Reactive power management of power networks with wind generation

Chapter 2
Facts Devices

In recent years technological advances in power electronics have facilitated the
development of electronic equipments that offer the ability to handle large amounts
of power; consequently, the use and application of this technology into electrical
power systems have increased significantly. These electronic devices, called
Flexible AC Transmission System (FACTS), are based on electronic power
converters and they provide the ability to make quick adjustments and to control
the electrical system. FACTS devices can be connected in series, in parallel, or in a
combination of both. The benefits they offer to the electrical grid are widely
referenced in scientific literature. These benefits include improvement of the
stability of the grid, control of the flow of active and reactive power on the grid,
loss minimization, and increased grid efficiency.
The installation of FACTS devices (with serial or parallel connections) in a wind
farm substation or in the terminals of wind turbines is increasing rapidly owing
mainly to the specifications listed in the Transmission System Operators’ (TSO)
grid codes which require that wind turbines should provide ancillary services
similar to those of conventional synchronous generators.

2.1 Static Var Compensator (SVC)

According to the IEEE definition, a Static Var Compensator (SVC) is a shunt-
connected static var generator or absorber whose output is adjusted to exchange
capacitive or inductive current to maintain or control specific parameters of the
electrical power system (typically, the bus voltage) [1].
Typical SVCs can be classified on Thyristor-Controlled Reactor (TCR),
Thyristor-Switched Reactor (TSR) or Thyristor-switched capacitors (TSCs). Figure 2.1
shows a TCR single-phase equivalent circuit in which the shunt reactor is dynamically
controlled from a minimum value (practically zero) to a maximum value by means of
conduction control of the by-directional thyristor valves. By this controlled action the
SVC can be seen as a variable shunt reactance established by the parallel connection of

H. Amaris et al., Reactive Power Management of Power Networks with Wind 9
Generation, Lecture Notes in Energy 5, DOI 10.1007/978-1-4471-4667-4_2,
# Springer-Verlag London 2013

10 2 Facts Devices

Fig. 2.1 Single-phase
equivalent circuit of the shunt i
SVC (TCR)

XL
U XC

the shunt capacitive reactance XC and the effective inductive reactance XL controlled
by the thyristor switching.

2.1.1 Mode of Operation

The instantaneous current supplied by SVCs is given by:
U
ðcos asvc À cos otÞ asvc ot asvc þ e
I¼ XL (2.1)
0 asvc þ e ot asvc þ p

Where:
U represents the SVC voltage at the Point of Common Coupling (PCC).
XL is the SVC total inductance.
asvc is the firing delay angle.
e is the SVC conduction angle given by

e ¼ 2ðp À asvc Þ (2.2)

It can be seen that as the delay angle asvc increases, the conduction angle 2 of
the valve decreases.
Figures 2.2, 2.3, and 2.4 show different current wave-shapes injected by the TCR
for diverse firing delay angles.
The SVC’s control of the output current is based on the control of the firing delay
of thyristors. Hence, the maximum injected current is obtained by a firing delay of
90 (full conduction). Meanwhile, the firing angle delays between 90 and 180
electrical degrees only indicate a partial current contribution. This fact contributes
to enhancing the device’s inductance and makes it possible, at the same time, to
decrease its contribution of reactive power and current.
The fundamental component of current is obtained by means of a Fourier
analysis (2.3) or in a reduced version (2.4):

2.1 Static Var Compensator (SVC) 11

Fig. 2.2 AC current wave shape for asvc ¼ 90


12 2 Facts Devices


2ðp À aSVC Þ þ sin 2aSVC
I1 ¼ U (2.3)
pXL

Which can be expressed as:

I1 ¼ BSVC ðaSVC ÞU (2.4)

Where:

2ðp À aSVC Þ þ sin 2aSVC
BSVC ðaSVC Þ ¼
pXL

The maximum value of Bsvc is 1=XL, which corresponds to a conduction angle of
180 and represents the condition for maximum conduction of the thyristor’s group.
The lowest value of Bsvc is 0 and it is obtained from a conduction angle equal to zero
or from a firing angle of 180 . Thyristor firing angles lower than 90 are not allowed
because they generate an asymmetric current wave with a high component of
continuous current.
The slope defined as the ratio between the voltage variation and the variation of
the SVC compensating current over the whole control range could be thus
expressed via the voltage–current characteristics:

U ¼ Uref þ XSL I (2.5)

2.2 Static Synchronous Compensator (STATCOM) 13

Fig. 2.5 Voltage–current
characteristics of the SVC U

1.0

i

ICMAX ILMAX

Typical values of XSL are located within the interval ranging from 0.02 to 0.05 p.u.,
referring to the SVC’s base magnitude. Under limit conditions the SVC will
become a fixed reactance. Figure 2.5 shows the characteristic curve of an SVC.
The reactive power supplied by the TCR could thus be calculated using (2.6):

U2
QSVC ðaSVC Þ ¼ À U 2 BSVC ðaSVC Þ (2.6)
XC

From the point of view of power system planning, localization and optimum
sizing of FACTS devices are the most important aspects for operating electric
networks with high wind power penetration while at the same time maintaining
the security and efficiency of the whole electric system.

2.2 Static Synchronous Compensator (STATCOM)

The concept of the STATCOM was proposed by Gyugyi in 1976. According to
IEEE a STATCOM can be defined as a static synchronous generator operated as a
shunt-connected static var compensator whose capacitive or inductive output
current can be controlled independent of the AC system voltage.
A STATCOM is a static compensator that it is connected to the grid in parallel
for the compensation of reactive power. It is able to inject or absorb reactive power
in a controlled way regardless of the grid voltage [1, 2]. The basic element is the
Voltage Source Converter (VSC) which converts an input DC voltage to an AC
voltage at the fundamental frequency with a given magnitude and a controllable
phase. The AC output voltage is dynamically controlled in order to provide the
required reactive power to the network.

14 2 Facts Devices

Fig. 2.6 Equivalent circuit of PCC
the statcom
IST PST +jQST

ZSH
Ui

UST

2.2.1 Mode of Operation

The VSC generates a voltage at the fundamental frequency !st ¼ Ust ffdst with
U
controllable voltage amplitude and phase. The VSC is connected to the grid
U ¼ Ui ffdi through an inductive impedance, Zsh , that represents the coupling
!i
transformer and the connection filters, the equivalent circuit is as shown in
Fig. 2.6.
The interchange of active and reactive power with the grid can be expressed as
follows:

Pst ¼ Ui 2 :gsh À Ui Ust ½gsh : cosðdi À dst Þ þ bsh : sinðdi À dst ÞŠ (2.7)

Qst ¼ ÀUi 2 :bsh À Ui Ust ½gsh : sinðdi À dst Þ À bsh : cosðdi À dst ÞŠ (2.8)

where Ysh ¼ Z1 ¼ gsh þ jbsh .
sh
The capacity for injecting reactive power into the grid is limited by the maxi-
mum voltage and the maximum current allowed by the semiconductors, as shown in
Fig. 2.7.
The principle of operation of the VSC-based STATCOM depends on the control
strategy for regulating the interchange of power between the converter and the grid
and it depends also on the output AC voltage of the converter. If the magnitude of
the voltage of the converter is equal to the voltage of the grid, Ust ¼ Ui, the
interchange of reactive power between the STATCOM and the grid is equal to zero.
In contrast, if the voltage of the converter is less that the grid voltage at the
PCC, Ust Ui, the STATCOM absorbs reactive power (draws lagging current).
However, if the STATCOM is controlled in such a way that the output voltage of
the converter is higher than the PCC voltage, reactive power is injected into the
grid [3].
In practice, it is also necessary to control the active power exchange of the
STATCOM by regulating the phase angle di st ¼ di À dst between the voltage at the
VSC ( !st ¼ Ust ffdst ) and the voltage at the PCC ( !i ¼ Ui ffdi ) so that the VSC
U U
absorbs active power from the grid to maintain a constant voltage for the DC-link.

