Power Converters and Control of Renewable Energy Systems
Frede Blaabjerg, Remus Teodorescu, Zhe Chen Marco Liserre
Aalborg University, Institute of Energy Technology, Politecnico di Bari, DEE
Denmark Italy
[e-mail], [e-mail], [e-mail] [e-mail]
Abstract  The global electrical energy consumption is steadily II. RENEWABLE ENERGY SOURCES
rising and therefore a continous demand to increase the power
generation capacity. A significant percentage of the required
Three different renewable energy sources are briefly
capacity increase can be based on renewable energy sources.
described. They are wind power, fuel cell and photovoltaic.
Wind turbine technology, as the most cost effective renewable
energy conversion system, will play an important part in our
future energy supply. But other sources like microturbines, A. Wind power conversion
photovoltaics and fuel cell systems may also be serious
The function of a wind turbine is to convert the motion of
contributors to the power supply. Characteristically, power
the wind into rotational energy that can be used to drive a
electronics will be an efficient and important interface to the
generator, as illustrated in Fig. 1. Wind turbines capture the
grid for the renewables and this paper will first briefly discuss
power from the wind by means of aerodynamically designed
three different alternative/renewable energy sources. Next,
blades and convert it into rotating mechanical power. At
various configurations of small and medium power conversion
present, the most popular wind turbine is the Horizontal
topologies are presented including their control (mainly for
PV-systems). Finally wind turbine configuration and their
Axis Wind Turbine (HAWTs) where the number of blades is
control are described.
typically three.
Wind turbine blades use airfoils to develop mechanical
I. INTRODUCTION
power. The cross-sections of wind turbine blades have the
shape of airfoils as the one shown in Fig. 2.
The energy consumption is steadily increasing and the Airflow over an airfoil produces a distribution of forces
deregulation of electricity has caused that the amount of along the airfoil surface. The resultant of all these pressure
installed production capacity of classical large power and friction forces is usually resolved into two forces and a
stations cannot follow the demand. A method to fill out the moment, lift force, drag force and pitching moment, as
gap is to make incentives to invest in alternative energy shown in Fig. 2.
sources like wind turbines, photovoltaic systems, The aerodynamic power, P, of a wind turbine is given by:
microturbines and also fuel cell systems. Two renewable
1
2v3C
P = �ĄR
energy systems are the most dominant so far which are the (1)
p
2
wind turbines and the photovoltaic systems. The wind
where � is the air density, R is the turbine radius, v is the
turbine technology is one of the most promising alternative
wind speed and CP is the turbine power coefficient which
energy technology [1]-[3]. The modern development started
represents the power conversion efficiency of a wind turbine.
in the 1980 s with sites of a few tens of kW to Multi-MW
CP is a function of the tip-speed ratio (), as well as the
range wind turbines today. E.g. Denmark has a high
penetration (> 20%) of wind energy in major areas of the blade pitch angle (�) in a pitch controlled wind turbine.  is
country and in 2003 15% of the whole electrical energy defined as the ratio of the tip speed of the turbine blades to
consumption was covered by wind energy. A higher wind speed, and given by:
penetration level will even be seen in the near future. As the
power range of the wind turbines increases the key
R �" &!
 = (2)
parameters like control of active and reactive power become
v
more and more important. The power electronics is the key-
where &! is the rotational speed of the wind turbine.
technology [4]-[5]to change the basic characteristic of the
The Betz limit, CP,max (theoretical) =16/27, is the maximum
wind turbine from being an energy source to be an active
theoretically possible rotor power coefficient. In practice
power source [6]-[36]. The power electronic possibilities are
three effects lead to a decrease in the maximum achievable
also used to interface other renewable energy sources [37]-
power coefficient [1]:
[46].
This paper will first explain the basic principles of wind
" Rotation of the wake behind the rotor
power conversion, fuel cells and photovoltaic. Next different
" Finite number of blades and associated tip losses
PV configurations are explained as well as power converters
" Non-zero aerodynamic drag
and their control. The three-phase inter-connection is also
discussed including control. Different wind turbine
configurations are finally reviewed together with their
control methods.
Electrical Power
Wind power
Gearbox (optional) Generator Power converter
Supply grid
Rotor
(optional)
Consumer
Power conversion &
Power conversion &
Power transmission Power conversion Power transmission
power control
power control
Fig. 1. Conversion from wind power to electrical power in a wind turbine [11].
Fig. 1. Conversion from wind power to electrical power in a wind turbine [11].
A typical CP- curve for a fixed pitch angle � is shown in The development in the wind turbine systems has been
Fig. 3. It can be seen that there is a practical maximum steady for the last 25 years and four to five generations of
power coefficient, CP,max. Normally, a variable speed wind wind turbines exist. It is now a proven technology.
turbine follows the CP,max to capture the maximum power up It is important to be able to control and limit the power at
higher wind speeds, as the power in the wind is a cube of the
to the rated speed by varying the rotor speed to keep the
wind speed.
system at the optimum tip-speed ratio, opt.
Wind turbines have to be cut out at a high wind speed to
As the blade tip-speed typically should be lower than half
avoid damage. A turbine could be designed in such a way
the speed of sound the rotational speed will decrease as the
that it converts as much power as possible in all wind speeds,
radius of the blade increases. For MW wind turbines the
but then it would have to be too heavy. The high costs of
rotational speed will be 10-15 rpm. A common way to
such a design would not be compensated by the extra
convert the low-speed, high-torque power to electrical
production at high winds, since such winds are rare.
power is to use a gear-box and a normal speed generator as
Therefore, turbines usually reach maximum power at a
illustrated in Fig. 1. The gear-box is optional as multi-pole
much lower wind speed, the rated wind speed (9-12 m/s).
generator systems are alternative solutions.
The power limitation may be done by one of the
aerodynamic mechanisms: stall control (the blade position is
fixed but stall of the wind appears along the blade at higher
Lift force Pitching moment
wind speed), active stall (the blade angle is adjusted in order
Drag force
to create stall along the blades) or pitch control (the blades
�
are turned out of the wind at higher wind speed).
Trailing edge
B. Fuel Cell power conversion
Ć ą
Angle of attack:ą
Leading edge
The fuel cell is a chemical device, which produces
Pitch angle: �
electricity directly without any intermediate stage and has
wind
recently received much attention [7]. The most significant
advantages are low emission of green house gases and high
power density. For example, a zero emission can be
Fig. 2. A simple airfoil used in wind turbines.
achieved with hydrogen fuel. The emission consists of only
harmless gases and water. The noise emission is also low.
The energy density of a typical fuel cell is 200 Wh/l, which
is nearly ten times of a battery. Various fuel cells are
available for industrial use or currently being investigated
for use in industry, including
" Proton Exchange Membrane
" Solid Oxide
" Molten Carbonate
" Phosphoric Acid
" Aqueous Alkaline
The efficiency of the fuel cell is quite high (40%-60%). Also
the waste heat generated by the fuel cell can usually be used
for cogeneration such as steam, air-conditioning, hot air and
Fig. 3. Typical Cp- curve for a wind turbine for a fixed angle �.
heating, then the overall efficiency of such a system can be
as high as 80%.
iPV
iSC id uPV
(a)
Fig. 4. V-I characteristics of a fuel cell [12].
