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Energy and Power Engineering, 2013, 5, 1209-1214
doi:10.4236/epe.2013.54B229 Published Online July 2013 (http://www.scirp.org/journal/epe)
PCHD-Based Passivity Control of VSC-HVDC
Connected Large Wind Farm
Xinming Fan1, Lin Guan1, Chengjun Xia1, He Jianming1, Xiaolin Li2, Shukai Xu2
1School of Electric Power, South China University of Technology, Guangzhou, China
2Electric Power Research Institute, CSG, Guangzhou, China
Email: [email protected]
Received March, 2013
ABSTRACT
Concentrated integration of large scale wind power demands stronger robustness of VSC-HVDC transmission. Based
on PCHD (Port Controled Hamiltonian with Dissipation) equation, the PCHD model of voltage source converter (VSC)
in abc frame and d-q rotating frame are built and the strict passivity of VSC is proved. Desired energy function is con-
structed and used as Lyapunov function by assigning link matrix and damping matrix. Impact from VSC equivalent dc
resistance is eliminated by additional d amping matrix. The IDA-PB (Interconnection and Damping Assignment Passiv-
ity-based) controller is designed based on desired equilibrium point and state variable. With different operation condi-
tions, VSC-HVDC and its control system are simulated by software PSCAD/EMTDC, the results show the proposed
control strategy has good performance and strong robustness.
Keywords: VSC-HVDC; Passivity; PCHD System; Damping Assignment; IDA-PB Control
1. Introduction
The use of wind power is a keystone in the policy of
every country for its renewable energy development
goals. Meanwhile wind farm is large-scalely developed
and the capacity of a single wind farm increases to hun-
dreds or thousands of MW [1]. HVDC with voltage
source converter (VSC-HVDC) has fine dynamic char-
acteristic and transmission flexibility, furthermore it im-
proves the stability of power system [2,3]. In addition,
VSC-HVDC is more economical for hundred megawatts
wind farm connection [4]. Therefore, VSC-HVDC has
obvious techno-economic advantages for the connection
of large scale wind farm. The VSC-HVDC system can be
operated in three modes: 1) constant dc voltage control
mode; 2) constant active and reactive power control
mode; and 3) constant ac voltage control mode[5]. And
one of converters has to control the dc voltage to make
power balanced and the dc voltage stable[6]. However
four control inputs of the VSC-HVDC and their interac-
tion make it a truly nonlinear multiple-input and multi-
ple-output system. Furthermore the fluctuation of wind
power will cause deviation of the electric variable in
connection point. So VSC-HVDC need strong robustness
to deliver power.
At present, voltage vector oriented double closed loop
PID control[7] based on synchronously rotating frame
and direct power control are commonly used. But they
both have weak robustness and it is difficult to tune PID
parameters. To eliminate the impacts of nonlinearity of
VSC-HVDC and improve its robustness, many research
works have been carried out, including feedback lineari-
zation and sliding mode control[5], adaptive
back-stepping control in Ref.[8], fuzzy PI control in
Ref.[9] and neural ne twork PID in Ref. [10 ]. Bu t it is still
difficult to achieve ideal effects because of the multi-
variable structure and highly coupled nonlinearity of the
VSC-HVDC system.
Passivity control is an emerging nonlinear control the-
ory based on the energy dissipation of system[11,12]. Its
profound physics meaning has significant relation with
Lyapunov function. IDA-PB control is a passivity control
based on PCHD. This paper, IDA-PB control strategy is
proposed based on the PCHD model of VSC-HVDC. The
control decreases dependence of system parameters and
makes VSC-HVDC connected large wind power has
smaller static error and stronger robustness. The simula-
tion results show its advantages.
2. Topology and Model of the VSC-HVDC
The single line diagram of the VSC-HVDC connected a
wind farm is shown in Figure 1.
The detailed structure of VSC is shown in Figure 2,
the transformer reactance and power loss are equivalent
to L and R, and the parameters of the three phase circuits
Copyright © 2013 SciRes. EPE
X. M. FAN ET AL.
1210
are assumed to be identical.
s
au,
s
bu and
s
cu
bu
dcu
are
phase voltage of the point of common coupling (PCC),
, and are line current at PCC. , and
are phase voltage at the ac side of the VSC, is
the dc voltage, is dc current in the dc transmission
line.
ai
cubiciau
dci
The mathematical model of the VSC-HVDC VSC in
the three phase static frame is
,,
,,
,,
1
3
1
3
1
3
()
()
()
a
s
aaa sadcaja
j abc
b
s
bbb sbdcbjb
j abc
c
s
ccc scdccjc
j abc
dc aabbcc dc
S
S
S
di
LuuRiuusR
dt
di
LuuRiuus R
dt
di
LuuRiuus Ri
dt
du
csisisii
dt
 
