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energies
Article

Coordinated Control for Large-Scale Wind Farms
with LCC-HVDC Integration
Xiuqiang He 1
1
2

*

ID

, Hua Geng 1, *, Geng Yang 1 and Xin Zou 2

Department of Automation, Tsinghua University, Beijing 100084, China;
he-xq16@mails.tsinghua.edu.cn (X.H.); yanggeng@tsinghua.edu.cn (G.Y.)
State Power Economic Research Institute, State Grid Corporation of China, Beijing 102209, China;
zouxin@chinasperi.sgcc.com.cn
Correspondence: genghua@tsinghua.edu.cn; Tel.: +86-10-6277-0559

Received: 30 July 2018; Accepted: 21 August 2018; Published: 23 August 2018




Abstract: Wind farms (WFs) controlled with conventional vector control (VC) algorithms cannot be
directly integrated to the power grid through line commutated rectifier (LCR)-based high voltage
direct current (HVDC) transmission due to the lack of voltage support at its sending-end bus. This
paper proposes a novel coordinated control scheme for WFs with LCC-HVDC integration. The
scheme comprises two key sub-control loops, referred to as the reactive power-based frequency (Q-f )
control loop and the active power-based voltage (P-V) control loop, respectively. The Q-f control,
applied to the voltage sources inverters in the WFs, maintains the system frequency and compensates
the reactive power for the LCR of HVDC, whereas the P-V control, applied to the LCR, maintains
the sending-end bus voltage and achieves the active power balance of the system. Phase-plane
analysis and small-signal analysis are performed to evaluate the stability of the system and facilitate
the controller parameter design. Simulations performed on PSCAD/EMTDC verify the proposed
control scheme.
Keywords: HVDC; line commutated converter; wind farm; frequency stability; frequency control;
voltage stability; voltage control; vector control; voltage-source converter

1. Introduction
The power system is facing unprecedented technical challenges due to abundant large-scale
renewable power plant integration [1–5]. In China, large-scale wind farms (WFs) are mainly built
in remote areas of the northwest. As the local alternating current (AC) network is quite weak and
the penetration level of wind power is extremely high, it is a critical technical issue to integrate and
deliver large-scale wind power into the southeastern power grid. Emerging ultra HVDC (UHVDC)
transmission technology is able to provide an available solution. To date, most of the UHVDC systems
that are being planned or that are already built are of the line commutated converter (LCC) type,
which are suitable for long-distance and large-capacity transmission, with advantages such as low
expenditure and power loss [4]. Recently, a ±800 kV UHVDC with 10 GW capacity is being planned
to deliver wind and solar power on the Tibetan Plateau into the eastern load center, and wind and
solar power accounts for about 85% of the transmission capacity. It is quite difficult for the system to
maintain stable operation when there is no traditional generating set that is available at the sending
end of the UHVDC, due to some special factors, e.g., circuit faults, but only islanded WFs and/or
photovoltaic power plants. Therefore, it is necessary to study the control scheme of large-scale WFs
with LCC-HVDC integration as a technical reserve [4–7].
Vector control (VC) algorithms are commonly used for the control of wind energy conversion
systems (WECSs). Conventional VC [8] is based on the orientation of the grid voltage vector, and
Energies 2018, 11, 2207; doi:10.3390/en11092207

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Energies 2018, 11, 2207

2 of 19

thus a stiff grid is required to ensure the stability of the systems [9]. Unlike the voltage source
converter in VSC-HVDC, the line commutated rectifier (LCR) in LCC-HVDC cannot actively generate
the referenced three-phase voltage, essentially because of the application of semi-controlled switching
devices, e.g., thyristors. Moreover, a steady and balanced commutation voltage is a prerequisite for the
operation of the LCR. Consequently, under the condition that there is no available voltage support at
the sending-end bus (SEB) of LCC-HVDC, the WFs with conventional VC algorithms cannot can be
integrated by the LCC-HVDC directly [10–12].
A simple approach is to introduce a static synchronous compensator (STATCOM) on the SEB
in order to provide the voltage support [10–12]. However, the extremely high reliability and large
capability is required for the STATCOM, which results in high operating costs and power loss [13].
Without voltage support, the critical issue in the system is to guarantee the stability of the SEB voltage
vector, including both the voltage stability and the frequency stability. Considering that the LCR is
controllable in terms of active power, both the frequency and voltage stability issues can be addressed
through the division of labor between the WF and the LCR [14–19], i.e., the voltage and the frequency
are controlled by the WF and the LCR respectively, or conversely.
For the doubly-fed induction generator (DFIG)-based offshore WF at steady states, the stator
voltage of the DFIG is the product of its stator flux and the SEB frequency [14]. Based on this
fact, the earliest approach, where the stator flux and the frequency are controlled by the WF and
the LCR respectively, is proposed in [14,15]. A similar approach can be found in [16], where the
stator voltage and the frequency are controlled by the WF and the LCR respectively. In both of the
approaches, the frequency is regulated by the active power of the WF, whereas the voltage is regulated
by the reactive power of the WF. Actually, there is a substantial amount of capacitive compensation
on the SEB of the LCC-HVDC or diode-based HVDC, leading to a strong coupling between the
bus voltage and the active power balance, and also between the frequency and the reactive power
balance [17,20–22]. Consequently, references [17,20–22] develop a novel control concept, where the
frequency is regulated by the reactive power, whereas the voltage is regulated by the active power.
There is another coordination approach developed in [18,19] where the voltage is controlled by both
the WF and the LCR. As a result, the strong coupling between the active and reactive power control
loops occurs, which would affect the dynamic performance of the system. Moreover, the frequency
stability was not addressed in the approach.
In the aforementioned approaches, the control algorithms of the WFs are based on the conventional
VC structure where phase-locked loops (PLLs) are employed to detect the phase-angle of the stator
voltage. It is reported that PLLs play an important role in the system dynamics, and the system stability
involving PLLs are quite complicated [9], especially when WFs are connected to the weak, or even
isolated grids [23,24]. There are some intensive studies regarding the PLL-less DFIG control algorithms
for standalone applications, referred to as the indirect self-orientated vector control (ISOVC) [25–28].
In the ISOVC, the phase-angle, adopted in the coordinate transformation between abc and dq reference
frames, is derived from a free running integral of the rated synchronous speed ω 0 instead of the PLL.
It is worth noting that the supplementary indirect orientation control is realized through modifying
the original active power loop, and thus the auxiliary torque and pitch angle control is required to
regulate the active power [25–28]. Since the probability of frequency instability due to the dynamic
characteristics of PLLs can be completely avoided in the ISOVC, it is applied to control standalone
DFIGs with LCC-HVDC integration in [29]. In order to be employed in multi-machine scenarios,
additional active power droop loop should be introduced into ω 0 to achieve synchronization and
power sharing among multiple machines [29,30]. Unfortunately, with such droop scheme, the WF
cannot always track its maximum power point with sacrificed economic benefits.
In this paper, a novel scheme with respect to the division of labor between the WF and the LCR is
proposed. On one hand, considering the coupling relationship between the frequency and the reactive
power balance [17–20], a novel indirect orientation control based on the reactive power loop instead
of the active power loop [25–28] is developed. In the scheme, reactive power droop is employed for

Energies 2018, 11, 2207

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Energies
2018, 11, x FOR
REVIEW
synchronization
andPEER
reactive
power

3 of 19
sharing among multiple machines. Therefore, it would not affect
the active power tracking of the WF. On the other hand, the control objective of the LCR is to maintain
voltage
the active
power
balance,
notthere
onlyiscan
the voltage
stability
be addressed,
also
WF
the SEB and
voltage
stability.
Actually,
since
a strong
coupling
between
the voltagebut
and
thethe
active
is
able
to
capture
the
maximum
active
power
with
the
proposed
scheme.
The
proposed
scheme
power balance, not only can the voltage stability be addressed, but also the WF is able to capture
comprises
two active
key sub-control
loops.
One is thescheme.
reactive The
power-based
(Q-f) control
the maximum
power with
the proposed
proposedfrequency
scheme comprises
twoloop
key
for
the
voltage
source
inverters
(VSIs)
in
the
WF,
where
a
novel
ISOVC
is
developed
to
maintain
the
sub-control loops. One is the reactive power-based frequency (Q-f ) control loop for the voltage source
SEB
frequency
and
compensate
reactive
power
for
the
LCR.
The
other
is
the
active
power-based
inverters (VSIs) in the WF, where a novel ISOVC is developed to maintain the SEB frequency and
voltage
(P-V)
control
loopfor
forthe
theLCR.
LCR,
through
the power-based
SEB voltage voltage
is controlled
to achieve
compensate
reactive
power
The
other iswhich
the active
(P-V) control
loop
the
active
power
balance.
for the LCR, through which the SEB voltage is controlled to achieve the active power balance.
The
rest of
of the
the paper
paper is
is organized
organized as
as follows.
follows. Section
Section 22 depicts
depicts the
the mathematical
mathematical models,
models, and
and
The rest
explains
active power
power balance,
balance, and
between the
explains the
the relationship
relationship between
between the
the voltage
voltage and
and the
the active
and also
also between
the
frequency
and
the
reactive
power
balance.
Section
3
proposes
the
Q-f
and
P-V
control
after
frequency and the reactive power balance. Section 3 proposes the Q-f and P-V control loops
loops after
analyzing
operational principles.
principles. Section
control
analyzing the
the operational
Section 44 demonstrates
demonstrates the
the stability
stability of
of the
the proposed
proposed control
scheme
parameters. Section
scheme and
and designs
designs the
the controller
controller parameters.
Section 55 shows
shows the
the simulation
simulation results
results and
and verifies
verifies the
the
feasibility
of
the
coordinated
control
scheme.
Section
6
concludes
this
paper.
feasibility of the coordinated control scheme. Section 6 concludes this paper.

2.
2. System
System Modeling
Modeling
The
topology of
the studied
studied system
system is
is shown
shown in
in Figure
Figure 1.
1. This
This study
study takes
takes permanent-magnet
permanent-magnet
The topology
of the
synchronous
asas
anan
example
to study
the coordination
between
WFs
synchronous generator
generator(PMSG)-based
(PMSG)-basedWECSs
WECSs
example
to study
the coordination
between
and
LCC-HVDC.
The
proposed
control
scheme
can
be
easily
extended
to
doubly-fed
induction
WFs and LCC-HVDC. The proposed control scheme can be easily extended to doubly-fed induction
generator
should
bebe
noticed
thatthat
thethe
Q-f Q-f
control
is applied
in grid-side
VSIs
generator (DFIG)-based
(DFIG)-basedWECSs.
WECSs.It It
should
noticed
control
is applied
in grid-side
of PMSG-based
WECSs,
whereas
it is applied
in rotor-side
converters
of DFIG-based
WECSs.
For
VSIs
of PMSG-based
WECSs,
whereas
it is applied
in rotor-side
converters
of DFIG-based
WECSs.
simplicity,
the
PMSG-based
WECS
can
be
equivalent
to
a
voltage
source
inverter
(VSI)
in
parallel
For simplicity, the PMSG-based WECS can be equivalent to a voltage source inverter (VSI) in parallel
with aadirect
directcurrent
current(DC)
(DC)
capacitor
a controlled
DC current
source
[31].
In to
order
to supply
with
capacitor
andand
a controlled
DC current
source
[31]. In
order
supply
energy
energy
for
the
system
startup,
batteries
are
installed
at
the
DC
bus
of
several
units
(no
need
all
for the system startup, batteries are installed at the DC bus of several units (no need for all for
units).
units).
Especially,
for
the
DFIG-based
WECSs,
rotor
excitation
of
DFIGs
should
be
provided
initially
Especially, for the DFIG-based WECSs, rotor excitation of DFIGs should be provided initially in the
in
the startup
process,
which
can be accomplished
the rotor-side
converters
by the
startup
process,
which can
be accomplished
throughthrough
the rotor-side
converters
poweredpowered
by the batteries.
batteries.
The
WECSs
are
connected
to
the
SEB
of
HVDC.
The
rectifier
is
of
the
LCC
type,
and
thus a
The WECSs are connected to the SEB of HVDC. The rectifier is of the LCC type, and thus a substantial
substantial
amount
ACconfigured
filters are at
configured
at mitigate
the SEB the
to mitigate
the current and
harmonics,
and
amount of AC
filtersofare
the SEB to
current harmonics,
meanwhile
meanwhile
they
provide
reactive
power compensation,
which
can be equivalent
to a capacitor
f at
they provide
reactive
power
compensation,
which can
be equivalent
to a capacitor
bankbank
Cf atCthe
the
fundamental
frequency.
fundamental frequency.