(uMPP, iMPP)
iSC IPV
A typical curve of the cell electrical voltage against current
density is shown in Fig. 4. It can be seen that there exists a
region where the voltage drop is linearly related with the
current density due to the Ohmic contact.
pMPP
Beyond this region the change in output voltage varies
rapidly. At very high current density, the voltage drops
significantly because of the gas exchange efficiency. At low
PPV
current level, the Ohmic loss becomes less significant, the
increase in output voltage is mainly due to the activity of the
uOC UPV
chemicals. Although the voltage of a fuel cell is usually
(b)
small, with a theoretical maximum being around 1.2 V, fuel
cells may be connected in parallel and/or in series to obtain
Fig. 5. Model and characteristics of a PhotoVoltaic (PV) cell.
the required power and voltage.
(a) Electrical model with current and voltages defined.
The power conditioning systems, including inverters and (b) Electrical characteristic of the PV cell, exposed to a given amount
of sunlight at a given temperature.
DC/DC converters, are often required in order to supply
normal customer load demand or send electricity into the
Several types of proven PV technologies exist, where the
grid.
crystalline (PV module light-to-electricity efficiency: � =
10% - 15%) and multi-crystalline (� = 9% - 12%) silicon
C. The photovoltaic cell
cells are based on standard microelectronic manufacturing
Photovoltaic (PV) power supplied to the utility grid is
processes. Other types are: thin-film amorphous silicon (� =
gaining more and more visibility due to many national
10%), thin-film copper indium diselenide (� = 12%), and
incentives [7]. With a continuous reduction in system cost
thin-film cadmium telluride (� = 9%). Novel technologies
(PV modules, DC/AC inverters, cables, fittings and man-
such as the thin-layer silicon (� = 8%) and the dye-sensitised
power), the PV technology has the potential to become one
nano-structured materials (� = 9%) are in their early
of the main renewable energy sources for the future
development. The reason to maintain a high level of
electricity supply.
research and development within these technologies is to
The PV cell is an all-electrical device, which produces
decrease the cost of the PV-cells, perhaps on the expense of
electrical power when exposed to sunlight and connected to
a somewhat lower efficiency. This is mainly due to the fact
a suitable load. Without any moving parts inside the PV
that cells based on today s microelectronic processes are
module, the tear-and-wear is very low. Thus, lifetimes of
rather costly, when compared to other renewable energy
more than 25 years for modules are easily reached. However,
sources.
the power generation capability may be reduced to 75% ~
The series connection of the cells benefit from a high
80% of nominal value due to ageing. A typical PV module is
voltage (around 25 V ~ 45 V) across the terminals, but the
made up around 36 or 72 cells connected in series,
weakest cell determines the current seen at the terminals.
encapsulated in a structure made of e.g. aluminum and tedlar.
An electrical model of the PV cell is depicted in Fig. 5.
6
2
1000 W/m
15oC
Power flow
40oC
4
2 Loads
600 W/m 75oC
Appliance
Power converter
Industry
Communication 2-3 2-3
2
Load /
2
200 W/m
generator
Generators
Wind
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Photo-voltaic
Fuel cell
Cell voltage [V]
Other sources
(a)
Control
2.5
o
15 C Reference (local/centralized)
2
o
40 C
o
1.5 75 C
Fig. 7. Power electronic system with the grid, load/source, power
converter and control.
1
0.5
III. SINGLE-PHASE PV-INVERTERS
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Cell voltage [V]
The first systems to be discussed will be single-phase
(b)
connected PV inverters. The general block diagram of a
Fig. 6. Characteristics of a PV cell. Model based on the British Petroleum
single-phase grid connected photovoltaic systems is shown
BP5170 crystalline silicon PV module. Power at standard test condition
in Fig. 8a. It consists of a PV array, a PV inverter with a
(1000 W/m2 irradiation, and a cell temperature of 25 �C): 170 W @ 36.0 V.
filter, a controller and the grid.
Legend: solid at 15 oC, dotted at 40 oC, and dashdot at 75 oC [7].
This causes reduction in the available power, which to
PV PV Inverter
Grid
some extent can be mitigated by the use of bypass diodes, in Array & Filter
parallel with the cells. The parallel connection of the cells
solves the  weakest-link problem, but the voltage seen at
the terminals is rather low. Typical curves of a PV cell
Control
current-voltage and power-voltage characteristics are plotted reference
in Fig. 6a and Fig. 6b respectively, with insolation and cell
a)
temperature as parameters. The graph reveals that the
captured power is determined by the loading conditions
(terminal voltage and current). This leads to a few basic
requirements for the power electronics used to interface the
PV module(s) to the utility grid.
The job for the power electronics in renewable energy
systems is to convert the energy from one stage into another
stage to the grid (alternative voltage) with the highest
possible efficiency, the lowest cost and to keep a superior
performance. The basic interfacing is shown in Fig. 7.
Usually the power converter interfacing a dc source to the
load and/or to the grid consists of a two stage converter: a
(b) (c) (d)
standard buck inverter and an ac/ac voltage amplifier or a dc
Fig 8. General schema for single-phase grid connected photovoltaic
boost converter [7]. The use of current source inverters is
systems. a) Block diagramof PV inverter; b) Central inverter; c) String
inverter; d) Module integrated inverter
quite limited because they require several devices producing
a large amount of conduction losses, sluggish transient
The PV array can be a single panel, a string of PV panels
response and high cost [66]. An interesting alternative
or a multitude of parallel strings of PV panels. Centralized
solution could be the use of a step-up inverter made by the
or decentralized PV systems can be used as depicted in Fig.
connection of two [67] or three [68] dc/dc boost converters
8b - Fig. 8d.
in order for the inverter and boost the voltage in only one
stage.
Central inverters
This power electronic system can be used with many
In this topology the PV plant (typical > 10 kW) is arranged
different loads and generators. In this case focus will be on
in many parallel strings that are connected to a single central
PV and wind turbines.
inverter on the DC-side (Fig. 8b). These inverters are
characterized by high efficiency and low specific cost.
However, the energy yield of the PV plant decreases due to
module mismatching and potential partial shading
Cell current [A]
Cell power [W]
conditions. Also, the reliability of the plant may be limited [38]. In the following, the different PV inverter power
due to the dependence of power generation on a single configurations are described in more details.
component: the failure of the central inverter results in that
the whole PV plant out of operation. on the LF side
with isolation
with DC-DC
String inverter on the HF side
converter
without isolation
Similar to the central inverter, the PV plant is divided into
PV
several parallel strings. Each of the PV strings is assigned to
Inverters
with isolation
a designated inverter, the so-called "string inverter" (see Fig.
without DC-DC
8c). String inverters have the capability of separate
converter
without isolation
Maximum Power Point (MPP) tracking of each PV string.
Fig. 9. Power configurations for PV inverters.