2.2 Static Synchronous Compensator (STATCOM) 15

Fig. 2.7 Voltage–current
characteristics of the U
STATCOM
1.0

i
Imin Imax
Capacitive Inductive

2.2.2 Control Techniques

There are various control techniques, as detailed in [4] where the two listed below
are the most typical:
• Voltage local control at the PCC voltage: In this control strategy, the purpose is to
regulate the PCC voltage, Ui, so that it is maintained constant at its reference value
Ui ref . Mathematically, this condition is expressed as a restriction of operation:

Ui À Ui ref ¼ 0 (2.9)

• Reactive Power control at the PCC: In many situations, the STATCOM is
required to inject reactive power into the grid according to the speciﬁcations
of the TSO. This form of control can be applied, for example, when a coordi-
nated control is required for FACTS devices and wind farms performing
reactive power delivery to the entire grid [5]. When this mode of operation is
desired, it must be expressed as a restriction of operation as follows:

Qst À Qst ref ¼ 0 (2.10)

2.2.3 Restrictions of Operation

In a STATCOM the maximum reactive power that can be supplied to the grid
depends on the maximum voltages and currents permitted by the power
semiconductors, so it is necessary to include the following internal restrictions:

16 2 Facts Devices

• The VSC output voltage must fall within the allowed limits of operation:

Ust;min Ust Ust;max (2.11)

where Ust;min and Ust;max are the limiting values of the minimum and maximum
voltages allowed by the semiconductors, respectively.
• The current injected by the STATCOM, Ist , must be less than the maximum
current allowed by the semiconductors, Ist;max :

Ist Ist;max (2.12)

Where:

Reactive power management of power networks with wind generation

st

• In contrast, it is necessary to include external restrictions of the grid voltage at
the PCC. According to the specific regulations of the grid operator the grid
voltage at the PCC must be maintained within certain allowed limits:

Ui;min Ui Ui;max (2.14)

2.2.4 Application of the STATCOM in Wind Farms

The first studies that analyzed the incorporation of STATCOMs in wind farms were
initiated at the end of the 1990s with the aim of improving the flicker and power
quality of fixed-speed wind turbines (Fig. 2.8). In these situations, the converter was
controlled with a unitary power factor so that there was not any interchange of
reactive power between the wind farm and the grid. This strategy has been followed
in [6] which demonstrated that by injecting reactive power it was possible to
improve the stability and the dynamic operation at the wind farm substation
(wind turbines and statcom).
´ ´
At the Rejsby Hede wind farm in Denmark a STATCOM was installed in 1998
with a rated power of 8 Mvar for compensating the reactive power of the wind farm.
The wind farm consisted of 40 turbines of 600 kW each with a total capacity of
24 MW [7]. The main objective was to improve power quality and to supply the
reactive power needed to operate the wind farm. It was noted that it was possible to
operate the wind farm with a unitary power factor (instead of regulating the reactive
power interchange between the wind farm and the grid) provided that the reactive
power demand of the wind farm were inferior to the maximum capacity of the
STATCOM; However, above 8 Mvar it was necessary to absorb reactive power
from the grid.

2.3 STATCOM Versus SVC 17

Fig. 2.8 Statcom installed at
the wind farm substation Wind
GRID
Farm

STATCOM

In recent years the new grid code specifications which refer to the regulation of
reactive power and Low-Voltage Ride-Through capability (LVRT) have again
generated interest in implementing SVCs or STATCOMs in wind farms. In [8]
the application of STATCOMs to improve voltage fluctuations is discussed and [9]
contains an analysis of how to improve the LVRT capability in fixed-speed wind
turbines if STATCOM devices are installed at the wind farm PCC instead of an
SVC. This last reference highlights the fact that STATCOMs have an inherent
ability to increase the transient stability margin by injecting an adjustable reactive
current to the grid regardless of the level of voltage supply; consequently, they are
ideal devices for offering LVRT capabilities against voltage dips.
In [10] the possibility of controlling the injection of reactive power of a
STATCOM in coordination with DFIG variable-speed wind turbines is analyzed.
The main purpose of the STATCOM is to inject reactive power in the PCC in order
to reduce the depth of the voltage dip at the wind farm terminal allowing DFIG
wind turbines to remain connected during voltage dip situations.

