Journal of International Council on Electrical Engineering Vol. 4, No. 1, pp.74~79, 2014
http://dx.doi.org/10.5370/JICEE.2014.4.1.074
A Voltage Stability Analysis Method of Multi-infeed HVDC Power Systems
Shao Yao†, Tang Yong*, Zhang Jian* and Li Baiqing*
Abstract – According to the Chinese power network planning, the risk of voltage instability at the
receiving-end AC power system will be increased significantly, where there will be more HVDC systems
feeding into a same AC grid in the future. At present, the effective voltage stability analysis methods of
multi-infeed DC (MIDC) system are few, the most widely used method with most research results is the
multi-infeed short-circuit ratio (MISCR) index at home and abroad. The deficiency of MISCR index is
pointed out. The relationship between multi-infeed interaction factor (MIIF) and the voltage stability of
the receiving-end AC system is discussed. Then a new method joint MIIF and MISCR indexes to
evaluate the voltage stability of MIDC system is put forward. Finally, simulation tests and analysis results
of a large actual grid prove the feasibility and good performance of the proposed new method.
Keywords: Multi-infeed DC power system (MIDC), Voltage stability, Multi-Infeed Interaction Factor
(MIIF), Multi-Infeed Short Circuit Ratio (MISCR)
Reference [5] proposes a novel structure-related index, i.e.
the transient voltage supporting index (TVSI) to evaluate
the interaction strength of the DC terminals, and it still is a
derivative of the concept of short-circuit ratio. However,
MISCR index is a relatively macroscopic structural indicator.
In some cases, it’s insufficient of using MISCR to determine
the voltage stability of MIDC systems.
In this paper, the defect of using MISCR method to
determine the MIDC system voltage stability is pointed out
based on a completely symmetrical two-infeed DC system.
The relationship between multi-infeed interaction factor
(MIIF) and the voltage stability of MIDC system is studied.
Then based on the above analysis, a new method using
MIIF and MISCR indexes to determine the voltage stability
of MIDC system is put forward. Finally, detailed analysis
and simulation tests are carried out in a large actual grid.
1. Introduction
There With the orderly constructions of China's power
grid, many UHV/EHV DC systems will be fed into the East
China Receiving-end Power Grid, where several of the DC
systems are located in the vicinity of each other. In multiinfeed DC (MIDC) systems, if the electrical couplings
between inverter stations are close and the dynamic reactive
power supports of the receiving-end AC system are
insufficient, when there are serious contingencies
happening in the AC system, the risk of the whole system
voltage collapse caused by simultaneous DC commutation
failure will increase[1]-[10].
At present, many voltage stability analysis methods of
MIDC system are derived from the research results of AC
system or single-infeed DC system, and the most widely
used method is multi-infeed short-circuit ratio (MISCR)
method. References [3]–[4] propose the definitions of
MISCR respectively. In [3], Node impedance matrix
elements are used to describe the effect of DC links, and in
[4], the change rate of voltage at converter buses after
reactive power disturbance is applied to indicate the
interactions between them. Reference [8] proves the
consistency of these two definitions based on a decoupled
model of MIDC system and gives the index of MISCR for
determining the strength of receiving-end AC system.
2. Evaluation indexes of MIDC system
2.1 Evaluation index for determining the strength of the
receiving-end AC system
Historically, an index known as Short Circuit Ratio
(SCR) was defined and intended to indicate the ac system
strength at the ac/dc interconnection point with respect to
the power rating of the single-infeed DC system. And
generally think, the higher the value of SCR, the stronger
the strength of receiving-end AC system, and the smaller
the probability of system voltage instability [1]-[7].
In multi-infeed DC system, considering the interactions
between DCs, MISCR is defined as:
†
Corresponding Author: China Electric Power Research Institute,
Haidian District, Beijing 100192, China (yaoshao@epri.sgcc.com)
*
China Electric Power Research Institute, Haidian District, Beijing
100192, China
Received: November 19, 2013; Accepted: January 6, 2014
74
Shao Yao, Tang Yong, Zhang Jian and Li Baiqing
M ISCR i =
Saci
Pdeqi
approximately zero, and each DC can be seen as a singleinfeed DC system. Simulations in [10] show that, for
MIIFji>0.6, the interaction between two DC systems is so
strong and the converters can be considered to be on the
same bus as regards to commutation failure (CF) behavior.