Local load
Tw
HVDC
Bus

WECS



Battery

SEB

Trc

Main grid
Filter

Filter

Figure 1. System
System topology.

For
clear description
description of
the system
system model,
model, it
it can
can be
be divided
divided into
into three
three subsystems:
subsystems: the
the WECS
WECS
For aa clear
of the
subsystem,
the
SEB
subsystem
and
the
HVDC
subsystem.
To
capture
the
fundamental
power
subsystem, the SEB subsystem and the HVDC subsystem. To capture the fundamental power dynamic
dynamic
characteristics
of thethe
system,
the switching
function
models
[10,11]
of the converters
are
characteristics
of the system,
switching
function models
[10,11]
of the
converters
are employed.
employed.
Moreover,
the
inverter
of
HVDC
can
be
equivalent
to
a
DC
voltage
source
[14,15]
since
it
Moreover, the inverter of HVDC can be equivalent to a DC voltage source [14,15] since it is subjected
is
subjected
to
a
constant-voltage
control
and
has
little
effect
on
the
other
subsystems
under
normal
to a constant-voltage control and has little effect on the other subsystems under normal operations.
operations.
Figure
2 depicts
the equivalent
circuit
of system,
the whole
system,
the significations
of the
Figure 2 depicts
the
equivalent
circuit of the
whole
where
the where
significations
of the electrical
electrical
variables
and
parameters
are
self-explanatory.
variables and parameters are self-explanatory.

Energies 2018, 11, 2207
Energies 2018, 11, x FOR PEER REVIEW

uwa Rw Lw iwa





uwb

iwb

uwc

iwc









VSI
WECS

Cf



uba

Rrc Lrc urca irca

ubb


ubc

ica icb icc

id Rd

urcb ircb



urcc ircc



udc
i1
Cdc

4 of 19
4 of 19

udr

Ld
udi

LCR
HVDC

SEB

Figure 2. Equivalent
Equivalent circuit,
circuit, where
where the
the wind
wind farm
farm (WF)
(WF) isis represented
represented by
by aa single
single wind
wind energy
energy
Figure
conversion systems
forfor
a simplified
system
model.
Note Note
that the
proposed
control control
scheme
conversion
systems(WECS)
(WECS)just
just
a simplified
system
model.
that
the proposed
is applicable
for multiple
WECSs WECSs
(see the (see
nextthe
section
morefor
details).
scheme
is applicable
for multiple
next for
section
more details).

2.1.
2.1. WECS
WECS Subsystem
Subsystem Model
Model
In
ω00,, the
In the rated synchronous reference frame (RSEF) with the rated frequency ω
the WECS
WECS model
can
can be written as:
(
di (ωb
 ubdbd+
mdm
udc
 0 Lω
i Lw iwq
Lw 
diLwd
dtb)dt= −RRwwiiwd
w /wd
wd − u
w 0wq

d udc +
(1)
(1)

LwdiLwq
/wq

ubqbq+mm
−0 Lωw0iwd
Lw iwd
(ωbdt
)dt= −RRwwiiwq
di


u
u
qdcu
dc
w
b
wq
q


Cdc dudc /(ωb dt) = i1 − md iwd + mq iwq
(2)
(2)
Cdc dudc b dt   i1  md iwd  mq iwq
where the subscripts d and q represent the variables transformed from the three-phase abc reference
where
thethe
subscripts
andωqb represent
variablessimilarly
transformed
from the three-phase abc reference
frame to
dq RSEF, dand
is the basethe
frequency,
hereinafter.
frame to the dq RSEF, and ωb is the base frequency, similarly hereinafter.
2.2. SEB Subsystem Model





2.2. SEB
Subsystem
Model
Similarly,
the SEB
model in the RSEF can be written as:
Similarly, the SEB model(in the RSEF can be written as:
C f dubd /(ωb dt) = iwd − ircd + ω0 C f ubq
dubd(ω
dt =iiwq
 i rcq−
0ωC0fCubq
C
f bq /
b ) 
wd − ircd
fCdu
b dt
f ubd

C
du

dt

i

i


C
u

0 f bd
 f bq  b  wq rcq
Let the amplitude and the phase-angle of the SEB voltage be:

(3)

(3)

Let the amplitude and the phase-angle of theqSEB voltage be:
Ubm =
u2bd + u2bq
(4)
Ubm  u 2  u2
bq
φ = arctan bdubq /u
bd , φ ∈ [0, 2π )
(4)
  arctan ubq ubd ,  0, 2 
It can be obtained in the polar coordinate system that [19,20]:
It can be obtained in the polar coordinate system that [19,20]:
2
0.5dUbm
/(ωb dt) = ( Pw − Prc )/C f
(5)
2
0.5 dUbm
bdt    Pw  Prc  C f
(5)


2
(6)
ω0 + dφ /(ωb dt) = ω1 = (− Qw + Qrc )/ C f Ubm
2
(6)
0  d b dt   1   Qw  Qrc  C f Ubm
where Pw = ubd iwd + ubq iwq and Prc = ubd ircd + ubq ircq are the active powers from the WECS, and they
are absorbed
Qw the
= –u
ubq iwd from
and Qthe
–ubd ircqand
+ uthey
rc =WECS,
where
Pw = ubdby
iwd the
+ ubqHVDC
iwq andrespectively.
Prc = ubdircd + uAlso,
bqircq are
active
powers
bd iwq +
bq ircd are
the reactive
from
the WECS Also,
and they
respectively,
and
absorbed
by powers
the HVDC
respectively.
Qw =are
–ubdabsorbed
iwq + ubqiwd by
andthe
QrcLCR
= –ubd
ircq + ubqircd are
theωreactive
1 is the
SEB
frequency.
powers from the WECS and they are absorbed by the LCR respectively, and ω1 is the SEB frequency.
Equations (5)
laylay
thethe
foundations
for this
From the
perspective
of the filter
capacitor
Equations
(5)and
and(6)(6)
foundations
for study.
this study.
From
the perspective
of the
filter
parallel branch,
thebranch,
WECS the
canWECS
be seencan
as abecontrolled
source
(Pw and
Qw ),(Pwhile
canthe
be
capacitor
parallel
seen as a power
controlled
power
source
w and the
Qw),LCR
while
seen
as
a
controlled
power
load
(P
and
Q
).
Given
that
the
WECS
and
the
HVDC
are
interconnected
LCR can be seen as a controlled power
load
rc
rc (Prc and Qrc). Given that the WECS and the HVDC are
by the filter capacitor,
can be drawn
from
capacitor
point
view. (1)
interconnected
by the two
filtersignificant
capacitor, results
two significant
results
canthe
be filer
drawn
from the
filerofcapacitor
The voltage
amplitude
Ubm is highly
coupled
the active
power
(Pthe

P
);
(2)
The
phase-angle
point
of view.
(1) The voltage
amplitude
Ubmwith
is highly
coupled
with
active
power
(P
w

Prc); (2)φ
w
rc
(or the
frequency ω
is highly
coupledωwith
reactive
power
(Qthe
Qrc ) [20].power
A physical
 1 )(or
The
phase-angle
the frequency
1) is the
highly
coupled
with
(Qw − mechanism
Qrc) [20]. A
w −reactive
explanation
is
given
as
follows.
physical mechanism explanation is given as follows.









It is known that the total instantaneous power of the three-phase balanced capacitor branch
equals its active power (which is zero) at steady states, and the power exchanged within the threephase capacitors charges/discharges the capacitors. As a result, the three-phase capacitor circuit as a

Energies 2018, 11, 2207

5 of 19

It is known that the total instantaneous power of the three-phase balanced capacitor branch equals
its active power (which is zero) at steady states, and the power exchanged within the three-phase
capacitors charges/discharges the capacitors. As a result, the three-phase capacitor circuit as a whole
exhibits a certain reactive power. However, this conclusion becomes invalid during dynamic processes.
For Equation (5), if there is an active power deviation, e.g., Pw − Prc > 0, this indicates that the active
power generated by the WECS is larger than that absorbed by the LCR, then the extra active power will
charge the capacitors. Consequently, the instantaneous current amplitude will increase, which leads
the instantaneous voltage amplitude to increase too. Similarly, if there is a reactive power deviation for
Equation (6), e.g., (–Qw + Qrc ) > 0, which indicates that the reactive power generated by the WECS is
smaller than that absorbed by the LCR, then the voltage phase-angle (i.e., the instantaneous frequency)
will increase, assuming that the voltage amplitude keeps unchanged. As a consequence, the capacitive
reactance will decrease due to the frequency increase, and therefore the capacitor will generate more
reactive power to try to balance the reactive power. In fact, the capacitive parallel branch is in a dual
relationship with the inductive series branch in traditional power systems, and thus it is not difficult to
understand the foregoing coupling relationship. Moreover, it can be also found that a smaller Cf (the
absolute minimum filter guarantees Cf > 0) can result in a stronger coupling.
2.3. HVDC Subsystem Model
In the RSEF, the HVDC model can be written as [11,12]:
(
Lrc dircd /(ωb dt) = − Rrc ircd + ubd − urcd + ω0 Lrc ircq
Lrc dircq /(ωb dt) = − Rrc ircq + ubq − urcq − ω0 Lrc ircd
(


urcd = Urcm ircd sin α + ircq cos α

urcq = Urcm ircd cos α − ircq sin α

(7)

(8)

udr = Urcm cos α

(9)

Ld did /(ωb dt) = udr − udi − Rd id

(10)

where α is the firing angle, and Urcm is the voltage amplitude in the rectifier bridge side. Note that the
variables are in the per-unit system, and thus the rectifier coefficient is eliminated. Also, both the (12k
± 1) order harmonics in ac side and the 12k order harmonics in DC side are neglected in the typical
12-plus HVDC model, since the events of major concern are the fundamental power conversion rather
than high frequency dynamic.
3. Coordinated Control Scheme
Prior to describing the proposed coordinated control scheme, the control requirements should be
emphasized first.
(1)
(2)
(3)
(4)

Voltage control: a stable voltage can offer voltage support for the WECSs, as well as the
commutation voltage for the LCR.
Frequency control: the frequency stability should be maintained so that multiple WECSs are able
to operate synchronously.
Active power balance: considering that the wind conditions are not controlled, the active power
generated from the WFs should be equal to that which is transmitted into the HVDC in real time.
Reactive power balance: considering that the reactive power compensation capability of AC
filters is discontinuous, the WECSs should be able to compensate and share the insufficient or
excessive reactive power automatically.

