56 for different values
of (Ma) and ( δ ) results in variation of both the DC output and the AC input
power
factor
.
To
illustrate
that,
simulation
Simulink/Matlab are plotted in the figures below.
116
results
obtained
using
Figure 62 DC output variation with amplitude modulation index for PWM
rectifier at constant δ=20o(values in boxes are for AC input power factor at
operating point)
Figure 63 DC output variation with power angle for PWM rectifier at constant
Ma=0.7
117
4.12 Conclusion
A study and computer simulation of the PWM three-phase voltage source
inverter/rectifier has been presented in this chapter. The performance of the bidirectional converter using sine-triangle PWM technique has been analyzed from
the prospective of input/output characteristics and harmonic content of output
voltage and current.
118
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119
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120
Appendix
%% Muthanna Abuhamdeh 2009%%
%%This function compares sinusoidal reference voltages with the
%%high frequency carrier to generate PWM gating signals for the 6
% switches in the bridge circuit
function y= comp(u)
%%inputs
tr=u(1);
% triangular wave
a=u(2);
% phase A reference voltage
b=u(3);
c=u(4);
if a>=tr
y(1)=1;
y(4)=0;
else
y(1)=0;
y(4)=1;
end
if b>=tr
y(3)=1;
y(6)=0;
else
y(3)=0;
y(6)=1;
end
if c>=tr
y(5)=1;
y(2)=0;
else
y(5)=0;
y(2)=1;
end
Matlab mfile listing for comparator.m
121
%% Muthanna Abuhamdeh 2009%%
%%This function generates triangular signal with peak of (k) V
function y= tria(u)
angle=u(1);
k=u(2);
if (0 < angle)&&(angle <= pi)
y = -2*k/pi*angle+k;
elseif (pi <= angle)&&(angle <= 2*pi)
y = 2*k*angle/(pi)-3*k;
else
y=0;
end
Matlab mfile listing for tria.m
122
Figure 64 Simulink model of switching pulses generation for 6-step inverter
123
Figure 65 Simulink model of switching pulses generation for sine-triangle PWM
124
Figure 66 Simulink model of three-phase voltage source full bridge inverter
125
Figure 67 Simulink model of three-phase voltage source full bridge rectifier
126