(1)
where, i is the number of DC converter station; Saci is the
ac short-circuit capacity at the i-th converter ac bus. Peqi is
the equivalent DC power considering the impacts of other
DC systems.
If the number of DC systems is m, through the Thevenin
equivalent method, (1) is extended to:
M ISCR i =
Saci
=
Pdeqi
3. Relationship between MIIF and voltage stability
of receiving-end AC system
3.1 Test system model
U N2 i / | Zeqii |
PdNi +
n
∑
j =1, j ≠ i
| Zeqij / Zeqii | PdNj
1
=
| Z eqii | PdNi +
m
∑
j =1, j ≠ i
In order to analyze the relationship between MIIF and
voltage stability of multi-infeed DC system, a completely
symmetrical test system of two DC infeeds connected
through a tie line (z12) is adopted. The circuit is shown in
Figure 1. Each DC system uses a standard control strategy
of constant current control at the rectifier and constant
extinction angle control at the inverter end respectively.
The parameters of each DC system are exactly the same.
The synthesis load mode, in which an impedance (40%)
and an induction motor (60%) are connected in parallel, is
used. And the resistances of AC lines are ignored.
(2)
| Z eqij | PdNj
where: UNi is the nominal voltage at the i-th converter
bus; PdNi, PdNj are the DC power ratings of the i-th, j-th DC
system, respectively; Zeq is the equivalent node impedance
matrix of the AC system seen from the ac converter buses;
Zeqij is the ith , jth of matrix Zeq; Zeqii is the ith , ith of matrix
Zeq.
Based on the value of multi-infeed critical SCR
(MCSCR) and the indexes of SCR proposed by IEEE,
reference[8] recommends indexes of MSCR as follows: (1)
very weak system: MSCRi<2; (2) weak system:
2<MSCRi<3; (3) strong system: MSCRi >3.
3.2 Relationship between MIIF and voltage stability
With the other parameters remaining constant, only
changing the value of z12, the relationship between MIIF
and MISCR of the above test system are listed in Table 1.
2.2 Evaluation index for determining the interaction
strength between DC systems
γ1
According to [4]–[9], an index known as MIIF, which
can be used to provides a first level indication of the degree
of the electrical coupling or interaction between two dc
systems, has been proposed as the ratio between the voltage
changes at inverter ac bus j and i due to a reactive ac power
change at inverter ac bus i, and given by:
X cI1
U&1
1: nI1
I&1
DC1
Qc1
Z12
X cI2
γ2
1: nI2
I&2
U& 2
Z load 2
DC2
M IIFji = ΔU j ΔU i
Z load 1
Qc 2
(3)
Fig. 1. A schematic diagram of the test system with two DC
infeed.
where, ΔU j is the observed voltage change at bus j for a
small induced voltage change at bus i; ΔU i is about 1%
voltage change at bus i.
Obviously, 0≤MIIFji≤1, the larger MIIFji or MIIFij is, the
stronger the interaction strength between DC i and DC j
will be. Reference [4] indicates that if MIIFji is less than 0.15
when the transmission power of DC i and DC j is similar,
the interaction between the two DC systems is
Table 1. MIIF and MISCR of the test system with two DC
infeed
No.
1
2
3
4
75
z12(p.u.)
1.31
0.631
0.131
0.001
MIIF21
0.393
0.488
0.686
0.990
MISCR 1
3.23
3.23
3.23
3.23
MISCR2
3.23
3.23
3.23
3.23
Design and Analysis of a Magnetless Flux-Switching DC-Excited Machine for Wind Power Generation
Seen from Table 1, with the decrease of z12, MIIF21 is
increasing, but MISCR1 and MISCR2 are remaining
unchanged. This is a special case which will be explained
as follows.
The test system shown in Fig. 1 can be equivalent to Fig. 2
under steady-state operation.