The proposed coordinated control scheme is able to achieve the requirements. The Q-f control
applied into the wind farm meets the requirements (2) and (4), whereas the P-V control applied into

Energies 2018, 11, 2207

6 of 19

Energies 2018, 11, x FOR PEER REVIEW

6 of 19

the HVDC rectifier meets the requirement (1) and (3). Thus, the wind farm and the HVDC cooperate
with Note
each other
system stability.
that to
theachieve
resynchronization
capability is also of much significance for the system
Note thatoperation
the resynchronization
capability
also
of muchthe
significance
for the system
uninterrupted
in the case of a fault.
Underis
fault
conditions,
back-end converters
can be
uninterrupted
operation
the case
of a fault.and
Under
faultbatteries
conditions,
theutilized
back-end
converters
controlled
to supply
zero in
power
temporarily,
then the
can be
again
to help
can be controlled
to supply
zero
and
then thedetails
batteries
be utilized
again
to help
generate
the SEB voltage
after
thepower
fault istemporarily,
cleared. More
technical
willcan
be given
in future
work.
generate the SEB voltage after the fault is cleared. More technical details will be given in future work.
3.1. Q-f Control of WECSs
3.1. Q-f Control of WECSs
In contrast to the ISOVC in [25–28], where the active power loop is adopted to achieve indirect
In contrast
to the ISOVC in [25–28],
active
power loop
is adopted
to achieve
indirect
orientation
and synchronization,
a novelwhere
ISOVCthe
will
be developed
here.
Since that
the relationship
orientation
synchronization,
a novel
ISOVC
will bein
developed
Since
that the
relationship
between
theand
frequency
and reactive
power,
as shown
Equationhere.
(6), the
reactive
power
loop is
between
the
frequency
and
reactive
power,
as
shown
in
Equation
(6),
the
reactive
power
loopQ-f
is
adopted to achieve Q-f control. As depicted in Figure 3, two key modifications are made in the
adoptedcompared
to achievewith
Q-f the
control.
As depicted
in Figure
3, two
key modifications
are made
in the Q-f
control
conventional
VC with
the unity
power
factor. One is that
the self-defined
control
compared
with
the
conventional
VC
with
the
unity
power
factor.
One
is
that
the
self-defined
phase-angle is:
phase-angle is:
Z
U    0
(11)
∠U =  ω00 + ∠
(11)
0

where 0 is an initial value, determined by the final value of the phase-angle at the end of system
where ∠0 is an initial value, determined by the final value of the phase-angle at the end of system
startup. The other is that the control object of the reactive power loop is regulating the q-axis voltage
startup. The other is that the control object of the reactive power loop is regulating the q-axis voltage
ubq instead of the reactive current iwq to zero. As a consequence, not only is the frequency ω1 clamped
ubq instead of the reactive current iwq to zero. As a consequence, not only is the frequency ω 1 clamped
when ubq = 0 since the actual phase-angle is consistent with the self-defined one, but the reactive
when ubq = 0 since the actual phase-angle is consistent with the self-defined one, but the reactive
current command iwq* can also be regulated automatically so that the WECS is able to compensate
current command iwq * can also be regulated automatically so that the WECS is able to compensate
reactive power for the LCR. Note that the active power control is still based on the maximum power
reactive power for the LCR. Note that the active power control is still based on the maximum power
point tracking (MPPT) control, as shown in Figure 3b. The operational principle of the Q-f control is
point tracking (MPPT) control, as shown in Figure 3b. The operational principle of the Q-f control is
described as follows.
described as follows.
+–


udc


iwq

PI 1

0


iwd
+–
iwd

PI 2

+–

PI 3

iwq

++

ud

++

ud
uq

uq
ubdq

iwdq

dq
abc
U b

SVPWM

udc

PLL

ubabc
iwabc

dq
abc

...

(a)


ubq
0



iw2 max

+

 –
udc
+–

ubq

2
 iwd

PI 1
PI 3

iwq

+–

PI 2
PI 4



++

ud

++

ud
dq

uq

uq

ubdq

dq
abc

ubabc

iwdq

dq
abc

iwabc

U  0  0

...

(b)

abc

SVPWM

udc


iwd
+–
i
 wd
iwq

Figure 3.
vector control
control (VC)
(VC) versus
versus (b)
(b) proposed
frequency
Figure
3. (a)
(a) Conventional
Conventional vector
proposed reactive
reactive power-based
power-based frequency
(Q-f ) control
control for
WECSs.
InIn
actual
practice,
thethe
controlled
variable
ubq
(Q-f)
for voltage
voltagesource
sourceinverters
inverters(VSIs)
(VSIs)ofof
WECSs.
actual
practice,
controlled
variable
can
be
replaced
by
the
local
voltage
information
instead
of
sending-end
bus
(SEB)
voltage
information.
ubq can be replaced by the local voltage information instead of sending-end bus (SEB) voltage
Since the critical
information
is the
voltage-phase
angle
rather than the
voltage
amplitude,
thevoltage
spatial
information.
Since
the critical
information
is the
voltage-phase
angle
rather
than the
distribution
feature
of
the
voltage
amplitude
has
litter
influences
on
the
Q-f
control
performance.
amplitude, the spatial distribution feature of the voltage amplitude has litter influences on the Q-f

control performance.

Assuming that the system is in a steady state, if the frequency ω 1 suddenly starts to increase due
Assuming that
the
system isincrease
in a steady
state,
if thepower
frequency
1 suddenly
starts U
tobincrease
due
to a disturbance,
e.g.,
a sudden
of the
reactive
Qrc , ω
the
voltage vector
and current
to
a disturbance,
e.g., a sudden
increase
of the
reactive
the voltage
Ub and current
vector
Iw under conventional
VC
is shown
in Figure
4a.power
It can Q
berc,observed
thatvector
the controller
tracks
vector
Iw underchange
conventional
VC is
shown
inreactive
Figure 4a.
It can
observed
the controller
tracks
the frequency
and cannot
output
the
power
to be
regulate
the that
frequency,
which further
the
frequency
change and
cannot output
the reactive
power
to regulate
the frequency,
which but
further
leads
to the instability
of frequency.
In Figure
4b, the
self-oriented
control
(11) is adopted,
the
leads to the instability of frequency. In Figure 4b, the self-oriented control (11) is adopted, but the
reactive power loop still regulates iwq to zero. Under this condition, Ub rotates counterclockwise an
angle ϕ due to the increase of frequency. Thus, although the WECS outputs reactive power, Ub no

Energies 2018, 11, 2207

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reactive power loop still regulates iwq to zero. Under this condition, U b rotates counterclockwise an
Energies 2018, 11, x FOR PEER REVIEW
7 of 19
angle φ due to the increase of frequency. Thus, although the WECS outputs reactive power, U b no
longer
coincides with
with the
the q-axis
q-axisbecause
becauseof
ofaalack
lackofofsynchronization
synchronizationcontrol.
control.Thereafter,
Thereafter,
the
and
longer coincides
the
d- dand
qq-axis
controls
are
no
longer
decoupled,
and
moreover,
multiple
WECSs
may
become
asynchronous
axis controls are no longer decoupled, and moreover, multiple WECSs may become asynchronous
due
to the
the accumulation
accumulationof
ofthe
theangle
angleerrors.
errors.InIn
Figure
issue
is completely
addressed
where
due to
Figure
4c,4c,
thethe
issue
is completely
addressed
where
the
the
control
object
is
u
=
0
instead
of
i
=
0.
In
other
words,
the
phase-angle
is
indirectly
controlled
wq
bq
control object is ubq = 0 instead of iwq = 0. In other words, the phase-angle is indirectly controlled to
to
follow
angle
generated
rated
frequency
controller
output
signal
is exactly
0 , and
follow
thethe
angle
generated
by by
thethe
rated
frequency
ω0,ωand
the the
controller
output
signal
is exactly
the
the
reactive
current
reference.
Consequently,
thirdproportional-integral
proportional-integral(PI
(PI3)3 )regulator
regulatorisis able
able to
reactive
current
reference.
Consequently,
thethethird
to
* under the condition that u = 0.
produce
an
exact
reactive
current
reference
i
*
wq
bq
produce an exact reactive current reference iwq under the condition that ubq = 0.
ωpll dpll

d

d

Ub
Iw
q qpll

d

Ub

Ub


ω0

Iw
ω0

q ubq

(a)



iwq

q

(b)

Iw
ω0

(c)

Figure 4.
4. Vector
Vector diagrams
diagrams in
in the
the rated
rated synchronous
synchronous reference
reference frame
frame (RSRF)
(RSRF) under
under different
different control
control
Figure
algorithms: (a)
(a) Conventional
Conventional VC
VC with
with iiwq == 0;
Self-oriented control
control with
with iiwq == 0;
Proposed Q-f
Q-f
algorithms:
0; (b)
(b) Self-oriented
0; (c)
(c) Proposed
wq
wq
control
with
u
bq = 0.
control with ubq = 0.

It should be noted that the PI3 regulator cannot work well in multi-WECS scenarios due to a
It should be noted that the PI3 regulator cannot work well in multi-WECS scenarios due to
reactive current circulation among the WECSs without a sharing scheme. To this end, a simple
a reactive current circulation among the WECSs without a sharing scheme. To this end, a simple
approach is to improve the PI-type regulator into a P-type one, resulting in a droop characteristic.
approach is to improve the PI-type regulator into a P-type one, resulting in a droop characteristic.
Thus, when a multi-machine system is subjected to the Q-f droop control, the reactive power can be
Thus, when a multi-machine system is subjected to the Q-f droop control, the reactive power can
compensated and shared automatically, and both the frequency stability and the synchronization
be compensated and shared automatically, and both the frequency stability and the synchronization
stability can be realized. With the P-type control, the voltage vector will no longer coincide with the
stability can be realized. With the P-type control, the voltage vector will no longer coincide with the
d-axis. By defining an appropriate range of the included angle between them, and thereby setting an
d-axis. By defining an appropriate range of the included angle between them, and thereby setting an
appropriate proportional coefficient, it is doable to ensure that the included angle is small enough
appropriate proportional coefficient, it is doable to ensure that the included angle is small enough and
and close to zero at steady states.
close to zero at steady states.
According to the P-type control, for one WECSj, it can be obtained that:
According to the P-type control, for one WECSj , it can be obtained that:

iwqj  kpj ubqj

(12)
(12)

iwqj = −k pj ubqj

where ubqj can be considered to be approximately the same for different units. For one thing, in actual
where
ubqjubqj
can= be
considered
be approximately
the from
same the
for different
units. For one
thing,
in
practice,
0 at
the time to
when
WECSj switches
pre-synchronization
stage
to the
actual
practice,
u
=
0
at
the
time
when
WECS
switches
from
the
pre-synchronization
stage
to
the
connection to thebqj
sending-end grid by means of jphase-locked loops. For another, after the connection
connection
to
the
sending-end
grid by meansloops
of phase-locked
loops.Then,
For another,
after the connection
to the sending-end grid, the phase-locked
are withdrawn.
the phase-angle
difference
to
the
sending-end
grid,
the
phase-locked
loops
are
withdrawn.
Then,
the
phase-angle
difference
between two units during normal operating conditions are also eliminated by their
initial
between
two units
during
normal operating conditions are also eliminated by their initial synchronous
synchronous
reference
frames.
reference
frames.
On the
basis of Equation (12), the reactive power can be written as:
On the basis of Equation (12), the reactive power can be written as:
Qwj  ubdj iwqj  ubqj iwdj  kpj ubdj  iwdj ubqj
(13)
 kpj ubqj
Qwj = −ubdj iwqj + ubqj iwdj = k pj ubdj + iwdj ubqj = k0 pj ubqj
(13)
Figure 5 shows the droop curves of the reactive currents and the reactive powers with respect to
the d-axis
It the
candroop
be observed
5a thatcurrents
a large and
proportional
coefficient
ablerespect
to result
Figurevoltage.
5 shows
curvesin
ofFigure
the reactive
the reactive
powers is
with
to
in
a
large
shared
reactive
current.
In
Figure
5b,
the
sharing
coefficient
is
given
by
Equation
(13).
Since
the d-axis voltage. It can be observed in Figure 5a that a large proportional coefficient is able to result
thea voltage
vectorreactive
and thecurrent.
d-axis are
not strictly
coincident,
the reactive
is inevitably
related
to
in
large shared
In Figure
5b, the
sharing coefficient
is power
given by
Equation (13).
Since
active current
iwdj. Even
so, ifare
a quite
large kpjcoincident,
is taken, then
the voltage
vector
and the d-axis
will
the voltage
vector and
the d-axis
not strictly
the reactive
power
is inevitably
related
to
substantially
coincide.
In this
is known
fromthen
Equation
(13) vector
that the
power
the
active current
iwdj . Even
so, ifpoint,
a quiteitlarge
kpj is taken,
the voltage
andreactive
the d-axis
will
contributed by
the active
current
small.
In short,
coefficient
of each
substantially
coincide.
In this
point,iwdjit is
is relatively
known from
Equation
(13)the
thatproportional
the reactive power
contributed
unitthecan
be current
calculated
designed
based
on Equation
(13). Incoefficient
practicalofapplications,
by
active
iwdj isand
relatively
small.
In short,
the proportional
each unit canthe
be
optimization
andbased
the quantitative
allocation
of reactive
power can the
be achieved
considering
calculated
andcontrol
designed
on Equation
(13). In practical
applications,
optimization
control
the unit capacity limit. For example, a large proportional coefficient can be set for the unit with a
small active power output so that it can share more reactive power.