 
 

i
i
(1)
where (j=a,b,c) is the logic switch function,
when the upper bridge arm is conductive and low-
er bridge arm is turn-off, when the contrary is the
case. By Park transformation matrix and its inverse ma-
trix, Equation (1) can be transformed to Equation (2) in
d-q rotating fram e
js1js0
js
22
33
d
s
dddq sdddcd
q
q
s
qqq dsqqdcqd
dc dd qqdc
di
LuuRiLiusuRiL
dt
di
LuuRiLiusuRiL
dt
du
csisii
dt

 
  

i
i
(2)
where and represent the d and q components of
the switch function,
dsqs
s
du and
s
quu
are the d and q
components of the voltage at PCC, and are the
d and q components of the voltage at ac side of VSC. The
active power and reactive power in the d-q
rotating frame are
dq
u
sPs
Q
T1
T2
PCC PCC
Figure 1. Wind farm VSC-HVDC connection topology.
a
i
b
i
ci
dc
i
s
a
u
R
L
1dc
U
2dc
U
1dc
i
s
b
u
s
c
u
a
u
b
u
c
u
Figure 2. VSC-HVDC circuit topology.
3
ssddsqq
2
3sd qsq d
s2
()
()
Q
ui ui
ui ui


(3)
When d axis is oriented at the vector of the voltage at
PCC, then 0squ
, and ssddi
3
2
Pu,3sd q
s2
Qui, so
controlling theand respectively can realize the
decoupled control of and.
diqi
sPs
Q
3. PCHD Model of VSC-HVDC Converter
Port-controlled Hamiltonian with Dissipation(PCHD)
model[13,14] is the form
T
()
[() ()]()
()
()
Hx
x
Jx xgxu
x
Hx
ygxx
 
(4)
where are the state variables,
n
RxT
()() R
nn
JxJ x
 
T() 0xx 
rep
is skew-symmetric matrix, (resents
the dissipation, () Rgx
)
nm
t matrix, ()
is inpu
H
xis
stem energy function, Rm
uare input variables
and yare outp variables. Evaluating the rate of change
of the system total energy, we obtain
the sy
ut
TT
() () ()
()
dH xHxH x
x
uy
dt xx

 

(5)
Because of T
()() 0xx
 , we obtain
T
()dH xuy
dt (6)
Therefo re energy input fr om external is always greater
than stored in the system, this makes the system passive.
Make the switch control variable ,,
1
3
ii
jabc
SKs
 j
,
where ,,i abc
, according to Equations (1) and (4), we
obtain the PCHD model of VSC in abc frame
()
[]
Hx
x
JG
x
 
u
(7)
T
1
2
()
H
xxMx
]
(8)
where ,
T
[]abc dcxiiiuT
[0sa sb scuuuu
000 /
000/
000/
/// 0
a
b
c
abc
KLC
KLC
JKLC
KLCKLCKLC
2
2
2
2
dc
00 0
/
00
/
00 0
/
000
1/( )
RL
RL
RRL
RC
0
Copyright © 2013 SciRes. EPE
X. M. FAN ET AL. 1211
,
1/0 0 0
01/00
001/0
0001/
L
L
GL
C






000
000
00 0
000
L
L
ML
C



and dcdc dc/
R
uii.e. the equivilent resistor at the dc side
of VSC. By Park transformation, Equation (7) can be
transformed to PCHD model in d-q synchronously rotat-
ing frame as Equation (9)
12
()
[] dc
Hx
x
JGu
x
 