This increases the energy yield via the reduction of
mismatching and partial shading losses. These superior
PV inverters with DC-DC converter and isolation
technical characteristics lead increase the energy yield and
The isolation is typically acquired using a transformer that
enhance the supply reliability. String inverters have evolved
can be placed on either the grid frequency side (LF) as
as a standard in PV system technology for grid connected
shown in Fig. 10a or on the high-frequency (HF) side in the
PV plants.
dc-dc converter as shown in Fig. 10b. The HF transformer
An evolution of the string technology applicable for higher
leads to more compact solutions but high care should be
power levels is the multi-string inverter [7]. It allows the
taken in the transformer design in order to keep the losses
connection of several strings with separate MPP tracking
low.
systems (via DC/DC converter) to a common DC/AC
inverter. Accordingly, a compact and cost-effective solution,
which combines the advantages of central and string
DC DC
PV
technologies, is achieved. This multi-string topology allows
Grid
Array
DC AC
the integration of PV strings of different technologies and of
various orientations (south, north, west and east). These
(a)
characteristics allow time-shifted solar power, which
optimizes the operation efficiencies of each string separately.
DC AC DC
The application area of the multi-string inverter covers PV
PV
Grid
Array
plants of 3-10 kW. AC DC AC
Module integrated inverter
(b)
This system uses one inverter for each module (Fig. 8d).
Fig. 10. PV inverter system with DC-DC converter
This topology optimizes the adaptability of the inverter to
and isolation transformer
the PV characteristics, since each module has its own MPP
a) on the Low Frequency (LF) side b) on the High Frequency (HF) side
tracker. Although the module-integrated inverter optimizes
the energy yield, it has a lower efficiency than the string
In the Fig. 11 is presented a PV inverter with HF
inverter. Module integrated inverters are characterized by
transformer using an isolated push-pull boost converter [41]
more extended AC-side cabling, since each module of the
PV plant has to be connected to the available AC grid (e.g.
230 V/ 50 Hz). Also, the maintenance processes are quite
complicated, especially for facade-integrated PV systems.
This concept can be implemented for PV plants of about 50-
400 W peak.
PV inverter
The PV inverter technology has evolved quite a lot during
Fig. 11. PV inverter with HF transformer in the dc-dc converter.
the last years towards maturity [42]. Still there are different
power configurations possible as shown in the Fig. 9.
Also, the dc-ac inverter in this solution is a low cost
The question of having a dc-dc converter or not is first of
inverter switched at the line frequency. The new solutions
all related to the PV string configuration. Having more
on the market are using PWM dc-ac inverters with IGBT s
panels in series and lower grid voltage, like in US and Japan,
switched typically at 10-20 kHz leading to a better power
it is possible to avoid the boost function with a dc-dc
quality performance.
converter. Thus a single stage PV inverter can be used
Other solutions for high frequency dc-dc converters with
leading to higher efficiency.
isolations includes: full-bridge isolated converter, Single-
The issue of isolation is mainly related to safety standards
Inductor push-pull Converter (SIC) and Double-Inductor
and is for the moment only required in US. The drawback of
Converter (DIC) as depicted in Fig. 12 [61].
having so many panels in series is that MPPT is harder to
achieve especially during partial shading, as demonstrated in
DC DC
PV
Grid
Array
DC AC
a)
(a)
b)
(b)
Fig. 13. PV inverter system with DC-DC converter without isolation
transformer a) General diagram
b) Practical example with boost converter and full-bridge inverter [39]
In Fig. 13b a practical example [39] using a simple boost
c)
Fig. 12. Dc-dc converter topologies with isolation. a) full-bridge; b) single- converter is shown. Another novel transformerless topology
inductor push-pull; c) double-inductor push-pull.
[39] featuring a high efficiency time-sharing dual mode
single-phase partially controlled sine-wave PWM inverter
In order to keep the magnetic components compact high
composed of quasi time-sharing sine-wave boost chopper
switching frequencies in the range of 20  100 kHz are
with a new functional bypass diode Db in the boost chopper
typically employed. The full-bridge converter is usually
side and complementary sine-wave PWM full-bridge
utilized at power levels above 750 W. The advantages of
inverter (Fig. 14).
this topology are: good transformer utilization  bipolar
magnetization of the core, good performance with current
programmed control  reduced DC magnetization of
transformer. The main disadvantages in comparison with
push-pull topology are the higher active part count and the
higher transformer ratio needed for boosting the dc voltage
to the grid level.
The single inductor push-pull converter can provide
boosting function on both the boosting inductor and
(a)
transformer, reducing the transformer ratio. Thus higher
efficiency can be achieved together with smoother input
current. On the negative side higher voltage blocking
switches are required and the transformer with tap point puts
some construction and reliability problems.
Those shortcomings can be alleviated using the double
inductor push-pull converter (DIC) where the boost inductor
has been split in two. Actually this topology is equivalent
with two interleaved boost converters leading to lower
ripple in the input current. The transformer construction is
(b)
more simple not requiring tap point. The single disadvantage
of this topology remains the need for an extra inductor.
Fig. 14. Time-sharing dual-mode sinewave modulated
single-phase inverter with boost chopper [40]
PV inverters with DC-DC converter without isolation
a) Circuit system configuration. b) Operating principle.
In some countries as the grid-isolation is not mandatory,
more simplified PV inverter design can be used, as shown in
Fig. 13.
PV inverters without DC-DC converter
In Fig. 16b, a typical transformerless topology is shown
The block diagram of this topology is shown in the Fig. using PWM IGBT inverters. This topology can be used
15a. when a large number of PV panels are available connected
in series producing in excess of the grid voltage peak at all
times.
DC
Another interesting PV inverter topology without boost
PV
Grid
Array and isolation can be achieved using multilevel concept. Grid
AC
connected photovoltaic systems with a five level cascaded
inverter is presented in Fig. 16c [41]. The redundant inverter
(a)
states of the five level cascaded inverter allow for a cyclic
switching scheme which minimizes the switching frequency,
equalizes stress evenly on all switches and minimizes the
voltage ripple on the DC capacitors.
IV. CONTROL OF SINGLE-PHASE PV-INVERTERS
Control of DC-DC boost converter
In order to control the output dc-voltage to a desired value, a
(b)
control system is needed which can automatically can adjust
the duty cycle, regardless of the load current or input
Fig. 15. PV inverter system without DC-DC converter
changes. There are two types of control for the dc-dc
and with isolation transformer
a) general diagram b) practical example with full-bridge inverter and grid-
converters: the direct duty-cycle control and the current
side transformer [39]
control [62]. (See Fig. 17).
In Fig. 15b are presented two topologies of PV inverters
vFC(t)
vDC(t)
are presented where the line frequency transformer is used.
iload(t)
Error Control
Converter
signal
For higher power levels, self-commutated inverters using
vref + signal
d(t)
Pulse-width
Compensator
Reference
thyristors are still being used on the market [39].
modulator
input -
Sensor gain
PV inverters without DC-DC converter and without
isolation
The block diagram of this topology is shown in Fig. 16a.
(a)
vFC(t)
vDC(t)
iload(t)
DC
Error Control
PV Converter
signal
Grid
vref + signal
d(t) iswitch(t)
Comparator and
Array
Compensator
AC
Reference
controller
input -
iswitch_ref(t)
iswitch(t)
(a)
Sensor gain
(b)
Fig. 17. Control strategies for switched dc-dc converters
a) direct duty-cycle control b) current control.