Energies 2018, 11, 2207

8 of 19

and the quantitative allocation of reactive power can be achieved considering the unit capacity limit.
For example, a large proportional coefficient can be set for the unit with a small active power output
Energies
11,share
x FORmore
PEER REVIEW
8 of 19
so
that 2018,
it can
reactive power.
Qw
Qw1

iwq
iwq1
iwq2

Qw2
ubqj ubq

kp2

ubqj ubq

kp1

k'p2 k'p1
(a)

(b)

Figure 5.
5. Reactive
sharing
relationship
with
thethe
P-type
droop
control.
(a)
Figure
Reactivecurrent
currentand
andreactive
reactivepower
power
sharing
relationship
with
P-type
droop
control.
Reactive
current
sharing
relationship;
(b)(b)
reactive
power
sharing
relationship.
(a)
Reactive
current
sharing
relationship;
reactive
power
sharing
relationship.

In order to maintain the active power benefit of WFs, the active power priority principle can be
In order to maintain the active power benefit of WFs, the active power priority principle can be
adopted. As shown in Figure 3, according to the real-time active current iwd, the reactive current iwq is
adopted. As shown in Figure 3, according to the real-time active current iwd , the reactive current iwq is
limited as follows:
limited as follows:
q
2
(14)
iwqlim
i =± ii22wmax−i 2iwd
(14)
wq lim

w max

wd

Equation (14) defines the reactive power margin. There is no steady-state equilibrium point
Equation (14) defines the reactive power margin. There is no steady-state equilibrium point of
of reactive power, assuming that the reactive power demand exceeds the reactive power margin.
reactive power, assuming that the reactive power demand exceeds the reactive power margin.
Considering that the reactive power demand can be adjusted by the centralized reactive power
Considering that the reactive power demand can be adjusted by the centralized reactive power
compensation device, and that a WF has the minimum reactive power compensation capability,
compensation device, and that a WF has the minimum reactive power compensation capability, this
this study recommends the following reactive power compensation scheme: (1) For the entire WF,
study recommends the following reactive power compensation scheme: (1) For the entire WF,
according to its rated capacity and maximum active power output to determine the minimum reactive
according to its rated capacity and maximum active power output to determine the minimum
power compensation capability. When the real-time reactive power output becomes larger than the
reactive power compensation capability. When the real-time reactive power output becomes larger
minimum compensation capacity, the centralized reactive power compensation should be adjusted
than the minimum compensation capacity, the centralized reactive power compensation should be
in time, such as the conventional filter or the high-performance static var compensator (SVC) or
adjusted in time, such as the conventional filter or the high-performance static var compensator (SVC)
STATCOM. Consequently, the reactive power demand becomes smaller, and within the minimum
or STATCOM. Consequently, the reactive power demand becomes smaller, and within the minimum
compensation capability. (2) For each unit, according to its real-time active current, adjust the limitation
compensation capability. (2) For each unit, according to its real-time active current, adjust the
of the reactive current according to Equation (14).
limitation of the reactive current according to Equation (14).
3.2. P-V Control of LCR
3.2. P-V Control of LCR
When the active power Pw from the WECS increases, it has been known that Ubm increases
When the active power Pw from the WECS increases, it has been known that Ubm increases
according to Equation (5) assuming that Prc remains constant. Actually, if Ubm increases, Prc will
according to Equation (5) assuming that Prc remains constant. Actually, if Ubm increases, Prc will
increase too. However, there is no doubt that the steady-state Ubm will become larger from the
increase too. However, there is no doubt that the steady-state Ubm will become larger from the
perspective of the whole circuit if the firing angle remains unchanged. Only if the LCR controller
perspective of the whole circuit if the firing angle remains unchanged. Only if the LCR controller
reduces the firing angle α, leading to more absorbed active power Prc by the LCR, can Ubm return back
reduces the firing angle α, leading to more absorbed active power Prc by the LCR, can Ubm return back
its reference value. A detailed analysis is performed as follows.
its reference value. A detailed analysis is performed as follows.
Based on the conclusions in [5], the time constant of the rectifier currents is quite small, about
Based on the conclusions in [5], the time constant of the rectifier currents is quite small, about
tens of milliseconds, under the constant-voltage control of the inverter of HVDC. Thus, the current
tens of milliseconds, under the constant-voltage control of the inverter of HVDC. Thus, the current
transients in Equations (7) and (10) can be ignored while analyzing the active power balance, which
transients in Equations (7) and (10) can be ignored while analyzing the active power balance, which
gives rise to:
gives rise to:
Peq = Ubm Urcm sin δ/(ω0 Lrc )
(15)
2 /(ω L )
QeqP=
U
UUrcm cos
ω00LLrcrc) − Urcm

U
sin δ/(
0 rc
bm
eq
bm rcm
(15)
2
Qeq and
Ubmreactive
Urcm cos power
Urcm
Lrc 
where Peq and Qeq are the active
and δ is the phase-angle
0 Lrcof rectifier
0bridge,
difference between U b and U rc , and it can be seen as a power angle. Note that the internal resistor Rrc
where
Peq in
and
Qeq are(15).
the Given
active that
andthe
reactive
of rectifier
δ is
the phase-angle
is
ignored
Equation
powerpower
factor angle
of the bridge,
rectifier and
bridge
(excluding
Rrc and
difference
between
U
b and Urc, and it can be seen as a power angle. Note that the internal resistor Rrc
Lrc ) is α, i.e.,:
is ignored in Equation (15). Given that theQpower
factor angle of the rectifier bridge (excluding(16)
Rrc
eq = Peq tan α
and Lrc) is α, i.e.,:
Qeq  Peq tan 

Combining Equations (9), (10), (15), and (16), it can be obtained that:

(16)

Energies 2018, 11, 2207
x FOR PEER REVIEW

9 of 19





Ubm(15),
cos and
  (16),
 uitdr can
 udibe obtained
id Rd  udi that:
Combining Equations (9), (10),

(17)

Furthermore, consideringUthe
effect
ofαthe
the
udr = uinductor
≈rc uon
(δ +
) =leakage
bm cos
di + id Rd L
di the power factor angle of (17)
LCR (including Trc), it exists as:
Furthermore, considering the effect of the leakage inductor Lrc on the power factor angle of the
udr  Ubm cos   id Rc
(18)
LCR (including Trc ), it exists as:
− id Rvalue
c
dr = Uwith
bm cos
where Rc is the equivalent commutation u
resistor
anαactual
6/πω0Lrc. Substituting Equation (18)
(18)
into Equations
(9)equivalent
and (10) yields
that:
where
Rc is the
commutation
resistor with an actual value 6/πω 0 Lrc . Substituting
Equation (18) into Equations (9) and (10) yields that:
Ubm cos   udi  id Rc  Rd
(19)





U cos α = udi + id ( Rc + Rd )
(19)
It can be assumed that both Ubm bm
and udi remain constant under the controls of both the rectifier
and inverter, and thus cos(δ + α) remains constant, according to Equation (17). Actually, when Pw
It can be assumed that both Ubm and udi remain constant under the controls of both the rectifier
increases, the power angle δ increases, whereas the firing angle α decreases along with the increase
and inverter, and thus cos(δ + α) remains constant, according to Equation (17). Actually, when Pw
of id in Equation (19). Therefore, δ + α remains approximately unchanged. Since that δ + α is the power
increases, the power angle δ increases, whereas the firing angle α decreases along with the increase of
factor angle between Ub and Irc:
id in Equation (19). Therefore, δ + α remains approximately unchanged. Since that δ + α is the power
factor angle between U b and Irc :
Prc  Ubm I rcm cos    
(20)
Prc = Ubm Ircm cos(δ + α)
Qrc  Ubm I rcm sin    
(20)
Qrc = Ubm Ircm sin(δ + α)

Let
Let U
Ubb be
beoriented
orientedto
tothe
thed-axis
d-axisof
ofthe
therated
ratedsynchronous
synchronous reference
reference frame
frame (RSRF)
(RSRF) (consistent
(consistent with
with
the
orientation
of
the
WECS),
and
the
vector
diagrams
of
the
SEB
is
depicted
in
Figure
6. Figure
In Figure
the orientation of the WECS), and the vector diagrams of the SEB is depicted in Figure 6. In
6a,
6a,
the
active
current
i
wd is smaller, and it can be assumed that the reactive current Ic from the filters
the active current iwd is smaller, and it can be assumed that the reactive current Ic from the filters
can
supplied to
rectifier exactly.
exactly. In
In Figure
Figure 6b,
6b, however,
however, iiwd becomes
larger, resulting in more
can be
be supplied
to the
the rectifier
wd becomes larger, resulting in more
required
reactive
power
for
the
LCR.
Assuming
that
I
c remains constant due to a time-delay to adjust
required reactive power for the LCR. Assuming that Ic remains constant due to a time-delay to adjust
the
ofU
Ub are
are controlled
controlled by
by the
the LCR
LCR and
the filters,
filters, the
the voltage
voltage amplitude
amplitude U
Ubm, ,and
andthe
thephase-angle
phase-angle φ of
and the
the
bm

b

WECS respectively,
respectively, and then the WECS can output the
the required
required reactive
reactive current
current automatically.
automatically. Thus,
Thus,
Icc,, together
with
i
wq
,
is
able
to
provide
the
reactive
current
of
the
LCR.
Moreover,
the
power
angle
together with iwq , is able to provide the reactive current of the LCR.
increases, whereas the firing angle decreases,
decreases, and
and U
Ubb remains constant.
d
Ub

d
Ub

j0 Lrc I rc

j0 Lrc I rc
Urc

Iw
q

Urc




(a)

iwd
Irc

Ic

q

Irc





Iw
I
i
c
wq
(b)

Figure 6. Vector diagrams under the condition that
that U
Ubb remains constant. (a) A smaller active current
(orPPww););(b)
(b)aalarger
largeractive
activecurrent
currentiwd
iwd
iwd
..
wd(or

After
of the
the system,
system, the
the P-V
P-V control
After analyzing
analyzing the
the power
power characteristics
characteristics of
control loop
loop can
can be
be designed
designed as
as
follows.
is aa linear
linear relationship
relationship between
between U
Ubmcosα
and
id.. In
fact,
α
follows. According
According to
to Equation
Equation (19),
(19), there
there is
cosα
and
i
In
fact,
α
bm
d

changes
within
a
narrow
range
of
around
20°
[14],
and
therefore,
it
can
be
approximately
considered
changes within a narrow range of around 20 [14], and therefore, it can be approximately considered
that
remains unchanged,
unchanged, leading
leading to
to an
an approximate
approximate linear
linear relationship
relationship between
between U
Ubm and
id.
that cosα
cosα remains
bm and id .
Consequently,
linearregulator,
regulator,such
such
employed
to control
bm, as shown in Figure 7,
Consequently, aalinear
asas
PI,PI,
cancan
be be
employed
to control
UbmU
, as
shown in Figure 7, and
and
its
output
is
the
DC
current
reference
i
d*. In the inner current loop, the typical regulator is applied.
its output is the DC current reference id *. In the inner current loop, the typical regulator is applied.
Note
obtain the
same
Note that
that the
the optional
optional compensation
compensation can
can be
be performed
performed in
in the
the outer
outer loop,
loop, so
so as
as to
to obtain
the same
control
gain
at
different
operating
points.
control gain at different operating points.

Energies 2018, 11, 2207
Energies 2018, 11, x FOR PEER REVIEW

10 of 19
10 of 19


compensation
U bm

U bm

PI 5



+–

id

PI 6

+–



id

cos 


+



Figure 7. Proposed power based voltage (P-V) control for LCR.