2.3 STATCOM Versus SVC

The main difference between a STATCOM and an SVC is the way they operate: a
STATCOM works as a controllable voltage source while an SVC works as a
dynamically controllable reactance connected in parallel.
Compared with an SVC, a STATCOM offers the possibility of feeding the grid
with the maximum available reactive current even at low voltage levels, this is
possible because in every equilibrium condition the injected reactive power varies
linearly with the voltage at the Point of Common Coupling (PCC) [11]. In contrast,
for an SVC there is a quadratic dependence of the reactive power on the voltage at
the PCC which means that to inject the same reactive power it is necessary to install
an SVC with a nominal capacity higher than that of a STATCOM.
With regard to the maximum transient capacitive current it is observed that in an
SVC the capacitive current is limited by the size of the capacitor and by the
magnitude of the AC voltage. In the case of a STATCOM the maximum capacitive
current that can be injected is limited by the maximum current capacity of the
semiconductors used [12] and is independent of the voltage level at the PCC.
Another feature of a STATCOM is that the DC-link capacitor serves as storage
for active power. Therefore in certain situations, depending on the capacitor size, it
is possible to regulate the interchange of active power with the grid also.

18 2 Facts Devices

PCC

Sensitive
GRID Loads

LC
Filter

Voltage
Source
Converter

UDC

Fig. 2.9 Equivalent circuit of a DVR connected to the grid

STATCOM devices are capable of much faster dynamic reaction (1/4-1 cycle)
than an SVC. In a STATCOM the speed of response is limited by the commutation
frequency of the IGBT’s (normally 1 kHz) [13].

2.4 Dynamic Voltage Restorer (DVR)

A DVR is composed of a Voltage Source Converter (VSC) that has an energy
storage connected to the DC link. The VSC is connected in series with the power
network by means of a series-connected injection transformer and coupling filters.
A DVR may be formed by three VSCs [14] where each one is connected to the
network through an LC filter (Lf, Cf) and a transformer. The capacitor filter is
connected across the secondary winding of the coupling transformer as shown
in Fig. 2.9.
The DVR is normally used to protect critical loads or sensitive installations from
the effects of faults at the point of common coupling. During a voltage dip the DVR
is able to inject the required voltage to reestablish the load supply voltages.
The typical DVR is based on IGBT solid-state power electronic switching
devices in a PWM converter structure and it is capable of independently generating
or absorbing controllable real and reactive power at its AC output terminals. For
line currents exceeding the inverter rating a bypass scheme can be incorporated to
protect the power electronic converter.
DVRs are installed at wind farms mainly for providing low-voltage ride-through
capability [14], as is shown in Fig. 2.10.

2.4 Dynamic Voltage Restorer (DVR) 19

Wind Farm

PCC WT1

GRID

LC WT2
Filter

...
Voltage
Source
Converter WTn
UDC

Fig. 2.10 Scheme of a DVR connected at wind farm substation

PCC WT1

GRID

Software Voltage dip LC WT2
PLL detection Filter ...
VSC
Voltage reference
control
generation
PWM WTn
DC UDC
Voltage
Control

Fig. 2.11 Control blocks at a DVR

2.4.1 DVR Control

The control structure of the DVR includes the following stages (Fig. 2.11): the
measured phase voltage before the DVR transformer is fed to the Phase-Locked-
Loop (PLL) to detect the phase angles and to generate synchronizing signals, Uref.
Additionally, the voltage before the DVR transformer is measured to detect and
estimate voltage dips. That information is sent to the Voltage reference generation
block where it is processed. The result is driven to the VSC Control – PWM, where
the switching signals for ﬁring the IGBTs are obtained. The DC voltage is measured
for feeding back the Voltage reference generation Control [15].

20 2 Facts Devices

Fig. 2.12 Pre-dip
UPCC
compensation strategy at the UDVR
DVR
jDIP

IWind Farm UWind Farm

2.4.1.1 VSC Control

The technique usually used to control the AC output voltage is Pulse Width
Modulation using the Park transformation [16].

2.4.1.2 Voltage Dip Detection

The objective of this task is to detect the start and finish of the voltage dip at the
PCC as soon as possible. This process can be very sensitive to disturbances and
noise signals. For this reason, the voltage dip detection block is required to be
reliable, generating a minimum number of false operations. Several methods have
been applied to detect the instant of time in which the voltage dip appears, such as
Kalman filters or wavelets [17].