Duty-Cycle control
The output voltage is measured and then compared to the
(b)
reference. The error signal is used as input in the
compensator, which will calculate it from the duty-cycle
reference for the pulse-width modulator.
Current Control
The converter output is controlled by the choice of the
transistor peak current. The control signal is a current and a
simple control network switches on and off the transistor
such its peak current follows the control input. The current
(c )
control, in the case of an isolated boost push-pull converter
has some advantages against the duty-cycle control like
Fig. 16. Transformerless PV inverter system without DC-DC converter
a) general diagram b) typical example with full-bridge inverter [39]
simpler dynamics (removes one pole from the control-to
c) multilevel [41]
output transfer function). Also as it uses a current sensor it
can provide a better protection of the switch by limiting the
ui*
ii
ii*
current to acceptable levels. GPI(s) Gd(s) Gf(s)
Another issue is the transformer saturation. In the
ii
ug
transformer a dc bias current generated by small voltage
imbalances can be induced due to the small differences in
boost inductors and/or switches. The dc current bias will
(a)
increase or decrease the transistor currents. The current
control will alter the duty cycles in the switch in a way that
ii* ui*
ii
these imbalances tend to disappear and the transformer volt-
Gc(s) Gd(s) Gf(s)
second balance to be maintained. Finally, the current
control is better suited to modularity where current sharing ii
needs to be solved when running in parallel. Gh(s)
Among the drawbacks of the current control it can be
mentioned that it requires an extra current sensor and it has a
(b)
susceptibility to noise and thus light filtering of feedback
signals is required.
Fig. 19. The current loop of PV inverter.
a) with PI controller; b) with P+Resonant (PR) controller
Control of DC-AC grid converter
For the grid-connected PV inverters in the range of 1-5 The PI current controller GPI(s) is defined as:
kW, the most common control structure for the dc-ac grid
converter is using a current-controlled H-bridge PWM
KI (1)
GPI (s) = KP +
inverter having a low-pass output filter. Typically L filters
s
are used but the new trend is to use LCL filters that have a
In order to get a good dynamic response, a grid voltage
higher order filter (3rd) which leads to more compact design.
feed-forward is used, as depicted in Fig. 19a. This leads in
The drawback is that due to its own resonance frequency it
turn to stability problems related to the delay introduced in
can produce stability problems and special control design is
the system by the voltage feedback filter.
required [43]. A typical dc-ac grid converter with LCL filter
In order to alleviate these problems, a second order
is depicted in Fig. 18.
generalized integrator (GI) as reported in [63] can be used.
The GI is a double integrator that achieves an infinite gain at
a certain frequency, also called resonance frequency, and
almost no gain exists outside this frequency. Thus, it can be
used as a notch filter in order to compensate the harmonics
in a very selective way. This technique has been primarily
used in three-phase active filter applications as reported in
[63] and also in [64] where closed-loop harmonic control is
introduced. Another approach reported in [65] where a new
ug
type of stationary-frame regulators called P+Resonant (PR)
Fig.18. The H-bridge PV coverter connected to the grid
is introduced and applied to three-phase PWM inverter
through an LCL filter
control. In this approach the PI dc-compensator is
transformed into an equivalent ac-compensator, so that it has
The harmonics level in the grid current is still a
the same frequency response characteristics in the
controversial issue for PV inverters. The IEEE 929 standard
bandwidth of concern. The current loop of the PV inverter
from year 2000 allows a limit of 5% for the current Total
with PR controller is depicted in Fig. 19b.
Harmonic Distortion (THD) factor with individual limits of
The P+Resonant (PR) current controller Gc(s) is defined as
4% for each odd harmonic from 3rd to 9th and 2% for 11th
[43], [63]:
to 15th while a recent draft of European IEC61727 suggests
something similar. These levels are far more stringent than
s
(2)
Gc (s) = KP + KI 2
other domestic appliances such as IEC61000-3-2 as PV
s2 + �o
systems are viewed as generation sources and so they are
subject to higher standards than load systems.
The harmonic compensator (HC) Gh(s) as defined in [43]:
Classical PI control with grid voltage feed-forward (Ug)
[11] as depicted in Fig. 19a is commonly used for current-
s
Gh (s) = KIh (3)
controlled PV inverters, but this solution exhibits two well "
2
h=3,5,7 s2 + �oh
( )
known drawbacks: inability of the PI controller to track a
sinusoidal reference without steady-state error and poor
is designed to compensate the selected harmonics 3rd, 5th and
disturbance rejection capability. This is due to the poor
7th as they are the most prominent harmonics in the current
performance of the integral action.
spectrum. A processing delay typical equal to Ts for the
25
PWM inverters [62] is introduced in . The filter Ig (exp) [5A/div]
Gd (s)
Ug (exp) [100/div]
20
transfer function Gf(s) is expressed in (4) [59].
15
10
2
s2 + zLC
( )
ii (s) 1
5
(4)
Gf (s) = =
2
ui (s) Lis 0
s2 +�res
( )
-5
-10
2 -15
Li + Lg �" zLC
-1 ( )
2 2
where and
Ą# ń#
zLC =
�res = -20
Ł#LgC f Ś#
Li
-25
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.0
time[sec]
The current error - disturbance ratio rejection capability at (a)
null reference is defined as:
25
Ig (exp) [5A/div]
Ug (exp) [100/div]
20
Gf (s)
� (s)
15
(5)
=
ug (s) 1+ Gc (s) + Gc (s) �"Gd (s) �"Gf (s) 10
()
ii* =0
5
0
where: � is current error and the grid voltage ug is
-5
considered as the disturbance for the system.
-10
The Bode plots of disturbance rejection for the PI and PR
-15
controllers are shown in Fig 20. As it can be observed, The
-20
PR provides much higher attenuation for both fundamental
and lower harmonics then PI. The PI rejection capability at -25
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.0
time[sec]
5th and 7th harmonic is comparable with that one of a simple
(b)
proportional (P) controller, the integral action being
irrelevant.
25
Ig (ex p) [5A /div]
Ug (ex p) [100/div]
Magnitude [dB]
20
0
15
10
-50
5
PR+HC
PI
P 0
-100
-5
-1 0
-150
-1 5
Phase angle (degrees)
-2 0
-270 -2 5
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
tim e[s ec ]
(c)
-360
Fig. 21. Experimental results at 3kW. Grid voltage and current. a) with PI
controller. b) with PR; c) with PR+HC.