Gi
(9)
where ,
T
[]dq dcxLiLiCuT
2[0 01]G
3
0Ls
2
3
2
33
22
0
0
d
q
dq
J
Ls
ss





]


,
00
00
000
R
R





1
100
010
000
G





, .
T
[0sdsquu u
The energy function of the system is defined as
22
12
111
223
() LLC
2
3
H
xxxx
(10)
4. IDA-PB Controller Design of Converter
According to IDA-PB control theory[14][15], it need to
find out functions ()
x
,a()
J
x,a()
x
and vector func-
tion ()
K
x
n
R for the desired stable equilibrium points
by assigning interconnection and damping ma-
rix and make they meet the Equation (11)
*
x
aa
aa
{[,( )]()[( )( )]}()
()
[()()][,()]
J
xxJxxxKx
Hx
Jxxgxx
x

 
(11)
They meets conditions as follows
T
da
()[,()] (){[,()] ()}
a
J
xJxxJx JxxJx


(12)
T
da a
()() ()[() ()]0xx xx x 
(13)
T
() ()Kx Kx
xx





, *
*()
()
x
x
Hx
Kx x
 (14)
The dc voltage is expect to be the reference value of
, and are determined by the requirements of
decoupled control of active power and reactive power.
Therefore, the anticipated stable equilibrium points are
*
dcu
*
1
di
*
d
qi
x
Li, *
q
*
2
x
Li, *
3dc*
x
Cu. The PCHD model
Equation (9) can be written as th e Equation (15)
1
()
[]
Hx
x
J
x
 
Gu
(15)
where
dc
00
00
003(2)
R
R
R






.
So dc equivalent resistor exist in converter dissipation
matrix. Its impacts are to be eliminated by assigning
damping matrix. Make that
a() 0Jx, a
dc
00 0
00 0
003(2 )R






According to Equations (11), (12) and (13), we obtain
Equation (16)
dd a
()
[()()] ()()Hx1
J
xxKxx G
x
 
u
(16)
Then the expasion of Equation (16) is Equation (17)
2
d21
3
2
q12
3
[() /]
[() /]
sd
sq
sLKRKuK
3
3
s
LK RKuK

 
(17)
Setting 111()
K
kx
,222()
K
kxand 333()
K
kx
,
according to Equation (14), we obtain
** *
111
** *
222
** *
333
()
()
()2 323
d
q
dc
kxxLi
kxxLi
kxx Cu
 
 
 
(18)
Based on above conditions, a set of solution for
1
K
,2
K
and 3
K
is
**
11 111
**
22 222
**
33 33
()( )
()()
()2 3()
kxx Lxx
kxxLx x
kxxCx x
  
 
 
3
(19)
where
,
,0
.
Substituting Eqation (19) to Eqation (17) and con-
sidering that the dc voltage of VSC is equal to desired
stable equilibrium voltage i.e. at steady state,
then the VSC con trol laws can be obtained and simplified
as
*
dc dc
uu
**
*2*
()
()
dsd qd
dqq
uuLiRLii
RiL ii