M ISCR1 =
=
E&1
z1
γ1
zc 2 z12 + z2 z12 + z2 zc 2 PdN1 + z2 zc 2 PdN2
1
Z 22 PdN2 + Z 21 PdN1
I&2d
zc1 z12 + z1 z12 + z1 zc1 PdN2 + z1 zc1 PdN1
E& 2
z2
γ2
z1 + z2 + z12
z1 z12 + 2 z2
(8)
M ISCR 2 =
z1 + z2 + z12
z2 z12 + 2 z1
(9)
And z1=z2, then
Fig. 2. A simplified model of the test system with two DC
infeed.
M ISCR1 =
In the test system, Y and Z are defined as the equivalent
node impedance matrix and node admittance matrix seen
from the ac converter buses, respectively:
⎤
− z12−1
−1 ⎥
z + zc−21 + z12
⎦
(4)
−1
2
⎤
z12−1
⎥
z + zc−11 + z12−1 ⎦
(5)
−1
1
)(
) (
)
Y = z1−1 + zc−11 z2−1 + zc−21 + z1−1 + z2−1 + zc−11 + zc−21 z12−1
Substituting the elements of (5) into (2), MISCR can be
rewritten as follows:
MIIF=0.393
MIIF=0.488
MIIF=0.686
MIIF=0.990
MIIF=0.393
MIIF=0.488
MIIF=0.686
MIIF=0.393
MIIF=0.990
1.1
DC2 power (MW)
0.9
1,000
0.8
0.7
0.6
(10)
MIIF=0.488
MIIF=0.686
MIIF=0.990
1,500
1,500
1
z1 + z1 + z12 1
= = M ISCR 2
z1 z12 + 2 z1 z1
As can be seen from (10), as long as the equivalent
impedances of AC system remain unchanged, MISCRs will
always be constant values.
Assuming there is a 3-phase fault occurring at bus 1 of
the AC tie line at 0.2s, and the line jumps at 0.3s after the
fault. Curves of voltages and DC powers are as shown in
Figure 3.
As can be seen from Fig. 3, with the increase of MIIF21,
the transient voltage stability of the receiving-end AC
system is deteriorated significantly. Even if the strength of
AC system is strong (MISCR1 =MISCR2=3.23), when
MIIF21 reaches a critical value, a serious AC disturbance
may cause the whole system to voltage instability.
where:
(
Y
M ISCR1 =
zc 2
1 ⎡ z2−1 + zc−21 + z12−1
⎢
Y ⎣
z12−1
(7)
z1 zc1 z12
Under the base of DC nominal power and nominal voltage
at the converter bus, (6) and (7) can be rewritten by:
z12
Z=
Y
In the actual power system, there is y1  yc1 , y2  yc 2 .
zc1
⎡ z −1 + zc−11 + z12−1
Y =⎢ 1
−1
− z12
⎣
(6)
z2 zc 2 z12
M ISCR 2 =
=
I&1d
1
Z11 PdN1 + Z12 PdN2
500
0.5
1,000
500
0.4
0
0
0.3
0.2
0
1
2
3
4
(a) bus voltage
5
6
0
1
2
3
4
5
(b) DC1 power at inverter side
6
0
1
2
4
5
(c) DC2 power at inverter side
Fig. 3. Simulation results when changing the interaction between DC systems.
76
3
6
Shao Yao, Tang Yong, Zhang Jian and Li Baiqing
between these DCs in addition to Shaox and Zhex inverter
stations.
Overall, the interactions between DC inverter stations fed
into East China power grid are not great.
4. The voltage stability analysis method joint MIIF
and MISCR
According to the analysis results of the previous section,
it’s not comprehensive enough of simply using MISCR to
determine the voltage stability of MIDC system. We should
consider both factors of MIIF and MISCR.
Therefore, this paper presents a new voltage stability
analysis method with use of MIIF and MISCR: for a MIDC
system, if MISCRs at the ac inverter buses are high and
MIIFs between DCs are small, the voltage stability of the
MIDC system is good; if MISCRs at the ac inverter buses
are small and MIIFs between DCs are high, the voltage
stability of the MIDC system is poor. For a same MIDC
system, the greater the MIIFs are, the higher the probability
of system voltage instability is.
And the local power grids with high MIIF between fed
DCs are weak areas responsible to voltage collapse in a
power system.