-450
The issue of stability when several PV inverters are
-540
1 2 3
10 10 10
running in parallel on the same grid is becoming more and
Frequency [Hz]
more important especially when LCL filters are used. In
[44] it is shown that in the case of a concentration of several
Fig. 20. Bode plot of disturbance rejection (current error ratio disturbance)
hundreds of solar roofs in Holland, resonance frequencies in
of the PR+HC, P and PR current controllers.
the range of 1-2 kHz are occurring as a result of the grid
Thus it is demonstrated the superiority of the PR controller interaction with the PV inverter. Thus, special attention is
in respect to the PI controller in terms of harmonic current required when designing the current control.
rejection. In [43] the discrete implementation into a low-cost
fixed-point DSP is demonstrated. In Fig. 21 some
MPPT
experimental results with a 3 kW PV inverter are shown
In order to capture the maximum power, a maximum
demonstrating the harmonic compensation using more
power point tracker (MPPT) is required. The maximum
advanced controllers.
power point of PV panels is a function of solar irradiance
and temperature as depicted in Fig. 6. This function can be
implemented either in the dc-dc converter or in the dc-ac
converter. Several algorithms can be used in order to conductance. The incremental conductance algorithm is then
implement the MPPT as followings [44]. used to determine the direction to move the operating point
of the MPPT. One disadvantage of this algorithm is that the
Perturb and Observe
parasitic capacitance in each module is very small, and will
The most commonly used MPPT algorithm is Perturb and
only come into play in large PV arrays where several
Observe (P&O), due to its ease of implementation in its
module strings are connected in parallel. Also, the DC-DC
basic form [45]. Fig. 6 shows the characterstic of a PV array,
converter has a sizable input capacitor used the filter out
which has a global maximum at the MPP. Thus, if the
small ripple in the array power. This capacitor may mask the
operating voltage of the PV array is perturbed in a given
overall effects of the parasitic capacitance of the PV array.
direction and dP/dV > 0, it is known that the perturbation
moved the operating point toward the MPP. The P&O
Constant Voltage
algorithm would then continue to perturb the PV array
This algorithm makes use of the fact that the MPP voltage
voltage in the same direction. If dP/dV < 0, then the change
changes only slightly with varying irradiances, as depicted
in operating point moved the PV array away from the MPP,
in Fig. 6. The ratio of VMP/VOC depends on the solar cell
and the P&O algorithm reverses the direction of the
parameters, but a commonly used value is 76% [45]. In this
perturbation. A problem with P&O is that it oscillates
algorithm, the MPPT momentarily sets the PV array current
around the MPP in steady state operation. It also can track in
to zero to allow a measurement of the array's open circuit
the wrong direction, away from the MPP, under rapidly
voltage. The array's operating voltage is then set to 76% of
increasing or decreasing irradiance levels. There are several
this measured value. This operating point is maintained for a
variations of the basic P&O that have been designed to
set amount of time, and then the cycle is repeated. A
minimize these drawbacks. These include using an average
problem with this algorithm is available energy is wasted
of several samples of the array power and dynamically
when the load is disconnected from the PV array, also the
adjusting the magnitude of the perturbation of the PV
MPP is not always located at 76% of the array s open circuit
operating point.
voltage.
Incremental Conductance
Anti-islanding
The incremental conductance algorithm seeks to overcome
In addition to the typical power quality regulations
the limitations of the P&O algorithm by using the PV array's
concerning the harmonic distortion and EMI limits, the grid-
incremental conductance to compute the sign of dP/dV
connected PV inverters must also meet specific power
without a perturbation [45]. It does this using an expression
generation requirements like the islanding detection, or even
derived from the condition that, at the MPP, dP/dV = 0.
certain country-specific technical recommendations for
Beginning with this condition, it is possible to show that, at
instance the grid impedance change detection (in Germany).
the MPP dI/dV = -I/V. Thus, incremental conductance can
Such extra-requirements contribute to a safer grid-operation
determine that the MPPT has reached the MPP and stop
especially when the equipment is connected in dispersed
perturbing the operating point. If this condition is not met,
power generating networks but impose additional effort to
the direction in which the MPPT operating point must be
readapt the existing equipments.
perturbed can be calculated using the relationship between
The European standard EN50330-1 (draft) [46] describes
dI/dV and -I/V. This relationship is derived from the fact
the ENS (the German abbreviation of Mains monitoring
that dP/dV is negative when the MPPT is to the right of the
units with allocated Switching Devices) requirement, setting
MPP and positive when it is to the left of the MPP. This
the utility fail-safe protective interface for the PV converters.
algorithm has advantages over perturb and observe in that it
The goal is to isolate the supply within 5 seconds after an
can determine when the MPPT has reached the MPP, where
impedance change of Z = 0.5 &!, which is associated with a
perturb and observe oscillates around the MPP. Also,
grid failure. The main impedance is typically detected by
incremental conductance can track rapidly increasing and
means of tracking and step change evaluation at the
decreasing irradiance conditions with higher accuracy than
fundamental frequency. Therefore, a method of measuring
perturb and observe. One disadvantage of this algorithm is
the grid impedance value and its changes should be
the increased complexity when compared to perturb and
implemented into existing PV-inverters.
observe. This increases computational time, and slows down
One solution is to attach a separate device developed only
the sampling frequency of the array voltage and current.
for the measuring purpose as depicted in Fig. 22a.
Parasitic Capacitance
The parasitic capacitance method is a refinement of the
incremental conductance method that takes into account the
parasitic capacitances of the solar cells in the PV array [45].
Parasitic capacitance uses the switching ripple of the MPPT
to perturb the array. To account for the parasitic capacitance,
the average ripple in the array power and voltage, generated
by the switching frequency, are measured using a series of
filters and multipliers and then used to calculate the array
Its control issues will be discussed starting from its
mathematical model both with L-filter and LCL-filter on the
grid side. Then simple controls as well as a few advanced
methods will be introduced and briefly discussed. Finally
some advanced topics and experimental results are shown.
Mathematical Model of the L-filter inverter
The state of the three-phase inverter is modelled by means
(a)
of a switching space-vector defined with the switching
functions p (t) (j = a, b, c)
j
2
(6)
p(t) = pa(t) + ą�" pb(t) + ą2 �" pc(t)
( )
3
then if the inverter is connected to the grid through an L-
filter (Fig. 23).
(b)
di (t)
(7)
v (t) = e (t) + Ri (t) + L
Fig. 22. Grid-impedance measurement for PV inverters. a) using external
dt
device; b) embedded on the inverter control using harmonic injection.
1
(8)
v(t) = p(t)vo(t)
2
This add-on option is being commonly used in the
commercial PV inverters, but the new trend is to implement
this function embedded into the inverter control without
extra hardware. Numerous publications exist in this field,
which offer measuring solutions for the grid impedance for a
wide frequency range from dc up to typically 1 kHz [47].
Unfortunately, not always can these methods easily be
embedded into a non-dedicated platform, i.e. PV-inverters
featuring typically a low-cost DSP. Specific limitations like
Fig. 23. L-filter inverter connected to the grid.
real-time computation, A/D conversion accuracy and fixed-
point numerical limitation, are typically occurring.
assuming to neglect the dc voltage dynamics as the dc
A novel approach presented in [48], [49] estimates the grid
voltage vo(t) is an input to the system. Moreover is the
v(t)
impedance on-line with the purpose of detection the step
change of 0.5 &! as required in [46] as shown in Fig. 22b. space-vector of the inverter input voltages; is the
i (t)
The solution is found by injecting a test signal through the
space-vector of the inverter input currents; is the
e(t)
inverter modulation process. This signal, an interharmonic
space-vector of the input line voltages.
current with a frequency close to the fundamental,
The mathematical model written in the state space form is
determines a voltage drop due to the grid impedance, which
is measured by the existing PV-inverter sensors. Then, the
di (t) 1 1
Ą#
(9)
same CPU unit that makes the control algorithm carries out = (t) - e(t) + p(t)vo (t)ń#
ó#-Ri Ą#
dt L 2
Ł# Ś#
the calculations and gives the grid impedance value [48].