4. Stability Analysis and Parameter Design
4.1. Stability Analysis of Q-f Control
Q-f
control
of of
thethe
WECS
subsystem,
the the
voltage
amplitude
Ubm
While analyzing
analyzingthe
thestability
stabilityofofthe
the
Q-f
control
WECS
subsystem,
voltage
amplitude
can
be assumed
to betoconstant,
andand
bothboth
the the
active
current
iwd and
thethe
reactive
power
QrcQare
seen
as
U
bm can
be assumed
be constant,
active
current
iwd and
reactive
power
rc are
seen
external
disturbances.
Moreover,
the
current
dynamics
can
be
neglected
since
they
are
generally
much
as external disturbances. Moreover, the current dynamics can be neglected since they are generally
faster faster
than those
power.
Considering
only the
outer
loop of
theof
Q-f
it canitbe
obtained
that:
much
than of
those
of power.
Considering
only
the outer
loop
thecontrol,
Q-f control,
can
be obtained
that:

iwq = k p3 + k i3 /s (0 − Ubm sin φ)
(21)
iwq  kp 3  ki 3 s  0  Ubm sin  
(21)
Let iwq = i0 wq + kp3 (0 − Ubm sin φ), and rewrite Equations (6) and (21) as:
Let iwq = i'wq + kp3(0 − Ubmsin  ), and rewrite Equations (6) and (21) as:


dφ /dt = ωb Ubm i0 wq − k p3 Ubm
sin φ cos
φ
(22)
U i   k U sin  cos
d dt  −
2
bm sin
wq φ +p 3Qrc
bm
Ubbm
]/ C f Ubm  − ωb ω0
 iwd
(22)
2
Ubm iwd sin   Qrc  C f Ubm
 b0
0
di wq /dt = −k i3 Ubm sin φ
(23)













From Equations (22) and (23), it candibe
thatsin
there
the
 observed
dt  ki 3U
 is a coupling relationship between(23)
wq
bm
0
state variables φ and i wq , which determines the reactive power-frequency dynamic characteristics.
The phase-plane
analysis
[32] it
can
bebe
performed
demonstrate
the stability
of the simplified
From
Equations (22)
and (23),
can
observed to
that
there is a coupling
relationship
between
second-order
nonlinear
system
consisting
of
Equations
(22)
and
(23).
Clearly,
the
equilibrium
point of
the state variables  and i′wq, which determines the reactive power-frequency dynamic
the system is:
characteristics.
(
= be
0 performed to demonstrate
The phase-plane analysis [32] φcan
the stability of the simplified

(24)
0
2
i wq = ofωEquations
Qrc and
/Ubm
second-order nonlinear system consisting
(23). Clearly, the equilibrium point
0 C f Ubm − (22)
of the system is:
Let a = ω b (kp3 Ubm + iwd )/(Cf Ubm ), and b = ki3 ω b /Cf . The linearized system at Equation (24) is ∆˙x
= A∆x with ∆x = [∆φ, ∆i0 wq ] and:

  0
(24)
 "
2
i   0C f Ubm
 Qrc Ubm #

 wq
−a
b/(k i3 Ubm )
A=
(25)
0
Let a = ωb(kp3Ubm + iwd)/(CfUbm), and b = −
ki3kωi3bU
/Cbm
f. The linearized
system at Equation (24) is Δẋ = AΔx
with Δx = [Δ  , Δi'wq] and:
The characteristic equation is λ2 + aλ + b = 0. Clearly, the system is small-signal stable, since
 will
 otherwise it is a stable node. In the
a be a bstable
a > 0 and b > 0. If a2 − 4b < 0, Equation (24)
 ki 3Ufocus,
bm 
A
(25)

former case, the motion near the equilibrium
in the form of oscillations. While
Ubm will 0converge
  ki 3point

in the latter case, there is no oscillation during the convergence and an asymptote exists around the
The characteristic
equation is λ2 + aλ + b = 0. Clearly, the system is small-signal stable, since a > 0
equilibrium
point:
2
and b > 0. If a − 4b < 0, Equation (24) will
focus,
it is a stable node. In the former
∆i0be
−k i3 U
∆φ
(26)
wq a=stable
bm /λ1otherwise
case, the motion near the equilibrium point will converge in the form of oscillations. While in the
where λ1 is the eigenvalue with a smaller modulus.
latter case, there is no oscillation during the convergence and an asymptote exists around the
Taking a concrete case as an example: Ubm = 1.0 pu, iwd = 0.8 pu, Qrc = Cf = 0.21 pu in an initial
equilibrium point:
state, and they remain unchanged in the following convergence process. Also, set kp3 = 0.6, ki3 =
is exactly
50. Since that the reactive power from Cfiwq
the
 ki 3Ubmsupplied
1  to Qrc , since Qrc = Cf , Qw = 0, and(26)
equilibrium point is the origin. As shown in Figure 8, the equilibrium points of Equation (22) and
where
λ1Equation
is the eigenvalue
a smaller
modulus.
those of
(23) formwith
the two
equilibrium
curves respectively in the φ − i0 wq phase plane, and
Taking a concrete case as an example: Ubm = 1.0 pu, iwd = 0.8 pu, Qrc = Cf = 0.21 pu in an initial state,
and they remain unchanged in the following convergence process. Also, set kp3 = 0.6, ki3 = 50. Since
that the reactive power from Cf is exactly supplied to Qrc, since Qrc = Cf, Qw = 0, and the equilibrium
point is the origin. As shown in Figure 8, the equilibrium points of Equation (22) and those of





Energies 2018, 11, x FOR PEER REVIEW
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11 of 19
11 of 19

Equation (23) form the two equilibrium curves respectively in the ϕ − i′wq phase plane, and the
intersection, i.e., the origin O, is the equilibrium point of the system. In Figure 8, the range of the state
the intersection, i.e., the origin O, is the equilibrium point of the system. In Figure 8, the range of the
variable i′wq is [i′0 wqmin, i′0 wqmax]. 0
state variable i wq is [i wqmin , i wqmax ].
2
 max  iwq max  kp 3Ubm sin   ip
iwq
 iwd  kp 3Ubm sin 
w max
2
wqmax = iwqmax + k p3 Ubm sin φ = piwmax − iwd + k p3 Ubm sin φ
 min
iwq
iwq min+kkp3p 3U
Ubm
sin    i 2 i2wmax
 iwd
kp+
U p3sin
i0 wqmin
= iwqmin
−
iwd
Ubm sin φ
bm sin φ = − w max
3 kbm

i0

(27)
(27)

ϕmax = π/2

2.0
1.5
P2
asymptote
1.0
i'wqmax
0.5
P3
P1
0.0
O
-0.5
i'wqmin
-1.0
-1.5
-2.0
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
ϕ (rad)
ϕmin = –π/2

i'wq (pu)

where
current of
ofthe
theWECS.
WECS.Moreover,
Moreover,
phase-angle
the
 should
where iwmax
the maximum
maximum current
thethe
phase-angle
φ should
be in be
theinrange
wmaxisisthe
(

π/2,
π/2)
so
as
to
ensure
the
negative
feedback
property
of
the
controller.
range (−π/2, π/2) so as to ensure the negative feedback property of the controller.
di'wq/dt = 0

di'wq/dt > 0
di'wq/dt < 0
dϕ/dt = 0
dϕ/dt > 0

dϕ/dt < 0

Figure 8.
8. Phase
Phase plane
plane φ
ϕ−
− i′iwq
the Q-f control.
0 with
Figure
wq with the Q-f control.

In Figure 8, the domain (−π/2, π/2) × [i′wqmin0, i′wqmax] 0is divided into four sections. In each section,
In Figure 8, the domain (−π/2, π/2) × [i
, i wqmax ] is divided into four sections. In each
the horizontal and vertical arrows indicate thewqmin
directions
of motions of Equations (22) and (23)
section, the horizontal and vertical arrows indicate the directions of motions of Equations (22) and (23)
respectively, and the actual direction of the state trajectory is the synthesis direction. Taking the initial
respectively, and the actual direction of the state trajectory is the synthesis direction. Taking the initial
point P1 as an example, as shown by the black arrow, the trajectory traverses the blue curve vertically
point P1 as an example, as shown by the black arrow, the trajectory traverses the blue curve vertically
and then enters the section where P2 is located. Then, it moves to the lower right, and traverses the
and then enters the section where P2 is located. Then, it moves to the lower right, and traverses the
red curve in a vertical direction. Thereafter,
the state trajectory will move along the asymptote to the
red curve in a vertical direction. Thereafter, the state trajectory will move along the asymptote to the
steady state point. Similar cases occur in other sections. Therefore, it can be concluded that the system
steady state point. Similar cases occur in other sections. Therefore, it can be concluded that the system
is locally asymptotically stable in the domain.
is locally asymptotically stable in the domain.
It should also be assumed that the initial point is I with the position (−0.1, 0.1), and the
It should also be assumed that the initial point is I with the position (−0.1, 0.1), and the
convergence process of the second-order simplified system is illustrated in Figure 9. From Figure 9a,
convergence process of the second-order simplified system is illustrated in Figure 9. From Figure 9a,
it can be observed that the system converges along the asymptote, since the equilibrium point is a
it can be observed that the system converges along the asymptote, since the equilibrium point is
stable node. In Figure 9b, the equilibrium point become a stable focus due to a large ki3. Thus, although
a stable node. In Figure 9b, the equilibrium point become a stable focus due to a large ki3 . Thus,
the convergence speed become large, there is an overshoot in the motion near the stable
focus.
although the convergence speed become large, there is an overshoot in the motion near the stable
Therefore, it can be concluded that a large ki3 can facilitate the system converge speed, causing both
focus. Therefore, it can be concluded that a large ki3 can facilitate the system converge speed, causing
overshoot and oscillation. A trade-off should be considered
to design an appropriate value for the
both overshoot and oscillation. A trade-off should be considered to design an appropriate value for
control parameter ki3. Similar work can be made to further study the effects of other parameters on
the control parameter ki3 . Similar work can be made to further study the effects of other parameters on
the system dynamic behaviors.
the system dynamic behaviors.
It is noteworthy that, when i0 wq reaches the limitation i0 wqmin or i0 wqmax , the system state moves
along the boundaries and it can still converge once the state reaches another section across the blue
curve as long as the equilibrium point is in the allowable domain. In Equation (27), the range of i0 wq
is related to iwd , i.e., the active power Pw . While in Equation (24), the equilibrium point is related
to the required reactive power Qw . The different equilibrium curves (or points) and domains under
different Pw and Qw are depicted in Figure 10. In particular, the equilibrium point P1 (P1 0 ) are beyond
the domain, when both Pw and Qw are quite large, such as 1.0 and 0.9 (−0.9). The problem must be
avoided in practice. To this end, a proper capacity of filters could be designed to result in a smaller Qw .

asympt

i'wq (pu)

di'wq/dt = 0

6
4
2

0

0.1000

4

0

2

dϕ/dt = 0

O

0

-10

0.1005
6

-5

10 10

5

0

5 ×0.01 0

0

0.0995

-4

0.05

ϕ (rad)

Energies 2018, 11, 2207
Energies 2018, 11, x FOR PEER REVIEW
0.05

0.10

0.15

12 of 19
12 of 19

t (s)

0.10

i'wq (pu)i'wq (pu)

8

×0.01

tI(s)

12
6 di'wq/dt = 0
10
I
4
8
6
2
dϕ/dt
==0 0
wq/dt
4 di'
O
0
2 dϕ/dt = 0
O
0 -10
-5
0
0
-2

4
0.15
6

0.1015

(a)

×0.01

0.05 -10
0
0.10
2

×0.01

10

asymptote

10
0.15

-6

-2

2

0.1010

8

×0.01

612
10
48
26
4
02
5 ×0.01 0
-2
ϕ (rad)
6 ×0.01

0

0.1005
0.1000
0

0.05

0.0995
10 10-4

5

0.10

0.15

t (s)
2

4

6

8

ϕ (rad) ×0.001

10

t (ms)

5
4

t (s)

(a)3

i'wq (pu)

2
1 ×0.01
×0.01
0
8
12
12
-1
10
10 t (ms)
10
-4
-2
0
2 ×0.001
I
8
(b)8
6
6
4 di'wq/dt = 0
4
Figure 9. Convergence process
of the
system composed
2 dϕ/dt
2
= 0second-order simplified
O
0
0
(23), from the initial point I. (a) kp3 = 0.6, ki3 = 50; (b) kp3 = 0.3, ki3 = 2000.
-2
-2
-10

-6

-2

2

6 ×0.01

0

2

4

6

8

of Equations (22) and

10

0
t (ms)
It is noteworthy that, when
i′wq reaches the limitation
, the system state moves along
ϕ (rad) ×0.001i′wqmin or i′wqmax
2
5
the boundaries and it can still4 converge once the state
4 reaches another section across the blue curve
3
2
6 is in the allowable domain.
as long as the equilibrium point
In Equation (27), the range of i′wq is related
1
0
8
to iwd, i.e., the active power Pw. While
in
Equation
(24),
-1 the equilibrium point is related to the required
t (ms)
10
-4
-2
0
2 ×0.001
reactive power Qw. The different equilibrium curves
(b) (or points) and domains under different Pw and
Qw are depicted in Figure 10. In particular, the equilibrium point P1 (P1′) are beyond the domain, when
Figure 9.
Convergence process
process of
of the
thesecond-order
second-order simplified
simplified system
system composed
composed of
of Equations
Equations (22)
(22) and
and
both Figure
Pw and9.QConvergence
w are quite large, such as 1.0 and 0.9 (−0.9). The problem must be avoided in practice. To
(23),
from
the
initial
point
I.
(a)
kkp3
=
0.6,
k
i3 = =
50;
(b)
k
p3
=
0.3,
k
i3 k
=
2000.
(23),
from
the
initial
point
I.
(a)
=
0.6,
k
50;
(b)
k
=
0.3,
=
2000.
this end, a proper capacity of filters p3
could bei3designed top3result ini3a smaller Qw.

