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UNIVERSITY OF STRATHCLYDE
Voltage Source Converter Modeling in DC Grid and Power System
Studies: appropriateness and limitations This work is part of twenties project-work package 5 and supported by European Union Under
Seventh Framework Program (FP7)
G.P. Adam, S.J. Finney and B.W. Williams
8/28/2012
This presentation tries to identify the attributes and limitations of the existing voltage source converter modeling approaches when used to analyzed hybrid
power systems that contain ac and dc networks. The importance of such work is that it may assist power systems engineers to conduct their studies with
appropriate converter models, knowing the scopes and limitations of each modeling approach. Therefore, brief discussions on converter modeling will be
presented that include detail switch model, switching function approach, and time average mode; and limitation of each approach will be highlighted. This
work will be substantiated by comparing the steady-state and transient responses of the four and six-terminals DC grids obtained from detail switch and
average models.
2
Fig. 1: Detail switch model
1. Could reproduce transients associated with fundamental
and harmonic voltages and currents, including interaction
between ac and dc sides.
2. Its switches mimic conduction of physical IGBT;
therefore, suitable for dc fault studies.
3. Suitable for wide range of studies where the detail
converter behavior is of great importance.
4. Prohibitively slow for large power system simulation.
5. AC harmonic filters must be included.
6. Not applicable for small signal stability.
Fig. 2: Ideal switch model (equivalent to switching function approach)
1. Its ideal switch representation does not permit reverse
current flow into dc side of when converter dc link is
suppressed; therefore, not suitable for dc fault studies of
traditional converters.
2. Could reproduce transients associated with fundamental
and harmonic voltages and currents. Could be used for
dynamic interactions between ac and dc sides during ac
network faults only.
3. AC harmonic filters must be included.
4. Prohibitively slow for large power system simulation.
5. Not applicable for small signal stability.
Vabc1
½Vdc
-½Vdc
0 t
Vgabc
Iabc
Va0
Zero power factor
line
Unity power factor
lineUnder excitation
Over excitation
Vc1
Vc1Vc1
Vc1
Vg
Vabc1
½Vdc
-½Vdc
0 t
Vgabc
Iabc
Va1
Zero power factor
line
Unity power factor
lineUnder excitation
Over excitation
Vc1
Vc1Vc1
Vc1
Vg
3
Fig. 3: Average model (controlled voltage source behind phase impedance)
1. This approach ignores any harmonics while
considers slow dynamics associated with power
frequency components only.
2. Could be used to analyze dynamic interactions
between ac and dc sides during ac network
faults only.
3. Not suitable for fast transients, including dc
network faults.
4. Relatively fast and suitable for transient
stability studies of medium-scale power
systems.
5. AC harmonic filters can be added to the model
to represent their effect at power frequencies.
6. Not applicable for small signal stability.
4
Fig. 4: Differential equations approach
DC side dynamics, including dc voltage controller:
1
*
*
1,
* 2 2
*
2 2
1
( )
( )
1( )
mdcj
dcjk
kj
dc
idc dcj dcj
m
dcjj pdc dcj dcj dc dcjk
k k j
dcj dcjj
dj q q dj qj
dj base
qj j j dj
qj
dj qj
dVI
dt C
dk V V
dt
I k V V I
V II V I R I I
V S
V P Q VI
V V
ξ
ξ
=
= ≠
=
= −
= − + −
= − − +
−=
+
∑
∑ (1)
AC side dyamics, including current controller:
*
*
( )
( )
( )
dqj
ii dqj dq
cdqj pi dqj dq j dqj dqj
dq cdqj dqj j dqj j dq
j
dk I I
dt
V k I I i L I
dI V V R I i L I
dt L
ψ
ω ψ
ω
= −
= − + +
− − −=
(2)
1. This approach considers only power frequency
dynamics. The converter model can be
expressed in abc or d-q synchronous reference
frame. However, modelling in d-q frame is
preferred.
2. When all controllers are incorporated, it can be
used to analyze transient and small signal
stability of large power powers. Also it can be
used to analyze dynamic interactions between
converters controls in dc grid and synchronous
machines in ac sides.
3. Small signal and transient analysis can be
conducted without the need for conventional or
sequential load flow, and manual linearization
of power system equations.
4. The DC current at the converter node is set by
the local dc voltage control loop and the current
from the DC link which is a function of the
local DC voltage and the voltages at all other
DC nodes, in the steady state the local control
will force the net current into the node to zero.
5
Fig. 5: Modular multilevel converter (M2C) detailed model
1. Reproduces all the transients
associated with power and
harmonic frequencies and detail
dynamic interactions between ac
and dc sides.
2. Takes into account all the
dynamics associated with
capacitor voltage balancing, phase
circulating and dc offset arm
currents.
3. Its switches mimic operation of
physical IGBTs, therefore suitable
for detail studies.
4. Prohibitively slow, therefore this
approach is not suitable for large
dc grids.
5. Not applicable to small signal
stability analysis.
6
Fig. 6: Modular multilevel converter (M2C) detailed model
1. Capable of reproducing power
frequency transients and ac/dc
dynamic interactions initiated by
disturbances in the ac side.
2. It is suitable for demonstration of
M2C active and reactive power
control, and voltage support
capability. Therefore, it may be
suitable for transient stability
studies of relatively large ac/dc
power systems.
3. This approach is unable to
reproduce the transients when the
M2C dc link is suppressed.
Therefore. Not suitable for dc
network fault studies.
4. Not applicable for small signal
stability; however, it can be twig
for small signal stability.
5. Dynamics of distributed M2C cell
capacitors can be modelled by
means of ‘virtual single lumped
capacitor and reflected current
source’. This models net energy
transfer between the M2C cells
and the AC and DC networks but
neglects sharing effects.