d
 
 (20)
**
*2*
()
()
qsqdq
qdd
uuLiRLii
RiL ii


q
 
 (21)
where and can be obtai n ed by outer-loop c o ntrol.
*
di*
qi
In order to facilitate active power setting and voltage
control for wind farm, active power and constant voltage
control are used at the outer-loop controller of sending
end, and constant dc voltage and constant voltage
controls are used at receiving end, Figure 3 shows the
control diagram.
5. Simulation and Analysis
The VSC-HVDC linked wind farm and its control strat-
egy are modeled and simulated by software PSCAD/
Copyright © 2013 SciRes. EPE
X. M. FAN ET AL.
1212
EMTDC. The rated dc voltage of the VSC-HVDC is
±160kV and the base capacity is 100 MVA. The power
production of the wind farm is 180 MW, the PCC voltage
of both ends is 110kV. The simulation time span is 20 s.
Comparison is made between PI double closed-loop con-
trol and IDA-PB control, and the outer-loop PI parame-
ters of both are identical so as to ensure co mpariso n valid.
Figure 4 to Figure 7 show the steady simulation results.
d
u
d
i
q
i
q
u
*
di
*
q
i
sd
u
sq
u
*
p
*
u
p
u
*
dc
u
dc
u
Figure 3. IDA-PB control strategy for both ends VSC.
(a) Voltage pu value in P CC under PI double clo sed-loop control
(b) Voltage pu value in PCC under IDA-PB conl
Figure control
Simulation resluts in Figure 4(b), Figure 5(b), Figure
6
ces,
m
nd has
litt
tro
4. Voltage value in PCC under two
strategies.
and Figure 7(b) show ac voltage, wind farm power
production, active power transmitted by VSC-HVDC, dc
voltage and direct current reach set value quickly and
keep stable, no oscillation and very small overshoot un-
der IDA-PB control. Comparison demonstrates that IDA-
PB control make the system has stronger robustness.
In order to compare dynamic response performan
ake the wind speed have a step change at 10 s and 15 s
under both control modes, as shown in Figure 8. Figure
9 shows the simulation results of each variable.
Figure 9(a) shows the dc voltage at sending e
le fluctuation and smaller flutter under IDA-PB con-
trol. The receiving end dc voltage is stabilized on set
value and error is ±0.05 kV under IDA-PB control, but it
fluctuates greatly and need much time to reach stability
under PI double closed-loop control, as shown in Figure
9(b).
(a) Wind power and transmited powoer under PI double closed-loop
control.
(b) Wind power and transmited powoer under IDA-PB control
Figwo ure 5. Wind power and transmited power under t
control strategies.
Figure 6. Direct voltage of receiving end under twcontrol o
strategies.
(a) Direct curren t under PI double closed-loop conol tr
(b) Direct c urrent under IDA-PB control
Figure 7.rategies. Direct current under two control st
C
opyright © 2013 SciRes. EPE
X. M. FAN ET AL. 1213
Figure 8. Wind speed.
(a) Direct voltage of sending end under two control st rategies
(b) Direct voltage of receiving end under two control strategies
F
igure 9. Direct voltage under step wind disturbance.
Figure 10. Voltage step change at PCC of receiving end.
Setting the voltage amplitude step change at the PCC
of
ac voltage has little ripple and
be
he VSC-HVDC transmission linked
receiving end to simulates voltage disturbance of con-
nected grid, as shown in Figure 10. Figure 11 and Fig-
ure 12 show the results.
Figure 11 shows the
tter steady and dynamic performance under IDA-PB
control when the voltage at PCC of receiving end
changes. And dc voltage at receiving end has smaller
static error, it recover to set value quickly after distur-
bance under IDA-PB control, as shown in Figure 1 2.
6. Conclusions
The robustness of t
large wind power is discussed, a IDA-PB control strategy
is proposed for converter in this paper. The proposed
(a) Voltage pu value in P CC under PI double clo sed-loop control
(b) Voltage pu value in PCC under IDA-PB control
Figure voltage 11. Voltage value in PCC under step
disturbance at PCC of receiving end.
Figure 12. Direct voltage of receiving end under step
ontrol strategy has merits as follows: ssivity character-
is
neral affine nonlinear struc-
tu
esign of
PC
he proposed strategy achieved decoupled control
of
7. Acknowledgements
the national high technology
voltage disturbance at PCC of receiving end.
c1) The system energy function has pa
tic. It is accord with Lyaapunov stability th eory and has
clear physical meaning, and ideal controller can be ob-
tained by making best of it.
2) PCHD function has ge
re. Its essence is a nonlinear control strategy and it is
apt to nonlinear characteristic of VSC-HVDC.
3) IDA-PB control simplified controller d
HD model. Damping assignment decrease the impact
from system parameter deviation and make the energy
function non-growth and minimum value at equilibrium
point.
4) T
four inputs. And the control law is easy and of practi-
cal value for engineering application.
This work was supported by
C
opyright © 2013 SciRes. EPE
X. M. FAN ET AL.
Copyright © 2013 SciRes. EPE
1214
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