This approach provides a fast and low cost solution to meet
A commonly used approach in analysing three-phase
the required standards and was succesfully implemented on
systems is to adopt a dq-frame that rotates at the angular
a TMS320F24x 16-bit fixed point DSP platform as an add-
speed � � (where � = 2Ąf and f is the fundamental frequency
on to the existing control.
of the power grid s voltage waveform). The space-vectors
which express the inverter electrical quantities are projected
V. CONTROL OF THREE-PHASE INVERTERS
on the d-axis and q-axis. As a consequence if a space-vector
with constant magnitude rotates at the same speed of the
The control of a three-phase inverter connected to the grid
frame, it has constant d- and q- components while if it
has more in common with the control of an active
rotates at a different speed or it has a time-variable
rectifier/filter rather than with the control of an adjustable
magnitude it has pulsating components. Thus in a dq-frame
speed drive. In fact with the first the distributed inverter
rotating at the angular speed � (7) becomes
shares the characteristic to be connected to the grid on the ac
side, while with second it shares the common characteristic
to have less responsibilities in the management of the dc- ż#did t
( ) 11
Ą#
-�iq t =
( ) ( ) ( ) ( ) ( )ń#
�#
ó#-Rid t - ed t + 2 pd t vo t Ą#
link voltage that is usually controlled by another converter
dt L
�# Ł# Ś#
(10)
�#
stage. Hence from the control perspective the three-phase
diq t
( )+ �id t =
11
Ą#
�#
distributed inverter has an advantage over the rectifier and a
( ) ( ) ( ) ( ) ( )ń#
ó#-Riq t - eq t + 2 pq t vo t Ą#
�#
dt L
Ł# Ś#
�#
disadvantage over the inverter for the motor.
 R1 1
Ą#ń#
ó#- � - 0 0 0 Ą#
L1 L1
ó#Ą#
R1 1
ó#Ą# 10 0
Ą#ń# Ą# ń#
ó#Ą#
i1d -� - 0 - 0 0 i1d ó#- 0 Ą# ó# 0 0 Ą#
Ą# ń# Ą# ń#
L1 L1 Ą#
L1
ó# Ą# ó# Ą# ó#Ą# ó# Ą#
i1q ó# 11 Ą# i1q
ó#
ó# Ą# ó# Ą# ó#Ą# ó# 0 0 Ą# (11)
1
0 0 � - 0
0 -
ó#Ą#
ó#vC d Ą#CC L1 Ą# ed ó# 0 0 Ą# vd
ó#vC d Ą# ó#
Ą# ń#
ff
d f f
ó#Ą#Ą# ń#
ó# Ą# ó# Ą# ó#Ą# ó# Ą#
=+ +
ó#e Ą#
Ą#ó#v Ą#
ó# Ą# ó# Ą# ó# 0 0 Ą# ó# Ą#
dt vC q ó# 11 vC q
1
qq
Ł# Ś#
f f
0 -� 0 0 - Ą#Ł# Ś#
ó# 0
ó# Ą# ó# Ą# ó#Ą# ó# Ą#
CC
ff
ó#Ą#
i2d i2d 0 0 L2
ó# Ą# ó# Ą# ó#Ą# ó# Ą#
ó#
ó# Ą#
1
1 R2 Ą# ó# i2q Ą# ó# 0 0 Ą# ó# 0 Ą#
i2q ó#Ą#
Ł# Ś# 0 0 - 0 - � Ł# Ś# ó#Ą# ó# Ą#
L2 L2 Ł#Ś# Ł# Ś#
0 0 L2
ó#Ą#
ó#
1 R2 Ą#
ó#
0 0 0 -� - Ą#
L2 L2 Ą#
ó#Ś#
Ł#
(10) shows how in the dq-frame the d- and q- differential The use of an LCL-filter claims for a deep dynamic and
equations for the current are dependent due to the cross- stability analysis of the current control loop [50]. In order to
highlight the stability problems that arise from the use of an
coupling terms �iq(t) and �id(t).
LCL-filter it is sufficient to show the d- or q-system plant in
Laplace domain. If the converter side current is sensed, the
Mathematical Model of the LCL-filter inverter
system plant is
In (11) the LCL-filter based inverter model is reported in
2
order to highlight the increased complexity of the system.
s2 + zLC
( )
i(s) 1
The system is shown in Fig. 24.
G(s) = = (12)
2
v(s) L2s
s2 + �res
()
If the grid side current is sensed, the plant for control is
2
i(s) 1 zLC
G(s) = = (13)
2
v(s) L2s
s2 + �res
( )
-1
2 22
Ą# ń#
where zLC = and �res = L1 + L2 zLC L2 .
Fig. 24. LCL-filter inverter connected to the grid. ( )
Ł#L1C f Ś#
AC Current control
In both cases the two poles related to the resonance of the
The ac current control (CC) is usually adopted because the
LCL-filter challenges the current control instability,
current controlled converter exhibits, in general, better
particularly the second one (sensing of the grid current)
safety, better stability and faster response [11].
generally leads to a more stable behavior [50].
This solution ensures several additional advantages. The
feedback loop also results in some limitations, such as that
Two axis-based current control
fast-response voltage modulation techniques must be
The most used control technique is the two axis-based
employed, like PWM. Optimal techniques, which use
method [11]. Then if the two-axis system is a stationary ą�-
precalculated switching patterns within the ac period, cannot
frame, the proportional plus resonant controller can be
be used, as they are not oriented to ensure current waveform
adopted [43] and it is
control [11].
Generally the current control is the most inner loop of a
Ks
Ą#K + i ń#
0
cascade control that employ a dc-link voltage level
p
ó# Ą#
s2 + �02
ó# Ą#
management system and active and reactive power
DPR (s)ą� = (14)
ó# Ą#
Ks
i
controller as shown in Fig. 25.
0 K +
ó# Ą#
p
s2 + �02 Ą#
ó#
Ł# Ś#
If the frame is a rotating dq-frame, classical PI controllers
can be used
Ki
Ą#K + 0 ń#
p
ó# Ą#
s
DPI (s)dq = ó# Ą# (15)
Ki Ą#
ó#
0 K +
p
ó# Ą#
Ł# s Ś#
If this controller is transformed into an ą�-frame then
Fig. 25. Block diagram of a typical three-phase distributed inverter.