Jiangsu
Power Grid
Xuzh
Nanj
Taizh
Jint
Liy
Zhengp
Huain
Suzh
Tongl
Shanghai
Power Grid
Anhui
Power Grid
Hux
Wann
Huax
Zheb
Fengj
Shaox
Zhex
Nanq
Fengx
Zhezh
Zhejiang
Power Grid
Fig. 4. 1000 kV network structure of East China power grid
with 10 DC infeed in 2015.
5. Simulation analysis
MISCRs of the DC inverter stations are shown in Table 3.
The results are shown that, MISCRs of Jint and Liy inverter
stations are greater than 2 and less than 3, MISCRs of other
inverter stations are greater than 3. Overall, East China
receiving-end power grid is a strong system that its voltage
stability supporting capacity to MIDC system is large.
The simulation model which is based on the summer
peak load operation mode in the planning of East China
power grid in 2015 is shown in Fig. 4. There are a total of
10 DC systems fed into the East China power grid.
By calculating, MIIFs between the 10 DC inverter
stations are listed in Table 2.
As seen from Table 2, MIIFs between the inverter
stations fed into the same local power grid are greatly
significantly greater than MIIFs between the inverter
stations fed into different local power grids. And the
interaction between Huax and Fengj inverter stations is
high; the local power grid with the two DC infeed is voltage
stability weak area. MIIFs between DCs fed into Zhejiang
power grid between the other DCs are smaller than 0.15.
Hence it can be approximated that there are no interactions
Table 3. MISCRs of DCs in East China Power Grid
DC
Zhengp
Jint
Nanq
Fengj
Shaox
MISCRi
3.43
2.09
3.64
3.22
3.26
DC
Tongl
Liy
Huax
Fengx
Zhex
MISCRi
2.73
2.10
3.61
3.87
3.98
In summary, according to the proposed analysis method,
the voltage stability of East China receiving-end power
system is good. And normal contingencies will not cause
Table 2. MIIFs between DCs in East China Power Grid
MIIFj,i
inverter
ac bus i
Zhengp
Tongl
Jint
Liy
Nanq
Huax
Fengj
Fengx
Shaox
Zhex
Zhengp
1.00
0.26
0.18
0.28
0.03
0.15
0.08
0.09
0.10
0.04
Tongl
0.32
1.00
0.17
0.16
0.04
0.30
0.14
0.13
0.07
0.03
Jint
0.31
0.24
1.00
0.34
0.03
0.19
0.10
0.10
0.07
0.03
inverter ac bus j
Nanq
Huax
0.09
0.16
0.13
0.25
0.06
0.12
0.05
0.09
1.00
0.11
0.38
1.00
0.31
0.33
0.38
0.28
0.06
0.08
0.03
0.03
Liy
0.47
0.22
0.33
1.00
0.02
0.15
0.08
0.09
0.09
0.03
77
Fengj
0.13
0.18
0.09
0.08
0.14
0.52
1.00
0.39
0.09
0.04
Fengx
0.09
0.11
0.05
0.05
0.10
0.27
0.24
1.00
0.09
0.03
Shaox
0.13
0.07
0.05
0.07
0.02
0.09
0.06
0.10
1.00
0.22
Zhex
0.04
0.02
0.02
0.02
0.01
0.04
0.03
0.04
0.21
1.00
Design and Analysis of a Magnetless Flux-Switching DC-Excited Machine for Wind Power Generation
the system to voltage instability. The results are further
verified by simulation tool.
Simulation results show that the transient voltage
stability of East China power grid in the summer peak load
operation mode in 2015 is very good. All unipolar block
faults occurred in DC systems, single faults occurred in AC
or DC system, three-phase permanent short-circuit fault,
which causes the tripout of two circuits, occurred in
UHVAC transmission line of receiving-end system and that
occurred in the line near commutation buses of inverter
stations and majority of DC bipolar block faults occurred in
DC systems will not lead to transient voltage instability of
East China receiving-end power grid.
The voltage curves of inverter station commutation buses
after three phase-to-ground N-2 faults occurring at 1000kV
ac lines are shown in Fig. 5.