½Vdc
-½Vdc
0 wt
Va1
VgabcVabc0
Vdc Iabc
Vce2
Vce1
iabc1
iabc2
1 1abc abcm i
2 2abc abcm i
7
Fig. 7: Hybrid cascaded multilevel converter detail model
1. Models transient associated with
power and harmonic frequencies,
dynamic interactions between ac
and dc sides that could be initiated
in ac or dc sides. Also it models
cell capacitor dynamics
accurately, including dc fault
reverse blocking capability.
2. Suitable for detail studies;
however, it is prohibitively slow.
Therefore, it is not suitable for
large power systems.
0xv
0av
tω
0( )a tv
π 2π
tωπ 2π
0( )xv t
π 2π
( )HBv t
tω
8
Fig. 8: Hybrid cascaded multilevel converter average model
1. Assumes ideal series active power
filter that is capable of attenuating
all the harmonics from the two-
level output voltage.
2. Suitable for ac side fault studies
of medium-scale dc grids, and
other applications that involve
manipulation of active and
reactive power exchange with ac
networks.
3. Relatively fast, therefore could be
used to model number of HVDC
links embedded in relatively large
power systems.
Va1
½Vd
c
-½Vdc
0
Va1Vc
Vdc
Vg
9
Simulations illustrate appropriateness and limitation of two-level converter models
a) Active and reactive power at B1 and B2
b) Active and reactive power at B3 and B4
10
Fig. 8: Waveforms illustrate responses of the detailed and average models of the two-level converter based dc grid to solid pole-to-pole dc fault at D5, with 200ms fault duration
a) Active and reactive power at B3 and B4 b) Active and reactive power at B3 and B4
11
Converter 3 dc link current Converter 3 dc link voltage
Voltage magnitude at B3
Fig. 9: Waveforms illustrate steady-state and responses of the detailed and averaged models of the two-level converter to three-phase fault at G3
12
Model validation of differential equations approach
(a) Six-terminal DC Grid illustrative model
(b) Active power VSC1, VSC2 and VSC3 inject into DC grid (c) Active power dc voltage regulator (VSC4, VSC5 and VSC6) inject in to AC grids 4,5 and 6
Idc1
Idc2
Idc3
Idc4
Idc5
Idc6
Ic1
Ic2
Ic3
Ic4
Ic5
Ic6
I14
I12
I23
I36
I45
I56
Vdc1
Vdc2
Vdc6 Vdc6
Vdc5
Vdc4V1
V2
V3
VSC1
VSC2
VSC3
VSC4
VSC5
VSC6
V4
V5
V6
I6
I5
I4I1
I2
I3
B1
B2
B3 B6
B5
B4
Vc2
Vc1
Vc3 Vc6
Vc5
Vc4
750MVA
400kV/300kV
Zt1=0.005+j0.2
750MVA
400kV/300kV
Zt2=0.005+j0.2
750MVA
400kV/300kV
Zt3=0.005+j0.2
750MVA
400kV/300kV
Zt4=0.005+j0.2
750MVA
400kV/300kV
Zt5=0.005+j0.2
750MVA
400kV/300kV
Zt6=0.005+j0.2
P14
P12
P45
P56P23
I25
P25
P36
P1
P2
P3 P6
P5
P4
Rc1 Rc4
Rc2 Rc5
Rc3 Rc6
13
(d) Voltage magnitude at the dc nodes (Vdc1, Vdc2, Vdc3, Vdc4, Vdc5 and Vdc6)
(e) Power flow in the DC lines (P14, P25 and P36)
(f) Power flow in the DC lines (P12, P23, P45 and P56)
Fig. 9: Key results illustrate validation of the presented DC grid mathematical model against detailed model that represents each converter station by its three-phase switch model (do lines represent detail model)
14
Table II: Eigenvalues demonstrate the stability of the DC grid in Fig, 1 under assumed operating condition
modes eigenvalues Damping time (s) Damping ratio
λ1,2 -359.0±j1960.1 0.00279 0.18
λ3,4 -359.2±j1208.8 0.00279 0.285
λ5,6 -359.1±j520.30 0.00279 0.568
λ7,8,9,10 -714.3 0.00140
λ11 -29.4 0.034
λ12,13 -29.3 0.034
λ14,15,16,17,18,19 -18.8±j46.3 0.053 0.376
λ20,21,22,23,24,25 -18.3±j46.5 0.053 0.366
λ26,27,28 -8.6 0.11627
λ29,33,38 -16.7 0.05988
λ30,31,32 -3983.3 0.0000251
λ34,35,40 -28.9 0.0346
λ36,37,39 -8.7 0.11494
Sample results illustrate response of M2C detail and average models to ac network faults
Active and reactive power converter exchanges with ac network
Current waveforms converter injects into ac network
15
Phase voltage at converter terminal relative to supply mid-point Voltages across the M2C cell capacitors
Sample waveforms illustrate M2C detail and average models responses during ac faults
Conclusions
• There is no single voltage source converter model that could be used in all power system studies.
• Model selection must be based on the scale and type of studies need to be conducted, taking into account the model
limitations.
• Detailed converter models could be used in conjunction with simplified converter models where is appropriate to represent
part of the network needs to be investigated in detail.
• Average voltage source converter model seems to be appropriate for power systems studies of relatively large hybrid ac/dc
power systems, where the focus on the dynamics due to ac network disturbances.
• Differential equations approach appears to be suitable and efficient for transient and small signal stability studies of very large
power systems. However, this has to be confirmed. The efficiency of this approach in very large power system could be
further improved using more advanced routines from IMSL and NAG libraries.