2.4.1.3 Voltage Reference Generation

This block is responsible for computing the voltage reference signal for the VSC
control. Its performance depends on the chosen compensation strategy. The basic
strategies are as follows [18]:
• Pre-dip compensation: The simplest solution is to reestablish the exact voltage
before the sag (magnitude and phase), see Fig. 2.12. The voltage at the PCC is
continuously tracked (UPCC), and with this information, the voltage injected by
the DVR (UDVR) is computed to maintain the voltage at the wind farm terminals
fixed to the pre-dip situation (UWind Farm).

UDVR ¼ UWindFarm À UPCC (2.15)

• In-phase compensation: This approach relies on compensating the voltage in
phase to the grid voltage after the voltage dip. It should be noted that using this
compensation strategy makes it possible to minimize the voltage magnitude but
the phase jump is not compensated.
• Energy-optimized compensation: This strategy consists of injecting the maxi-
mum reactive power by drawing as much active power from the grid as possible.
By using this compensation strategy it is possible to restore the voltage but a

2.4 Dynamic Voltage Restorer (DVR) 21

Fig. 2.13 Single-phase iac uf
equivalent circuit of the DVR
Cf
is

Zf LT
PCC uC Wind Farm
Bus Bus

phase jump occurs. This compensation strategy only works properly with small
voltage depths.
The single-phase equivalent circuit of the DVR is shown in Fig. 2.13, in which
the following parameters are considered:
• uc corresponds to the switching voltage generated at the AC converter terminals.
• LT represents the leakage inductance of the series transformer.
• The LC filter is composed of a filter inductance Lf and a capacitor filter Cf. The
voltage across the capacitor filter is denoted as uf .
• The impedance Zf ¼ Rin þ joLf is composed of both the resistance Rin which
represents the switching losses of the converter and the filter inductance Lf.
From the single-phase equivalent circuit the differential equations of the con-
troller using the state space methodology may be obtained:

0 1=Cf 0 À1=Cf u
x¼ xþ : c (2.16)
À1=LT ÀRin =LT Udc =Lf 0 is

where the state vector is:

uf
x¼ (2.17)
iac

Equation 2.16 is used to obtain the control law for the series compensator. The
controller determines the voltage that has to be injected into the grid to compensate
for the voltage dips.

2.4.2 Numerical Results

In this section different simulations are carried out in a wind farm of 20 MVA at a
nominal voltage of 11 kV that is composed of fixed-speed wind turbines. Each
electrical machine consists of an induction generator of 690 V and 750 kW.
Induction generators are provided with bank capacitors for reactive power compen-
sation. The distribution line is represented by its p equivalent circuit and a series

22 2 Facts Devices

Fig. 2.14 Voltage evolution
under fault conditions without
DVR

DVR is installed at the wind terminals. Its performance is tested under symmetrical
three-faults and unbalanced faults.
The wind farm is assumed to be formed by n generators in parallel all of them
with similar characteristics. All the simulations were performed assuming that the
whole wind farm is operating at 0.99 leading power factor. For simplicity it has
been assumed that each of the turbines experiences the same wind speed, therefore,
the whole farm may be represented by its equivalent induction generator.

2.4.2.1 Wind Turbine Performance Under Fault Conditions Without DVR

In this first simulation the DVR is not connected at the wind farm bus. Consequently
when a three-phase fault appears at the wind farm terminals (Fig. 2.14) the fixed-
speed wind farm is not able to withstand the voltage dip and the angular velocity of
the rotor under fault conditions starts to increase, increasing the probability of
stability problems, as is depicted in Fig. 2.15.

2.4.2.2 Wind Turbine Performance Under a Three-Phase Fault with DVR

In this scenario the DVR is connected at the wind farm bus. A symmetrical three-
phase fault is simulated at the wind terminals with a voltage depth of 50 % and a
phase jump of 20 at the beginning of the voltage dip. The voltage dip at the PCC
lasts from instant of time t ¼ 0.9 ms to t ¼ 1.1 ms.
In Fig. 2.16 it can be noted that the DVR detects the voltage dip efficiently and
injects the required voltage to restore the voltage seen by the wind farm.
It should be highlighted that by using the pre-dip compensation strategy the wind
farm’s active and reactive power injected to the network is not affected by the
voltage dip (Fig. 2.17) and remains almost fixed at the reference values. The angular
velocity and the electromagnetic torque of the equivalent wind turbine (Fig. 2.18)
recover nominal values after the voltage dip.

Reactive power management of power networks with wind generation

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