As seen from Fig. 5, after the faults, bus voltages of the
receiving-end AC system drop significantly. But with the
fault clearing, bus voltages can restore to new stable values
after a period of slight fluctuations. During the fault period,
voltage stability at commutation buses in Huax and Fengj
inverter stations are worse than the other commutation
buses. The local power grid where Huax and Fengj DCs fed
into is the voltage stability weak area. The conclusions are
泰泰－泰泰泰
浙浙泰－浙浙泰
泰泰泰－南南泰
西泰－浙浙泰
西泰－ 泰泰
1
0.8
0.8
泰泰泰－南南泰
西泰－浙浙泰
西泰－ 泰泰
西泰－ 泰泰
泰泰－泰泰泰
浙浙泰－浙浙泰
1
/pu
母
0.8
0.6
0.4
0.4
0.2
0.2
0.2
0
0.5
1
(a)
泰泰泰－南南泰
西泰－浙浙泰
1.5
/s
2
2.5
0
3
0.5
Huax
1
1.5
/s
2
2.5
3
0
泰泰－泰泰泰
浙浙泰－浙浙泰
泰泰泰－南南泰
Taizh -Nanj UHV
西泰－浙浙泰
Hux-Zheb
UHV
西泰－ 泰泰
0.6
泰泰
西泰－ UHV
Hux-Suzh
泰泰－泰泰泰
Suzh
-Taizh UHV
浙浙泰－浙浙泰
Zheb-Zhezh
UHV
/pu
0.8
0.6
1
1.5
/s
(d) Tongl
2
2.5
3
2.5
3
泰泰－泰泰泰
浙浙泰－浙浙泰
西泰－ 泰泰
0.8
0.6
0.4
0.2
0.2
0.2
2
1
0.4
0.4
1.5
/s
(c) Nanq
母
Bus voltage
母
/pu(pu)
0.8
0.5
1
泰泰泰－南南泰
西泰－浙浙泰
1
0
0.5
(b) Fengj
1
/pu
泰泰－泰泰泰
浙浙泰－浙浙泰
0.6
0.6
0.4
母
(1) It’s not comprehensive enough of only using MISCR
index to determine the voltage stability of systems
with multiple DC infeed. Both factors of MIIF and
MISCR indexes should be considered.
(2) MIIF, which is an evaluation index of the degree of
voltage interaction between two DC links, can reflect
the voltage stability weak areas of receiving-end
system: the local power grid with high MIIF between
fed DC links is weak area responsible to voltage
collapse in a power system.
(3) A new method joint MIIF and MISCR to evaluate the
voltage stability of systems with multiple DC infeed
is proposed: for a MIDC system, if MISCRs at the ac
inverter commutation buses are high and MIIFs
between DCs are small, the voltage stability of the
/pu
1
6. Conclusion
母
Bus voltage
/pu(pu)
母
泰泰泰－南南泰
西泰－浙浙泰
exactly the same with the results concluded from Table 2.
Obviously, the simulation results prove the accuracy of
the proposed new method united MIIF and MISCR indexes
to evaluate the voltage stability of systems with multiple
DC infeed.
0
0.5
1
1.5
s /s
(e) Jint
2
2.5
3
0
0.5
1
1.5
/s
2
2.5
3
(f) Shaox
Fig. 5. Voltage curves of inverter station commutation buses after three phase-to-ground N-2 fault occurring at 1000 kV ac
lines in East China power grid.
78
Shao Yao, Tang Yong, Zhang Jian and Li Baiqing
MIDC system is good; if MISCRs at the ac inverter
commutation buses are small and MIIFs between
DCs are high, the voltage stability of the MIDC
system is poor. For a same MIDC system, the greater
the MIIFs are, the higher the probability of system
voltage collapse is.
Theoretical analysis and simulation results of a large
actual grid prove the accuracy of the proposed new method.
SHAO YAO is currently an engineer in the Electric Power
Research Institute of China. Her research interests are
power system voltage stability and control, AC/DC systems
characteristics analysis
TANG YONG is a research fellow engineer in the Electric
Power Research Institute of China. His research interests
are power system simulation and analysis, voltage stability
and control, load modeling and simulation.
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ZHANG JIAN is a senior engineer in the Electric Power
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79