Ks �0Ki new sensors because this voltage is near to the grid, which is
Ą#K + i ń#
p
ó#
normally sensed. Moreover, in [52] an interesting approach
s2 + �02 s2 + �02 Ą#
ó#Ą#
DPI (s)ą� = (16)
to perform active damping has been proposed: a virtual
ó#Ą#
�0Ki Kis
K +
ó# - Ą#
p
resistor is added. The virtual resistor is an additional control
s2 + �02 s2 + �02 Ś#
ó#Ą#
Ł#
algorithm that makes the LCL-filter behaving as if there was
a real resistor connected to it. However, an additional
In Eq. (16) it is equal to (14) except for non-diagonal terms.
current sensor is needed if the virtual resistor is connected in
Hence the PI controller in the dq-frame and PR controller in
series to the filter inductor or capacitor. Further an
the ą�-frame can achieve similar performances.
additional voltage sensor is needed, if it is connected in
In the case of a dq-frame, if it is oriented such as the d-
parallel. Basically all these approaches are multiloop-based
axis is aligned on the grid voltage vector the control is called
[53] while an alternative solution consists of adopting a
Voltage Oriented Control (VOC) (Fig. 26). The reference
more complex controller acting as a digital filter around the
current d-component i*d is controlled to manage the active
resonance frequency of the LCL-filter [50].
power flow while the reference current q-component i*q is
controlled to manage the reactive power flow. To have the
Direct power control
grid current vector in phase with the grid voltage vector, i*q
In the last years the most interesting emerging technique has
should be zero.
been the direct power control developed in analogy to the
well known direct torque control used for drives. In DPC
Grid voltage harmonic compensators there are no internal current loops and no PWM modulator
The grid voltage is usually affected by a background block because the converter switching states are
distortion that can result in a high harmonic distortion of the appropriately selected by a switching table based on the
grid current. This problem can be solved both in a stationary instantaneous errors between the commanded and estimated
values of active and reactive power [11], [54], [55] see Fig.
ą�-frame and in a rotating dq-frame. In the first case it is
27. The main advantage of the DPC is in its simple
sufficient to plug in other resonant controller also called
algorithm while the main disadvantage is the need for a high
harmonic compensators
sampling frequency to obtain satisfactory performance.
s
GR (s)ą� = kih
" (17)
2
h=3,5,7 s2 + �0 �" h
( )
Reduction of the number of sensors
The basic number of needed sensors is 4 (two ac currents
where h is the order of the harmonic to be compensated.
and two ac voltages). However this number can be reduced
If the controller adopts a rotating dq-frame approach it is
avoiding the use of grid voltage vector with implementing a
possible to introduce other dq-frame rotating at multiple
virtual sensor or using a zero crossing detector in order to
speed in respect to the fundamental one and adopting
have the phase reference for the current. Moreover if a
standard PI-controllers in each of them. In both the cases it
feedforward current control technique is adopted the grid
is necessary that the harmonics to be compensated stay
current sensors can be avoided but it is essential to provide a
within the bandwidth of the current controller otherwise
method for overcurrent protection in industrial applications.
stability problems may arise [37].
Fig. 27. Direct Power Control based on the active and reactive power
calculation.
In [56] an algorithm to estimate the position of line
Fig. 26. Voltage Oriented Control based on the use of a rotating dq-frame.
voltage is presented. The proportional-plus-integral current
Current control active damping
regulator is modified to obtain the angle error signal driving
This solution seems very attractive especially in
an observer, similar in structure to a phase-locked loop,
applications above several kW, where the use of a damping
which provides the angle of line voltages.
resistor increases the encumbrances, the losses could claim
for forced cooling and the efficiency decrement becomes a
Non-ideal conditions
key point. In [51] a lead-lag network has been used on the
The non-ideal conditions are many and they can affect
filter capacitor voltage and it is possible to avoid the use of
very much the overall system performance such as too long
computation time, presence of acquisition filters, ac phase
unbalance, location of the grid voltage sensors after a
dominant reactance and passive damping if an LCL-filter is
used. A proper design to take them into consideration them
should be provided [57].
It is well known that the grid unbalance causes even
harmonics at the dc output and odd harmonics in the input
current [58]. Some solutions have been studied such as the
use of negative sequence in the reference current that
unfortunately leads to uncontrollability of the power factor
or the use of two current controllers for positive and
negative sequences, which also can create stability problems.
EMC-issues
The main EMC-issues are related to the low frequency
Fig. 29. Compensation of grid background distortion: grid currents [2
range and thus to the correct control of the current. Thus the
A/div] and grid voltage [100 V/div] (sampling/switching 10 kHz, active
use of a LCL-filter on the ac side is an interesting solution:
power 2 kW, PR-controllers in a ą�-frame).
the reduced values of the inductance can be achieved and
the grid current is almost ripple free. The design of the LCL-
filter has been investigated [59].
Results
Some tests results, obtained on the set-up shown in Fig.
28, are reported in order to evaluate the impact of the non-
ideal conditions on the behaviour of a PR-based controller in
ą�-frame (Fig. 29), the use of harmonic compensator in a
stationary ą�-frame to mitigate these effects (Fig. 30) and
finally the effect of active damping (Fig. 31).
Fig. 30. Compensation of grid background distortion: grid currents [2
A/div] and grid voltage [100 V/div] (sampling/switching 10 kHz, active
power 2 kW, PR-controllers in a ą�-frame with 5th and 7th harmonic
compensators).
Fig. 28. Laboratory set-up to test three-phase power converter control.
Fig. 31. Control change from active damping to no damping (t=40 ms): grid
currents [2 A/div] (sampling/switching 10 kHz, active power 2 kW, PR-
controllers in a ą�-frame).
VI. CONVERTER TOPOLOGIES FOR WIND TURBINES
In a fixed speed wind power conversion system, the
power may be limited aerodynamically either by stall, active
IV
W ounded Rotor
stall or by pitch control [6], [7]. Normally induction
Induction
generator
generators are used in fixed speed systems, which are almost
Grid
Gear
independent of torque variation and operate at a fixed speed
(slip variation of 1-2%). Fig. 32 shows different topologies
Resistance
for the first category of wind turbines. Pitch
control
Reactive
with PE
All three systems are using a soft-starter (not shown in
compensator
Fig. 32) in order to reduce the inrush current and thereby
(a)
limit flicker problems on the grid. They also need a reactive
power compensator to reduce (almost eliminate) the reactive
V
Doubly-fed
power demand from the turbine generators to the grid. induction generator
It is usually done by continuously switching capacitor
Grid
Gear
banks following the production variation (5-25 steps). Those
solutions are attractive due to cost and reliability but they
Pitch
are not able (within a few ms) to control the active power
AC DC
very fast. The generators have typically a pole-shift AC
DC
possibility in order to maximize the energy capture.
Pref Qref
The next category is variable speed systems [6]-[36] where
(b)
pitch control is typically used. Variable speed wind turbines
may be further divided into two parts, one with partially
Fig. 33. Wind turbine topologies with partially rated power electronics and
rated power electronic converters and one with fully rated limited speed range, (a) Rotor-resistance converter (System IV) (b) Doubly-
fed induction generator (System V).
power electronic converters.
I
Induction
Fig. 33 shows wind turbines with partially rated power
generator
electronic converters that are used to obtain an improved
Grid
Gear
control performance. Fig. 33a shows a wind turbine system
where the generator is an induction generator with a
wounded rotor. An extra resistance is added in the rotor,
Pitch
which can be controlled by power electronics. This is a
Reactive
compensator
dynamic slip controller and it gives typically a speed range
of 2-10 %. The power converter for the rotor resistance
(a)
control is for low voltage but high currents. At the same
time an extra control freedom is obtained at higher wind
II
Induction
speeds in order to keep the output power fixed. This solution
generator
still needs a soft-starter and a reactive power compensator.