ϕmin = –π/2

ϕmax = π/2

i'wq (pu)

It is noteworthy that,
when i′wq reaches the limitation i′wqmin or i′wqmax, the system state moves along
1.5
the boundaries and it can still converge
once the state reaches another section across the blue curve
i'wqmax
1.0 point is in the allowable domain.
P1
as long as the equilibrium
In Equation (27), the range of i′wq is related
to iwd, i.e., the active power
P
w
.
While
in
Equation
(24),
the
equilibrium
point is related to the required
0.5
reactive power Qw. The different equilibrium curves (or points) and domains under different Pw and
0.0
Qw are depicted in Figure
10. In particular, the equilibrium point P1 (P1′) are beyond the domain, when
both Pw and Qw are quite
large,
such as 1.0 and 0.9 (−0.9). The problem must be avoided in practice. To
-0.5
this end, a proper capacity of filters could be designed
P1'to result in a smaller Qw.
-1.0

i'wqmin

1.5
-1.5

1.0

-2

-1.5
i'wqmax -1

-0.5

0
ϕ (rad)
P1

0.5

1

1.5

2

i'wq (pu)

Figure 10. Different equilibrium curves and domains under different Pw and Qw.
Figure 10.0.5Different equilibrium curves and domains under different Pw and Qw .
ϕmax = π/2

ϕmin = –π/2

4.2. Stability Analysis of0.0
P-V Control
4.2. Stability Analysis of P-V Control
-0.5
A simplified second-order
equation of the HVDC subsystem can be obtained when the current
A simplified second-order equation of the HVDC subsystem can be obtained when the current
P1'
transients are ignored.-1.0
i'wqmin
transients are ignored.

id i≈  k p5
Ubm−
(28)
-1.5
bm )
kp 5 +
 kkii55 /s
s (U
UU
(28)
d
bm
bm
-2
-1.5
-1
-0.5
0
0.5
1.5
2
ϕ (rad)
1
2
dUbm
/dt ≈ 2ωb Pw − udi id − Rd i2d /C f
(29)







Figure 10. Different equilibrium curves and domains under different Pw and Qw.

According to Equations (28) and (29), when Pw increases, the voltage amplitude Ubm will increase,
andStability
thus theAnalysis
control of
loop
4.2.
P-VEquation
Control (28) will adjust the DC current reference. Once the firing angle
regulated by the inner loop decreases, the actual DC current id will increase. According to Equation (29),
A simplified second-order equation of the HVDC subsystem can be obtained when the current
Ubm will stop increasing and start to decrease, and finally the system will reach a new steady state.
transients are ignored.






id  kp 5  ki 5 s Ubm
 Ubm



(28)

According to
to Equations
Equations (28)
(28) and
and (29),
(29), when
when P
Pww increases,
increases, the
the voltage
voltage amplitude
amplitude U
Ubm
bm will
will increase,
increase,
According
and
thus
the
control
loop
Equation
(28)
will
adjust
the
DC
current
reference.
Once
the
firing
angle
and thus the control loop Equation (28) will adjust the DC current reference. Once the firing angle
regulated by
by the
the inner
inner loop
loop decreases,
decreases, the
the actual
actual DC
DC current
current iidd will
will increase.
increase. According
According to
to Equation
Equation
regulated
(29), U
Ubm
bm will
will stop
stop increasing
increasing and
and start
start to
to decrease,
decrease, and
and finally
finally the
the system
system will
will reach
reach aa new
new steady
steady
(29),
Energies 2018, 11, 2207
13 of 19
state.
state.

dc
uudc

uubq

bq

PI11
PI

++––

PI33
PI
–1
–1

++––

PI22
PI
LLww
LLww
PI44
PI

+
++–– u
u wd

Linearizing urcd
bd
rcd Linearizing urcd
wd
uubd
iircd
Eq.(1) iiwd
wd Eq.(1)
Eq.(3)
Eq.(7)
Eq.(8) and
and u
Eq.(3)
Eq.(7)
Eq.(8)
Eq.(2) iiwq
udrdr
wq
bq
rcq
uubq
iircq
uuwq Eq.(2)
(9)
+ wq
rcq
(9)
uurcq
+++
+

WECS
WECS
model
model

VSI controller
controller
VSI

Eq.(10)
Eq.(10)

4.3. Small-Signal
Small-Signal Analysis and
and Parameters Design
Design
4.3.
4.3. Small-Signal Analysis
Analysis and Parameters
Parameters Design
Taking one
one of
of typical
typical operating
operating points,
points, i.e.,
i.e., P
Pw = 0.8 pu
pu and Q
Qrc = 0.21 pu;
pu; as an
an example, the
the
Taking
Taking one of
typical operating
points, i.e.,
Pww == 0.8
0.8 pu and
and Qrcrc == 0.21
0.21 pu; as
as an example,
example, the
small-signal model
model of
of the
the overall
overall system
system can
can be
be established
established in
in the
the RSEF,
RSEF, as
as shown
shown in
in Figure
Figure 11.
11. For
For
small-signal
small-signal model of the overall system can be established in the RSEF, as shown in Figure 11. For the
the inner
inner loop regulator,
regulator, PI
PI22 and
and PI
PI4,, of
of the
the WECS,
WECS, the
the parameters
parameters can
can be set as
as kkp2p2 (k
(kp4)) is
is 1.0,
1.0, and kki2i2
the
inner looploop
regulator, PI2 and
PI4 , of 4the
WECS,
the parameters
can be setbeasset
kp2 (kp4
) isp41.0,
and kand
i2 (ki4 )
(ki4i4)) is
is 10,
10, leading
leading to
to aa closed-loop
closed-loop bandwidth
bandwidth about
about 167
167 Hz.
Hz. Moreover,
Moreover, typical
typical parameters such
such
(k
is 10, leading
to a closed-loop
bandwidth about 167
Hz. Moreover,
typical parametersparameters
such as kp1 = 4.0,
as
k
p1
=
4.0,
k
i1
=
50
can
be
set
for
the
outer
loop
active
power
regulator
PI
1
,
leading
to
a
closed-loop
as
= 4.0,
ki1 =set50for
can
set for
theactive
outerpower
loop active
power
leading to abandwidth
closed-loop
ki1 k=p150
can be
thebeouter
loop
regulator
PI1 ,regulator
leading toPIa1,closed-loop
of
bandwidth of
of about
about 20
20 Hz.
Hz.
bandwidth
about 20 Hz.
U bm
LinearizingU
bm
Linearizing
PI55 ––+ PI
PI66
PI
Eq.(4)
+
Eq.(4)

iidd


SEB model
model
SEB

LCRcontroller
controller
LCR

Figure
11.
Small-signal
model
of
the
system.
Figure
Figure 11.
11. Small-signal
Small-signal model
model of
of the
the system.
system.

(a)
axis
Imag.axis
(a) Imag.

In particular,
particular, attention
attention should
should be
be paid
paid to
to the
the parameters
parameters of
of the
the developed
developed outer
outer loop
loop reactive
reactive
In
In particular, attention should be paid to the parameters of the developed outer loop reactive
power
control.
As
shown
in
Figure
12a,
when
k
i3
becomes
larger,
the
damping
of
PI
3
increases.
power control. As shown in Figure 12a, when ki3 becomes larger, the damping of PI3 increases.
power control. As shown in Figure 12a, when ki3 becomes larger, the damping of PI3 increases.
However, the
the loop
loop will
will couple
couple with
with the
the DC
DC voltage
voltage when
when kki3i3 is
is too
too large,
large, resulting
resulting in
in aa pair
pair of
of
However,
However, the loop will couple with the DC voltage when ki3 is too large, resulting in a pair of conjugate
conjugate modes.
modes. It
It can
can be
be seen
seen from
from Figure
Figure 12b
12b that
that when
when kkp3p3 increases,
increases, the
the damping
damping of
of PI
PI33 decreases,
decreases,
conjugate
modes. It can be seen from Figure 12b that when kp3 increases, the damping of PI3 decreases, which
which
thereafter
leads
to
the
coupling.
However,
the
coupling
disappears
as
k
p3
continues
to
increase.
which thereafter leads to the coupling. However, the coupling disappears as kp3 continues to increase.
thereafter leads to the coupling. However, the coupling disappears as kp3 continues to increase. Finally,
Finally,
k
p3

[1.5,
2.0],
and
k
i3

[20,
140]
can
be
taken.
Within
the
tuned
parameter
ranges,
the
closedFinally, kp3  [1.5, 2.0], and ki3  [20, 140] can be taken. Within the tuned parameter ranges, the closedkp3 ∈ [1.5, 2.0], and ki3 ∈ [20, 140] can be taken. Within the tuned parameter ranges, the closed-loop
loop bandwidth
bandwidth is
is about
about 40
40 Hz.
Hz.
loop
bandwidth is about 40 Hz.
10
10
55

00
-5
-5

PI3+Δu
+Δudcdc
PI
Δudcdc3
Δu

PI11
PI

-10
-10
-80
-80

(b)
axis
Imag.axis
(b) Imag.

PI5,6
5,6
PI
PI2,4
2,4
PI

PI33
PI

-60
-60

10
10

55

PI33
PI

-40
-40

-20
-20

Real axis
axis
Real

PI33+Δu
+Δudcdc
PI

Δudcdc
Δu

00

-10
-10

-100
-100

-80
-80

-60
-60

Real axis
axis
Real

00

PI5,6
5,6
PI
PI
2,4
PI2,4
PI11
PI
PI5,6
5,6
PI

PI33
PI

-5
-5

-120
-120

PI5,6
5,6
PI

-40
-40

-20
-20

00

Figure 12.
12. Root loci
loci of the
the small-signal
small-signal model.
model. (a)
(a) kkp3p3 == 1.3
1.3 and kki3i3 changes
changes from 50
50 to
to 140;
140; (b)
(b) kki3i3 == 130
130
Figure
Figure 12. Root
Root loci of
of the small-signal
model. (a)
kp3 = 1.3 and
and ki3 changes from
from 50 to
140; (b)
ki3 = 130
and
k
p3
changes
from
0.3
to
2.0.
and
and kkp3 changes
changesfrom
from0.3
0.3to
to2.0.
2.0.
p3

A similar
similar analysis
analysis can
can be
be performed
performed to
to tune
tune the
the parameters
parameters of
of the
the rectifier
rectifier P-V
P-V controller.
controller. In
In
A
A
similar
analysis
can
be
performed
to
tune
the
parameters
of
the
rectifier
P-V
controller.
Figure 13a,
13a, when
when kki5i5 becomes
becomes larger,
larger, the
the oscillation
oscillation mode
mode in
in PI
PI5,6
5,6 disappears,
disappears, but
but the
the damping
damping of
of PI
PI66
Figure
In Figure
13a, when
ki5 the
becomes
larger,
the oscillation
mode
in PI
disappears,
but the
damping
of
5,6
tends
to
decrease
and
damping
characteristics
of
both
the
voltage
and
current
of
the
SEB
are
tends to decrease and the damping characteristics of both the voltage and current of the SEB are
PI6 tends to decrease
and
thethe
damping
of the
bothdamping
the voltage
andofcurrent
the SEBkp5are
deteriorated.
In Figure
Figure
13b,
larger kkcharacteristics
p5 is,
is, the
the smaller
smaller
factor
PI5,6
5,6 is.
is.of
Finally,

deteriorated.
In
13b,
the larger
p5
the damping
factor
of PI
Finally,
kp5 
deteriorated.
In
Figure
13b,
the
larger
k
is,
the
smaller
the
damping
factor
of
PI
is.
Finally,
k

p5
p5
[0.2, 0.5],
0.5], kki5i5 
 [40,
[40, 100]
100] can
can be
be selected.
selected. Note
Note that
that typical
typical parameters
parameters such
such as
as kkp6p6 == 5,6
2.0 and
and kki6i6 == 20
20 are
are
[0.2,
2.0
[0.2, 0.5], ki5 ∈ [40, 100] can be selected. Note that typical parameters such as kp6 = 2.0 and ki6 = 20 are
employed in the inner loop. Within the suggested parameter ranges, the outer and inner closed-loop
bandwidths are approximately 5 Hz and 110 Hz respectively.

Energies
Energies2018,
2018,11,
11,xxFOR
FORPEER
PEERREVIEW
REVIEW

14
14of
of19
19

employed
inner
employed
in
the
innerloop.
loop.Within
Withinthe
thesuggested
suggestedparameter
parameterranges,
ranges,the
theouter
outerand
andinner
innerclosed-loop
closed-loop
Energies
2018,in
11,the
2207
14 of 19
bandwidths
are
approximately
5
Hz
and
110
Hz
respectively.
bandwidths are approximately 5 Hz and 110 Hz respectively.
axis
Imag.axis
(a) Imag.
(a)

10
10

5
5
0
0
-5
-5

-10
-10

PI
PI5,65,6
PI
Δu
3
PI3 Δudcdc PI
PI6 6PI
PI1 1

Δi
dc
Δid+Δu
d+Δudc

Δi
+Δubd
2000
Δi
Δircd
2000
rcd+Δubd
Δiwqwq+Δu
+Δubqbq
1000
1000
0
Δi
wd
0
Δi
Δi
d
wd
-1000
Δid
-1000
wd+PI5
-2000 Δi
-2000 Δiwd+PI5
-1200
-1000
-800
-600
-400
-200
-1200
-1000
-800
-600
-400
-200

-150
-150

-100
-100

Real
Realaxis
axis

PI
PI2,42,4

-50
-50

0
0

axis
Imag.axis
(b) Imag.
(b)

10
10

PI
PI5,65,6
PI
PI2,42,4
PI
PI5,6

5
5

0
0
-5
-5

PI
PI1 1

5,6

-10
-10
-20
-20

-15
-15

-10
-10

-5
-5

Real
Realaxis
axis

0
0

Figure
model.
(a)
(b)
i5 =
Figure
13.
Root
loci
of
the
small-signal
0.4
and
changes
from
50
to
1000;
50
Figure13.
13.Root
Rootloci
lociof
ofthe
thesmall-signal
small-signalmodel.
model.(a)
(a)kkp5
kp5p5===0.4
0.4and
andkkki5i5i5changes
changesfrom
from50
50to
to1000;
1000;(b)
(b)kkki5
i5 =
=50
50
and
k
p5
changes
from
0.1
to
2.0.
and
changes from
from 0.1
0.1 to
to 2.0.
2.0.
and kkp5
p5 changes

5.
5. Simulation
Simulation Results
Results
Simulations
to
the
control
scheme.
The
are
carried
out
on
PSCAD/EMTDC
to verify
verify
the proposed
proposed
control
scheme.
The
Simulations are
arecarried
carriedout
outon
onPSCAD/EMTDC
PSCAD/EMTDC
to verify
the
proposed
control
scheme.
simulated
system
is
shown
in
Figure
14,
and
the
detailed
parameters
of
the
system
are
listed
in
Table
1.1.
simulated
system
is
shown
in
Figure
14,
and
the
detailed
parameters
of
the
system
are
listed
in
Table
The simulated system is shown in Figure 14, and the detailed parameters of the system are listed
The
employed
monopole
LCC-HVDC
model
is
from
the
CIGRE
benchmark
model
[33],
both
the
The
employed
monopole monopole
LCC-HVDC
model is from
theis CIGRE
benchmark
model [33],
both[33],
the
in
Table
1. The employed
LCC-HVDC
model
from the
CIGRE benchmark
model
rectifier
inverter
which
LCC-based.
The
isis1000
MVA,
and
rectifier
and
inverter
of
whichare
arewhich
LCC-based.
Therated
ratedcapability
capability
ofthe
thesystem
system
1000
MVA,
and
both
theand
rectifier
andof
inverter
of
are LCC-based.
The
rated of
capability
of the
system
is 1000
the
power
capability
each
11/13
filters
isis50
The
increase
thereactive
reactive
power
capability
ofcapability
eachset
setof
of
AC
11/13
order
harmonic
filters
50MVar.
MVar.
The
increase
MVA,
and the
reactive
powerof
ofAC
each
set order
of
ACharmonic
11/13 order
harmonic
filters
is 50
MVar.
and
decrease
of
the
DC-side
current
of
the
WECS
can
simulate
the
changes
of
the
input
power
the
and increase
decreaseand
of the
DC-side
of thecurrent
WECS of
can
simulate
the changes
the
input power
of
the
The
decrease
of current
the DC-side
the
WECS can
simulateof
the
changes
of theof
input
back
end.
back end.
power
of the back end.
Wind
WindFarm
Farm
35kV
35kV

0.5968H0.5968H
0.5968H0.5968H
2.5Ω
2.5Ω
2.5Ω
2.5Ω

500kV
500kV

26.0uF
26.0uF

35:213.5
35:213.5
YY ∆∆

209.2:230
209.2:230
∆∆ YY

YY YY
11/13th
11/13th

YY YY
11/13th
11/13th

Figure
Figure14.
14.Simulated
Simulatedsystem.
system.
Figure
14.
Simulated
system.
Table
Table1.
1.Parameters
Parametersof
ofthe
thesimulated
simulatedsystem.
system.
Table
1.
Parameters
of
the
simulated
system.

CCdcdc 90,000
90,000uF
uFfor
for1.5
1.5MVA
MVAcapacity
capacity
Cdc Rw 90,000 uF for 0.001
1.5 MVA
capacity
Wind
Energy
Conversion
System
pu
Wind
Energy
Conversion
System
R
w
0.001
pu
Wind Energy Conversion System
Rw
0.001 pu
Lw
0.3 pu
Lw Lw
0.30.3
pu pu
Sending-End
Bus
C
f
0.05
pu
for
each
set of
Sending-End
Bus
C
f
0.05
pu
for
each
offilter
filter
Cf
Sending-End Bus
0.05 pu for each set set
of filter
RRrcrc
0.001
pu
0.001 pu
Rrc Lrc
0.001
pupu
0.18
L
rc
0.18
pu
High
Voltage
Direct
Current
L
0.18
pu
High
Voltage
Direct
Current
System
rc
High Voltage Direct Current System Ld
1.1936
1.1936
H
System
Ld Ld
1.1936
HH
R
d
5
Ω
Rd Rd
5 Ω5 Ω
5.1.
5.1.
System Startup
Startup
5.1.System
The
The WF
WF is
is equivalent
equivalent to
to aa single
single WECS,
WECS,and
andthe
thesystem
systemstartup
shownin
startup process
processisis shown
shown
in Figure
Figure 15.
15.
Before
the
system
startup,
the
capacitor
of
the
WECS
is
charged
by
the
configured
battery,
and
Before
startup,
thethe
capacitor
of the
is charged
by the configured
battery, and
thereafter
Beforethe
thesystem
system
startup,
capacitor
ofWECS
the WECS
is charged
by the configured
battery,
and
thereafter
the
voltage
of
generated
WECS
as
the
three-phase
AC voltageAC
of the
SEB can
be SEB
generated
by
the WECSby
atthe
0–0.3
s, as at
shown
15a.
thereafter
thethree-phase
three-phase
AC
voltage
ofthe
the
SEBcan
canbe
be
generated
by
the
WECS
at0–0.3
0–0.3ins,s,Figure
asshown
shown
At 0.3 s, the DC-side current of the WECS starts to increase, and then the HVDC is unblocked, with the

Energies 2018, 11, x FOR PEER REVIEW
Energies 2018, 11, 2207

15 of 19
15 of 19

(f) WECS (e) WECS dc-side (d) SEB voltage (pu) (c) Reactive power (pu) (b) Active power (pu) (a) Voltage and
freq. (pu)
voltage (pu)
current (pu)

in Figure 15a. At 0.3 s, the DC-side current of the WECS starts to increase, and then the HVDC is
unblocked,
P-V control
in the
whereas the
constant-voltage
control
in the inverter.
P-V controlwith
in thethe
rectifier
whereas
therectifier
constant-voltage
control
in the inverter.
Henceforth,
the DC
Henceforth,
the
DC
voltage
of
HVDC
is
generated
gradually,
as
shown
in
Figure
15g.
0.4 s, the
voltage of HVDC is generated gradually, as shown in Figure 15g. At 0.4 s, the batteryAt
configured
battery configured at the DC bus of the WECS is withdrew, and the Q-f control in the WECS is
at the DC bus of the WECS is withdrew, and the Q-f control in the WECS is switched on. Then, the
switched
on. Then, the active power continues increasing until to the rated point, as shown in Figure
active power continues increasing until to the rated point, as shown in Figure 15b,f. In Figure 15a,
15b,f. In Figure 15a, it can be observed that both the system frequency ω1 and the voltage of the SEB
it can be observed that both the system frequency ω 1 and the voltage of the SEB Ubm remain stable
Ubm remain stable and are maintained at 1.0 pu in the final steady state. The active power generated
and are maintained at 1.0 pu in the final steady state. The active power generated from the WECS
from the WECS can be delivered into the receiving end grid through the LCC-HVDC transmission.
can be delivered into the receiving end grid through the LCC-HVDC transmission. The AC filters are
The AC filters are connected to the SEB gradually when the reactive power from the WECS Qw is
connected to the SEB gradually when the reactive power from the WECS Qw is large than 0.1 pu (see
large than 0.1 pu (see Figure 15c), which can be regarded as the reactive power limit of the WECS.
Figure 15c), which can be regarded as the reactive power limit of the WECS. The reactive current iwq
The reactive current iwq of the WECS is regulated automatically, so as to compensate the reactive
of the WECS is regulated automatically, so as to compensate the reactive power for the LCR under
power for the LCR under the condition that ubq = 0, as shown in Figure 15d,f. Moreover, Figure 15e
the condition that ubq = 0, as shown in Figure 15d,f. Moreover, Figure 15e indicates that the DC-side
indicates that the DC-side voltage of the WECS remains stable under the active power control of the
voltage of the WECS remains stable under the active power control of the WECS after the battery
WECS after the battery is withdrawn.
is withdrawn.
1.2

1
0.9
0.8

0

0.5

1

1.5

2

2.5

1
0.8

3

Pw
Prc
Piv

0.6

0.4
0.2
0
0

0.5

1

1.5

2

2.5

3

0.6

0.4

Qw
Qfilter
Qrc

Add a set of filter once Qw > 0.1 pu

0.2
0
0

0.5

1

1.5

2

2.5

3

1.5
1

ubd
ubq

0.5
0
-0.5

0

0.5

0

0.5

1

1.5

2

2.5

3

1.5

2

2.5

3

1.2

1.1
1
0.9
0.8

Battery is withdrew
1

0.9

iwd
iwq

0.5
0.1
-0.3

(g) HVDC voltage
and current (pu)

Ub m
ω1

1.1

0

0.5

1

1.5

2

2.5

1
0.8
0.6
0.4
0.2
0

3

udr
id
udi
0

0.5

1

1.5

2

2.5

3

Time (s)

Figure
startup.
(a) (a)
Sending-end
busbus
voltage
andand
frequency;
(b)
Figure 15.
15. Simulation
Simulationresult
resultofofthe
thesystem
system
startup.
Sending-end
voltage
frequency;
active
power;
(c)
reactive
power;
(d)
dq-axis
sending-end
bus
voltage;
(e)
WECS
DC-link
voltage;
(f)
(b) active power; (c) reactive power; (d) dq-axis sending-end bus voltage; (e) WECS DC-link voltage;
WECS
output
current;
(g) (g)
HVDC
DC-link
voltage
andand
current.
(f) WECS
output
current;
HVDC
DC-link
voltage
current.

Energies 2018, 11, 2207

16 of 19

Energies 2018, 11, x FOR PEER REVIEW

16 of 19

5.2.Operation
Operationunder
underDisturbances
Disturbances
5.2.