Grid
A second solution of using a medium scale power
Gear
converter with a wounded rotor induction generator is
shown in Fig. 33b [18]-[26]. Slip-rings are making the
Stall electrical connection to the rotor. A power converter
Reactive
controls the rotor currents. If the generator is running super-
compensator
synchronously electrical power is delivered through both the
rotor and the stator. If the generator is running sub-
(b)
synchronously electrical power is only delivered into the
III
rotor from the grid. A speed variation of ą30 % around
Induction
synchronous speed can be obtained by the use of a power
generator
Grid converter of 30 % of nominal power.
Gear
Furthermore, it is possible to control both active (Pref) and
reactive power (Qref), which gives a better grid performance,
and the power electronics enable the wind turbine to act
Active
Stall more as a dynamic power source to the grid. The solution
Reactive
compensator
shown in Fig. 33b needs neither a soft-starter nor a reactive
power compensator. The solution is naturally a little bit
(c)
more expensive compared to the classical solutions shown
in Fig. 32 and Fig. 33a. However, it is possible to save
Fig. 32. Wind turbine systems without power converter but with
aerodynamic power control. money on the safety margin of gear, reactive power
Pitch controlled (System I) b) Stall controlled (System II) c) Active stall
compensation units and it is possible to capture more energy
controlled (System III).
from the wind.
 The wind turbines with a full-scale power converter power converter to the grid enables the system very fast to
between the generator and grid give extra losses in the control active and reactive power. However, the negative
power conversion but it may be gained by the added side is a more complex system with a more sensitive
technical performance [9]. Fig. 34 shows four possible electronic part.
solutions with full-scale power converters. By introducing power electronics many of the wind
turbine systems get a performance like a power plant. In
respect to control performance they are faster but of course
VI
the produced real power depends on the available wind. The
Induction
reactive power can in some solutions be delivered without
generator
Grid
having any wind.
AC DC
Gear
DC AC Fig. 34 also indicates other important issues for wind
turbines in order to act as a real power source for the grid.
Pref Qref
Pitch
They are able to be active when a fault appears at the grid
(a) and so as to build the grid voltage up again quickly; the
systems have the possibility to lower the power production
even though more power is available in the wind and
DC
thereby acting as a rolling capacity. Finally, some are able to
VII AC
operate in island operation in the case of a grid collapse.
Grid
AC DC
Gear
VII. CONTROL OF WIND TURBINES
DC AC
Synchronous
Pitch
Generator
P Q Controlling a wind turbine involves both fast and slow
ref re f
control. Overall the power has to be controlled by means of
the aerodynamic system and has to react based on a set-
(b)
point given by dispatched center or locally with the goal to
maximize the production based on the available wind power.
The power control system should also be able to limit the
DC
power. An example of an overall control scheme of a wind
VIII AC
turbine with a doubly-fed generator system is shown in Fig.
Grid
35.
AC DC Below maximum power production the wind turbine will
DC AC typically vary the speed proportional with the wind speed
Synchronous
and keep the pitch angle � fixed. At very low wind the speed
Generator
Pitch
Pref Qref
Multi-pole of the turbine will be fixed at the maximum allowable slip in
order not to have overvoltage.
(c)
A pitch angle controller will limit the power when the
turbine reaches nominal power. The generated electrical
IX PM-synchronous power is done by controlling the doubly-fed generator
Generator
through the rotor-side converter. The control of the grid-side
Multi-pole
Grid
AC DC converter is simply just keeping the dc-link voltage fixed.
DC AC
Internal current loops in both converters are used which
typically are linear PI-controllers, as it is illustrated in Fig.
Pitch
Pref Qref
36a. The power converters to the grid-side and the rotor-side
(d)
are voltage source inverters.
Another solution for the electrical power control is to use
Fig. 34. Wind turbine systems with full-scale power converters.
the multi-pole synchronous generator. A passive rectifier
a) Induction generator with gear (System VI)
b) Synchronous generator with gear (System VII) and a boost converter are used to boost the voltage at low
c) Multi-pole synchronous generator (System VIII)
speed. The system is industrially used today. It is possible to
d) Multi-pole permanent magnet synchronous generator (System IX).
control the active power from the generator. The topology is
shown in Fig. 36b. A grid inverter is interfacing the dc-link
The solutions shown in Fig. 34a and Fig. 34b are
to the grid. Here it is also possible to control the reactive
characterized by having a gear. A synchronous generator
power to the grid. Common for both systems are they are
solution shown in Fig. 34b needs a small power converter
able to control reactive and active power very fast and
for field excitation. Multi-pole systems with the
thereby the turbine can take active part in the power system
synchronous generator without a gear are shown in Fig. 34c
control.
and Fig. 34d.
The last solution uses permanent magnets, which are still
becoming cheaper and thereby more attractive. All four
solutions have the same controllable characteristics since the
generator is decoupled from the grid by a dc-link. The
Measurement
Measurement
grid point M
grid point M
N
N
AC DC
AC DC
AC
AC
DC
DC
T
T
meas
meas
U PWM
U PWM
dc
dc
PWM
meas
Iac
Iac
meas
meas
�
�
Pgrid
Pgrid
Rotor side
Rotor side Grid side
Rotor side Grid side
meas
meas
Irotor converter controller converter controller meas
I
rotor
converter controller
converter controller converter controller
meas
Qgrid
Qgrid
DFIG control
DFIG control
conv,
conv,
Qgrid ref ref
Qgrid ref ref
U
U
dc
dc
conv,
conv,
meas Pgrid ref
meas Pgrid ref
�gen
�
gen
Grid
Grid
meas
meas
operators
operators
Pgrid
Pgrid
cross-coupling
cross - coupling
control system
control system
Power controller Speed controller
Power controller Speed controller
Power controller Speed controller
rat
rat
Pgrided , ref
Pgrided , ref
Wind turbine control
Wind turbine control
Fig. 35. Control of wind turbine with doubly-fed induction generator system [35 ].
DFIG
Transformer
Grid
Gear
Rotor-side Grid-side
Inductance
�r
converter converter
Pgrid
Q
grid
3
vra, vrb,vrc
vga,v vgc
gb,
i irb,irc
ra,
iga, igb,igc
vDC Grid
Rotor
Pref Qref
control control
(a)
Generator Grid
PMG
rectifier inverter
Inductance
Grid
vDC
vga,v vgc
gb,
vDC
iga, igb,igc
Power Grid
Pref control
Q
control
ref
(b)
Fig. 36. Basic control of active and reactive power in a wind turbine [11].
a) Doubly-fed induction generator system (System V)
b) Multi-pole synchronous generator system (System VIII)
[20] D. Arsudis,  Doppeltgespeister Drehstromgenerator mit
VIII. CONCLUSION
Spannungszwischenkreis Umrichter in Rotorkreis f�r Wind
Kraftanlagen, Ph.D. Thesis, 1998, T.U. Braunschweig, Germany.
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Power Systems, Vol. 18, No. 2, May 2003, pp. 803- 809.
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