(d) ubq and iwq (pu)

(c) Reactive power (pu) (b) Active power (pu) (a) Voltage, Freq (pu)

Underdisturbances,
disturbances,such
suchasasfluctuations
fluctuationsofofactive
activepower
powerand
andreactive
reactivepower,
power,the
thesimulation
simulation
Under
results
are
shown
in
Figure
16,
where
the
WF
is
equivalent
to
a
single
WECS
with
the
PI-type
Q-f
results are shown in Figure 16, where the WF is equivalent to a single WECS with the PI-type Q-f
control.InInFigure
Figure
s, the
DC-side
current
of the
WECS
starts
to decrease,
which
simulates
control.
16,16,
at at
0.50.5
s, the
DC-side
current
of the
WECS
starts
to decrease,
which
simulates
the
the
decrease
of
the
input
active
power
from
the
front
end
of
the
WECS.
Figure
16a
shows
that
a
small
decrease of the input active power from the front end of the WECS. Figure 16a shows that a small
dropofofthe
theSEB
SEBvoltage
voltageUUbmbmoccurs.
occurs.Then,
Then,the
thevoltage
voltagereturns
returnstotothe
therated
ratedvalue
valueunder
underthe
theP-V
P-Vcontrol.
control.
drop
At2.0
2.0s,s,the
theDC-side
DC-sidecurrent
currentrises
risestotothe
theoriginal
originalvalue,
value,and
andaacontrary
contraryphenomenon
phenomenoncan
canbe
beobserved
observed
At
in
Figure
16b.
It
should
be
noticed
that
the
AC
filters
cannot
be
removed
or
added
due
to
a
time
delay.
in Figure 16b. It should be noticed that the AC filters cannot be removed or added due to a time delay.
Therefore,
the
reactive
power
difference
between
Q
and
Q
can
be
compensated
by
Q
.
From
filtercan be compensated by Qww
Therefore, the reactive power difference between Qrcrc and Qfilter
. From 44ss
severalsets
setsof
offilters
filters are
are added
added and
and removed
removed intentionally,
toto99s,s,several
intentionally,in
inorder
ordertotoverify
verifythe
theperformance
performanceof
the
Q-f
control.
From
Figure
16d,
it
can
be
observed
that
the
reactive
current
i
automatically
changes
wq
of the Q-f control. From Figure 16d, it can be observed that the reactive current
iwq automatically
with thewith
demand
for reactive
theunder
condition
that ubq =that
0, guaranteeing
the frequency
changes
the demand
for power
reactiveunder
power
the condition
ubq = 0, guaranteeing
the
stability.
Accordingly,
the
reactive
power
differences
between
Q
and
Q
can
be
automatically
rc
filter
frequency stability. Accordingly, the reactive power differences between Qrc and Qfilter can be
compensatedcompensated
by the WECS,by
asthe
shown
in Figure
16c.in Figure 16c.
automatically
WECS,
as shown
1.1

Ubm
ω1

1.05
1
0.95

0.9
1.1
1
0.9
0.8
0.7
0.6
0.5

0

2

4

8

10

Pw
Prc
Piv

Input active power increases
0

1

2

3

0.6
0.5
0.4
0.3
0.2
0.1
0
-0.1

6

Input active power decreases

4

5

6

7

8

Remove two sets of
filters
Add two sets of
filters

0

1

2

3

4

5

6

7

9

10

Qw
Qfiter
Qrc

8

9

10

0.2

ubq
iwq

0.1

0
-0.1

-0.2

0

1

2

3

4

5

Time (s)

6

7

8

9

10

Figure 16. Simulation results under external disturbances, where the WF is represented by a single
Figure 16. Simulation results under external disturbances, where the WF is represented by a single
WECS with the PI-type Q-f control. (a) Sending-end bus voltage and frequency; (b) active power; (c)
WECS with the PI-type Q-f control. (a) Sending-end bus voltage and frequency; (b) active power;
reactive power; (d) dq-axis sending-end bus voltage.
(c) reactive power; (d) dq-axis sending-end bus voltage.

In order to evaluate the performance of the Q-f droop control in a multi-machine WF, the WF is
In order
evaluate
thewith
performance
of the
Q-f control.
droop control
in a multi-machine
the WF
represented
bytotwo
WECSs
a P-type Q-f
droop
The capabilities
of the twoWF,
WECSs
areis
represented
by
two
WECSs
with
a
P-type
Q-f
droop
control.
The
capabilities
of
the
two
WECSs
are
the same (500 MVA) but the droop coefficients are different (2.0 versus 1.0). The simulation result the
is
same (500
MVA) 17.
butThe
the droop
coefficients
arethe
different
(2.0
versus 1.0).
simulation
result is
shown
in Figure
DC-side
currents of
WECSs
decrease
at 0.5The
s and
then increase
at shown
2.5 s.
in Figure
Thes,DC-side
of the
WECSs
decrease atto0.5
s and
increase
at 2.5
s. From
4.5 s
From
4.5 s17.
to 7.5
several currents
sets of AC
filters
are connected
the
SEBthen
gradually.
The
similar
results
to 7.5 s, several
sets of16
AC
filters
are connected
to thethere
SEB is
gradually.
The similar
compared
compared
with Figure
can
be obtained.
However,
a small static
error inresults
ubq1,2 because
of
with
Figure
16
can
be
obtained.
However,
there
is
a
small
static
error
in
u
because
of
the
bq1,2
the adopted P-type droop control, as shown in Figure 17d. Moreover, from Figure 17d, it can adopted
be also
P-type droop
as shown
in Figure
17d.
from
Figurethat
17d,of
it can
be 2also
that
observed
that control,
the shared
reactive
current
by Moreover,
WECS1 iwq1
is twice
WECS
iwq2,observed
due to the
relationship between their droop coefficients.

Energies 2018, 11, 2207

17 of 19

the shared reactive current by WECS1 iwq1 is twice that of WECS2 iwq2 , due to the relationship between
17 of 19
their droop coefficients.
(c) Reactive power (pu) (b) Active power (pu) (a) Voltage, Freq (pu)

Energies 2018, 11, x FOR PEER REVIEW

1.05

Ubm
ω1

1.025
1
1.002
1.000
0.998

0.975

4

0.95
0

2

3

4

5

5

6

6

7

7

8

8

9

1

Pw1
Pw2
Pr c

0.8

Input active power increases

0.6
0.4
0.2

Input active power decreases
0

1

2

3

4

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-0.1
0.15
0.1
0.05
0
-0.05
-0.1
-0.15

5

6

7

1

2

ubq1

0

1

3

ubq2

2

4

iwq1

3

4

5

8

9

Qw1
Qw2
Qfilter
Qr c

Add five sets of filters

0

(d) ubq and iwq (pu)

1

6

7

8

9

6

7

8

9

iwq2

5

Time (s)

Figure 17.
external
disturbances,
where
the WF
represented
by two by
WECSs
Figure
17. Simulation
Simulationresults
resultsunder
under
external
disturbances,
where
theisWF
is represented
two
with thewith
P-type
droop
control.
Sending-end
bus voltage
frequency;
(b) active power;
(c)
WECSs
theQ-f
P-type
Q-f
droop (a)
control.
(a) Sending-end
busand
voltage
and frequency;
(b) active
reactive
power;
(d)
dq-axis
sending-end
bus
voltage.
Note
that
P
,
P
denote
the
active
powers
w1
w2
power; (c) reactive power; (d) dq-axis sending-end bus voltage. Note that Pw1, Pw2 denote the active
outputted
by both by
theboth
WECSs,
respectively,
similar for
Qw1 , for
Qw2Q. w1
Q,filter
the reactive
power
powers
outputted
the WECSs,
respectively,
similar
Qw2denotes
. Qfilter denotes
the reactive
generated
by
the
filters.
power generated by the filters.

It should
should be noted
noted that the dynamic
dynamic behaviors
behaviors of
of the
the system
system is
is affected
affected by both the system
system
parameters
small-signal
stability
analysis
performed
in Section
4.3 just
parameters and
and control
controlparameters.
parameters.The
The
small-signal
stability
analysis
performed
in Section
4.3
illustrates
the results
of oneofofone
the of
typical
operating
points. points.
Similar repetitive
work canwork
be made
to
just illustrates
the results
the typical
operating
Similar repetitive
can be
further
thestudy
effectthe
of effect
control
on the system
at different
operating
points.
made tostudy
further
ofparameters
control parameters
on the stability
system stability
at different
operating
Furthermore,
as shown
in Figure
9, the
phase-plane
analysis,
together
points. Furthermore,
as shown
in Figure
9, the
phase-plane
analysis,
togetherwith
withtime-domain
time-domain state
state
trajectory based
based on
on Equations
Equations(22)
(22)and
and(23),
(23),ororEquations
Equations
(28)
and
(29)
employed
to evaluate
(28)
and
(29)
cancan
be be
employed
to evaluate
the
the
effects
of the
system
parameters
control
parameters
dynamic
behaviors
system
effects
of the
system
parameters
andand
control
parameters
on on
thethe
dynamic
behaviors
of of
thethe
system
in
in
practical
applications.
practical
applications.
6. Conclusions
Conclusions
6.
This paper
paper proposed
proposed aa novel
novel coordinated
coordinated control
control scheme
scheme for
for WFs
WFs with
with LCC-HVDC
LCC-HVDCintegration.
integration.
This
The
scheme
comprises
the
Q-f
control
loop
in
the
WECSs,
and
the
P-V
control
loop
in
the LCR.
The scheme comprises the Q-f control loop in the WECSs, and the P-V control loop in the LCR.
The
Thecontrol
Q-f control
maintains
the system
frequency
and compensates
forreactive
the reactive
forLCR
the
Q-f
maintains
the system
frequency
and compensates
for the
powerpower
for the
LCR automatically,
whereas
thecontrol
P-V control
maintains
bus voltage
and realizes
thepower
active
automatically,
whereas
the P-V
maintains
the ACthe
busAC
voltage
and realizes
the active
power balance
the sending-end
bus
of HVDC.
the HVDC.
Thus,
scheme
addressesboth
boththe
thevoltage
voltage and
and
balance
of the of
sending-end
bus of
the
Thus,
thethe
scheme
addresses
frequency stability, based on the
the coordination
coordination between
between the
the WF
WF and
and the
the LCR.
LCR.
The
distinguishing
features
of
the
scheme
can
be
concluded
as
follows:
(1) there (1)
are no
commonly
The distinguishing features of the scheme can be concluded as follows:
there
are no
used
PLLs
in
the
controllers
of
WECSs,
and
consequently,
the
frequency
and
synchronization
stability
commonly used PLLs in the controllers of WECSs, and consequently, the frequency
and
issues introducedstability
by PLLsissues
can be
avoided; (2)
reactive
droop
of thepower
active power
synchronization
introduced
bythe
PLLs
can bepower
avoided;
(2)instead
the reactive
droop

instead of the active power droop is adopted while being applied to achieve synchronization control
and reactive power sharing in multi-machine systems, and therefore, the maximum power point
tracking of WFs remains unaffected; (3) the scheme can be utilized in more universal scenarios, as
long as the core topology is the VSI with LCR connection, such as WFs and photovoltaic power plants

Energies 2018, 11, 2207

18 of 19

droop is adopted while being applied to achieve synchronization control and reactive power sharing in
multi-machine systems, and therefore, the maximum power point tracking of WFs remains unaffected;
(3) the scheme can be utilized in more universal scenarios, as long as the core topology is the VSI
with LCR connection, such as WFs and photovoltaic power plants with LCC-based rectifier HVDC
integration. Our future work will focus on the control and protection algorithms during fault operation,
e.g., voltage-dependent current order limits (VDCOLs) for LCC-HVDC and low voltage ride-through
(LVRT) for WECS.
Author Contributions: Conceptualization, X.H. and H.G.; Methodology, X.H.; Validation, X.H, H.G. and G.Y.;
Writing—Original Draft Preparation, X.H.; Writing—Review & Editing, H.G., G.Y. and X.Z.; Supervision, H.G.
and X.Z.; Project Administration, G.Y.
Funding: This work was supported by the National Natural Science Foundation of China (Nos. 61722307, U1510208,
and 51711530235).
Conflicts of Interest: The authors declare no conflict of interest.

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